COUPLING OF RANSE-CFD WITH VPP METHODS: FROM THE NUMERICAL TANK TO VIRTUAL BOAT TESTING C Boehm, Delft University of Technology, NL K Graf, University of Applied Sciences Kiel, GER SUMMARY The paper proposes a new method to evaluate the performance of sailing yachts which directly implements the prediction of sailing equilibrium in a RANSE flow solver. This is done by coupling the prediction of sail forces with the hydrodynamic forces calculated by the flow code and solving the resulting imbalance in the equations of motion in the RANSE solver. The paper discusses implementation steps for the inclusion of the sail forces into the flow code as well as calculation and grid setup. Some first results of the method christened RVPP are shown for a generic yacht design and are compared with results from a classical VPP approach on the same design. The paper finishes with a discussion of the pros and cons of the method. NOMENCLATURE β Leeway angle (°) δ Rudder angle (°) μ Dynamic viscosity (Pa s) υ Kinematic viscosity ( m² s-1) υT Turbulent viscosity (m² s-1) ρ Density of water (kg m-3) τ Tab angle (°) τi Viscous stress (Pa) Ω Control Volume (m³) ω Specific turbulent dissipation (s-1) ω Angular velocity of rigid body (rad s-1) ASails Total Sail Area (m²) AW Apparent wind vector (m s-1) AWA Apparent Wind Angle (°) AWS Apparent Wind Speed (m s-1) b Body forces, normalized by mass (N) BOA Breadth over all (m) c Volume-of-Fluid Fraction (-) cD Drag Coefficient (-) cDTotal Aggregate Drag Coefficient (-) CE Efficiency coefficient (-) CE Aerodynamic Centre of Efficiency (m) cL Lift Coefficient (-) cLTotal Aggregate Lift Coefficient (-) cM Added mass coefficient (-) CV Control Volume (m³) CWL Construction Water line (m) FH Lift due to heel (N) FHß Lift due to leeway (N)
FHδ Lift due to rudder (N)
FHτ Lift due to trim tab (N) FAero Total Sail Force Vector (N) FHydro Hydrodynamic Fluid Force (N) FExt External Force (N) FSail Sail Force (N) FSA Added mass Force sails (N) flat Flattening factor of sails (-) g Gravity vector (m s-2) I Tensor of moment of Inertia (kg m²)
k Turbulent kinetic energy (m s-1) LOA Length over all (m) LCG Longitudinal Centre of Gravity (m) m Mass (kg) MHydro Hydrodynamic Fluid Moment (Nm) MExt External Moment (Nm) n Surface normal (-) p Pressure (N m-2 ) RH Added Resistance due to Heel (N) RI Induced Resistance (N) RPP Parasitic profile drag (N) RTot Total Resistance (N) RU Upright Resistance (N) RWaves Added Resistance due to sea state (N) Reef Reefing factor (-) Si Control Volume Face Surface (m²) T Total draft (m) TCB Draft Canoe Body (m) TCG Transverse Centre of Gravity (m) TWA True Wind Angle (deg) TWS True Wind Speed (m s-1) u Flow velocity (m s-1) us velocity of sails due to rotation (m s-1) uB Boat velocity (m s-1) ux,uy Components of boat velocity (m s-1) VCG Vertical Centre of Gravity (m) v Linear velocity (m s-1) xi CV face centre vector (m) xG Vector to centre of gravity (m) zceAero Aerodynamic vertical centre of
efficiency (m) 1. INTRODUCTION A conventional velocity prediction program for sailing yachts (VPP) relies on a set of aero- as well as hydrodynamic coefficients, describing the respective properties of the yacht for a given set of state variables, velocity u, heeling angle ϕ, leeway angle β and rudder angle δ. These coefficients are usually provided as tabulated values, The generation of hydrodynamic coefficients using a RANSE flow simulation method
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resembles procedures from towing tank testing: Within a predefined test matrix, flow forces for a permutation of boat speeds, heel, leeway and rudder angles are analyzed. This usually causes a large number of computational runs to be carried out, including many off-equilibrium states, necessary for interpolations purposes, however rarely encountered by the sailing yacht. This results in large computational overhead. A remedy to the drawbacks of the method described above is to calculate aerodynamic forces conventionally, however directly include the prediction of sailing equilibrium into a RANSE solver, which calculates the hydrodynamic forces on the fly. Solving for sailing force equilibrium by including the equation of motion into the RANSE solution, the window is opened wide to predict boat performance not only in calm water conditions but also in dynamic, instationary states, for example in natural seaways or while maneuvering. The R&D-project RVPP, carried out by YRU-Kiel, addresses this topic. While RVPP obviously calculates hydrodynamic forces from a RANSE simulation, aerodynamic forces are predicted from wind tunnel data or conventional (HAZEN-like) sail force models. This approach does not only reduce the computational costs of the method, it allows to easily involve the necessary optimization to reflect the sail trimming process carried out in the wind tunnel or by the sailor on board a racing yacht. The paper describes the method and discusses pros and cons. First implementation steps are presented and some first results will be shown. 