The goal of the present work is to improve the prediction of propeller performance at model-scale using a local correlation transition model. Results are presented for two marine propellers for which paint-tests have been conducted and experimental open-water data is available. The numerical results using the k-\omega SST turbulence model and the \gamma-Re_\theta transition model are compared with the experiments. In order to distinguish between numerical and modelling errors in the comparison with experimental results, a verification study using a range of geometrically similar grids with different grid densities is made. The influence of the turbulence inlet quantities on the numerical results is discussed and boundary-layer characteristics are presented. Finally, the numerical predictions are compared with the experimental results. An improvement in the flow pattern is achieved with the transition model. However, the model strongly depends on the turbulence inlet quantities for the prediction of the transition location. Both propellers show an increase in thrust of 2% to 4% and similar torque when using the transition model.

1. On the Use of the γ − ˜Reθ Transition Model
for the Prediction of the Propeller Performance
at Model-Scale
J. Baltazar1, D. Rijpkema2, J.A.C. Falc˜ao de Campos1
1Instituto Superior T´ecnico, Universidade de Lisboa, Portugal
2Maritime Research Institute Netherlands, Wageningen, the Netherlands
smp’17 Espoo, Finland June 12-15 1

2. Introduction
smp’17 Espoo, Finland June 12-15 2

3. Introduction
Full-scale prediction propellers mostly based on simple
extrapolation methods from model-scale experiments
smp’17 Espoo, Finland June 12-15 2

4. Introduction
Full-scale prediction propellers mostly based on simple
extrapolation methods from model-scale experiments
RANS solvers may be used at both model and full scale and
offer an alternative scaling method
smp’17 Espoo, Finland June 12-15 2

5. Introduction
Full-scale prediction propellers mostly based on simple
extrapolation methods from model-scale experiments
RANS solvers may be used at both model and full scale and
offer an alternative scaling method
Requires accurate prediction at both Reynolds numbers
smp’17 Espoo, Finland June 12-15 2

6. Introduction
Turbulence models (k − ω, SST, k −
√
kL, etc.) are known to
provide a good prediction for fully developed turbulent flows
smp’17 Espoo, Finland June 12-15 3

7. Introduction
Turbulence models (k − ω, SST, k −
√
kL, etc.) are known to
provide a good prediction for fully developed turbulent flows
However, these models predict transition at lower Reynolds
number than seen in experiments
smp’17 Espoo, Finland June 12-15 3

8. Introduction
Turbulence models (k − ω, SST, k −
√
kL, etc.) are known to
provide a good prediction for fully developed turbulent flows
However, these models predict transition at lower Reynolds
number than seen in experiments
Model-scale experiments in critical Reynolds number regime
smp’17 Espoo, Finland June 12-15 3

9. Introduction
Turbulence models (k − ω, SST, k −
√
kL, etc.) are known to
provide a good prediction for fully developed turbulent flows
However, these models predict transition at lower Reynolds
number than seen in experiments
Model-scale experiments in critical Reynolds number regime
Improve the prediction of the propeller performance prediction at
model-scale using the RANS equations complemented with the
k − ω SST turbulence model and the γ − ˜Reθ transition model
smp’17 Espoo, Finland June 12-15 3

10. Overview
smp’17 Espoo, Finland June 12-15 4

11. Overview
Two marine propellers: conventional and skewed propellers
smp’17 Espoo, Finland June 12-15 4

12. Overview
Two marine propellers: conventional and skewed propellers
Estimation of the numerical errors: round-off error (negligible),
iterative error and discretisation error
smp’17 Espoo, Finland June 12-15 4

13. Overview
Two marine propellers: conventional and skewed propellers
Estimation of the numerical errors: round-off error (negligible),
iterative error and discretisation error
Influence of the turbulence inlet quantities
smp’17 Espoo, Finland June 12-15 4

14. Overview
Two marine propellers: conventional and skewed propellers
Estimation of the numerical errors: round-off error (negligible),
iterative error and discretisation error
Influence of the turbulence inlet quantities
Comparison with paint-tests
smp’17 Espoo, Finland June 12-15 4

