最終報告書
平成２４年 3 月
日本船舶海洋工学会
摩擦抵抗低減研究委員会
まえがき
日本船舶海洋工学会摩擦抵抗低減研究委員会
委員長
大阪大学
戸田保幸
摩擦抵抗低減研究委員会（略称Ｓ７委員会）は、26 期国際試験水槽会議（ITTC）に設置され
表面処理に関する専門家委員会（Specialist Committee on Surface Treatment、以下 ITTC 委
員会）の活動に対応する委員会として、日本船舶海洋工学会に設置されたストラテジー委員会で、
平成 21 年度より 3 年間活動してきました。目的は「摩擦抵抗低減法に関しての実船性能推定手
法など、今後利用される可能性のあるペイント・空気潤滑などによる摩擦抵抗低減技術、および
模型試験等に基づく摩擦抵抗推定法に関する共同研究を実施すること」としておりましたが、共
同研究は行わず、これまでの研究をまとめて、新しい塗膜などに対してどのような推定法を作れ
ばよいのかなどを討議してきました。
本委員会では、ITTC 委員会の日本からの委員をサポートするのが大きな目的であることから、
表面処理による摩擦抵抗等を推定、低減する技術に関する文献調査及び表面処理による摩擦抵抗
等を推定、低減する技術に関するレビューと理論的検討を行った。前者については昨年約 80 編
の文献について、その概要を英和両文で１編あたり１ページの体裁で要約集としてとりまとめ、
「塗膜、汚損等の表面摩擦抵抗に関する文献調査集」を印刷、製本し配布しました。後者につい
ての各委員からの発表資料を取りまとめたものが今回の最終報告書です。
後者の活動を紹介いたしますと委員会は摩擦抵抗に対して大きな低減効果がある空気潤滑法
等は取り扱わず、ITTC 委員会との関連から主に塗膜面の摩擦抵抗を調査しました。ただし摩擦
抵抗変化により伴流係数が変化するなどは共通のことであるのでこの委員会でも検討すること
になりました。内容は塗膜面の試験法としてどのようなものがあるかを調査し、回転円筒を用い
た計測、パイプによる計測、平板による試験、数式船型を用いた曳航試験など試験可能なレイノ
ルズ数範囲とこれらの試験で得られた結果から高いレイノルズ数の実船相当の抵抗を推定する
方法を調査検討してきました。その中には最近開発された海上技術安全研究所の高精度な平行平
板を用いた手法も紹介されました。また表面の性質（たとえば幾何学的な粗度と流体力学的に考
察しやすい等価な砂粗度など）が分かったとしてそれをどのように使っての実船の性能推定等に
ついても検討しました。また粘性抵抗変化によりプロペラ面平均流速推定法も変える必要がある
こと、相関としてのΔCF と表面状況によるものの分離などが話し合われています。しかしなか
なか一致した方法が提案できる状況までは至っておりませんが、いくつかの考え方が資料で示さ
れています。またこの委員会のあと共同研究を行うプロジェクト委員会についても話し合いがも
たれましたが、全機関が参加できるものはなかなか難しいという結論となりました。たとえば粗
度に関するデータベースを作るという提案に対しても各機関計測は行いたいが、公表してデータ
を共有することには参加しにくいというものなどどうしても集まっていただいたすべての機関
がデータを共有するようなプロジェクトは難しく、実船のさまざまな計測手法などであれば共同
開発可能であろうかということで新しいプロジェクト研究委員会の提案を行わないまま、ストラ
テジー研究員会（S７委員会）の活動を終わることになりました。研究活動としては半ばという
感じですがこの資料集が今後のこの分野の研究を行う方々への一助となれば幸いです。
これまで活動としては、下記の表に示すように 3 年間で 10 回の会合を持ち、各委員からの資
料に対して検討を行ってまいりました。この報告書にのせたもの以外にも各委員から発表がなさ
1
れましたが、一部は図のみであったりしたため省略させていただきました。また造船各社からの
委員には、実船摩擦抵抗推定に関し多くの有益な意見をいただきました。最後に委員名簿と、こ
れまでオブザーバーとして討論に参加していただいた方々の名簿を示します。
委員会開催履歴
第1回
2009/06/09
広島大学学士会館
8名
第2回
2009/11/14
大阪大学 大学院工学研究科船舶海洋部門
10 名
第3回
2010/01/21
日本船舶海洋工学会事務局会議室
10 名
第4回
2010/04/16
日本船舶海洋工学会事務局会議室
7名
第5回
第6回
第7回
第8回
第9回
第 10 回
2010/06/25
2010/10/08
2011/01/21
2011/04/22
2011/09/16
2011/12/09
大阪大学 大学院工学研究科船舶海洋部門
日本船舶海洋工学会事務局会議室
日本船舶海洋工学会事務局会議室
日本船舶海洋工学会事務局会議室
大阪大学大学院工学研究科船舶海洋部門
日本船舶海洋工学会事務局会議室
9名
8名
7名
9名
12 名
10 名
委員およびオブザーバー
委員長
戸田 保幸（大阪大学大学院）
委員
川村 隆文（東京大学）
委員
甲斐 寿（横浜国立大学大学院）
委員
藪下 和樹（防衛大学校）
委員
勝井 辰博（神戸大学）
委員
土岐 直二（愛媛大学）
委員
日夏 宗彦（海上技術安全研究所）
委員
川島 英幹（海上技術安全研究所）
委員
木村 校優（三井造船昭島研究所）
委員
村上 恭ニ（住友重機械マリンエンジニアリング）
委員
長屋 茂樹（ＩＨＩ技術研究所）
委員
川北 千春（三菱重工業）
委員（事務局）
田中 寿夫（ユニバーサル造船）
委員代理
池田 剛大（三井造船昭島研究所）
オブザーバー
山盛 直樹（日本ペイントマリン）
オブザーバー
肥後 清彰（日本ペイントマリン）
オブザーバー
高井 章（日本ペイントマリン）
オブザーバー
柳田 徹郎（MTI）
オブザーバー
安藤 英幸（MTI）
2
次ページ以降は各委員による発表をまとめたものである。配布資料として配布されたもの、
発表用パワーポイントファイルを印刷したもの、発表資料から少し文章をつけたものなど
さまざまな形があるが、再度形式をそろえて書き直す時間も考えてそのままの形で収録す
ることとした。それぞれの委員ごとにまとめている。内容も計測法について過去の研究を
レビューしたもの、過去に委員の機関が行ったものなどさまざまである。また ITTC 委員会
対応の委員会であったので、ブラジルで 2011 年 9 月に開催された総会でのレポートと関連
のグループディスカッションでの発表も資料をいただき収録している。簡単な目次は以下
のとおりである。
川村委員
4
川村「実船スケールレイノルズ数の CFD について」
5
川村、柳田「プロペラ性能に対する表面粗さの影響の CFD による推定」
17
田中委員
25
田中「粗度高さ定義比較」
26
田中「管内流を利用した摩擦抵抗の計測」
27
田中「回転円筒を用いた摩擦抵抗の計測」
32
勝井委員
46
勝井「粗度影響を考慮した平板摩擦抵抗の算定について」
47
勝井,泉「等価砂粗度による平板摩擦抵抗係数の増加量-計算結果の表示について」 52
勝井「後流関数を考慮した平板摩擦の粗度影響について」
54
日夏、川島委員
57
NMRI 流体設計系「平行平板曳航法による平板の摩擦抵抗評価」
58
日夏、川島「摩擦応力計測法について」
72
戸田委員
87
資料１
Hoang, Toda, Sanada ISOPE2009 論文
資料 2 Yamamori, Toda, Yano
資料 3 戸田、眞田、植原
88
ISME2009 論文
94
摩擦抵抗低減に関する考察
100
資料 4 塗膜模型船を用いた水槽実験
111
資料 5 深江丸の推力、トルク計測
118
資料 6 ITTC 表面処理委員会レポート
121
資料７
ITTC
グループ討議 Green Ship
Atlar 教授資料
資料 8 山盛氏による防汚塗料についての解説資料
3
152
157
川村委員の発表資料
川村「実船スケールレイノルズ数の CFD について」では高レイノルズ数まで CFD コード
で計算した例をもとに様々な説明がなされた。
川村、柳田「プロペラ性能に対する表面粗さの影響の CFD による推定」では表面粗度の影
響を考慮した CFD 計算を行い、性能の変化を示して ITTC1978 の式との比較を行った例が
説明された。
4
ᐇ⯪䝇䜿䞊䝹䝺䜲䝜䝹䝈ᩘ䛾
CFD䛻䛴䛔䛶
䠄ᰴ䠅ᩘ್ὶయຊᏛ䝁䞁䝃䝹䝔䜱䞁䜾
ᕝᮧ㝯ᩥ
⫼ᬒ
• ≀⌮ⓗ䛺ไ⣙䛜䛒䜛ᶍᆺᐇ㦂䛷䛿䚸ᚲ䛪䝺䜲䝜䝹䝈
ᩘ䛾ᙳ㡪䜢ཷ䛡䜛䛯䜑䚸ᐇ⯪㤿ຊ䛾᥎ᐃ䛻䛚䛔䛶
䛿⤒㦂ⓗ䛺ಟṇ䛜ᚲせ䛷䛒䜛䚹
• ⤒㦂ⓗ䛺ಟṇ䛿㐣ཤ䛾䝕䞊䝍䛻ᇶ䛵䛔䛶⾜䜟䜜䜛
䛯䜑䚸⯪ᆺ䜔୺せ┠䛜㐣ཤ䛾䝕䞊䝍䛛䜙እ䜜䛶䛔
䜛ሙྜ䛿ಙ㢗ᛶ䛜༑ศ䛷䛺䛔䛸䛔䛖ၥ㢟䛜䛒䜛䚹
• ୍᪉䚸䠟䠢䠠䛻䛚䛔䛶䛿ᐇ⯪䝇䜿䞊䝹䛾ィ⟬䛜ཎ⌮
ⓗ䛻䛿ྍ⬟䛷䛒䜛䛯䜑䚸ィ⟬䛾ಙ㢗ᛶ䜢㧗䜑䜛䛣䛸
䛷䚸ᐇ⯪㤿ຊ䛾᥎ᐃ⢭ᗘ䜢ྥୖ䛥䛫䜛䛣䛸䛜ฟ᮶䜛
䛾䛷䛿䛺䛔䛰䜝䛖䛛䚹
5
ෆᐜ
•
㐣ཤ䛾ᐇ⯪䝇䜿䞊䝹䝺䜲䝜䝹䝈ᩘ䛾ィ⟬䛾䝺䝡䝳䞊
1. Y. Tahara, T. Katsui, Y. Himeno: Computation of Ship Viscous
Flow at Full Scale Reynolds Number, Journal of The society of
Naval Architects of Japan,Vol.192,2002,pp.89-101
2. ᮧୖ䚸ᕝᮧ䚸᭷஭䠖ᩘ್䝅䝭䝳䝺䞊䝅䝵䞁䛻䜘䜛㧗ᥭຊ⯦䛾ᑻᗘᙳ
㡪䛾ホ౯䚸᪥ᮏ⯪⯧ᾏὒᕤᏛ఍ㅮ₇఍ㄽᩥ㞟 (4), 305-308,
2007
3. ᕝᮧ䚸኱᳃䠖䝥䝻䝨䝷༢⊂ᛶ⬟䛻ᑐ䛩䜛䝺䜲䝜䝹䝈ᩘ䛾ᙳ㡪䚸᪥ᮏ
⯪⯧ᾏὒᕤᏛ఍ㄽᩥ㞟(10), 29-36, 2009
4. 㯤䚸ᒣཱྀ䚸ᕝᮧ䚸኱᳃䠖 ᐇ⯪䝇䜿䞊䝹䛻䛚䛡䜛⯪య᢬ᢠ䛾ᩘ್ண
䚸ᖹᡂ22ᖺᗘ᪥ᮏ⯪⯧ᾏὒᕤᏛ఍ᮾ㒊ᨭ㒊⛅Ꮨㅮ₇఍ㅮ₇ㄽ
ᩥ㞟䚸2010
•
⪃ᐹ䛸ㄢ㢟
ὀ┠Ⅼ
• ᐇ⯪䝇䜿䞊䝹䝺䜲䝜䝹䝈ᩘ䛻䛚䛡䜛ᦶ᧿᢬ᢠ
ಀᩘ
• 䛂⾲㠃⢒䛥䛃䛾ᙳ㡪䛾ᙳ㡪
• ᙧ≧ᙳ㡪ಀᩘ䠄⢓ᛶᅽຊ᢬ᢠ䠅䛻ᑐ䛩䜛䝺䜲
䝜䝹䝈ᩘᙳ㡪
6
Y. Tahara, T. Katsui, Y. Himeno (1)
• 2-Layer k-H䝰䝕䝹䛸Wall-function k-H䝰䝕䝹䛻䜘䜛
ᐇ⯪䝺䜲䝜䝹䝈ᩘ䛾ᖹᯈ䛸Series 60࿘䜚ὶ䜜䛾ィ
⟬⤖ᯝ
2-Layer
Wall function
⁥䜙䛛䛺ᖹᯈ≧䛾ὶ㏿ศᕸ
Y. Tahara, T. Katsui, Y. Himeno (2)
⁥䜙䛛䛺ᖹᯈ䛾ᦶ᧿᢬ᢠಀᩘ
7
Y. Tahara, T. Katsui, Y. Himeno (3)
• ⢒䛥䛾ᙳ㡪䛻䛴䛔䛶䠄ᖹᯈ䠅
Y. Tahara, T. Katsui, Y. Himeno (4)
Series 60࿘䜚ὶ䜜䠄Wall-Function k-H䠅
• 1+K䛾್(Schoenherr䝧䞊䝇)
– ᶍᆺᐇ㦂
– ᶍᆺReィ⟬
– ᐇ⯪Reィ⟬
ᐇ⯪Re䛻䛚䛡䜛కὶศᕸ
1.18
?
1.20
• ᦶ᧿᢬ᢠಀᩘ䛜ᖹᯈ䛾ሙྜ
䛸ྠ䛨䛸䛩䜛䛸1+K䛻䛿ᐇ㉁ⓗ
䛻䝺䜲䝜䝹䝈ᩘᙳ㡪䛿↓䛔䛸
ᛮ䜟䜜䜛䚹
8
ᮧୖ䚸ᕝᮧ䚸᭷஭ (1)
• ప䝺䜲䝜䝹䝈ᩘᆺSST-k-Z䝰䝕䝹䛻䜘䜚䝅䝸
䞁䜾䝷䝎䞊䛸ᬑ㏻⯦䠄NACA0017䠅䛾᢬ᢠಀ
ᩘ䛾䝺䜲䝜䝹䝈ᩘ౫Ꮡᛶ䜢ホ౯
¾ 䝧䜽䝒䜲䞁A
¾ ᬑ㏻⯦
(NACA0017)
¾ 䝧䜽䝒䜲䞁B
¾ ⯦C-1
¾ ⯦C-2
ᮧୖ䚸ᕝᮧ䚸᭷஭ (2)
㻜㻚㻜㻤
㻝㻚㻡
㻟㻰ィ⟬
ᐇ㦂㻔ᅇὶỈᵴ㻕㻭
㻝
㻞㻰ィ⟬
㻟㻰ィ⟬
ᐇ㦂䠄ᅇὶỈᵴ䠅㻭
ᐇ㦂䠄ᅇὶỈᵴ䠅㻮
㻜㻚㻜㻣
㻜㻚㻜㻢
㻜㻚㻜㻡
㻯㻸
㻯㻰
㻜㻚㻡
㻜㻚㻜㻠
㻜㻚㻜㻟
㻜
㻜㻚㻜㻞
㻙㻜㻚㻡
㻜㻚㻜㻝
㻙㻝
㻙㻣㻡
㻙㻡㻜
㻙㻞㻡
㻜
䃐㼇㼐㼑㼓㼉
㻞㻡
㻡㻜
㻜
㻝㻚㻜㻜㻱㻗㻜㻠
㻣㻡
㻝㻚㻜㻜㻱㻗㻜㻡
㻝㻚㻜㻜㻱㻗㻜㻢
㻾㼑
CD 䛸Reᩘ䛾㛵ಀ
CL 䛸㏄ゅ䛾㛵ಀ
9
㻝㻚㻜㻜㻱㻗㻜㻣
ᮧୖ䚸ᕝᮧ䚸᭷஭ (3)
㻢
㻭
㻮
㻯㻙㻝
㻯㻙㻞
㻺㻭㻯㻭㻜㻜㻝㻣
㻡
㻝㻗㻷
㻠
䝅䝸䞁䜾䝷䝎䞊
㻟
㻞
NACA
㻝
㻜
㻝㻚㻜㻜㻱㻗㻜㻠 㻝㻚㻜㻜㻱㻗㻜㻡 㻝㻚㻜㻜㻱㻗㻜㻢 㻝㻚㻜㻜㻱㻗㻜㻣 㻝㻚㻜㻜㻱㻗㻜㻤
㻾㼑
ᮧୖ䚸ᕝᮧ䚸᭷஭ (4)
㻜㻚㻜㻤
䝧䜽䝒䜲䞁A -2 [deg]
㻯㼐䠖᢬ᢠಀᩘ
C
D 䠖᢬ᢠಀᩘ
C
㻯㼐㼜䠖ᅽຊ᢬ᢠಀᩘ
DP 䠖ᅽຊ᢬ᢠಀᩘ
㻜㻚㻜㻣
㻜㻚㻜㻢
C
㻯㼒䠖ᦶ᧿᢬ᢠಀᩘ
f 䠖ᦶ᧿᢬ᢠಀᩘ
2Cf
㻯㼒㻜䠖ᖹᯈᦶ᧿᢬ᢠಀᩘ
0䠖ᖹᯈᦶ᧿᢬ᢠಀᩘ
㻜㻚㻜㻡
㻜㻚㻜㻠
㻜㻚㻜㻟
㻜㻚㻜㻞
㻜㻚㻜㻝
㻜
㻝㻚㻜㻜㻱㻗㻜㻠
㻝㻚㻜㻜㻱㻗㻜㻡
㻝㻚㻜㻜㻱㻗㻜㻢
㻾㼑
10
㻝㻚㻜㻜㻱㻗㻜㻣
㻝㻚㻜㻜㻱㻗㻜㻤
ᮧୖ䚸ᕝᮧ䚸᭷஭ (5)
㻜㻚㻜㻢
㻯㼐㼜䠖ᅽຊ᢬ᢠಀᩘ
㻯㼐㼎㼜䠖䝧䞊䝇㒊ศ
㻯㼐㼜㻙㻯㼐㼎㼜䠖䝧䞊䝇㒊ศ௨እ
㻯㼒㻜䠖ᖹᯈᦶ᧿᢬ᢠಀᩘ
㻜㻚㻜㻡
㻜㻚㻜㻠
㻜㻚㻜㻟
䝧䞊䝇㒊ศ
㻜㻚㻜㻞
㻜㻚㻜㻝
䝧䞊䝇㒊ศ௨እ䛾ᅽຊ᢬ᢠ䛿
㧗䛔Reᩘ䛷Cf0䛻ẚ౛䠛
㻜
㻝㻚㻜㻜㻱㻗㻜㻠 㻝㻚㻜㻜㻱㻗㻜㻡 㻝㻚㻜㻜㻱㻗㻜㻢 㻝㻚㻜㻜㻱㻗㻜㻣 㻝㻚㻜㻜㻱㻗㻜㻤
㻾㼑
ᕝᮧ䚸኱᳃ (1)
• ప䝺䜲䝜䝹䝈ᩘᆺSST-k-Z䝰䝕䝹䛻䜘䜚䝥䝻䝨䝷䛾
༢⊂ᛶ⬟䛾䝺䜲䝜䝹䝈ᩘ౫Ꮡᛶ䜢ホ౯
0.8
Exp.
Cal. k-ω
Cal. k-ω-trans
0.7
ηO
KT, 10KQ, ηO
0.6
0.5
0.4
10KQ
0.3
0.2
KT
0.1
0
0.1
㟷㞼୸CP
0.2
0.3
0.4
0.5
0.6
J
Rn( K ) 3.23 u 105
11
0.7
0.8
0.9
1
D=0.25mᶍᆺ䝇䜿䞊䝹
ᕝᮧ䚸኱᳃ (2)
1.2
Exp.
Cal. k-ω
Cal. k-ω-trans
KT, 10KQ, ηO
1
0.8
ηO ᐇ㦂
㒊ศ஘ὶィ⟬
0.6
඲㠃஘ὶィ⟬
10KQ
0.4
0.2
KT
0
0.2
0.4
0.6
0.8
1
1.2
J
MP282
Rn( K ) 3.5 u105
D=0.25mᶍᆺ䝇䜿䞊䝹
ᕝᮧ䚸኱᳃ (3)
䝺䜲䝜䝹䝈ᩘᙳ㡪䛻䛴䛔䛶䛾⪃ᐹ
KT
KTf 'KT
↓㝈䝺䜲䝜䝹䝈ᩘ䛷䛾್
'KT
KQ
᭷㝈䝺䜲䝜䝹䝈ᩘᙳ㡪
'KTP KTV
ᅽຊᡂศ䛾ኚ໬
K Qf 'K Q
'K Q
'K QP K QV
ᦶ᧿ᡂศ䛾ኚ໬䠙ᦶ᧿ᡂศ
12
ᕝᮧ䚸኱᳃ (4)
0.004
ΔKTV
0.002
0.002
Seiunmaru CP J=0.6
Seiunmaru CP J=0.4
MP282 J=1.1
ΔKQP, ΔKQV
-0.002
-0.004
ΔKTP
0.0005
0
-0.0005
ΔKQP
-0.001
-0.008
-0.0015
-0.01
100000
1e+06
1e+07
1e+08
-0.002
100000
1e+06
1e+07
1e+08
Rn(K)
Rn(K)
ᕝᮧ䚸኱᳃ (5)
0.025
Seiunmaru CP J=0.6
Seiunmaru CP J=0.4
MP282 J=1.1
0.02
⣙3%
10ΔKQ
0.015
0.01
ΔKT, 10ΔKQ
ΔKTP, ΔKTV
ΔKQV
0.001
0
-0.006
Seiunmaru CP J=0.6
Seiunmaru CP J=0.4
MP282 J=1.1
0.0015
4Cf0
0.005
0
-2.5Cf0
-0.005
ΔKT
-0.01
⣙4%
-0.015
-0.02
0
0.001
0.002
0.003
Cf0
0.004
0.005
0.006
Kempf䛾䝺䜲䝜䝹䝈ᩘ䛻䛚䛡䜛ᖹᯈᦶ᧿᢬ᢠಀᩘ
13
㯤䚸ᒣཱྀ䚸ᕝᮧ䚸኱᳃(1)
• SST-k-Z䝰䝕䝹䛻䜘䜛䝍䞁䜹䞊⯪ᆺ࿘䜚䛾ィ⟬
• Re=1e7䡚ᐇ⯪䝇䜿䞊䝹
㻜㻚㻜㻜㻠㻜
㻯㼢㼜㼋㼏㼍㼘
㻯㼒㼋㼏㼍㼘
㻜㻚㻜㻜㻟㻡
㻯㼠㼋㼏㼍㼘
㻯㼒㻜
㻜㻚㻜㻜㻟㻜
㻜㻚㻜㻜㻞㻡
㻜㻚㻜㻜㻞㻜
㻜㻚㻜㻜㻝㻡
㻜㻚㻜㻜㻝㻜
㻜㻚㻜㻜㻜㻡
㻜㻚㻜㻜㻜㻜
㻝㻚㻜㻱㻗㻜㻢
㻝㻚㻜㻱㻗㻜㻣
㻝㻚㻜㻱㻗㻜㻤
㻝㻚㻜㻱㻗㻜㻥
㻝㻚㻜㻱㻗㻝㻜
㻾㼑㼥㼚㼛㼘㼐㼟㻌㼚㼡㼙㼎㼑㼞
㯤䚸ᒣཱྀ䚸ᕝᮧ䚸኱᳃(2)
㻲㼛㼞㼙㻌㼒㼍㼏㼠㼛㼞
K_cal / K_exp
㻝㻚㻢㻜
㻝㻚㻠㻜
㻝㻚㻞㻜
㻷㻛㻷㼋㼑㼤㼜
㻷㻓㻛㻷㼋㼑㼤㼜
㻷㻓㻓㻛㻷㼋㼑㼤㼜
㻝㻚㻜㻜
㻜㻚㻤㻜
㻝㻚㻜㻱㻗㻜㻢
㻝㻚㻜㻱㻗㻜㻣
㻝㻚㻜㻱㻗㻜㻤
㻝㻚㻜㻱㻗㻜㻥
㻾㼑㼥㼚㼛㼘㼐㼟㻌㼚㼡㼙㼎㼑㼞
14
㻝㻚㻜㻱㻗㻝㻜
㻯㼠㻌㻌㼣㻛㼛㻌㻯㼣
㯤䚸ᒣཱྀ䚸ᕝᮧ䚸኱᳃(3)
㻜㻚㻜㻜㻞㻡
㻔㻝㻗㻷㼋㼑㼤㼜㻕㻖㻯㼒㼟㻗䂴㻯㼒
㻜㻚㻜㻜㻞㻠
㻯㼢㼜㼋㼏㼍㼘㻗㻯㼒㼋㼏㼍㼘
㻜㻚㻜㻜㻞㻟
㻜㻚㻜㻜㻞㻞
㻜㻚㻜㻜㻞㻝
㻜㻚㻜㻜㻞㻜
㻜㻚㻜㻜㻝㻥
㻜㻚㻜㻜㻝㻤
㻤
㻤㻚㻡
㻥
㻥㻚㻡
㻝㻜
㻸㼛㼓㻔㻾㼑㻕
⪃ᐹ
• Cf䛾ィ⟬್䛿䝰䝕䝹䛾ಀᩘ䛻౫Ꮡ䛩䜛䛯䜑䚸
ィ⟬䛛䜙᪂䛯䛺▱ぢ䜢⏕䜏ฟ䛩䛣䛸䛿ᅔ㞴䛷
䛒䜛䚹
• ⩼ᆺ䛾䜘䛖䛺᏶඲䛺ὶ⥺ᆺ䛾ሙྜ䛿1+K䛿
Cf䛻ẚ౛䛩䜛䛜䚸᏶඲䛺ὶ⥺ᆺ䛷䛺䛔ሙྜ
䛿䚸㧗䝺䜲䝜䝹䝈ᩘ䛻䛚䛔䛶್䛜ቑຍ䛩䜛䚹
• ᐇ⯪㤿ຊ᥎ᐃ䛻䛚䛡䜛'Cf䛻䛿⢒䛥䛾ᙳ㡪䛸
1+K䛾ቑຍ䛾ᙳ㡪䛜ྵ䜎䜜䜛䚹
• 1-t䛻ᑐ䛩䜛䝺䜲䝜䝹䝈ᩘᙳ㡪䛿䛒䜛䛾䛛䠛
• Cw䛻ᑐ䛩䜛䝺䜲䝜䝹䝈ᩘᙳ㡪䛿䛒䜛䛾䛛䠛
15
ᐇ⯪䝇䜿䞊䝹CFD䛾ㄢ㢟(1)
• k-w䝰䝕䝹䛾ḞⅬ
Cf䛾཰᮰䛜ᝏ䛔䠄y+䜢㠀ᖖ䛻ᑠ䛥䛟䛩䜛ᚲせ䛜䛒䜛䠅
㻝㻚㻞
㻯㼒㻛㻯㼒䛾཰᮰್
㻝㻚㻝㻡
㻝㻚㻝
㻝㻚㻜㻡
㻲㼘㼡㼑㼚㼠
㻻㼜㼑㼚㻲㻻㻭㻹
㻝
㻜㻚㻥㻡
㻜㻚㻥
㻜㻚㻤㻡
㻜㻚㻤
㻜㻚㻜㻝㻜
㻜㻚㻝㻜㻜
㻝㻚㻜㻜㻜
㼥㻗
㻝㻜㻚㻜㻜㻜
㻝㻜㻜㻚㻜㻜㻜
ᐇ⯪䝇䜿䞊䝹CFD䛾ㄢ㢟(2)
• 䝯䝑䝅䝳䛾ၥ㢟
Re=1e9䛸䛩䜛䛸Cf0=0.0015
Lpp=1䛸䛩䜛䛸y+=0.1䛸䛩䜛䛻䛿'y=3.6e-9
ಸ⢭ᗘ䛷䜒䝯䝖䝸䝑䜽䛾ィ⟬䛷᱆ⴠ䛱䛜Ẽ䛻䛺䜛
䠄୍㒊䛾䝋䝣䝖䛷䛿䝯䝑䝅䝳సᡂ᫬䛛䝯䝖䝸䝑䜽䛾ィ⟬䛷䜶
䝷䞊䛻䛺䜛䠅
• ᙧ≧ฎ⌮䛾ၥ㢟
⯦䛾᭷↓䜔䚸䝅䝱䝣䝖䚸䝪䝇䛾ฎ⌮䛻1+K䛜౫Ꮡ䛩䜛䚹
16
䝥䝻䝨䝷ᛶ⬟䛻ᑐ䛩䜛⾲㠃⢒䛥䛾ᙳ㡪䛾
䠟䠢䠠䛻䜘䜛᥎ᐃ
䠄ᰴ䠅ᩘ್ὶయຊᏛ䝁䞁䝃䝹䝔䜱䞁䜾 ᕝᮧ㝯ᩥ
䠄ᰴ䠅MTI ᰗ⏣ᚭ㑻
┠ⓗ
• ⯪⯧䛾᥎㐍ᛶ⬟䛿䚸⯪య䛸䝥䝻䝨䝷䛾ởᦆ䛻䜘䜚పୗ䛩䜛䚹
• ᭱㐺䛺䝯䞁䝔䝘䞁䝇䛾䛯䜑䛻䛿䚸⯪య䛾ởᦆ䛸䝥䝻䝨䝷䛻䜘
䜛ởᦆ䛾ᙳ㡪䜢⢭ᐦ䛻ண ཬ䜃ホ౯䛩䜛䛣䛸䛜㔜せ䛷䛒䜛䚹
• ㏻ᖖ䛿㏿ຊ䛸ᅇ㌿ᩘ䛸䝖䝹䜽䛾䜏䛜ィ 䛥䜜䛶䛔䜛䛜䚸䛣䜜
䛻ຍ䛘䛶᥎ຊ䛾ィ 䜢⾜䛖䛣䛸䛻䜘䜚䚸⯪య䛸䝥䝻䝨䝷䛾ở
ᦆ䛾ᙳ㡪䜢ศ㞳䛩䜛䛣䛸䛜ฟ᮶䜛䚹
• ୍᪉䚸䝥䝻䝨䝷䛾䝖䝹䜽䛾ኚ໬䛸᥎ຊ䛾ኚ໬䛾㛵ಀ䛜ศ䛛䛳
䛶䛔䜜䜀䚸ィ 䛧䛯䝖䝹䜽䛛䜙᥎ຊ䛾ኚ໬䜢᥎ᐃ䛷䛝䜛䚹
• 䛥䜙䛻䚸ୖ䛾୧᪉⾜䛖䛣䛸䛻䜘䜚┦஫䛻᳨ド䛜ྍ⬟䛸䛺䜚䚸⢭
ᗘ䛾ྥୖ䛜ᮇᚅ䛷䛝䜛䚹
• ᮏ◊✲䛷䛿䚸CFD䛻䜘䜚䝥䝻䝨䝷䛾䝖䝹䜽䛸᥎ຊ䛾ኚ໬䛾ண
䜢⾜䛖䚹
17
ඛ⾜◊✲
• Wan et al., The Experiment and Numerical Calculation of
Propeller Performance with Surface Roughness Effects,
㛵す㐀⯪༠఍ㄽᩥ㞟 (238), 49-54, 2002
• ୓ ☐⋢䜙䚸ᐇᾏᇦ⯟⾜୰⯪⯧䛾᥎㐍ᛶ⬟ศᯒἲ䛻㛵䛩䜛
◊✲ : ⯪⯧䝥䝻䝨䝷⾲㠃⢒ᗘᙳ㡪䛾ホ౯䚸㛵す㐀⯪༠఍ㄽ
ᩥ㞟 (239), 55-60, 2003
– ⢒ᗘ䜢௜䛡䛯䝥䝻䝨䝷ᶍᆺ䛾ᐇ㦂
– ቃ⏺ᒙ⌮ㄽ䛻䜘䜛ᩘ್ィ⟬
– ⚄ᡞၟ⯪኱䛾⦎⩦⯪䛂῝Ụ୸䛃䛾ᐇ⯪ィ • ᕝᮧ 㝯ᩥ䚸኱᳃ ᣅஓ䚸䝥䝻䝨䝷༢⊂ᛶ⬟䛻ᑐ䛩䜛䝺䜲䝜䝹
䝈ᩘ䛾ᙳ㡪䚸᪥ᮏ⯪⯧ᾏὒᕤᏛ఍ㄽᩥ㞟(10), 29-36,
2009
– ᦶ᧿᢬ᢠಀᩘ䛾ኚ໬䠄䝺䜲䝜䝹䝈ᩘ䛻䜘䜛䠅䛻䜘䜛䝥䝻䝨䝷༢⊂ᛶ⬟
䛾ኚ໬䛾CFD䛻䜘䜛ண ᐇ᪋ෆᐜ
• 䛒䜛䝁䞁䝔䝘⯪䛾䝥䝻䝨䝷䜢౛䛻䚸⾲㠃⢒ᗘ䜢ኚ໬
䛥䛫䛶䝥䝻䝨䝷༢⊂ᛶ⬟䛾ண ィ⟬䜢ᐇ⯪䝺䜲䝜䝹
䝈ᩘ䛷⾜䛖䚹
• 䝥䝻䝨䝷ᛶ⬟䛾ィ⟬䛿Fluent䜢⏝䛔䛶䚸㐣ཤ䛾◊✲
䛸ྠᵝ䛾᪉ἲ䛷⾜䛖䚹
• ⾲㠃⢒ᗘ䛾ᙳ㡪䛿k-w-SST䝰䝕䝹䛾⢒ᗘ䝰䝕䝹䛻
䜘䜚⾜䛖䚹
• 䠄ᐇ⯪䝕䞊䝍䛸䛾ẚ㍑᳨ド䜢⾜䛖䠅
18
ᑐ㇟䝥䝻䝨䝷
୺せ┠
㻰
㼆
㻼㻛㻰㻌㼍㼠㻌㻜㻚㻣㻾
㼏㻌㼍㼠㻌㻜㻚㻣㻾
㻱㻭㻾
㻿㼑㼏㼠㼕㼛㼚
㻮㼛㼟㼟㻌㻾㼍㼠㼕㼛
⣙㻥
㻢
⣙㻝
⣙㻟
⣙㻜㻚㻥
㻺㻭㻯㻭
㻜㻚㻝㻥㻜
㼙
㼙
POT䛸䛾ẚ㍑
1
CFD
Exp.
0.9
10KQ
0.8
ηo
KT, 10KQ, ηo
0.7
KT
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
J
0.8
1
⁥㠃䜢᝿ᐃ䛧䛯ィ⟬䠄Rn(K)=2.9e5䠅
䝥䝻䝨䝷䜸䝣䝉䝑䝖䛜䛺䛟䚸ᙧ≧䛿୍㒊᥎ᐃ
19
1.2
ᖹᯈ䛾⢒ᗘ䛸ᦶ᧿᢬ᢠಀᩘ䛾㛵ಀ
• ᖹᯈ䛾㛗䛥䛿⣙3m 䠄0.7R䛾䝁䞊䝗㛗䠅
• 䝺䜲䝜䝹䝈ᩘ䛿ᐇ⯪䛾Kempf䛾䝺䜲䝜䝹䝈ᩘ
Re
⢒㠃ᖹᯈ䛾ᦶ᧿᢬ᢠಀᩘ䛾ィ⟬್
ks
㼗㼟㻌㻔P㼙㻕
㼗㼟㻛㻯㻜㻚㻣㻾 㼗㼟㻗
㻯㼒
㻜㻚㻜 㻜㻚㻜㻜㻱㻗㻜㻜
㻜㻚㻜 㻞㻚㻜㻢㻱㻙㻜㻟
㻟㻚㻝 㻝㻚㻜㻜㻱㻙㻜㻢
㻟㻚㻝 㻞㻚㻜㻣㻱㻙㻜㻟
㻢㻚㻟 㻞㻚㻜㻜㻱㻙㻜㻢
㻢㻚㻞 㻞㻚㻞㻜㻱㻙㻜㻟
㻝㻡㻚㻣 㻡㻚㻜㻜㻱㻙㻜㻢
㻝㻡㻚㻢 㻞㻚㻡㻢㻱㻙㻜㻟
㻟㻝㻚㻠 㻝㻚㻜㻜㻱㻙㻜㻡
㻟㻝㻚㻞 㻞㻚㻥㻤㻱㻙㻜㻟
㻢㻞㻚㻤 㻞㻚㻜㻜㻱㻙㻜㻡
㻢㻞㻚㻠 㻟㻚㻠㻟㻱㻙㻜㻟
㻝㻡㻢㻚㻥 㻡㻚㻜㻜㻱㻙㻜㻡
㻝㻡㻡㻚㻥 㻠㻚㻜㻞㻱㻙㻜㻟
䠖➼౯◁⢒ᗘ
k s uW
Q
'㻯㼒
㻜㻚㻜㻜㻱㻗㻜㻜
㻝㻚㻥㻞㻱㻙㻜㻡
㻝㻚㻠㻟㻱㻙㻜㻠
㻡㻚㻜㻠㻱㻙㻜㻠
㻥㻚㻞㻝㻱㻙㻜㻠
㻝㻚㻟㻤㻱㻙㻜㻟
㻝㻚㻥㻢㻱㻙㻜㻟
㻠㻚㻡㻜㻱㻙㻜㻟
㻠㻚㻜㻜㻱㻙㻜㻟
㻟㻚㻡㻜㻱㻙㻜㻟
㻟㻚㻜㻜㻱㻙㻜㻟
㻞㻚㻡㻜㻱㻙㻜㻟
㻯㼒
㻯㼒㻜
㻯㼒
㻞㻚㻜㻜㻱㻙㻜㻟
㻝㻚㻡㻜㻱㻙㻜㻟
㻝㻚㻜㻜㻱㻙㻜㻟
㻡㻚㻜㻜㻱㻙㻜㻠
㻜㻚㻜㻜㻱㻗㻜㻜
㻜㻚㻜
㻞㻜㻚㻜
㻠㻜㻚㻜
㻢㻜㻚㻜
㻤㻜㻚㻜
㻝㻜㻜㻚㻜
㼗㼟㻌㻔䝬䜲䜽䝻䝯䞊䝖䝹㻕
㻝㻞㻜㻚㻜
㻝㻠㻜㻚㻜
㻝㻢㻜㻚㻜
㻝㻤㻜㻚㻜
㻞㻚㻡㻜㻱㻙㻜㻟
㻞㻚㻜㻜㻱㻙㻜㻟
㻝㻚㻡㻜㻱㻙㻜㻟
㻰㼑㼘㼠㼍㻌㻯㼒
ks
9.66 u 10 7
㻰㼑㼘㼠㼍㻌㻯㼒
㼥㻩㻜㻚㻜㻜㻝㻠㻣㻌㼤㻌㻙㻌㻜㻚㻜㻜㻝㻞㻡
㻝㻚㻜㻜㻱㻙㻜㻟
㻡㻚㻜㻜㻱㻙㻜㻠
㻜㻚㻜㻜㻱㻗㻜㻜
㻝㻚㻜
㻝㻜㻚㻜
㻝㻜㻜㻚㻜
㼗㼟㻌㻔䝬䜲䜽䝻䝯䞊䝖䝹㻕
20
㻝㻜㻜㻜㻚㻜
⢒䛥䛾䛒䜛ᐇ⯪䝥䝻䝨䝷䛾ィ⟬
ks
0, 5, 10, 20, 50, 100, 200Pm 1
CFD Smooth
CFD ks=200μm
Est. Full
0.9
10KQ
0.8
ηo
KT
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
J
0.8
1
1.2
㻜㻚㻞㻡㻤
㻜㻚㻞㻡㻢
㻜㻚㻞㻡㻠
㻜㻚㻞㻡㻞
㻷㼀
㻜㻚㻞㻡
㻜㻚㻞㻠㻤
㻜㻚㻞㻠㻢
㻜㻚㻞㻠㻠
㻜㻚㻞㻠㻞
㻜㻚㻞㻠
㻜
㻡㻜
㻝㻜㻜
㻝㻡㻜
㼗㼟㻌㻔䝬䜲䜽䝻䝯䞊䝖䝹㻕
㻞㻜㻜
㻞㻡㻜
㻜
㻡㻜
㻝㻜㻜
㻝㻡㻜
㼗㼟㻌㻔䝬䜲䜽䝻䝯䞊䝖䝹㻕
㻞㻜㻜
㻞㻡㻜
㻜㻚㻜㻠㻡㻤
㻜㻚㻜㻠㻡㻢
㻜㻚㻜㻠㻡㻠
㻜㻚㻜㻠㻡㻞
㻷㻽
KT, 10KQ, ηo
0.7
㻜㻚㻜㻠㻡
㻜㻚㻜㻠㻠㻤
㻜㻚㻜㻠㻠㻢
㻜㻚㻜㻠㻠㻠
㻜㻚㻜㻠㻠㻞
タィⅬ (J=0.7)䛻䛚䛡䜛➼౯◁⢒ᗘ䛸KT䛸KQ䛾㛵ಀ
21
㻜
㻜
㻜㻚㻜㻜㻜㻡
㻜㻚㻜㻜㻝
㻜㻚㻜㻜㻝㻡
㻜㻚㻜㻜㻞
㻜㻚㻜㻜㻞㻡
㻙㻜㻚㻜㻜㻞
㻙㻜㻚㻜㻜㻠
㻰㼑㼘㼠㼍㻌㻷㼀
㻙㻜㻚㻜㻜㻢
㻙㻜㻚㻜㻜㻤
㻙㻜㻚㻜㻝
㼥㻌㻩㻌㻙㻢㻚㻡㻞㻤㻣㼤
㻙㻜㻚㻜㻝㻞
㻙㻜㻚㻜㻝㻠
㻙㻜㻚㻜㻝㻢
㻰㼑㼘㼠㼍㻌㻯㼒
㻜㻚㻜㻜㻝㻠
㻜㻚㻜㻜㻝㻞
㻜㻚㻜㻜㻝
㻰㼑㼘㼠㼍㻌㻷㻽
㼥㻌㻩㻌㻜㻚㻡㻤㻝㻟㼤
㻜㻚㻜㻜㻜㻤
㻜㻚㻜㻜㻜㻢
㻜㻚㻜㻜㻜㻠
㻜㻚㻜㻜㻜㻞
㻜
㻜
㻜㻚㻜㻜㻜㻡
㻜㻚㻜㻜㻝
㻜㻚㻜㻜㻝㻡
㻜㻚㻜㻜㻞
㻜㻚㻜㻜㻞㻡
㻰㼑㼘㼠㼍㻌㻯㼒
ᦶ᧿᢬ᢠቑຍ'Cf䛸'KT, 'KQ䛾㛵ಀ
ITTC1978䛸䛾ẚ㍑
ITTC1978䛷䛿䚸䝥䝻䝨䝷䛾ᑻᗘᙳ㡪䛻䛴䛔䛶௨ୗ䛾ᘧ䛜♧䛥䜜䛶䛔䜛䚹
C P
'K T 0.3Z
'C D
DD
'K Q
0.25Z
C
'C D
D
ୖ䛛䜙'CD䜢ᾘཤ䛧䚸䝢䝑䝏ẚ1.05䜢௦ධ䛩䜛䛸
'K T
1.26'K Q
୍᪉䚸௒ᅇ䛾ィ⟬⤖ᯝ䛛䜙䛿
' K T 6 .5 ' C f
'K Q
0.58'C f
'K T
11.2'K Q
ITTC1978䛾ᘧ䛿᥎ຊ䛾ኚ໬䜢㐣ᑠホ౯䛩䜛䚹
䠄䛣䛾䛣䛸䛿୓䜙䜒ᣦ᦬䛧䛶䛔䜛䠅
22
ITTC1978䛸䛾ẚ㍑䠄⥆䛝䠅
ITTC1978䛾ᘧ䛾ᐃᩘ㒊ศ䛰䛡䜢௒ᅇ䛾ィ⟬⤖ᯝ䛷⨨䛝᥮䛘䜛䛸௨ୗ
䛾䜘䛖䛻䛺䜛䚹
'K T
2.96 Z
'K Q
0.28Z
C P
'C f
DD
C
'C f
D
'K T
0.3Z
C P
'C D
DD
'K Q
0.25Z
C
'C D
D
ITTC1978
䛺䛚䚸ITTC1978䛾'CD䛿᩿㠃䛾᢬ᢠಀᩘ䛺䛾䛷䚸
'C D | 2 ' C f
䛷䛒䜛䚹
୓䚸すᕝ䜙䛻䜘䜛ᐇ⯪ィ 䛸䛾ẚ㍑
௒ᅇ䛾CFD䛻ᇶ䛵䛟ಀᩘ
'K T
9 .0 ' K Q
ITTC1978䛾ಀᩘ
'K T
23
1.02'K Q
䜎䛸䜑
• ⾲㠃⢒ᗘ䜢⪃៖䛧䛯CFDィ⟬䛻䜘䜚䚸⾲㠃䛾ᦶ᧿᢬ᢠಀᩘ
䛾ቑຍ䛸䝥䝻䝨䝷ᛶ⬟䛾ኚ໬䛾㛵ಀ䜢ホ౯䛧䛯䚹
• ᦶ᧿᢬ᢠ䛾ቑຍ('Cf)䛸KT䚸KQ䛾ኚ໬('KT,'KQ)䛿ẚ౛㛵
ಀ䛻䛒䜛䚹
• ᚑ䛳䛶䚸'KT䛸'KQ䛿ẚ౛㛵ಀ䛻䛒䜛䚹
• ITTC1978䛾┦㛵ᘧ䛿'KT䜢୍᱆㏆䛟㐣ᑠホ౯䛧䛶䛔䜛ྍ⬟
ᛶ䛜㧗䛔䚹
• 䝺䜲䝜䝹䝈ᩘ䚸⢒ᗘ䛸'Cf䛾㛵ಀཬ䜃䝥䝻䝨䝷୺せ┠䛸'Cf 䛸
'KT䛸'KQ䛾㛵ಀ䛻䛴䛔䛶ᩚ⌮䛩䜛䛣䛸䛻䜘䜚䚸୍⯡໬䛥䜜
䛯䝥䝻䝨䝷ᛶ⬟ኚ໬䛾ண ᘧ䜢స䜛䛣䛸䛜ฟ᮶䜛䛸ᛮ䜟䜜䜛䚹
24
田中委員の発表資料
田中「粗度高さ定義比較」では様々な粗度の定義（計測器も含めて）があるが、同じ粗度
高さであっても、どの定義を使っているか認識することが必要との話がなされた。
田中「管内流を利用した摩擦抵抗の計測」では、これまでのパイプを使った研究がレビュ
ーされた。チャンネル流れでの計測との比較もなされた。
田中「回転円筒を用いた摩擦抵抗の計測」ではこれまで田中委員により行われた回転円筒
試験装置による試験が説明された。
25
2010/04/16
粗度高さ定義の比較
ユニバーサル造船
26
田中
管内流を利用した摩擦抵抗の計測
ユニバーサル造船 田中寿夫
1
直線円管を用いた摩擦抵抗計測：概要
•
•
•
•
山崎・小野木・仲渡・姫野・田中・鈴木：「表面粗
度による抵抗増加の研究（第１報告）、日本造
船学会論文集１５３号、１９８３
小野木・山崎・仲渡・姫野・田中・鈴木：「表面粗
度による抵抗増加の研究（第１報告）、日本造
船学会論文集１５５号、１９８４
直線円管における圧力損失を計測することによ
り、円管内面の摩擦抵抗を計測
円管内面の粗度あるいは塗装状態が摩擦抵抗
に及ぼす影響を明らかにすることが目的
27
2
直線円管を用いた摩擦抵抗計測：抵抗の計測方法
•
内径50mm・全長
4,000mmの直線円管を
使用
•
側壁に設けた静圧孔を
用いて管路の圧力損失
を計測し、これをDarcy
の摩擦抵抗係数に換算
•
静圧孔から総圧管を挿
入して円管断面内の流
速分布も計測
3
直線円管を用いた摩擦抵抗計測：粗度の計測方法
28
•
円管内側に研磨用砂
を接着して砂粗度を模
擬
•
円管内側の粗度を計
測する代わりに、同様
の方法で作成した粗
度平板について、ＢＳ
ＲＡ式可搬型粗度計で
表面粗度を計測
•
ＢＳＲＡ粗度は、タング
ステン球を対象面に
接触させ、面に沿って
100mm移動させたとき
の最大粗度を示す
4
直線円管を用いた摩擦抵抗計測：管内の速度分布
•
総圧管を断面内でトラ
バースさせて、速度分
布を計測
•
管直径の40倍程度の
助走区間をとっている
ため、計測部では安
定した速度分布が得
られている
5
直線円管を用いた摩擦抵抗計測：滑面の摩擦抵抗
• 圧力損失から求めた管摩擦抵抗係数ｆをPrandtlの実験式と比較
• 広範囲のReynolds数にわたって、実験値とよく一致
• ばらつきも少ない
29
6
直線円管を用いた摩擦抵抗計測：粗面の摩擦抵抗
•
ほとんどの供試粗面
円管はReynolds数に
よらず一定値の摩擦
抵抗となっている→流
体力学的に完全粗面
の状態
•
管摩擦抵抗係数ｆは
Reynilds数に依存せ
ず,Nikuradseの砂粗度
ks/Dの関数となってい
る
7
直線円管を用いた摩擦抵抗計測：粗度の影響
Pipe No.
ｆ
Ｋｓ／Ｄ
Ｋｓ
（μｍ）
ＫＢＳＲＡ
（μｍ）
Ｋｓ／ｋＢＳＲＡ
２
０．０１８ ０．０００７
３６
６４
０．４９
３
０．０２８ ０．００３８
１９６
１３０
１．５１
４
０．０３１ ０．００５４
２６６
２０２
１．３２
５
０．０４４ ０．０１５１
７７８
５３８
１．４５
６
０．０５９ ０．０３２４
１６８５
１１３２
１．４６
30
8
直線円管を用いた摩擦抵抗計測：粗度の影響
•
計測された摩擦抵抗
係数から求めた
Nikuradseの砂粗度ｋｓ
と、BSRAの粗度は比
例関係にある
•
粗度が小さい場合は、
必ずしも比例にはなら
ない
•
新造船の場合の粗度
は高々５０～１５０μｍ
程度であり、比例関係
が当てはまるとは言い
切れない
9
溶接ビードが摩擦抵抗に及ぼす影響
・「白勢：粗面と溶接ビードによる船の抵抗増加（西部造船会報75
号）」
・「白勢：粗面と溶接ビードによる船の抵抗増加（西部造船会報75号）」
・Ｌpp=225m
の船体が10
10ブロックからなると仮定
ブロックからなると仮定
・Ｌpp=225mの船体が
・溶接ビードは幅20mm
・高さ5mm
5mmと仮定
と仮定
・溶接ビードは幅20mm・高さ
・摩擦抵抗に及ぼす影響は２％程度⇒粗度の1/10
オーダー
・摩擦抵抗に及ぼす影響は２％程度⇒粗度の1/10オーダー
5mm
31
10
Ｓ７委員会＃６
回転円筒を用いた
摩擦抵抗の計測
ユニバーサル造船 田中寿夫
回転円筒試験装置（外観）
モーター
トルク計
外円筒（固定）
32
回転円筒試験装置（内部）
回転軸
エンドプレート
（２次流れを抑制）
供試円筒
（側面を塗装）
実船における摩擦抵抗推定法
1. 回転円筒－固定円筒管に生じる境界層内にお
ける速度分布に壁法則を仮定
2. 壁法則から円筒表面に作用する平均摩擦応力
を推定
3. 回転円筒試験で得られた摩擦抵抗係数に一致
するように壁法則で等価砂粗度Ｋｅを決定
4. 得られた等価砂粗度によって実船尺度におけ
る摩擦抵抗の増減量を評価
33
流速分布の比較
－人工粗度円筒の場合－
1
•境界層内速度分
布に壁法則を仮定
•表面粗度の異なる
円筒の実験値と比
較
•等価砂粗度Ｋｅを
仮定して求めた速
度分布は実験結
果と定量的に良好
な一致を示す
Estimated (Bout=500m)
Ks= 0m
Ks= 34m
Ks=121m
Measured
RF1(Rz= 6.2m)
RF3(Rz= 16.6m)
RF5(Rz=100.5m)
0.9
0.8
0.7
u/U
0.6
0.5
0.4
0.3
0.2
0.1
0
1
1.5
2
2r/D
2.5
3
平均摩擦応力の比較
－人工粗度円筒の場合－
0.0036
0.0035
0.0034
Estimated (Log law×1.96)
Ks= 0m
Ks= 34m
Ks=121m
Measured
RF1(Rz= 6.2m)
RF3(Rz= 16.6m)
RF5(Rz=100.5m)
0.0033
0.0032
Ct
0.0031
0.003
0.0029
0.0028
0.0027
0.0026
2
3
4
5
6
7
Rn
8
9
10
34
11
12
+6
[10 ]
•流速分布から
決定した等価
砂粗度Ｋｅを用
いて供試円筒
に作用する平
均摩擦応力を
推定
•レイノルズ数の
変化が摩擦応
力に及ぼす影
響はよく推定さ
れている
塗膜面の表面状態変化を
考慮した摩擦抵抗の計測法
１）供試塗膜を側面に塗装した円筒を作製
２）試験装置で回転数0～700rpmの範囲で回
転トルクを計測→摩擦抵抗係数を算出
３）表面粗度をＪＩＳ方式で計測
４）エイジング用池で１ヶ月間連続回転（円筒
表面における回転速度が４．５ノット相
当）
５）２）～４）の過程を３ヶ月間繰り返す
エイジング装置
新鮮な海水が常時循環するプール内で供試円筒を連続回転
実船まわり流れにおける塗膜面の暴露状態を模擬
35
供試塗膜の要目
No.
初期粗度 消耗度 接触角
(μm)
(μm/年) (°)
性質
RF1 無塗装滑面（基準円筒）
11.9
－
－
SF1
自己研磨型
32.3
78.0
－
SF3
自己研磨型
45.6
41.0
－
SF5
自己研磨型
32.5
162.0
－
SF5R
自己研磨型
87.3
162.0
－
SW1
SF5R
撥水性アクリル系
23.1
－
85
撥水性シリコン系
24.0
－
129
初期粗度：ＪＩＳ方式で計測した最大値
消耗度：１５ノット相当回転速度で研磨した場合の値
エイジングによる生物付着
（撥水性塗膜）
エイジング過程でスライム（藻類の死骸）が付着
初期状態
１ヶ月経過
36
自己研磨型塗膜の抵抗係数
（初期状態）
初期粗度大のＳＦ５Ｒの抵抗が非常に大きい
他の塗膜面は滑面を若干上回る程度
0.0036
0.0035
0.0034
0.0033
0.0032
Ct
0.0031
0.003
0.0029
0.0028
0.0027
00/09/11
RF1
SF1
SF3
SF5
SF5R
0.0026
2
3
4
5
6
7
Rn
8
9
10
11
12
+6
[10 ]
自己研磨型塗膜の抵抗係数
（３ヶ月経過後）
初期粗度大のＳＦ５Ｒの抵抗が大幅に低下
他の塗膜面の抵抗は微増傾向
0.0036
0.0035
0.0034
0.0033
0.0032
Ct
0.0031
0.003
0.0029
0.0028
0.0027
00/12/18
RF1
SF1
SF3
SF5
SF5R
0.0026
2
3
4
5
6
7
Rn
37
8
9
10
11
12
+6
[10 ]
塗膜面摩擦抵抗の経時変化
3.5
3.4
3.3
RF1
SF1
SF3
SF5
SF5R
SW1
SW3
3.1
3.0
2.9
2.8
2.7
2.6
2.5
Sep
Oct
Nov
Dec
平均粗度Rzの経時変化
100
5.5kt 10.1kt
90
SF1
80
SF1R
70
SF3
60
SF5
50
Rz(m)
Ct×1000
3.2
SF5R
40
SF5RR
30
20
10
0
0
100
38
Day
200
平均粗度Rzと抵抗係数の相関
4
at Rn=8,000,000
5.5kt
10.1kt
SF–1
SF–1R
SF–3
1000Cf
SF–5
SF–5R
SF–5RR
Estimated
3
4
5
10
10
L/Rz
平均摩擦応力の比較
－自己研磨型塗膜の場合－
SF5R Series
0.0036
0.0035
0.0034
0.0033
0.0032
Ct
0.0031
0.003
0.0029
0.0028
0.0027
Exp.(Rmax)
Cal.
00/09/11(87m)
Ke=115m
00/10/10(79m)
Ke= 75m
00/11/13(74m)
Ke=60m
00/12/18(59m)
0.0026
2
3
4
5
6
7
Rn
39
8
9
10
11
12
+6
[10 ]
最大粗度Rzmaxと
等価砂粗度Κｅの相関
200
180
160
140
Ke(m)
120
100
at Rn=8,000,000
5.5kt 10.1kt
80
SF–1
SF–1R
SF–3
SF–5
SF–5R
SF–5RR
60
40
20
0
0
20
40
60
80 100 120 140 160 180 200
Rzmax(m)
ΔＣＦとレイノルズ数の関係
Ｗｈｉｔｅの式を用いて等価砂粗度ＫｅからΔＣＦを推定
相対粗度高さ一定の場合のΔＣＦの変化を表示
0.002
Ke/L=1×10
–5
Ke/L=5×10
CF
0.001
Ke/L=1×10
–5
–6
–6
Ke/L=5×10
–7
0 6
10
Ke/L=1×10
7
8
10
10
Rn
40
10
9
10
10
実船におけるΔＣＦの推定
船速１５ノット、海水温度１５℃と仮定
等価砂粗度高さを一定とした場合のΔＣＦを表示
ＳＦ５Ｒの研磨によるΔＣＦの低下量は０．０００２程度
0.0008
Ke=200m
CF
0.0006
ITTC1978
Ke=100m
0.0004
Ke=50m
Ke=25m
0.0002
0
100
200
300
L(m)
撥水性塗膜の摩擦抵抗係数
（初期状態）
0.0036
0.0035
0.0034
0.0033
0.0032
Ct
0.0031
0.003
0.0029
0.0028
0.0027
00/09/11
RF1
SW1
SW3
0.0026
2
3
4
5
6
7
Rn
41
8
9
10
11
12
+6
[10 ]
撥水性塗膜の摩擦抵抗係数
（３ヶ月経過状態）
0.0036
0.0035
0.0034
0.0033
0.0032
Ct
0.0031
0.003
0.0029
0.0028
0.0027
00/12/18
RF1
SW1
SW3
0.0026
2
3
4
5
6
7
Rn
8
9
10
11
12
+6
[10 ]
生物付着による摩擦抵抗増加
直径・高さとも１ｍｍ
の円柱状の生物（セル
プラ）が１０ｃｍ角の
範囲に約４０個付着
42
生物付着影響の推定例
u/U
u/U
0.4
0.4
RF1 1
RF1 2
RF1 3
SF1（未使用、傷あり）
SF5
SF5R
SW3
0.3
RF1 1
RF1 2
RF1 3
SF1（未使用、傷あり）
SF5
SF5R
SW3
0.3
0.2
1
1.5
2
1
r/R
1.1
1.2
1.3
r/R 1.4
(c)　計測速度分布(拡大）
(a)　計測速度分布
u/U
u/U
0.4
0.4
0μ
50μ
100μ
0μ
50μ
100μ
•セルプラの付
着による影響
を等価砂粗度
Ｋｅで評価する
と１００μｍに
相当する
0.3
0.3
0.2
1
1.5
1
2
1.1
1.2
1.3
r/R
1.4
r/R
(b)　計算速度分布
(d)　計算速度分布（拡大）
トムズ効果の検証
－回転円筒試験装置による計測例－
0.005
1st
0.0045
2nd
PEO3(0ppm)
PEO3(118ppm)
Ct
0.004
PEO3(350ppm)
分子量１００万のＰＥ
Ｏ水溶液で最大１８％
の抵抗低減を確認
0.0035
0.003
0.0025
0.002
1
2
3
4
5
6
7
Re
8
9
43
10
11
12
13
[10
+6
]
トムズ効果の検証
－効果の持続性－
7
6.9
6.8
長時間にわたって剪
断力を加えると、摩
擦抵抗低減効果が消
失する
↓
添加物の物性が変化
する？
PEO3(0ppm)
6.6
PEO3(118ppm)
6.5
6.4
6.3
6.2
6.1
6
5.9
0
10
20
Time(min)
30
40
トムズ効果の検証
－物性値との関係－
せん断率大で粘性係数小
（Stress Thinning）
↓
摩擦抵抗低減効果あり
0.0014
せん断粘性係数(Pa・s)
Q(Nm)
6.7
0.0012
0.001
せん断率大で粘性係数大
↓
摩擦抵抗低減効果なし
0
100
44せん断率(1/s)
200
まとめ
－塗膜面と摩擦抵抗の関係－
• 自己研磨型塗膜は研磨作用により表面粗度が
低下し初期状態より抵抗が低減する
• 自己研磨型塗膜の抵抗が滑面の抵抗を下回る
ことはない
• 撥水性塗膜には摩擦抵抗低減効果は認められ
ない
• 強い撥水性があっても生物付着は生じる
• 回転円筒試験の結果から塗膜面の等価砂粗度
を決定すれば、これを用いて実船スケールにお
ける摩擦抵抗の増減量を推定することができる
45
勝井委員の発表資料
勝井「粗度影響を考慮した平板摩擦抵抗の算定について」では勝井委員が行なっている後
流関数を考慮した摩擦抵抗計算法に粗度の影響を入れた方法が説明された。
勝井「等価砂粗度による平板摩擦抵抗係数の増加量―計算結果の表示について」では勝井
委員が行なっている後流関数を考慮した摩擦抵抗計算法に粗度の影響を入れた方法の結果
が説明された。
勝井「後流関数を考慮した平板摩擦の粗度影響について」後流関数を考慮していない阪大
の方法との比較が示された。
46
摩擦抵抗低減ストラテジ研究委員会資料
平成 22 年 1 月 21 日
粗度影響を考慮した平板摩擦抵抗の算定について
神戸大学大学院
海事科学研究科
勝井 辰博
1. 平板摩擦抵抗係数 C F の算定手法
(1) 運動量積分式
二次元の圧力勾配のない平板周りの流れを考えると，運動量積分公式は以下のようになる．
τ
dθ
1
= w 2 = cf
dx ρU
2
θ ：運動量厚さ，τ w ：壁面せん断応力，ρ：流体の密度， U ：一様流速，
c f ：局所摩擦抵抗係数
(1)
運動量厚さの定義は
θ ≡∫
δ
0
u
u
1 − dy
U U
(2)
u ：主流方向の流速，δ：境界層厚さ
これを x = 0 すなわち平板前縁で運動量厚さ θ が 0 となる条件のもと積分すれば
x
θ=
x ∫0 τ w dx 1
= CF x
21
2
2
ρU x
2
(3)
C F ：平板摩擦抵抗係数
となる．つまり，運動量厚さ θ を定義する乱流境界層内の速度分布が分かれば，(2)，(3)式より
平板摩擦抵抗係数 C F を算定することが可能となる．
(2) 平板の乱流境界層内速度分布
平板の乱流境界層内速度分布は Fig.1 に示すような摩擦速度を用いた相似則が知られている．図
中に示したように境界層は I．粘性応力が卓越する粘性底層，II．粘性応力とレイノルズ応力が
同程度の Buffer 層，III．レイノルズ応力が卓越する対数領域から外層，の 3 領域に分類され，
それぞれの領域で速度分布は異なる．粘性底層，Buffer 層の速度分布が C F に与える影響は微小
である．そこで本研究では，境界層内で，レイノルズ応力が卓越する対数領域から外層域の速
度分布を境界層内速度分布として用いた．その領域での速度分布は，Coles Law と呼ばれ，以
下のような式で与えられる．
Coles Law
( )
 + 1
Π δ +  y+ 
+
w +  − F
u = ln y + C +
κ
κ

