In this paper a comparison between RANSE simulations carried out with the k-\omega SST turbulence model and \gamma-Re_\theta transition model, and experimental measurements for marine propeller P4119 is made. The experiments were conducted at the David Taylor Model Basin and comprehended three-dimensional velocity components measurements of the blade boundary-layer and wake using a LDV system in uniform conditions. The present work includes an estimation of the numerical errors that occur in the simulations, analysis of the propeller blade flow, chordwise and radial components of the boundary-layer velocities and boundary-layer characteristics. From this comparison and depending on the selected turbulence inlet quantities, we conclude that the transition model is able to predict the extent of laminar and turbulent regions observed in the experiments.

1. Analysis of the Blade Boundary-Layer Flow
of a Marine Propeller With RANSE
J. Baltazar1
, D. Melo1
, D. Rijpkema2
1Instituto Superior Técnico, Universidade de Lisboa, Portugal
2Maritime Research Institute Netherlands, Wageningen, the Netherlands
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2. Objectives
Comparison between RANS simulations and experimental data
from LDV measurements in the DTRC water tunnel for marine
propeller P4119 (Jessup, 1989):
D [m] 0.3048
c0.7R [m] 0.1409
Z 3
P/D0.7R 1.0839
AE /A0 0.5
Contribute to the understanding of the blade boundary-layer flow
modelling.
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3. Performance Prediction at Model-Scale
RANSE solver ReFRESCO
Finite-volume discretisation
Flow variables defined in cell-centres
Turbulence model:
– k − ω SST (Menter et al., 2003)
– Not developed for transition
Transition model:
– γ − R̃eθt (Langtry and Menter, 2009)
– Strong dependency to turbulence intensity Tu
and eddy-viscosity ratio µt/µ
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4. Numerical Set-Up
Cylindrical domain (5D)
6 multi-block structured grids: 1M to 38M cells
No wall functions are used (y+
∼ 1)
Uniform inflow (open-water)
Discretisation of convective flux:
– Momentum: QUICK
– Turbulence/Transition: Upwind
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5. Grid Generation
Grid Volume Blade y+
max
G1 37.6M 73.9k 0.20
G2 21.0M 42.3k 0.24
G3 9.9M 25.6k 0.31
G4 6.1M 18.6k 0.39
G5 1.9M 8.6k 0.51
G6 0.9M 4.9k 0.66
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6. Results Summary
RANS simulations at model-scale (Re ' 9.5 × 105
)
Comparison with experimental data (Jdesign = 0.833)
Evaluation of numerical errors:
– Iterative errors
– Numerical uncertainty estimation
Influence of turbulence quantities:
– Blade flow (limiting streamlines and skin friction)
– Propeller forces
Chordwise and spanwise velocity profiles
Boundary-layer parameters
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7. Evaluation of Iterative Error
k − ω SST turbulence model (Tu =1.0% and µt/µ = 1)
Iteration
L
∞
0 20000 40000 60000 80000 100000
10
-8
10
-7
10-6
10
-5
10
-4
10
-3
10
-2
10
-1
UX
UY
UZ
P
k
ω
L∞
Norm
Iteration
L
2
0 20000 40000 60000 80000 100000
10
-10
10
-9
10-8
10
-7
10
-6
10
-5
10
-4
10
-3
UX
UY
UZ
P
k
ω
L2
Norm
Iteration
0 20000 40000 60000 80000 100000
0.10
0.15
0.20
0.25
0.30
Iteration
0 20000 40000 60000 80000 100000
0.10
0.15
0.20
0.25
0.30
KT
10KQ
Propeller Force Coefficients
