singularity maxi: a comparison of cfd and tank test results · the upright position. with the help...
TRANSCRIPT
5th High Performance Yacht Design Conference
Auckland, 10-12 March, 2015
Singularity MAXI:
A comparison of CFD and Tank test results
Oleg Gulinsky, [email protected]
Andrey Rogatkin, [email protected]
Vadim Vorobyov, [email protected]
Abstract. The boat concept of Lutra 80 Singularity was to create a true dual-purpose yacht that rewards its owner with
racecourse performance and a high level of interior luxury. The hull form and underwater appendages combined with an
aggressive sail plan showed impressive results on the racecourse. This task has required a significant amount of tank and
tunnel tests. Not all the planned tests could be carried out within a limited time and with a certain constraint on the budget.
This report presents the results of a series of CFD experiments based on the OpenFOAM platform.
Marin tank test gave results which were confirmed in the real tests in the sea. The main purpose of our computations at this
stage is to reproduce the resistance (drag) curves at various heeling angles. We used meshes of the various size and
configurations. In general, we achieved a good correspondence (within 10%) between CFD and Marin tank test results.
However this correspondence is not uniform. For more accurate results, it is necessary to apply refinement of the mesh, and
continue to search for suitable regularization parameters.
NOMENCLATURE
w Wall shear stress
α Relative amount of water in computational cell
ρ Weighted media density
ρw Water density
ρa Air density
µ Weighted dynamic viscosity
µt Turbulence dynamic viscosity
ν w Water kinematic viscosity
ν a Air kinematic viscosity
ν weighted kinematic viscosity
U Velocity vector field
P Pressure field
y+
Dimensionless wall distance
u+
Dimensionless velocity
κ Von Karman constant
FB Body forces
1. INTRODUCTION
Lutra 80 Singularity was designed by Lutra Yacht
Design Group. The boat concept was to create a true
dual-purpose yacht that rewards its owner with
racecourse performance and a high level of interior
luxury. In racing mode, the Singularity concept provides
a sophisticated competitive edge. The hull form and
underwater appendages combined with an aggressive sail
plan showed impressive results on the racecourse. This
task has required a significant amount of tank and tunnel
tests. Nevertheless, certainly not all the planned tests
could be carried out within a limited time and with a
certain constraint on the budget. The purpose of the
present project is the following. Using the results of real
tank tests we wanted to work out and test a reliable and
stable solver based on the OpenFOAM platform, version
2.1.0-2.3.0. With this in hand we plan to perform a series
of numerical experiments based on the Lutra 80 concept.
Figure 1. Singularity yacht on a racecourse
2. COMPUTATIONAL PROCEDURE
2.1. Navier-Stokes numerical solving
The starting point is the Navier-Stokes equation, which is
now believed to embody the physics of all fluid flows,
including turbulent ones (in the simple form appropriate
for analysis of incompressible flow of a fluid whose
physical properties may be assumed constant):
· 0, U
(𝜌𝑼)𝑡 + ∇ ∙ (𝜌𝑼𝑼) = −∇�̅� + ∇ ∙ [𝜇∇𝑼] + 𝑭𝑩
There are several approaches to the construction of
approximate solutions of the equations such as RANS,
LES and DNS. For detailed discussion LES, DNS and
RANS see for example [1]. On this stage of study we
basically used RANS. For more information on CFD
theory see [2].
2.2. Two phase fluid
A yacht hull design problem is commonly referred to a
hydrodynamic one. However, this can lead to confusion,
because in fact it is substantially a two-phase flow
problem. Indeed, the wave drag force is essential for
conventional ships and not for submarines in deep water.
Consequently, we need to simulate a boat moving in a
two-phase medium and, what is most important, an
interaction between the air and water phases. On the
other hand, the forces acting on hull are not equally
affected by these two phases. As the density of air is
much less than the density of water, it makes no sense to
model an exact air velocity field and a pressure
distribution. However, what we do need to determine is
the air-water interface precise position and the air-water
mixing proportions in a region where such mixing exists.
