A method is presented to predict propeller performance in an artificially generated wake field using body forces calibrated iteratively. The full RANSE approach and body force method show minor differences of 1.8% in mean propeller force coefficients. Reasons for differences include the artificial wake differing from the actual wake by over 10% near the hub, and using a nominal wake without the hull for the propeller simulations.

1. Propeller Performance Prediction in an
Artificially Generated Wake Field Using RANSE
J. Baltazar1
, B. Schuiling2
, D. Rijpkema2
1Instituto Superior T´ecnico, Universidade de Lisboa, Portugal
2Maritime Research Institute Netherlands, Wageningen, the Netherlands
NuTTS 2019 Tomar, Portugal 29 September - 1 October 1

2. Outline
Motivation
Propeller-Ship Simulations (KCS)
(Nominal) Wake Field Generation
Propeller in Behind Condition (w/o Ship)
Conclusions
NuTTS 2019 Tomar, Portugal 29 September - 1 October 2

3. Propeller Performance in Behind Condition
Full Propeller-Ship Simulations
NuTTS 2019 Tomar, Portugal 29 September - 1 October 3

4. Propeller Performance in Behind Condition
Propeller Simulations
NuTTS 2019 Tomar, Portugal 29 September - 1 October 4

5. Propeller Performance in Behind Condition
NuTTS 2019 Tomar, Portugal 29 September - 1 October 5

6. Propeller Performance in Behind Condition
NuTTS 2019 Tomar, Portugal 29 September - 1 October 6

7. KRISO Container Ship
Model geometry:
Lpp = 7.2786 m
d = 0.3418 m
Sw = 9.4379 m2
Vm = 2.196 m/s
Model propeller:
D = 0.25 m
P/D0.7R = 0.9967
Ae/A0 = 0.800
Z = 5
Full scale:
LPPS = 230 m
VS = 24 kt
Propeller plane:
x/Lpp = 0.4825
from midship
NuTTS 2019 Tomar, Portugal 29 September - 1 October 7

8. Viscous Flow Simulations
RANSE solver ReFRESCO
Finite volume discretisation
k − ω SST turbulence model (Menter et al., 2003)
No wall functions are used (y+
∼ 1)
Discretisation of the convective flux:
Momentum: QUICK
Turbulence: upwind
Time integration: implicit 2nd order scheme
NuTTS 2019 Tomar, Portugal 29 September - 1 October 8

9. Full Propeller-Ship Simulations
Fn=0.26, Re=1.4×107
and fixed free surface (18.4M + 2.9M cells)
NuTTS 2019 Tomar, Portugal 29 September - 1 October 9

10. Full Propeller-Ship Simulations
Fn=0.26, Re=1.4×107
and fixed free surface (18.4M + 2.9M cells)
Azimuth [deg]
KT
72 144 216 288 360
0.010
0.020
0.030
0.040
0.050
0.060
Propeller in Behind Hull
Blade Thrust Coefficient
Azimuth [deg]
10KQ
72 144 216 288 360
0.030
0.040
0.050
0.060
0.070
0.080
0.090
0.100
Propeller in Behind Hull
Blade Torque Coefficient
Azimuth [deg]
KT
72 144 216 288 360
0.160
0.162
0.164
0.166
0.168
0.170
0.172
Propeller in Behind Hull
Propeller Thrust Coefficient
Azimuth [deg]
10KQ
72 144 216 288 360
0.290
0.295
0.300
0.305
Propeller in Behind Hull
Propeller Torque Coefficient
NuTTS 2019 Tomar, Portugal 29 September - 1 October 10

11. Bare Hull Simulations
Fn=0.26, Re=1.4×107
and fixed free surface (18.8M cells)
NuTTS 2019 Tomar, Portugal 29 September - 1 October 11

12. Bare Hull Simulations
Fn=0.26, Re=1.4×107
and fixed free surface (18.8M cells)
y/R
-1.0 -0.5 0.0 0.5 1.0
-1.0
-0.5
0.0
0.5
1.0
Vx: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33
z/R
VS
Vwx /VS:
NuTTS 2019 Tomar, Portugal 29 September - 1 October 12

13. Nominal Wake Field Generation
Uniform flow at inlet (ship’s speed)
Body-forces upstream of propeller plane at 1D
Iterative calibration of body-forces:
F
(i)
x = −1/2ρ VS − V
(i)
wx VS + V
(i)
wx
1
∆V 1/3
F
(i)
y = 1/2ρ VS + V
(0)
wx V
(i)
wy
1
∆V 1/3
F
(i)
z = 1/2ρ VS + V
(0)
wx V
(i)
wz
1
∆V 1/3
with V
(i)
wx,y,z = V
(0)
wx,y,z − β V
(i−1)
wx,y,z − V
(0)
wx,y,z
where V
(0)
wx,y,z represents the nominal wake field
and β = 0.5 is a relaxation factor.
NuTTS 2019 Tomar, Portugal 29 September - 1 October 13