δ 

+
+
w y  = 1 − cos π ⋅ y 
 δ+ 
 δ + 



 
+
+
u = u Uτ ， y = Uτ ⋅ y ν ，δ + = Uτ ⋅ δ ν ，
( )
47
(4)
摩擦抵抗低減ストラテジ研究委員会資料
平成 22 年 1 月 21 日
(
)
U τ = τ w ρ ：摩擦速度， κ = 0.41 ：カルマン定数，
ν ：動粘性係数， C = 5.0 ：（平板のとき）， y ：平板からの距離，
Π (δ + ) = 0.62 − 1.21exp(− δ + 290 ) ：後流パラメタ， w ：後流関数
ここで式中 F は，粗度によって境界層内の速度分布が一様に減速する効果を表しており，粗面
の特性に応じて変化する．以後この F を F = ∆u U τ とし，粗度関数と呼ぶことにする．
30
Ⅰ
Ⅱ
Ⅲ
u+
20
Ⅰ: linear sublayer
10
Ⅱ: buffer layer
Ⅲ: log region and outer layer
0
100
101
102
y+
103
Fig.1 Similarity law of velocity profile in turbulent boundary layer.
(3) 粗度関数
砂粗面的性質をもつ粗面の場合は摩擦速度 U τ と粗度高さ k で表される粗度レイノルズ数
k + (= U τ ⋅ k ν ) の増加とともに粗度関数 ∆u U τ が大きくなる．砂粗面の粗度関数 ∆u U τ は，
White3)による実験式が与えられており，粗度レイノルズ数 k + が境界層内速度分布に与える影響
は(2-1-2-1)式のように表される．
∆u / U τ =
1
κ
(
ln 1 + 0.3 ⋅ k +
)
(5)
この式を(4)式の F に代入することにより，砂粗面での，粗度影響を含む平板乱流境界層内速度
分布が得られる．
(4) 平板摩擦抵抗係数を求めるための微分方程式
(4), (5)式より砂粗面の平板乱流境界層内速度分布式は(6)式のように表わされる．
u+ =
1
κ
( )
ln y + + C +
( ) w y
Πδ+
κ
+
 1
+
 δ +  − κ ln 1 + 0.3 ⋅ k


(
 y+
w +
δ
)


y+ 
 = 1 − cos π ⋅ + 

 δ 
平板乱流境界層の外端 y = δ で，流速 u が一様流速 U となるから
( )
U
1
2Π δ +
1
= ln δ + + C +
− ln 1 + 0.3 ⋅ k +
Uτ κ
κ
κ
( )
(
(7)式から(6)式を引けば，速度欠損は
48
)
(6)
(7)
摩擦抵抗低減ストラテジ研究委員会資料
平成 22 年 1 月 21 日
( )
 y+
Πδ+ 
U −u
1
 +
= − ln y + / δ + +
−
2
w

κ
κ 
Uτ
δ
(
)



(8)
となる。両辺に u/Uτ を加え、さらに両辺を U/Uτ で割ると
( )
 y + 
Πδ+ 
U
u
1
 + 
=
− ln y + / δ + +
2
−
w

κ 
Uτ Uτ κ
 δ 
 y + 
U Πδ+ 
u Uτ Uτ 1
 + 
1=
ln y + / δ + + τ
2
w
−
−

Uτ U
U κ
U κ 
 δ 
すなわち速度欠損則は，無次元摩擦速度 σ (= U τ U ) を用いて，
σ
Π
σ ⋅ u + = 1 + ln η + − σ ⋅ ⋅ 2 − w η +
(
)
(
κ
ただし，η
+
( )
)
( )
κ
(
( ))
(9)
(10)
(11)
+
≡ y+ δ
+
(2)式で定義される運動量厚さ θ は定義式において y を y+ に変数変換すれば u = σ ⋅ u ，
y + = U τ y /ν ( dy = ν / U τ dy + )より
1 δ+
θ
= + ∫ σ ⋅ u + (1 − σ ⋅ u + )dy +
δ
δ
(12)
0
と変換できる．同様に(3)式は
R ⋅σ
θ 1
= CF x +
δ 2
δ
(13)
ただし， R x = Ux /ν ：平板長さ x に対するレイノルズ数
となる．よって(12)，(13)式より
∫
δ+
0
u + (1 − σ ⋅ u + )dy + =
1
C F Rx
2
(14)
の関係が得られる．左辺の積分を計算することで，(14)式は
F1 (δ + ) − σ ⋅ F2 (δ + ) =
1
C F Rx
2
(15)
ただし，
F1 (δ + ) =
(1 + Π(δ )) ， F (δ ) =
κ
1
+
+
2
π
sin θ
0
θ
Si(π ) = ∫
1 
3Π 2
Si (π )  


2
+
+ 2Π 2 1 +

2 
2
π  
κ 

dθ ：積分正弦関数
と表される．
ここで，無次元摩擦速度 σ には，局所摩擦抵抗係数 c f との間に
σ≡
Uτ
=
U
τw
1
=
cf
2
2
ρU
(16)
という関係がある．また，局所摩擦抵抗係数 c f と平板摩擦抵抗係数 C F には，(3)式の微分と(1)
式から
dθ 1 dC F
1
1 U dC F
1
1
=
x + CF =
x + CF = c f
dx 2 dx
2
2 ν dRx
2
2
となり、
49
摩擦抵抗低減ストラテジ研究委員会資料
平成 22 年 1 月 21 日
c f = C F + Rx ⋅
dC F
dRx
(17)
という関係が得られる．よって無次元摩擦速度 σ は
C F + Rx ⋅
σ =
dC F
dR x
(18)
2
と表される．(15)，(18)式より，
C F + Rx ⋅
( )
F1 δ + −
が成り立つ．ここで， RnL
dC F
dRx
( )
1
CF Rx
2
⋅ F2 δ + =
(19)
2
= ln (R x ) という変数変換を行うと，
dC F
1 dC F
=
dRx
R x dRnL
(20)
となることから，
dC F
dRnL
X =
(21)
とおけば，(19)式から
(
)
( )
f X , δ + = F1 δ + −
CF + X
1
⋅ F2 δ + − C F ⋅ exp(RnL ) = 0
2
2
( )
(22)
のように砂粗面での平板摩擦抵抗係数 C F を算定する微分方程式が得られる．
+
しかしながら，この式は X = dC F / dRnL と δ の２つの未知数を持つ方程式であるから，これだけで
は，粗面での平板摩擦抵抗係数 C F を算定することができない．そこで，平板乱流境界層外端で，流
速が一様流速となることを考慮すれば，(7)式より，無次元摩擦速度 σ を用いて，(23)式が成り立つ必
要がある．
1
=
σ
1
κ
( )
ln δ + + C +
( ) − 1 ln (1 + 0.3 ⋅ k )
κ
κ
2Π δ +
+
(23)
+
また，式中，粗度レイノルズ数 k は，定義式から無次元摩擦速度 σ を用いて
U τ Ux k U τ
R k
L k
k
=
⋅ R x ⋅ ⋅ = σ ⋅ R x ⋅ n ⋅ = σ ⋅ Rn ⋅
U ν x U
x L
ν
Rx L
L
 UL 
ただし， R n  =
 ：平板長さに対するレイノルズ数
 ν 
k+ =
Uτ k
=
となることから，(23)式は
1
σ
=
1
κ
( )
ln δ + + C +
( ) − 1 ln1 + 0.3 ⋅ σ ⋅ R
2Π δ +
κ
κ

