Investigation of modern sailing yachts using a new free...

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/m3)

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

mailto:[email protected]




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


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.


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


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


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


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


INNOV'SAIL 2017 73

https://en.wikipedia.org/wiki/en:Creative_Commons

https://creativecommons.org/licenses/by/2.0/deed.en

https://creativecommons.org/licenses/by/2.0/deed.en

Computational grids of 5.8 million cells were used for

the flat water case, while 8.6 million grid cells were used

for the wave case, using fine resolution for the entire wave

height.

Fig 20 depicts the total resistance of the two hull

variants on flat water over simulation time. Clearly the

scow bow form generates more resistance than the

conventionally shaped hull (V18).

Fig 21 shows the longitudinal flow force on the two

hulls for the investigated case of sea waves. It can be

observed, that the oscillating flow forces acting on the

scow hull are generally a bit higher.

The average resistance has been derived from these

diagrams by building the average over the flow forces over

the last 60% of the simulation time for the flat water case

and the average over the last 8 encountering waves for the

head sea case. These averages are:

Flat water:

Scow Bow: RTOT=1528 N

V18 Bow: RTOT=1466 N

Head sea:

Scow Bow: RTOT=2726 N

V18 Bow: RTOT=2290 N

The result is clear: for flat water the resistance

increase due to the scow bow is about 4.2%. For the head

sea the average resistance increase is a hefty 19%.

Fig 20: Flat water resistance over simulation time

Fig 21: Longitudinal flow force over simulation time

The reason for this resistance increase can clearly

be detected by analyzing the flow pattern at the bow, Fig

22. While the local water elevation at the bow is similar

for both hull shape, it covers a wider area on scow bow.

Fig 22: Flow pattern around scow and conventional bow

The test case shown here is quite an extreme one.

Wave lengths of 1.5*boat length usually generate the

maximum of added resistance in sea waves. With a boat

speed of 4.4 m/s the encounter frequency is quite high.

When sailing in a head sea of this wave length and height

this boat speed certainly cannot be maintained. Last but

not least when sailing in a sea wave the boat speed does

not remain constant. It is known from tank testing, that

keeping boat speed constant when sailing in a head sea

leads to an overestimation of the resistance.

In addition, it has to be mentioned that the scow

bow hull generates significantly higher righting arms due


INNOV'SAIL 2017 74

to a fuller flotation plane. Some VPP investigation showed

that this additional sail carrying power can equalize higher

flat water resistance due to the bow shape. However, it can

be doubted that this is still the case, when sailing in sea

waves.

7 SAILING YACHT IN A FOLLOWING SEA

Sailing in a following sea way is of extraordinary

fun for most sailors. On a modern light-weight boat very

high boat speed can be achieved. On the other hand in

strong wind condition surfing a wave needs special

attention of the sailors to maintain control and cope with

potential instabilities.

Simulating the flow around a boat in a running

wave and predicting its behaviour provides some

challenges for the simulation setup. In particular, mean

flow and wave propagation have to oriented in opposed

directions.

A simulation has been set up where this condition

is established. A new boundary condition is used allowing

to define a wave superimposed by a mean flow in opposed

direction. In addition the boat can arbitrary accelerate.

This is established by either defining time dependent

velocities or by an external force acting on the yacht. The

acceleration is established by an additional source term in

the momentum equations. The outer bounds of the grid

still do not move. The boat may freely pitch and sink, but

longitudinal motions of the yacht are realized by changing

the flow speed respectively.

This setup is used to investigate the sailing yacht

YIP+ from chapter 3. Boat main dimensions and the

computational grid remain unchanged. The wave

parameters and the boat speeds are:

Wave length: 20.0 m

Wave height: 0.8 m

Boat Speed: 3.0 m/s

The simulation starts at boat speed of u=0m/s and

sinkage and pitch is set non-captive from the beginning

on. The wave is pre-initialized in the entire flow domain.

Simulations in a running sea way are particularly

expensive in terms of computational runtime. The

encounter frequency is quite low, making it necessary to

simulate long time periods in order to cover at least two to

three wave periods in fully developed flow and boat speed

Fig 23 depicts flow forces acting on the bare hull of

the yacht, plotted over simulation time. Only two wave

periods are taken into account for the running wave case.

The low encounter frequency for the running wave case

can clearly be detected. It can be observed that the

oscillation of the flow forces is of same order of magnitude

for both the head wave and the running wave, however an

offset can be detected. Averaging the flow forces over a

time period corresponding to two wave periods of the

running wave case yields the following result:

Flat Water: RTOT: 306 N

Head Waves: RTOT: 479 N

Running Waves: RTOT: 223 N

While the change of the resistance due to the

waves is quite obvious, it has to be mentioned again

that the assumption of a constant speed (after the

acceleration phase) will lead to an overestimation of

the wave effects.

