3KDVH&KDQJH(YDSRUDWRU'HVLJQIRU1DWXUDO5HIULJHUDWLRQ6\VWHP
௙
$VXWRVK3UDVDG௙
2UL6DFV.DQG5DM&7KLDJDUDMDQ
&RUUHVSRQGLQJDXWKRU$72$6FLHQWLILF7HFKQRORJLHV3YW/WG5HJHQW3ULPH:KLWHILHOG0DLQ
5RDG:KLWHILHOG%HQJDOXUX,QGLDZZZDWRDFRP௙
F RUSKT#DWRDFRP
$EVWUDFW
1DWXUDO UHIULJHUDWLRQ LV DQ DJH ROG SURFHVV DQG WKH
UHFHQW LQWHUHVW LV GXH WR JUHHQ DQG DOWHUQDWH HQHUJ\
LQLWLDWLYHV 7KH 3KDVH FKDQJH SK\VLFDO SKHQRPHQD LV
DQ HIIHFWLYH DSSURDFK WR WKHUPDO HQHUJ\ PDQDJHPHQW
IRU LQQRYDWLYH HQJLQHHULQJ DSSOLFDWLRQV 2QH RI WKH
PDMRU DSSOLFDWLRQ RI 3KDVH FKDQJH SK\VLFV LV
(YDSRUDWLYH&RROLQJ(YDSRUDWLYHFRROLQJSKHQRPHQD
SOD\V D PDMRU UROH IRU FRROLQJ RI OLTXLG SDUWLFOHV LQ D
1DWXUDO UHIULJHUDWLRQ V\VWHP GHVLJQ 5HIULJHUDWLRQ LV
WKH SURFHVV RI WUDQVIHUULQJ KHDW IURP RQH VRXUFH WR
DQRWKHU DV SHU UHTXLUHPHQW IRU GHVLUHG DSSOLFDWLRQ
(YDSRUDWLYH FRROLQJ SURFHVV FRPHV ZLWK YDULRXV
WHFKQLFDO FKDOOHQJHV $PELHQW WHPSHUDWXUH 5HODWLYH
+XPLGLW\ 7KHUPDO &RQGXFWLYLW\ (YDSRUDWLQJ
6XUIDFH PHGLXP DIIHFWV WKH FRROLQJ SURFHVV ,Q WKLV
SDSHU WKH FRROLQJ SHUIRUPDQFH RI WZR GHVLJQV KDV
FRPSDUHG FRQVLGHULQJ WKH GLIIHUHQW VXUIDFH DUHD RI
HYDSRUDWLQJ PHGLXP ZKLOH NHHSLQJ RWKHU SDUDPHWHUV
DVFRQVWDQW
,QWURGXFWLRQ
:LWK RQVHW RI HQHUJ\ FULVLV DQG HQYLURQPHQW
SUREOHPV FDXVHG E\ FRQYHQWLRQDO UHIULJHUDWRUV
LPSRUWDQFH RI HYDSRUDWLYH FRROLQJ KDV JURZQ
&RQYHQWLRQDO UHIULJHUDWLRQ FRPHV ZLWK LW¶V RZQ
GLVDGYDQWDJHV DIIHFWLQJ QDWXUDO HQYLURQPHQWV E\
GLVSRVLQJ FKHPLFDO JDVHV ZKLFK ZLOO KDUP WKH2]RQH
OD\HU5HIULJHUDWLRQE\HYDSRUDWLQJFRROLQJKDVSURYHG
WR EH D VXFFHVVIXO DOWHUQDWLYH WR FRQYHQWLRQDO
UHIULJHUDWRU (YDSRUDWLYH FRROLQJ SURFHVV LV
LQH[SHQVLYH HQYLURQPHQW IULHQGO\ DQ HIIHFWLYHZD\
WR SUHVHUYH IRRG DJULFXOWXUDO SURGXFWV 7KRXJK WKH
PHWKRGV RI HYDSRUDWLQJFRROLQJKDVEHHQLQXVHIURPD
GHFDGH DJR WKH LPSURYHPHQW LQ YDULRXV GHVLJQ DQG
FRROLQJ SHUIRUPDQFH WR SUHVHUYH IRRG PHGLFLQHVDUH
WKHPDLQIRFXVLQUHFHQWGHYHORSPHQW