n
⋅
(24)
k

L
(25)
となる．この式に(18)を代入し，先ほど用いた変数変換を行うことで，
(
)
g X ,δ + =
( )
CF + X
2
1
2Π δ +
1 
k
+
− ln δ − C −
+ ln1 + 0.3 ⋅
⋅ Rn ⋅  = 0
CF + X κ
κ
κ 
2
L
( )
(26)
+
を得る．(26)式も(22)式同様 X = dC F / dRnL と δ の２つの未知数を持つ方程式であり， k / L を与え
+
れば，(26)式と(22)式を連立させて解くことで，各レイノルズ数に対して dC F / dRnL と δ が得られ
るから順次 dC F / dRnL を積分すれば平板摩擦抵抗係数が得られる．
50
摩擦抵抗低減ストラテジ研究委員会資料
平成 22 年 1 月 21 日
2. 平板摩擦抵抗係数に与える粗度影響の計算例
(1) 計算条件
平板長さ：L=300 [m]
粗度高さ：k=0, 0.03, 0.3, 3, 30, 150 [µm]
計算レイノルズ数：Rn=1.0*105 ~ 1.0*109
(2) 計算結果
1.4
k=0 (smooth)
k=0.03[µm]
k=0.3 [µm]
k=3 [µm]
k=30 [µm]
k=150 [µm]
1.2
CF*102
1
0.8
0.6
0.4
0.2
0
105
106
107
108
109
Rn
Fig. 2 Frictional resistance coefficient of flat plate with sand roughness
0.5
k=0 (smooth)
k=0.03[µm]
k=0.3 [µm]
k=3 [µm]
k=30 [µm]
k=150 [µm]
CF*102
0.4
0.3
0.2
0.1
0
107
108
109
Rn
Fig.3 Frictional resistance coefficient of flat plate with sand roughness in high Reynolds number.
51
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摩擦抵抗低減ストラテジ研究委員会資料
平成 22 年 10 月 8 日
後流関数を考慮した平板摩擦の粗度影響について
-
阪大の方法との比較 神戸大学大学院海事科学研究科
勝井 辰博
1. 速度一定の場合 (実線：神戸大学、破線：大阪大学)
計算条件
速度：U=8.0,12.0,16.0,20.0,24.0 [knot]
粗度高さ：k=0.0,100.0,160.0,240.0,320.0,400.0 [µm]
計算レイノルズ数
：Rn=1.0*106 ~ 1.0*1010
0.012
k=400.0μm
k=400.0μm
k=320.0μm
k=320.0μm
k=240.0.μm
k=240.0μm
k=160.0μm
k=160.0μm
k=100.0μm
k=100.0μm
k=0.0μm
k=0.0μm
U=8.0(knot)
0.01
CF
0.008
0.006
0.004
0.002
106
107
108
109
1010
Rn
0.012
k=400.0μm
k=400.0μm
k=320.0μm
k=320.0μm
k=240.0μm
k=240.0μm
k=160.0μm
k=160.0μm
k=100.0μm
k=100.0μm
k=0.0μm
k=0.0μm
U=12.0(knot)
0.01
CF
0.008
0.006
0.004
0.002
106
107
108
Rn
54
109
1010
摩擦抵抗低減ストラテジ研究委員会資料
平成 22 年 10 月 8 日
0.012
k=400.0μm
k=400.0μm
k=320.0μm
k=320.0μm
k=240.0μm
k=240.0μm
k=160.0μm
k=160.0μm
k=100.0μm
k=100.0μm
k=0.0μm
k=0.0μm
U=16.0(knot)
0.01
CF
0.008
0.006
0.004
0.002
106
107
108
109
1010
Rn
0.012
k=400.0μm
k=400.0μm
k=320.0μm
k=320.0μm
k=240.0μm
k=240.0μm
k=160.0μm
k=160.0μm
k=100.0μm
k=100.0μm
k=0.0μm
k=0.0μm
U=20.0(knot)
0.01
CF
0.008
0.006
0.004
0.002
106
107
108
Rn
55
109
1010
摩擦抵抗低減ストラテジ研究委員会資料
平成 22 年 10 月 8 日
0.012
k=400.0μm
k=400.0μm
k=320.0μm
k=320.0μm
k=240.0μm
k=240.0μm
k=160.0μm
k=160.0μm
k=100.0μm
k=100.0μm
k=0.0μm
k=0.0μm
U=24.0(knot)
0.01
CF
0.008
0.006
0.004
0.002
106
107
108
109
1010
Rn
2. 平板長さ一定の場合(実線：神戸大学、破線：大阪大学)
計算条件
平板長さ：3.0[m]
速度：U=1.0~10.0 [knot]
粗度高さ：k=0.0,100.0,160.0 [µm]
計算レイノルズ数：Rn=1.0*106 ~ 2.0*107
0.006
k=0.0μm(OSAKA)
k=100.0μm(OSAKA)
k=160.0μm(OSAKA)
k=0.0μm(KOBE)
k=100.0μm(KOBE)
k=160.0μm(KOBE)
CF
0.005
0.004
0.003
0.002
106
Rn
56
107
日夏、川島委員の発表資料
NMRI 流体設計系「平行平板曳航法による平板の摩擦抵抗評価」では、様々な水槽試験で
の影響を除去して高精度に平板摩擦抵抗を計測する方法について示され、適用例が示され
た。
日夏、川島「摩擦応力計測法について」では摩擦応力の計測法について広範囲にレビュー
した結果を紹介した。
57
平行平板曳航法による
平板の摩擦抵抗評価
海上技術安全研究所
流体設計系
研究の背景と目的
船舶の全抵抗の内、摩擦抵抗成分が50%∼80%を占めるため、
摩擦抵抗の低減が可能であれば、船舶の省エネ化に有効
NEDOプロジェクト
海水摩擦抵抗を低減する船舶用塗料の基礎技術の研究開発
・塗料の種類による摩擦抵抗の差を精密に評価したい
・1%程度の摩擦抵抗の差を正確に評価することが目標
58
1
開発目標
●塗料の種類による摩擦抵抗の差を精密に評価する。
●外部流れでの摩擦抵抗を評価する。
●発達した乱流境界層での摩擦抵抗を評価する。
●なるべく実船に近いレイノルズ数で摩擦抵抗を評価する。
●実船と同程度の局所摩擦応力（剪断応力）の条件で摩擦抵抗
を評価する。
●１％程度の摩擦抵抗の差を評価可能とする。
35
実船14kt
30
平板4.5m/s
τw
25
Re =
平板4m/s
20
L ×V
µ
L
：代表長さ
10
V
：速度
5
µ
：動粘性係数
15
0
0
50
100
150
200
250
300
350
L (m)
長水槽での摩擦抵抗評価における誤差要因
長水槽における曳航試験で摩擦抵抗を評価する場合の誤差要因
●計測系起因の誤差
・検力計の精度
・計測装置の可動部、摺動部の摩擦、変形部のバネ定数等の誤差
・計測値の振動と平均値の求め方
●水槽試験起因の誤差
・静振、残留、水温の不均一と変化、レール高さ、速度制御
●抵抗成分の影響
・造波抵抗成分、形状抵抗成分、浸水表面積に占める被検部面積
の割合、造波による浸水表面積の変化
●被試験体の影響
・模型の製作精度、模型の設置状態
・乱流遷移の安定性
59
2
平行平板曳航法の精度向上のための工夫
●２枚の試験用平板を同時に曳航・計測することで、水槽内の残流、
静振、温度勾配、レール高さの変動、曳航台車の速度変動、計測区
間の設定などの誤差要因が、両平板におなじように影響を与える
ようにして、緩和させた。
●試験用平板は前後の板バネを介してブランコ式にぶら下げることで、
摩擦・摺動抵抗の影響を無くし、装置起因のヒステリシスが小さくなる
ようにした。
●試験用平板は、高精度圧延アルミニウム板に、精密に機械加工した
整流部を取り付ける構造として、個体差により生じる誤差を小さくした。
●長さ2.25m厚さ10mmのごく薄い平板模型を用いることで、
造波抵抗成分、形状抵抗成分が極力小さくなるようにした。
●流体力学的な干渉の影響が無視できる距離をCFDにより計算して
平板の間隔を2.0mとした。
●後部整流覆いに設置した高精度水温計で水温を常時モニタ。
平行平板曳航法による摩擦抵抗計測装置
試験用平板
全長 2250mm(内前後250mmは、円弧翼型フェアリング)
全高 1160mm（喫水760mm）
厚さ 10mm
平板の間隔
2000mm
検力計
抵抗計測用１分力計２台（定格200N、誤差0.02%）
平板の固定方法
平板の進行方向の軸のみ自由、他は拘束
吊り下げ方式
板バネ方式
乱流促進
スタッド方式（2mm角、高さ2mm、間隔10mm、1条）
試験平板の取付調整 レーザーシート光を基準面とする
喫水線
平板間距離2000(mm)
760(mm)
2250(mm)
側面図
正面図
60
3
摩擦抵抗計測方法模式図
計測方法模式図（抵抗計測時）
進行方向
検力計
板バネ
曳航ロッド
試験用平板
側面図
検力計と曳航ロッドの取り付け状態
検力計
曳航ロッド
61
4
乱流促進装置とブランコの板バネ
乱流促進装置
（2mm角立方体を
10mm間隔で配置）
板バネ
前部整流覆いと乱流促進装置
平板をつり下げる板バネ
試験用平板取り付け調整方法
レーザーシート光を
基準面にして試験用平板
を取り付け・調整する。
計測レールの駒を基準に
レーザーシート光で基準面をつくる
平板とレーザーシート光の
距離を計測する
62
5
計測装置水槽設置状態
乱流状態の確認
0.005
CT, CF
全抵抗係数、摩擦抵抗係数
0.0045
0.004
0.0035
0.003
0.0025
0.002
CT (FAPB)
CT (FBPA)
CF (Shoenherr)
CF*1.03
0.0015
0.001
0.0005
0
0.0E+00
2.0E+06
4.0E+06
6.0E+06
8.0E+06
1.0E+07
1.2E+07
Re
Shoenherrの式で求められる摩擦抵抗係数との比較
63
6
抵抗成分の分離
RT = RR + RFleading −edge + RFtest − surface + RFtrailing −edge + RFbottom −end
RR ：剰余抵抗（造波抵抗及び形状抵抗）
RT ：全抵抗
RFtest − surface ：検査面の摩擦抵抗
RFleading −edge ：前部整流覆の摩擦抵抗
RFtrailing −edge ：後部整流覆の摩擦抵抗
RFbottom −end ：下部整流覆の摩擦抵抗
喫水線
125mm
1150mm
750mm
乱流促進
検査面
125mm
2000mm
10mm
前部整流覆
後部整流覆
下部整流覆い
抵抗成分の割合
100%
90%
80%
70%
剰余抵抗
60%
整流覆摩擦抵抗部分
50%
試験部摩擦抵抗成分
40%
30%
20%
10%
0%
0.5
1
1.5
2
2.5
3
3.5
4
4.5
試験速度(m/s)
64
7
計測装置の精度①
検力計を装置に取り付けた状態での精度を以下に示す。
精度の確認は平板を取り付けた状態で、校正用プーリーを
用いて定格容量の490Nまで実施。
右検力計
490N
直線性
ヒステリシス
(%)
(%)
0.07
0.04 -0.03
左検力計
490N
0.06 -0.06
定格
0.06
計測装置の精度②（精度確認試験）
・試験対象
同一寸法、同一形状の無塗装アルマイト地肌の基準板
・抵抗試験
速度範囲
0.5m/s∼4.5m/s
Re数：1×106∼1×107
・繰り返し試験
速度：4.0m/s
試験回数：10回
65
8
計測装置の精度③整流部の固有抵抗
整流部、板の交換による整流部固有抵抗差の確認
FA：フェアリングA、FB：フェアリングB、PA：平板A、PB：平板B
2.00%
FBPA-FAPB
FAPA-FBPB（フェアリング交換）
FBPA-FAPB（フェアリング戻し）
FAPB-FBPA（平板左右交換）
全抵抗の差[%]
1.50%
1.00%
0.50%
0.00%
-0.50%
0
1
2
3
4
5
-1.00%
-1.50%
Vm[m/s]
左右の前部フェアリングの固有抵抗の差が0.3%程度あることが判った。
計測装置の精度②繰り返し試験結果①
同一形状・材質の試験用平板２枚の繰り返し試験結果（4m/s）
計測された全抵抗値の差は0.18％の範囲に分布
1.00%
0.80%
FAPB-FBPA（4m/s）
dR/R[%(15℃)]
左右平板の抵抗差（％）
0.60%
0.40%
0.18%
0.20%
0.00%
-0.20%
0
1
2
3
4
5
6
7
8
9
10
11
-0.40%
-0.60%
-0.80%
-1.00%
Test Number
66
9
計測装置の精度③繰り返し試験結果②
全抵抗値の分布の範囲は、左側平板で0.46%、右側平板で0.45%
左右の平板を同時に計測することにより、試験状態の相違が緩和されていることが判る
1.0%
Right plate（4m/s）
Left plate(4m/s)
0.6%
0.4%
0.2%
0.0%
-0.2%
0.45%
0 0.46%
1
2
3
4
5
6
7
8
9
10
11
-0.4%
-0.6%
-0.8%
-1.0%
Test Number
計測装置の精度④平板の脱着
同一形状・材質の試験用平板の検査面を左右取り替えて計測
平板の脱着による差は最大で0.1%程度
0.50%
FAPA-FBPB
0.45%
dR/R[%]
左右平板の抵抗差（％）
平板抵抗値の平均値との差（％）
0.8%
0.40%
FAPB-FBPA
0.35%
0.1%程度
0.30%
0.25%
0.20%
0.15%
0.10%
0.05%
0.00%
5.0E+06
6.0E+06
7.0E+06
8.0E+06
9.0E+06
1.0E+07
Re
67
10
舶用塗料の評価①（試験条件）
・試験対象
無塗装アルマイト地肌の基準板
加水分解型塗料A塗装板
シリコン系塗料B塗装板
サンドブラスト加工粗度板
・速度範囲
0.5m/s∼4.5m/s
Re数：1×106∼1×107
加水分解塗料A
シリコン系塗料B
舶用塗料の評価②（塗膜の厚みの影響の補正）
depth (m)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.75 average
9.99 10.00 10.00 10.00 10.00 10.00
10.00
Bare plate 10.00 10.00
thickness
10.56 10.50 10.54 10.48 10.49 10.47 10.47 10.49
10.50
(mm) Paint A
Paint B
10.97 10.98 10.93 10.94 10.92 10.92 10.94 10.98
10.95
0.1
With 12 sheets
0.09
0.08
DCR/CR
0.07
0.06
0.05
With 6 sheets
0.04
0.03
0.02
0.01
0
0
0.2
0.4
0.6
Additional thickness of the plates (mm)
0.8
1
DCR = CRsheets − CR0
CR0：厚みが付加されていない状態
CRsheets：厚みが付加された状態
での剰余抵抗係数
での剰余抵抗係数
68
11
舶用塗料の評価③（摩擦抵抗計測結果）
0.0041
Bare plate 1 （vs Roughness）
Bare plate 2 (vs Paint A)
0.0039
Bare plate 3（vs Paint B）
0.0037
Paint A (vs Bare plate）
Paint A (vs Paint B）
CF
0.0035
Paint B (vs Bare plate)
0.0033
Paint B （vs Paint A）
Roughness (vs Bare plate)
0.0031
0.0029
0.0027
0.0E+00
2.0E+06
4.0E+06
6.0E+06
8.0E+06
1.0E+07
1.2E+07
Re
舶用塗料の評価④（同時計測の摩擦抵抗の評価）
1.035
1.03
1.025
CF/CF
1.02
1.015
Roughness／Bare plate
Paint A／Bare plate
Paint B／Bare plate
Paint B／Paint A
1.01
1.005
1
0.995
0.99
0.0E+00
2.0E+06
4.0E+06
6.0E+06
8.0E+06
1.0E+07
1.2E+07
Re
69
12
舶用塗料の評価④（試験平板の表面粗度）
走査型共焦点レーザー顕微鏡 非接触レーザー変位計
2.5mm×1.9mm
30mm×30mm
2Ra
Rzjis
Rz
Rz
Paint A
3.22
6.48
10.48
100
粗度(μm) Paint B
0.74
1.64
2.62
106
Roughness plate 15.04
33.86
48.59
61
測定範囲
粗度定義
粗度と摩擦抵抗の関係（Schlichtingの図表から）
走査型共焦点レーザー顕微鏡 非接触レーザー変位計
2.5mm×1.9mm
30mm×30mm
2Ra
Rzjis
Rz
Rz
Paint A
6.99E+05 3.47E+05 2.15E+05
2.25E+04
粗度（k/L) Paint B
3.04E+06 1.37E+06 8.59E+05
2.12E+04
Roughness plate 1.50E+05 6.65E+04 4.63E+04
3.69E+04
測定範囲
粗度定義
1.35
CF(rough)/CF(smooth)
1.3
1.25
1.2
1.15
1.1
1.05
1
0.95
0.9
0.E+00
5.E+04
1.E+05
2.E+05
2.E+05
3.E+05
L/k
70
13
まとめ
・左右の平板を同時に計測することにより、水槽試験に
つきものの計測毎の条件の相違が緩和され、抵抗の差
がより精度良く評価できる。
・繰り返し試験の結果、左右平板の抵抗差の再現性は
非常に高い。
・摩擦抵抗の差1%以下の２種類の船舶用塗料の摩擦抵抗
を評価できた。
・塗膜の表面粗度は、波長の大きいうねり成分ではなく、
波長の短い粗度で評価する必要がある。
謝辞
本研究は (独)新エネルギー・産業技術総合開発機構による
「海水摩擦抵抗を低減する船舶用塗料の基礎技術
の研究開発」の一部として実施しました。
ここに謝意を表します。
71
14
摩擦応力計測法について
摩擦抵抗低減ストラテジー委員会
平成23年1月21日
海技研 日夏宗彦、川島英幹
摩擦応力計測法(チャンネル流）についてのレビュー
摩擦応力計測法について、1950年代から70年代にかけて活発に行われた。
今回の紹介ではチャンネル流にとらわれず、摩擦応力計測法に関する過去の文献から、
以下の４件を取り上げて、紹介することとする。これらの論文では、摩擦応力計測法に関
するレビューや考察が詳細に記述されており、一読しておく価値のある文献と思われる。
1)Direct Measurements of Skin Friction, b y S.Dhawan, NACA Report 1121 (1953)
2）Skin-Friction Measurements in Incompressible Flow, by D.W.Smith & J.H.Walker
NACA-TN-4231, (1958)
3) Calibration of the Preston tube and limitations on its use in pressure gradients, by
V.C.Patel, JFM vol23, part 1, 185-208 (1965)
4) The Measurement of Skin Friction in Turbulent Boundary Layers with Adverse
Pressure Gradients, by K.C.Brown, P.N.Joubert, JFM Vol.35 part 4, 737-757 (1969)
72
摩擦応力計測法(チャンネル流）についてのレビュー
我が国(船舶系）においても下記のような摩擦応力計測に関する研究が行われている。
（今回は紹介を割愛した）
1)A New Skin Friction Meter of Floating-Element Type and the Measurements of
Local Shear Stress by T.Hotta, JSNAJ Vol. 138, (1976)
2）表面粗度による抵抗増加に関する研究（第１，2報）､山崎､小野木他、造論153号
(1983)、155号(1984)
3)油膜を用いた限界流線と壁面摩擦応力の計測、奥野他、造論176号、(1994)
4)船体表面の摩擦応力分布および境界層内の2次流れに関する研究、奥野、造論139号、
(1976)
なお、今回のレビューの最後に光学的手法による最近の論文を簡単に紹介した。先の英
文４件とは異なる手法であるため、新しい動向の自答という位置づけで取り上げた。
また、ここで紹介する４件の英文論文や上記の論文は著名なものばかりなので、既に読ま
れた方がほとんどと思われるが、復習の意味も込めてご容赦願いたい。
Dhawan の論文
概要：
超音速域での摩擦抵抗式を求める。従来の計測法についてのレビューをした結果、直接法を採用し
た。本論ではレビュー内容が詳細に述べられている。
直接法に対しても、圧縮性流体を視野に入れているので、温度計測による方法もレビューしている。
最終的には直接摩擦応力を計測する方法を採用。
Floatingタイプの方法を採用。
・floatingタイプの場合、センサー板と支持部のgap影響は？ Gap前後の境界層速度分布を計測。
影響なしと判断。
73
Dhawan の論文
微小力の計測方法：
いくつかの方法があり、それぞれについてレビューの後、reactanceタイプを採用。外部の振動影響を
除去、温度変化(±20度）による出力変化がないことを確認。
計測部のピックアップ部
風胴に取り付けられた摩擦応力計測装置の詳細(図では0.2cmx2cmの受感板だが、これは音速用）
(非圧縮、低音速の場合は、1.15cmx6.3cmとした）
校正では、直線性、繰り返し荷重による再現性等も確認した。
Dhawan の論文
実験時のセットアップ：
受感板が長方形のため、tilt影響による
誤差修正も考慮。
境界層速度分布計測例
層流境界層の判定として、熱線データか
らTS波が検出されるか否かでも判断
74
Dhawan の論文(圧縮性の部分は省略）
摩擦応力係数の結果非圧縮の場合）
層流の場合、計測した速度分布と右図に示す圧力勾配デー
タからzero圧力勾配下のデータに修正。
乱流の場合、1/7乗則で速度分布を近似
Smith & Walkerの論文
概要：
Zero圧力勾配下での摩擦応力計測について詳述。3つの方法で計測。
・境界層速度分布計測から境界層パラメータを求め運動量積分式からcfを計算。
・直接法：floatingタイプ
・Preston管
試験のセットアップ（単位はインチ）
前縁の小孔から空気を
吹き出して、遷移させ
ている
75
Smith & Walkerの論文
摩擦応力計測装置
境界層速度分布計測用の平型Pitot管
Smith & Walkerの論文
Preston管
ゼロ圧力勾配の確認
乱流境界層の見かけの始点は、d(log 2θ)/dxで決定
76
Smith & Walkerの論文
境界層速度分布計測例
乱流境界層の見かけの始点は、d(log 2θ)/dxで決定
形状係数Hとレイノルズ数の関係
Smith & Walkerの論文
77
Smith & Walkerの論文
境界層速度分布結果から運動量厚さ経由
でCFを推定した値と、Ｃｆ計測結果を積分し
た結果の比較
Smith & Walkerの論文
今回の結果(tableIV)と従来の試験結果の比較
78
Smith & Walkerの論文
今回の結果(tableIV)と従来の試験結果の比較
Smith & Walkerの論文
直接摩擦応力計測法とPreston管で得た結果の比較。Preston管の方が小さいが、Prestonの
校正曲線が正しくないことが原因と考えられる。(Patelらの指摘に通じる）
79
V.C.Patelの論文
概要：
Preston管による摩擦抵抗計測法を考案したPrestonが提案した式は誤差が大きい。正し
い、校正式を提案する。さらに圧力勾配下で、この式がどの程度正しいか見極める。
試験方法：
パイプ流れを用いる。真とする摩擦抵抗の値は圧力降下で求める。14種類のPreston管
で試験。(圧力勾配の影響小のとき）
V.C.Patelの論文
境界層を下記3つの領域に分ける。て、それぞれについて定式化
それぞれについて下記のように定式化
80
V.C.Patelの論文
圧力勾配があるとき
右図のような実験装置で
実験
Ｐｒｓｔｏｎ管には新たにフェ
ンスが設けられている。
フェンス前後の圧力差を
計測
前述の校正曲線が圧力
勾配下でどの程度使える
のか調べルことを目的と
したが、難しいことがわ
かった。
圧力勾配下での速度分
布の考察を行う。
V.C.Patelの論文
Preston管の読みとフェンス前後の圧力差の読みが圧力勾配の影響を受けないとすると、これらの関係は一つの線
に乗る。しかし、実際はPreston管の読みとフェンス前後の圧力差の関係が一つの曲線に乗らない。
Preston管は圧力勾配下では摩擦力を過大評価している傾向にあるように見える。順圧力勾配下では、Preston管径
が小さくなるほど、誤差は増加。 当初の予期とは異なる。 速度分布の変化にテーマを変えた。
81
V.C.Patelの論文
Δ=
速度は0.054インチ径のピトー管で計測
摩擦応力はフェンス前後の圧力差で決める。(別途校正）
著者が導いたPreston管の使用限界
Brown & Joubertの論文
概要：
逆圧力勾配下での摩擦抵抗計測を行う。種々の方法をレビューし、その結果直接計測法を採用。
著者らの摩擦応力計測法の分類
論文では上記手法について興味深いレビューがされている。
82
Brown & Joubertの論文
直接計測法の模式図。ギャップによ
る影響について考察されている。
右図は著者らの摩擦応力計測装置
Aの計測部の直径は3/4インチ
ギャップは.003インチ、
Cの青銅板バネで支持、
Dはダンパーで風洞の振動影響を除
去
Brown & Joubertの論文
キャリブレーションの方法(2種類でチェック） (b)では糸の角度が必要、写真で読み取る。
試験風洞
総圧管の径：0.04インチ
Preston管の径:
0.0362、0.029、0.02イ
ンチ
Preston管の校正係数
はPatelの結果を使用
83
Brown & Joubertの論文
結果
Clauserの方法は、次ページに示すClauserのチャートに境界層速度分布をプロットし、Cfを補間して決定
直接法とPreston管の違いは、圧力勾配によるslight secondary force、アラインメントの誤差等の影響と考えられ
る。
Brown & Joubertの論文
84
Brown & Joubertの論文
圧力勾配下での結果
Preston管と速度分布から摩擦応力を決める。
圧力勾配下でのPreston管の精度限界マップ
Patelの6%リミットは楽観的
Brown & Joubertの論文
直接法における圧力勾配によるsecondary forceの影響マップ
摩擦応力はPreston管の読みを用いた。
1.0のときsecondary force
の影響なし
85
最近の論文より
COHERENT STRUCTURES AND THEIR CONTRIBUTION TO TURBULENT
INTENSITY IN TURBULENT CHANNEL FLOW
S. Imayama、Y.Yamamoto、YTsuji
（名大 辻先生より原稿入手）
最近の論文より
uk:フリンジ速度, n:屈折率、Δh：両隣のフリンジ高さの差 h0：オイルフィ
ルム端の最初のフリンジ高さ
86
戸田委員による報告の概要
１．資料１の論文と発表資料により、空気潤滑法であるがこの結果により摩擦抵抗低減が
あるとプロペラ面流速（1-w）に変化があり、この場合は同じ回転数、同じ CPP 翼角
で摩擦抵抗が減ると、船速はほとんど増加せず、馬力が下がる。これを推力、トルク
計測を行なっていたため抵抗が小さくなり、1-w が大きくなっていることがわかったこ
とを説明し、抵抗が下がっても単純に速度が上がる場合ばかりではないことを説明し
た。これにより摩擦抵抗が変わると当然 1-w の推定もやり直す必要があること、推力
を実船で計測が可能であれば直接船体抵抗に関連するものが取られるということを説
明し、燃料消費や馬力での検討より少し細かい内容が分かることを説明した。
２．資料２の論文と発表資料（報告書では省略)により、塗膜の種類によっては同じような
幾何学敵粗度であっても、抵抗が異なる場合があること、かなり平滑面に近づくよう
な場合もあることが紹介された。回転円筒装置と 3m の模型船を使った検討で、ある種
の親水性塗料では浸漬後計測すると等価砂粗度がかなり小さくなり、この等価なもの
を用いて実船を推定した結果なども示された。またこの推定により同じ等価砂粗度高
さで長さを変化した時の変化を ITTC の手法と比較して説明した。現在の ITTC の相関
に関するものと粗度に関するものの粗度の部分とは少し異なる傾向があることを示し
た。
３．資料３のパワーポイントにより、粗度の影響を考慮した境界層計算を行い、等価砂粗
度が変わる塗膜を半分塗る場合、前半でも後半でも同じことを示した。これは境界層
厚さの発達が異なるためで、資料４の空気潤滑でも同じことが得られることやこれは
青雲丸の実験でも見られたことなどが紹介された。
４．資料４により大学のような専門家がいないところでは浮かす単純船型模型による実験
が今までの経験上再現性が高く、その方法を様々な塗膜に行い、データベースにより
さまざまな塗膜にたいする実船推定法の考察を示した。
５．深江丸のドック前後の推力、トルク計測結果を示し、推力トルク計測を行うことで汚
損の船体への影響とプロペラへの影響が分離可能ではないかという報告がなされた。
資料５
６．ITTC の表面処理委員会のレポート（資料６）と、グループディスカッションでの関連
講演の資料（資料７）が示され概略が説明され、粗度計測装置について概略が示され
た。これは資料４に示した。
７．なお山盛オブザーバによる解説も戸田委員よりお願いしたのでここに資料 8 として入
れる
87
Full scale experiment for frictional resistance reduction using air lubrication method
C.L. Hoang, Y. Toda, Y. Sanada
Department of Naval Architecture and Ocean Engineering, Graduate school of Engineering, Osaka University
Suita, Osaka, Japan
the previous two experiments, the full-scale experiment using the same
ship, Pacific Seagull, was carried out in 2008.
This full-scale experiment was conducted by the cooperative
research project with National Maritime Research Institute Japan
(NMRI), Hokkaido university, Osaka university and Azuma shipping
company. New Energy and Industrial Technology Development
Organization (NEDO) sponsored for this project. Kodama (2008)
showed a brief summary of this full-scale experiment with about 4%
net fuel consumption reduction in case of full load condition and 7% in
case of ballast condition. In this paper, the results from shear stress,
thrust and torque measurement done by the authors are presented and
considered using simple momentum integral equation of the boundary
layer. The data was taken from January 6th to 11th, 2008.
ABSTRACT
This paper describes the full scale experiment using air lubrication
method to reduce the frictional resistance. The full scale experiment
with the cement carrier Pacific Seagull was conducted from January to
March, 2008. Torque and thrust are decreased due to the effect of
bubbles. If we assume the value of thrust deduction is constant with
and without bubbles, the effect of bubbles in reducing frictional
resistance or ship resistance is clearly proved by the experimental
results. The maximum total resistance reduction in case of ballast
condition and full load condition are about 11% and 6% respectively.
The mean propeller inflow velocity was increased for with air
lubrication from no air condition due to the viscous resistance reduction.
This phenomenon was considered using very simple boundary layer
method.
KEY WORDS:
EXPERIMENTAL EQUIPMENTS
General Arrangement of Experimental Equipments
Full scale experiment; energy saving; air
The principal dimensions of Pacific Seagull ship are shown in table 1.
In order to conduct the full scale experiment, the ship was equipped
with experimental equipments such as blowers, cameras, ultrasonic
velocity profiler (UVP), thrust and torque gauge on the propeller shaft,
shear stress sensor on the hull surface and etc.
lubrication; frictional resistance reduction.
INTRODUCTION
Air lubrication method is a promising method to reduce frictional
resistance which is nearly 70% of total resistance of low speed ship.
Bubbles were injected at the fore bottom part of the ship. After
injection, it is expected that bubbles will cover all the bottom part
downstream and take effect on local frictional resistance reduction.
In 2002, the full-scale experiment was carried out in SR 239 project for
the first time using the training ship Sein-maru. The net energy saving
in that experiment was 2% at air injection rate 40 m3/min. Based on
this result, the effect of bubbles on frictional resistance reduction of
ship was proved (Nagamatsu et al. 2003).
There are 5 sets of blowers, 3 on starboard and 2 on the port side.
The pressure is 100 kPa. The ability of air supply of one blower is
about 22 m3/min, so maximum bubble generation is 110 m3/min. Air
was fed from blowers to bubble generation device using the related
piping system which was installed from the main deck to the bottom of
ship. Three cameras were installed at propeller plane, bubble injector
position and near shear stress sensors position. The main purpose of
these cameras is to capture the images of bubble when blowers were
active.
Three years later, in 2005, the second full-scale experiment was done
using the cement carrier Pacific Seagull. This ship has a box shape hull
and was equipped with blowers which could be used to supply air for
bubbles. However, injected bubbles did not cover the bottom of ship
sufficiently so maximum frictional resistance reduction was only 1% at
air injection of 50 m3/min (Kodama et al. 2007).
In order to keep bubble more efficiently inside the bottom area of
ship, end plates were welded along the side end under the bottom of
ship. These end plates have the same height of 0.15 m and the total
length of end plates is 47.2 m. Figure 1 shows the general arrangement
of equipments in full scale experiment.
Overall brief description of experiments was shown in Kodama(2008).
Based on the results and accumulation of experience obtained from
88
are shown in Toda et al.(2005) and the size of the fairing plate was
changed to 1174x1174 mm to reduce the effect of the mound. The flat
part is 400x400 mm, so the 27 mm height is reduced using 387 mm
slope (less than 1/14). In this experiment, 3 sensors were installed
under the bottom of the ship. 2 sensors were on the starboard and the
other one was on the port side. The position of these sensors was 50 m
toward the stern direction from the bubble injection position.
Table 1. Principal dimensions of Pacific seagull
Length over all
Length between perpendiculars
Breadth
Depth
Draft (designed full)
Draft (Full experiment)
Draft (ballast) in experiment
Speed (service)
Main engine
Propeller
Diameter of propeller
126.6 m
120.0 m
21.4 m
9.9 m
7.1m
7.0 m even
4.0 m (trim by stern 1.5 m)
12.4 kt
3883 kW x1
4 blades CPP
3.6 m
Blower
Thrust and torque gauge
Bubble generator
Air pipe
Fig. 2 Thrust gauge and torque gauge
End plate
Shear stress sensor
UVP transducers
Camera
Fig. 1 General arrangement of equipment
Strain Gauge and Shear Stress Sensor
To measure the thrust and torque, the strain gauges were attached on
the shaft directly and to minimize the temperature effect, Hylarides
method (Hylarides, 1974) with dummy plate and temperature insulation
using two direction strain gauges were employed to measure thrust and
torque. In figure 2, two pictures on top were focused on the images of
torque gauge and thrust gauge. To minimize the misalignment, the
10mm gauge length was used for measurement as shown in Fig. 2.
Here, torque gauge is the strain gauge on the left and thrust gauge is the
strain gauge on the right. The remain two pictures of Fig. 2 show the
installation work from the beginning when the first strain gauges were
glued on propeller shaft to until the entire job have been done.
Preamplifier with transmitters and batteries were tied with belts around
the shaft. After finished the installation, propeller shaft was covered
with thermal insulation material. The system which was constituted
from these strain gauges will detect thrust, torque and temperature and
transmit the measuring data as radio signals to the data acquisition
system via telemeter.
Fig. 3 Shear stress sensor
EXPERIMENTAL RESULTS
During the operation of ship, the large difference in ship speed
between with and without bubble injection was not observed. The
measurements were carried out for full load and ballast conditions and
the blade pitch angle of controllable pitch propeller was changed to
change the average speed.
Figure 3 shows the images of shear stress sensor before and after it
was installed under the bottom of the ship in the dockyard. As shown in
the left figure, the sensing plate was held with three blade springs and
frictional stress was detected by load cell. The sensing plate was made
of acrylic resin and in a square shape with dimensions of 200 mm x 200
mm, 5 mm in thickness and 238 g in weight. The height of sensor was
quite thin and 27 mm. The right figure shows the installation by stud
bolts. After this installation, the fairing plate was installed as shown in
the bottom figure. It was suitable for mounting sensor to the ship
surface smoothly with fairing. Fairing plates were installed to the
sensor to reduce the height difference between the sensor plate and the
surrounding surface. Detailed information and structure of this sensor
Figure 4 shows the example of shear stress measurement results for
sensor No. 1 (near the bilge keel on starboard side) and sensor No. 2
(near the centre plane). From the figure, the clear reduction of local
skin friction for both sensors can be seen at 50 m downstream from the
injection point and the time lag from the start time of blower operation
due to the distance from the injection point. It shows that the effect of
bubbles remains whole bottom area and the larger reduction seems to
be obtained in the upstream region. This result can be referred to the
result obtained from the 50 m model experiment in NMRI (Kodama et
89
al. 2007). From the figure, the amount of reduction depends on the
location and the reduction rate is larger near the centre plane. About
40% reduction was observed for sensor No. 2.
5
[×10 ]4
Thrust (N)
Shearing Force (N)
~ 5%reduction
3
Shearing Force (N)
Without bubble and with bubble by 2 blowers (No.3,4)
Propeller pitch 16.2degree, ship speed 13.1kt and 12.9kt
∼20% reduction
2
∼40% reduction
Blower On
Blower Off
1
Sensor No.1
t(s)
~ 5%reduction
Torque(N.m)
Sensor No.2
t(s)
t(s)
00
500
1000
Fig. 6 Example of raw time history of thrust and torque without
bubble and with bubble by 2 blowers in full load condition
Fig. 4 Example of raw time history of the local shear force
(acting on the sensing plate) when five blowers were active
From the thrust identity analysis using measured thrust and the
propeller open characteristics measured in NMRI, the effective mean
velocity at propeller plane is estimated. Figure 7 shows the ratio of
resistance and effective wake fraction between with and without bubble.
As showed in this figure, with the appearance of bubble, ratio of
resistance decreased opposite with the increasing tendency of ratio of
effective wake fraction. It means the mean flow in the propeller plane
increases due to the skin friction reduction.
Figs. 5~6 show two examples of thrust and torque measurement in
two cases: ballast condition and full load condition. As shown in these
figures, torque and thrust are decreased due to the effect of bubble and
similar time delay can be observed due to the distance between the
injection point and the propeller. The value of thrust deduction can be
assumed constant with and without bubble, because the main cause of
thrust deduction is the upstream pressure drop by producing the thrust.
So, in this case the total resistance seems to be reduced about 10% in
Fig. 5 and about 5% in Fig. 6. The total resistance reduction of the ship
is about 11% and 6% in case of ballast condition and full load
condition, respectively.
1.2
R/R0, (1-w)/(1-w)0
1.1
In experiment, number of revolution was fixed, so the torque
reduction means the power reduction. It means that the fuel
consumption should be reduced by this reduction.
1
0.9
0.8
0.7
R/R0
(1-w)/(1-w)0
0.6
0.5
0
1
2
3
4
5
6
Number of blower
Fig. 7 Analyzed ratio of R and 1-w between with and without
bubble for ballast condition, pitch angle 16.9 degree
Propeller pitch 16 degree, ship speed 13.1 and 13.2kt
Total resistance consists of 30% wave making resistance and 70%
viscous resistance based on full scale prediction from model
experiment. The ship which was used in full-scale experiment has large
bottom area and this area is nearly 50％ of wetted surface area in
ballast condition. The effect of bubble was only observed at the bottom
of ship. It means that 11% total resistance reduction obtained in
experiment is the reduction in viscous resistance of bottom part. From
the above analysis, if we consider only bottom area of ship, the viscous
resistance reduction of covered area by bubbles will be 35%. From
Fig. 7, if resistance is reduced 11%, nearly 12% of increase of
1-w is observed. The ratio of resistance and 1-w is shown for
one condition in table 2.
Fig. 5 Example of raw time history of thrust and torque without
bubble and with bubble by 5 blowers in ballast condition
90
dθ
7 υ 14
)
= 0.0225(
dx
72 θU
Table 2. Values of 1-w, 1-t and total resistance rate when 5 blowers
were active and propeller pitch angle was set 16.9 degree.
Total resistance ratio
Viscous resistance ratio
of bottom area
1-w
1-t (assumed constant
from model exp.)
Without bubble
1
1
With bubble
0.89
0.65
0.573
0.81
0.638
0.81
This is the well known relation and the non-dimensional form is as
following. The over bar￣ represents the non-dimensional value.
1
−
dθ
7 14 − 14
= 0.0225(
) θ = a ( Rnθ ) 4
72 Rn
dx
where
From table 2, 1-w is increased by 0.65. The viscous wake wv is
estimated from ITTC procedure (wv = w-wp = w-(t+0.04), wv: viscous
wake component, wp: invisid wake component, 0.04: rudder effect). If
wv for with bubble condition is estimated using wv is proportional to
viscous resistance of bottom viscous resistance because the propeller
plane flow almost comes from the bottom area, predicted 1-w is 0.642.
This value is a little bit higher than the measured value, but the increase
of mean velocity can be explained by the resistance decrease in bottom
area considering that the density change and details of the flow field
were ignored.
a = 0.0225(
4
ν
: Reynolds number
1
⎛ 5 ⎞5 −
C f = 2a ⎜ a ⎟ Rn 5 x
⎝4 ⎠
(7)
1
−
1
5
(8)
When bubbles were injected, due to the effect of bubbles, frictional
coefficient will be smaller. Assume that we can express the relation
between Cf (local frictional coefficient with bubble) and Cf0 (local
frictional coefficient without bubbles for same momentum thickness
Reynolds number) like the equation below:
We assume velocity distribution in boundary layer by using the 1/7
power law like in Eq. 1
⎛ Uθ ⎞
C f = k (ta , void fraction distribution)C f 0 ⎜
⎟
⎝ υ ⎠
1
(1)
(9)
In Eq. 9, ta is air layer thickness. The value of ta is expressed as follow.
And using the following local skin friction law
1
UL
Using Eq. 2 with the value of momentum thickness received from
Eq. 7, we obtain
The simple integral method for two dimensional boundary layer is
employed to consider the phenomena obtained in the full scale
experiment. For without bubble conditions, the following equation is
well known as the simple method (Schlichting, 1979).
⎛ υ ⎞4
τ = 0.0225ρU ⎜ ⎟
⎝δ ⎠
Rn =
⎛ 5 ⎞5 −
θ ( x) = ⎜ a x ⎟ Rn 5
⎝4 ⎠
4
7
4
7 14
)
72
(6)
After solving the above equation, momentum thickness will be
represented as
CONSIDERATION USING SIMPLE INTEGRAL METHOD
u ⎛ y ⎞7
=⎜ ⎟
U ⎝δ ⎠
(5)
ta =
1
τ
⎛ υ ⎞4
Cf =
= 2i0.0225 ⎜
⎟
1
⎝ δU ⎠
ρU 2
2
(2)
Qa
( BaU )
(10)
where, Qa is injected air flow rate, Ba is the width of the
injection plate. Therefore
B
Where δ: boundary layer thickness, U: the uniform flow velocity
L: ship length, θ : momentum thickness
y: the distance from the surface, ρ: the density
τ: shear stress, Cf: local skin friction coefficient
υ: kinematic viscosity
δ
u
U
0
θ =∫
⎛ u
⎜1 −
⎝ U
7
⎞
⎟dy = δ
72
⎠
1
1
−
−
dθ 1
= kC f 0 = kaRn 4 θ 4
dx 2
To the point x = x0 (injected point), we obtain the momentum thickness
using original Eq. 7. So, the momentum thickness at x0 is shown as
follows
(3)
The momentum integral equation is shown as the following.
dθ
τ
=
dx ρU 2
(11)
5
5
4
−
1
θ ( x0 ) 4 = aRn 4 x0
(4)
(12)
Momentum thickness at initial value of x = x0 must be the same in case
of bubbles and without bubbles. So, we can obtain the momentum
thickness for with bubble condition as follows
Where x : the distance from the leading edge in flow direction
So the momentum thickness will be obtained as follow
91
5
−
5
4
1
5
4
−
1
position x0 and k. In full scale experiment, bubbles were injected at
26 m downstream from the bow. In other words, injected bubble
location is about 20% from the bow when it is compared with the
length of real ship. From this and the above mentioned analysis, as
shown in Fig 9, in case x0 = 0.2, k = 0.5 total frictional resistant
coefficient reduction between with and without bubbles is 35%. This
value shows a good agreement with the aforementioned result obtained
in full scale experiment.
5
θ 4 ( x) = kaRn 4 x − kaRn 4 x0 + θ 4 ( x0 )
After transformation, this equation become
4
1
−
⎛5
⎞5
θ ( x) = ⎜ aRn 4 k x + (1 − k ) x0 ⎟
⎝4
⎠
(
)
(13)
From Eq. 13 the value of local frictional coefficient will be obtained as
follow:
−
⎛5
C f = 2akRn ⎜ aRn
⎝4
1
−
4
1
−
4
⎞
( k x + (1 − k ) x ) ⎟
0
Figure 10 displays the momentum thickness for k=0.5 along with
without bubble condition at different air injection positions. The solid
curve depicted the momentum thickness without bubble. At the
injection points x0 = 0.2 and x0 = 0.4 momentum thickness changed to
dash curve and dash dot curve, respectively. Boundary layer
development will change due to the local skin friction reduction. This
phenomenon could be used to explain the increasing tendency of 1-w
when bubble takes effect at the bottom of ship.
1
5
(14)
⎠
In case k ＝ 1/2 , Eq. 14 can be rewritten as follow:
−
1
−
⎛5
⎞
C f = aRn ⎜ aRn 4 x + x0 ⎟
⎝8
⎠
−
(
1
4
)
1
5
(15)
The calculated value is decided by the value without bubbles and
shown in Fig. 8. The Cf00 is the value for without bubble condition.
Although we assume the constant k=0.5, the value of Cf/Cf00 is
increasing towards the downstream from the injection point. This
tendency is similar as the results obtained in NMRI using 50 m model
with end plates (Kodama et al., 2007).
x0=1
x0=0.2
x0=(0:1)
x0=0
Cf/Cf00
ｋ
Fig. 9 CF/CF0 at different x0
k= 0.5, x0= 0.2
θ .Rn
1
5
x
Fig. 8 Cf/Cf00 at ｋ = 0.5, x0 = 0.2
Total frictional resistance coefficient is shown as follows
CF =
R
1
ρU 2 L
2
= θ (1)
L
k=0.5
1
1
R = ∫ τ dx = ρU 2 L ∫ C f d x
2
0
0
(16)
Where R: total frictional resistance
So, the value of frictional coefficient can be obtained by Eq. 7 and
Eq. 13 for without and with bubble conditions, respectively.
Fig. 10 Momentum thickness at different x0
Fig. 9 shows the relation among the ratio of total frictional resistant
coefficient between with and without bubbles CF/CF0, injected bubble
92
CONCLUSIONS
REFERENCES
The effect of bubbles in reducing frictional resistance or ship
resistance is clearly proved by full scale experiment result. The mean
velocity at propeller plane is increased due to the viscous resistance
reduction from the thrust measurement results. It seems the cause of the
small speed gain against the large resistance reduction. The torque
reduction is also observed and the required power reduction is shown.
The phenomena are considered using very simple boundary layer
theory. But the mechanism of frictional resistance reduction by bubbles
is complicated. It is necessary to have further research to elucidate this
problem.
Hylarides. “Thrust Measurement by Strain Gauge without the Influence
of Torque” Shipping World and Shipbuilder, Dec. 1974,
pp. 1259-1260
Kodama, Y, Takahashi, T, Makino, M., Hori, T, Kawashima, H, Ueda,
T, Suzuki, T, Toda, Y, Yamashita, K (2005). “microbubbles – a
large scale model experiment and a new full-scale experiment”
Proceedings of the 5th Osaka colloquium, pp. 62-66.
Kodama, Y, Hinatsu, M, Kawashima, H, Hori, T, Makino, M, Ohnawa,
M, Takeshi, H, Sakoda, M, Kawashima, H, Maeda, M(2007). “A
progress report of a research project on drag reduction by air
bubbles for ships” 6th International conference on multiphase flow,
ICMF 2007.
Kodama, Y et al. (2008). “A full-scale air lubrication experiment using
a large cement carrier for energy saving-result and analysis”,
Conference proceedings, the Japan Society of Naval Architects and
Ocean Engineers, pp. 163-166 (in Japanese)
Nagamatsu, T et al (2002). “A Full-scale Experiment on Microbubbles
for Skin Friction Reduction Using ”SEIUN MARU” - Part 2: The
Full-scale Experiment-”, Journal of the Society of Naval Architects
of Japan, No. 192.
ACKNOWLEDGEMENTS
This study is sponsored by NEDO and done as the cooperative
research project with NMRI, Azuma Shipping Co. Ltd., Hokkaido
University and University of Tokyo. The authors appreciate of those
supports. The authors would like to express the special thanks to Dr.
Yoshiaki Kodama and Munehiko Hinatsu for the guidance of the
project. The special thanks are extended to the crew members of Pacific
Seagull.
Schlichting, H. (1979). “Boundary layer theory-seventh edition”
McGraw – Hill, pp. 636-639
Toda, Y, Suzuki, T, Yuda, N, Lee, Y.S(2005). “Shear stress sensor for
full-scale experiment” Proceedings of the 5th Osaka colloquium,
pp. 67-75.
93
International Symposium on Marine Engineering (ISME) 2009, BEXCO, Busan, Oct. 2009
Frictional Resistance Reduction using Lower Frictional Paint
N.Yamamori 1, Y. Toda 2, Y. Yano 3
1. Nippon Paint Marine Coating Co, Ltd., 19-17 Ikedanakamachi, Neyagawa City,
Osaka572-8501, Japan, [email protected]
2. Osaka University, Department of Naval Architecture and Ocean Engineering 2-1 Yamadaoka,
Suita City, Osaka 565-0871, Japan, [email protected]
3. Kobe University, Training Ship Fukae Maru, 5-1-1 Fukaeminamimachi, Higashinadaku,
Kobe City, Hyogo 658-0022, Japan, [email protected]
Corresponding author Y. Toda
Abstract
The effect of paint coating on hull surface to the ship frictional resistance is studied. The frictional
resistance acting on the newly developed anti-fouling Lower Frictional paint (LFC-AF) is compared
with that on the conventional Self Polishing Copolymer (SPC) through rotational cylinder tests,
towing tank experiment. The viscous resistance reduction using LFC was observed in those
experiments. The results show the promising results. So, the full scale experiment and full scale
monitoring during actual service voyages were conducted and the lower fuel consumption was
obtained for the condition with LFC surface. This paint seems to reduce the roughness effect in the
water.
Keyword: Ship Resistance, Lower Friction Paint, Surface Roughness, Towing tank Experiment
1. Introduction
Energy-saving technology is studied in various fields with the pressure from environmental
protection and the unpredictable fuel price. In the field of ship building and operation, the energysaving by reducing the ship resistance or high efficiency propulsion system have been investigated by
many researchers, for example, the group discussion 3 in 25th ITTC[1]. In this study, the Lower
Frictional paint (LFC) on ship surface is studied through rotational cylinder test, towing tank
experiment, full scale experiment and full scale monitoring during actual service voyages. The paint is
developed by Nippon Paint Marine Coating Co. Ltd. to get the lower frictional resistance than the
conventional Self Polishing Copolymer(SPC).
In the rotational circular cylinder tests, LFC surface shows 5% lower frictional resistance than the
conventional SPC for around 100μm.
In the towing tank experiment, three same geometry ship models which have different surface
condition were tested. Two of them were painted with new LFC and Self-polishing paint (SPC),
respectively. These two model have similar roughness(150μm). The remaining one was not painted
and the FRP surface was polished to make the surface smooth (very low roughness). The resistance
tests and velocity measurement in boundary layer were conducted. From the results of resistance test,
total resistance coefficient of LFC surface model was about 6% lower than that of SPC surface model
where fluid number was 0.25 to 0.4. And viscous resistance coefficient of LFC model was about 10%
lower than that of SPC model where Reynolds number was 3.5 million to 5.5 million. From the
velocity measurement, the axial velocity component in the boundary layer around new paint surface
was larger than that around SPC surface. Therefore, roughness effect of LFC should be smaller than
that of actual roughness. The simple consideration using White’s equation was done based on the
measured results. In result, roughness effect of LFC on geometrical roughness of 153μm was
94
N. Yamamori, Y. Toda and Y. Yano
equivalent to that of 50μm. The full scale performance was estimated using equivalent roughness. The
LFC seems to have the potential to reduce fuel by 5 % for 150μm roughness.
The results of monitoring for actual ships and full scale experiment of ship resistance are also
presented and the results show very promising feature.
2. Laboratory Experiment
In the laboratory, the rotating cylinder test and resistance test using 3m model were carried out. The
measurement of roughness was made by non-contact type roughness meter using laser displacement
meter. The roughness of test cylinder surface was measured directly by special device. The roughness
of the model surface was measured by measuring the replica surface taken from the model surface.
2.1 Rotating circular cylinder test
To measure the difference of frictional resistance acting in the paint surface, the rotational cylinder
testing device was used to select the good paint. It is similar as the device used in Tanaka and Toda et.
al[2] and the size of the cylinder is different and the devices have the similarity. The cylinder size is
10cm diameter and 10cm height. It was rotating in the 30cm diameter cylinder tank. The side surfaces
of the cylinders were painted by several paints and top and bottom surfaces were treated as smooth
surface. Before the tests using paint surfaces, the cylinders that have the artificial roughness similar as
sand roughness were tested and the device was checked. The results show the test device can show the
change of frictional resistance due to roughness.
The measurement device is shown Fig.1. The torque acting on the rotating cylinder was measured
by subtracting the torque acting on the shaft and by the support bearings using the test without a
cylinder (shaft only). The examples of results are shown in Fig.2. In the figure, the torque is nondimensionalized using surface velocity and side surface area as shown in Eq.(1) and plotted versus
Reynolds number Rn based on the circumferential length and surface velocity. Ct means frictional
resistance coefficient or local skin friction coefficient.
Ct 
Torque
1
D
2
  nD   D 2 
2
2