14. Nominal Wake Field Generation
Vinlet = VS (3.2M cells)
NuTTS 2019 Tomar, Portugal 29 September - 1 October 14

15. Nominal Wake Field Generation
Calibrated vs hull simulation
y/R
-1.0 -0.5 0.0 0.5 1.0
-1.0
-0.5
0.0
0.5
1.0
Vx2: 0.33 0.41 0.49 0.57 0.65 0.73 0.81 0.89
z/R
VS
Vwx /VS:
y/R
-1.0 -0.5 0.0 0.5 1.0
-1.0
-0.5
0.0
0.5
1.0
Vx2: 0.33 0.41 0.49 0.57 0.65 0.73 0.81 0.89
z/R
VS
Vwx /VS:
NuTTS 2019 Tomar, Portugal 29 September - 1 October 15

16. Nominal Wake Field Generation
Convergence history and circumferential averaged wake field
Iteration
max|eVw|[%]
mean|eVw|[%]
1 2 3 4 5 6 7 8 9 10 11 12 13
0
20
40
60
0
2
4
6
8
10
12mean|eVwx |
max|eVwx
|
mean|eVwy
|
max|eVwy
|
mean|eVwz
|
max|eVwz |
r/R
0.2 0.4 0.6 0.8 1.0 1.2
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
Vwx /VS: Bare Hull Simulation
Vwx
/VS
: Generated Wake Field
Vwr
/VS
: Bare Hull Simulation
Vwr
/VS
: Generated Wake Field
Vwθ
/VS
: Bare Hull Simulation
Vwθ
/VS
: Generated Wake Field
NuTTS 2019 Tomar, Portugal 29 September - 1 October 16

17. Propeller in Behind Condition (w/o Ship)
JS = 0.901 and n = 9.75rps (2.8M + 2.1M cells)
NuTTS 2019 Tomar, Portugal 29 September - 1 October 17

18. Propeller in Behind Condition
Comparison of force coefficients
Azimuth [deg]
KT
72 144 216 288 360
0.010
0.020
0.030
0.040
0.050
0.060
Propeller in Behind Hull
Propeller in Artificial Wake
Blade Thrust Coefficient
Azimuth [deg]
10KQ
72 144 216 288 360
0.030
0.040
0.050
0.060
0.070
0.080
0.090
0.100
Propeller in Behind Hull
Propeller in Artificial Wake
Blade Torque Coefficient
Azimuth [deg]
KT
72 144 216 288 360
0.160
0.162
0.164
0.166
0.168
0.170
0.172
Propeller in Behind Hull
Propeller in Artificial Wake
Propeller Thrust Coefficient
Azimuth [deg]
10KQ
72 144 216 288 360
0.290
0.295
0.300
0.305
Propeller in Behind Hull
Propeller in Artificial Wake
Propeller Torque Coefficient
NuTTS 2019 Tomar, Portugal 29 September - 1 October 18

19. Propeller in Behind Condition
Mean, first and second harmonic amplitudes of the blade frequency
Behind Hull Artificial Wake
n K
(n)
T 10K
(n)
Q K
(n)
T 10K
(n)
Q
0 0.1660 0.2985 0.1630 0.2930
1 0.0025 0.0034 0.0017 0.0019
2 0.0002 0.0002 0.0002 0.0003
KT,Q (θ) = K
(0)
T,Q + K
(1)
T,Q sin Zθ + φ(1) + K
(2)
T,Q sin 2Zθ + φ(2)
NuTTS 2019 Tomar, Portugal 29 September - 1 October 19

20. Conclusions
NuTTS 2019 Tomar, Portugal 29 September - 1 October 20

21. Conclusions
A method for the prediction of the propeller unsteady
performance in an artificially generated wake field using
(iteratively calibrated) body-forces is presented.
NuTTS 2019 Tomar, Portugal 29 September - 1 October 20

22. Conclusions
A method for the prediction of the propeller unsteady
performance in an artificially generated wake field using
(iteratively calibrated) body-forces is presented.
This method offers an alternative to the full RANSE approach.
NuTTS 2019 Tomar, Portugal 29 September - 1 October 20

23. Conclusions
A method for the prediction of the propeller unsteady
performance in an artificially generated wake field using
(iteratively calibrated) body-forces is presented.
This method offers an alternative to the full RANSE approach.
The two approaches are compared, where minor differences in
the order of 1.8% are obtained for the mean propeller force
coefficients.
NuTTS 2019 Tomar, Portugal 29 September - 1 October 20