7UDGLWLRQDO UHIULJHUDWRUV UHTXLUH HOHFWULFLW\ WR UXQ
ZKLFK LV LQFUHDVLQJ HOHFWULFLW\ GHPDQG LQ WKLV DJH RI
HQHUJ\ VFDUFLW\ 0RVW RIWKHXQGHUGHYHORSHGFRXQWULHV
DQG UXUDO DUHDV GRHV QRW KDYH VXIILFLHQW HYHQ LI
PLQLPDO DFFHVV WR HOHFWULFLW\ 3UHVHUYDWLRQ RIIRRGDQG
DJULFXOWXUDO SURGXFWV LQ UXUDO DUHDV LV DQ REVWDFOH WR
KXPDQOLIHVXVWHQDQFHH[SORULQJDOWHUQDWLYHWR
FRPPHUFLDO UHIULJHUDWRUV 1DWXUDO UHIULJHUDWRUV ZLOO
SOD\ DQ LPSRUWDQW UROHLQIXWXUHWRSUHVHUYHIRRGLWHPV
ZKLFK ZLOO OHDGV WR UHYROXWLRQ LQ UHIULJHUDWLRQ
LQGXVWU\ 7KHVH UHIULJHUDWRUV ZLOO EH LQH[SHQVLYH
HDVLO\ DYDLODEOH DQG VKRXOG EH HQYLURQPHQW IULHQGO\
5HIULJHUDWLRQ E\ HYDSRUDWLYH FRROLQJ LV IRXQG WR EH
VXFFHVVIXOIRUWKLVSXUSRVH
(YDSRUDWLYH&RROLQJ
(YDSRUDWLYH FRROLQJ LV D KHDW DQG PDVV WUDQVIHU
SURFHVV LQ ZKLFK VRPH VHQVLEOH KHDW IURP WKH
VXUURXQGLQJ RI D ZHW VXUIDFH LV XVHG WR HYDSRUDWH
PRLVWXUH LQWR WKH DLU WKXV LW LV FRQYHUWHG WRODWHQWKHDW
RI WKH PRLVWXUH 7KLV LV D DGLDEDWLF VDWXUDWLRQ SURFHVV
LQ ZKLFK KHDW LV WDNHQ IURP WKH ZHW VXUIDFH WR WKH
DPELHQW DLU KHQFH LQFUHDVLQJ PRLVWXUH FRQWHQW DQG
ZHWEXOE WHPSHUDWXUH RI WKH VXUURXQGLQJ DLU ,Q WKLV
SURFHVV VRPH HQHUJ\ ORVWGXHWRSKDVHFKDQJHRIZDWHU
PROHFXOHV KHQFH FUHDWH D FRROLQJ HIIHFWV IRUWKHZDWHU
SDUWLFOH OD\ EHKLQG DQG WKH SURFHVV FRQWLQXHWRFUHDWH
D FRROUHJLRQ&RQVLGHULQJWKHDERYHSURFHVVD1DWXUDO
UHIULJHUDWRU FDQ EH GHVLJQHG WR SUHVHUYH IRRG SURGXFWV
IRUVHYHUDOKRXUVZLWKRXWORVLQJWKHQXWULHQWV
:RUNLQJ3ULQFLSOHRI1DWXUDO5HIULJHUDWLRQ
7KH ZRUNLQJ SULQFLSOH RI QDWXUDO UHIULJHUDWLRQ E\
HYDSRUDWLYH FRROLQJ LQYROYHV D VWRUDJH VSDFH FRYHUHG
E\ WZR VLQJOH OD\HUV RI SRURXV DQG QRQSRURXV
PHGLXP ZLWK HYDSRUDWLYH OLTXLG ZDWHU LQ EHWZHHQ
7KH ERWWRP SRUWLRQ DQG LQVLGH QRQSRURXV OD\HUV ZLOO
QRW DOORZ WKH VHHSDJH RI WKH HYDSRUDWLYH OLTXLG WR
RXWVLGH HQYLURQPHQW DV ZHOO DV LQVLGH VWRUDJH RI WKH
UHIULJHUDWRU UHVSHFWLYHO\ 7KH RSHQLQJ RI WKH
UHIULJHUDWRU LV HLWKHU FRYHUHG ZLWK D SRO\PHURUSRURXV