Torque
Rn 
1
 2 n 2 D 5
4
n 2 D 2
(1)

where
n: number of revolution of cylinder per second D:Diameter of circular cylinder
 :density  : kinematic viscosity
0.0070
0.0065
0.0060
従来型 1
SPC１
従来型２
SPC２
従来型３
SPC３
LFC1
LFC2
LFC3
従来型４
SPC４
Ct
0.0055
0.0050
0.0045
0.0040
0.0035
0.0030
1
Fig.1 Experimental device for rotating cylinder.
6
11
16
21
26
31
36
41
46
[x10 5]
Fig.2 Example of test results.
Re
In Fig.2, frictional resistance with several LFC surface are compared with frictional resistance with
conventional SPC surface. Those surfaces have similar surface roughness around 90-100  m .
Although those surface have the similar roughness, frictional resistance acting on the LFC surface
clearly lower than that on SPC surface for all surface speed range. The frictional resistance acting on
the smooth surface finished by buffing is lower than those results. To investigate the paint surface
effect on the frictional resistance, the frictional resistance increase from smooth surface to paint
surface is shown in Fig.3 at Rn=4,000,000 for LFC and SPC surface with various roughness.
95
N. Yamamori, Y. Toda and Y. Yano
Fig.3 frictional resistance increase due to paint surface versus surface roughness
As shown in figure, the frictional resistance of LFC group is lower than that of SPC group. Usual
paint surface using usual painting device is 100-150  m , so LFC surface frictional resistance seems to
be lower around 5% than usual SPC surface. LFC surface seems to reduce the effect of roughness.
2.2 Towing tank experiment
To measure the effect to the frictional resistance in the developing boundary layer due to painted
surface, usual resistance tests using 3 m mathematical models were conducted in Osaka University
towing tank (length: 100m, width: 8m, depth: 4.35m). The model geometry is shown by Eq.(2).
y
B  z 
1   
2   d 
2
  2 x  2 
1

  L  


L  3.0m B  0.5m d  0.2m
where x : distance from midship in lengthwise direction
y : distance from center plane in lateral direction
z : distance from still water plane in depthwise direction
(2)
The three FRP models were made from same mold and geometry of the models were checked
before painting. The conventional SPC and present LFC chosen by rotating cylinder tests were painted
on two model surface by same painting procedure, respectively. The roughness of conventional SPC
surface and LFC surface were 160  m and 153  m , respectively. The other model surface was
finished by buffing to the hydrodynamically smooth surface (the roughness 11  m ). The surface
roughness was the mean of the measured values on the replica surfaces taken from several model
surface points. The photographs of the model are shown in Fig.4. After painting, the models were
dipped into artificial seawater for three weeks and tested. Four resistance tests were conducted every
one month and the painted models were dipped between the tests. Before the fresh water towing tank
test, then models were washed by water. The test results for four tests were very similar, so the final
test result is shown in this paper. As shown in top photographs, no turbulence stimulation device was
installed on the model. The resistance test was conducted using usual two yawing guides,
dynamometer (100N full scale) and towing rod as shown in the bottom photographs. The displacement
weight (bare hull weight +ballast weight) of the models was kept to same value (1,306N) during
experiment. The carriage speed U was changed from 0.4m/sec to 2.4m/sec. The example of resistance
test result is shown in Fig.5. Fig.5(a) shows the measured resistance and (b) shows the total resistance
coefficient. The resistance coefficient curve shows the laminar effect at low Froude number (Fn) and
usual curve which has the large wave making resistance at high Fn. The resistance increase of the
painted surface from the smooth surface due to the roughness is observed in the figure. But, the
increase is clearly different between SPC surface and LFC surface. From the comparison between two
painted surface, even in (a), the clear resistance reduction for LFC surface model from conventional
SPC model resistance is observed in high speed range. From Fig.5 (b), the resistance reduction due to
LFC paint compared with the model of SPC paint is seen in all speed range. The reduction is 4-5%.
Although two painted models have similar roughness on their surface, the resistance of LFC model
increases only 3-4% on the contrary that of SPC model is 8-10%.
96
N. Yamamori, Y. Toda and Y. Yano
Fig.4 Models for towing tank experiment and resistance test apparatus
(a)
(b)
CT 
R
1
U 2 S
2
Fn 
U
Lg
R :Total resistance (N)
L: Model length(m)
S :Wetted surface area(m 2 )
 :Water density(Kg/m3 )
g :gravity acceleration(m/sec 2 )
Fig.5 Results of resistance tests
To investigate the effect of paint surface to viscous resistance, usual analysis of resistance test was
done for hydrodynamically smooth surface model. Form factor K is estimated as 1.11 from low Fn
data. Wave making resistance coefficient was estimated by subtracting viscous resistance (1+K)CF0
from CT total resistance coefficient. Frictional resistance coefficient CF0 of equivalent flat plate is
calculated by Schonherr equation. For painted models, the viscous resistance coefficient is estimated
by subtracting wave making resistance at same Fn from total resistance coefficient due to the same
geometry. Fig.5 shows the total and resistance coeeficient for three models along with frictional
resistance coefficient of the equivalent flat plate and wave making resistance. The viscous resistance
coefficient of the painted models is larger than the smooth model due to roughness.
R
UL
Rn 
1

U 2 S
2
R :Total resistance (N)
L: Model length(m)
CT 
CF 0 
0.242
log10 ( RnCF 0 )
S :Wetted surface area(m 2 )
 :Water density(Kg/m3 )
 : kinematic vis cos ity (m 2 /sec)
K : Form Factor
CT ( smooth)  (1  K )CF 0  CW ( Fn )
(a)
CV ( smooth)  (1  K )CF 0 ( K :determined at low Fn )
(b)
CV (SPC or LFC)  CT (SPC or LFC)  CW ( Fn )
Fig.5 Resistance coefficient and ratio of resistance coefficient versus Reynolds number
97
N. Yamamori, Y. Toda and Y. Yano
The increase due to roughness on painted surface is smaller for LFC than for conventional SPC and
the viscous resistance for LFC is smaller than for SPC. The ratio of resistance coefficient is also
shown in Fig.5. From Fig.5(b), viscous resistance for LFC is lower around 10% than for SPC around
Rn =3.5 to 5.5 million. The ratio of viscous resistance between two models increases as Rn increases,
while the ratio of total resistance shows similar value for all Rn due to the ratio of viscous resistance
and wave making resistance. From these results, LFC seems to have low equivalent hydrodynamic
roughness.
To investigate this effect, the simple consideration using White’s equation [3] was done based on
the measured results. In the equation, equivalent roughness height k is used. Frictional resistance
coefficient increase CF 0 of equivalent flat plate for a certain k was obtained by the total frictional
resistance coefficient calculated by same equation (k=0) from the total resistance coefficient calculated
for a certain k. Viscous resistance of painted model was estimated by adding CF 0 to viscous
resistance of smooth model. The result is shown in Fig.6.
Fig. 6 Prediction by White equation
Fig.7 Full scale prediction
Fig.8 Boundary layer profiles
As shown if Fig.6, the prediction using k=160  m agrees well with experiment for SPC, on the
contrary the prediction using k=50  m agrees well with that for LFC. It means that LFC has the effect
to reduce the roughness effect. In result, roughness effect of LFC on geometrical roughness of 153μm
was equivalent to that of 50μm. The full scale viscous resistance for ship length 50 to 300m was
predicted by assuming equivalent roughness 160  m and 50  m for SPC and LFC, respectively. The
ship speed was assumed 15kt. Note that k/L decreases as ship length increases due to the constant k.
Result is shown in Fig.7. Viscous resistance can be reduced by using LFC instead of SPC in case of
painted rough surface(around 150  m roughness). If viscous resistance and wave making resistance
are similar, the total resistance can be reduced about 5%. The reduction rate depends on hull form and
Froude number (the ratio of wave making resistance and viscous resistance). The boundary layer
measurement at 95% length position(x/L=0.95) was conducted for three models. The velocity profile
shows that the velocity in boundary layer for LFC is higher than that for SPC. It also show that LFC
reduce the roughness effect and momentum loss.
3. Deceleration test using training ship ‘Fukae Maru’
To investigate the effect of paint on the full scale ship, deceleration test using the training ship ‘Fukae
Maru’ of Kobe University was conducted in 2006 and 2007 after docking. In 2006, LFC was painted
on the former paint and conventional SPC was painted in 2007 in similar way. So, the roughness was
similar for both experiments. The test was conducted for similar draft and inside the breakwater of
Kobe port to minimize the wave, wind and tidal current effect as shown in Fig.9. The four tests were
carried out for following wind, head wind, port side beam wind and starboard side beam wind case.
CPP propeller is installed on the ship, so the experiment was done as following. The steady speed was
accomplished at S/B Full Ahead Engine(CPP blade pitch angle 20degree) around 10knot for some
98
N. Yamamori, Y. Toda and Y. Yano
period and the pitch angle was changed to Stop Engine condition(pitch angle -1degree). After this
change, the ship speed and position were recorded. Stop Engine condition means that the propeller
does not produce the thrust at zero advance speed, so the propeller produce the drag force
approximately proportional to U2. If the total resistance acting on hull is assumed to be constant
around some speed, the total drag force including propeller and hull is proportional to U2. So, if the
viscous resistance coefficient is smaller around 8kt, the period for deceleration from 8kt to 6kt is
longer and the distance is longer. The example of ship speed time history is shown in Fig.10. From
these time histories, the coefficient related to drag force is calculated by using the data between 8kt
and 6kt and compared for two paint conditions. If this coefficient a is smaller, the drag force is smaller.
Fig. 9 Example of experimental route
Fig.10 Example of ship speed time history
Table 1 shows the analyzed coefficient a. The averaged values of a for LFC(No.4-10) and SPC(No.1116) are 12.017 and 12.650, respectively. It means the total resistance of LFC surface is 5% lower than
that of SPC surface. By monitoring the real operation from docking to docking for some Ferry and
PCC, the fuel consumption per mile or hour was reduced by LFC. From those results, LFC seems to
reduce the fuel consumption about 5% by reducing the roughness effect.
Table 1 analyzed coefficient related to drag
4. Conclusion
The viscous resistance of newly developed anti-fouling Lower Frictional paint (LFC-AF) was
investigated through rotational cylinder test, towing tank model experiment, full scale experiment and
full scale fuel consumption monitoring. In the laboratory experiment, the viscous resistance of LFCAF is clearly lower than that of conventional Self Polishing Copolymer (SPC). LFC seems to have the
effect to reduce the roughness effect of real geometrical roughness. In the full scale tests, the results
shows LFC paint is very promising.
References
[1] Hubregtse A.(Chaiman), “Group Discussion 3: Global Warming and impact on ITTC Activities”,
Proc. of 25th ITTC, Vol.III, Fukuoka, Japan (2009).
[2] Tanaka H., Toda Y. Higo K. Yamashita K ., “Influence of Surface Properties of Coatings to
Frictional Resistance”, Journal of Kansai Soc. Nav. Archi., Japan, No.239(2003) .
[3] White F. M., “Viscous Fluid Flow : 2nd Edition”, McGraw-Hill, (1991).
99
資料３
親水性ペンキによる
摩擦抵抗 減
摩擦抵抗低減に関する一考察
す
考察
大阪大学
戸田保幸、眞田有吾、植原靖子
今回のものは委員会での話の中で出てきた部分的に高性能塗
料を利用する等のことに対して検討したものであり、簡単な検
討を行った手始めで論文にまとめるほどのものではないと思わ
れるが1考察としてお話させていただく
• ISME2009のYamamori,Toda,Yanoの結果がベースでるのでそ
れを少し見ていただいた後今回の説明をさせていただく。
100
1
Ship Models
Wigley船
L=3000mm
B=500mm
d=200mm
排水量 33 3k f
排水量=133.3kgf
図1 Plain (無塗装船)
図2 LFCN30 (親水性塗料) 図3 LFC46(自己研磨型塗料)
図２ LFC46表面状態
(粗度 160μm)
図１ LFCN30表面状態
(粗度 153μm)
粗度の影響を計算式で表すために、レプリカで計測された10点平均
粗度の影響を計算式で表すため
、
リカで計測された 点平均
粗度高さRzを用いた。等価砂粗度との関係はこの程度の平均波長
の場合1/2の高さの砂粗度となる。
101
2
実験時の摩擦抵抗推定法
山盛らではWhiteの近似式を用いて推定されてい
た。
今回はこれを直接運動量積分式を解くことによって
高価な塗料を塗る位置などについても検討。より複
雑な境界層内速度分布に対しても簡単に拡張可能
（たとえば勝井らの摩擦抵抗式を求めた速度分布な
ど）
今回のアプローチ
①摩擦抵抗係数ＣFを、近似式ではなく運動量積
分式を直接解いてもとめる
分式を直接解いてもとめる。
②実船で考えた場合、親水性塗料にどれほど省
エネルギ 効果があるのかを調べるとともに
エネルギー効果があるのかを調べるとともに
一部に用いた場合の効果などについても検討
102
3
粗度を考慮した平板周りの境界層
d

1
cf


dx U 2 2
運動量積分式
運動量厚さの定義
 

u
u
(1  )dy
U
U
0
乱流境界層内の速度分布
u
1 u* y
u
 ln(
)  5.5 ΔB　:

U
u* 
*

U
2
粗度関数ΔＢ
①Whiteの式
B 
1



ln(1  0.3
0 3k )
k 
u *k

②CebeciらのNikuradseの粗度を考慮した式
k ＜2.25　B  0
2.25  k ＜90 B  ( B  8.5 
90  k  B  ( B  8.5 
1

103
1

ln k  ) sin(0.4258(ln k   0.811))
ln k  )
4

u
u
(1  ) dy　U
U
1
1
1
   (1   ln  )(  ln  )d
 
0





    ln   ( ln  ) 2 d
0

 


2
  (  2 2 ) 

U 1 u*
1
)  5.5  ln(1  0.3k  )
 ln(
*



u
*
U u 1 u 
1 u* y

ln(
)

ln(
)




u*
1 
 ln
 y
0
1
1

ln(
u
1 u* y
ln
 1
U
U 
1
y
 1   ln

:
u
u*

ln(
u*



U

e e
B '  5.5 - B
1

 B ')

 e  e  B '


  B '
1

)  (
u*
*
U
) B' 

u
*

e  e  B '
1

( 2 2)


subroutine bibun(y,f,U)
y: momentum thickness θ non-dimensional
ｆ：ｄθ/dx nondimensional
real k,Rn,c,L,U,m
k=0.4
c=0.0001
L=300.
am 1.11
am=1.11
z0=0.02
Rn=(U*L*1.e6)/am
do i=1,50
B=5.5-1/k*log(1+0.3*Rn*c/L*z0)
z=k/(log(Rn*y/exp(-k*B)/(1/k-2*z0/k*k))
zsa=abs(z-z0)
if(zsa.lt.1.e-12) then
go to 200
else
z0=z
endif
end do
200 continue
f=z0*z0
return
end
104
5
Rougness function ΔＢ
14
12
ΔB
10
ΔB
8
ΔB=ln(1+0.3k)/κ
6
4
2
0
‐2
0
100
200
300
400
k+
k ＜2.25　B  0
2.25  k ＜90 B  ( B  8.5 
90  k  B  ( B  8.5 
1

1

ln k  ) sin(0.4258(ln k   0.811))
ln k  )
Momentum thickness
L=3m
L
3m
0 004
0.004
0.0003
0.002
0.0002
0.001
0
0
k=160μm
k=50μm
plain
運動量厚さ　θ
運動量厚さ　θ
k=160μm
k=50μm
plain
0.003
L=200m
L
200m
0 0004
0.0004
0.0001
1
2
Rn
0
0
3
[10 ]
U  1.0(m / s )   1.11*106 CF 
1
2
Rn
6
3
4
[107]
2
CF : Frictional Resistance Coeffi
L
105
6
Frictional Resistance
摩擦
擦抵抗係数CF
-6
10
0* -6
84 10
=3 0* -6
*k 0 0
U =32 0*1 -06
*k 6 1
U =25 20* -06
*k 19 1-6
U k= 00*10
*
U =12 0* -6
0
*k 0 0
U k=1 0*1-6
* 0 0
U k=8 *1 -6
* 0
U =60 * 1 0
*k 0
U =4 0
*k
U
0.003
k/L=1.0*10-6
0.002
-6
k/L=0.5*10
-6
6
k/L=0.25*10
0.001 7
10
108
plain
109
Rn
実験の摩擦抵抗と計算値の比較
6
3
10 CF
5
103ΔCF0
4
Cv (plain)
実験値Cv (k=160μm)
実験値Cv (k=153μm)
(k 153
)
計算値 CF（k=160μm)
計算値 CF(k=50μm)
計算値 CF(plain)
3
2
1
0
1
2
3
4
Rn×10-6
5
ΔCF0 (k=160μm)
ΔCF0 ((k=153μm)
μ )
ΔCF0 (k=160μm)
ΔCF0 (k=50μm)
ただし、Ｌ＝3m,動粘性係数  1.109256*106
Ｕ=0.4～2.4（m/s)
106
7
速度ごとの実船の摩擦抵抗推定値
0.003
摩擦抵抗係
係数　CF
摩擦抵抗
抗係数　CF
0.003
U=8.0knot
0.0025
0.002
0.0015
0 002
0.002
0.0015
0.001
0.0005
50
U=12knot
0.0025
0.001
50
100 150 200 250 300 350 400
100 150 200 250 300 350 400
船長　L(m)
U=16.0knot
0.0025
U=24.0knot
0.0025
0.002
0.0015
0.001
50
船長　L(m)
0.003
摩擦抵抗係数　C
CF
摩擦抵抗係数　CF
0.003
0.002
0.0015
100
150
200
250
300
船長　L(m)
350
0.001
50
400
ｋ=50,80,120,160,200μm
100 150 200 250 300 350 400
船長　L(m)
親水性塗料による摩擦抵抗値減少率
16.00
実船レベルでのCF減少率
14.00
CF減少率(%)
12.00
10.00
U=8.0(knot)
U=12.0(knot)
8.00
U=16.0(knot)
6.00
U=20.0(knot)
U=24 0(knot)
U=24.0(knot)
4 00
4.00
2.00
0.00
50
150
250
350
450
船長L(m)
107
8
cf
L=3m
0 01
0.01
L=200m
0 006
0.006
局部
部的摩擦抵抗係数　cff
局部
部的摩擦抵抗係数　cff
局部摩擦抵抗係数
k=160μm
k=50μm
plain
0.005
0.008
0.004
0.006
0.003
0.004
0.002
0 4
10
0.002
k=160μm
k=50μm
plain
105
0.001
106
0 6
10
107
Ux/ν
107
108
Ux/ν
U  1.0(m / s )   1.11*106
1.40E+00
摩擦抵
抵抗係数 ＣF
1.20E+00
1.00E+00
8.00E‐01
6.00E‐01
4.00E‐01
2.00E‐01
0.00E+00
1
①plain
②ks=50(μm)
2
3
③ks=160(μm)
108
4
④f:ks=50(μm)
b:ks=160(μm)
5
⑤f:ks=160(μm)
b:ks=50(μm)
9
③k=160
⑤back k=50
④front k=50
②k=50
①plain
運動量厚さ　θ
0.001
0.0008
0.0006
0.0004
0 0002
0.0002
0
0
0.2
0.4
0.6
0.8
1
x
③k=160
⑨中央k=50
⑥両端k=50
⑧後方2/3 k=50
⑦前方2/3 k=50
②k=50
①plain
運
運動量厚さ　θ
0.001
0.0005
局部摩擦抵抗
抗係数　cf
0
0
0.2
0.4
0.6
0.8
1
0.0025
0.002
0.0015
0
0.2
0.4
0.6
0.8
1
③k=160
⑨中央k=50
⑥両端k=50
⑧後方2/3 k=50
⑦前方2/3 k=50
②k=50
①plain
x
109
10
ただしこれは平板での検討で
あるので船尾付近のガース長
さの減少や逆圧力勾配による
境界層の厚くなる部分では異
なると思われる。これについて
は粗度関数への圧力勾配影
響も加味して積分型解法で検
討予定
塗料の部分使用
摩擦抵抗が小さいと考えられる塗料の塗り方による違いは
、塗布領域以上の効果は見込めなかった。
摩擦が高い前半部に塗るのも後半部に塗るのも摩擦抵抗
に違いはないという計算結果になった。
現在模型を5mとし検討中（次ページ）
110
11
１．
初めに
５ｍ数式模型船を用いて水槽実験により塗膜の抵抗特性を求めた。塗膜はかなり表面粗
度が大きいものをつくり模型船における計測でも大きな差が出るものを作成し調査したも
塗装模型船を用いた水槽実験。
のである。
２．
5m の FRP 模型船を多数作成し、その表面をさまざまな粗度で塗装した（粗度１2,3,4）
模型船 4 隻を用意し抵抗試験を行った。これに加え表面が滑面である無塗装模型船も実験
した。また無塗装、粗度 1 と 2 については、抵抗の差と速度分布や乱れ度の大きさの変化
の差を比較するためステレオ PIV 装置による流場計測も行ったが委員会では省略する。ま
た粗度１と２については表面粗度計を試作し表面形状の計測を行い、実際の幾何粗度計測
も行った。また、抵抗から等価砂祖度を推定し、実船推定の方法を提案した。以下それら
について示す。また PIV 試験用に黒色に塗装した。
２．１模型船
5000mm
ま伸ばした垂直舷側
喫水より上部は喫水の形をそのま
z : 水面からの深さ L : 全長
x：長さ方向距離船体中心より
B
z
2x
y  (1 ( )2 )(1 ( )2 )
d
L
2
y : 各点の幅 B : 全幅　d : 喫水
模型船は表 1 に示す主要目を持つ Wigley 船型で船型を表す数式は表に入れている
全長
600mm
表 1 模型船主要目
全幅
399.8kgf
300mm
排水量
400mm
喫水
全深さ
模型船の写真を図１、図２に示す。図１が無塗装滑面模型船であり、PIV 計測のため船尾
部分を艶消しブラックで薄く塗装し研磨して滑面とした。図２は今回作成した塗装表面を
持つ模型船の一例である。塗装模型船は全体の写真は同じように見えるので表面の写真を
図３に示す。
図１
滑面模型船
抵抗試験
(a) 概要
２．２
図３ 各塗装模型船の表面
図２
塗装模型船の一例
大阪大学船舶海洋試験水槽(長水槽)において、抵抗試験を表２のような日程と水温の下で
実施した。模型船は外形は完全に仕上げられているが、FRP の厚み等が異なるため模型船
重量は異なる。そのため抵抗試験に必要な治具を取り付けたのち重量を測定し、排水量が
同じになるようにバラスト重量を調整した。また船体に引いた喫水線によりトリムの調整
表 ２ 実験条件
使用した模型船
PLAIN船
LFC(粗度大)
LFC(粗度小),LFC(粗度中)
SPC(粗度中)
水温(℃)
23.4
23.4
23.2
23.2
は行った。トリム、シンケージのみフリーとしたので重心高さは厳密に調整していない。
実施日
9.12
9.13
9.14
9.15
111
が粗い。見た目の粗度の大きいほどこの場合では抵抗が大きい。
図に示すように明らかに粗度の影響が表れていることがわかる。粗度は番号が少ないほう
それを模型船中央にピン接続し、各種船速(0.4m/s～2.8m/s まで 0.2m/s 毎)で曳航し、模型
す。
抵抗を無次元化し全抵抗係数で示したものを図７に示す。図中の PLAIN は滑面模型船を示
図 4、図 5 に示すように斜航軸(曳航ロッド)に検力計(型式：LMC-3502-20)を取り付け、
船抵抗(全抵抗値:Rt)を計測した。その際に、模型船が斜航、ロールをしないように模型船
図 5 斜航軸(曳航ロッド)
る。これは理論的な考察から得られるものと
高速になるほど境界層が薄くなるため粗度の影響が出やすく差が大きくなる様子が見られ
抗試験解析より得られた造波抵抗係数を示す。粘性抵抗にすると同じ模型船租度であれば、
め全体の粘性抵抗傾向を見るために使用する。図８に粘性抵抗係数と滑面模型船の通常抵
塗装面での粘性抵抗を求めた。これは計測値の引き算が入るためばらつきが大きくなるた
が同じであるので造波抵抗を各フルード数で全抵抗からさし引くことにより、それぞれの
（低速で造波抵抗を０と仮定することにより０.０５が得られた）と造波抵抗を求め、船型
さの順に変化している。次に滑面模型船で通常の抵抗試験解析をおこない、形状影響係数
の全抵抗の差がありかなり大きな差が生じている。抵抗は滑面より目視による粗度の大き
全抵抗係数にするとより粗度による抵抗変化が顕著に見える。滑面とは粗度１で約１２％
図７ 全抵抗係数
の前後端付近にガイドを挿入した。
図 4 抵抗試験の様子
抵抗試験結果
計測した全抵抗値 Rt を図６に示す。横軸をフルード数、縦軸を全抵抗値 Rt とする。
(b)実験結果
図６
112
図８
粘性抵抗係数
等しい傾向であるのでこの図から等価砂祖度を算出する。
（ｃ）砂粗度による粗度関数を仮定した計算との比較による等価砂粗度の算定
2
f
: 壁 面 せ ん 断 応 力 , : 流 体 の 密 度
1

c
2
運動量積分式は二次元の圧力勾配のない平板周りの流れを考えると運動量積分式は以下
のようになる．
w
d

U
dx
 :運動量厚さ, 
w
U :一 様 流 速 , c : 局 所 摩 擦 抵 抗 係 数
f
ここで，運動量厚さの定義は

u 
 u 
 1   dy
U 
0 U 
 
u : 主 流 方 向 の 流 速 , : 境 界 層 厚 さ
これを x=0 つまり平板全縁で運動量厚さθが 0 となる条件で積分すると，
x
x 0  w dx
1
 
 CF x
2 1 U 2 x 2
2
CF : 平板摩擦抵抗係数
となる．運動量厚さθを定義する乱流境界層内の速度分布がわかれば，平板摩擦抵抗係数
CF を算定することができる．
平板の乱流境界層内速度分布に対して粗度の影響を考慮した乱流境界層内の速度分布を次
式で表わす．
u 1  u* y 
 ln 
  5.5  B
u*    
  0.41 : カ ル マ ン 定 数
y : 平板表面から法線方向の距離
u * (  /  ) : 摩 擦 速 度,
w
 : 動粘性係数,

u *k
ここで， B は粗度関数とよばれ，粗度の影響を含む項である．今回は White の式を
1

ln(1  0.3 k  ) k  
用いた．White の式を以下に示す．
B 
k : 砂粗度高さ
これらを用いて、模型船の抵抗試験範囲のスピードに対し等価平板の摩擦抵抗曲線を計算
した。これをさまざまな等価砂粗度に対して示したものが図９である。図９でも実験結果
の粘性抵抗と同様の傾向を示している。ただしこの計算により得られる滑面の摩擦抵抗係
CV ( k )
と表わすこと
数は若干シェーンヘルの式と値が異なるため粗度面と滑面の差をシェーンヘルに加えたも
のを各粗度の摩擦抵抗係数としている。
以下，粗度 k(μm)の摩擦抵抗係数，粘性抵抗係数をそれぞれ C F ( k ) ，
にする． C F ( k ) のグラフを以下に示す．粗度を 0μm から 200μm まで変化させて計算し
113
た．
図９摩擦抵抗係数 CF (k ) 計算結果
図９の摩擦抵抗係数と形状影響係数を用い粘性抵抗を推定したものが、計算の粘性抵抗で
それを作っておき実験をプロットし全体で傾向の合ように等価砂祖度を推定した。推定の
ために実験値をのせたものを図 10 に、推定した等価砂粗度による粘性抵抗計算値と実験を
図１０に示す。
図 10 作成した図９に実験の粘性抵抗を表示したもの
図 10:実験値と等価砂粗度の曲線の比較
114
される．この計算結果と実験結果の比較により，水中では LFC 粗度１が 100μm，粗度２
このように全体の傾向が一致するように等価粗度を決めることで，細かい実験誤差は除去
図 12 に今回試作した装置を示す。これにより実船塗膜なども計測可能と考えられるが、そ
た計測装置を試作した。
粗度１、２について粗度を計測した。このためにレーザー距離計とトラバース速度を用い
２．３
粗度計測
が 50μm，粗度３が 25μm，粗度４が 10μm の砂粗度と等価であることが確認できた．
表３
粗度計測結果
粗度を計測すれば等価砂祖度を推定できる可能性もある。
膜面でも実粗度の約半分の高さの等価砂粗度が得られており同じような塗装面であれば実
表３に示す。等価砂祖度の比率とほぼ同じように得られており相関がある。また以前の塗
子を図１６に示す。得られた結果を図 17，18 に示す。これを用いて粗度を算出したものを
船首付近、船体中央付近、船尾付近の三点で船の深さ方向に変位測定を行った。計測の様
1000μs に設定した。水槽実験を行った模型船の内、粗度１と粗度２２隻についてそれぞれ
計測はレーザの移動速度を 2.0mm/s,移動距離を 50.0mm,データのサンプリング周期を
図 12 面粗度計測装置
れによるデータベース蓄積と公表は委員会では否定的であった。
この等価砂粗度を用いて実船の抵抗を推定する方法を考察する．
船の長さをさまざまに変えて同じフルード数で計算した、摩擦抵抗曲線を図 11 に示す。
これによると実船で差がある粗度であれば模型船でも差があること、また模型の計測精度
が高いことを考えれば実船で有意な差が生じる表面粗度の影響は 5m 程度の模型船で十分
同じフルード数で試験することが可能であるとみることもできる。したがって今回のよう
な数式船型で数多くの塗装面に対して等価砂祖度を得ておけばその粗面に対する実船の摩
擦抵抗、あるいは粘性抵抗が推定可能である。通常の滑面模型船で通常の模型試験を行い
形状影響係数 K と各フルード数での造波抵抗係数がわかれば、図 11 の対応する塗装面で対
応する長さの船の摩擦抵抗曲線を（１＋K）倍し、それに造波抵抗を足すのが 1 つの方法で
あるが、これまでの相関との関係から、デザインスピードでのこれまで使用してきた塗膜
さまざまな船長に対する摩擦抵抗曲線
と新しい塗膜のΔCF の差を図 11 から推定し通常の推定結果にそれをたしひきする方法も
考えられる。
図１１
115
(a) 船首面粗度計測の様子
図１3 計測
(b)
船体中央付近面粗度計測の様子
得られた全データを最小二乗法で三次多項式に近似し、求めた曲線と各データの最短距離
Zp5th
Zv4th
Zp3th
Zv2th
lr
Zp1th=Rp
Zv1th=Rv
面粗度の基本パラメータ
Zp2th
Zv5th
Zp4th
Zv3th
図１７
0.25
0.2
0.15
0.1
0.05
0
-0.05
-0.1
図１８
20
X
30
表面形状計測結果
10
表面形状計測結果
50
LFC 粗度大
40
LFC 粗度中
116
を船体表面粗度として算出した。得られた船体表面粗度から(6. 1),(6. 2)でそれぞれ定義され
る最大高さ粗さ、十点平均粗さを求めた。
RZ : 最大高さ粗さ
V
 基準長さにおける輪郭曲線の

山高さの最大値と谷深さの最大値との和
P
R R R
Z
R ZJIS : 十点平均粗さ
1 5
 ( Z PJ  ZVJ )
5 j 1
 粗さ曲線で最高の山頂から高い順に