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8. Evaluation of Iterative Error
γ − R̃eθt
transition model (Tu =1.5% and µt/µ = 500)
Iteration
L
∞
0 5000 10000 15000 20000 25000
10
-7
10
-6
10-5
10
-4
10
-3
10
-2
10
-1
100
10
1
UX
UY
UZ
P
k
ω
γ
Reθ
L∞
Norm
Iteration
L
2
0 5000 10000 15000 20000 25000
10
-9
10-8
10
-7
10
-6
10
-5
10
-4
10-3
10
-2
10
-1
10
0
UX
UY
UZ
P
k
ω
γ
Reθ
L2
Norm
Iteration
0 5000 10000 15000 20000 25000
0.10
0.15
0.20
0.25
0.30
Iteration
0 5000 10000 15000 20000 25000
0.10
0.15
0.20
0.25
0.30
KT
10KQ
Propeller Force Coefficients
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9. Numerical Uncertainty Estimation
Eça and Hoekstra (2014) procedure
hi
/h1
K
T
0 1 2 3 4
0.140
0.142
0.144
0.146
0.148 k-ω SST : p=0.96 , Unum
=0.55 %
γ-Reθ
: p=1.16 , Unum
=1.03 %
hi
/h1
10K
Q
0 1 2 3 4
0.270
0.273
0.276
0.279
0.282
0.285 k-ω SST : p=1.84 , Unum
=0.20 %
γ-Reθ
: p=1.64 , Unum
=0.51 %
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10. Limiting Streamlines and Skin Friction Coefficient
γ − R̃eθt
transition model (Tu =1.2% and µt/µ = 500)
Pressure Side Suction Side
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11. Limiting Streamlines and Skin Friction Coefficient
γ − R̃eθt
transition model (Tu =1.5% and µt/µ = 500)
Pressure Side Suction Side
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12. Limiting Streamlines and Skin Friction Coefficient
k − ω SST turbulence model (Tu =1.0% and µt/µ = 1)
Pressure Side Suction Side
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13. Influence of Turbulence Quantities
Thrust and torque coefficients (pressure p and friction f contributions)
Model Tu µt/µ KTp KTf
KT
γ − R̃eθt 1.2% 500 0.1498 -0.002470 0.1473
γ − R̃eθt 1.5% 500 0.1476 -0.003373 0.1442
k − ω SST 1.0% 1 0.1463 -0.004460 0.1419
Exp. – – – – 0.146
Model Tu µt/µ 10KQp 10KQf
10KQ
γ − R̃eθt 1.2% 500 0.2529 0.01771 0.2706
γ − R̃eθt 1.5% 500 0.2489 0.02422 0.2731
k − ω SST 1.0% 1 0.2472 0.03117 0.2784
Exp. – – – – 0.280
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14. Blade Boundary-Layer Flow
Chordwise velocity profiles: r/R = 0.7 (suction side)
Vs /Vref
100
y/c
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
γ-Reθt , Tu=1.2%, µt /µ=500, 100δ/c=0.29
γ-Reθt , Tu=1.5%, µt /µ=500, 100δ/c=0.34
k-ω SST, Tu=1.0%, µt /µ=1, 100δ/c=0.63
Experimental (Tripped Blade)
Experimental (Smooth Blade)
s/c=0.3
Vs /Vref
100
y/c
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
γ-Reθt , Tu=1.2%, µt /µ=500, 100δ/c=0.49
γ-Reθt , Tu=1.5%, µt /µ=500, 100δ/c=0.78
k-ω SST, Tu=1.0%, µt /µ=1, 100δ/c=1.01
Experimental (Tripped Blade)
Experimental (Smooth Blade)
s/c=0.5
Vs /Vref
100
y/c
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.3
0.6
0.9
1.2
1.5
1.8
γ-Reθt , Tu=1.2%, µt /µ=500, 100δ/c=0.92
γ-Reθt , Tu=1.5%, µt /µ=500, 100δ/c=1.24
k-ω SST, Tu=1.0%, µt /µ=1, 100δ/c=1.48
Experimental (Tripped Blade)
Experimental (Smooth Blade)
s/c=0.7
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15. Blade Boundary-Layer Flow
Chordwise velocity profiles: r/R = 0.7 (pressure side)
Vs /Vref
100
y/c
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
γ-Reθt , Tu=1.2%, µt /µ=500, 100δ/c=0.31
γ-Reθt , Tu=1.5%, µt /µ=500, 100δ/c=0.32
k-ω SST, Tu=1.0%, µt /µ=1, 100δ/c=0.75
Experimental (Tripped Blade)
Experimental (Smooth Blade)
s/c=0.39
Vs /Vref
100
y/c
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.3
0.6
0.9
