Numerical Studies for Verification and Validation of Open-Water Propeller RANS Computations

Numerical Studies for
Verification and Validation of
Open-Water Propeller RANS Computations
J. Baltazar1, D. Rijpkema2, J.A.C. Falcão de Campos1
1Instituto Superior Técnico, Universidade de Lisboa, Portugal
2Maritime Research Institute Netherlands, Wageningen, the Netherlands
MARINE 2015 Rome, Italy 15 - 17 June 1

Introduction
With the increase of computing power, RANS methods are
becoming an useful numerical tool for the analysis and design
of marine propulsors;

Introduction
The knowledge on the inﬂuence of the grid topology,
discretisation level, domain size, turbulence model, Reynolds
number, etc., are important for cost-eﬀective accurate numerical
predictions;

Introduction
predictions;
This knowledge can be improved by analysing a wide range
of propeller geometries using numerical uncertainty analysis
(E¸ca and Hoekstra, 2014) for series of grids to quantify the
diﬀerent sources of errors;

Introduction
predictions;
This knowledge can be improved by analysing a wide range
of propeller geometries using numerical uncertainty analysis
(E¸ca and Hoekstra, 2014) for series of grids to quantify the
diﬀerent sources of errors;
In this work, viscous ﬂow calculations using a RANS code are
presented for two marine propellers in open-water conditions
at model-scale.

RANS Code ReFRESCO
Viscous ﬂow CFD code developed within a cooperation led by
MARIN;

RANS Code ReFRESCO
MARIN;
Solves the incompressible RANS equations, complemented with
turbulence models;

RANS Code ReFRESCO
MARIN;
turbulence models;
The equations are discretised using a ﬁnite-volume approach
with cell-centred collocation variables;

RANS Code ReFRESCO
MARIN;
turbulence models;
Flow is considered turbulent, κ − ω SST 2-equation model
proposed by Menter (1994) is used;

RANS Code ReFRESCO
MARIN;
turbulence models;
Second-order convection scheme (QUICK) is used for the
momentum equations;

RANS Code ReFRESCO
MARIN;
turbulence models;
momentum equations;
First-order upwind scheme is used for the turbulence model;

RANS Code ReFRESCO
MARIN;
turbulence models;
momentum equations;
First-order upwind scheme is used for the turbulence model;
No wall functions are used (y+
∼ 1).

ReFRESCO Calculations
Computational domain and boundary conditions

Test Cases
Propellers S6368 (left) and S6408 (right)
S6368 S6408
D [m] 0.2714 0.3010
c0.7R [m] 0.0694 0.0794
Z 4 4
P/D0.7R 0.757 0.711
AE /A0 0.456 0.481

Grid Sizes
S6368 S6408
Volume Blade y+
Volume Blade y+
G1 34.8M 39K 0.34 41.3M 51K 0.27
G2 17.8M 25K 0.42 23.7M 35K 0.37
G3 8.0M 15K 0.52 11.3M 21K 0.32
G4 4.3M 10K 0.62 6.9M 15K 0.40
G5 2.2M 6K 0.78 2.3M 7K 0.59
G6 1.0M 2K 0.95 1.0M 4K 0.63

Error Estimation
Numerical errors involved on a CFD prediction:

Error Estimation
Round-oﬀ error: due to the ﬁnite precision of computers.
Considered to be low;

Error Estimation
Iterative error: related to the non-linearity of the transport
equations. Monitored from the residuals;
L∞(φ) = max |res(φi )|, L2(φ) =
Ncells
i=1
res2(φi ) Ncells

Error Estimation
Iterative error: related to the non-linearity of the transport
equations. Monitored from the residuals;
L∞(φ) = max |res(φi )|, L2(φ) =
Ncells
i=1
res2(φi ) Ncells
Discretisation error: discrete representation (space and time)
of a (partial) diﬀerential equation. Monitored from grid
reﬁnement studies.

Iterative Error
Propeller S6368 at J = 0.3
Iteration
1000 2000 3000 4000 5000
10
-7
10
-6
10-5
10
-4
10
-3
10-2
10-1
10
0
VX
VY
VZ
p
κ
ω
L∞
Iteration
1000 2000 3000 4000 5000
10-7
10
-6
10-5
10
-4
10
-3
10-2
10-1
10
0
VX
VY
VZ
p
κ
ω
L∞
Iteration
1000 2000 3000 4000 5000
10
-9
10
-8
10-7
10-6
10-5
10
-4
10-3
10-2
10-1
10
0
VX
VY
VZ
p
κ
ω
L2
Iteration
1000 2000 3000 4000 5000
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
KT
Iteration
1000 2000 3000 4000 5000
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
10KQ

Iterative Error
Iteration
1000 2000 3000 4000 5000
10
-7
10
-6
10
-5
10
-4
10-3
10-2
10-1
100
10
1
VX
VY
VZ
p
κ
ω
L∞
Iteration
1000 2000 3000 4000 5000
10-7
10
-6
10
-5
10
-4
10-3
10-2
10-1
100
10
1
VX
VY
VZ
p
κ
ω
L∞
Iteration
1000 2000 3000 4000 5000
10
-9
10
-8
10-7
10-6
10-5
10
-4
10-3
10-2
10-1
10
0
VX
VY
VZ
p
κ
ω
L2
Iteration
1000 2000 3000 4000 5000
0.24
0.25
0.26
0.27
0.28
0.29
0.30
KT
Iteration
1000 2000 3000 4000 5000
0.24
0.25
0.26
0.27
0.28
0.29
0.30
10KQ