We use VOF method which consider two immiscible
fluids as one effective fluid in the domain, the physical
properties of which are calculated as weighted averages:
(1 )w a ,
(1 )w w a a ,
𝜈 =𝜇
𝜌 ,
∇ ∙ 𝑼 = 0 ,
(𝜌𝑼)𝑡 + ∇ ∙ (𝜌𝑼𝑼) = −∇�̅� + ∇ ∙ [(𝜇 + 𝜇𝑡)∇𝑼]
2.3. Equation discretization
At this stage, our goal was to construct a reliable and
stable computational scheme, so in some cases we chose
the lower order schemes which at the same time provide
a bounded solution. To that end, we have chosen the
finite volume method (FV). In this method physical
properties of the flow for each cell assumed constant in
this cell and are attributed to the cell geometric center.
For interpolation of the divergent term in the turbulence
model equation we applied the Upwind Differencing
(UD) discretization scheme. Boundedness of the UD
solution is guaranteed through the sufficient boundedness
criterion for systems of algebraic equations. However,
boundedness of UD is insured at the expense of the
accuracy.
2.4. Dynamic Mesh handling
Apart from the problem of simulating a turbulent
environment and modelling a two-phase fluid, we face
the challenge of fixing a precise position of the boat,
changing under the influence of hydrodynamic forces.
The OpenFOAM dynamic mesh tool is crucial to
determine the exact position of the boat. In particular, the
dynamic mesh allows to analyze trim and heel and to
optimize mass distribution and weight. We used the
laplacian mesh solver with cell diffusivity proportional to
inverse distance to the hull. We created the mesh using
snappyHexMesh 2.3 (fig. 2).
Figure 2. Surface mesh on a keel, bulb and dagger board on
Mesh2
We developed four various meshes. The overview of the
meshes is given in the table below
Name Number of
cells
Minimal
cell size,
cm
Sublayer
refinement,
Hull/appendages
Mesh1 300k 4 No/No
Mesh2 500k 2 No/No
Mesh3 1.1 M 0.6 Yes/No
Mesh4 1.11M 0.1 Yes/Yes
2.5.Turbulence modelling
For the calculation of the boundary conditions in the
model of turbulence, we used the lin-log wall-function
(see fig. 3).It is well known [2] that in order to obtain
reliable results, the values of the dimensionless quantity
y+ must be in the logarithmic region 30-300. Fig. 4-6
show the distribution of the values of y+ on hull surface
for different meshes.It should be noted that the fourth
grid is constructed specifically for obtaining a uniform
distribution of values, and indeed it has the best
properties although it has almost the same number of
cells as the Mesh3.
Figure 3. the law of the wall, dimensionless horizontal
velocity near the wall
Figure 4. y+ on Mesh2, number of cells 0.5M
Figure 5. y+ on Mesh3, number of cells 1.103M
Figure 6. y+ on Mesh4, number of cells 1.109M
2.6 Computational parameters
Boat mass: 23800 kg.
Boat length: 80ft.
Figure 7. Singularity yacht geometry. Left – Tank test
model, right – computer model
Computational domain: 200x120x20 meters (fig. 11)
Solver: interDyMFoam OpenFOAM 2.1.0. version
Meshes: ~ [500 000, 1100000] cells, hexahedral
Mesh generator: snappyHexMesh OpenFOAM 2.3.0
version with explicit feature edge handling
Time step: ~0.001 s.
