Investigation of modern sailing yachts using a new free-surface RANSE code K. Graf, Univ. Appl. Sciences Kiel, Germany, [email protected]J. Meyer, R&D-Center Univ. Applied Science Kiel, Yacht Research Unit, Germany, [email protected]H. Renzsch, Fluid Engineering Solutions GmbH, Germany, [email protected]C. Preuß, Univ. Appl. Sciences Kiel, Germany, [email protected]A new free surface flow RANSE solver has been developed based on the OpenFOAM framework. The solver addresses some of the main deficiencies of OpenFOAM’s standard free surface solver. It uses advanced higher order discretization schemes for the volume of fluid variable, a reconstruction of the pressure at the free surface for proper treatment of the jump of the pressure gradient at the free surface and a special method for the generation and damping of sea waves and ship generated waves at inlet and outlet of the flow domain. This new solver is used for the simulation of advanced flow problems for sailing yachts and small boats: resistance investigations at very high Froude number, investigation of the behaviour of sailing yachts in head waves and the surfing behaviour of a sailing yacht in following waves. The paper outlines the new solver and presents some case studies demonstrating its abilities. NOMENCLATURE A Control volume face area vector (m²) a acceleration (m/s²) B Beam over all (m) BWL Beam in waterline (m) F Force acting on boat (N) Fx,y,z Force component (N) Fn Froude number (u/(g LWL) 0.5 ) H Water height (m) LoA Length over all (m) LWL Length of water line (m) m Boat mass (kg) m´´ Added mass (kg) PD Power delivered (kW) RTOT Total resistance (N) t Time (s) T Yacht draft (m) u Velocity vector (m/s) u Boat speed (m/s) V Volume (m³) Volume fraction (-) ∆ Yacht displacement (kg) Density of water (kg/m 3 ) Kinematic viscosity (m²/s) 1 INTRODUCTION Simulation of viscous and turbulent free surface flow is still a field of intensive research activities. The prediction of the flow around a ship or yacht sailing on flat water or in a sea way provides some challenges: maintaining a sharp interface between water and air, generation and damping of waves, numerical stability and general accuracy of the predicted flow forces. The most common algorithms solve the time averaged Navier Stokes equation. To account for the free surface, the conservation equations are solved for a two- media mixture flow. An additional scalar variable, the volume fraction, is used to quantify the fraction of the two media, air and water, in a computational cell. For the calculation of this variable, an additional conservation equation is solved. Wackers et.al. [1] give a detailed summary of the methods behind the above-described general approach. Some commercial flow solvers are available implementing these methods. Widely used in ship hydrodynamics are StarCCM+ of Siemens and FineMarine of Numeca. The public domain framework OpenFOAM is widely used in academia and to a lesser extend in industry as well. It is free and offers a great flexibility, however at the cost of lower user convenience. Prince and Claughton [2] compared hydrodynamic investigations using the above-mentioned flow codes. Simulation results of flow around a contemporary racing yacht design have been compared with respective tank test results. One of their findings was that in many test cases the OpenFOAM simulation results did not show the same quality as the other flow codes. OpenFOAM is a free open-source software. The structure of the source-code intends to ease modification and enhancements. The motivation behind the study presented here is to add more advanced and proven algorithms to OpenFOAM in order to increase simulation accuracy and numerical robustness. In the following, the modifications to the OpenFOAM code are sketched. Then, some examples are shown, demonstrating the abilities of the new code: general resistance investigation of a yacht hull, sailing yacht behaviour in a head sea, flow simulation at very high Froude number and the behaviour of a yacht surfing in a following sea. 2 THE OPENFOAM FRAMEWORK OpenFOAM is a framework of software libraries, executables and utilities to manipulate field variables in a continuum. OpenFOAM is widely used but not limited to solve the governing equations of viscous turbulent flow. A standard solver for free surface flow is available, interFoam. It can be used for the simulation of The Fourth International Conference on Innovation in High Performance Sailing Yachts, Lorient, France INNOV'SAIL 2017 67
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Investigation of modern sailing yachts using a new free-surface RANSE code
flow around ships; however, test calculations have shown
its limitations.
2.1 OPENFOAM STANDARD SOLVER FOR FREE
SURFACE FLOW
The OpenFOAM interFoam solver implements
the volume-of-fluid method. An additional compressive
term is used in the transport equation for the volume
fraction in order to achieve a sharp interface. The transport
equation is solved using the multi-dimensional limiter for
explicit solution (MULES). It uses an implicit predictor
based on upwind differencing for the convective term.