PHGLD DV UHTXLUHG )LJXUH VKRZV WKH ZRUNLQJ
SULQFLSOHRID1DWXUDOUHIULJHUDWLRQV\VWHPGHVLJQ
:KHQ WKH UHIULJHUDWRU LV VXEMHFWHG WR DPELHQW GU\
DLU WKH ZDWHU GLIIXVHV WKURXJK WKH SRURXV PHGLXP WR
WKH RXWHU VXUIDFH DQG HYDSRUDWHG LQWR WKH VXUURXQGLQJ
DLU
Excerpt from the Proceedings of the 2015 COMSOL Conference in Pune
)LJXUH௙
:RUNLQJSULQFLSOHRIHYDSRUDWLYHFRROLQJQDWXUDOUHIULJHUDWRU
7KH VHHSDJH RI ZDWHU RXW RI WKH SRURXVPHGLXPWRWKH
H[WHUQDO VXUIDFH RI WKH UHIULJHUDWRU LV FDXVHG E\ WKH
JUDYLWDWLRQDO SUHVVXUH KHDG DQG K\GUDXOLFV IRUFH RI
ZDWHU LQVLGH WKH OLTXLG FKDPEHU 7KH FDSLOODULW\ DQG
'DUF\¶V /DZ LQ SRURXV PHGLD SOD\V D PDMRU UROH IRU
VHHSDJH RI ZDWHU PROHFXOH WR H[WHUQDO VXUIDFH RI WKH
SRURXV PHGLXP 7KH WKHUPDO HQHUJ\ UHTXLUHG IRU WKH
HYDSRUDWLRQ RQ WKH H[WHUQDO VXUIDFH RI WKH UHIULJHUDWRU
LV GUDZQ IURP WKH VWRUDJH VSDFH KHQFH JHQHUDWH
FRROLQJ HIIHFW LQVLGH WKH VWRUDJH FKDPEHU LQWHQGHGIRU
SUHVHUYLQJIRRGLWHPVIRUVHYHUDOKRXUV
$$WPRVSKHULF7HPSHUDWXUH
7KH DWPRVSKHULF WHPSHUDWXUH SOD\V DQ LPSRUWDQW
UROH LQ HYDSRUDWLYH FRROLQJ SURFHVV 6LQFH IRU
HYDSRUDWLQJ FRROLQJ WKH UDWH RI GLIIXVLRQ RI ZDWHU
PROHFXOH IURP WKH HYDSRUDWLQJ PHGLXP QHHG WR EH
KLJK KHQFH KLJKHUWKHDWPRVSKHULFWHPSHUDWXUHKLJKHU
ZLOO EH WKH UDWH RI HYDSRUDWLRQ OHDGLQJ WR EHWWHU
FRROLQJ RI WKH VWRUDJH VSDFH IRU IRRGSUHVHUYDWLRQ)RU
EHWWHU SHUIRUPDQFH RI HYDSRUDWLYH FRROLQJ LQ QDWXUDO
UHIULJHUDWRU WKH GU\EXOE WHPSHUDWXUH ℃℃ DQG
ZHWEXOE WHPSHUDWXUH ℃ VKRXOG EH PDLQWDLQ IRU
DQH[WHQGHGSHULRGRIWLPH
)DFWRUVDIIHFWLQJ(YDSRUDWLYH&RROLQJ
7KRXJK WKH FRQFHSW RI HYDSRUDWLYH FRROLQJFRPHV %$PELHQW5HODWLYH+XPLGLW\
ZLWK YDULRXV DGYDQWDJHV ZHFDQQRWLJQRUHWKHIDFWRUV DIIHFWLQJ LQ FRROLQJ SURFHVV 7KH GLIIHUHQW IDFWRUV $PELHQW UHODWLYH KXPLGLW\ GHVFULEH WKH DPRXQW RI
ZDWHU PROHFXOH SUHVHQW LQ WKH DPELHQW DLU 6LQFH WR
DIIHFWLQJHYDSRUDWLYHUHIULJHUDWLRQDUH
PDLQWDLQ PDVV HTXLOLEULXP LQ WKH V\VWHP ZDWHU