Courant Number: in water 0.4, in air 2
Turbulence model: RANS kOmegaSST
Dynamic mesh: Laplacian solver with diffusivity
proportional to inverse distance to the hull
Constraints: allowed only motion along vertical axis and
only pitch angular motion
Regularization: accelerating damping coefficient = 0.7
Figure 8. Computational domain, virtual Tank
The set of boundary conditions for the particular faces is
given in the table below
inletWater
U fixedValue; value uniform (-9 0 0)
P zeroGradient
fixedValue; value uniform 1
k fixedValue; value uniform 0.00015
fixedValue; value uniform 2
T fixedValue; value uniform 5e-07
inletAir
U fixedValue; value uniform (-9 0 0)
P zeroGradient
fixedValue; value uniform 0
k fixedValue; value uniform 0.00015
fixedValue; value uniform 2
T fixedValue; value uniform 5e-07
outlet
U zeroGradient
P fixedValue; value uniform 0
zeroGradient
k zeroGradient
inletOutlet; inletValue uniform 2
T zeroGradient
sides
U fixedValue; value uniform (-9 0 0)
P zeroGradient
zeroGradient
k symmetryPlane
symmetryPlane
T symmetryPlane
hull
U movingWallVelocity; value uniform (0 0 0)
P buoyantPressure; value uniform 0
zeroGradient
k kqRWallFunction; value uniform 0.00015
omegaWallFunction; value uniform 2
T symmetryPlane; type nutkWallFunction;
value uniform 0
atmosphere
U type pressureInletOutletVelocity; value
uniform (-9 0 0)
P totalPressure; p0 uniform 0; U U; phi phi;
rho rho; psi none; gamma 1; value uniform 0
inletOutlet; inletValue uniform 0; value
uniform 0
k inletOutlet; inletValue uniform 0.00015;
value uniform 0.00015
inletOutlet; inletValue uniform 2; value
uniform 2
T zeroGradient
Interpolating schemes which we used Value Scheme Accuracy
order
Time Implicit Euler 1
Spatial gradient Central
Differencing
2
div(rho*phi,U) 2nd
order Upwind 2
div(phi,alpha) TVD vanLeer 2
div(phi,k) Upwind 1
div(phi,omega) Upwind 1
laplacianSchemes linear corrected 2
We used the following regularization parameters:
acceleration of the boat after calculating multiplied by
0.3 (acceleration damping coefficient = 0.7) acceleration
of the boat was limited by 1 m / s ^ 2 This allowed the
boat to reach quickly the equilibrium position ( to the
equilibrium angle of attack) and thus to limit the
influence non-physical forces acting in the first second
calculation. Since we are looking for the stationary flow
solutions, the use of these parameters has no significant
effect on the actual forces acting on the boat, allowing us
to reduce the time for which the calculation stabilizes
3. RESULTS
The main objective of this phase of work is to make sure
that CFD gives reasonable results, from a physical point
of view. To this end the tank test results are important
bench marks to checking the CFD numbers.
In the Singularity case the Marin test gave results which
were confirmed in the real tests in the sea. We would like
to mention that we did not try to match our result to tank
test. Our approach is to find an appropriate
approximation to the Navier-Stokes equation.
The main result of hydrodynamic tank tests are the
resistance (drag) curves at various heeling angles.
Therefore, the main purpose of our computations at this
stage is to reproduce these results. As a first step we have
taken the study of the canoe body. These results are
given in [1]. Unfortunately we have no tank test data for
the canoe body to compare them with our calculations, so
we will not replay it here. The CFD analysis of yacht
with all appendages with dynamic mesh handling is an
issue of the current paper. The main challenge in this
case is creating a proper calculating mesh for complex
geometries.
Mesh1 was used mainly to obtain the reference data in
the upright position. With the help of Mesh2 we obtained
the base data for the upright position and for different
angles of the hull and keel (see fig. 4). Mesh3 is a step
towards obtaining the analogous results with an
appropriate value for y+
(see fig. 5) Mesh4 allows
achieving a good distribution of y+ values on the surface
of the hull, but the computational process at the time of
writing this version of the text was not yet over
(see fig. 6).
We calculated the drag curve for the yacht with all
appendages, including keel, daggerboard, rudder and
bulb in upright position (fig. 9)
Figure 9. Drag curves for yacht with all appendages in
upright position
and with some heel angles and canting keel position (fig.
10). In general, one can see a good correspondence
(within 10%) between CFD and Marin tank test results.
However, the coincidence is not uniform. We note that in
the range 6-12 knots there is a very good agreement of all
CFD parameters with tank test data. At speeds of 12-16
knots the discrepancy between the CFD results and tank
test data was higher than 10%. We are not accurate in the
point where the flow is very complex and unstable and
therefore very sensitive to the input parameters. We plan
to fine-tune the parameters of the calculation in the
vicinity of the point where the boat is in semi-planning
regime. At the same time it may be noted that the
calculations, performed on the Mesh3, yield results
which are in better agreement with the experimental data.
These results allow us to hope that the completion of
calculations on the Mesh4 can provide further
improvements in 12-16 knots range.
We also see the reduction in drag force in case of canted
keel (fig. 10). There is a great temptation to attribute the
observed reduction in drag force to the lift force
generated by the canting keel. However, an analysis of
the sinkage curve (fig. 11) does not give a clear
confirmation of this phenomenon.