５番目までの山高さの平均と,
 最深の谷底から深い順に

５番目までの谷深さの平均の和
R ZJIS 
ROUGHNESS, zero
0
0
100
1
0 .9
0 .8
0 .7
0 .6
0 .5
0 .4
0 .3
0 .2
0 .1
0
Vx
100
境界層でも差が出ていたので概略を示す。粗度１、粗度２、PLAIN であればこの順に協会
0
y
層の厚さが大きい。乱れ強度もこの順に大きい。
-1 0 0
-5 0
-1 0 0
-1 5 0
-2 0 0
-2 5 0
-3 0 0
-3 5 0
y
図 30Plain 32×32pixel 解析
-1 0 0
Vx
-2 0 0
-200
-1 0 0
-100
0.8
0.7
y
0
-5 0
-1 0 0
-1 5 0
-2 0 0
-2 5 0
-3 0 0
-3 5 0
0.6
0.6
0
0
y
0
0.3
-50
0.5
-100
0.3
0.5
0.3
0.7
0.6 0.4
-150
0.6
0.7
0.7
-200
0.8
0.4
0.4
0.5
1
0.7
0.6
0.9
1
-250
1
0.3
0.8
0.8
0.9
0.9
1 1
1
0.9
100
1
0 .9
0 .8
0 .7
0 .6
0 .5
0 .4
0 .3
0 .2
0 .1
0
Vx
100
図３２:粗度２32×32pixel 解析結果
0.9
0.9
0.8
1
0 .9
0 .8
0 .7
0 .6
0 .5
0 .4
0 .3
0 .2
0 .1
0
-300
1
-350
0.9
図３３:３隻の比較(赤：粗度１，青：粗度２，黒：PLAIN)
1
0.4
0
-5 0
-1 0 0
-1 5 0
-2 0 0
-2 5 0
-3 0 0
-3 5 0
粗度１32×32pixel 解析結果
0.5
0.6
0.5
0.6
0.9
0.4
117
z
z
1
-2 0 0
-2 0 0
図３０
0.8
z
z
資料５
深江丸を用いての推力トルク計測
３．１概要
通常船舶では馬力は計測される場合が多いが、推力は計測されることは少ない。プロペ
ラ作動時の船体抵抗とプロペラ推力は釣り合うので、推力を計測すれば推力減少率の変化
が小さいと考えれば船体抵抗の増減がわかり、馬力はそのほかの影響、たとえばプロペラ
汚損による効率の低下（同じスラストを出すために必要なトルクの増加）が入っているた
め、それらを分離して船体の抵抗の変化のみを計測できる。したがって推力を計測するこ
とは大きな意味を持つ。計測手法は軸にゲージを張り付ける資料１の方法である。
３．２計測器の概要
神戸大学海事科学部の練習船深江丸がドックにおいて新しい塗料を塗装する前に深江丸
の中間シャフト（直径 145mm）にゲージを張り付けスラストトルクを計測した。装置の概
要図 36 に示す。図に示すようにシャフトに直接ゲージを張り、その出力をテレメータで送
信している。シャフト温度等も計測し温度の影響も考慮している図 37 に受信機側の表示を
示す。
図３６
シャフト直貼りによるスラストトルク計測装置概要
図３７
受信機とデータ取得用パソコン
118
3.3 計測結果
回転数 305rpm、可変ピッチ翼角 12，14，16，18 度において速力とスラストトルクの関係
を求めた。速度は深江丸の計測機によるものである。図 38 に推力、トルクの時系列を示す。
馬力
(PS)
推力
(ton)
時間(分）
図３８
推力馬力の時系列
同じ翼角で 2 回とっているが安定しており、速度が増加するときは、速度が上がる前は翼
角が大きくなると推力、馬力とも先に一度大きくなっていることがわかる。これなスピー
ドが小さく前進率が小さい部分で回っているためで、翼角を落とすときは逆の現象がみら
れる。この平均値を横軸に船速を取り書いたものが推力の図 39 と馬力の図４０である。
119
スラスト
（ton）
船速（Kt）
図３９
船速(kt)とスラスト(ton)の関係
同じ船速で見ると推力は下がっており、新しい塗料を塗った直後は大きく抵抗が下がって
いることがわかる。しかし同じ翼角では推力が同じで船速が大きくなった結果が出ている。
これは J の大きいところで同じ推力を出せることを意味し、揚力特性がよくなっているこ
とがわかる。これはプロペラの汚損による影響であると思われる。船速と馬力の関係を見
ると推力よりも大きく減少しており、プロペラの効率改善が大きいことがわかる。ドック
前には非常にプロペラが汚損していたものと思われる。
馬力（PS）
船速(Kt)
図４０
船速と馬力（PS）の関係
120
Proceedings of 26th ITTC – Volume I
419
Specialist Committee on Surface Treatment
1.
Membership
Introduction
1.
2.
3.
4.
Review state of the art of different
surface treatment methods
Review the possible impact on ship
performance in the following areas in
the light of the recent rapid
development of coating systems:
a.)
Resistance (friction line)
b.)
Propeller characteristics
c.)
Cavitation behavior
d.)
Comfort (propeller induced
noise)
e.)
Acoustic signature
Review the existing measurement
methods for surface roughness at
model-scale and at full-scale
Propose methods that take into
account surface roughness and other
relevant characteristics of coating
systems in model testing.
a.)
Check the need for changes to
the existing extrapolation laws
b.)
Study the roughness allowance
for high-speed and
conventional ships (hull,
appendages and propellers)
Final report and recommendations to the 26th ITTC
1.1.
Meetings
R. Anzböck, VMB, Austria, (Chairman)
M. Leer-Andersen, SSPA, Sweden,
(Secretary)
M. Atlar, Newcastle University, UK
J. H. Jang, Samsung HI, Korea,
H. Kai, Yokohama National University, Japan
E. Carillo, CEHIPAR, Spain
M. Donnelly, NSWCCD, USA, left the
committee on 29-01-2010
1.2.
Tasks
The committee met 4 times:
November 24, 25, 2008, Vienna
May 11, 12, 2009, Madrid
February 1, 2, 2010, Daejeon
October 28,29, 2010, Gothenburg
1.3.
Below we list the tasks given to the
committee by the 25th ITTC
Specialist Committee on Surface Treatment
420
Fouling: Self cleaning from 8knots.
Silicon polymers form a hydrogel microlayer
between the paint surface and the seawater,
resulting in enhanced antifouling capability,
and improved self-cleaning potential.
Service inter: 90months
Toxicity:
low toxicity, biocide free
(VOC=Volatile organic compound)
TASK 1:
REVIEW STATE OF THE ART OF DIFFERENT SURFACE TREATMENT
METHODS
The committee found practically no
support from paint manufacturers; except
brochures where they claim reduction of fuel
consumption up to 10 % neither reliable
measurements nor serious data were provided
by the industry. In the following a short
overview over the products of several paint
manufacturers given and a few essential
comments are added to the single products.
Hempel:
Hempasil X3
Type: Silicone Hydrogel, low surface energy
Friction: Hempel does not claim
reduction in frictional resistance per se, but
claims reduced resistance due to less fouling.
They claim 4-8% fuel savings (see
XXXXXX). Tested at Force towing tank,
plates of about 1m2. Have not obtained test
report.
121
Proceedings of 26th ITTC – Volume I
HEMPASIL 77500
Type:
Silicone, water repellent low
surface tension, second generation
Toxicity: biocide free
Fouling:
Self cleaning above 8knots
Service inter: 40months
421
Friction: As seen below they claim big
improvements in power, however underlying
data must be investigated if possible. They
claim AHR of 20micron compared to 125-150
for convetional
Friction: self smoothing, exists in low
(deep sea) and high polishing (coastal)
Friction: self smoothing, exists in low
(deep sea) and high polishing (coastal)
Fouling: self polishing toxic anti fouling
self smoothing
Service inter:?
Friction: self smoothing, exists in low
(deep seae) and high polishing (coastal)
Figure1:Comparedtoselfpolishingantifouling
Anti-fouling nanocapsule,
Cuprous oxide and other
GLOBIC NCT
Type:
Toxicity:
biosides
fibres,
fibres,
Fouling: self polishing toxic anti fouling
self smoothing
Service inter:60months
OLYMPIC
Type:
Anti-fouling mineral
high mechanical strength
Toxicity:
Low level of VOC
(400g/litres)
OCEANIC
Type:
Anti-fouling mineral
medium mechanical strength
Toxicity:
Fouling:
Service inter:36month
fouling
OCEANIC
Very good
Fair
60
10-30knot
Very good
430g/litre
Zinc carboxylate
Medium
OLYMPIC
good
Neutral
36
10-25knot
good
450g/litre
Natural rasin
Fair
The following graphs, which are copies of
the manufacturer’s brochure, show, what
“International” claims for their products
“Intersleak 700” and “Intersleak 900”. They
promise a reduction of the friction coefficient
of 38% without any proof; nevertheless a fuel
reduction of 6% is guaranteed ignoring the
type of ship, the Froude numbers and the ratio
of frictional resistance to total resistance.
claims better efficiency parameter (wave
length). With below method claiming 38%
lower Cf than intersleek 700
Friction: Claims 4% fuel savings
compared to traditional SPC. Average AHR
100
Service inter:36month
GLOBAL NCT
Excellent
High
60
0-35knot
Excellent
400g/litre
Nanocapsule
High
Specialist Committee on Surface Treatment
422
Hempasil
Exellent
Exellent
+60
>13kn
None
275g/litre
Silicon
None
Comparison of Hempel paints
Mechanical
Fuel saving
Drydock inter
Speed
Self polishing
VOC
Binder
Biocide efficiency
elastomer
INTERNATIONAL
INTERSLEEK 700
Type:
Silicone
release, self cleaning
Toxicity:
None
Fouling:
Speed: 15-30knots
INTERSLEEK 900
Type: Fluropolymer fouling release, self
cleaning
Toxicity:
None
Fouling: Hydrophobic waterreppelent
surface, 40% lower barnacle shear adhesion
strength than intersleek 700. Better slime
repellent
Speed: >10knots
Service inter:36month
Friction: Claims 6% fuel savings
compared to intersleek 700. Average AHR 75
(Intersleek 700 AHR=100, typical SPC(Self
Polishing
copolymer)=125micron.
Also
122
Proceedings of 26th ITTC – Volume I
INTERSWIFT 655
Type: Self polishing copolymer (SPC)
Toxicity:
Copper Acrylate biocide
release
INTERSMOOTH 746
Type: Self polishing copolymer (SPC), lower
solvent emission
Toxicity:
Copper Acrylate biocide
release
INTERSHIELD 163 INERTA 160
Type: Anti-corrosive, Ice resistant, no ice
adhesion, high mechanical strength, low
temperature
Toxicity:
Low VOC (40g/litre)
Fouling:
Biocide release
Service inter:36month
Friction:
No info found
Fouling:
Biocide release
Service inter:up to 60month
Friction:
No info found
423
Fouling:
No anti fouling normally
Service inter:No information found
Friction:
Claims 7-10% fuel saving
compared to traditional ani corrosive paint.
Specialist Committee on Surface Treatment
424
Comparisons between International paints
Data taken from http://www.international-marine.com/Literature/HRPC_Folder_Paper.pdf ”Hull
roughness calculator”
Figure2:Savings
123
Proceedings of 26th ITTC – Volume I
Fouling:
Service inter:>60month
Friction:
No information found
425
Figure3:Fuelincreaseusage(hybrid=mixofCDPandSPC(Interswift),CDP=ControlledDepletionPolymer(Interspeed),SPC=Self
polishingcopolymer(Intersmooth),Foulrelease(Intersleek)).Allfigureshavesamedescription?
JOTUN
Very little information found
SEALION
Type: Foul release Silicone elastomer
Toxicity:
Fouling:
Service inter:
Friction:
SeaQuantum
Type: Self smoothing and self polishing
(SPC) Hydrolising
Toxicity:
Specialist Committee on Surface Treatment
426
Paintsfordifferentapplicationareas
Figure1:Typicalpaintsystemsfordifferentapplication
Typesoffouling
Severalthousandspeciesofmarineorganismscanfoulthesurfaceofaship.Mostwillstayattachor
releasewhentheshipspeedisabove45knots.Whichorganismscanattachisaffectedbymany
factorssuchaspH,temperature,salinity,dissolvedsaltsandoxygenconcentration.
Figure2:MainMarinefoulingorgasms
Typeofantifoulingpaintsinsecondhalfof20thcentury
Allthoughthesepaintshavebeenlargelyphasedoutsomewherestilluseduntil2001whereIMObannedthe
useofTBTpaintsworldwide,becauseoftheirtoxiceffectsonmarinelife.
124
Proceedings of 26th ITTC – Volume I
Specialist Committee on Surface Treatment
order to take surface roughness effect into
account. In order to determine the velocity
shift function by surface roughness,
experiment using long pipe in which the wall
can be roughened is taken place. Full scale
skin friction calculated by “SHIPFLOW” is
shown in Fig.14. We can not see any reliable
experiment data in this paper.
428
TASK 2:
REVIEW THE POSSIBLE IMPACT ON SHIP PERFORMANCE IN THE
FOLLOWING AREAS IN THE LIGHT OF THE RECENT RAPID DEVELOPMENT OF
COATING SYSTEMS
1. Resistance (friction line)
2. Propeller characteristics
3. Cavitation behavior
4. Comfort (propeller induced noise)
427
Task 2.1. Impact on the Resistance (friction line)
In the following an overview over the recent papers concerning the impact of coating systems on
the resistance of a ship is given:
Lars-Erik Johansson, “The Local Effect of
Hull Roughness on Skin Friction.
Calculations Based on Floating Element
Data and Three-dimensional Boundary
Layer Theory”, Read in London at a
meeting oh the Royal Institution of Naval
Architects on April 11, 1984
The effect of surface roughness on skin
friction is calculated. The author takes place
experiment using floating element and
measure both skin friction and velocity profile
in boundary layer. Using those data obtained,
velocity shift is determined. A boundary layer
program for three-dimensional turbulent
boundary layers is employed. Roughness
effect upon flat plate and two ship hulls are
presented. Increase in viscous resistance due
to roughness from painted surface of ship is
shown in Fig.14.
This paper firstly shows cause of hull
roughness. The effect of coating on ship
performance is calculated by some formula.
The effect of biocide free foul release coating
to fuel saving is shown. The author concludes
foul release products give lower hull
roughness than biocidal AF and lower
environmental impact whereas higher initial
costs.
2.1.2. Ship Resistance: Resistance Data are not published
Y. Yano, N. Wakabayashi : “Presumption of
Bottom Fouling in Real Ship”, J. of Japan
Institute of Navigation , 2008
The authors attempted to presume the
degree of bottom fouling of real ship by trial
test. They conducted short stopping test with
conventional paint and new type paint. From
experimental data, they obtained coefficient
of stain. From its value, the degree of bottom
fouling was assumed and the effect of paint
was investigated.
Friction drag by slime and shell and weed
are discussed. Research history about them is
shown. Methods to measure the hard paint
roughness of antifouling coatings are
summarized. The author refers to the relation
between surface roughness and skin friction.
Economic considerations are also made.
Y. Yamazaki, H. Onogi, M. Nakato, Y.
Himeno, I. Tanaka, T. Suzuki :
“Resistance Increase due to Surface
Roughness (2nd Report)”, Journal of the
Five roughed plate which were obtained in
hull of real ships were tested in the circulating
water channel and measured frictional
resistance coefficient. Speed decrease
estimated by plate frictional resistance
coefficient was 0.2 ~ 2 knot in case of blunt
ships, and 0.3 ~ 3 knot in case of high speed
ships.
H. Doi, O. Kikuchi : “Frictional Resistance
Due to Surface Roughness (1st Report) Effect on Reducing of Ship's speed by
Roughness Models –“, Journal of the
Kansai Society of Naval Architects, Japan,
No.194 , 1984
Leer-Andersen M, Larsson L, “An
experimental/numerical approach for
evaluating skin friction on full-scale ships
with surface roughness”, J. of Marine
Science and Technology Vol. 8, No1, 2003
J. Willsher : “The Effect of Biocide Free Foul
Release Systems on Vessel Performance”,
SHIP EFFENCY, 1st International
Conference, Hamburg, October 8-9 , 2001
Townsin RL : “The ship hull fouling penalty”,
International Congress on Marine
Corrosion and Fouling No11, San Diego,
California , 2003
The authors evaluate the increased skin
friction of full-scale ships by surface
roughness. CFD code “SHIPFLOW” is
modified and velocity shift function is used in
Speed trial data of training ship during
past 8 years are shown. Variations of Ship
speed, shaft horse power, fuel consumption
are shown in order to estimate the effect of
bottom fouling. The results show shaft horse
power increases about 20% in full speed
condition because of fouling. Trial data are
analyzed and variations of friction resistance
are also shown. We can see the shaft-horse
power and fuel consumption versus days after
dock with self-polish.
K. Yokoi, “On the Influence of Ship's Bottom
Fouling upon Speed Performance”,
Toyama National College of Maritime
Technology, Bulletin of Toyama National
College of Maritime Technology in
Japan2004
decreases about 10% due to propeller
polishing. We can see the increase of
resistance(%) to days for developments.
2.1.1. Ship resistance: Resistance Data are published
M. P. Schultz, “Effects of coating roughness
and biofouling on ship resistance and
powering”, Biofouling, 2007, Vol. 23,
No.5, pp.331-341
Increased resistance of full-scale ship by
surface roughness is calculated in some
roughness conditions. Calculation methods
are based on model ship resistance results and
boundary layer similarity law analysis. The
calculation results show increased resistance
in heavy calcareous fouling is up to 86%.
Values of shaft power of full-scale ship
obtained by trial data are given and compared
to calculation results. Both results agree well
with each other. The resistance coefficient Ct
of typical naval ship is shown in Fig.1.
However, the data in this figure is NOT so
reliable.
T Munk, M Sc, “Fuel Conservation through
Managing Hull Resistance”, Motor ship
Propulsion Conference, Copenhagen April
26th, 2006
In this paper, variations of increased
resistance of some actual ships in service are
shown. The data shows clearly the effect of
dry-dock and propeller polishing. One
example shows increase of resistance
decreases over 20% thanks to dry-docking.
Another example shows increase of resistance
125
Proceedings of 26th ITTC – Volume I
Society of Naval Architects of Japan,
No.153 , 1984
Since hydrodynamic characteristics of
sand roughened surface and painted surface
were different in previous report, the author
investigated this problem experimentally
using simple wavy roughened surfaces.
Frictional resistance and velocity distribution
in boundary layer were measured in wavy
surfaces. Roughness functions were obtained
by experimental results.
Y. Yamazaki, H. Onogi, M. Nakato, Y.
Himeno, I. Tanaka, T. Suzuki :
“Resistance Increase due to Surface
Roughness (1st Report)”, Journal of the
Society of Naval Architects of Japan,
No..155 , 1983
The authors conducted experiments using
roughened pipes in order to measure frictional
resistance and velocity distribution in
boundary layer. Relation between roughness
height measured by BSRA analyzer and
equivalent sand roughness was obtained.
Velocity shift by surface roughness is used in
order to get resistance increase.
K. Tokunaga, E. Baba :” Approximate
Calculation of Ship Frictional Resistance
Increase due to Surface Roughness”,
Journal of the Society of Naval Architects
of Japan · No.152 , 1982
In order to calculate frictional resistance
of a ship by surface roughness, the authors
applied a-two dimensional turbulent boundary
2.1.3. Resistance of Flat Plates
M. Candries, M. Atlar : “Experimental
Investigation of the Turbulent Boundary
Layer of Surfaces Coated With Marine
Antifoulings”, 2005
Velocity distributions on turbulent
boundary layers on flat plates coated with two
429
layer theory for rough surface to potential
streamlines over the hull surface. Potential
streamlines were calculated by Hess-Smith
method. Increased resistance in full-scale ship
was calculated.
M. Sone : “Influence of the Fouled Ship
Bottom on the Propulsion Horsepower of
the Seikan Ferry-boats”, J. of the Marine
Engineering Society in Japan, Vol.16,
No.2 , 1981
Variations of Propulsion horsepower and
fuel consumption of Seikan-Ferry boats were
investigated in 10 years using measurement
and abstract log-book data. This ship is
docked every year and annual increase in
delivered horse power due to the ship bottom
fouling is about 8%. Since the paint was
changed from higher-toxic one to lower toxic
one, increase of propulsion horsepower seems
to become higher.
H. Orido, M. Kakinuma : “Speed Decrease
Due to Hull Surface Roughness (in
Japanese)”, Bulletin of the Society of
Naval Architects of Japan · Vol.616 , 1980
The authors showed practical analysis
using data of some ships in service. Relation
between surface roughness and ship age was
shown. Empirical approximate formula was
also shown in the graph and compared with
measured data. However, the accuracy of
analysis seemed not to be high since the
theory was not established enough.
different new generation marine antifouling
paints were measured. The two paints were
Foul Release paint and Tin-free SPC
respectively. Smooth flat plate and plate
covered with sand grit were also used in order
to make sure the performance of two new
paints. Remarkable point is that LDV
Specialist Committee on Surface Treatment
430
measurements for marine coatings have been
published in the open literature.
M. P. Schultz : “Frictional resistance of
antifouling coating systems”, Journal of
fluids engineering, vol. 126, No.6, 2004
resistance of 6.3 m long plate coated with
Foul Release coating was 1.4% lower on
average than that coated with SPC.
Roughness functions of two paintings were
shown.
Towing test is carried out on three surface
conditions in order to compare drag
characteristics. The surface conditions are
Aluminum, SPC and Foul Release coating
respectively. From the experimental results,
above Reynolds number 2 * 10^7, it is shown
total drag coefficient of the foul release
surface was on average 1.41% lower than the
SPC surface.
Candries M., Atlar, M. and Anderson, C.D. :”
Low-energy surfaces on high-speed craft”,
Proceedings HIPER '01, Hamburg, 2001
Frictional
resistance
and
velocity
distribution on several ship hull coatings in
the unfouled, fouled, ad cleaned conditions
were measured. Test surface coated with
silicone, ablative copper, SPC copper and
SPC TBT were used. The experimental results
indicated little difference in frictional
resistance coefficient among the coatings in
the unfouled condition, however, after 287
days of marine exposure, test surface coated
with silicone showed the largest increases in
frictional resistance coefficient.
M. P. Schultz : “Turbulent Boundary Layers
on Surfaces Covered With Filamentous
Algae”, Journal of fluids engineering, Vol.
122, No.2, 2000
Turbulent boundary layers over natural
marine biofilms and a smooth plate were
compared. Profiles of the mean and
turbulence velocity components were
measured. An average increase in the skin
friction coefficient was 33 to 187 % on the
fouled specimens. The skin friction
coefficient was found to be dependent on both
biofilm thickness and shape of surface.
M. P. Schultz and G. W. Swain : “The Effect
of Biofilms on Turbulent Boundary
Layers”, Journal of fluids engineering, Vol.
121, No.1, 1999
The effect of algae to frictional resistance
was investigated. The surfaces covered with
filamentous algae were prepared and put in a
closed return water tunnel. A two-component
LDV was used to obtain velocity distribution
in turbulent boundary layer. Significant
increases in the skin friction coefficient for
the algae-covered surfaces were measured.
M. P. Schultz :” The Relationship Between
Frictional Resistance and Roughness for
Surfaces Smoothed by Sanding”, Journal
of Fluids Engineering, Vol.124, 2002
The effect of sanding on surface
roughness was investigated. The author
prepared 7 kinds of plates. One of them was
not sanded and the others were sanded by
different fineness. Plates were towed and
frictional resistance was measured in each
case. The results showed resistance increase
of unsanded plate against polished one was
5% in average. Roughness function ೼U was
shown of all plates.
M. Candries, M. Atlar, A. Guerrero and C.D.
Anderson : “Lower frictional resistance
characteristics of Foul Release systems”,
Pro. of the 8th Int. Symp. on the PRADS,
Vol. 1, 2001
The roughness and drag characteristics of
surface painted with SPC (tin-free SelfPolishing Co-Polymer) and non-toxic Foul
Release were investigated. Two plates coated
with these two paints were towed in tank and
drag was measured. The results showed total
126
Proceedings of 26th ITTC – Volume I
2.1.4. Resistance of Circular Cylinders
S.M. Mirabedini, S. Pazoki, M. Esfandeh, M.
Mohseni, Z. Akbari : “Comparison of drag
characteristics of self-polishing copolymers and silicone foul release
coatings: A study of wettability and
surface roughness”, Progress in organic
coatings, Vol. 57, No.4, 2006
Drag on some surfaces coated with some
paints is measured using a smooth aluminum
cylinder connected to a rotor device.
Downward shift of the velocity distributions
and frictional resistance coefficients for each
test cylinder by Reynolds number are also
measured. The drag characteristics of a
surface are affected by its free energy and
roughness parameters.
Weinell CE, Olsen KN, Christoffersen MW, et
al. : “Experimental study of drag
resistance using a laboratory scale rotary
set-up”,
Biofouling,
International
Congress on Marine Corrosion and
Fouling No11, San Diego, California,
2003
431
A laboratory scale rotary set-up was used
to measure the drag resistance, and the surface
roughness of the samples was measured.
Measurements on pure paint systems and
measurements on large-scale irregularities
were investigated. The contribution from a
modern self-polishing antifouling or silicone
based fouling-release paint was negligible
compared to the one from irregularities of hull
of ship.
Hisao TANAKA, Yasuyuki TODA, Kiyoaki
HIGO,
Kazuharu YAMASHITA :
“Influence of Surface Properties of
Coatings to Frictional Resistance”, ournal
of the Kansai Society of Naval Architects,
Vol.239, Japan, 2003
A. Matsuyama, T. Nishiya, T. Araki , T.
Imada :” Studies on Propulsive
Performance by Marine Fouling of Shiphull and Propeller”, Bulletin of the Faculty
of Fisheries, Nagasaki University No.83,
2001
In order to investigate effect of surface
properties of coatings to frictional resistance,
experiments were carried out using a rotating
cylinder type dynamometer built by the
authors. Frictional resistance and velocity
distribution in turbulent boundary were
measured. The aging effect of paints on
surface roughness was shown.
M. Miyamoto :” Estimation and Evaluation of
Ship Performance in Actual Seas - Review
and Evaluation of Fouling, Aging Effect
and Sea Condition-“, Journal of the Japan
Society of Naval Architects and Ocean
Engineers, Vol.4 2007
In order to investigate the effect of marine
fouling on ship hull and propeller, the author
analyzed the log-book data from 1990 to 1998.
Shaft horse power, amount of fuel
consumption, admiralty coefficient and ship
speed were investigated. It was recognized
that fuel consumption increases up to 22%
from the value of 1990.
2.1.5. Interaction Ship and Propeller
The author estimates the effect of fouling,
aging effect and sea condition upon real ships.
The approximate method exploited by the
author is verified by comparing with
measured data and data of abstract log-book.
As a result, it is shown that the accuracy
seems to be quantitatively practical. The
approximate method could be applied to
design stage.
Specialist Committee on Surface Treatment
N. Nakai, S. Suzuki : “On the Presumption of
Bottom's Roughness with Making Use of
Propeller Efficiency on CPP”, Bulletin of
Kobe Marchant Ship University Vol.32,
Japan, 1984
432
K. Nagatomo, H. Matsushita, E. Inui, Y.
Miyoshi : “Studies on Marine Fouling of
the Bottom Plates and Propeller Surface –
1”, The Journal of Shimonoseki Univ. of
Fisheries, Vol.41, No.4, 1993
In order to estimate the bottom fouling of
real ship, practical method was presented. The
speed trial test was taken place before and
after docking. Surface roughness in fouled
condition was estimated by the increase of
frictional
resistance
using
Bowden
formulation. The results showed after docking,
surface roughness became about 6.2 mm from
145ജm in cleaned condition.
The foul condition on bottom and
propeller of real ship was investigated.
Because of long-time mooring during August
to October, fouling was progressed so much.
According to speed trial, ship speed became
about 70% compared to cleaned condition.
The cause of speed decrease came from ship
hull fouling by two-third; the rest came from
propeller fouling.
N. Nakai, S. Suzuki : “On the Effect for
Propelling Performance in Consequence
of Marine Fouling and the Practical
Method of Presumption of Bottom's
Roughness on FUKAE MARU before
Autumnal Docking”, Bulletin of Kobe
Marchant Ship University Vol.32, Japan ,
1983
The increased resistance caused by
adhesion of barnacle to propeller was
calculated. Firstly, the situation of foul of
propeller was measured. The measurement
results showed barnacle adhered near trailing
edge near boss. Barnacles were approximated
as a half-cylinder solid and loss-horse power
was calculated. The calculation results
showed loss horse power was over 1%.
N. Nakai, S. Suzuki : “The Effect of Marine
Fouling -On the Result of Actual
Experiments with the Ship Installed CPP-“,
J. of Japan Institute of Navigation, 1983
Bottom and propeller fouling of real ship
was investigated through one year. It was
known the kind of marine fouling organisms
and process of attachment. The effect of
marine fouling prevention by pouring sea
water with dissolved innoxious copper-ion
which was supplied by the system into the
dome of bow-thruster was also investigated.
K. Sato, K. Inoue, E. Takeda, H. Akizawa, Y.
Mine, Y. Koike, Y. Miyazaki :
“Experimental Study of Prevention of
Bottom and Propeller Foulings with
Regard to Energy Saving of Fishing
Boats”, Journal of Tokyo Univ. of
Fisheries, Vol.74, No.2, 1987
In order to investigate the effect of marine
antifouling paints on propulsion performance
of actual ships, firstly some test plates coated
with some paints were put in seawater and
performance of paints was studied. Secondly,
speed trial tests were taken place. Variations
of BHP and surface roughness just after
painting, before docking, and after docking
were shown.
E. Nishikawa, M. Uchida :” On Propulsion
Property of FUKAE MARU Equipped
CPP and its Deterioration due to Surface
Fouling”, Bulletin of Kobe Marchant Ship
University Vol.33, 1985
The effect of surface fouling on the
propeller and ship were investigated. Trial sea
data of training ship equipped with CPP were
obtained just before docking and just after
docking in 3 years. Performances of
propulsion property with and without fouling
were compared. The results showed change of
propulsion performance with CPP was
different from the one with FPP.
127
Proceedings of 26th ITTC – Volume I
2.1.6. Further Papers of possible Interest
2.1.6.1. Paint
Elisabete Almeida, Teresa C. Diamantino,
Orlando de Sousa :” Marine paints: The
particular case of antifouling paints”, 2007
The authors presented a general overview
of marine antifouling paints. Firstly,
interaction between ship hull and sea water
was explained. Marine organisms that adhere
to ship hull were shown. The history of the
development of antifouling technology was
explained. As a next generation marine paints,
more
environment
and
man-friendly
antifouling paints, such as CDPs, TF-SPCs
and Biocide-free paints were shown.
Chambers LD, Stokes KR, Walsh FC, et al. :
“Modern approaches to marine antifouling
coatings”, 2006
This article reviews the development of
marine
antifouling
coatings.
Historic
antifouling methods were shown. Over 100
papers were review in it. Among them, 10
major paper were chosen and introduced.
Performances of some coatings are compared.
Tin-free self-polishing copolymer (SPC) and
foul release technologies are current
applications however many alternatives have
been suggested.
Casse F, Swain GW : “The development of
microfouling
on
four
commercial
antifouling coatings under static and
dynamic immersion”, 2006
Four test panels coated with paints were
immersed in seawater in order to compare
their performance against microfouling under
static and dynamic immersion. Three paints
were biocide based (tributylin self-polishing,
copper self-polishing, copper ablative) and
one was biocide free (silicone fouling release).
It was know that total bacteria counts were
433
similar on all coatings after static immersion,
but after dynamic immersion the largest
decrease in numbers was seen on the fouling
release coating.
Tetsuya SENDA : “Ship Bottom Anti Fouling
Coating and Marine Environment (in
Japanese)”, 2006
History of development of anti-fouling
coating is summarized. Since restrictions
against toxic coating have become harder in
recent years in terms of protection of marine
environment, the author evaluates the
environmental risk for anti-fouling coating.
The author says it is necessary to establish the
way to evaluate properly environmental
effects of anti-fouling substances, and to find
some low-risk substances.
Anderson, C.D., Atlar, M., Candries, C.,
Callow, M.E., Milne, A. and Townsin,
R.J : “The development of Foul Release
coatings for seagoing vessels”, 2004
This paper describes the history of
development of antifouling paint. Firstly,
some marine fouling organisms are explained.
Secondly, some explanation about antifouling
painting is done. The method how fluid drag
on foul-release coating is calculated is
explained. Lastly, performance of antifouling
coating is shown. Reading this paper, reader
can get the overall knowledge of antifouling
painting.
Kazuya OGAWA : “The Prevention of Marine
Fouling on FRP Ship Hull by Coating a
Non-polluting and Anti-fouling Paint 2 Relation
between
Preventative
Performance and Physical Properties of
Silicone Coated Film-“, 1996
Specialist Committee on Surface Treatment
434
In the second report, the author
investigates the reason why the proposed new
coating method has an effectiveness for the
prevention of bio-foulings on FRP ship hulls.
The physical properties of the coated film are
investigated. The author measures a contact
angle and a sliding angle of a drop of water
on the silicone coated film. The author also
observes the repelling appearance of colored
water sprayer on this film.
Kazuya OGAWA : “The Prevention of Marine
Fouling on FRP Ship Hull by Coating a
Non-polluting and Anti-fouling Paint 1 Effectiveness of Silicone Coated Film
against Marine fouling-“, 1996
In the first report, the author develops new
coating method by using a nontoxic paint
instead of toxic paints. FRP test plane with
some coating are put in sea for several month
2.1.6.2. Marine Creature
Schultz MP, Kavanagh CJ, Swain GW :
“Hydrodynamic forces on barnacles:
Implications on detachment from foulingrelease surfaces”, 1999
In this paper, lift and drag acting on
barnacles were measured. The results were
compared to the results obtained by
and antifouling performance are compared
with each other. The paint which shows the
best antifouling performance is painted to real
ship and its performance is confirmed.
Nobuyoshi HIROTA : “Non-Toxic Anti
Fouling Coating without Adhesion of
Marine Creatures (in Japanese)”, 1985
Development and application of non-toxic
anti fouling coating called “Bioclean”
developed by CHUGOKU MARINE PAINTS
LTD is explained. In case of the application to
the propeller of the 200 thousand DW ore
carrier, it is reported that no adhesion of
marine creatures occurred in half year after
launching. In case of the application to the
propeller of the support ship of national
defense ministry, it is reported that no
adhesion of marine creatures occurred in one
year.
hemisphere, cube and pyramid. Lift
coefficient remained nearly constant over the
range of Reynolds numbers tested, however
drag coefficient decreased slightly with
increasing Reynolds number.
A table of the literature checked for task
2a is attached in appendix 1 to this report.
review of reasons and associated different
coating methods reported in the open
literature are given. Based on this review
since the Foul Release (FR) coating systems
have been developing as the prime propeller
coating system, in 2.2.4 a brief background to
this coating system is given with a view to the
TASK 2.2: IMPACT OF PROPELLER COATING SYSTEMS ON PROPELLER
CHARACTERISTICS
2.2.1. Introduction
This section gives a background on
propeller coating systems and their influence
on propeller characteristics. In item 2.2.2. the
important aspect of the propeller surface
measurements
and
representation
are
reviewed. This is followed by 2.2.3. where the
128
Proceedings of 26th ITTC – Volume I
propeller coating. Item 2.2.5. presents the
recent applications and review of the effect of
the FR coatings on the efficiency, cavitation
and underwater acoustics of propellers as well
as the interaction of this coating system with
bio-fouling. Finally, 2.2.6. presents the
concluding remarks from the review and
recommendations for further research on
propeller coating.
When the loss in ship performance is
associated with the condition of the ship hull,
the effect of the propeller surface condition is
often overlooked. Mosaad (1986) stated that
in absolute terms, the effect of the propeller
surface condition is less important than the
hull condition, but significantly more
important in terms of energy loss per unit area.
In economic terms, high return of a relatively
cheap investment can be obtained by propeller
maintenance. This has been well recognised
by cautious ship operators who regularly
polish the propellers of their vessels. While
this is a good practice, the inconvenience of
finding suitable time and place as well as the
associated cost favour for the alternative
means of keeping propellers clean by coating,
especially after the recent introduction of Foul
Release (FR) type coating. Besides, there has
always been an interest to the coating of
propellers to avoid or reduce fouling growth
and galvanic corrosion of ship hull and as
well as to resist to cavitation erosion if it is
ever possible.
Propeller coating applications have been
growing with increasing applications of foul
release (FR) coatings on ship hulls during the
last fifteen years or so, especially on the
propellers of large cargo vessels. According
to the data base of one of the major coating
manufacturers, the current breakdown of the
ship antifouling applications, about a 5% of
their hull coating applications is with the FR
type and this ratio has been increasing
considerably due to environmental scrutiny
and competitions amongst newly emerging
other FR brands. This type of coating is
favoured for the propeller applications due to
435
their smoother finish and improved
application as well as longevity relative to the
Self-Polishing Copolymer (SPC) types. In
fact some paint manufacturers have been
offering free of charge paint applications to
ship owners who are willing to paint their
vessels by FR coating. Again, according to
the data base of the above mentioned major
paint manufacturer the number of the coated
propellers has reached to more than 250
during the last 10 years.
The main objective of propeller coating is
to control fouling growth beside other
potential benefits in association with
improved condition of the blade surfaces
including propeller efficiency, cavitation and
noise. However prior to exploring these
effects, one needs to clarify differences
amongst surface deterioration and fouling.
Surface deterioration may be caused by
corrosion, impingement attack, cavitation
erosion or improper maintenance whilst
fouling is mainly due to marine growth of the
animal type, acorn barnacles and tubeworms
as well as the slime type, Atlar et al (2002).
Depending upon its extent while the surface
deterioration can be represented by surface
roughness the representation of fouling is
rather complex and hence its effect upon the
propeller is difficult to quantify since very
little theoretical and experimental work done
on the subject. However it is a well-known
fact that, whether it is a surface deterioration
or fouling, any micro or macro level change
in the blades surfaces will increase the
propeller loss due to the viscous friction effect
in addition to the potential axial and rotational
losses. The frictional loss can be as high as
15% of the total propeller losses depending
upon the propeller’s loading condition,
Glover (1991). It is therefore beneficial to
keep the propeller surface free from marine
fouling and as smooth as possible to reduce
the frictional loss beside other consequences
of these causes that may lead onto undesirable
earlier inception and further development of
cavitation as well as increased underwater
noise.
Specialist Committee on Surface Treatment
436
This was then used to calculate a value for
the Average Propeller Roughness (APR). This
is a weighted average, so the roughness closer
to the tip has a much greater influence than
the same roughness would, if placed nearer
the blade root. Five sections were suggested
and given the weights shown in Table 1.
h ' | 0 .0147 R a2 ( 2 .5 ) PC
In an attempt to establish a standard
methodology for the propeller roughness
measurements Townsin et al. (1985)
proposed the following procedure: each blade
surface is divided into a number of roughly
uniform radial strips, for each of which 3
measurements were taken with a cut-off
length of 2.5mm. At that time this was
designed for use a stylus type roughness
device, the Surtronic 3 instrument, so Ra (the
mean line average roughness amplitude) and
Pc (the Peak Count per unit length, which is a
texture parameter) were recorded for later
conversion into Musker’s “Apparent” or
“Characteristic” roughness parameter, h’, by
the approximation below.
give a wide range of values for all roughness
parameters; therefore for any point on the
blade, an average of many samples is needed
to reach a representative figure. However
these values of average roughness will vary
hugely over the blades surface, meaning that
the roughness needs to be measured at many
locations. This is important as the same level
of roughness will cause very different effects
on section drag, depending upon where on the
blade it is located. Fouling and damage, such
as galvanic or cavitation erosion, can have a
massive effect upon the roughness measured
and hence the section drag. Most importantly,
there was no agreed standard methodology for
measuring roughness, no matter how
arbitrarily defined.
2.2.2. Measurement and representation of propeller surface condition
Before the effects of roughness upon the
performance of a propeller can be quantified
the roughness of the surface has to be
measured. There are various methods for
doing this, such as using a propeller
roughness comparator, by using a portable
stylus instrument or by taking a replica of the
surface of the blades and measuring it with
laboratory equipment such as optical
measurement systems. A detailed description
of both the stylus (by mechanical contact with
the surface) and optical measurement systems
can be found in e.g. Thomas (1999). On the
other hand the propeller roughness
comparator is a simple gauge by which the
roughness of a propeller can be compared to a
surface of known roughness. The most wellknown example of this is the Rubert propeller
roughness comparator. The gauge consists of
six examples (A, B, C, D, E and F) of surface
finish that range from an average meanline
roughness amplitude Ra = 0.65μm to an
amplitude of Ra = 29.9μm, see, e.g. Carlton
(2008). The examples represent the surfaces
of actual uncoated propeller blades. Examples
A and B represent the surface roughness of
new or reconditioned propeller blades while
the remaining examples are replicas of surface
roughness taken from propellers eroded by
periods of service. C, D, E and F can be used
to assess and report upon the propeller blade
surface condition after periods of service.
The measurement of propeller roughness,
whichever method is used, presents a number
of problems which are similar problems to
those of measuring hull roughness. They stem
from the very nature of propeller blade
roughness, with its wide variety of amplitudes,
textures and locations. Townsin et al (1981)
discussed
the
propeller
roughness
measurement problems and concluded the
following: any one small area of a blade will
Table 1. Weights suggested for calculating
APR, based on 5 sections.
129
Region
0.20.5
0.50.7
0.70.8
0.80.9
0.9tip
Weight
0.07
0.22
0.21
0.27
0.23
3
437
fully turbulent frictional drag expression for
the propeller blade surfaces in ITTC’78
procedure, will not be suitable for
representing the effect of coatings on
propellers. This is not only on the ground that
this expression is based on the Nikuradse
approach of sand roughness, since actual
propeller roughness is different than the sand
roughness, but also on the ground of
neglecting the effect of surface texture.
Although a surface may have relatively large
average roughness amplitude its texture may
have a long wave length sinusoidal texture.
This type of surface may cause lower drag
when compared to a surface consisting of
smaller amplitudes but with a jagged texture
consisting of closely packed sharp peaks
surface as claimed by Grigson (1982). This
claim was further proved by Candries (2001)
through comprehensive boundary layer, drag
and roughness measurements and analysis of
flat plates coated with two different marine
coatings which were a commercial FR and a
tin free Self-Polishing Copolymer (SPC) type.
In this study it was shown that the FR coated
system belonged to the former surface type
while the SPC coated surface belonged to the
second type suggested by Grigson as typified
in their comparative roughness profiles shown
in Figure 1. It can be seen that when longwavelength waviness, which is unlikely to
have any effect upon the drag, has been
filtered out, two striking features appear: not
only are the amplitude parameters (i.e. Ra, Rq,
Rt) of the FR profiles typically lower, the
texture parameter of the surface, which is
represented by the slope (Sa), is significantly
lower. In metrological terms this type of
texture is known as “open” whereas the
spikier texture of a tin-free SPC surface is
known as “closed”.
5
10
20
25
30
35
Foul Release Roughness profile:
Ra = 1.10
Rq = 1.21
Rt = 4.50
Sk = -0.87
Ku = 5.04
Sa = 0.33
15
mm
40
45
Specialist Committee on Surface Treatment
0
438
20
15
10
5
0
-5
-10
-15
2.2.3. Review of propeller coatings
50
As it is noted in the above review, an
accurate representation of blades surfaces by
characteristic roughness parameter requires
relatively sophisticated measurement devices
for proper analysis of the surfaces. These
devices are preferred to be optical and
portable as well as practical that can be used
in dry docks etc. Unfortunately such systems
currently are not available although there are
increased activities in this field especially
after the introduction of the FR coatings. As
discussed earlier these coatings do not readily
allow themselves to be measured by practical
stylus type devices although they are
currently being used on based on certain skills
involving some errors in measurements.
Although taking replica (print) from the
actual blade surfaces is relatively direct and
hence more accurate way measurement
method, it is rather impractical and it has its
20
15
0
5
10
-5
-10
-15
0
5
10
20
25
30
35
Tin-free SPC Roughness profile:
Ra = 3.26
Rq = 4.04
Rt = 19.98
Sk = 0.01
Ku = 3.29
Sa = 2.57
15
mm
40
45
50
In demonstrating the effect of fouling on
propellers and its prevention by coating Kan
et al (1958) investigated the characteristics of
conducted in order to conserve the scarce
alloys usually used for propellers. Cast steel is
much cheaper than bronze, can be easier to
coat and requires less exacting manufacturing
technology, so was proposed as an alternative.
At least 4 ships had coated steel propellers
installed during the war. Three of them were
sunk and unfortunately no follow-up was
made on the fourth Dashnaw et al., (1980).
own problems. At this point, until such
devices are available, it is plausible to think of
establishing a new comparator system, which
is based on a similar idea to the Rubert
comparator. However this new comparator
can be developed for foul release coated
sample surfaces which are graded based on
different paint applications varying from good
to bad since the application grade is an
important parameter in the texture and
roughness parameters for newly applied
coatings. Of course these samples will be
indirect and will not necessarily represent the
actual coated blades after a period in service.
However, as long as they are not damaged,
FR coating systems can maintain they
roughness and texture characteristics similar
to the new condition except the effect of slime.
There may be ways including this effect but
requiring further research.
Figure 1 – Characteristics of a typical foul release (Intersleek 700 – on the left) and tin-free SPC (Ecoloflex – on the right) roughness profiles taken by
laser profilometry, Candries et al (2001).
micron
Proceedings of 26th ITTC – Volume I
i
1
2
3
4
5
1 º
ª 5
3
«¦ Wi (h'i ) »
¬1
¼
By assuming h’ is constant within each
weighting band; APR for the 5 bands is given
by,
APR
3
mn5
A more generalized form for APR,
suitable if a survey of the entire blade
roughness is not available (the missing values
should not just be assumed to be zero) is
given by
APR
1 º
ª n
3
« ¦Wi (h'i ) »
« m n
»
«
¦m Wi ¼»»
¬«
The weights are evaluated such that for a
uniform distribution of roughness, APR = h’.
In the above procedure “characteristic”
roughness parameter h’ was obtained from a
drag-roughness correlation with replicated
coated surfaces based on Mosaad’s (1986)
extensive measurements. This parameter was
originally proposed by Musker (1977) to
characterize a surface by a single parameter
taking both the amplitude and texture of the
roughness into account. At this point it must
be noted that a single parameter (such as
average roughness height) as those measured
by Broersma and Tasseron (1967) or
equivalent sand roughness height (ks) of the
The idea of coating a marine propeller is
not a new one. The first recorded idea was by
Holzapel (1904) who claimed two major
reasons for the coating of marine propellers,
as true today, namely to prevent fouling and
to reduce galvanic corrosion. Unfortunately
his comments were not taken up at the time
and further investigation into the concept of
coating marine propellers was not conducted
for some time. It was not until the second
World War that further development of
protective coatings for marine propellers was
130
micron
figures was presented. Three coatings were
proposed for further evaluation and were
coated onto blades of a 6.5m bronze propeller.
The two coatings were polyurethane
formulations and one was an undisclosed
formulation (known as Y-1). They were
inspected after 2 and 11 months in service. It
was found that the polyurethanes had quickly
delaminated from the propeller. Y-1 had fared
better. From these trials they realised that for
any propeller coating, the bond strength of the
adhesive/primer
was
of
fundamental
importance. They recommended that for the
broad surface area of the blades, under low
hydrodynamic loading, the coating needed an
adhesion strength of at least 8.92 kN/m (50
lb/in.) of width. Near the edges of the blades,
where the surface was under high and
dynamic hydrodynamic loading, a much
higher strength would be needed.
Proceedings of 26th ITTC – Volume I
a fouled propeller using self-propulsion tests
and full-scale trials with the propeller covered
in various rubber sheets to mimic the fouling.
They found that small increases in roughness
will cause large increases in delivered
horsepower (DHP), producing a worse effect
on propulsive efficiency than hull fouling but
the reduction in thrust due to roughness was
very small. These experiments, however, did
not give very good agreement with their fullscale results. The full-scale measurements
showed that the rate of increase of DHP will
decrease as the roughness increases; the initial
roughness has the greatest effect on
performance. Because of propeller fouling,
the DHP decreases by 20% and from these
results, it can be seen that the effects of
propeller fouling in terms of a power penalty
are much greater than those of surface
roughness.
439
Further work was conducted from the 50’s
to the 80’s particularly focusing upon the
prevention of cavitation damage e.g. by
Heathcock et al. (1979), Angell et al (1979)
and Akhtar (1982). These mostly used
ceramic coatings and were not just interested
in propellers but also, rudders, A-brackets and
turbine blades.
Foster (1989) described trials on 2
Canadian naval vessels that had their
propellers coated with a 3-layer vinyl
antifouling system that used a cuprous oxide
containing topcoat. This was at the time the
standard system used on the hulls of the
Canadian naval fleet. The first vessel, CFAV
Endeavour, found that, after 2 years in service,
the coated propeller (the ship had twin screws
and only was one coated) was fouling free
and only had small amounts of paint loss on
the leading edges of the blades. They also
found that the shaft grounding current of the
coated propeller was reduced to about a third
of the uncoated one (the information on
current demand was taken from the monthly
cathodic protection reports of both ships). The
second ship, the naval frigate HMCS
MacKenzie had both of her propellers coated.
They were examined by divers after 6 months
and again in dry-dock after 2.5 years in
service. The divers found that the coating was
fouling free and almost intact except for some
detachment along the leading edges and some
small isolated spots on the back of the blades.
They also noted that the coating was still red
in color suggesting that little copper had
leached out. Once in dry-dock, it was found
Dashnaw et al. (1980) published their
work studying a large number of coatings and
surface finishes, in order to investigate those
that might prevent cavitation damage and
corrosion while still providing a smooth
surface to minimise the hydrodynamic drag.
Their theory being that, if a suitable covering
system could be found it might be possible to
replace the expensive materials propellers that
are usually made from by cheaper steel. They
conducted tests using a 24 inch rotating disc
apparatus and found that certain urethane
coatings could produce less drag than bare
steel discs even with a higher value of the
root-mean-squared roughness amplitude, Rq.
They concluded that there was a 10% change
in drag approximating to a 1% change in
power at the propeller, although no
explanation as to how they arrived at these
Specialist Committee on Surface Treatment
440
that while still free from fouling, the damage
had grown. The small isolated spots on the
back of the blade, most likely caused by
cavitation, had grown to a diameter of 530mm. A 30mm wide strip had been eroded
along the trailing edge and the top-coat had
been removed from the leading edge back to
about the mid-chord. The cathodic protection
reports showed that the current demand had
dropped by about 30% while at rest and at sea
by about 20% compared to the pre-coated
condition. They maintained these figures
throughout the 2.5 years in service.
Coldron and Condé (1990) reported on
the Shell Engineer, a 1300dwt coastal tanker,
generating 905kw at 250rpm through a 4
bladed nickel-aluminum-bronze propeller,
2.44m in diameter. In 1983 it was selected to
trial the effect of a TBT-SPC based coating
on its propeller. This system was suggested
by the wealth of published data on the
coatings performance on ships hulls. The
propeller was removed, faired, wet blasted
and then dried before the coating system was
applied. Two alternate blades were coated
with a vinyl shop primer and 2 with a 2 layer
epoxy primer. The whole propeller was then
coated with two layers of the TBT-SPC
system (an extra coating was also added to the
outer half of the blades. The roughness of the
propeller before and after coating can be seen
in Table 2.
Table 2. A comparison in the roughness of the
surface both before and after painting
110.3Pm
43.7Pm
60.38%
Rtm (2.5)
Coldron and Conde (1990)
Ra (2.5)
Prior
to
23.2Pm
Painting
14.2Pm
After Painting
38.79%
% Change
The propeller was inspected after both 6
and 12 weeks and was found that the TBTSPC coatings had rapidly been removed from
the vinyl primer. The SPC on the epoxy
performed better with only some mechanical
damage to the tip. The polishing rate of the
SPC was found to be very low when
compared to that expected of a ship’s hull.
The epoxy was slowly ‘stripped’ back along
the suction side from the tip inwards so that
25% had been removed after only 3 months.
In 1989, after 6 years in service, 20% of the
epoxy, near the blade roots, still remained on
the propeller