Future research will address this: in a first step a

constant driving force will be used and the boat speed

in the waves will be traced. As the next step the

change of the driving force due to a change of boat

speed will be taken into account. This will finally lead

to a dynamic VPP, since the change of the driving

forces due to changes of boat speed will be calculated

from an aerodynamic model, predicting the

aerodynamic forces from sail force coefficients of a

respective sail set to be used when sailing downwind.

Fig 23: Longitudinal flow forces acting on the bare hull

for flat water conditions, for a heading sea wave and for a

running sea wave

Fig 24: Running wave passing the boat


INNOV'SAIL 2017 75

8 CONCLUSIONS

A new RANSE-based free surface flow

simulation method has been developed using the

OpenFOAM framework. Within the development special

attention has been paid to computational efficiency. In

particular the method can use large time steps for the

simulation of unsteady flow problems compared to the

standard OpenFOAM free surface solver.

This method is capable to simulate the flow

around yachts sailing at very high Froude number and the

behaviour of sailing yachts in head waves as well as

running waves. While flat water flow simulations have

been validated and show good agreement with respective

towing tank test results, validation of the results of

simulations taking sea waves into account is subject to

future research.

ACKNOWLEDGEMENTS

The research project around the Kiel Classic 24

is funded by the German Ministry of Economics and

Energy via the ZIM program: Zentrales

Innovationsprogramm Mittelstand (Central Innovation

Program for SMEs).

The development of the free surface flow solver

is part of the project Scour Prediction, funded by the

Ministry of Economics, Agriculture and Energy

Schleswig-Holstein.

REFERENCES

1. Wackers, J.; Koren, B.; Raven, H.C. et al.: Free

Surface viscous flow simulation methods for ship

hydrodynamics, Arch Computat Methods Eng , 2011.

2. Prince, M. and Clauthon, A.: The SYRF Wide

Light Project. In: Society of Naval and Marine Engineers

(Hg.): The Twenty-Second Chesapeake Sailing Yacht

Symposium. March 18-19, 2016.

3. Meyer, J.; Renzsch, H; Graf, K.; Slawig, T.:

Advanced CFD-Simulations of free-surface flows around

modern sailing yachts using a newly developed

OpenFOAM solver. In: Society of Naval and Marine

Engineers (Hg.): The Twenty-Second Chesapeake Sailing

Yacht Symposium. March 18-19, 2016.

4. Meyer, J.; Graf, K. and Slawig, T.: A new

adjustment –free damping method for free-surface waves

in numerical simulations, Preprint submitted to: VII

International Conference on Computational Methods in

Marine Engineering, Nantes/France, 2017

5. Söding, H.: How to Integrate Free Motions of

Solids in Fluids, 4th Numerical Towing Tank Symposium,

Hamburg-Germany, 2001.

6. Keuning, J.A.; Vermeulen, K.J.: A Bare Hull

Resistance Prediction Method Derived from Results of the

Delft Systematic Yacht Hull Series, Proc. Intl. Conference

on Innovations in High Performance Sailing Yachts,

Lorient/Fr., 2008.

7. http://www.flickr.com/photos/agecombahia/629

6869520/in/set-72157628015380898, 1.4.2017

8. Jacobsen, N.G.; Fuhrmann, D.R. and Fresdoe, J.:

A wave generation toolbox for the opensouce CFD library

OpenFOAM, Intl. J Numerical Methods in Fluids, 2012.

AUTHORS BIOGRAPHY

K. Graf is a professor for ship hydrodynamics at the

University of Applied Sciences Kiel/Germany and

founder of the University’s Yacht Research Unit. He has

been involved in many professional sail sport campaigns

since many years.

J. Meyer is a PhD candidate at the Christian Albrecht

University Kiel/Germany and works at the Yacht

Research Unit Kiel on the development of new

OpenFOAM based flow simulation methods.

H. Renzsch is an independent flow analysist working on

the development and application of advanced flow

simulation methods. Since his graduation from the

University of Applied Science Kiel about 12 years ago, he

has contributed to America’s Cup and Volvo Ocean Race

campaigns as flow and performance analyst.

C. Preuß graduated from the University of Applied

Sciences Kiel in 2016 and joined the Yacht Research Unit

as a flow analyst, specialized in OpenFOAM based flow

simulations, focussing on flow simulations at very high

Froude numbers.


INNOV'SAIL 2017 76

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