1.2
1.5
γ-Reθt , Tu=1.2%, µt /µ=500, 100δ/c=0.39
γ-Reθt , Tu=1.5%, µt /µ=500, 100δ/c=0.51
k-ω SST, Tu=1.0%, µt /µ=1, 100δ/c=1.09
Experimental (Tripped Blade)
Experimental (Smooth Blade)
s/c=0.608
Vs /Vref
100
y/c
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.4
0.8
1.2
1.6
2.0
γ-Reθt , Tu=1.2%, µt /µ=500, 100δ/c=0.50
γ-Reθt , Tu=1.5%, µt /µ=500, 100δ/c=0.99
k-ω SST, Tu=1.0%, µt /µ=1, 100δ/c=1.53
Experimental (Tripped Blade)
Experimental (Smooth Blade)
s/c=0.859
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16. Blade Boundary-Layer Flow
Spanwise velocity profiles: r/R = 0.7 (suction side)
Vt /Vref
100
y/c
-0.05 0.00 0.05 0.10 0.15
0.0
0.2
0.4
0.6
0.8
γ-Reθt , Tu=1.2%, µt /µ=500, 100δ/c=0.29
γ-Reθt , Tu=1.5%, µt /µ=500, 100δ/c=0.55
k-ω SST, Tu=1.0%, µt /µ=1, 100δ/c=0.64
Experimental (Smooth Blade)
s/c=0.31
Vt /Vref
100
y/c
-0.05 0.00 0.05 0.10 0.15
0.0
0.2
0.4
0.6
0.8
1.0
1.2
γ-Reθt , Tu=1.2%, µt /µ=500, 100δ/c=0.49
γ-Reθt , Tu=1.5%, µt /µ=500, 100δ/c=0.78
k-ω SST, Tu=1.0%, µt /µ=1, 100δ/c=1.01
Experimental (Smooth Blade)
s/c=0.5
Vt /Vref
100
y/c
-0.05 0.00 0.05 0.10 0.15
0.0
0.4
0.8
1.2
1.6
γ-Reθt , Tu=1.2%, µt /µ=500, 100δ/c=1.07
γ-Reθt , Tu=1.5%, µt /µ=500, 100δ/c=1.39
k-ω SST, Tu=1.0%, µt /µ=1, 100δ/c=1.60
Experimental (Smooth Blade)
s/c=0.77
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17. Boundary-Layer Characteristics
(Streamwise)
Boundary-layer thickness δ estimation:
– total pressure-loss:
∆pt = P + 1/2ρV 2
t − Pinlet − 1/2ρ
V 2
inlet + (Ω0.7R)2
– C∆pt = ∆pt/(1/2ρV 2
ref ) = −0.01 (Vδ = 0.995Ve)
with V 2
e = Vs(δ)2 + Vt(δ)2
Displacement thickness δ∗
= 1
Ve
δ
R
0
(Vs(δ) − Vs(y))dy
Momentum thickness θ = 1
V 2
e
δ
R
0
(Vs(δ) − Vs(y))Vs(y)dy
Shape factor H = δ∗
θ
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18. Boundary-Layer Characteristics
r/R = 0.7 (suction side)
s/c
100δ/c
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
1.5
2.0
2.5
γ-Reθt , Tu=1.2%, µt /µ=500
γ-Reθt , Tu=1.5%, µt /µ=500
k-ω SST, Tu=1.0%, µt/µ=1
Boundary-Layer Thickness
s/c
100δ
*
/c
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.1
0.2
0.3
0.4
γ-Reθt , Tu=1.2%, µt /µ=500
γ-Reθt , Tu=1.5%, µt /µ=500
k-ω SST, Tu=1.0%, µt/µ=1
Experimental (Tripped Blade)
Experimental (Smooth Blade)
Displacement Thickness
s/c
H
0.0 0.2 0.4 0.6 0.8 1.0
0.5
1.0
1.5
2.0
2.5
3.0
γ-Reθt , Tu=1.2%, µt /µ=500
γ-Reθt
, Tu=1.5%, µt
/µ=500
k-ω SST, Tu=1.0%, µt
/µ=1
Experimental (Tripped Blade)
Experimental (Smooth Blade)
Shape Factor
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19. Boundary-Layer Characteristics
r/R = 0.7 (pressure side)
s/c
100δ/c
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
1.5
2.0
γ-Reθt , Tu=1.2%, µt /µ=500
γ-Reθt , Tu=1.5%, µt /µ=500
k-ω SST, Tu=1.0%, µt
/µ=1
Boundary-Layer Thickness
s/c
100δ
*
/c
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.1
0.2
0.3
0.4
γ-Reθt , Tu=1.2%, µt /µ=500
γ-Reθt , Tu=1.5%, µt /µ=500
k-ω SST, Tu=1.0%, µt
/µ=1
Experimental (Tripped Blade)
Experimental (Smooth Blade)
Displacement Thickness
s/c
H
0.0 0.2 0.4 0.6 0.8 1.0
1.0
1.5
2.0
2.5
3.0
γ-Reθt , Tu=1.2%, µt /µ=500
γ-Reθt
, Tu=1.5%, µt
/µ=500
k-ω SST, Tu=1.0%, µt
/µ=1
Experimental (Tripped Blade)
Experimental (Smooth Blade)
Shape Factor
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20. Conclusions
Evaluation of numerical errors:
– γ − R̃eθt model does not satisfy iterative convergence criterion.