2. PERFORMANCE PREDICTION A sailing yacht is a complex physical system of aerodynamic as well as hydrodynamic wings positioned in the interface of two fluids, air and water. It interacts simultaneously with them and relies solely on the interaction of fluid forces for its propulsion, which in turn depend on changing environmental conditions, in particular wind speed and direction. This makes it difficult to predict the velocity of sailing yachts from the scratch. Thus the need for special calculation procedures, so called Velocity Prediction Programs (VPPs), arise to predict the yachts performance. 2.1 APPROACH USING CONVENTIONAL VPP Conventional VPPs usually rely on a pre-calculated database of aerodynamic and hydrodynamic characteristics of a yacht. Using input values of true wind speed (TWS) and true wind angle (TWA) the force components are then balanced by setting up and solving the resulting non-linear system of equations. In order to maximize the velocity of the yacht, an optimizer is used to simulate the trimming of the sails. The aerodynamic database usually compromises of coefficients of drag and lift, cD and cL, as functions of the apparent wind angle
(AWA). These coefficients are stored for various single sails or sail sets and are generated by means of wind tunnel testing or numerical investigation. The hydrodynamic part of the database can be generated in two ways. Firstly, one can use empirical regressions derived from results of towing tank tests on systematically varied hull forms (e.g. Delft Systematic Yacht Hull Series). This approach is rather often used for custom builds with a limited budget, but due to its generic approach obviously it lacks the accuracy of dedicated investigations of the individual hull form. The second approach is to investigate the individual hull by means of towing tank testing, be it numerical or physical. Here the different components that make up total resistance and total lift of a sailing yacht have to be considered. The total resistance can be decomposed into:
( )WavesPPIHUTot RRRRRR ++++= ∑ (1) Here RTot is total resistance, RU upright resistance at non-lifting condition, RH added resistance due to heel, RI induced resistance due to production of lift and RPP parasitic profile drag of blade and rudder profile. RWaves represents the added resistance due to sea state and is often neglected since it is difficult to generalize. Total lift FH generated by the sailing yacht hull may be decomposed as:
τδβ HHHH FFFF ++= (2) Here FHß is lift generated due to leeway, FHδ is Lift due to rudder angle and FHτ is lift generated by a trim tab, if applicable.
Figure 1: Towing Tank Test Matrix for Sailing Yachts
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To capture the influence of differing sailing states, the yacht is tested at permutations of speed, heel angle, leeway angle and rudder angle. A typical test matrix is depicted in Figure 1. Typical values for generating the test matrix are:
• Non-Lifting tests o 10-20 boat speeds
• Leeway angle tests o 3-4 heel angles o 4-6 leeway angles o 5-13 boat speeds
• Rudder angle tests o 3-4 heel angles o 3-5 rudder angles o 5-13 boat speeds
This leads to a large number of test runs, normally ranging in between 100 to 300 runs. To a certain degree, the matrix can be curtailed by making it dense at special points of interest and sparse at points which are a bit out of place of expected performance. After performing the investigations, hydrodynamic coefficients are derived from the resulting forces and moments. These coefficients allow quantifying the characteristics of a sailing yacht at every occurring state by means of interpolation. Figure 2 shows a surface of the dimensionless coefficient for added resistance due to heel over boat speed and heel angle.