Further trials were conducted, this time
using a ceramic coating, in order to try and
prevent a problem with localized but random
cracking of the propellers of the Shell
Marketer class of vessels Coldron and
Condé (1990). Two blades were, cleaned,
degreased, preheated and the grit blasted
before being coated not more than 40 mins
after the surface preparation. The coating used
was a ceramic mix, with an alumina base,
with 13% titanium added (this improves the
impact resistance but reduces the electrical
resistance). The coating was applied using a
plasma
flame
spray
system
with
argon/hydrogen plasma gas. The two
remaining blades were prepared to the
manufacturer’s standard finish. After a period
of 4 years, the propeller was inspected to find
that the coated blades had actually become
smoother compared to their initial roughness
after coating. The uncoated blades, however,
had deteriorated to a surface about 50%
rougher than their initial value. The coating
had managed to remain attached, even in an
area where mechanical damage had removed
part of the coating, there was no evidence of
‘creep back’. Although it should be
considered highly unreliable, due to the
complex nature of the effect of propeller
condition on ship performance, it was also
noted that the Shell Marketeer was
performing 6% (in terms of nautical miles per
tonnes of fuel) better than its sister-ship, the
Shell Seafarer, whose blades had not been
131
Proceedings of 26th ITTC – Volume I
coated, but were of a similar roughness to the
Shell Marketeer’s blades prior to their coating.
Matsushita et al. (1993) noted that
because the training ship of the Yuge National
College of Maritime Technology in Japan, the
Yuge-Maru, was at anchor for long periods,
the propeller had a serious problem with
biofouling. The seawater around its home port
ranged from 8-9°C to 27-28°C, a wide variety
of adhesive sea life were present in the
surrounding waters, including at many
different species of barnacle (such as
Tintinnabulum rosa, Amphitrite tesselatus and
Amphitrite
hawaiiensis),
Bryozoans
(calcarious colonial animals, similar to
corals), Serpulids (a type of tubeworm),
mussels, oysters, algae and bacterial biofilm.
Therefore researchers at the college, as part of
a wider investigation into the effect of a non
toxic coating of silicone resin decided to coat
the ship’s propeller. The coating system had
been developed as an industrial, non-polluting
paint in such areas as seawater suction pipes
and cooling pipes of nuclear plants. Since
there was no toxin present in the coating
chemistry it was considered safe to the
environment. The surface had similar
properties to the modern Foul Release
properties, with a low surface energy and high
water repellence. The antifouling ability was
derived from the low attachment strength of
marine fouling organisms to the surface. This
was then the first reported experiment with a
FR coating on a marine propeller. The
propeller was first cleaned and then allowed
to foul over a six month period. Upon
inspection after this period it was found that
the propeller was heavily coated in fouling
(mostly bryozoans and serpulids) particularly
441
in areas of slow flow speed over the surface
e.g. the boss and blade roots. After the
inspection the propeller was then re-cleaned
and coated with silicone resin paint. 6 months
after coating, the propeller was again
inspected. The coating was found to be intact
and free from fouling except for a few flat
bryozoans on the root. After a further 6
months the propeller was inspected a third
time, again no damage to the coating was
found, there was however, some bryozoans
and slime fouling present. These results were
the first to show that a foul release coating
can remain attached to a propeller and achieve
effective antifouling in actual service.
In addition to the propeller inspections
described above the fuel consumption was
recorded for both the un-coated and coated
propellers were recorded over the course of
three months during the summer fouling
breeding season. It was found that the fuel
consumption with the 6.2% lower when the
propeller was coated although the lack of
details about the change in hull condition over
the trial period mean that this change cannot
be attributed to the condition of the propeller
alone.
The Yuge-Maru also had a large number
of sacrificial zinc anodes attached around the
hull to protect the hull from electrochemical
corrosion by galvanic action in seawater,
caused by the copper alloy propeller. Each
side of the ship has 23 anodes attached to the
shell plating, one in the bow thruster tunnel,
one on each of the upper and lower bearings
of the rudder post and one at the end of the
stern tube, see Figure 2.
Specialist Committee on Surface Treatment
442
Within the framework of galvanic
corrosion Atlar (2004) noted that some ship
owners and propeller manufacturers may
think that partially coated propellers, which
can represent possible damage to paint or a
paint failure, could be subjected to complex
corrosion effect due to inherent differences in
two surfaces. Although such corrosive
damage has not been reported in any of the
vessels with coated propellers, within the
capability of modern cathodic protection
systems this should not be a problem. His
consultation with a major UK propeller
manufacturer revealed that the final surface
finish of a large propeller by hand may take
about a month of time while with a machine
this will take at least a half of this period. In
the mean time, the application of coating on
propeller surface would require relatively
rough surface, which is obtained by grid
blasting, to provide the coatings with a
necessary grip to stick on the surface. Based
upon this requirement, the propeller
manufacturer does not perform the final finish,
and hence save labour cost and delivery time,
but this was still much lower than the current
output of the uncoated disc. Although done on
a small scale, this is further strong evidence
that the coating will reduce the galvanic
current caused by the propeller.
Figure 2 - Arrangement of Sacrificial Anodes (Zn Plates) on ship body of Yuge-Maru (Matsushita
et al., 1993).
Table 3 shows the amount of degradation
of the anodes of the course of a year without
the propeller being coating and as a
comparison the levels of degradation of the
replacement anodes over a year once the
propeller was coated. The level of
deterioration was low for both cases (less than
5%); suggesting that the number of anodes
attached to the ship was excessive. The results
did show however, as expected, the anodes
near the propeller were the most reduced
(except number 3, inside the bow thruster
tunnel). The difference between anode
degradation in the uncoated and coated
propeller condition was approximately 30% in
favour of the coated propeller condition. This
suggests that the propeller coating stopped or
significantly reduced the galvanic current. In
fact this has since been confirmed by more
recent research by Anderson et al. (2003)
who conducted further testing of new
generation FR system, on the propellers (and
replacement metal discs) of a 100th detailed
scale model of a frigate, to investigate the
effect of a propeller coating upon the current
output of an Impressed Current Cathodic
Protection (ICCP) system. They found that
the use of the coating “markedly reduced” the
ICCP current output. When the coating was
damaged, there was an increase in the output,
132
Proceedings of 26th ITTC – Volume I
while the paint manufacturer will apply grid
blasting directly on this surface. This way all
three
parties:
the
owner;
propeller
manufacturer and paint manufacturer can
benefit as well as the environment
Table 3. Consumption of Sacrificial Anodes
(Zn plates) of the TS Yuge-Maru.
(Matsushita et al., 1993)
A
B
C
95.4
5.2
2.2
4.0
5.5
12.6
2.2
4.0
Total
A
B
C
95.4
5.2
2.2
4.0
3.95
4.5
8.4
6.2
Non-Propeller Coating
Propeller Coating
(07.03.1989-28.02.1990)
(10.03.1990-04.03.1992)
Zinc Anode New Zinc Rate of Zinc Zinc Anode New Zinc Rate of Zinc
Position
Weight Consumption Position
Weight Consumption
(Kg)
(%)
Number
(Kg)
(%)
Number
1
3.5
2.1
1
3.5
3.1
2
3.5
2.1
2
3.5
3.6
3
3.5
14.2
3
3.5
14.9
4
3.5
3.5
4
3.5
3.0
5
3.5
2.4
5
3.5
3.4
6
3.5
2.7
6
3.5
4.3
7
3.5
3.0
7
3.5
3.6
8
3.5
3.1
8
3.5
3.9
9
3.5
3.4
9
3.5
2.7
10
3.5
2.5
10
3.5
3.1
11
3.5
2.7
11
3.5
2.5
12
3.5
2.3
12
3.5
1.9
13
3.5
1.4
13
3.5
2.2
14
3.5
1.2
14
3.5
2.6
15
3.5
1.5
15
3.5
3.1
16
3.5
3.1
16
3.5
4.3
17
3.5
4.6
17
3.5
3.9
18
3.5
2.9
18
3.5
2.9
19
3.5
8.9
19
3.5
0.4
20
3.5
9.1
20
3.5
3.1
21
3.5
2.5
21
3.5
2.1
22
3.5
6.1
22
3.5
3.0
23
3.5
9.6
23
3.5
4.7
24
3.5
13.6
24
3.5
4.9
Subtotal
84.0
4.5
Subtotal
84.0
3.65
Total
=
=
=
=
Shell Plate (B-4)
Upper Gudgeon
Lower Gudgeon
End of Stern Tube
1-24
A
B
C
Another Japanese trial was conducted, this
time using the training ship Kakuyo Maru
Araki et al., (2000) and Araki et al. (2001).
The ship’s 2.85m diameter propeller was
coated with a silicone resin (Bioclean DX –
Chugoku Marine Paint Company Ltd.). After
1 year in service, the propeller was inspected
to find only light slime on the blades, with
only a little paint having been removed from
the tips of the blades. Improvements were
also noted in the rate of fuel oil consumption,
fuel oil pump index, and shaft horse power
required, compared to the fouled propeller,
443
although it was unlikely that this was due to
the condition of the propeller alone.
Over the years propeller coatings have
been tested that have a wide range of
properties that effect propeller performance
and durability of coating. In the search for the
perfect propeller coating a number of
attributes have been highlighted as desirable.
Coldron and Condé (1990) defined the
attributes of an ideal propeller coating as
follows:x Exhibit adequate erosion, abrasion,
corrosion and cavitation resistance and
be resistant to impact damage and
penetration.
x Posses anti-fouling characteristics or
be smooth to simplify removal of
marine biofouling.
x Retain an acceptable level of
properties when exposed to seawater
with low water permeability to prevent
degradation of bond strength by
corrosion of the coating/substrate
interface.
x Possess adequate bond strength
initially and after prolonged seawater
immersion to withstand the operating
conditions, including maintenance
procedures.
x Be non-conducting to reduce cathodic
protection current requirements by
limiting the cathodic area.
x The materials should be cheap, readily
available, and relatively easy to apply
and repair.
x The coating must be capable of
inspection for quality assurance
purposes.
x The coating must be sufficiently thin
that it can be applied within the blade
thickness tolerance range and not
require expensive re-design of the
propeller. In practice this implies a
coating in the thickness range of 100
to 250μm.
To the above list it can be added two
further attributes, that have become more
Specialist Committee on Surface Treatment
444
desirable in the years since Coldron and
Condé published their list:
x The
coating
must
be
as
environmentally benign as possible.
x Preferred to reduce any radiated
signatures emanating from the
propeller as much as possible
(especially important for naval vessels
and cruise ships).
A number of possible propeller coating
types have been developed that each have
some of the above attributes but not all of
them. The possible types were listed by
Coldron and Condé (1990) as in the
following
Organic Coatings
This is a wide ranging group of coating
types that includes both current SPC
technology and Foul Release antifouling
coating technologies, epoxies, vinyls,
neoprenes, urethanes and polyamides (nylons).
There are a wide range of possible application
methods such as airless spray, brush and
roller. Some can even be coated onto the
propeller in either a fluid or powdered state
and then autoclaved to give the final coating,
although such methods are hard to use for
large modern merchant propellers, due to the
need for an autoclave of sufficient size.
Metallic Coatings
A wide variety of metallic coating could
be considered for marine propellers. Some
may even have antifouling properties, if they
contain compounds metals with known
antifouling properties such as Copper, Zinc,
Tin or other heavy metals. They could, in
theory, be deposited a number of different
methods, such as by electroplating, thermal
spray, weld overlay or vapour deposition.
This group could also include, laser surface
melting, when a thin layer of the surface is
heating to improve the surfaces resistance to
cavitation, e.g. Tang et al., (2004, 2005). The
development of these coating would require
large scale facilities to allow merchant
propeller, typically of 5-10m diameter to be
treated economically. Metallic coatings also
suffer from the problem of, if two dissimilar
metals are in contact, a galvanic cell will form
causing accelerated corrosion. This is why
little research has been done on this type of
coating for use on propellers.
Ceramic Coatings
This type of coating are created a
powdered mix of mineral substances
including clays and metal oxides (aluminum,
chrome and titanium oxides are widely used)
that are then fired (or specialist techniques,
such as thermal spray processes can be used)
to produce a dense, low porosity coatings.
The properties vary widely, depending on
what chemicals are what proportions of each
chemical are used. They can be insulating or
semi-conducting and the hardness can be
varied. They are
usually inert in seawater but not all can
withstand high levels of cavitation. Expensive
research into the ideal chemical formula
would be needed before their use as a
propeller coating will become widespread.
No coating has yet been found to have all
the attributes in the list, so the perfect coating
is still elusive. The current leading contenders
for a suitable propeller coating and their
properties
compared
to
the
above
requirements can be seen (not in any order of
importance) in Table 4.
Table 4. The four systems currently most
likely to be developed as a propeller coating
are the two leading types of antifouling
system (silicone based foul release and copper
based SPC) and metallic and ceramic type
coatings. The qualities of each coating system
compared to the desired attributes are shown.
Those coloured green indicate that the system
exhibits that attribute successfully, orange
indicates that the system may exhibit that
attribute or no evidence for the system
displaying that attribute was available and red
indicates that the attribute is not exhibited.
133
Proven antifouling
ability
Inert in seawater
Silicone
Foul
Release
Softer coating
Proceedings of 26th ITTC – Volume I
Resilience
to
Damage
Antifouling Ability
Inert in Seawater
Copper SPC
Hard coating
Metallic Coating
Hard coating
Ceramic Coating
Non toxic
Unproven,
No
mechanism known
Inert in seawater
Hard coating
Proven attachment
to propellers
Non conductor
Strong Attachment
Proven antifouling
ability
Leaches away with
time
Proven attachment
to propellers
Unknown,
may
conduct
Already
in
production
Non Conducting
in
Already
production
Proven attachment
to propellers
Depends
upon
ceramic used
Development and
material
costs
required
Depends on coating
used
Thin coating likely
Cheap to develop
and produce
Unproven, possible
with some metals
Depends upon the
chemistry used
Unknown
attachment ability
Likely
to
be
conductor
Development and
material
costs
required
Depends on coating
used
Thin coating likely
No effect likely
upon
No effect likely
Depends
coating used
445
analysis, using a variety of diagnostic liquids,
measuring the angles that the liquid droplets
make with the coated surface. It is the surface
tension of a polymer which is the property
that has most commonly been correlated with
resistance to befouling, Brady and Singer
(2000). A generalised relationship between
Surface Tension and the Relative amount of
bio Adhesion has been established and
presented in a graph commonly known as the
“Baier curve”, which does not display the
minimum relative bio adhesion (22~24
mN/m) at the lowest surface energy. A variety
of explanations has been given to account for
this including the effects of elastic modulus
(E), thickness and surface chemistry of
coatings as discussed by Anderson et al
(2002). Elastic modulus is key factor in bio
adhesion and hence ability of organisms to
“release” from a coating, Brady and Singer
(2000) and Berling et al (2003). The
calculated Critical Free Surface Energy (c)
for a range of different polymers indicated
that there was a better correlation between the
relative bio adhesion and (cE)1/2 than with
either surface energy or elastic modulus,
of the attributes when compared to the other
types of coating as will be discussed further in
the next.
Coating easy to
inspect
Coating thins over
time
No effect likely
Inspection
of
Coating
Thickness
of
Coating
Noise Reduction
Toxic leachate
to
Coating easy to
inspect
~350mic, 3 layer
system
Pliable, may reduce
Noise
Non toxic
Harmful
environment
From the table it can be seen that silicone
based fouling release systems displays more
2.2.4. Review of foul release coating technology
Foul Release (FR) coating technology is
the fore runner of the modern coating systems
for ship propellers. In comparison to
traditional antifouling technologies, FR
technology relies on a fundamentally different
concept of fouling prevention. Instead of
using the slow release of a biocide into the
surrounding water, FR coatings work by
providing a surface to which fouling species
find it difficult to attach securely, this is
known to be “low free surface energy”
surface. The fouling is then removed from the
surface by hydrodynamic shear force.
The free energy of a surface, which is
commonly referred to as “surface energy” or
“surface tension”, is the excess energy of the
molecules on the surface compared with the
molecules
in
the
thermodynamically
homogenous interior. The size of the surface
energy represents the capability of the surface
to interact spontaneously with other materials,
Brady (1997). The surface energy and the
critical surface tension of surface are
determined by comprehensive contact angle
Specialist Committee on Surface Treatment
446
Brady and Singer (2000). Thickness is
another characteristic of low surface energy
coatings that plays an important role in bio
adhesion. It has been found that below
~100μm dry film thickness barnacles can “cut
through” to the underlying coats and thus
establish firm adhesion. Above this thickness
there is no marked increase in FR properties.
The majority of current FR coatings are based
on the molecule Polydimethylsiloxane
(PDMS) which are generally formed by a
condensation mechanism. This long chain
polymer has a long flexible ‘backbone’ that,
along with the low intermolecular forces
between the methyl groups, allows it to adopt
the lowest surface energy configuration.
PDMS has, in air, a surface energy of 23-35
mN/m and such lower value of surface energy
and its elastic nature makes PDMS perfectly
suited for use as a FR type coating, Brady
and Singer (2000). In fact, for PDMS and
other silicone material, J C E , was found to
be at least an order of magnitude lower than
that of other materials (Singer et al., 2000). It
has been found that incorporation oils can
enhance the FR properties of PDMS polymers,
Milne (1977). Oils, by their nature, are
lubricants and therefore should decrease the
friction, but this is not the main reason for the
efficacy of PDMS. This is thought to be due
to the surface tension and hydrophobicity
changes that the oils effect during the curing
process and after immersion, Truby et al
(2003).
When Foul Release coatings were
commercially introduced in the mid-1990s
and applied to a high-speed catamaran ferry,
replacing a toxic Controlled Depletion
Polymer (CDP) antifouling, the recorded fuel
consumption was lower at the same service
speed, implying lower drag characteristics as
reported by Millett and Anderson (1997). As
a consequence a research project was set up at
Newcastle University with the objective of
collecting data on the drag, boundary-layer
and roughness characteristics of Foul Release
and tin-free SPC coatings, and to compare
them systematically, Candries (2001) The
coatings used were a PDMS Foul Release and
a tin-free copper-pigmented acrylic SPC that
contained zinc pyrithione as a booster biocide.
Drag measurements were carried out in
towing tank experiments with two friction
planes of different size (2.5m and 6.3m long),
which showed that the Foul Release system
exhibits less drag than the tin-free SPC
system when similarly applied. The difference
in frictional resistance varied between ca. 2
and 23%, depending on the quality of
application as reported by Candries et al.
(2001). Rotor experiments were also carried
out to measure the difference in torque
between uncoated and variously coated
cylinders. In addition to coatings applied by
spraying, a Foul Release surface applied by
rollering was included because there were
indications that this type of application might
affect the drag characteristics. The
measurements indicated an average 3.6%
difference in local frictional resistance
coefficient between the sprayed Foul Release
and the sprayed tin-free SPC, but the
difference between the rollered Foul Release
and the sprayed tin-free SPC was only 2.2%,
Candries et al. (2003)
The friction of a surface in fluid flow is
caused by the viscous effects and turbulence
production in the boundary layer close to the
surface. A study of the boundary-layer
characteristics of the coatings was therefore
carried out in two different water tunnels
using four-beam two-component Laser
Doppler Velocimetry (LDV) and the coatings
were applied on 1m long test sections that
were fitted in a 2.1m long flat plate set-up,
Candries and Atlar (2005). Velocity profiles
were measured at five different streamwise
locations and at five different free-stream
velocities. A rollered surface and a sprayed
Foul Release surface were tested to
investigate the effect of application method.
The measurements showed that the friction
velocity for Foul Release surfaces is
significantly lower than for tin-free SPC
surfaces, when similarly applied. This
134
Proceedings of 26th ITTC – Volume I
indicated that at the same streamwise
Reynolds number the ratio of the inner layer
to the outer layer is smaller for Foul Release
surfaces. The inner layer is that part of the
boundary layer where major turbulence (and
hence drag) production occurs. Statistical
analysis of the values of the roughness
function obtained by means of multiple
pairwise comparison, using Tukey’s test,
indicated that the roughness function for Foul
Release surfaces is significantly lower than
for tin-free SPC surfaces at a 95% confidence
level. These findings are consistent with the
drag characteristics measured in the water
tunnel and rotor experiments
In addition to the difference in frictional
resistance and the roughness function, the
roughness characteristics of each of the
surfaces were investigated. The average
values of their roughness were measured
using the BMT Hull Roughness Analyser,
which is the stylus instrument in common use
in dry-docks or underwater, for standardised
hull roughness measurement. It measures Rt
(50), which is the highest peak to lowest
valley roughness height over a sampling
length of 50mm. Successive values are
averaged over a surface. It is clear from the
rotor experiments and the large plate towing
tank experiments that this single amplitude
parameter does not correlate with the
measured drag increase for Foul Release
surfaces, as it does with SPC surfaces.
A detailed non-contact roughness analysis
was carried out with an optical measurement
system fitted with a 3mW laser.
Measurements were taken on sample plates
coated alongside the surfaces tested in the
towing tank and water tunnel, and were thus
assumed representative of the test surface
characteristics. In the case of the cylinders
used in the rotor experiments, sections were
cut from the cylinders after testing, for use in
the optical measurements. A moving average
was applied to filter long-wavelength
curvature. The upper bandwidth limit or cutoff length was set at 2.5 and 5mm, whereas
447
the lower bandwidth limit or sampling
interval was set at 50mm.
The detailed roughness analysis revealed
that when long-wavelength curvature has
been filtered out, the amplitude parameters of
the sprayed Foul Release surfaces are in
general lower than those of the rollered Foul
Release surfaces and the SPC surfaces.
However, the rollered Foul Release surfaces
display a roughness height distribution which
is considerably more leptokurtic (i.e. exhibits
a larger number of sharp roughness peaks)
than the sprayed Foul Release surfaces. The
greater number of high peaks on the rollered
Foul Release surfaces is expected to engender
higher drag than sprayed Foul Release
surfaces.
The main difference between the Foul
Release and the tin-free SPC systems lies in
the texture characteristics, as shown in Figure
3 for two typical roughness profilogram of
such coatings, applied by spraying. Whereas
the tin-free SPC surface displays a spiky
“closed” texture, the wavy “open” texture of
the Foul Release surface is characterised by a
smaller proportion of short-wavelength
roughness. This is particularly evident in
texture parameters such as the mean absolute
slope and the fractal dimension. There is
relatively little data available in the literature
of irregularly rough surfaces on the influence
of texture only on drag. Grigson (1982) has
mentioned explicitly that open textures have a
beneficial effect on drag.
It is clear that in order to correlate with
drag, the roughness of the generality of
irregularly rough surfaces needs to take both
amplitude and texture parameters into account,
e.g. Musker (1977) and Townsin and Dey
(1990). Based on the experiments presented,
it was thought that the rheology of the paint,
which is significantly different for foulrelease and tin-free SPC coatings, had a direct
effect on its texture, whereas amplitudes
depend significantly on the application quality.
A correlation analysis of the texture
Specialist Committee on Surface Treatment
448
parameters with the amplitude parameters,
however, has shown that the two are interrelated, so that bad application can be
expected to have a knock-on effect on the
texture parameters
At present, the procedure adopted by the
International Towing Tank Committee
(ITTC) to correlate roughness with drag only
accounts for a single roughness amplitude
parameter, ITTC (1990). The procedure
hinges on the use of a practical formula for
the added ship resistance (or roughness
correlation allowance), which was proposed
by Townsin and Dey (1990) in terms of
Average Hull Roughness for the moderately
rough ship range where Rt(50) is less than
Pm. Unfortunately, this procedure may
not work for foul-release surfaces, unless a
texture parameter is included in the roughness
characterisation. For a selection of 41
different coated surfaces, including 8 newly
applied foul-release surfaces, Candries and
Atlar (2003) found that the measured drag
correlated reasonably well best when the
roughness measure, h, is characterised by h =
1/2Ra.'a where Ra is the average roughness
amplitude while'a is the mean absolute slope.
There was a need for further testing and
correlation studies to provide further support
for this correlation.
Figure 3. Typical roughness profilograms taken from a tin free SPC coated surface, Ecoloflex,
(above) and Foul Release, Intrersleek 700, coated surface (below) using laser profilometry,
Candries and Atlar (2003)
135
Proceedings of 26th ITTC – Volume I
449
University propeller coating research, and
some numerical and experimental work was
conducted with the scaled model of this
propeller with the following main particulars
given in Table 5 and operating conditions
given in Table 6.
scaled service condition of the propeller) a
slight drop in efficiency (2.48%) was noted.
Neither of these values was large enough to
say that the coating made a significant change
to the propeller efficiency beyond that of
experimental error. It was noted that with the
coating the inception of the tip vortex
cavitation appeared at approximately a 5%
lower value of the rpm for the uncoated
propeller, although this could easily be due to
the poor application of the coating (applied by
brush) or mechanical damage on the leading
edges of the blades. No adverse effect of the
coating to the extent of the cavitation was
noted whilst the coating stayed intact until the
end of these tests except small peeling off at
the sharp edges, Candries et al. (1999). In
addressing at the second stage investigations
(2) more through and long term research was
planned. This has involved numerical and
experimental investigations as well as fullscale trials / observations to demonstrate if
there were any benefits or disadvantages of
applying FR coating on propellers in terms of
propeller efficiency, effect on cavitation
inception, type and extent of cavitation and
underwater noise emission from propellers.
The following section gives a brief review
and findindgs from these investigations.
2.2.5. Foul release coating research – as applied to propellers
While the earlier summarized research on
the FR coatings was continuing to understand
their general drag reduction mechanism, there
was further interest from industry to research
on the application of these coating systems on
propellers in the following two areas: (1) if
the FR coatings can successfully stay on yacht
propellers in arduous conditions; (2) if the FR
coatings can display any performance benefit
for a large commercial vessel propeller that
was coated with the earlier mentioned FR
system, Intersleek 700 (IS700). In addressing
at the first investigation area (1), a pilot
experimental study was conducted with a 3bladed, 300mm diameter, aluminum alloy
model of a commercial motorboat propeller.
The model was coated by IS700 using a
rollering technique as opposed to spraying to
simulate a real life scenario for small craft
owners. Open water tests were conducted in
the Emerson Cavitation Tunnel of Newcastle
University in atmospheric and reduced
vacuum condition. In the latter case the
propeller was exposed to several hours of
cavitating condition to check on the adherence
resilience of the FR system. In the
atmospheric condition a slight increase in
propeller efficiency of 0.16% was recorded.
In a vacuum condition (equivalent to the
2.2.6. Effects on propeller efficiency
Based upon some plausible fuel saving
reports after the application of IS700 coating
on the propeller of a 100,000 DWT tanker, it
was decided to use the propeller of this vessel
as the benchmark propeller for the Newcastle
6.85 m
Deadweight
Length Overall,
LOA
Ship type
Propeller
Table 5. Main particulars of the basis vessel and propeller
Diameter, D
0.699
0.524
Vessel
Medium sized
tanker
96920 tonnes
243.28 m
Pitch Ratio, P/D
Expanded Blade Area Ratio,
AE/A0
Max Draught, T
9893 kW
14.86 knots
13.62 m
Specialist Committee on Surface Treatment
450
Speed
1992
4
Power(installed)
Number of Blades, Z
Year built
0.48
19.57
Right/H
Design Advance Coefficient, JA
Direction of rotation
4.66
0.334
Table 6. Operational conditions
10
Fully Loaded
Condition
0.520
104
In consultation with a major UK propeller
manufacturer, it was assumed that a
roughness equivalent to Rubert A represented
a degree of smoothness unlikely to be
achieved in practice. Rubert B was considered
characteristic of a new or well polished
propeller and Rubert D to E would be
equivalent to the blade roughness after 1 to 2
years in service. In the numerical analysis it
was assumed that the new or polished
propeller had Rubert B blade surfaces, the
drag of which was represented by the design
CD values taken from Burrill (1955-56). The
increase in CD caused by blade roughening
was then given by the difference between the
' CD values corresponding to the Rubert
surface in question and that for Rubert B. The
effect of the increased roughness on the drag
coefficient for the section at r/R = 0.7 is
shown in Table 8.
The total drag coefficient was represented
by the sum of the frictional drag and the form
drag as in the following where t is being the
thickness of the blade section:
' C D 2 (1 t / c ) ' C F
0.48
0.486
0.75, 0.70, 0.65, 0.60, 0.55, 0.50, 0.45, 0.40
100
Ballast Condition
Scale ratio, O
Cavitation number, V
Propeller immersion, H (m)
Propeller speed (RPM)
Design JA
J range tested
ª1
º
8.1 Re 0.093 « h ' c 4.5 Re 1 / 3 »
¬3
¼
Atlar et al (2002) conducted numerical
investigations on the open water performance
analysis of this propeller by using a boundary
element theory based lifting surface analysis
tool in which the effect of the FR coating was
simulated in the appropriately selected drag
coefficients of the propeller blade section. In
this selection the increase in section frictional
drag due to roughness was represented by the
expression given by Mosaad (1986) as:
1000 'C F
Where
Re is the blade section
Reynolds’ Number; c is the section chord
length; h’ is the roughness parameter as
defined by Musker described earlier. Values
for h’ for the various Rubert surfaces were
calculated by Mosaad and are given in Table 7.
Table 7. Musker’s characteristic roughness
measure of Rubert gauge surfaces.
1.32
3.4
h' ( P m)
14.8
A
B
Rubert Surface
C
160
49.2
252
D
F
E
136
Proceedings of 26th ITTC – Volume I
Surface
0.0083
38
Design
Rubert
D
0.0100
3
19.7
Rubert
E
0.0113
8
35.8
Rubert
F
0.0120
6
43.9
Table 8. Drag coefficients of Rubert surfaces
(Design = Rubert B).
CD
%
Increase
The key decision on this analysis was the
determination of characteristic roughness
values (h’) for the foul release coated blade
surfaces. In this decision the measurements
made with the FR coated flat plates by
Candries (2001) played an important role.
The surface characteristics of 5 different
applications were studied using a UBM
Optical Measurement System from which it
was found that the roughness measure h’
varied between 0.5 and 5Pm. The quality of
application ranged from excellent to good, so
that it was considered appropriate to assume a
value of h’ = 5Pm. The calculated values
were negligibly different from those
calculated when using the Design CD values.
From this it can be inferred that a foul release
coated blade surface was equivalent to the
new or well polished blade surface.
Based on the above assumption the
sectional drag coefficients in the numerical
tool was modified and the propeller
performance with the design CD values was
first was calculated for varying operating
(advance coefficient) conditions and this
procedure was then repeated with the drag
coefficients corresponding to Rubert D, E and
F surfaces for the same conditions. The
results of the comparisons were presented in
the open water curves of this propeller as
shown in Figure 4 where the predominant
effect of an increase in the roughness of the
propeller blades was an increase in the
propeller torque. The decrease in propeller
thrust that accompanies the increased torque
was too small to be obvious on the figure’s
scale.
451
Figure 4. Propeller open water characteristics
for various values of blade surface roughness,
Atlar et al (2002).
The loss in propeller efficiency (KRas the
propeller blades roughen, to a base J, is
shown by Figure 5. Performance data for the
subject vessel from which the propeller was
modelled showed that on average propeller
worked at a value of J = 0.48. As shown in
Figure 3 the propeller efficiency losses due to
blade roughening (or gains by keeping
propeller clean) were about 3%, 5% and
6%for surfaces of roughness represented by
Rubert D, E and F, respectively. In summary,
this numerical investigation showed that
significant losses in propulsive efficiency
resulting from blade roughening can be
regained by cleaning and polishing of the
blades. Alternatively, the efficiency losses
could be avoided, perhaps indefinitely, by the
application of a paint system that gives a
surface finish equivalent to that of a new or
well-polished propeller. A foul release
coating could be such a paint system.
Atlar et al (2003) conducted the similar
analysis, this time applied on high-speed and
large surface area propellers. The simulations
for the open water performance of the GawnBurrill Series based propeller of a twin-screw
patrol gun boat indicated rather plausible
efficiency gain (or loss) which was almost
twice the maximum efficiency gain (or loss)
Specialist Committee on Surface Treatment
452
obtained with the earlier reported tanker
propeller. This was related to the high speed
and larger blade surface area of the propeller.
While the above described numerical
investigations revealed attractive potential of
the FR coating for efficiency gain,
experimental investigations were conducted
to confirm on this potential with a scaled
model of the earlier described basis tanker
propeller in the Emerson Cavitation Tunnel.
The model was constructed from aluminium
to a scale of 1:19.57 so that multiple sets of
blades, manufactured with great accuracy can
be installed or replaced easily.
polymer top coat and a tie coat between these
two for good bonding. The whole system
dried to a film thickness of between 320 and
360mic. The uncoated and coated propeller
model can be seen in Figure 6.
Figure 5. Loss in efficiency in going from Design Drag Coefficient to specified Rubert Surfaces,
Atlar et al (2002).
This allowed rapid and reversible changes
between the coated and uncoated condition.
One set of blades was coated with the IS700
FR system which was a three layer system
consisting of an epoxy basecoat, a silicon
Figure 6. Model Propeller with uncoated (left) and coated (right) blades, Mutton et al (2005)
slight change was due to the slight decrease in
the measured torque as observed in the
numerical simulations. The open water tests
were repeated at a reduced vacuum, which
corresponded to the fully-loaded condition of
the vessel. This did not show any change in
the efficiency at the design operating
condition.
Results from the tests were discussed by
Mutton et al (2005) and Figure 7 shows the
findings from the open water tests. As shown
in this figure there was little difference
between the coated and uncoated condition
for the favour of the coated condition at
higher values of advance coefficients. The
137
0.35
0.45
Advance Coefficient, J
0.55
0.65
0.75
0.85
uncoated Kt
uncoated 10Kq
uncoated Efficiency
coated Kt
coated 10Kq
coated Efficiency
Comparison of Open Water Characteristics in Atmospheric condition
(water speed 4ms-1, Confidence limits 95%)
Proceedings of 26th ITTC – Volume I
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.25
453
However in their experimental study,
Korkut and Atlar (2009) withdrew attention
coating technology. In parallel to this
development, in the early stages of the above
described research at Newcastle University
the commercial FR system used was
International Paint’s Intersleek 700 (IS700).
After the introduction of the recent
commercial product, Intersleek 900 (IS900),
the above propeller performance tests were
repeated with this latest coating system
applied on the same model propeller by
Korkut and Atlar (2009). Using the latest
application technology it was possibly to
achieve a dry film thickness of 250Pm with
the three layer coating system as opposed to a
350Pm thickness of the earlier tests. The open
water performance tests revealed an average
1% difference in the efficiency values over
the entire J range for the favour of uncoated
blades. Both thrust and torque values were
slightly increased by 1.9% and 0.9% with the
effect of coating, respectively. In overall the
difference in the average efficiency was
within the uncertainty level of the open water
tests which was 3%, similar to the
conclusions by Mutton et al (2005) although
the trend in the previous tests was in favour of
coated blades.
Figure 7. Open water curves for the uncoated and coated propeller. A slight reduction in torque at higher
advance coefficient has led to an increase in efficiency for the coated propeller. The design operating
condition for this propeller is J=0.48; no difference is detected in performance at this condition, Mutton et al
(2005).
Examination of full-scale propellers
coated with FR systems has demonstrated that,
like all propeller coatings, the Foul Release
coating is prone to suffering damage from to
cavitation and hitting objects in the water.
This is usually about 5-10% of the coating
surface area and predominantly on the blades
leading edge, trailing edge and tip regions. It
was suggested that this damage may
significantly affect the performance of the
propeller as well as promoting early
cavitation inception and encourage further
cavitation development in the damaged areas.
To investigate these effects Mutton et al
(2005) imparted different levels of typical
damages onto this model propeller’s coating
to investigate the damage effects. These tests
indicated that the damage to the coating had
to be extensive before significant reduction in
efficiency to occur.
One of the important aspects affecting the
foul releasing ability of these coatings is the
lower threshold of a vessel’s continuous
operational speed. Early generation FR
coatings had relatively high threshold (e.g. 18
knots and beyond) to be effective whilst this
limit has been reducing (e.g. 12 knots and
below) with recent development in this
Specialist Committee on Surface Treatment
454
on the applied paint thickness such that,
owing to the practical limitation of the
application technique of the particular coating,
which was airless spraying, the coating
thickness applied on the model propeller was
almost similar to the coating thickness at fullscale. This would require further investigation
on scaled coating thickness and appropriate
scaling law.
Within the same framework another recent
experimental investigation on the application
of new FR coating on model propeller
performance was reported by Atlar et al
(2010) as part of the recently completed ECFP6 integrated R&D project AMBIO which
aimed to develop non-toxic antifouling
benefited from nano technology engineering
to prevent or reduce the growth of biofouling
in the marine environment, AMBIO (2010).
In this project, one of many newly formulated
and tested FR coatings was TNO-008 which
was based on nano-engineered Sol-gel
technology by TNO. This coating was applied
on the earlier described benchmark model
propeller using spraying technique and cured
by heating up to 125 deg. The nature of the
coating and the application technology
enabled to apply this coating at a desired
thickness such that it was possible to achieve
an average roughness which was 54% less
than the roughness achieved with the
Intersleek 900 (IS900). The comparisons of
the open water test results of the model
propeller with the IS900 and TNO-E008
coatings showed similar torque characteristics,
with little difference observed between the 2
coatings. However the TNO-E008 coating
gave a higher thrust value for the same rpm
when compared to the IS900 coating such that
the efficiency increase could be as high as 4%
when compared to the IS900 at the maximum
efficiency. Whilst this finding appears to be
too plausible requiring further investigations
at least by applying on other types of
propellers and to test, the most interesting
nature of this new coating technology was the
flexibility in the application thickness that can
be adjusted to meet a scaling criterion that can
be found between the model and full-scale
paint thickness.
In order to investigate the effect of
propeller coating on ship’s performance in
full-scale and controlled manner, Mutton et
al (2003) conducted a series of comparative
dedicated full scale trials for the first time
with the FR coated and uncoated propellers.
This was over a measured mile with
Newcastle University’s Ex-R/V Bernicia
which was based on the design of a fishing
vessel and mainly used for estuarine and
coastal research. The main particulars of the
R/V and its single screw are given in Table 8
and 9, respectively.
Table 9. The general particulars of RV Bernicia
Overall length
16.2 m
Beeam
4.72m
Draft
2.59m
Gross tonnage
46.25 tons
Engine (MCR)
150HP @ 1500rpm
Gear box ratio
3.4:1
Maximum ship speed
9 knots
Table 10. Main particulars of the R/V Bernicia propeller
Diameter
1.14m
Mean face pitch
0.9m
Expanded BAR
0.466
Blade numbere
4
Rotation
Right hand
Max rpm
440
138
Kt, 10Kq, Efficiency
Proceedings of 26th ITTC – Volume I
455
Mutton et al (2003). As shown in Figure 8,
despite the weather affecting the coated trials,
the results showed little difference between
the shaft power performance of the coated and
uncoated propellers.
9.00
9.50
Although
the
sea
trials
proved
inconclusive due to poor weather, in
measuring the short term increase in
performance due to the application of the
coating, in the first three years since the trials
took place, the propeller was inspected at both
12, 24 and 36 months’ The state of the
propellers at these inspections are shown at
pictures in Figure 9, Mutton et al (2005).
Errors estimated at 10%
8.00
8.50
Final Power Curve Comparison
Uncoated Trial
Coated Trial
7.50
Tide Corrected Speed over Ground (knots)
7.00
Specialist Committee on Surface Treatment
456
4
6
8
10
New Coating
18
20
22
Coating After 1yr in Service
16
Uncoated Propeller
14
Ra value (microns)
12
24
Ra Frequency Distribution for the Uncoated Propeller, the Newly Coated
Propeller and after 1yr in Service
2
26
28
was significantly different in favour of the
coated propeller. There was some measured
difference between the newly applied coating
and the coating after 12 months in service.
This was mostly due to the presence of the
slime layer on the blades which can easily be
removed and some slight mechanical damage
to the coating.
12 months
24 months
36 months (back)
Figure 9.: The coated propeller of Bernicia after 12, 24 and 36 months in service, Mutton et al
(2005)
0
Roughness measurements were taken on
the Bernicia propeller using stylus type
roughness gauge (Surtronic 3+) before and
after the coating applied as well as after 1
year vessel was in service with the coated
propeller. As shown in Figure 10 the average
of the mean roughness amplitude (Ra, with a
cut-off length of 2.5mm) and its distribution
40.00%
35.00%
30.00%
25.00%
20.00%
15.00%
5.00%
10.00%
0.00%
Figure 11 shows the mean spacing distance
between profile peaks frequency distribution
(Sm) measured on the Bernicia’s propeller.
This is a measure of the surface texture where
the larger the value, the more ‘open’ the
texture. The coated propeller exhibits a much
wider range of mean spacing, while the
uncoated propeller had a much smaller range.
As shown in Figure 11, after a year in service
the frequency distribution of Sm has changed
little and still exhibited the wider range.
Mutton et al (2005) concluded that the
coating significantly changed the roughness
characteristics of the propeller blade surface
and that the roughness did not change
significantly after 12 months in service. The
coating had the effect of preventing the
increases in roughness usually seen with
uncoated propellers as well as keeping the
R/V propeller remarkably free from major
fouling more than 3 years which was
impossible with her uncoated propeller.
Figure 10. The mean roughness amplitude, Ra, frequency distributions measured on the propeller of
R/V Bernicia before coating, after coating and after a period with the coating in service.
% Frequency
The initial trials were conducted with its
clean but uncoated propeller before being
placed on the slip and its propeller removed to
be coated by IS700 using spraying at the paint
manufacturer’s site. Another series of
measured mile trials were then conducted for
the same loading conditions applied with the
uncoated propeller trials. Shaft torque,
shaft/vessel speeds and all other relevant
parameter measurements were recorded for
analysis and further corrections. The conduct
of the trials and analyses were carried out
using the BSRA standard procedure and
details of these measurements can be found in
6.50
propeller. What fouling was returned is a light
‘slime’ layer that could be easily removed
with a damp cloth. This was very different for
the uncoated propeller where after 14 months
in service after a polish, hard shelled
barnacles were present to about half the blade
radius that can only be removed by scrubbing..
139
140000.00
120000.00
100000.00
80000.00
60000.00
40000.00
20000.00
0.00
6.00
As shown in these pictures the coating
was found to be in good condition, 95% intact,
except for slight removal of the coating at the
edges and tip of the blades. The results have
shown that despite the vessel operating in a
heavy fouling, coastal and estuarine
environment, little fouling was returned to the
Figure 8: The final Results of the Bernicia sea trials show no statistical difference between the two
curves. The trials were particularly affected by the weather leading to large error estimates and
making the results inconclusive, Mutton et al (2005).
Corrected Shaft Power (Watts )
0
500
1000
2500
New Coating
1yr in Service
Uncoated Propeller
2000
Sm Value (Microns)
1500
3000
3500
Sm Frequency Distribution for the Uncoated propeller, Newly Applied
Coating and After 1yr in Service
Proceedings of 26th ITTC – Volume I
90.00%
100.00%
80.00%
70.00%
60.00%
50.00%
40.00%
30.00%
20.00%
10.00%
0.00%
4000
457
Figure 11. The mean spacing between profile peaks, Sm, frequency distribution. Measured on the
propeller of Bernicia before coating, after coating and after a period with the coating in service.
In the case of a “surface” cavitation, as
oppose to a “vortex” type, inception occurs in
the region of the boundary layer transition. In
this respect, propeller blade roughness
stimulates the transition of the boundary layer
from laminar to turbulent flow and hence
causes cavitation inception. The Foul Release
coatings are expected to delay such transition
from the laminar to the turbulent flow and
hence the associated delay in cavitation
inception will also be expected. However, this
effect may not be so important for full-scale
propellers which operate in fully turbulent
regime. Even if it is limited to the leading
edge regions, this effect can be important for
special propellers designed to avoid cavitation.
Another interesting nature of the visco-elastic
materials, like the silicon coating, is their
effect to alter the turbulence characteristics of
the flow near the wall and even “relaminarise” the turbulent flow. This will not
only affect the cavitation inception but also
influence the characteristics of the developed
cavitation. In contrast, the protuberances of
uncoated and not well-maintained rough blade
surfaces are expected to destabilise the
vortices more quickly and creating bubble
residence locations, and hence reduce the
cavitation strength of the water.
Task 2.3. The Effect of Coating on the Cavitation Behaviour
The effect of coating on the cavitation
performance of a propeller can be as
important as on its efficiency or even more
for a quiet propeller. Nevertheless, there is
hardly any data reported on this subject in the
open literature except some anecdotal
reporting from full-scale and limited
experimental investigations conducted at
Newcastle University. These investigations
have focused on the effect of different types
FR coatings on the cavitation inception, and
type and extent of fully developed cavitation
observed on the earlier mentioned bench mark
tanker propeller tests summarised in the
following.
Cavitation inception is a complex
phenomenon which is far from being
completely understood at present. The
mechanisms underlying this phenomenon are
thought to be threefold: (1) water quality
(mainly nuclei content and its statistics); (2)
the growth of the boundary layer over the
blade sections; and (3) type of cavitation to be
developed. Amongst them, it is most likely
that the growth of the boundary layer will be
most affected by the presence of coating
while the type of cavitation may also be
affected.
Specialist Committee on Surface Treatment
458
In the case of “vortex” type cavitation,
particularly in the tip vortex type, the nature
of the vortex is strongly dependent upon the
nature of the boundary layer over blade in the
tip region, which can be affected by the
coating. If the boundary layer separates near
the tip then the tip vortex will be attached to
the blade while the preservation of a laminar
flow near the tip can avoid the detachment of
tip vortices.
The effect of FR coating on the cavitation
inception was first reported by Mutton et al
(2006) on the tests conducted in the Emerson
Cavitation Tunnel with the earlier described
benchmark tanker propeller. The model of
this propeller was tested with its blades
uncoated and coated with Intersleek 700
(IS700) in uniform flow at reduced vacuum
levels simulating the loaded and ballast
operating conditions of the tanker. Careful
recordings of the cavitation inception of a thin
unattached tip vortex indicated slight delay in
inception due to the FR coating in the loaded
condition whilst this trend was somehow
reversed in the ballast condition. In overall it
was concluded that the effect of coating on
cavitation inception was not significant. On
the other hand, the nature and extent of the
developed cavitation patterns, which were
mainly tip vortex and sheet cavitations, were
somehow different such that the uncoated
propeller tip vortex was thicker while the
extent of sheet cavitation was relatively large
compared to the coated propeller blade
cavitations. However, the uncoated propeller
cavitation pattern was more stable compared
to the coated one. The unstable nature of the
coated sheet cavitation sometimes caused it to
break up into misty and cloud types of
cavitation along the lower boundary of the
cavity sheet. Although it was not published
the effect of coating damage on cavitation
was also explored by various scenarios and no
evidence was found that the coating damage
would cause further cavitation on this
propeller model.
In a recent follow up investigation to the
above study, Korkut and Atlar (2009)
conducted further experimental investigations