Figure 10. Drag curve for yacht with all appendages in
different positions
We estimated the pitch angle of a boat running at
different speeds. The curve shows correspondence with
the tank test results (fig. 12).
Figure 11. Sinkage curves on 20 degrees heel angle.
Figure 12. Pitch angle curves
As a qualitative result we can compare wave patterns for
CFD and experiment. In fig. 13 (top) we present a stern
wave image of the yacht on a full close-hauled course at
speed about 14 knots with about 10 degrees of heel angle
and 35 degrees canting keel. In fig. 12 (bottom) we
depict a CFD modelled wave at 14 knots of boat speed.
There is a solid stern wave on the starboard side of the
stern wave pattern due to the heeling of a boat.
Figure 13. Water surface visualization
4. ACCURACY ESTIMATION
The quality of the calculations is commonly estimated using the
graphs presented in fig. 14. Although the accuracy of the
calculations depends of course not only on the size of the cells
in the grid but also on many other parameters of the grid,
following the tradition, we present the results in fig. 14. As
already noted, some of the procedures used in the calculation
are of the first order, which of course reflected in the form of
the graphs for the Meshes 1,2,3.
Figure 14. Drag force sensitivity to mesh variation
Fig. 15 shows drag force versus time for the speed 6
knots, respectively, where time is understood as a
parameter (physical) in the equation. At the speed of 6
knots after a transition period (about 10 sec.), the flow
and the position of the boat on the water stabilize and
drag force overlooks the stable constant through damped
harmonic oscillation, which is generally considered as a
sign of reasonable computational value. To obtain the
drag force value we applied the averaging filter. The
average standard deviation from the filtered values is
about 3%.
Fig. 15. Typical drag force time convergence (6 knots)
5. CONCLUSIONS
The present report is a part of ongoing project. The main
goal of this stage was to work out and test a reliable and
stable solver based on the OpenFOAM platform version
2.1.x-2.3.x with the idea to perform a series of numerical
experiments based on the Lutra 80 concept. To this end
the tank test results are important bench marks for
checking the CFD numbers. At the same time we did not
try to match our result to Tank test. Our approach is to
find a "good" approximation to the Navier-Stokes
equation. In general, we can claim a good
correspondence (within 10%) between CFD and Marin
tank test results. However, the coincidence is not
uniform. At speeds of 12-16 knots the discrepancy
between the CFD results and tank test data is higher than
in others ranges. We are not accurate where the flow is
very complex and unstable and therefore very sensitive
to the input parameters. For more accurate results, it is
necessary to apply refinement of the mesh with a suitable
mesh geometric properties (skewness, orthogonality,
aspect ratio); and continue to search for suitable
regularization parameters.
Acknowledgements
We are grateful for the continued assistance and support
delivered by “Lutra Design Group” of relevant
particulars concerning SY “Singularity”.
We are also grateful to the the “University Cluster”
program (see [4]) for providing the computational
We would like to thank the reviewers for deep and
thoughtful analysis of our work. l resources on the
UniHUB platform (see [5]), as well as for educational
programs and consultations on CFD.
Also we would like to thank the referees for a friendly
and comprehensive analysis.
References
1. O.Gulinsky, A.Konynendyk, A.Rogatkin,
V.Vorobyov. “OpenFOAM hydrodynamics for yacht
design: the case of Lutra 80 Singularity”, 1st
OpenFOAM User Conference, Frankfurt, 2013.
2. Ferziger, J. H. and Peric, M., Computational
Methods for Fluid Dynamics, 2nd ed., Springer-
Verlag (2001).
3. singularitymaxi.com
4. unicluster.ru/en
5. unihub.ru
6. H. Jasak PhD Thesis. Error Analysis and Estimation
for the Finite Volume Method with Applications to
Fluid Flows (1996)
7. H.Rusche. PhD Thesis. Computational Fluid
Dynamics of Dispersed Two-Phase Flows at High
Phase Fractions (2002)
8. M.S. Darwish F. Moulkalled, TVD schemes for
unstructured grids. International Journal of Heat and
Mass Transfer 46 (2003) 599 611