Ɣ $WPRVSKHULF7HPSHUDWXUH
Ɣ $PELHQW5HODWLYH+XPLGLW\
PROHFXOHV QHHG WR HYDSRUDWH IURP ZHW VXUIDFH WR WKH
Ɣ *HRPHWULF6XUIDFHDUHDRI(YDSRUDWLQJ0HGLXP
DPELHQW DLU KHQFH OHVV ZLOO EH WKH DPELHQW UHODWLYH
Ɣ 7KHUPDOFRQGXFWLYLW\RIUHIULJHUDWRUSK\VLFDOERG\
KXPLGLW\ PRUH ZLOO EH WKH UDWH RI HYDSRUDWLRQ
Ɣ +\GUDXOLF&RQGXFWLYLW\RISRURXVPHGLD
UHVXOWLQJEHWWHUFRROLQJSHUIRUPDQFH
Ɣ 0RYHPHQWRIVXUURXQGLQJDLU
Excerpt from the Proceedings of the 2015 COMSOL Conference in Pune
&*HRPHWULF6XUIDFHDUHDRI(YDSRUDWLQJ0HGLXP
,W LV SURYHQ DQDO\WLFDOO\ WKH UDWH RI HYDSRUDWLRQ LV
GLUHFWO\ SURSRUWLRQDO WR WKH VXUIDFH DUHD RI WKH
HYDSRUDWLQJ PHGLXP GLUHFW LQ FRQWDFW ZLWK WKH
DPELHQWDLU
7R REWDLQ D EHWWHU FRROLQJ SHUIRUPDQFH IRU D
FHUWDLQ YROXPH WKH VXUIDFH WR YROXPH UDWLR VKRXOG EH
KLJK DV SRVVLEOH ,Q WKLV SDSHU DQ XQLTXH GHVLJQ KDV
LQYHVWLJDWHG RQ WKH HIIHFW RI ODUJH RXWVLGH VXUIDFHDUHD
RIWKH5HIULJHUDWRU
' 7KHUPDO FRQGXFWLYLW\ RI UHIULJHUDWRU SK\VLFDO
ERG\
/RZ WKHUPDO FRQGXFWLYLW\ UHTXLUHG IRU WKH
PDWHULDOV XVHG WR FRQVWUXFW WKH SK\VLFDO ERG\ RI
QDWXUDO UHIULJHUDWRU DV SRVVLEOH WR REWDLQ SOHDVDQW
FRROLQJ UHJLRQ /RZHU ZLOO EH WKH WKHUPDO
FRQGXFWLYLW\ KLJKHU ZLOO EH WKH KHDW GLVVLSDWLRQ UDWH
DQGFRROLQJSHUIRUPDQFH
(+\GUDXOLF&RQGXFWLYLW\RISRURXVPHGLD
7R DFKLHYH FRQVWDQWGLIIXVLRQRIZDWHUPROHFXOHWR
WKH H[WHUQDO VXUIDFH RI WKH UHIULJHUDWRU SHUIHFW
K\GUDXOLF FRQGXFWLYLW\ RI SRURXV PHGLXP LV UHTXLUHG
IRU SURSHU VHHSDJH RI ZDWHU PROHFXOH WR WKH DPELHQW
DLU 7KH VHHSDJH RI ZDWHU PROHFXOH WKURXJK SRURXV
PHGLD VKRXOG QRW EHWRRKLJKDQGWRRORZIRUDFHUWDLQ
DPRXQWRIZDWHUYROXPH
)0RYHPHQWRIVXUURXQGLQJDLU
7KH PRYHPHQW RI WKH VXUURXQGLQJDLULQFUHDVHVWKH
HYDSRUDWLRQ UDWH KHQFH LQFUHDVH LQ FRROLQJ
SHUIRUPDQFH RI WKH UHIULJHUDWRU +LJKHU YHORFLW\ RI DLU
DURXQG WKH UHIULJHUDWLRQ LV UHTXLUHG WR LQFUHDVH WKH
HYDSRUDWLRQ UDWH KHQFH LQFUHDVH LQ FRROLQJ
SHUIRUPDQFH
)LJXUH௙
௙
6WDQGDUGHYDSRUDWLQJUHIULJHUDWRUGHVLJQ