Afterwards the solution is corrected with an explicit
corrector using the 2nd order van Leer discretization
scheme, which belongs to the TVD scheme family.
Some test calculation showed that interFoam has some
severe limitations: time discretization relies on small step
size for numerical stability. The interface between air and
water tends to smear, resulting in ventilated regions that
are expected to be fully submerged and wetted. Internal
test calculations showed that reasonable results only could
be achieved with very large grids and small time-step
sizes, giving unacceptable high computational costs. The
interFoam solver often needs additional user adjustment
to achieve a stable solution; for some large grids it is not
possible to get a stable simulation at all. To some degree,
this is in-line with the findings of Prince and Claughton
[2].
2.2 NEW FREE SURFACE FLOW SOLVER
The new free surface solver has been developed
with the intention to implement some of the advanced
algorithms available:
A high resolution scheme for the discretization of
the convective term of the volume-of-fluid
conservation equation.
Pressure reconstruction for proper modelling of
the pressure gradient near the free surface.
A variation of the turbulence model taking into
account the variable density in a mixture of two
fluids.
A stable algorithm for the generation of seaways.
A reliable, non-reflective damping of waves at
the exit of the flow domain.
A stable method for the solution of the equation
of motion to trace ship movement in a seaway.
Details of the theory and implementation of the new
solver are given in [3] and [4]. Only an overview is given
here.
VOF discretization schemes:
For the prediction of the location of the free
surface the volume fraction of water (or air) in a volume
has to be calculated using:
0A
V dt
u A
(1)
Special care has to be taken for the discretization
of the convective term. Well-known discretization
schemes are the HRIC, BICS and BRICS schemes, the
latter ones described in [1]. These schemes ensure higher
order discretization, satisfy the boundedness criterion and
avoid oscillating solutions. They allow Courant numbers
larger than 1 which is crucial for the computational
efficiency of the method. All of the mentioned methods
have been implemented in the new OpenFOAM solver in
a deferred correction manner, saying that only first order
discretization is taken into account implicitly while a
higher order explicit correction is added based on the last
time step values of the fractional volume of fluid α. The
test cases shown later are investigated using the BRICS
scheme, which showed a bit smoother results than the
other methods.
Pressure Reconstruction:
Pressure reconstruction describes an operation
applied to the pressure in order to take the discontinuity
of the pressure gradient at the free surface into account in
a precise manner. The general idea behind pressure
reconstruction is to predict the pressure and its gradient at
a cell face by taking the exact distance of the cell centres
to the face and local non-orthogonality into account. The
method uses the known discontinuous density to calculate
the discontinuous behavior of the pressure gradient at the
free surface. For the Rhie-Chow implementation the face-
normal component of the pressure gradient is built at the
cell-face but in a form normalized with the reversed linear
interpolated density. This normalized gradient is
reconstructed to the cell-center and multiplied with the
density at the cell center. Additional explicit terms are
used to achieve a correct treatment on non-orthogonal
grids.
Without pressure reconstruction, severe non-
physical air over-speeds occur driven by the large density
difference of air and water. However, practical
investigation show that even with pressure reconstruction
over-speeds cannot be avoided at any time. Therefore, a
simple explicit limiting is implemented additionally,
setting the velocity magnitude back whenever it exceeds a
given threshold.
Turbulence model re-implementation:
For external flow at low Mach number, air and
water can be assumed incompressible. In one-phase flow
the density may be excluded from time or spatial
derivations. This is also done in OpenFOAM’s
incompressible turbulence models, although the density is
varying in time or space due to the volume-of-fluid
mixture approach. As a remedy the incompressible 2-
equation turbulence models available in OpenFOAM have
been rewritten such that the density is included in the
different derivations.
Generation of sea waves:
For the generation of sea waves a modified
version of the publicly available OpenFOAM extension
waves2Foam [8] is used. At the inlet, the values for the
The Fourth International Conference on Innovation in High Performance Sailing Yachts, Lorient, France
INNOV'SAIL 2017 68
velocities and volume fractions are prescribed according
to Stokes waves of 5th order. An equation for the pressure
value itself or the pressure gradient is missing, which is a
significant problem. The implemented solution is using a
Neumann boundary condition with a zero gradient for the
pressure. Certainly, the assumption of a zero gradient is
wrong in the presence of a wave and for many 3D
simulations the wave will collapse behind the inlet.