15. Overview
Two marine propellers: conventional and skewed propellers
Estimation of the numerical errors: round-off error (negligible),
iterative error and discretisation error
Influence of the turbulence inlet quantities
Comparison with paint-tests
Boundary-layer analysis
smp’17 Espoo, Finland June 12-15 4

16. Overview
Two marine propellers: conventional and skewed propellers
Estimation of the numerical errors: round-off error (negligible),
iterative error and discretisation error
Influence of the turbulence inlet quantities
Comparison with paint-tests
Boundary-layer analysis
Prediction of open-water performance
smp’17 Espoo, Finland June 12-15 4

17. RANS Code ReFRESCO
smp’17 Espoo, Finland June 12-15 5

18. RANS Code ReFRESCO
Viscous flow CFD solver developed within a cooperation led by
MARIN
smp’17 Espoo, Finland June 12-15 5

19. RANS Code ReFRESCO
Viscous flow CFD solver developed within a cooperation led by
MARIN
Solves the incompressible RANS equations, complemented with
turbulence/transition models
smp’17 Espoo, Finland June 12-15 5

20. RANS Code ReFRESCO
Viscous flow CFD solver developed within a cooperation led by
MARIN
Solves the incompressible RANS equations, complemented with
turbulence/transition models
The equations are discretised using a finite-volume approach
with cell-centred collocation variables
smp’17 Espoo, Finland June 12-15 5

21. Performance Prediction at Model-Scale
smp’17 Espoo, Finland June 12-15 6

22. Performance Prediction at Model-Scale
Turbulence model: k − ω SST 2-equation model proposed by
Menter et al. (2003)
smp’17 Espoo, Finland June 12-15 6

23. Performance Prediction at Model-Scale
Turbulence model: k − ω SST 2-equation model proposed by
Menter et al. (2003)
Transition model: γ − ˜Reθ model proposed by Langtry and
Menter (2009)
smp’17 Espoo, Finland June 12-15 6

24. Performance Prediction at Model-Scale
Turbulence model: k − ω SST 2-equation model proposed by
Menter et al. (2003)
Transition model: γ − ˜Reθ model proposed by Langtry and
Menter (2009)
Second-order convection scheme (QUICK) is used for the
momentum equations
smp’17 Espoo, Finland June 12-15 6

25. Performance Prediction at Model-Scale
Turbulence model: k − ω SST 2-equation model proposed by
Menter et al. (2003)
Transition model: γ − ˜Reθ model proposed by Langtry and
Menter (2009)
Second-order convection scheme (QUICK) is used for the
momentum equations
First-order upwind scheme is used for the turbulence/transition
models
smp’17 Espoo, Finland June 12-15 6

26. Performance Prediction at Model-Scale
Turbulence model: k − ω SST 2-equation model proposed by
Menter et al. (2003)
Transition model: γ − ˜Reθ model proposed by Langtry and
Menter (2009)
Second-order convection scheme (QUICK) is used for the
momentum equations
First-order upwind scheme is used for the turbulence/transition
models
No wall functions are used (y+
∼ 1)
smp’17 Espoo, Finland June 12-15 6

27. Test Cases
Propellers S6368 (left) and S6698 (right)
S6368 S6698
Diameter D [m] 0.2714 0.233
Chord length at r = 0.7R [m] 0.0694 0.121
Number of blades 4 4
Pitch ratio P/D at r = 0.7R 0.757 1.224
Blade-area ratio AE /A0 0.456 0.729
smp’17 Espoo, Finland June 12-15 7

28. Mesh and Numerical Set-up
Multi-block structured grids (GridPro)
Cylindrical Domain (5D):
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29. Mesh and Numerical Set-up
Multi-block structured grids (GridPro)
Cylindrical Domain (5D):
Grid Sizes:
S6368 S6698
Volume Blade y+ Volume Blade y+
G1 34.8M 39K 0.3 64.9M 151K 0.2
G2 17.8M 25K 0.4 31.7M 96K 0.2
G3 8.0M 15K 0.4 15.6M 60K 0.3
G4 4.3M 10K 0.5 8.2M 38K 0.4
G5 2.2M 6K 0.7 3.4M 22K 0.5
G6 1.0M 2K 0.8 1.6M 13K 0.6
smp’17 Espoo, Finland June 12-15 8