onto the effect of coatings on the cavitation
inception and cavitation extent on the same
benchmark propeller but using latest
commercial FR product, IS900. Furthermore
they also explored the effect of non-uniform
flow by testing the model propeller behind a
wake screen. The results of the
inception/desinence test are shown in Table
11 where the cavitation inceptin number is
defined based on the resultant flow velocity
combined with the advance speed and
rotational speed at 0.7R.
0.606
0.683
0.685
0.611
0.677
0.679
0.701
0.980
0.982
0.695
0.983
0.984
Table 11. Cavitation inception test results with uncoated and coated blades in uniform and nonuniform flow cases, Korkut & Atlar (2009)
Uniform
Non-Uniform
Uncoated Coated Uncoated
Coated
Cavitation Type
Unattached tip vortex
cavitation-inception
Unattached tip vortex
cavitation-desinence
Attached to all blades
140
% Frequency
Proceedings of 26th ITTC – Volume I
As shown in the table the coating of the
blade did not change the cavitation inception
characteristics of the model propeller
(difference is less than 1%), if the coating
applied correctly (i.e. avoiding sagging of
paint at sharp blade edges that may cause
unrealistic cavitation pattaern and singing).
Korkut and Atlar related this to the similar
roughness and surface texture characteristics
of both uncoated and coated blades measured
with the model. However this may not be the
case in full-scale applications, where some
advantage of smooth FR surface finish can be
expected, by delaying the inception of
cavitation.
As far as the cavitation extent was
concerned, the uncoated blades displayed
slightly more extended cavitation than those
of the coated blades from tip vortex to sheet
vortex type for both loading conditions as
459
shown in Figure 12 for the fully loaded
condition.
In a recent study by Sampson and Atlar
(2010) the cavitation inception and extent
characteristics of the same model propeller
were compared as uncoated, coated with
IS900 and the earlier described AMBIO
project coating (TNO-E008). These tests
indicated some delay in cavitation inception
for IS900 compared to the uncoated and
TNO-008 coated blades. Analysis of the
cavitation patterns was subjective owing to
the resolution of the video camera. The
predominant cavitation on the blade was
steady sheet cavitation and developed tip
vortex cavitation in the propeller slipstream
which had greater extent on the uncoated
blade and similar but slightly less presence on
the coated blades with non-discernable
difference between them as shown in Figure
13.
J=0.50 Uniform
J=0.50 Non-Uniform
J=0.40 Non-Uniform
J=0.40 Uniform
Specialist Committee on Surface Treatment
460
(a)
(b)
Figure 12. Cavitation developments in uniform and non-uniform flow conditions at varying advance
coefficients for fully loaded condition: (a) uncoated; (b) coated by IS900.
Korkut & Atlar (2009)
Figure 13. Cavitation comparison of the 3 blades (Uncoated, IP900, TNO-E008)
at J = 0.35 and atmospheric condition. Atlar et al (2010)
Similar to the lack of research on
cavitation, virtually there is also no published
data on the effect of FR coating on propeller
noise available in the open literature, apart
from the limited investigation conducted at
Newcastle University by Mutton et al (2006)
and Korkut & Atlar (2009).
Of the above four mechanisms of
generating propeller noise the first two are
associated with “non-cavitating” propeller
flow while the latter two with the “cavitating”
water by the blade profiles; (2) immigration
of flow from the pressure to the suction side
of the blades in developing thrust; (3)
fluctuating volume of cavitation on the blades
when cavitation develops on the blades of
propeller operating in non-uniform wake
flow; and (4) collapse of cavitating bubble
and/or bursting of a cavitating vortex.
Task 2.4. The effect of Coating on Comfort (Propeller noise)
There are four principal mechanisms by
which a propeller can generate sound
pressures in water, Carlton (2009). These are
associated with: (1) the displacement of the
141
Proceedings of 26th ITTC – Volume I
flow. The non-cavitating component of sound
pressures will have distinct tones – known as
the blade rate noise- associated with discrete
(lower) blade frequencies together with a
broad-band noise at higher frequencies. The
blade rate noise is closely associated with the
unsteadiness caused by circumferentially
varying wake field in which the propeller
operates. This causes a fluctuation in the
angle of attack of the propeller blade sections
and hence sound pressure. However this can
hardly be affected by the presence of the
coating. On the other hand the broad-band
noise is mostly affected by the level of
turbulence in the incident flow and its
interaction with the wall boundary layer
which will be affected by the coating. One of
the important mechanisms contributing to the
broad-band noise is the trailing edge noise,
which is perhaps the least well understood
mechanism. The role of the turbulence in the
boundary layer is a crucial parameter, which
will be affected by the presence of coating,
while this noise component would suffer from
the effect of possible fouling with uncoated
propeller as well as from hydro-elastic effects
of the coated blades. The collapse of
cavitation bubbles creates shock waves and
hence cavitation noise. This is manifested as
mostly ‘white noise’ in a frequency band up
to around 1MHz. It is thought that the coating
will mostly affect the trailing edge noise and
may even act as a damper by absorbing the
energy of cavitation noise due to its flexible
nature.
The investigation of the effect of FR
coating on propeller noise was also part of the
experimental work on the efficiency and
cavitation investigations with the benchmark
propeller reviewed earlier. The noise
investigations therefore conducted at two
experimental campaigns: in the first, the
benchmark model propeller uncoated and
coated with IS700 tested in uniform flow; in
the second campaign the same model
propeller coated with IS90 and tested behind
non-uniform flow as well as the uniform flow.
461
The comparative results of the first
experimental measurements, which were
analysed using the ITTC analysis and
correction procedure, presented as the net
sound pressure level of the propeller against
the centre frequencies for the uncoated and
coated blades at the fully loaded and ballast
conditions as reported by Mutton et al (2006).
The comparisons indicated that there was
some effect of the coating and the beneficial
effect appeared limited to the broadband
frequencies and the higher advance
coefficients. At smaller values of advance
coefficients, which covered the design
advance coefficient, the uncoated propeller
exhibited reduced noise levels compared to
the coated one. In the discrete frequency
range there was hardly any discernable
difference between the two. As the cavitation
increased (as in the ballast condition) the
difference between the noise levels of the
uncoated and coated propeller at smaller
advance coefficient diminished.
The recent follow up investigations by
Korkut and Atlar (2009) measured the
comparative noise levels of the benchmark
model propeller, and analysed and presented
in the similar manner to the previous
investigation. However they used IS900 to
coat the blades and also included the effect of
flow non-uniformity by wake screen. Typical
comparative
presentation
of
their
measurements in uniform flow is shown in
Figure 14 for fully loaded condition. From
these measurements it was concluded that
whilst the coating of the blades reduced the
noise levels in non-cavitating condition (i.e.
higher advance coefficients, J=0.75-0.60), it
slightly increased in the developed cavitation
condition. This finding applied to both fully
loading and ballast condition in uniform and
non-uniform flows.
Interaction with bio-fouling
As stated earlier the effect of fouling is a
rather important but complex phenomenon
and hence to prevent and reduce the fouling
Specialist Committee on Surface Treatment
462
settlement on any surfaces, including
propeller blades, should be the prime target
rather than assessing or modelling of the
fouling effects. Within this framework
numerous end-user-testimonies and 4 years of
monitoring of the Newcastle University R/V
Bernicia propeller reveal that FR coating can
effectively stay on blades more than 3 years
almost 85-90% percent of the coating intact.
For example, Figure 14 shows the state of the
FR coating (IS700) on the propeller of the
earlier mentioned tanker vessel after 37
months in service. During this period the
coating has clearly prevented the major
fouling development except the slime fouling.
This beneficial effect was even more
obvious on the Newcastle University R/V
propeller as shown in Figure 15 where the
uncoated propeller (after 14 months) is
compared with the FR (IS700) coated
propeller (after 24 months). It was noted that
the uncoated propeller was covered with hard
shelled barnacles that had to be removed by
abrasive means or scrapers, Mutton et al
(2003). In contrast the slime or even barnacles
that may be attached to FR coated surfaces
could be removed by pressure washing or
gentle sweeping action.
The effect of slime on any type antifouling is a pretty well-known and complex
issue, and experience so far with FR coatings
indicates that this coating type suffers more
from the slime compared to other types, since
slime film will attach more strongly to foul
release surfaces than other fouling organisms.
Experimental studies with FR coatings
indicated that increasing the flow shear can
reduce the thickness of the slime layer but not
remove completely, e.g. Klijsnstra et al
(2002). While this may compromise the initial
drag benefits of FR coatings, at higher speeds
that propeller blades operate, this benefit may
still persists due to thinner layer of slime film
as discussed by Candries et al (2003). This is
a rather topical issue currently attracting much
research supported by paint manufacturers
and ship owners.
In an attempt to model the coating
roughness including the bio-fouling effect on
ship resistance the recent study by Schultz
(2007) is worthy to note. In this study the
resistance-roughness characteristics of some
coating types on flat surfaces, which are
exposed to different grades of roughness and
bio-fouling (varying from slime to heavy
calcareous types) settled in a controlled
environment, have been established by using
a similarity law scaling procedure proposed
by Granville (1958) and (1987) based on
the similarity between smooth and rough
wall boundary layers.
142
Proceedings of 26th ITTC – Volume I
463
Figure 14. Effect of coating on noise levels of model propeller for at varying advance coefficients in
uniform flow for fully loaded condition.
Specialist Committee on Surface Treatment
464
Figure 14. Face and back view of the benchmark tanker propeller painted by IS700 FR coating after
37 months in service without any cleaning
x
Propeller coating has always been
interest to ship owners by multiple
Although this study is only representative and
requires further proof, its potential
implication in assessing performance losses
due to deteriorated blade surfaces including
various grades of bio-fouling can be plausible
since the procedure is generic and technically
can be applied to the blade sections based on
the flat plate approach as applied in e.g. Atlar
et al (2002). However further roughness data
of different types of coating in controlled
environment may be required for the
simulation of typical propeller surfaces.
Figure 15. R/V Bernicia propeller uncoated after 14 months in service (left); coated by IS700 after
36 months in service without cleaning (right)
This procedure enabled Schultz to predict
the effect of a given roughness on the
frictional resistance of a plate of arbitrary
length (i.e. representing ship surface) based
on laboratory-scale measurements of the
frictional resistance and roughness function of
a smaller flat plate covered with the same
roughness. Schultz applied this procedure to
predict the roughness and fouling penalties of
a US frigate demonstrating as high as 86%
penalty for the heavy calcareous fouling case.
Concluding remarks
143
Proceedings of 26th ITTC – Volume I
x
In spite of various anecdotal claims
there has been no credible evidence
from full-scale to demonstrate any
gain/loss from a vessel fitted with
newly polished propeller and FR
coated one. However there is limited
evidence that these coatings can
provide the propeller surface with
roughness and texture levels similar
to newly polished surfaces for a long
time after its applications. This will
provide
savings
in
propeller
efficiency and maintenance cost
relative to the efficiency and cost of
unpolished propellers in-service.
reasons
amongst
which
the
prevention/reduction of galvanic
corrosion and that of bio-fouling are
the well recognised ones. Recent
developments in foul release coating
technology and increasing number of
FR coated propellers indicates that
these coatings have most of the
desired properties of propeller
coating and currently the most
suitable system for development of a
propeller coating.
x
There is no published report of
dedicated trial or model test on the
comparative efficiency, cavitation
and noise emission characteristics of
a propeller as uncoated and coated
with FR coatings apart from a single
source. Limited amount of tests
conducted in this source with a
model propeller with the coated and
uncoated blades have not revealed
any remarkable difference in the
open water efficiency, cavitation
inception and extent as well as the
REFERENCES
Mosaad, M., 1986, “Marine propeller
roughness penalties”, Ph.D. Thesis,
University of Newcastle upon Tyne.
465
x
x
x
Validation and verification studies
involving model and full-scale
performance of coated propeller will
require
standard
measurement
procedures and reliable measurement
tools, which are preferably optical
and practical to use in model and
full-scale, for the measurement of
appropriate
blade
surface
characteristics.
Semi-empirical expressions used for
the frictional drag coefficient of
uncoated propeller blade sections
need to be modified to take into
account surface roughness effect of
coated sections properly. This will in
turn
require
drag-roughness
correlation studies with foul release
coated surfaces, preferably including
the effect of slime.
Propeller model tests with coated
blades suffer from appropriate paint
thickness at model scale due to
practical limitation of the application
method with commercial FR coatings.
This requires further investigations.
measured noise levels despite some
small
variations
in
these
characteristics due to the effect of
coating.
x
There is a need for dedicated
comparative full-scale trials and
observations to accurately assess the
effect of coatings on the propeller
efficiency, cavitation and noise
emission.
Glover, E.J, 1987, “Propulsive devices for
improved propulsive efficiency”, Trans.
IMar(TM), Vol. 99, Paper 31, London.
Specialist Committee on Surface Treatment
466
Thomas, T.R., 1999, “Rough surfaces”, 2nd
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Carlton, J., 2007, “Marine propellers and
propulsion”, Butterworth- Heinemann Ltd.,
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Townsin, R.L., Byrne, D., Svensen, T.E.,
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roughness”,
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Grigson, C.W.B., 1982, “Propeller roughness,
its nature and its effect upon the drag
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Candries, M., 2001, “Drag, boundary-layer
and roughness characteristics of marine
surfaces coated with antifoulings”, PhD
Thesis, University of Newcastle upon
Tyne.
Candries, M., Atlar, M., Anderson, C.D., 2001,
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craft”, HIPER 2001, 2nd International
conference on high-performance marine
vehicles, 2-5 May, Hamburg.
Holzapfel,
A.C.A.,
1904,
“Ships
compositions”, Trans Institution of Naval
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Kan, S., Shiba, H., Tsuchida, K., Yokoo, K.,
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and
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performance”, International Shipbuilding
Progress, Vol. 5, pp.
Dashnaw, F.J., Hochrein, A.A, Weinreich,
R.S., Conn, P.K., Snell, I.C., 1980, “The
development of protective covering
systems for steel and bronze ship
propellers”, Trans. SNAME Vol. 88.
Coldron, J.O. and Conde, J.F.G., 1990,
“….”Intl workshop on marine roughness
and drag, Paper 5, RINA.
Matsushita, K., Ogawa, K., 1993, “Ship hull
and propeller coatings using non polluting
and anti-fouling paint”, Paper 24, ICMES
93-Marine System Design and Operation..
Anderson, C.D., McKenzie, R.R., Ransom,
C.J., Tighe-Ford, D.J., 2003, “Effect of a
Paint Coating upon the Modulations of
ICCP Current Outputs Produced by Model
Warship
Propeller
Rotation”,
2nd
International Warship Cathodic protection
Symposium and equipment Exhibition,
Shrivenham, UK.
Atlar, M., 2003, “More than antifouling”,
Marine Engineers Review, March.
Brady, R.F., 1997, “In search of non-stick
coatings”, Chemistry and Industry.
Brady, R.F., Singer, I.L., 2000, “Mechanical
Factors favouring release from Fouling
Release coatings”, Biofouling, Vol 15.
Anderson, A.C., Atlar, M., Callow, M.,
Candries, M., Townsin, R.L., 2002, The
development of foul-release coatings for
seagoing vessels”, Journal of marine
design and operations, Part B4, IMarEST.
Berglin, M., Lnn, N. and Gatenholm, P.,
2003, “Coating Modulus and Barnacle
Bioadhesion”, Biofouling, Vol 19S.
144
Proceedings of 26th ITTC – Volume I
Milne, A., 1977, “Coated marine surfaces”,
UK Patent 1470465 and “Antifouling
marine compositions”, US Patent 4025693.
Truby, K., Wood, C., Stein, J., Cella, J.,
Carpenter, J., Kavanagh, C., Swain, G.,
Wiebe, D., Lapota, D., Meyer, A., Holm,
E., Wendt, D., Smith, C. and Motemorano,
J., 2000, “Evaluation of the performance
enhancement of silicone biofoulingrelease coatings bu oil incorporation”,
Biofouling, Vol 15.
Millett, J., Anderson, C.D., 1997, “Fighting
fast ferry fouling”, FAST'97, Vol. 1.
Townsin, R.L., Dey, S.K., 1990, “The
correlation of roughness drag with surface
characteristics”, International Workshop
on Marine Roughness and Drag, R.I.N.A.,
London.
Candries, M., Atlar, M., Mesbahi, E., Pazouki,
K., 2003, “The measurement of the drag
characteristics of Tin-free Self-Polishing
Co-polymers and Fouling Release
coatings using a rotor apparatus”,
Biofouling,19S.
Candries, M and Atlar, M., 2003, “On the
drag and roughness characteristics of
antifoulings”, Intl. Journal of Maritime
Engineering, RINA, Vol. 145, A2.
Candries, M., Atlar, M., 2005, “Experimental
investigation of the turbulent boundary
layer of surfaces coated with marine
antifoulings”,
Journal
of
Fluids
Engineering, ASME, Vol 127.
I.T.T.C., 1990, Report of the Powering
Performance Committee, Proceedings of
the 19th International Towing Tank
Conference, Madrid.
Candries, M., Atlar, M., Paterson, I., 1999,
“Cavitation tunnel tests with coated model
propeller”, Marine technology report,
University of Newcastle.
467
Atlar, M., Glover, E.J., Candries, M., Mutton,
R., Anderson, C.D., 2002, “The effect of a
Foul Release coating on propeller
performance”, Conference Proceedings
Environmental Sustainability (ENSUS).
University of Newcastle.
Burrill, L.C., 1955-56, “The optimum
diameter of marine propellers: A new
design approach”, Trans. N.E.C.I.E.S., Vol.
72.
Atlar, M., Glover, E.J., Mutton, R., and
Anderson, C.D., 2003, “Calculation of the
effects of new generation coatings on high
speed propeller performance”, 2nd Intl
Warship Cathodic Protection Symposium
and Equipment Exhibition, Cranfield
University, Shrivenham.
Mutton, R.J., Atlar, M., Downie, M.,
Anderson, C.D., 2005, “Drag prevention
coatings for marine propellers”. 2nd
International Symposium on Seawater
Drag Reduction, Busan, Korea.
Korkut, E. and Atlar, M., 2009, “An
experimental study into the effect of foul
release coating on the efficiency, noise and
cavitation characteristics of a propeller”,
SMP’09, Trondheim.
website,
Atlar M., Unal B., Unal, U.O., Sampson R,
Politis, G., 2010. “WP5.2 Hydrodynamic
Testing- Executive Summary”, AMBIO
Project Report, Deliverable 5.2b1.
AMBIO,
2010,
Official
http://www.ambio.bham.ac.uk/,
Approached December 2010.
Mutton, R.J., Atlar, M., Paterson, I., Sampson,
R., 2003, “The Effect of a Foul Release
Coating on the Research Vessel Bernicia”,
Report MT-2003-048, School of Marine
Science and Technology, University of
Newcastle.
Specialist Committee on Surface Treatment
468
Mutton, R.J., Atlar, M., Downie, M.,
Anderson, C.D., 2005, “Drag Prevention
Coatings for Marine Propellers”. 2nd
International Symposium on Seawater
Drag Reduction, Busan, Korea.
Mutton, R.J., Atlar, M., Downie, M.,
Anderson, C.D., 2006, “The effect of a
foul release coating on propeller noise and
cavitation” Advance materials and
coatings symposium, RINA, London.
Klijnstra, J.W., Overbeke, K., Sonke, H.,
Head, R. and Ferrari, G.M., 2002, “Critical
speeds for fouling removal from a silicone
coating”, 11th International congress on
marine corrosion and fouling, San Diego.
Candries, M., Atlar, M. and Anderson, C.D.,
2003, “Estimating the Impact of newgeneration
antifoulings
on
ship
performance: The Presence of slime”.
Journal of Marine Engineering and
Technology, Part A, Procs. IMarEST, (A2).
Schultz, M. P., 2007, “Effects of coating
roughness and biofouling on ship
resistance and powering”, Biofouling,
23:5.
for
surface
Granville, P.S., 1958, “The frictional
resistance and turbulent boundary layer of
rough surfaces”. Journal of Ship Research
2: 52-74.
methods
The following table gives an overview
over the most common formulas how to
calculate roughness. Each of the formulas
listed in the table assumes that the roughness
profile has been filtered from the raw profile
data and the mean line has been calculated.
The roughness profile contains n ordered,
equally spaced points along the trace where yi
represents the vertical distance from the mean
line to the ith data point.
most common one. Since these parameters
reduce all of the information in a profile to a
single number great care must be taken in
applying and interpreting them.
Task 3: Review the existing measurement
roughness at modelscale and at full scale
3.1. Roughness Parameters
Surface roughness in general is a measure
of the of the texture of a surface. It is
quantified by the vertical deviation of the real
surface from its ideal form; in case of large
deviations we speak about a rough surface.
Roughness values can either be calculated on
a profile or on a surface. Profile roughness
parameters (Ra, Rq….) are more common
whereas area roughness parameters (Sa,
Sq,….) give more significant values.
There are many different roughness
parameters in use, but Ra (Rah) is by far the
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Proceedings of 26th ITTC – Volume I
The most commonly used roughness
parameter is the Average Hull Roughness
parameter Rah representing the mean of all
the vessel’s hull roughness readings.
3.2. Measurement Techniques
For the measurement of roughness stylus
instruments and optical instruments are in use.
In the shipbuilding industry the BMT Sea
469
The standard roughness unit is the peak to
trough height in microns per sample (one
sample is of 50 mm length of the underwater
hull).
Tech Hull Roughness Analyser (a stylus
instrument with a surface probe) is accepted
as the industry standard instrument for the
measurement of hull roughness.
Specialist Committee on Surface Treatment
470
3.3. Full Scale Measurements
The hull roughness normally is measured
in the way that the hull is divided into 10
equal sections with 10 measurements each, 5
on the port and 5 on the starboard side. A total
3.4. Roughness Measurements on Ship Models
of 50 readings are taken on each side, 30 on
the vertical sides and 20 on the flats. From the
100 measuring locations, the Average Hull
Roughness is calculated.
Roughness measurements on ship models are carried out (e.g. MARIN, SSPA) but the results of the
measurements are used for quality assurance and not for further investigation.
Most of the Model Basins do not measure the roughness of the model’s hull.
1. Measurement equipment
Task 4: Propose methods that take into account surface roughness
and other relevant characteristics of coating systems; check the need
for changes to the existing extrapolation laws.
This chapter will outline recommendations
regarding procedures in measuring skin
friction on rough surfaces aimed at the
maritime sector.
Several different techniques can be used
for measuring skin friction on rough surfaces
some better suited than others. In no specific
order the following can be mentioned:
Flat plate in towing tank
Flat plate in cavitation tank
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Proceedings of 26th ITTC – Volume I
Flat plate in towing tank
Flat plate in open water channel
Pipe friction device
Flow cell
Couette cell
Other shapes than flat plate in towing
tank or the like such as ax symmetric
body or model ship
Full scale tests
1.1.
In the committees opinion the best
combination of accuracy and complexity.
Usually a quite large surface can be coated,
and if care is taken with the setup and rigging
of the plate, reproducibility is usually
excellent.
The longer and thinner the plate is the
better, as skin friction resistance ratio to total
resistance will increase with those parameters.
Towing speed is limited (to usually around
5m/s) which does require some more
extrapolation to full scale than for instance
cavitation tank.
Re-rigging after a new surface has been
applied can be quite sensitive, therefore
control of reproducibility is very important.
Time between tows can also be important as a
flat plat (especially if towed horizontally) is
sensitive to small changes to angle of attack
caused by vortical flow remaining in the
towing tank after a test.
1.2.
471
Flate plate in Cavitation tank
Skin friction measurements can be achieved
by two methods.
1.2.1. Floating element measurements
A plate is built with the sample coated on
the plate (and/or before the plate), with a very
small gap between the measurement plate and
the flush surrounding plate. This plate is
suspended in such a way that it is fixed, but
shear forces can recorded, usually by strain
gauges.
To avoid edge effects the gap is critical,
and step changes in roughness should be
avoided by coating before and after the test
section.
1.2.2. Boundary layer measurements
Measuring the boundary layer by for
instance LDV (Laser Doppler Velocimeter),
the velocity shift in logarithmic boundary
layer can be recorded.
where U+ is the non-dimensional wall
velocity, y+ the wall distance and
is the
velocity shift function, also known as the
roughness function. Critical is the extraction
of the friction velocity u and several methods
have been proposed. This committee has no
recommendations regarding which one to use.
Specialist Committee on Surface Treatment
472
1.3.
Pipe Friktion Measurements
The above equations can be used for any
type of skin friction measurements, the
difference between boundary layer methods is
that friction velocity is used directly, whereas
resistance measurements should use the
second version of the equation.
Boundary layer measurements are very time
consuming and requires expensive and
sensitive measurement equipment. But better
control of displacement thickness is possible
than indirect methods.
or if boundary layer measurements are not
available (as for instance towed plate or
floating element measurements)
Figure 4: Velocity profile measurements on different rough surfaces
Once the velocity shift function is
established by boundary layer measurements,
it relates to the skin friction coefficient as
where s and r refers to smooth and rough
respectively. Therefore for all boundary layer
measurements
(and
skin
friction
measurements in general) it is important to
measure the hydraulically smooth case. The
above equation is a simplification of
integration of the log-law boundary layer
equation, and assumes that the displacement
thickness is constant. Depending on the type
of measurement, care must be taken to either
ensure that the assumption holds, or otherwise
correct for the simplification. For boundary
layer measurements for example momentum
or outer similarity methods can be used, but
will not be described further in this report, see
for example.
Finally, skin friction can be related roughness
by the non-dimensional roughness height
Pipe friction measurements is probably the
most cost effective method along with
Couette Cell flow. It is also well suited for
tests with for example bio fouling as the test
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Proceedings of 26th ITTC – Volume I
pipes can be transported relatively easy
between test site and fouling site.
Flow Cell
Measurement method is indirect as
measured parameters is average flow velocity
and pressure drop over test section. Accuracy
is much lower than for instance towed flat
plate however for surfaces with high skin
friction increase it is deemed sufficient (as for
instance barnacle surface). Boundary layer is
not free (confined by the pipe radius) and
correction to flat plate skin friction must be
performed.
1.4.
Couette Cell
Mainly mentioned to include types of tests.
Flow cell is not well suited skin friction
measurements within the maritime sector as
Reynolds number is very low and requires too
extensive extrapolation to full scale skin
friction.
1.5.
Couette cell is relatively simple in
construction and build cost. It does however
produce results which is difficult to interpret
accurately due to mainly the formation
Taylor-Couette cells, complex axially nonuniform boundary layer and boundary layer
development, but also issues such as
increasing water temperature during tests.
Reynolds Number
473
Therefore, some difficulty exists calculating
Cf based on torque measurements, but [Arcapi,
1984] suggested
where is the von Karman constant and Reh
is the Reynolds number based on the gap
length between cylinders.
Other shapes
Advantage with Couette cells is that it is
rather easy to apply a new surface, and
especially
for
tests
which
require
measurements over long time (for example to
test self polishing) Couette cell is well suited.
1.6.
Generally using other shapes than flat
plate for towing, seems like an unnecessary
complication in model scale. The goal of skin
friction measurements is to acquire skin
friction lines which can be extrapolated to full
scale. Using for example a ship model will
introduce much higher residual and wave
resistance than for a flat plate, but even more
important large variations of skin friction
locally due to accelerating flow around the
model. This makes it difficult to interpret
extracted increase in resistance. It is therefore
not a recommended procedure.
There is another reason to keep Reynolds
number relatively high which is that the
results will require less extrapolation to full
scale.
Cf smooth can be taken from any source, for
example Cf,ITTC.
case the Reynolds number is too low for
measuring any effect related to skin friction
(exceptions does exist as for example ribblets
or active surfaces), and results will be of very
questionable value.
2. Test Procedure Recommendations
2.1.
It must be ensured that the Reynolds
number is sufficiently high. The lower the
Reynolds number the higher the risk is that
the surface becomes hydraulically smooth.
This is the case no matter what measurement
equipment is being used.
Theoretically, the surface is hydraulically
smooth when y+ is lower than 5. If this is the
Flow speed
Specialist Committee on Surface Treatment
474
2.2.
At least 2m/s above hydraulically smooth
must be tested. If not it will be difficult to
perform regression analysis and extract
parameters such as efficiency for the given
surface. Ideally points should be fairly dense
for more confidence in regression analysis,
but also to identify possible problems with the
test equipment/measurement method.
Reference surface
For some test equipment this can present a
problem, especially in a towing tank.
Therefore it is recommended that it is possible
to fulfil this recommendation before tests
commences.
2.3.
To be able to compare different surfaces
skin friction, it is imperative that all
measurements are completed with reference
to a hydraulically smooth surface. Most
measurements are unfortunately reference to
another rough surface, for example SPC to
silicone. This makes it impossible, or at the
very least quite difficult to collect results from
many different sources. Therefore at least one
measurement must be carried through with a
hydraulic smooth surface
Reproducability
where y+=5 is the limit. This value will for
most test setups be in the range 5-50m, so
some polishing of for example a primer will
usually be necessary.
2.4.
Reproducability will vary quite a lot
between different measurement equipment.
Two levels of reproducibility exists, with and
without re-rigging. A full ITTC uncertainty
analysis would be the best procedure to
follow, but at least for some measurement
techniques will require too much additional
work.
Minimum. Repeat 3 measuring points 3 times
without re-rigging
Recommended. Same as test 1, but completed
twice between re-rigging. Re-rigging implies
that the setup is dismantled to a degree where
a new surface can be applied.
Surface
Reproducibility is paramount, especially
for testing for example coatings, as difference
between coatings and hydraulically smooth is
quite low (below 20% for most cases and
Reynolds
numbers),
between
most
commercial coatings below 10%. If
reproducibility is only 5% it will have a
significant impact on the analysis.
Many
factors
can
produce
low
reproducibility. This committee is aware of
the following error sources.
Towing tank: Poor alignment of plate, too
little time between tests, suspension allowing
plate to bend or Yaw.
Cavitiation tank: Not stiff enough floating
element increasing gap size, test section not
flush with surroundings, scatter in LDV
measurements.
Pipe friction device: Reproducability in
measurement of average flow velocity, nonflush pressure tap.
Couette cell: Temperature change between
and under tests
2.5.
Two aspects of the surface must be
considered
Application
Roughness height (and possibly other
parameters)
Application of commercial coatings must
be completed in a fashion similar to the
procedure at the shipyard. For instance,
temperature and humidity range from the
supplier must be followed, if high pressure
spray system is required the surface topology
and roughness height can change significantly
from the intended if a low pressure system or
roller is used.
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Proceedings of 26th ITTC – Volume I
The committee agrees that steel/primer
surface need not be considered. Even though a
real untreated hull surface is not smooth,
applying the coating system usually
consisting of multiple layers, most of the steel
roughness will be masked by the coating. This
is off course not the case for welding seems
for example, but taking such imperfections
into account will be practically impossible. A
further (very small) added friction could
eventually be proposed.
Roughness height measurement should
preferably be completed with a BMT
roughness analyser. However, other devices
can be used, if they as a minimum produce a
measure of Ra. MA can perhaps add to this.
Other parameters can be added such as
average distance between roughness elements
for barnacles for instance. This might be
usefull at a later stage when a relatively high
number measurements are collected.
3. ITTC Rough Skin Friction
Database
It is proposed that an international
database of skin friction measurements are
created. Many different researchers have
measured skin friction on a lot of different
surfaces seen on a ship hull. This includes
coatings, bio-fouling and bio-films.
As no single facility will have the funding
available to test every coating, bio-fouling
and bio-film surface, the second best option is
to analyse results following the same
guidelines and procedures.
Tests have been completed with test
equipment as described in section 1.1 at
varying Reynolds numbers, facilities, surface
size, roughness height measurement method
(if any) and so forth. Many tests are also
referenced to another coating and not a
hydraulically smooth surface.
Procedure
475
It is therefore at present difficult to collect
skin friction lines and present them in the
same figure. For experiments which fulfil the
test procedure recommendations in chapter 2,
it will however be possible to collect and
compare the results.
3.1.
SSPA and Newcastle University will
jointly be responsible for creation and
maintaining the homepage, and evaluate and
present new results.
Submission of results
After submission of results hydro
dynamist from either SSPA or Newcastle Uni.
will evaluate results submitted (see 3.2), and
determine if results can be used. After
analysis is completed results will be
publically available on the homepage.
3.2.
Any party can submit results completing
the submission form and appending data in
electronic form. At a minimum raw
measurement data and analysis to skin friction
coefficient must be supplied, along with
description of analysis method.
Unless requested otherwise all material
submitted will be publically available. It is
assumed that at a minimum the material can
be used to extract necessary data by RSFD
and present it together with other results.
RSFD will evaluate the material in
accordance to items described in Chapter 2,
and decide a confidence level and whether or
not results will be added to the database. The
submitter will have the option to comment on
the results before they are made public on the
homepage.
Skin friction line, velocity shift function
parameters and roughness height will be the
main publicised results compared to CF,ITTC.
All supplied material will be made available
on ftp server (or links to for example papers)
Specialist Committee on Surface Treatment
476
Analysis Procedure.
unless otherwise requested by the submitter in
the submission form.
3.3.
3.3.1. Velocity shift function
If results are accepted the analysis procedure
will be as follows. Velocity shift function
will be used regressively on each skin friction
line, however using only one parameter (h)
will not be sufficient. Part of the ultimate
outcome of SFRD will be to specify the
efficiency parameter for various types of
surfaces. Bowden added resistance main
shortfall is that it is based on a one parameter
description of the surface topology which is
not sufficient as can be seen in several
articles.
Many different two (and more) parameter
function have been investigated, but it is this
committees conviction that using an
additional parameter which is not directly
measurable by analysing the surface topology
is the most viable method. This additional
parameter is the efficiency parameter.
In stead of using
for description of the velocity shift as a
function of roughness height, the efficiency
parameter C will be introduced as
For each measurement added to the
database either the velocity shift (boundary
layer measurements) or Cf rough and smooth
and roughness height will be known and C
can be calculated (by least squares method
along the Reynolds number range measured).
It is the hope that collecting many
measurements of different types of surfaces,
for example silicone surfaces, will reveal a
fairly constant value of C, even with varying
roughness heights. This will produce a
method of calculating the full scale skin
friction using the roughness height and a type
specific efficiency parameter, rendering a
much more reliable method than the Bowden
added resistance used today.
Velocity shift function also have the
advantage that it can be used locally with for
example thin boundary layer methods or Elog
method for RANS solvers.
3.3.2. Comparison of results
The only reliable way to compare results
from
different
institutions/measurement
methods is to reference the measurements to a
surface with known skin friction line. This
can in principle be any type of surface for
example a specific SPC coating applied
exactly the same way each time. However, the
only practical procedure is to always use
hydraulically smooth surface.
As residual resistance (and wave
resistance for some methods) is different for
each measurement equipment and design,
skin friction lines cannot be compared
directly. Therefore, raw results will be reevaluated using the smooth skin friction
measurements under the assumption that the
only resistance component that changes
between tests of different surfaces is the skin
friction. Thus only added skin friction
resistance will be used
The velocity shift function will then be
evaluated using a know smooth skin friction
line such as CF,ITTC or other lines if deemed
more warranted.
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Proceedings of 26th ITTC – Volume I
This procedure will to a large degree
remove problems with comparing results
between measurement techniques at different
facilities. It does require measurements of
hydraulically
smooth
surface,
which
unfortunately is not available in many
measurements.
It is conceivable that measurements
eventually can be added to the database using
other reference surface, but several surface
with the correct reference line is necessary
before such measurements can be added with
confidence.
Conclusion and
Recommendations
1 ExtrapolationMethods
1.1 Conclusions
At this time no evidence suggests that the
recommendation of the 25’th Specialist
Committee
on
Powering
Performance
Prediction regarding the use of the Townsin
roughness allowance should be revoked. This
does not imply that the committee believes that
Townsin/Bowden roughness allowance is an
accurate and universal roughness allowance,
but that at this point nothing better seems to be
available.
Based on a skin friction model test
measurement database a new or modified
roughness allowance should be suggested.
Considering the variety of surface roughness
on a ship (coating, damage, slime, fouling) it is
likely that this new formulation will either be
several formulations or at least one formulation
but with roughness type dependent parameters.
A most likely candidate for an improved
roughness allowance is the velocity shift
function (Roughness Function), used to
generate Bowden or Townsin type formulation
for the full scale ship using CFD analysis
supported by experimental and full-scale data.
477
Arpaci V.S., Larsen P.S., Convection Heat
Transfer, Prentice-Hall, Englewood Cliffs,
NJ, USA, 1984
Leer-Andersen M., Larsson L., Andreasson H.,
Skin Friction Measurements on Rough
Surfaces and Full Scale evaluation, 2nd
International Symposium on Seawater
Drag Reduction, Busan, Korea, 2005
Leer-Andersen M., Larsson L., An
experimental/numerical approach for
evaluating skin friction on full-scale ships
with surface roughness, J. Mar Sci
Technol, 2003
All antifoulings suffer from micro-slime
(slime) even in newly applied condition. Foul
release coating particularly suffers from slime
effect due to their non-biocidal defence
mechanism which requires shear stress to keep
slime free.
Recommendations
There is a lack of data on the dragroughness correlation of AF-coatings as well as
of a new generation of self-polishing types to
improve the performance extrapolations not
only for the “as newly applied” (trial) condition
but also for the “after some time” (in-service)
condition. Limited drag-roughness correlation
studies indicate that the skin friction of “newly
applied” foul release coated surfaces does not
correlate with single hull roughness parameters.
1.2
It will not be possible to generate a new
formulation without an extensive database of
skin friction measurements. A relatively small
number of existing datasets which is the basis
for all formulations today does not lend
credibility to a new formulation which can be
used with higher confidence.
There is a need for investigation to establish
a relationship between the drag-roughness
characteristics of surfaces coated either with
foul release coatings or with the new
Specialist Committee on Surface Treatment
Roughness measurement should as a
minimum include Ra. Including more surface
parameters such as Rt, profile measurements
and so forth adds value to the measurements.
Foul release coated surfaces suffer from
inaccurate measurements in full-scale (as well
as in model-scale with relatively large surfaces)
with stylus type mechanical surface
measurement devices.
478
generation of self-polishing coatings to
improve the performance extrapolations. These
investigations should be extended for coated
surfaces
“in-service”
as
the
surface
characteristics of coatings change progressively
in service, particularly in case of self-polishing
coated surfaces. Although this is a challenging
task it is the reality in predicting power inservice.
2.2
Recommendation
Regarding future work one issue which this
committee feels can progress the confidence
and accuracy greatly for roughness allowance
and its application range is to establish a
comparative database for skin friction
measurements.
3 PropellerCoatings
Conclusions
In spite of various anecdotal claims there
has been no credible evidence from full-scale
measurements to prove any gain or loss from a
vessel fitted with a coated propeller compared
to a newly polished uncoated propeller.
However there is limited evidence that the foul
release based coatings can provide the
propeller surfaces with roughness and texture
levels similar to newly polished uncoated
surfaces and even better for a long time after its
applications. There is also evidence that these
Propeller coating has always been of
interest to ship owners by multiple reasons
amongst which the prevention and/or reduction
of galvanic corrosion and that of biofouling
control are well recognized. Recent
developments in foul release coating
technology and an increasing number of coated
propellers indicates that this paint technology
has most of the desired properties of propeller
coating and is currently the most suitable
system for development of a propeller coating.
3.1
Initially as much data as possible following
the recommendation for test procedure at least
to an extent should be collected and compared
after which alternative roughness allowance
There is need for data concerning the
roughness-drag correlations of flat plat plates
coated with foul release as well as with the
modern day self-polishing type coatings.
Investigations to collect appropriate data are
required.
The effect of micro scale biofouling (slime)
on the paint performance should be included in
the performance predictions and hence
investigations should be widened to cover this
effect which is a hot issue in foul release
coatings.
2 ModelTestProcedures
2.1 Conclusions
The most accurate method for skin friction
measurements probably is the flat plate in the
towing tank, but several other methods,
including boundary layer measurements, can
produce valid results.
Tests should be carried out at Reynolds
numbers which produce a flow above the
“hydraulically smooth surface” to have any
meaningful results. For comparison with other
experiments it is of high importance that a
reference surface is tested which is
hydraulically over the Reynolds range. If this is
not the case it is impossible to compare tests
coming from different facilities.
Reproducibility should be tested especially
for equipment which needs to be re-installed
when changing the surface, e.g. in case of a flat
plate in towing tank. Reproducibility with and
without re-installing should be checked.
150
Proceedings of 26th ITTC – Volume I
coatings can maintain the blade surface free
from major fouling for long time without any
maintenance. This suggests potential savings in
propeller efficiency and maintenance cost
relative to the efficiency and cost of unpolished
propellers in-service.
There is no published report of dedicated
trials or model tests on the comparative
efficiency, cavitation and noise emission
characteristics of a propeller uncoated and
coated with foul release coatings apart from a
single source. Limited amount of tests
conducted with model propellers with coated
and uncoated blades have not revealed any
remarkable difference in open water efficiency,
cavitation inception and extent as well as the
measured noise levels despite some small
variations in these characteristics due to the
effect of coating.
Recommendations
Propeller model tests with coated blades
suffer from appropriate paint thickness in
model scale due to application methods with
commercial coatings.
Although this conclusion applies to any
coating, as a generic problem of the foul
release type coatings, any validation and
verification investigation involving the model
and full-scale performance of foul release
coated propeller will require a standard
measurement
procedure
and
reliable
measurement
tools
for
the
surface
measurements.
3.2
There is growing number of full-scale
applications and an increasing interest on
propeller coatings. Investigations therefore
should continue in this field.
There is a need for dedicated model tests,
full-scale trials and progressive docking
observations to accurately assess the effect of
coatings on the propeller efficiency, cavitation
and noise performance. At least limited amount
round robin tests for open water performances
amongst the ITTC community may resolve
some current model test related issues.
479
As a generic problem of the foul release
type coatings, investigations on the application
and measurement of coatings on model
propellers (and full-scale) should continue with
the objective of devising standard procedures
and resolving the scale effect issue involving
paint thickness.
Semi-empirical expressions used for the
frictional drag coefficient and perhaps the lift
coefficient of uncoated blade profiles need to
be modified to take into account the coating
effect.
As a generic problem of any coating
applied surface the technology investigation of
coatings should be extended for the effect of
biofouling, at least for the effect of slime which
is the natural conditioner of any coating but
particularly affecting the performance of foul
release coatings.
4 StateoftheArtCoatings
Specialist Committee on Surface Treatment
480
measured surfaces. There is a need for the
development
of
“non-contact”
based
measurement devices providing options for
more parameters and hence investigations in
this areas should continue
Company/institution
Submission date
Adress
Phone
Public (Yes/no)
Other parameters
ITTC Skin Friction Data Submission Form
Contact person
Appendix:
e-mail
Appended material (raw data, analysed data, reports, papers)
File name (description)
1.
2.
3.
Test description
1. Equipment (see document XXX, section 1.1, 1-8). If other please specify
2. Reynolds number range
3. Flow speed range
Deliverables Description
1. (name or description)
2.
Additional information
Roughness height
4. Roughness height measurement type (device and parameter)
Short description of test equipment if not standard
Conclusions
4.1
3.
Surfaces tested
Anti fouling technology is under further
scrutiny due to environmental concerns. As a
result, although currently in small proportion,
the applications of foul releasing (non-biocidal)
type antifoulings are increasing worldwide
requiring further attention and hence further
investigation.
Recommendation
Solid evidence comparing the skin friction
characteristics between majorities of coatings is
non-existing. Different model evaluation,
application and measuring techniques make it
very difficult to compare measurements for
which reason most of the measurements are
only able to state that this coating is xx% better
than another coating.
4.2
Measurements of hull surfaces coated with
foul release surfaces in dry docks suffer from
“contact” problems of stylus in mechanical
devices. Furthermore, a single hull roughness
parameter is not sufficient to characterize the
151
1
ON
THE IMPORTANCE OF ANTIFOULINGS
FOR
GREEN SHIPS
By
y
Prof. Mehmet Atlar
Antifouling economies – SPC Coatings
3
EARLY 1990s
data, A. Milne
Indirect reduced costs (e.g. bunker transport)
1080M $/y
Reduced dry docking costs
800M $/y
Extended docking intervals
409M $/y
Reduced fuel cost
720M $/y
TOTAL
SAVING
3,000M $/year
Main objective of antifoulings
 Preventing the attachment of fouling and
hence minimising drag is the main
objective of marine antifoulings (A/F)
 Improved drag reduces fuel consumption
and in turn GHG emission
 There are other ways of keeping ship hulls
clean but none so far proven to be viable for
the vast majority of the world’s
world s fleet
 Keeping ships’ propellers free of fouling
is also important from the ship performance
point of view
NOx
SOx
• Total CO2 saving:
20M tonnes / year
• Rate of CO2 emission:
3.1 ton / Ton-Fuel
• Annual fuel saving:
7.4 M tonnes
• 2% saving due to
improved antifouling
performance
• 2% saving due to
smoother hulls
Impact on GHG emission – SPC Coatings
COx
GHG
&
Ozon
Depleters
EARLY 1990s
data, A. Milne
2
4
1
152
Antifouling – Current drivers
 Ship operators are looking at cost more closely than ever
 Ever increasing and unpredictable fuel prices; financial climate
 IMO and National Legislations
g
- IMO/AFS Convention (October 2001)
 Ship operators have A/F high on the agenda by law
 New coating technologies and associated products
 Biocidal / Hybrid/ Non-biocidal ; Ship operators are confused by the claims
and counter claims regarding to A/F
 Operators
O
t
wantt to
t be
b environmentally
i
t ll compliant
li t (ISO)
 The environment matters more than ever
 Ships have to be energy efficient by design (EEDI) and operation (EEIO) –
IMO-MEPC 58-59 report on “IMO GHG Study 2009” (April 2009)
Biocidal options
Currently 90% of the world fleet use these products
SPC
“Controlled Depletion Polymer”
Hybrid
SPC
“Self-Polishing Copolymer”
CDP
PRICE
5
7
Antifouling technology options
Controlled Depletion Polymer (CDP)
Self-Polishing Copolymer (SPC)
Hybrid SPC
1. Biocidal option