Therefore, a relaxation zone behind the inlet is used, about
one wavelength long. It applies fully implicit relaxation
for the momentum and volume-of-fluid equation. Full
relaxation is applied at the inlet going to no relaxation at
the end of the generation-zone. The target values for the
velocity and the volume-fraction are calculated with the
chosen wave theory.
This is implemented as an implicit relaxation,
e.g. the blending is built into right as well as the left side
of the transport equations for momentum and volume
fraction.
Damping of sea waves and yacht generated waves:
Corresponding to the entrance zone for the
generation of sea waves an exit zone close to the flow
domain outlet is used. The exit zone with a length of about
one wavelength is used to damp sea waves and boat-
generated waves in order to avoid reflexions.
A new approach for the wave damping in the exit
zone has been developed, which has been published only
recently [4]. Available methods usually damp the sea
waves by adding some external force into the momentum
equation. These methods need some adjustment to the
actual wave scale to be damped. The new approach uses a
relaxation scheme, e.g. a prescribed solution is available
at the exit zone, which is blended into the calculated
solution. In the case of wave damping, the prescribed
solution is a target value for the vertical component of the
momentum. The z-component of the velocity in the wave-
damping zone is calculated from:
(1 )Z CZ tZu u u
(2)
where uCZ is the vertical flow speed calculated from the
momentum equation while utZ is the target value of the
vertical flow speed. ω is a relaxation factor. It is set to 1 at
the upstream border of the wave damping zone while it is
set to 0 at the outlet of the flow domain. A target value of
utZ=0 is used. It successfully smooths the wave elevation
to vanishing and generates parallel outflow at the flow
domain outlet.
The method is implemented implicitly, saying
that (2) is integrated into the momentum equation. This is
done in a deferred correction manner.
Ship motion prediction:
For the prediction of the motion of a ship sailing
at the free surface the equation of motion has to be
integrated:
mF a
(3)
where { , , , , , }T
X Y Z X Y ZF F F M M MF, m is the inertia
matrix and a is the vector of the translational and rotational
accelerations of the yacht. This is done using trapezoidal
integration.
Söding [5] showed that that the semi-implicit
nature of the coupling of motion and flow solution lead to
stability issues as soon as added masses (resulting in
motion-dependent forces proportional and opposed to the
acceleration) are equal or larger than the actual physical
mass. This happens due to the fact that in this particular
kind of iterative coupling the individual iterations of the
motion solution are effectively explicit extrapolations and
implicit or strong coupling are only achieved by iteration
of the coupled system.
To stabilise the system the added masses need to
be approximated. Söding proposes to compute this added
mass matrix m'' from the resulting reaction forces from a
known acceleration vector. This leads to:
ˆ( )m m m a F a F (4)
Yacht motion is integrated into the flow
simulation process using a morphing grid: in the far-field
the grid is rigid and not moving. In the vicinity of the yacht
the grid moves together with the yacht. In the intermediate
zone the grid is deformable and moving in order to
maintain integrity between the near-field and the far-field.
This approach is favourable compared to a rigid moving
grid, since grid resolution close to and alignment with the
water surface can be maintained in the far-field.
The methods mentioned here are described in
detail in [3] and [4]. They are implemented as a new
OpenFOAM solver and as enhancements of existing
boundary conditions.
3 VALIDATION
The new solver has been validated against towing
tank tests carried out on flat water with the Sysser sailing
yacht from the Delft Systematical Yacht Hull Series.
Validation includes integral values as flow forces and
wave field measurements near the yacht. The result of the
validations study confirmed that the new OpenFOAM
solver was able to achieve the same quality of results at
approximately the same computational run time than the
commercial RANSE solver StarCCM+. Agreement with
the towing tank results of the Sysser was fairly well. This
validation study is described in detail in [3].
Special attention has been paid to a validation
against the results of the Wide Light Project of the Sailing
Yacht Research Foundation [2]. The study showed that the
standard OpenFOAM solver for free surfaces lacks some
accuracy and is computationally expensive. The
development described here is partly motivated by these
results. In the following a comparison of the results
generated with the new solver and the known results from
the Wide and Light study is presented.
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INNOV'SAIL 2017 69
2.1 GENERAL
A limited test matrix is chosen with focus on
upright resistance (bare hull symmetrical) and heel / yaw
effects (fully appended, heeled by 25°) with single rudder.
