Institutt for marin teknikk
1
Making speed-power predictions
from model tests
Sverre Steen
ITTC’57 Correlation Line
0.02
0.018
ITTC'57 Friction line CF
Institutt for marin teknikk
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
1.0E+03
2
1.0E+04
1.0E+05
1.0E+06
1.0E+07
Reynolds number Rn
1.0E+08
1.0E+09
1.0E+10
Friction lines
(formulas to calculate the frictional coefficient)
Turbulent flow
Institutt for marin teknikk
3
Institutt for marin teknikk
4
Scaling of Resistance
Institutt for marin teknikk
= Calculated from
empirical formulas
Total Resistance, ship
=
Measured resistance of model
Correlation allowance
-
+
Viscous resistance, model
Viscous resistance, ship
-
+
Air resistance, model
+
=
Residuary resistance, model
5
Air resistance, ship
=
Residuary resistance, ship
Ship Resistance Scaling
Viscous resistance
Residual resistance model
=
Residual resistance ship
Full scale
resistance components
Institutt for marin teknikk
CRm = CTm − (1 + ko ) ⋅ CFm − CAAm − CBDm = CRs
Correlation coef. Transom stern drag
CTs = CRm + (CFs + ∆CF ) ⋅ (1 + ko ) + CA + CAAs + CBDs
Full scale resistance
6
Air resistance Transom stern drag
Model scale
resistance components
Measured model resistance
Viscous resistance
Air resistance
Calculated resistance components
•
Institutt for marin teknikk
7
Total resistance coef., model CTm =
ρm
2
RTm
⋅Vm2 ⋅ Sm
AT ⇒ C ≈0.8
D
S
Air resistance coefficient
CAA = 0.001⋅
•
Transom stern resistance
0.029⋅ (SB / S )3/ 2
CBD =
(CF )1/ 2
•
Appendage resistance
•
Viscous Resistance
•
Institutt for marin teknikk
8
Frictional Resistance
CF =
0.075
(log Rn − 2)2
(ITTC’57)
•
Form factor
•
2
Roughness allowance ∆CF = 110.31⋅ ( H ⋅Vs )0.21 − 403.33 ⋅ CFs
[
]
Determining the form factor
•
Institutt for marin teknikk
9
When wave resistance, air resistance, and base drag is subtracted
from total resistance, you are left with viscous resistance
CTm = (1 + ko ) ⋅ CFm + C AAm + CR + CBDm
•
⇒
⇒
⇒
How can the form factor (1+k) be determined?
By running at low speed so that CR≈0 (typically Fn=0.1)
By using Prohaska’s method
By using an empirical method
Prohaska’s metode for å finne
formfaktor
1.8
1.4
y = 62.981x + 1.251
1.2
CT/CF
Institutt for marin teknikk
1.6
1
0.8
(1+k)=1.251
0.6
0.4
0.2
0
0
0.0005
0.001
0.0015
0.002
0.0025
Fn4/CF
10
0.003
0.0035
0.004
0.0045
0.005
Prohaska’s
method
Institutt for marin teknikk
11
The exponent for Fn
is chosen so that the
data points fall on a
line that is as
straight as possible
The exponent should
be in the order of 2-9
MARINTEK Form Factor
Institutt for marin teknikk
12
•
Based on a regression, instead
of measurements on each
model
•
Intentionally excludes viscous
pressure resistance, since
pressure resistance should be
scaled as wave resistance
•
ko = 0.6ϕ + 75ϕ 3
Form factor
where ϕ = CB
LWL
(TAP + TFP ) ⋅ B
Correlation Coefficient CA
Institutt for marin teknikk
13
•
•
•
•
Accounts for systematic errors in the scaling method
Derived from analysis of full scale speed trials
-0.15E-03 ≤ CA ≤ -0.3E-03 for conventional ships. Value depend
on stern shape and appendix arrangement
It is important to get access to full scale trial results of high
quality to maintain a good correlation!
Propulsion Test
Institutt for marin teknikk
14
Measurement of:
Torque Q
Thrust T
Rate of revolutions n
Tow rope FD
Dynamometer
T
ρ ⋅ n 2 ⋅ D4
Q
K
=
Torque Coefficient Q
ρ ⋅ n2 ⋅ D5
Thrust coefficient KT =
Open Water Test
10*KQ
KT
V
KT =
T
ρ ⋅ n2 ⋅ D4
thrust coefficient
KQ =
Q
ρ ⋅ n 2 ⋅ D5
torque coefficient
KT ⋅ J
KQ ⋅ 2π
propeller efficiency in open water
ηO =
15
Efficiency η
KT, 10*KQ
Institutt for marin teknikk
Measurement of:
Torque Q
Thrust T
Rate of revolutions n
Speed V
Advance number J =
VA
n⋅D
Analysis of Propulsion Test
Efficiency η0
10*KQ
KQ0
Enter with KT
from propulsion test
Advance number J =
16
Results:
VA
n⋅D
JO
V
n⋅ D
Wake fraction:
w =1 −
Relative rotative efficiency:
ηR =
Hull efficiency:
ηH =
Quasi-propulsive coefficient:
ηD = ηO ⋅ηH ⋅ηR
Thrust deduction fraction:
t = 1−
KT
to find J0
Institutt for marin teknikk
KT, 10*KQ
Open water diagram:
KQO
KQ
1− t
1− w
RT − FD
T
Performance Prediction
Institutt for marin teknikk
17
•
•
ηR and thrust deduction t are assumed free of scale effects
Wake of single-screw vessels is scaled according to:
C + ∆CF
ws = wo + (wm − wo ) Fs
where
wo = 0.04 + t
CFm
•
The full scale propulsion point J* is found from solving the
equation:
From towing test
From open water test
RTs
KT
=
J 2 ρ ⋅ (1 − t ) ⋅ D2 ⋅Vs2 ⋅ (1 − ws )2
From propulsion test
Performance Prediction (cont.)
•
Rate of revolutions
RPM =
Institutt for marin teknikk
60⋅ (1 − ws ) Vs
⋅
D
J*
This KQ is found from the full scale open water diagram for J
•
•
Delivered power
Brake power
RPM 3 KQ
2π
5
⋅ ρ ⋅ D ⋅(
) ⋅
PD (kW ) =
ηR
1000
60
PB (kW ) =
PD
ηM
A procedure for powering prediction is given in Annex E in the lecture note
18
Load-varied propulsion tests – British
method
•
Institutt for marin teknikk
19
•
•
Thrust T, torque Q and propeller speed n in model scale is
known as functions of the tow rope force FD
Interpolate (or extrapolate linearly) to find the model resistance:
RTM=Thrust when FD=0
Calculate correct FD for each speed and find actual values of
Thrust T, Torque Q, and propeller speed n.
– From here on the procedure is the same as for the continental
method
Multiple-screw propulsion
•
Institutt for marin teknikk
20
•
If the propulsors are equal: use average values of thrust and
torque when calculating propulsive factors and determining the
propulsion point
If the propulsors aren’t equal: do a separate analysis of each
propulsor, finding it’s full scale RPM and power
– Problem: special tests are generally required to determine the part
of the resistance carried by each propeller
Possible solution: make an assumption about how the thrust
deduction is distributed between the propulsors
– Example: A double-ended ferry using both forward and aft
propulsors during transit.
The forward propulsor will have much higher thrust deduction that
the aft propulors. Tests running each propulsor separately can be
used to determine the thrust deduction of each unit