24. Conclusions
Main reasons for the differences:
NuTTS 2019 Tomar, Portugal 29 September - 1 October 21

25. Conclusions
Main reasons for the differences:
Artificial wake field present differences higher than 10% (at
inner radii) in respect to the ship velocity. Attributed to the
strong interaction between the axial and transversal wake flows.
NuTTS 2019 Tomar, Portugal 29 September - 1 October 21

26. Conclusions
Main reasons for the differences:
Artificial wake field present differences higher than 10% (at
inner radii) in respect to the ship velocity. Attributed to the
strong interaction between the axial and transversal wake flows.
The nominal wake field is considered for the propeller
simulations without hull. May contribute for the
under-prediction of the propeller forces.
NuTTS 2019 Tomar, Portugal 29 September - 1 October 21

27. Thank You!
c new wave media
NuTTS 2019 Tomar, Portugal 29 September - 1 October 22

28. Wake Field Modelling
Computational domain and boundary conditions
Cylindrical domain (size 5D)
Inflow b.c./body forces
Hub field: r/R < 0.2
Wake field: 0.2 ≤ r/R ≤ 1.2
Transition field: 1.2 < r/R < 2.0
Uniform inflow field: r/R ≥ 2.0
Tu=1% and µt/µ = 1
Farfield: pressure b.c.
Outlet: outflow b.c.
NuTTS 2019 Tomar, Portugal 29 September - 1 October 23

29. Wake Field Modelling
Boundary condition at the inlet/force field
Hub field: cubic
Hermite interpolator
Wake field:
Fourier function
Transition field: cubic
Hermite interpolator
Uniform infow field:
Vwx /VS = 1.0
y/R
z/R
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0 V23: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33
Vwx / VS:
Hub Field
Uniform Inflow Field
Transition Field
Wake Field
NuTTS 2019 Tomar, Portugal 29 September - 1 October 24

30. Decomposition of the Wake Field for a Propeller
Total velocity is the velocity at the propeller plane when the propeller is operating at the stern of the ship.
Nominal velocity is the velocity at the propeller plane when the propeller is absent.
Propeller induced velocity is the velocity at the propeller plane induced by the propeller.
Interaction velocity is the velocity at the propeller plane due to the interaction of the propeller with the nominal wake.
Effective velocity = Total velocity - Propeller induced velocity.
Effective velocity = Nominal velocity + Interaction velocity.
NuTTS 2019 Tomar, Portugal 29 September - 1 October 25

31. Nominal Wake Field Generation
Questions
NuTTS 2019 Tomar, Portugal 29 September - 1 October 26

32. Nominal Wake Field Generation
Iterative Convergence
Iteration
0 5000 10000 15000
10-7
10-6
10-5
10
-4
10-3
10-2
10-1
10
0
VX
VY
VZ
p
k
ω
L∞
Iteration
0 5000 10000 15000
10-9
10-8
10-7
10
-6
10-5
10-4
10-3
10
-2
VX
VY
VZ
p
k
ω
L2
NuTTS 2019 Tomar, Portugal 29 September - 1 October 27

33. Nominal Wake Field Generation
Iterative calibration of the body forces - Iter 1
y/R
z/R
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0Vwx: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33Vwx / VS:
VS
Iteration
max|eVw|[%]
mean|eVw|[%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
0
2
4
6
8
10
12mean|eVwx |
max|eVwx
|
mean|eVwy
|
max|eVwy
|
mean|eVwz
|
max|eVwz |
NuTTS 2019 Tomar, Portugal 29 September - 1 October 28

34. Nominal Wake Field Generation
Iterative calibration of the body forces - Iter 2
y/R
z/R
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0Vwx: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33Vwx / VS:
VS
Iteration
max|eVw|[%]
mean|eVw|[%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
0
2
4
6
8
10
12mean|eVwx |
max|eVwx
|
mean|eVwy
|
max|eVwy
|
mean|eVwz
|
max|eVwz |
NuTTS 2019 Tomar, Portugal 29 September - 1 October 29

35. Nominal Wake Field Generation
Iterative calibration of the body forces - Iter 3
y/R
z/R
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0Vwx: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33Vwx / VS:
VS
Iteration
max|eVw|[%]
mean|eVw|[%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
0
2
4
6
8
10
12mean|eVwx |
max|eVwx
|
mean|eVwy
|
max|eVwy
|
mean|eVwz
|
max|eVwz |
NuTTS 2019 Tomar, Portugal 29 September - 1 October 30

36. Nominal Wake Field Generation
Iterative calibration of the body forces - Iter 4
y/R
z/R
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0Vwx: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33Vwx / VS:
VS
Iteration
max|eVw|[%]
mean|eVw|[%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
0
2
4
6
8
10
12mean|eVwx |
max|eVwx
|
mean|eVwy
|
max|eVwy
|
mean|eVwz
|
max|eVwz |
NuTTS 2019 Tomar, Portugal 29 September - 1 October 31

