Modelling of Laminar-to-Turbulent Flow Transition on a Marine Propeller Using a RANS Solver

Modelling of Laminar-to-Turbulent Flow Transition
on a Marine Propeller Using a RANS Solver
J. Baltazar1
, B. Schuiling2
, M. Kerkvliet2
1Instituto Superior Técnico, Universidade de Lisboa, Portugal
2Maritime Research Institute Netherlands, Wageningen, the Netherlands
NuTTS 2023 Ericeira, Portugal 15-17 October 1

Introduction

Introduction
Full-scale prediction propellers mostly based on simple
extrapolation methods from model-scale experiments

Introduction
RANS solvers may be used at both model and full scale and
offer an alternative scaling method

Introduction
RANS solvers may be used at both model and full scale and
offer an alternative scaling method
Requires accurate prediction at both Reynolds numbers

Introduction
Turbulence models (k − ω, SST, k −
√
kL, etc.) are known to
provide a good prediction for fully developed turbulent flows

Introduction
√
However, these models predict transition at lower Reynolds
number than seen in experiments

Introduction
√
Model-scale experiments in critical Reynolds number regime

Introduction
√
Model-scale experiments in critical Reynolds number regime
Propeller performance prediction at different Reynolds number
regimes using the γ − R̃eθ transition model and compare with
the k − ω SST turbulence model

IST/MARIN Research Project 2021
Improving Propeller Computations at Model-Scale

Extensive experimental campaign carried out at MARIN
in 2020 (4 propellers)

RANS solver ReFRESCO: k − ω SST and γ − R̃eθt

Numerical Studies:
- estimation of the numerical errors
- influence of inlet turbulence quantities
- identification of blade flow regime
- comparison with paint-tests

Numerical Studies:
- estimation of the numerical errors
- influence of inlet turbulence quantities
- identification of blade flow regime
- comparison with paint-tests
J. Baltazar, 2022. Laminar-Turbulent Transition Modelling
on Propellers in Open-Water Conditions with RANS Code
ReFRESCO. IST/MARETEC-TR-3600-7.

Propeller S6368
D [m] 0.2714
c0.7R [m] 0.0694
Z 4
P/D0.7R 0.757
AE /A0 0.464

Experimental Data
n [rps] 6.6(6)1 10.01 12.52 15.01 15.03 20.01
J KT
0.300 0.2344 – 0.2360 0.2390 0.2353
0.568 0.1259 0.1307 0.1290 0.1307 0.1301 0.1279
n [rps] 6.6(6)1 10.01 12.52 15.01 15.03 20.01
J 10KQ
0.300 0.2769 – 0.2712 0.2758 0.2704
0.568 0.1743 0.1731 0.174 0.1724 0.1752 0.1718
1
B. Schuiling, M. Kerkvliet, D. Rijpkema, 2021. How to Paint a Propeller. A Practical Guide to Performing Propeller Paint
Tests and Visualize Turbulence Transition. MARIN Report No. 80358-1-RD.
2
A. Boorsma, 2000. Improving Full Scale Ship Powering Performance Predictions by Application of Propeller Leading Edge
Roughness. Part 1: Effect of Leading Edge Roughness on Propeller Performance. Master Thesis, TU Delft.
3
A. Jonk, H. Willemsen, 1994. Calm Water Model Tests for a 300,000 DWT Crude Oil Carrier. MARIN Report No.
012383-1-VT.

Grid Generation
Volume Blade hi /h1 y+
G1 34.8M 39K 1.0000 0.37
G2 17.8M 25K 1.2495 0.46
G3 8.0M 15K 1.6327 0.58
G4 4.3M 10K 2.0101 0.69
G5 2.2M 6K 2.5038 0.86
G6 1.0M 2K 3.2654 0.95

Iterative Errors
Monitored from the residuals
Turbulence model:
- residuals < 10−6
Transition model:
- residuals ∼ 10−3 to 10−6, γ ∼ 10−1
Fast iterative convergence of the propeller forces

Discretisation Errors
Numerical uncertainty analysis for n = 15 rps (Eça and Hoekstra, 2014)
hi /h1
0 1 2 3 4
0.200
0.210
0.220
0.230
0.240
0.110
0.115
0.120
0.125
0.130
J=0.300: Unum
=2.51%
J=0.568: Unum
=3.37%
KT
(J=0.3)
(J=0.568)
hi /h1
0 1 2 3 4
0.255
0.260
0.265
0.270
0.275
0.280
0.155
0.160
0.165
0.170
0.175
0.180
J=0.300: Unum
=1.09%
J=0.568: Unum
=1.62%
10KQ
(J=0.3)
(J=0.568)