30. Estimation of Numerical Errors
smp’17 Espoo, Finland June 12-15 9

31. Estimation of Numerical Errors
Iterative errors: monitored from the residuals
smp’17 Espoo, Finland June 12-15 9

32. Estimation of Numerical Errors
Iterative errors: monitored from the residuals
Turbulence model: residuals ∼ 10−4 to 10−6
smp’17 Espoo, Finland June 12-15 9

33. Estimation of Numerical Errors
Iterative errors: monitored from the residuals
Turbulence model: residuals ∼ 10−4 to 10−6
Transition model: residuals ∼ 10−3 to 10−5, γ ∼ 10−1
smp’17 Espoo, Finland June 12-15 9

34. Estimation of Numerical Errors
Iterative errors: monitored from the residuals
Turbulence model: residuals ∼ 10−4 to 10−6
Transition model: residuals ∼ 10−3 to 10−5, γ ∼ 10−1
The transition model is not as numerically robust as the
turbulence model: iterative convergence becomes more difficult!
smp’17 Espoo, Finland June 12-15 9

35. Estimation of Numerical Errors
Iterative errors: monitored from the residuals
Turbulence model: residuals ∼ 10−4 to 10−6
Transition model: residuals ∼ 10−3 to 10−5, γ ∼ 10−1
The transition model is not as numerically robust as the
turbulence model: iterative convergence becomes more difficult!
Fast iterative convergence of the propeller forces
smp’17 Espoo, Finland June 12-15 9

36. Estimation of Numerical Errors
Iterative errors: monitored from the residuals
Turbulence model: residuals ∼ 10−4 to 10−6
Transition model: residuals ∼ 10−3 to 10−5, γ ∼ 10−1
The transition model is not as numerically robust as the
turbulence model: iterative convergence becomes more difficult!
Fast iterative convergence of the propeller forces
Dicretisation errors: estimated from a numerical uncertainty
analysis
smp’17 Espoo, Finland June 12-15 9

37. Estimation of Numerical Errors
Iterative errors: monitored from the residuals
Turbulence model: residuals ∼ 10−4 to 10−6
Transition model: residuals ∼ 10−3 to 10−5, γ ∼ 10−1
The transition model is not as numerically robust as the
turbulence model: iterative convergence becomes more difficult!
Fast iterative convergence of the propeller forces
Dicretisation errors: estimated from a numerical uncertainty
analysis
Convergence of the propeller forces with grid density.
Differences lower than 1% for grids with 8M cells
smp’17 Espoo, Finland June 12-15 9

38. Estimation of Numerical Errors
Iterative errors: monitored from the residuals
Turbulence model: residuals ∼ 10−4 to 10−6
Transition model: residuals ∼ 10−3 to 10−5, γ ∼ 10−1
The transition model is not as numerically robust as the
turbulence model: iterative convergence becomes more difficult!
Fast iterative convergence of the propeller forces
Dicretisation errors: estimated from a numerical uncertainty
analysis
Convergence of the propeller forces with grid density.
Differences lower than 1% for grids with 8M cells
Numerical uncertainties are in the order of 1%-2%
smp’17 Espoo, Finland June 12-15 9

39. Influence of Turbulence Inlet Quantities
smp’17 Espoo, Finland June 12-15 10

40. Influence of Turbulence Inlet Quantities
Turbulence models predict strong decay of turbulence quantities
from the inlet along the streamwise direction. Analytical solution
for uniform axial flow
smp’17 Espoo, Finland June 12-15 10

41. Influence of Turbulence Inlet Quantities
Turbulence models predict strong decay of turbulence quantities
from the inlet along the streamwise direction. Analytical solution
for uniform axial flow
Small influence of the turbulence inlet quantities for common
turbulence models. Default values of Tu=1% and µt/µ = 1
smp’17 Espoo, Finland June 12-15 10