0XOWLSK\VLFV0RGHOLQJ6LPXODWLRQ
,Q WKLV SDSHU D PRGHO RI QDWXUDO UHIULJHUDWRU KDV
GHVLJQHG DQG VLPXODWHG LQ &2062/ 0XOWLSK\VLFV
7KLV H[SHULPHQW GHVFULEHV WKH VLPXODWLRQ RI
HYDSRUDWLYH FRROLQJ HIIHFWV LQ D QDWXUDO UHIULJHUDWRU
FRQVLGHULQJZDWHUDQGDLUDVZRUNLQJIOXLG
7KH FRROLQJ HIIHFW RI DQ LQQRYDWLYH GHVLJQ KDV
FRPSDUHG ZLWK D VWDQGDUG GHVLJQ )LJXUHVKRZV
WKHFRPSDULVRQEHWZHHQWZRGHVLJQV
)LJXUH௙
&RUUXJDWHGUHIULJHUDWRUGHVLJQ
Excerpt from the Proceedings of the 2015 COMSOL Conference in Pune
$ERYH DUH WKH WZR D[LV\PPHWULF UHIULJHUDWRU
GHVLJQV LQYHVWLJDWHG LQ WKLV H[SHULPHQW WR FRPSDUH
WKH FRROLQJ SHUIRUPDQFHV 7KHVH DUH WKH ' FURVVVHFWLRQDO SURILOHV RI F\OLQGULFDO UHIULJHUDWRU
GHVLJQ DVVXPHG WR EH F\OLQGULFDOO\ V\PPHWU\ 7KH
FRUUXJDWHG W\SH H[WHUQDO VXUIDFH RI WKH UHIULJHUDWRU
LQFUHDVHV WKH VXUIDFH DUHD WR YROXPH UDWLRFRPSDUHGWR
D FRQYHQWLRQDO GHVLJQ /DUJH VXUIDFH DUHD H[SRVHG WR
DPELHQW DLU IORZ HYDSRUDWHV PRUH ZDWHU PROHFXOH WR
WKH DWPRVSKHUH KHQFH LQFUHDVHV WKH FRROLQJ
SHUIRUPDQFH
0RGHO'HILQLWLRQ
7KH ' KDOI FURVVVHFWLRQDO PRGHOV RI WZR
&2062/0RGHORIFRUUXJDWHGHYDSRUDWLQJ
UHIULJHUDWLRQ GHVLJQV KDV GHVLJQHG LQ &2062/ )LJXUH௙
H[WHUQDOGHVLJQ
&$'(QYLURQPHQWVKRZQLQ௙
)LJXUH
,Q
0XOWLSK\VLFV
6LPXODWLRQ
RI HYDSRUDWLYH FRROLQJ
WKUHHSK\VLFDOHIIHFWVZHUHWDNHQLQWRDFFRXQW
Ɣ 7XUEXOHQWIORZRIDLUDURXQGWKHUHIULJHUDWRU
Ɣ +HDWWUDQVIHULQDOOGRPDLQRIWKHUHIULJHUDWRU
Ɣ 7UDQVSRUW RI ZDWHU YDSRU WR DLU IURP H[WHUQDO
VXUIDFHRIWKHUHIULJHUDWRU
7XUEXOHQW)ORZ
)LJXUH௙
&2062/0RGHORI௙
6WDQGDUGHYDSRUDWLQJ
H[WHUQDOGHVLJQ
7KH WXUEXOHQW IORZ FKDUDFWHULVWLFV RI DPELHQW DLU
HQKDQFHV WKH GLIIXVLRQ RI ZDWHU PROHFXOHV WR
DWPRVSKHUH LQFUHDVLQJ WKH HYDSRUDWLYH FRROLQJ UDWH
7XUEXOHQW IORZ /RZ 5H .İ LQWHUIDFH RI &2062O
0XOWLSK\VLFV KDV WDNHQ LQWR DFFRXQW WR VLPXODWH
WKH DLUIORZ DURXQG WKH UHIULJHUDWRU 7KHIORZ RIDLUDQG
WXUEXOHQFH HTXDWLRQ DUH DVVXPHG WR EH
FRPSUHVVLEOH0D 5$16 5H\QROGV $YHUDJHG