Techniques to Control the Decay of Turbulence

Large µt/µ to reduce the decay:
k∗
= k∗
inlet

1 + β(x∗
− x∗
inlet)
k∗
inlet
(µt inlet/µ)
Re
−β∗/β
ω∗
= ω∗
inlet

1 + β(x∗
− x∗
inlet)
k∗
inlet
(µt inlet/µ)
Re
−1
with x∗
= x/Lref, k∗
= k/U2
∞, ω∗
= ωLref/U∞, β∗
/β = 1.087.

k∗
= k∗
inlet

1 + β(x∗
− x∗
inlet)
k∗
inlet
(µt inlet/µ)
Re
−β∗/β
ω∗
= ω∗
inlet

1 + β(x∗
− x∗
inlet)
k∗
inlet
(µt inlet/µ)
Re
−1
with x∗
= x/Lref, k∗
= k/U2
∞, ω∗
/β = 1.087.
Frozen region upstream of propeller: Dk = Dω = 0
xfrozen = 1.0R, µt/µ = 25

k∗
= k∗
inlet

1 + β(x∗
− x∗
inlet)
k∗
inlet
(µt inlet/µ)
Re
−β∗/β
ω∗
= ω∗
inlet

1 + β(x∗
− x∗
inlet)
k∗
inlet
(µt inlet/µ)
Re
−1
with x∗
= x/Lref, k∗
= k/U2
∞, ω∗
/β = 1.087.
Frozen region upstream of propeller: Dk = Dω = 0
xfrozen = 1.0R, µt/µ = 25
Total pressure head: C∆pt = 0 ⇒ Dk = 0 (not available AFM)

Transition Identification
Limiting streamlines
Skin friction distribution: Cf
Skin friction gradient: ∂Cf
∂s
Intermittency threshold: γ = 0.03
Intermittency gradient:
q
(∂γ
∂x
)2 + (∂γ
∂y
)2 + (∂γ
∂z
)2
Turbulence index: iT = 7.4∂k0.31
∂n
ν
u1.62
τ
(Sclafani et al., 2012)

Influence of Inlet Turbulence Quantities
J = 0.568, n = 15rps, Re0.7R = 5.6×105
Tu = 1.0% Tu = 2.0% Tu = 5.0% Tu = 10.0%

Comparison with Paint Tests
J = 0.568, n = 6.6(6) rps, Re0.7R = 2.5×105
J = 0.568, n = 15.0 rps, Re0.7R = 5.6×105

J = 0.568, n = 20.0 rps, Re0.7R = 7.5×105
Model Inlet n = 6.6(6) n = 15.0 n = 20.0
Tu µt /µ KT 10KQ KT 10KQ KT 10KQ
k − ω SST 1.0% 1.0 0.1095 0.1660 0.1129 0.1652 0.1140 0.1649
γ − R̃eθt
1.0% 25.0 0.1157 0.1633 0.1226 0.1634 0.1234 0.1619
2.0% 25.0 0.1168 0.1630 0.1176 0.1622 0.1179 0.1631
4.0% 25.0 0.1150 0.1638 – – – –
5.0% 25.0 – – 0.1161 0.1643 0.1166 0.1644
8.0% 25.0 0.1144 0.1655 – – – –
10.0% 25.0 – – 0.1159 0.1646 0.1164 0.1645
Experiments – – 0.126 0.174 0.131 0.172 0.128 0.172

J = 0.3, n = 15.0 rps, Re0.7R = 5.5×105
J = 0.3, n = 20.0 rps, Re0.7R = 7.5×105

Model Inlet n = 15.0 n = 20.0
Tu µt /µ KT 10KQ KT 10KQ
k − ω SST 1.0% 1.0 0.2265 0.2685 0.2273 0.2675
γ − R̃eθt 1.0% 25.0 0.2353 0.2690 0.2367 0.2692
2.0% 25.0 0.2310 0.2672 0.2312 0.2674
4.0% 25.0 0.2291 0.2673 0.2297 0.2675
10.0% 25.0 0.2283 0.2675 0.2292 0.2675
Experiments – – 0.236 0.271 0.235 0.270

Conclusions

Conclusions
The γ − R̃eθt turbulent-transition model is strongly dependent
on the inlet turbulence quantities.

Conclusions
Therefore, their use for propeller performance prediction relies on
experimental data (turbulence quantities at the inlet are scarcely
available).

Conclusions
available).
The inlet turbulence quantities are selected to match
qualitatively the experimental transition location from
paint-test photos.

Conclusions
available).
The inlet turbulence quantities are selected to match
qualitatively the experimental transition location from
paint-test photos.
The selected inlet turbulence quantities (which may not be
realistic from the physical point of view) are dependent on the
Reynolds number and propeller loading condition.

Modelling of Laminar-to-Turbulent Flow Transition on a Marine Propeller Using a RANS Solver

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