42. Influence of Turbulence Inlet Quantities
Turbulence models predict strong decay of turbulence quantities
from the inlet along the streamwise direction. Analytical solution
for uniform axial flow
Small influence of the turbulence inlet quantities for common
turbulence models. Default values of Tu=1% and µt/µ = 1
γ − ˜Reθ model shows a strong sensitivity to the turbulence inlet
quantities
smp’17 Espoo, Finland June 12-15 10

43. Influence of Turbulence Inlet Quantities
Turbulence models predict strong decay of turbulence quantities
from the inlet along the streamwise direction. Analytical solution
for uniform axial flow
Small influence of the turbulence inlet quantities for common
turbulence models. Default values of Tu=1% and µt/µ = 1
γ − ˜Reθ model shows a strong sensitivity to the turbulence inlet
quantities
Sensitivity study of the turbulence inlet quantities for
turbulence/transition models
smp’17 Espoo, Finland June 12-15 10

44. Influence of Turbulence Inlet Quantities
Turbulence models predict strong decay of turbulence quantities
from the inlet along the streamwise direction. Analytical solution
for uniform axial flow
Small influence of the turbulence inlet quantities for common
turbulence models. Default values of Tu=1% and µt/µ = 1
γ − ˜Reθ model shows a strong sensitivity to the turbulence inlet
quantities
Sensitivity study of the turbulence inlet quantities for
turbulence/transition models
May result in unrealistic turbulence levels at the inlet for
γ − ˜Reθ model
smp’17 Espoo, Finland June 12-15 10

45. Influence of Turbulence Inlet Quantities
Propeller S6368 at J = 0.568 and Re=4.5×105
Inlet x/R = 10 x/R = 1 Forces
Model Tu µt/µ Tu µt/µ KT 10KQ
k − ω SST 1.0% 1 0.2% 0.8 0.112 0.166
k − ω SST 1.0% 500 1.0% 115.3 0.112 0.166
k − ω SST 2.5% 500 2.2% 489.2 0.112 0.166
γ − ˜Reθ 1.0% 1 0.2% 0.8 0.121 0.163
γ − ˜Reθ 1.0% 500 1.0% 109.3 0.121 0.163
γ − ˜Reθ 2.5% 500 2.2% 489.4 0.117 0.164
γ − ˜Reθ 5.0% 500 3.3% 467.3 0.116 0.167
smp’17 Espoo, Finland June 12-15 11

46. Influence of Turbulence Inlet Quantities
γ − ˜Reθ Model: Propeller S6368 at J = 0.568 and Re=4.5×105
Tu=1.0% Tu=1.0% Tu=2.5% Tu=5.0%
µt/µ = 1 µt/µ = 500 µt/µ = 500 µt/µ = 500
smp’17 Espoo, Finland June 12-15 12

47. Influence of Turbulence Inlet Quantities
γ − ˜Reθ Model: Propeller S6368 at J = 0.568 and Re=4.5×105
Tu=1.0% Tu=1.0% Tu=2.5% Tu=5.0%
µt/µ = 1 µt/µ = 500 µt/µ = 500 µt/µ = 500
smp’17 Espoo, Finland June 12-15 12

48. Influence of Turbulence Inlet Quantities
γ − ˜Reθ Model: Propeller S6368 at J = 0.568 and Re=4.5×105
Tu=1.0% Tu=1.0% Tu=2.5% Tu=5.0%
µt/µ = 1 µt/µ = 500 µt/µ = 500 µt/µ = 500
smp’17 Espoo, Finland June 12-15 12

49. Influence of Turbulence Inlet Quantities
γ − ˜Reθ Model: Propeller S6368 at J = 0.568 and Re=4.5×105
Tu=1.0% Tu=1.0% Tu=2.5% Tu=5.0%
µt/µ = 1 µt/µ = 500 µt/µ = 500 µt/µ = 500
smp’17 Espoo, Finland June 12-15 12

50. Influence of Turbulence Inlet Quantities
γ − ˜Reθ Model: Propeller S6368 at J = 0.568 and Re=4.5×105
Tu=1.0% Tu=1.0% Tu=2.5% Tu=5.0%
µt/µ = 1 µt/µ = 500 µt/µ = 500 µt/µ = 500
smp’17 Espoo, Finland June 12-15 12