Discretisation Error
Grid reﬁnement study for Propeller S6368
J 0.30 0.65
Grid ∆KT ∆KQ ∆η0 ∆KT ∆KQ ∆η0
1.0M 1.5% 3.1% -1.5% 3.9% 5.8% -1.8%
2.2M 1.0% 1.6% -0.5% 2.0% 2.6% -0.6%
4.3M 0.5% 0.8% -0.2% 1.0% 1.4% -0.5%
8.0M 0.3% 0.4% 0.0% 0.5% 0.7% -0.3%
17.8M 0.0% 0.0% 0.0% 0.0% 0.1% -0.2%
34.8M – – – – – –

Discretisation Error
Grid reﬁnement study for Propeller S6408
J 0.2 0.5
Grid ∆KT ∆KQ ∆η0 ∆KT ∆KQ ∆η0
1.0M 0.6% 2.0% -1.4% 2.8% 3.9% -1.0%
2.3M 0.6% 1.1% -0.7% 1.8% 2.2% -0.3%
6.9M 0.4% 0.4% -0.4% 0.9% 0.9% 0.0%
11.3M 0.2% 0.3% -0.4% 0.6% 0.7% 0.0%
23.7M 0.0% 0.1% -0.4% 0.1% 0.2% 0.0%
41.3M – – – – – –

Veriﬁcation Procedure (E¸ca and Hoekstra, 2014)
The goal of veriﬁcation is to estimate the uncertainty of a given
numerical prediction Unum:
φi − Unum ≤ φexact ≤ φi + Unum

Numerical Uncertainty:
Unum = Fs| |

Numerical Uncertainty:
Unum = Fs| |
Estimation of the discretisation error :
= φi − φ0 = αhp
i
Unknowns: φ0, α and p.

Veriﬁcation Study
hi
/h1
0 1 2 3 4
0.224
0.226
0.228
0.230
p=1.63, Unum=0.43 %
KT
hi
/h1
0 1 2 3 4
0.265
0.270
0.275
0.280
p=2.00, Unum=1.17 %
10KQ

Veriﬁcation Study
hi
/h1
0 1 2 3 4
0.245
0.250
0.255
0.260
α1
h+α2
h2
, Unum
=2.0 %
KT
hi
/h1
0 1 2 3 4
0.288
0.291
0.294
0.297
p=1.88, Unum=0.31 %
10KQ

Limiting streamlines on the suction side
Propeller S6408 at J = 0.2. Grids with 1M (left) and 41M (right) cells

Inﬂuence of domain size and boundary conditions

Propeller S6408
Domain J = 0.2 J = 0.5
Size KT 10KQ η0 KT 10KQ η0
3D 0.2544 0.2915 0.278 0.1284 0.1748 0.585
5D 0.2528 0.2902 0.277 0.1278 0.1745 0.583
10D 0.2523 0.2889 0.278 0.1276 0.1736 0.585

Propeller S6408
Domain J = 0.2 J = 0.5
Size KT 10KQ η0 KT 10KQ η0
3D 0.2544 0.2915 0.278 0.1284 0.1748 0.585
5D 0.2528 0.2902 0.277 0.1278 0.1745 0.583
10D 0.2523 0.2889 0.278 0.1276 0.1736 0.585
Boundary Boundaries:
Conditions Farfield Outflow Tunnel Outflow
BC1 const. pressure zero normal derivative zero normal derivative
BC2 slip-wall const. pressure const. pressure
BC3 slip-wall const. pressure zero normal derivative
Boundary J = 0.2 J = 0.5
Conditions KT 10KQ η0 KT 10KQ η0
BC1 0.2528 0.2902 0.277 0.1278 0.1745 0.583
BC2 0.2533 0.2907 0.277 0.1280 0.1747 0.583
BC3 0.2530 0.2902 0.278 0.1277 0.1743 0.583

Comparison Between Numerical and Experimental
Results
J
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Experiments
ReFRESCO
KT
10KQ
0
S6368
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
ReFRESCO
KT
10KQ
S6408

Results (Comparison Error E)
KT KQ η0
J E Unum E Unum E Unum
S6368
0.30 -5.19% 0.43% -2.36% 1.17% -2.9% 0.68%
0.65 -18.63% 1.50% -7.92% 2.17% -11.7% 0.63%
S6408
0.20 -3.70% 2.00% 0.55% 0.31% -4.5% 0.46%
0.50 -6.44% 1.77% 2.35% 0.73% -8.6% 0.43%

Results (Rijpkema et al., 2015)

Conclusions
The inﬂuence of the iterative errors, discretisation errors, domain size
and boundary conditions on the propeller forces has been analysed;

Conclusions
Small iterative errors are expected due to its fast convergence. The
discretisation error has been estimated from a veriﬁcation study and
numerical uncertainties in the order of 0.4%-2.2% are obtained;

Conclusions
The inﬂuence of the domain size and boundary conditions is found to
be smaller than 1%;

Conclusions
be smaller than 1%;
Large diﬀerences are found between the numerical and experimental
results, suggesting that the comparison error (E) is dominated by the
modelling error;

Conclusions
be smaller than 1%;
Large differences are found between the numerical and experimental
results, suggesting that the comparison error (E) is dominated by the
modelling error;
Since the experiments are made in the critical Reynolds number
range (5.0 − 7.0 × 105), different flow regimes (laminar and
turbulent) may occur simultaneously on the propeller blades.

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