Expected small influence on propeller forces
– Low numerical uncertainties ( 2%) for force coefficients
k − ω SST model correctly predicts the velocity profiles in fully
turbulent region (tripped blade)
γ − R̃eθt model predicts laminar-turbulent transition:
– Strong sensitivity to inlet turbulence quantities
– Selection based on experimental velocity profiles (smooth blade)
– However, may limit the predictive capabilities of the model!
Evolution of the streamwise boundary-layer quantities show
typical laminar and turbulent flow behaviours
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21. Influence of Grid Refinement
Variation of propeller force coefficients
Model k − ω SST γ − R̃eθt
Grid ∆KT ∆KQ ∆η0 ∆KT ∆KQ ∆η0
0.9M 1.0% 1.4% -0.4% -0.6% 2.4% -2.8%
1.9M 0.6% 0.8% -0.3% -0.7% 1.4% -2.1%
6.1M 0.4% 0.3% 0.0% -0.6% 0.6% -1.1%
9.9M 0.2% 0.2% 0.0% -0.6% 0.3% -0.8%
21.0M 0.1% 0.1% 0.0% -0.2% 0.1% -0.3%
37.6M 0.1416 0.2779 0.676 0.1450 0.2722 0.706
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22. Influence of Grid Refinement
Suction side, s/c = 0.2, r/R = 0.7
Vs /Vref
100
y/c
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.1
0.2
0.3
0.4
0.5
Grid with 9.9M cells
Grid with 37.6M cells
k-ω SST Turbulence Model
Vs /Vref
100
y/c
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.1
0.2
0.3
0.4
Grid with 9.9M cells
Grid with 37.6M cells
γ-Reθt
Transition Model
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23. Blade Boundary-Layer Flow
Chordwise velocity profiles: r/R = 0.7 (suction side)
Vs /Vref
100
y/c
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
γ-Reθt , Tu=1.2%, µt /µ=500, 100δ/c=0.23
γ-Reθt , Tu=1.5%, µt /µ=500, 100δ/c=0.22
k-ω SST, Tu=1.0%, µt /µ=1, 100δ/c=0.42
Experimental (Tripped Blade)
Experimental (Smooth Blade)
s/c=0.2
Vs /Vref
100
y/c
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.3
0.6
0.9
1.2
1.5
γ-Reθt , Tu=1.2%, µt /µ=500, 100δ/c=0.69
γ-Reθt , Tu=1.5%, µt /µ=500, 100δ/c=0.98
k-ω SST, Tu=1.0%, µt /µ=1, 100δ/c=1.23
Experimental (Tripped Blade)
Experimental (Smooth Blade)
s/c=0.6
Vs /Vref
100
y/c
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
1.5
2.0
2.5
γ-Reθt , Tu=1.2%, µt /µ=500, 100δ/c=1.47
γ-Reθt , Tu=1.5%, µt /µ=500, 100δ/c=1.83
k-ω SST, Tu=1.0%, µt /µ=1, 100δ/c=2.09
Experimental (Tripped Blade)
Experimental (Smooth Blade)
s/c=0.9
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24. Blade Boundary-Layer Flow
Spanwise velocity profiles: r/R = 0.7 (suction side)
Vt /Vref
100
y/c
-0.05 0.00 0.05 0.10 0.15
0.0
0.2
0.4
0.6
0.8
1.0
γ-Reθt , Tu=1.2%, µt /µ=500, 100δ/c=0.36
γ-Reθt , Tu=1.5%, µt /µ=500, 100δ/c=0.55
k-ω SST, Tu=1.0%, µt /µ=1, 100δ/c=0.82
Experimental (Smooth Blade)
s/c=0.4
Vt /Vref
100
y/c
-0.05 0.00 0.05 0.10 0.15
0.0
0.4
0.8
1.2
1.6
γ-Reθt , Tu=1.2%, µt /µ=500, 100δ/c=0.69
γ-Reθt , Tu=1.5%, µt /µ=500, 100δ/c=0.98
k-ω SST, Tu=1.0%, µt /µ=1, 100δ/c=1.21
Experimental (Smooth Blade)
s/c=0.6
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