For the symmetrical bare hull case a mesh of about 2.2
million cells is used, for the heeled appended case about
5.6 million cells. The meshes are generated using a
snappyHexMesh in a fully scripted procedure ensuring
consistency of relevant meshing parameters (global and
local and wall resolution). Turbulence is modelled by the
k-w-SST model.
Using a quasi-static body motion approach for
free trim and sinkage the bare hull cases take about 6h on
a dual-XEON E5-2650 (2.0GHz) workstation, the fully
appended cases about 14h to convergence of forces and
position.
The results are compared to the experimental
data as well as to the results generated using STAR-CCM+
and FINE|MARINE as provided in [2].
2.2 RESULTS
In Figures 1 to 6 resistance, side-force (where applicable),
heave and sinkage are given for the tested cases. The same
format as in [2] is used and experimental as well as STAR-
CCM+ and FINE|MARINE results are given for
comparison.
Fig 1: Resistance bare hull upright
Fig 2: Trim / sinkage bare hull upright
Fig 3: Resistance heeled, fully appended at Fn 0.35 (solid)
and 0.50 (dashed)
Fig 4: Side-force heeled, fully appended at Fn 0.35 (solid)
and 0.50 (dashed)
Fig 5: Heave heeled, fully appended at Fn 0.35 (solid) and
0.50 (dashed)
Fig 6: Trim heeled, fully appended at Fn 0.35 (solid) and
0.50 (dashed)
As can be clearly seen, the obtained results –
forces as well as motion – fit in very well with those from
The Fourth International Conference on Innovation in High Performance Sailing Yachts, Lorient, France
INNOV'SAIL 2017 70
the towing tank and commercial CFD codes. Similar
accuracy has been demonstrated on fundamentally
different hull shapes, e.g. container vessels and mega
yachts.
Figure 7 gives an example of the resulting wave pattern.
Fig 7: Wave pattern at 25° heel, Fn 0.5, -2° yaw
4 SAILING YACHT RESISTANCE
INVESTIGATION
Predicting the flat water resistance of a sailing
yacht is the standard task for RANSE-based free surface
flow investigations. As an example an investigation of a
9m-daysailer yacht with conventional ship lines is shown
here. Main dimensions and line drawings are shown
below:
LoA: 9.16 m
LWL: 9.00 m
B: 2.50 m
BWL: 2.15 m
T: 1.99 m
∆: 1950 kg
Fig 8: Line drawings of the YIP+29 daysailer
A computational grid of 2.48 million grid cells is
used. To predict the resistance at a single boat speed,
computational runtime of 18 h is needed on a Linux
workstation (Intel Xeon E5-2470 CPU). For an entire
resistance diagram a sequence of acceleration phases and
phases with constant velocity are performed within a
single computational run. To predict the resistance for 6-8
boat speeds, the total computational runtime is about 2-4
days, still on a workstation.
Fig 9 shows the resistance diagram of the yacht.
Maximum Froude number investigated is Fn=1.05
corresponding to a boat speed of 22 kts.. For Froude
numbers up to Fn=0.62 the resistance curve from the flow
simulation is compared to resistance prediction based on a
regression of the Delft Systematically Yacht Hull Series,
[6]. Agreement is reasonable with derivations of 12% at a
Froude number of Fn=0.4. It is below 4% at any other
Froude number. Obviously a regression method cannot be
used to validate the results.
Fig 10 shows the wave pattern at a Froude
number of Fn=0.5. Note that ship waves vanish about 5
boat lengths aft of the boats transom. This intended feature
of the simulation has been established using the wave
damping method described above.
Fig 9: Resistance curve of the YIP+29 daysailer
Fig 10: Wave pattern at Fn=0.5
5 MOTORBOAT AT VERY HIGH FROUD
NUMBER
The Kiel Classic 24 is a motorboat manufactured
in Northern Germany by the small boat yard Marina
Brodersby. She is designed as a tender for lovers of classic
design and is built in small numbers, Fig 11.