51. Influence of Turbulence Inlet Quantities
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.05
0.08
0.10
r/R=0.70
Cf
smp’17 Espoo, Finland June 12-15 13

52. Influence of Turbulence Inlet Quantities
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.05
0.08
0.10
r/R=0.70
Cf
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.05
0.08
0.10
r/R=0.70
Cf
Tu=1.0%, µt
/µ=1, k-ω SST
smp’17 Espoo, Finland June 12-15 13

53. Influence of Turbulence Inlet Quantities
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.05
0.08
0.10
r/R=0.70
Cf
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.05
0.08
0.10
r/R=0.70
Cf
Tu=1.0%, µt
/µ=1, k-ω SST
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.05
0.08
0.10
r/R=0.70
Cf
Tu=1.0%, µt
/µ=1, γ-ReθTu=1.0%, µt
/µ=1, k-ω SST
smp’17 Espoo, Finland June 12-15 13

54. Influence of Turbulence Inlet Quantities
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.05
0.08
0.10
r/R=0.70
Cf
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.05
0.08
0.10
r/R=0.70
Cf
Tu=1.0%, µt
/µ=1, k-ω SST
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.05
0.08
0.10
r/R=0.70
Cf
Tu=1.0%, µt
/µ=1, γ-ReθTu=1.0%, µt
/µ=1, k-ω SST
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.05
0.08
0.10
r/R=0.70
Cf
Tu=1.0%, µt
/µ=1, γ-Reθ
Tu=2.5%, µt
/µ=500, γ-Reθ
Tu=1.0%, µt
/µ=1, k-ω SST
smp’17 Espoo, Finland June 12-15 13

55. Influence of Turbulence Inlet Quantities
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.05
0.08
0.10
r/R=0.70
Cf
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.05
0.08
0.10
r/R=0.70
Cf
Tu=1.0%, µt
/µ=1, k-ω SST
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.05
0.08
0.10
r/R=0.70
Cf
Tu=1.0%, µt
/µ=1, γ-ReθTu=1.0%, µt
/µ=1, k-ω SST
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.05
0.08
0.10
r/R=0.70
Cf
Tu=1.0%, µt
/µ=1, γ-Reθ
Tu=2.5%, µt
/µ=500, γ-Reθ
Tu=1.0%, µt
/µ=1, k-ω SST
s/c
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.03
0.05
0.08
0.10
r/R=0.70
Cf
Tu=1.0%, µt
/µ=1, γ-Reθ
Tu=2.5%, µt
/µ=500, γ-Reθ
Tu=5.0%, µt
/µ=500, γ-Reθ
Tu=1.0%, µt
/µ=1, k-ω SST
smp’17 Espoo, Finland June 12-15 13

56. Comparison with Paint-Tests
Propeller S6368 at J = 0.568 and Re=4.5×105
smp’17 Espoo, Finland June 12-15 14

57. Comparison with Paint-Tests
Propeller S6368 at J = 0.568 and Re=4.5×105
k − ω SST γ − ˜Reθ Paint
Tu=1.0% Tu=2.5% Tests
µt/µ = 1 µt/µ = 500
(Suction Side)
smp’17 Espoo, Finland June 12-15 14

58. Comparison with Paint-Tests
Propeller S6368 at J = 0.568 and Re=4.5×105
k − ω SST γ − ˜Reθ Paint
Tu=1.0% Tu=2.5% Tests
µt/µ = 1 µt/µ = 500
(Pressure Side)
smp’17 Espoo, Finland June 12-15 15

59. Pressure and Friction Contributions
Propeller Forces for S6368 at J = 0.568 and Re=4.5×105
Model Tu µt/µ KTp KTf
KT
γ − ˜Reθ 1.0% 500 0.122 -0.00107 0.121
γ − ˜Reθ 2.5% 500 0.118 -0.00177 0.117
k − ω SST 1.0% 1 0.115 -0.00241 0.112
Exp. – – – – 0.129
Exp. (LER) – – – – 0.118
Model Tu µt/µ 10KQp 10KQf
10KQ
γ − ˜Reθ 1.0% 500 0.151 0.0118 0.163
γ − ˜Reθ 2.5% 500 0.145 0.0197 0.164
k − ω SST 1.0% 1 0.141 0.0258 0.166
Exp. – – – – 0.174
Exp. (LER) – – – – 0.176
smp’17 Espoo, Finland June 12-15 16