Foul Release (non-stick)
2. Non-biocidal option

Foul Release
Non - biocidal option
CDP
TBT free SPC
Hybrid SPC
Durable & Long lasting
Less weight
Less paint
Lower M&R costs
Foul Release
Potential fuel savings
and lower emissions
Currently less than 10% of the world fleet use this product
No biocides
Low VOC
Antifouling Performance
Keeps fouling off propellers
6
8
2
153
 Noise unsteadiness due to fouling during operations needs separate study –
IMO-MEPC 59/19 Correspondence Group report “Noise from commercial
shipping and its adverse impacts on marine life“ (April 2009)
PE
ERFORMANCE
Current R & D needs
There is increasing interest and applications of foul release coatings due to their
environmental and other benefits.
Relative merits of these coatings, especially for drag benefits on hulls and
p p
propellers,
, need further R&D including:
g
 To develop a robust, industry based device to measure roughness characteristics
of hulls and propellers coated with FR paints in dry docks and labs
 To establish new skin friction data base and hence roughness allowance
associated with these coatings for power estimations
 Foul release coatings appears to be more vulnerable to slime growth than biocidal
coatings. Their drag performance in the presence of slime effect should be evaluated
using
i special
i l model
d l and
d full
f ll scale
l testing
t ti facilities
f iliti
 Real performance evaluation of hulls and propellers with different coatings needs
dedicated full-scale trails with special performance monitoring devices on board
 Foul release coatings can take advantage of nano-engineered surface patterning that
can be further exploited for drag benefits with close collaboration between
chemist, marine biologist and hydrodynamicst at the development stage of these
coatings
9
Laser profilometer
Current R&D Examples
New BMT-HRA device
11
12
10
Stylus based BMT -HRA
Laser sensor based
prototype BMT – HRA
Current R & D examples
 New BMT- HRA using laser sensor
Current R&D Examples
25:1
2.3m x 0.25m x
0.01m

A unique facility, which is fully-turbulent flow channel (FLOW CELL), has
been established to study the adhesion and friction drag characteristics of
foul release coatings in the presence of marine bio-fouling, in particular
“slime”
Measuring
section size
(L x B x H)
FLOW CELL
Contraction
ratio
256kPa
13.4 m/s
14 slides
76mm x 26mm
or
single plate
185mm x76mm
Max water
velocity
Test slide
capacity
Fresh/sea water
at 280C-300C
Max shear
stress
Operating
medium
3
154

Current R&D Examples
3.35
0.4
0.02
1.5
6
0.6 x 0.28
10
287
167
Umean (m/s)
2
5
7
10
τw (Pa)
11
48
87
167
13

AMBIO (Advanced Nanostructure Surfaces for the Control of Biofouling) was an
EU-FP6 Integrated Project. The 5-year project completed in 2010 was highly
interdisciplinary including nanotechnology, polymer science, surface science, coating
technology, hydrodynamics and marine biology. Project integrated 31 Partners from
industries, universities and research organisation and significant end-users
industries
end users involved

There is a need for field data on
service performance of coatings
using “removable
removable test patches”
patches
and novel ideas for “in-situ
measurements” (e.g. using
research vessels fitted with
special equipment).
Current R&D Examples

Current R&D Examples
Such test (research) vessels
with the state-of-the-art
f
it i systems
t
performance
monitoring
(including thrust gauge) will
make more realistic contribution
into analysis of hydrodynamic
performance of different
coatings

10000
Re 
15000
20000
AKZO19 Cf (B)
AKZO20 Cf (B)
AKZO21 Cf (B)
AKZO28 Cf (B)
INT900 Cf (B)
STEEL Cf (B)
AKZO 19 (Flourinated Slicone blend) displayed
favourable skin friction over major commercial
brands and patented by IP
0.0034
0.0032
0.003
0.0028
0.0026
0.0024
5000
14
16
4
155
Another facility to investigate the service performance of SPC coatings is
“AGING FLUME” which simulates the polishing activity in laboratory
condition using seawater in fully turbulent flow condition.
Measuring section length (m)
Measuring section width (m)
Measuring section height (m)
Development length (m)
Number of plates
Size of coated area/plate L×B (m)
Water velocity (m/s)
Water flow rate (m3/h)
Maximum wall shear stress (Pa)

Approximately 500 different foul release nano-structured coatings, representing 64
generic coating chemistries were prepared at laboratory-scale and evaluated for their
antifouling and foul release performance. Of these, 15 were down-selected for
testing in a range of field and end-user tests. Several coatings showed promise in
these trials, and have either been commercialized, or have the potential to be so after
further develop. 5 novel coatings were patented.
Current R&D Examples

www.ambio.bham.ac.uk
Some of these coatings showed great potential for drag reduction characteristics for
hull and propeller applications e.g.
e g Fluorinated silicone blends and nano-hybrid
nano hybrid sol-gel
sol gel
coatings with clay nanofilllers, respectively.
15
C f (B)
Chemists
MARINE
ANTIFOULING
Marine
Biologists
Current R&D Examples
Ship
Owner
Naval
Architect
17
THANK YOU
Marine
S h l off
School
Science and Technology
[email protected]
18
[email protected]
5
156
2010年４月16日
ITTIC資料
防汚塗料について
日本ペイントマリン㈱
山盛 直樹
船底防汚塗料の現状
157
防汚の歴史
BC.400
アリストテレス：船低に“Echeniis”が付着すると船速が低下
BC.300～200
船底の汚損防止にピッチ、蝋、タール、アスファルトを使用
BC 287～212
アルキメデス：船底に鉛を用い、銅のボルトで締める
キメデ 船底に鉛を用
銅 ボ ト 締める
ﾙﾈｻﾝｽ時代
レオナルド・ダ ビンチ 熔融鉛を船底の汚損防止用に使用
1625年
1685年
1776年
19世紀
1881年
1885年
生物付着防止用に船底を銅板で被服（特許）
船底を虫食いから防止するためタールを塗装（船底塗料の最初の特許）
英国艦隊はすべて銅板で覆う
英国艦隊はす
て銅板で覆う
鉄船の時代に入る
⇒ ＡＣ塗料の出現
光明社創設
日本特許第1号 「錆止め塗料及びその塗り方」
代表的な付着生物（１）
158
代表的な付着生物（２）
代表的な付着生物（３）
159
防汚塗料の組成
樹脂（塩化ゴム
（塩化ゴム・加水分解型アクリル樹脂
加水分解型アクリル樹脂
・ロジン等）
可塑剤
防汚塗料
体質顔料
着色顔料
添加剤（タレ止め剤 沈降防止剤等）
添加剤（タレ止め剤・沈降防止剤等）
防汚剤
溶剤
船底塗料の世界的動向
（有機スズ防汚剤規制）
2001年10月の国際海事機構（IMO）外交会議での有害な防汚
方法の規則に関する国際条約が採択された。
方法の規則に関する国際条約が採択された
１．2003年1月1日以降すべての船舶に殺生物剤として機能す
る有機スズ化合物（ﾄﾘﾌﾞﾘﾙｽｽﾞ化合物、ﾄﾘﾌｪﾆﾙｽｽﾞ化合物）
を含有する防汚塗料の塗装の禁止
２．2008年1月1日以降すべての船舶の船体外部表面に殺生物剤
として機能する有機スズ化合物を含有する防汚塗料の存在の禁止
（ブラストし非有機スズ船底塗料に塗り替え、シーラーコート
で有機スズ船底塗料を被服する。）
160
船底塗料の法的規制
- 船底塗料はBiocidal Productsとして分類される。
products は殺虫剤／殺草剤のような規制を受ける。
- Biocidal p
塗膜表面の防汚剤
分解
海水中 防汚剤
海水中の防汚剤
堆積物中の防汚剤
環境に対する３つのポイント:
防汚剤の分解速度
付着生物以外の生態 の毒性
付着生物以外の生態への毒性
生体蓄積性
防汚剤の種類
No.
CAS. No.
防 剤名
防汚剤名
1
1111-67-7
ロダン銅
2
1317-39-1
化
亜酸化銅
3
137-30-4
Ziram (P
4
330-54-1
DCMU (Preventol A6)
5
971 66 4
971-66-4
P idi t i h
Pyridine-triphenylborane
lb
(PK)
6
1085-98-9
Dichlofluanid ((Preventol A4)
7
13108-52-6
Tems pyridine (Densil S-100)
8
13167-25-4
Trichlorophenyl-maleimid（IT-354）
9
13463-41-7
Zinc pyrithione
10
14915-37-8
Copper pyrithione
11
28159-98-0
Irgarol 1051
12
64359-81-5
Seanine-211
13
1897-45-6
Chlorothalonil
14
12122-67-7
Zineb
15
137-26-8
137
26 8
Thiram
161
分解
付着生物と防汚剤
動物
TBT Cu 防汚助剤
外殻をもつもの
フジツボ
セルプラ
イガイ
外殻をもたないもの
ヒドロ
ホヤ
植物
藻類
緑藻
褐藻
紅藻
珪藻類
“緑色スライム"
“黒色スライム"
防汚剤登録（日本塗料工業会）
2004年以降
「IMO・2001年の船舶に有害な防汚方法の規制に関する
国際条約への適合性に関する（社）日本塗料工業会自主
管理登録品」
として登録および情報公開
162
船底塗料国登録
登録が必要な国々
アメリカ
カナダ
スウェーデン
オランダ
アイルランド
ベルギー
フィンランド
オーストリア
マルタ
ホンコン
オーストラリア
ニュージーランド
船級登録
船舶の安全航行における環境負荷の低減
Lloyd
Germanischer Lloyd
DNV
KR
をはじめとする各船級への登録
163
LF-Sea
船底塗料の分類
船底塗料
分類
（低摩擦）
加水分解型
自己研磨型A/F
SPC
(従来型）
水和分解型
溶出型
燃
費
崩壊型A/F
拡散型A/F（溶出型A/F)
表面物性
非溶出型
忌避
電気的 等
自己研磨型樹脂の特徴
海水中
+
加水分解
《樹脂が親水化・溶出》
ＫＬ/510浬
セルフポリッシング（自己研磨作用）
70
Insoluble spot
（平均運行速度：２０ノット）
消費
費燃料
60
拡散型塗膜
消耗膜厚
50
自己研磨型塗膜
基盤
40
0
1
2
3
4
5
6
7
8
9
10
11
経過月数
図　運行燃費節減効果
運航後の塗膜の断面写真
164
12
加水分解機構
銅アクリル樹脂
Ｙ
C=O
C=O
XY
O
（海水：PH=8.2)
Ｘ
O
O
＋
Cu++
＋
C=O
R
Cu
海水中に溶出
O
C=O
R
加水分 型
加水分解型（＝自己研磨型）塗料用樹脂
磨型 塗 用
有機錫アクリル樹脂
Bu
銅／亜鉛アクリル樹脂
シリルアクリル樹脂
C=O
C=O
C=O
O
O
O
Sn
Bu
Bu
Me
O
C=O
R
M
Me：
C or Zn
Cu
Z
165
R
Sｉ
R
R
各種錫フリー船底塗料の特徴（溶出型）
経時表面変化
塗装直後
加水分解型A/F
水和分解型・
崩壊型A/F
拡散型A/F
(μg/cm2 /day)
防汚剤放出
出速度[Cu
u]
60
50
拡散型
（塩化ゴム/ロジン）
40
30
自己研磨型（SPC)
20
10
生物が付着する放出量
が 着
0
２
４
６
８
10
測定期間（月）
図
防汚剤（Ｃｕ 2 Ｏ）の放出速度
166
12
スズフリー自己研磨型樹脂
（比較的古いタイプの樹脂）
銅アクリル樹脂
亜鉛アクリル樹脂
C=O
C=O
O
O
Cu
Zn
O
O
C=O
C=O
R
R
シリルアクリル樹脂
C=O
O
iPr
Ｓｉ
iPr
iPr
（当社塗料には使用しておりません）
新規加水分解型樹脂（HyB）
シリルアクリル樹脂A/Fの難点を克服するため、従来の
金属含有アクリル樹脂技術 を組み合わせ新規樹脂を開発
銅アクリル樹脂
シリルアクリル樹脂
O
Cu
O
＋
iPr
C=O
O
O
O
Ｓｉ
シリル・ 銅アクリル樹脂
C=O
C=O
C=O
ハイブリッド化樹脂
Cu
iPr
O
iPr
C=O
C=O
C
O
R
R
167
iPr
Ｓｉ
iPr
iPr

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