0
1000
2000
3000
4000
5000
6000
7000
0 0.2 0.4 0.6 0.8 1 1.2
Tota
l Res
ista
nce
[N
]
Froude-number [-]
OpenFOAM FS-Solver
DSYHS-Regression
The Fourth International Conference on Innovation in High Performance Sailing Yachts, Lorient, France
INNOV'SAIL 2017 71
Fig 11: Kiel Classic 24 motorboat
The main dimension are:
LoA: 7.33 m
LWL: 6.80 m
B: 2.41 m
∆: 2.1 t
PD: 103 – 195 kW w. Z-Drive
Fig 12: Kiel Classic 24 line drawings
For a project concerning resistance optimization
methods based on innovative appendages, it was
necessary to predict the flat water resistance as a base for
comparison.
The Kiel Classic 24 is rather heavy compared to
a sailing yacht of same dimensions. It can achieve a boat
speed of 35 kts. corresponding to a Froude number of
Fn=2.2. This high boat speed provides many problems for
hydrodynamic investigations, experimentally as well as
numerically. Motions of the boat are large, when reaching
top-speed and the wave system is very pronounced. Free
surface RANSE simulations only converge with very
small time steps making these simulations
computationally expensive.
The investigations shown here have been
conducted using a grid of 2.9 million grid cells. A
hexahedral grid is used in the far-field, allowing simpler
definition of the boundary conditions and the wave
damping. In the near-field unstructured polyhedral grid
cells are used, Fig 13.
The simulations for an individual boat speed took
approximately 6 h for Fn=0.2 and up to 48 h for Fn=2.2
on three nodes and 36 cores on an Infiniband-connected
compute cluster.
Fig 13: Computational grid around Kiel Classic 24
Fig. 14 shows the resistance curve of the Kiel
Classic. A comparison with the regression methods of
Savitsky and Blount&Fox show reasonable agreement at
Froude numbers of Fn>1. The simulated resistance curve
shows two steep resistance increases at Fn≈0.4 and
Fn≈0.9. It is assumed that the resistance increase at the
higher Froude number is due to shallow water effects. The
computational domain has a water draft of 8 m. At a
Froude number of Fn=0.9 the Froude depth number /Fn u gH
is close to 1.
Fig. 14: Resistance diagram of the Kiel Classic 24
Fig 15 and Fig 16 show the wave pattern at
Froude number of Fn=0.5 and Fn=2.0 respectively. At the
higher Froude number the opening angle of the trailing
wave system is getting very small as expected.
Fig 17 shows the resistance decomposed into
frictional and pressure resistance. The pattern observed
here shows that at low Froude number of Fn≈0.4 the
resistance is dominated by pressure resistance, accounting
for more than 80% of the total resistance. However, for
high Froud numbers of Fn>1.5 frictional and pressure resistance are of same order of magnitude. For any resistance optimization method it has to be taken into account, that only those methods will succeed, which
zz
x
x
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
Tota
l Res
ista
nce
[N
]
Froude number [-]
Savitsky Planing Resistance [N]
Blount and Fox Planing Resistance [N]
OpenFOAM FS-Solver
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INNOV'SAIL 2017 72
address the frictional as well as the pressure resistance.
Fig 15: Kiel Classic at Fn=0.5
Fig 16: Kiel Classic at Fn=2.0
Fig 17: Resistance decomposition Kiel Classic 24
6 COMPARISON OF TWO BOW SHAPES IN A
HEAD SEA
2011 David Raison won the Mini-Transat race
with a self-developed yacht with a quite uncommon scow
bow, (Fig 18).
Fig 18: Mini-Transat yacht Teamwork
Source: Creative Commons License: Attribution 2.0
Generic, [7]
Scow bows on dinghies are well-known, f.x
Melges’ E-Scow, however using this bow on seagoing
yachts raises questions about their behaviour in waves. In
a collaborative project with French designer VPLP design
it has been investigated if this concept of a scow bow can
be adapted to the Class 40, a yacht sailed with small crew
on distance races. To this end, a variation of an existing
design of a Class 40 has been developed, featuring a scow
bow, see Fig 19.
Fig 19: Class 40 scow bow and conventional design
The main dimensions of both yachts were kept constant:
LoA: 12.19 m
∆: 4925 kg
The yachts have been investigated for the following
states:
Boat speed: 4.4 m/s
Leeway angle: 3°
Heel angle: 15°
The following conditions were investigated
Flat water
Wave Length: 18 m, Wave Height: 0.4 m
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
Res
ista
nce
[N
]
Froude number [-]
Total Resistance
Pressure Resistance
Frictional Resistance
The Fourth International Conference on Innovation in High Performance Sailing Yachts, Lorient, France