37. Nominal Wake Field Generation
Iterative calibration of the body forces - Iter 5
y/R
z/R
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0Vwx: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33Vwx / VS:
VS
Iteration
max|eVw|[%]
mean|eVw|[%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
0
2
4
6
8
10
12mean|eVwx |
max|eVwx
|
mean|eVwy
|
max|eVwy
|
mean|eVwz
|
max|eVwz |
NuTTS 2019 Tomar, Portugal 29 September - 1 October 32

38. Nominal Wake Field Generation
Iterative calibration of the body forces - Iter 6
y/R
z/R
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0Vwx: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33Vwx / VS:
VS
Iteration
max|eVw|[%]
mean|eVw|[%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
0
2
4
6
8
10
12mean|eVwx |
max|eVwx
|
mean|eVwy
|
max|eVwy
|
mean|eVwz
|
max|eVwz |
NuTTS 2019 Tomar, Portugal 29 September - 1 October 33

39. Nominal Wake Field Generation
Iterative calibration of the body forces - Iter 7
y/R
z/R
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0Vwx: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33Vwx / VS:
VS
Iteration
max|eVw|[%]
mean|eVw|[%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
0
2
4
6
8
10
12mean|eVwx |
max|eVwx
|
mean|eVwy
|
max|eVwy
|
mean|eVwz
|
max|eVwz |
NuTTS 2019 Tomar, Portugal 29 September - 1 October 34

40. Nominal Wake Field Generation
Iterative calibration of the body forces - Iter 8
y/R
z/R
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0Vwx: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33Vwx / VS:
VS
Iteration
max|eVw|[%]
mean|eVw|[%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
0
2
4
6
8
10
12mean|eVwx |
max|eVwx
|
mean|eVwy
|
max|eVwy
|
mean|eVwz
|
max|eVwz |
NuTTS 2019 Tomar, Portugal 29 September - 1 October 35

41. Nominal Wake Field Generation
Iterative calibration of the body forces - Iter 9
y/R
z/R
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0Vwx: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33Vwx / VS:
VS
Iteration
max|eVw|[%]
mean|eVw|[%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
0
2
4
6
8
10
12mean|eVwx |
max|eVwx
|
mean|eVwy
|
max|eVwy
|
mean|eVwz
|
max|eVwz |
NuTTS 2019 Tomar, Portugal 29 September - 1 October 36

42. Nominal Wake Field Generation
Iterative calibration of the body forces - Iter 11
y/R
z/R
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0Vwx: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33Vwx / VS:
VS
Iteration
max|eVw|[%]
mean|eVw|[%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
0
2
4
6
8
10
12mean|eVwx |
max|eVwx
|
mean|eVwy
|
max|eVwy
|
mean|eVwz
|
max|eVwz |
NuTTS 2019 Tomar, Portugal 29 September - 1 October 37

43. Nominal Wake Field Generation
Iterative calibration of the body forces - Iter 12
y/R
z/R
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0Vwx: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33Vwx / VS:
VS
Iteration
max|eVw|[%]
mean|eVw|[%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
0
2
4
6
8
10
12mean|eVwx |
max|eVwx
|
mean|eVwy
|
max|eVwy
|
mean|eVwz
|
max|eVwz |
NuTTS 2019 Tomar, Portugal 29 September - 1 October 38

44. Nominal Wake Field Generation
Iterative calibration of the body forces - Iter 13
y/R
z/R
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0Vwx: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33Vwx / VS:
VS
Iteration
max|eVw|[%]
mean|eVw|[%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
0
2
4
6
8
10
12mean|eVwx |
max|eVwx
|
mean|eVwy
|
max|eVwy
|
mean|eVwz
|
max|eVwz |
NuTTS 2019 Tomar, Portugal 29 September - 1 October 39

45. Nominal Wake Field Generation
Iterative calibration of the body forces - Iter 14
y/R
z/R
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0Vwx: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33Vwx / VS:
VS
Iteration
max|eVw|[%]
mean|eVw|[%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
0
2
4
6
8
10
12mean|eVwx |
max|eVwx
|
mean|eVwy
|
max|eVwy
|
mean|eVwz
|
max|eVwz |
NuTTS 2019 Tomar, Portugal 29 September - 1 October 40

46. Nominal Wake Field Generation
Iterative calibration of the body forces - Iter 15
y/R
z/R
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0Vwx: -0.89 -0.81 -0.73 -0.65 -0.57 -0.49 -0.41 -0.33Vwx / VS:
VS
Iteration
max|eVw|[%]
mean|eVw|[%]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
20
40
60
0
2
4
6
8
10
12mean|eVwx |
max|eVwx
|
mean|eVwy
|
max|eVwy
|
mean|eVwz
|
max|eVwz |
NuTTS 2019 Tomar, Portugal 29 September - 1 October 41