1DYLHU 6WRNH UHVSHFWLYHO\ 7KLV DOORZV WR FDOFXODWH
WKH WXUEXOHQW IORZ ILHOG DURXQG WKH UHIULJHUDWRU LQ
DGYDQFH DQG WKHQ FDQ EH XVHG DV LQSXW IRU WKH KHDW
WUDQVIHUDQGVSHFLHVWUDQVSRUWHTXDWLRQV
+HDW7UDQVIHU 7KH KHDW WUDQVIHU IURP H[WHUQDO VXUIDFH RI WKH
UHIULJHUDWRU WR WKH DPELHQWDLULVGXHWRFRQYHFWLRQDQG
LQVLGHWKHUHIULJHUDWRULVFRQGXFWLRQ
Excerpt from the Proceedings of the 2015 COMSOL Conference in Pune
7KH WXUEXOHQW IORZ RI DLU LQFUHDVHV WKH KHDW
GLVVLSDWLRQ UDWHIURPH[WHUQDOVXUIDFHRIWKHUHIULJHUDWRU
WR WKH DWPRVSKHUH 'XULQJ HYDSRUDWLRQ ODWHQW KHDW
UHOHDVHG IURP WKH H[WHUQDO ZHW VXUIDFH GXH WR SKDVH
FKDQJH RI ZDWHU PROHFXOHV IURP OLTXLG WR YDSRU
UHVXOWLQJHQHUJ\ORVVZKLFKFUHDWHVFRROLQJHIIHFW7KH
+HDW WUDQVIHU PRGXOH RI &2062/ KDV WDNHQ LQWR
DFFRXQW WR VLPXODWH KHDW WUDQVIHU SKHQRPHQD RI WKH
UHIULJHUDWRU *RYHUQLQJ HTXDWLRQ IRU KHDW WUDQVIHU LV
JLYHQEHORZ
QN▽7 +௙
Q'▽FXF
YDS௙
:KHUH+௙
LVWKHODWHQWKHDWRIYDSRUL]DWLRQ
YDS௙
5HVXOW'LVFXVVLRQ
7KH SHUIRUPDQFH RI HYDSRUDWLRQ FRROLQJ KDV
DQDO\VHG DQG FRPSDUHG IRU WZR GLIIHUHQW GHVLJQV 7KH
HIIHFWV RI VXUIDFH WR YROXPH UDWLR RQ HYDSRUDWLYH
FRROLQJ SHUIRUPDQFH KDV PDQLSXODWHG LQ WKLV
H[SHULPHQW )LJXUH UHSUHVHQWV WKH WHPSHUDWXUH
GLVWULEXWLRQIRUFRQYHQWLRQDOFRUUXJDWHGVXUIDFHDUHD
UHIULJHUDWRU
7UDQVSRUWRI:DWHU9DSRU
7KH DPRXQW RI ZDWHU ZKLFK LV HYDSRUDWH IURP WKH
ZDWHU FKDPEHU WR DLU GRPDLQ SOD\V DQ LPSRUWDQW UROH
WR HQKDQFH WKH SHUIRUPDQFH RI UHIULJHUDWRU 7KH ZDWHU
PROHFXOH GLIIXVLRQ UDWH LQ ODUJH VXUIDFH ZLOO EH PRUH
FRPSDUHG WR D SODQHU VXUIDFH UHVXOWLQJ LQFUHDVH LQ
FRROLQJ HIILFLHQF\ RI WKH UHIULJHUDWRU ,Q WKLV
H[SHULPHQW LW LV SURYHQ WKDW E\ LQFUHDVLQJ WKH VXUIDFH
WR YROXPH UDWLR IRU D FHUWDLQ DPRXQW ZLOO LQFUHDVH WKH
HYDSRUDWLRQ UDWH 7UDQVSRUW RI 'LOXWHG 6SHFLHV
LQWHUIDFH RI &2062O KDV XVHG IRU DLU GRPDLQ WR
FDOFXODWH WKH DPRXQW RI ZDWHU WUDQVSRUWHG IURP WKH
UHIULJHUDWRU WR DPELHQW DLU ,Q WKLV H[SHULPHQW WKH