60. Boundary-Layer Analysis
Chordwise Vs and radial Vt velocity profiles (s/c = 0.6 and r/R = 0.3)
(Suction) (Pressure)
V/(ΩR)
n/R
0.0 0.1 0.2 0.3 0.4 0.5
0.000
0.002
0.004
0.006
Vs: k-ω SST, Tu=1.0%, µt /µ=1
Vt
Vs: γ-Reθ , Tu=2.5%, µt /µ=500
Vt
k-ω SST: δ/R=0.0044
γ-Reθ
: δ/R=0.0037
V/(ΩR)
n/R
0.0 0.1 0.2 0.3 0.4
0.000
0.003
0.006
0.009
Vs: k-ω SST, Tu=1.0%, µt /µ=1
Vt
Vs: γ-Reθ , Tu=2.5%, µt /µ=500
Vt
k-ω SST: δ/R=0.0070
γ-Reθ: δ/R=0.0051
smp’17 Espoo, Finland June 12-15 17

61. Comparison with Paint-Tests
Propeller S6698 at J = 0.87 and Re=7.3×105
k − ω SST Paint
Tu=1.0% Tests
µt/µ = 1
(Suction Side)
smp’17 Espoo, Finland June 12-15 18

62. Comparison with Paint-Tests
Propeller S6698 at J = 0.87 and Re=7.3×105
γ − ˜Reθ Paint
Tu=2.5% Tests
µt/µ = 500
(Suction Side)
smp’17 Espoo, Finland June 12-15 19

63. Comparison with Paint-Tests
Propeller S6698 at J = 0.87 and Re=7.3×105
k − ω SST Paint
Tu=1.0% Tests
µt/µ = 1
(Pressure Side)
smp’17 Espoo, Finland June 12-15 20

64. Comparison with Paint-Tests
Propeller S6698 at J = 0.87 and Re=7.3×105
γ − ˜Reθ Paint
Tu=2.5% Tests
µt/µ = 500
(Pressure Side)
smp’17 Espoo, Finland June 12-15 21

65. Open-Water Prediction
S6368 S6698
J
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Experiments
Experiments (LER)
k-ω SST: Tu=1.0%, µt /µ=1
γ-Reθ: Tu=2.5%, µt /µ=500
KT
10KQ
η
J
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Experiments
k-ω SST: Tu=1.0%, µt /µ=1
γ-Reθ: Tu=2.5%, µt /µ=500
KT
10KQ
η
smp’17 Espoo, Finland June 12-15 22

66. Comparison Between Numerical and Experimental
Results (Comparison Error E)
Model J
KT KQ
E Unum E Unum
S6368
k − ω SST 0.300 -5.61% 0.49% -3.08% 1.16%
k − ω SST 0.568 -13.31% 1.13% -5.05% 1.70%
γ − ˜Reθ 0.300 -3.35% 1.72% -3.34% 1.38%
γ − ˜Reθ 0.568 -9.46% 0.88% -6.36% 0.84%
S6698
k − ω SST 0.300 0.30% 0.57% 0.89% 1.58%
k − ω SST 0.870 -1.67% 1.51% 3.60% 0.34%
γ − ˜Reθ 0.300 1.59% 1.41% 1.61% 1.40%
γ − ˜Reθ 0.870 0.51% 0.56% 3.03% 0.34%
smp’17 Espoo, Finland June 12-15 23

67. Conclusions
smp’17 Espoo, Finland June 12-15 24

68. Conclusions
Turbulence model is insensitive to the inlet turbulence
parameters. A (fully) turbulent flow solution is obtained
smp’17 Espoo, Finland June 12-15 24

69. Conclusions
Turbulence model is insensitive to the inlet turbulence
parameters. A (fully) turbulent flow solution is obtained
A strong sensitivity to the inlet turbulence parameters
(Tu and µt/µ) is found for the transition model
smp’17 Espoo, Finland June 12-15 24