FRQFHQWUDWLRQ LV FKRVHQ DV SHU DQ LQLWLDO UHODWLYH )LJXUH௙
7HPSHUDWXUHGLVWULEXWLRQLQDVWDQGDUGGHVLJQ
KXPLGLW\ RI 7KH LGHDO JDV ODZ DW VDWXUDWLRQ
SUHVVXUH KDV DSSOLHG DV ERXQGDU\ VRXUFH RI
YDSRULVDWLRQWRWKHH[WHUQDOVXUIDFHRIWKHUHIULJHUDWRU
F௙
YDS
P sat
RgT
F௙
YDS LV WKH VSHFLILF FRHIILFLHQW RI
YDSRULVDWLRQ 3௙
LV WKH FRQVWDQW VDWXUDWLRQ SUHVVXUH
VDW ௙
:KHUH
5௙
LV WKH JDV FRQVWDQW DQG ௙
7 LV WKH WHPSHUDWXUH7KH
J ௙
WUDQVSRUW HTXDWLRQVIRUDLUGRPDLQIXUWKHUXVHVWKHIORZ ILHOG UHVXOWV VROYHG ZLWK 7XUEXOHQFH /RZ 5H .İ LQWHUIDFH /DWHU IROORZLQJ HTXDWLRQ KDV LPSOHPHQWHG
DVWXUEXOHQWGLIIXVLYLW\WRWKHGLIIXVLRQWHQVRU
vT
'௙
ScT
,
7௙
:KHUH Y7 LV WKH WXUEXOHQFH NLQHPDWLF YLVFRVLW\
6F7 LV WKH WXUEXOHQW 6FKPLGW QXPEHU DQG ௙
, WKH 8QLW
PDWUL[
)LJXUH௙
7HPSHUDWXUHGLVWULEXWLRQLQFRUUXJDWHG
GHVLJQ
Excerpt from the Proceedings of the 2015 COMSOL Conference in Pune
6LPXODWLRQ UHVXOWV VKRZV WKH WHPSHUDWXUH GLVWULEXWLRQ
IRU HYDSRUDWLRQ FRROLQJ LQ ERWK GHVLJQV 1DWXUDO
FRROLQJ VKRZV WKH SRWHQWLDO WR ORZHU WKH WHPSHUDWXUH
E\ DERXW ℃ IURP WKH LQLWLDO FRQGLWLRQ 7KH
FRUUXJDWHG GHVLJQ VKRZV SRWHQWLDO WR IXUWKHU ORZHULQJ
WKH WHPSHUDWXUH DURXW 7HPSHUDWXUH GLIIHUHQFH RI
℃ KDV REWDLQHG ZLWK ODUJH HYDSRUDWLYH VXUIDFH DUHD
FRPSDUHGWRVWDQGDUGGHVLJQ
7KH HYDSRUDWLYH FRROLQJ HIIHFWV LQ ERWK GHVLJQV
ZHUH FRPSDUHG 7KH UHDO WLPH FRXSOHG PXOWLSK\VLFV
LQYROYHG LQ HYDSRUDWLYH FRROLQJ SURFHVV KDV VROYHG
XVLQJ&2062/0XOWLSK\VLFVVLPXODWLRQVRIWZDUH
7KH GHULYHG UHVXOWV IURP VLPXODWLRQ UHVXOWV ZHUH
FRPSDUHG UHVSHFWLYHO\ 7KH SKDVH FKDQJH SK\VLFV
PRGHO KHOSHG WR RSWLPLVH WKH HYDSRUDWRU GHVLJQ IRU
HIILFLHQW SHUIRUPDQFH 7KH FRUUXJDWHG HYDSRUDWLYH
VXUIDFH GHPRQVWUDWHG UHGXFWLRQ LQ WHPSHUDWXUH
FRPSDUHG WR VWDQGDUG GHVLJQ 7KLV PXOWLSK\VLFV
PRGHOLQJPHWKRGRORJ\FDQIXUWKHUEHXVHGWRRSWLPLVH
HYDSRUDWLYH FRROLQJ EDVHG ORZ FRVW SURGXFWV ZLWK
VXSHULRUSHUIRUPDQFHIRUUHDOLVWLFZHDWKHU
௙
$FNQRZOHGJHPHQW
7KLV UHVHDUFK ZDV VXSSRUWHG E\ 5,'HSDUWPHQW
RI $72$ 6FLHQWLILF 7HFKQRORJLHV %HQJDOXUX ,QGLD
7KH DXWKRU ZRXOG OLNH WR WKDQN WKH WHFKQLFDO WHDP
ZKR SURYLGHG LQVLJKW DQG H[SHUWLVH WKDW JUHDWO\
DVVLVWHGWKHUHVHDUFK
5HIHUHQFHV
>@³5HIULJHUDWLRQDQG$LU&RQGLWLRQLQJ´E\0DQRKDU3UDVDG
>@³(QJLQHHULQJ7KHUPRG\QDPLFV´E\3.1DJ
>@³+HDW0DVV7UDQVIHU´E\5.5DMSXW
>@³(YDSRUDWLYH&RROLQJRI:DWHULQ(DUWKHQ3RWV LQ4XLHVFHQW
$LU´ - $ 2ORUXQPDL\H 'HSDUWPHQW RI 0HFKDQLFDO
(QJLQHHULQJ8QLYHUVLW\RI,ORULRQ1LJHULD
)LJXUH௙
7HPSHUDWXUHGURSFRPSDULVRQ
0DWKHPDWLFDO 0RGHO RI DQ (YDSRUDWLYH &RROLQJ 3DG
7KH HYDSRUDWLYH FRROLQJ HIIHFWV IRU ERWK >@³$
8VLQJ 6LQWHUHG 1LJHULDQ &OD\´ &KXNZXQHNH -HUHPLDK
GHVLJQV ZHUH HYDOXDWHG DQG WHPSHUDWXUH GURS /HNZXZD $MLNH &KLQDJRURP 2JEX $FKHEH &KLQRQVR
YDOXHV IRU ERWK GHVLJQV IRU VSHFLILF WLPH GXUDWLRQ +XEHUW 2NROLH 3DXO &KXNZXOR]LH 'HSDUWPHQW RI0HFKDQLFDO
KDV FRPSDUHG DV VKRZQ LQ )LJXUH ࣡
)URP WKLV (QJLQHHULQJ 1QDPGL $]LNLZH 8QLYHUVLW\30%$ZND
1LJHULD
H[SHULPHQW D WHPSHUDWXUH GLIIHUHQFH RI ℃ KDV DFKLHYHG )URP WKLV H[SHULPHQW LW LV SURYHQ WKDW >@³+HDW DQG 0DVV 7UDQVIHU LQ 'LUHFW (YDSRUDWLYH &RROHU´ 6
HYDSRUDWLYH UHIULJHUDWRUV PDGH ZLWK ODUJH 6 .DFKKZDKD DQG 6XKDV 3UDEKDNDU 'HSDUWPHQW RI
HYDSRUDWLYH VXUIDFH DUHD KDYH PRUH FRROLQJ UDWH 0HFKDQLFDO(QJLQHHULQJ'HOKL7HFKQRORJLFDO8QLYHUVLW\
FRPSDUHGWRVWDQGDUGGHVLJQV
>@³$Q ,QYHVWLJDWLYH 5HYLHZ RQ 5HFHQW 'HYHORSPHQWV LQ
5HIULJHUDWLRQ E\ (YDSRUDWLYH &RROLQJ´ ,QWHUQDWLRQDO -RXUQDO
RI (QJLQHHULQJ 7UHQGV DQG 7HFKQRORJ\ ,-(77 9ROXPH &RQFOXVLRQV
1XPEHU0D\
7KH SURFHVV RI HYDSRUDWLYH FRROLQJ IRU QDWXUDO UHIULJHUDWLRQ V\VWHP KDV H[SODLQHG7KHHIIHFWVRIODUJH >@³(YDSRUDWLQJ &RROLQJ RI :DWHU´&2062/0RGHO7XWRULDO
VXUIDFH WR YROXPH UDWLRLQHYDSRUDWLQJFRROLQJSURFHVV JXLGH&2062/
KDV LQYHVWLJDWHG 7ZR GLIIHUHQW H[SHULPHQWDO PRGHO KDVVLPXODWHGQXPHULFDOO\
Excerpt from the Proceedings of the 2015 COMSOL Conference in Pune
Excerpt from the Proceedings of the 2015 COMSOL Conference in Pune