70. Conclusions
Turbulence model is insensitive to the inlet turbulence
parameters. A (fully) turbulent flow solution is obtained
A strong sensitivity to the inlet turbulence parameters
(Tu and µt/µ) is found for the transition model
Inlet turbulence values are recommended (Tu=2.5% and
µt/µ = 500) for the transition model. A qualitative agreement
is found between the paint-tests and the limiting streamlines
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71. Conclusions
Turbulence model is insensitive to the inlet turbulence
parameters. A (fully) turbulent flow solution is obtained
A strong sensitivity to the inlet turbulence parameters
(Tu and µt/µ) is found for the transition model
Inlet turbulence values are recommended (Tu=2.5% and
µt/µ = 500) for the transition model. A qualitative agreement
is found between the paint-tests and the limiting streamlines
Transition model versus turbulence model:
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72. Conclusions
Turbulence model is insensitive to the inlet turbulence
parameters. A (fully) turbulent flow solution is obtained
A strong sensitivity to the inlet turbulence parameters
(Tu and µt/µ) is found for the transition model
Inlet turbulence values are recommended (Tu=2.5% and
µt/µ = 500) for the transition model. A qualitative agreement
is found between the paint-tests and the limiting streamlines
Transition model versus turbulence model:
Increase in thrust (2-4%) due to higher lift forces (cambering)
and lower shear stresses
smp’17 Espoo, Finland June 12-15 24

73. Conclusions
Turbulence model is insensitive to the inlet turbulence
parameters. A (fully) turbulent flow solution is obtained
A strong sensitivity to the inlet turbulence parameters
(Tu and µt/µ) is found for the transition model
Inlet turbulence values are recommended (Tu=2.5% and
µt/µ = 500) for the transition model. A qualitative agreement
is found between the paint-tests and the limiting streamlines
Transition model versus turbulence model:
Increase in thrust (2-4%) due to higher lift forces (cambering)
and lower shear stresses
Small variation in torque due to higher lift and lower friction
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74. Conclusions
Turbulence model is insensitive to the inlet turbulence
parameters. A (fully) turbulent flow solution is obtained
A strong sensitivity to the inlet turbulence parameters
(Tu and µt/µ) is found for the transition model
Inlet turbulence values are recommended (Tu=2.5% and
µt/µ = 500) for the transition model. A qualitative agreement
is found between the paint-tests and the limiting streamlines
Transition model versus turbulence model:
Increase in thrust (2-4%) due to higher lift forces (cambering)
and lower shear stresses
Small variation in torque due to higher lift and lower friction
Better agreement (1-10%) for the conventional propeller
(S6368) with transition model and similar results
(1-9%) for skewed propeller (S6698)
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75. Boundary-Layer Thickness
Estimated from total pressure loss: C∆pt = −0.01
s/c
δ/c
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
r/R=0.30 - k-ω SST: Tu=1.0%, µt /µ=1
r/R=0.50
r/R=0.70
r/R=0.30 - γ-Reθ : Tu=2.5%, µt /µ=500
r/R=0.50
r/R=0.70
s/c
δ/c
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.00
0.01
0.02
0.03
0.04
0.05
r/R=0.30 - k-ω SST: Tu=1.0%, µt /µ=1
r/R=0.50
r/R=0.70
r/R=0.30 - γ-Reθ : Tu=2.5%, µt /µ=500
r/R=0.50
r/R=0.70
(Suction Side) (Pressure Side)
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76. Pressure and Friction Contributions
Propeller Forces for S6698 at J = 0.87 and Re=7.3×105
Model Tu µt/µ KTp KTf
KT
γ − ˜Reθ 1.0% 500 0.166 -0.00330 0.163
γ − ˜Reθ 2.5% 500 0.162 -0.00520 0.157
k − ω SST 1.0% 1 0.160 -0.00638 0.154
Exp. – – – – 0.1555
Model Tu µt/µ 10KQp 10KQf
10KQ
γ − ˜Reθ 1.0% 500 0.310 0.0229 0.333
γ − ˜Reθ 2.5% 500 0.300 0.0421 0.342
k − ω SST 1.0% 1 0.296 0.0499 0.346
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