U [kts]468101214
Heel [°]
1020
3040
r H[- ]
-0.05
0
X
Z
Y
Added Heeling Drag Ratio
Figure 2: Coefficients for Added Resistance due to Heel The database of hydrodynamic coefficients is fed into the VPP program. In conjunction with the aerodynamic coefficients, the VPP calculates polar plots of optimal boat speed as function of TWA and TWS. 2.2 APPROACH USING RVPP RVPP is an attempt to directly implement the calculation of sailing equilibrium into a RANSE Solver. To do so, not only the RANS equations have to be solved, but also
the equations of motions of the sailing yacht, which is considered to be a rigid body. To account for the aerodynamic forces imposed by the sails, an additional, external force is modelled which is acting on the rigid body “yacht”. Since this external sailing force vector FAero is of unsteady nature, modelling of this vector implicitly requires that its calculation routine is directly coupled with the rigid body motion module. Along with gravity force and hydrodynamic forces acting on the yacht, this sailing force vector is used to solve the equations of motion. The sailing force vector itself is calculated using a HAZEN-like Sail force model. As described for the conventional VPPs, the sailing forces coefficients cD and cL as functions of AWA are stored in a database. The procedure is modified to take into account additional force components originating from movement and orientation of the boat, allowing calculating its influence on boat movement as a time series. This approach wilfully keeps up the paradigm of separation of aerodynamic and hydrodynamic investigation for several reasons: It allows taking into account sailing force data from virtually any source, in conjunction with depowering algorithms, resembling the trimming of the sail carried out by sailors. It simplifies the analysis of cause and effect of changes in aerodynamic or hydrodynamic parts of a yacht. Finally it allows to take into account advanced techniques for the prediction of aerodynamic forces, e.g. fluid structure interaction methods. In contrary to the conventional VPP approach, this procedure has no need for a database of hydrodynamic coefficients. The hydrodynamic data of the yacht is directly calculated via the RANSE solver. This has a direct impact on the number of runs necessary to predict boat velocity. Results of a VPP analysis are usually displayed in a polar plot depicting boat speed for a given true wind speed over true wind angle. On average such a plot will show 3-5 polar lines for upwind and for downwind courses.
• 3 – 5 true wind speeds • 30° – 120° TWA Upwind • 90° - 180° TWA Downwind
This gives about 60 – 100 simulation runs, which is much less than the numbers needed for a conventional VPP. Additionally, it is possible to investigate only the areas most interesting for a specific boat type, for example maximum VMG (Velocity made good) upwind and downwind, which further reduces the number of necessary runs dramatically to about 24 - 40. Another benefit of this procedure is that the impact of the hydrodynamics of the yacht on its performance should be
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captured more accurately since there is no interpolation involved in this part of the VPP investigation. The downside of the method is that the results are only valid for a specific sailing set. If an existing hull shall be fitted with a new sail set, a whole new simulation series is necessary. 3. THEORETICAL METHOD 3.1 FLOW SOLVER A RANSE solver is used to calculate the flow around the fully appended hull. Descriptions of RANSE methods are widely available, see Ferziger [2] as the authors` favourite. The governing equations of RANSE methods will be sketched here only briefly. RANSE solver use a volume based method to solve the time-averaged Navier-Stokes equations in a computational domain around the investigated body. The RANS equation evolves from time averaging mass and momentum conservation for a continuous flow. In the method used it is assumed that the Reynolds stress evolving from time averaging is modelled using the eddy viscosity hypothesis and two-equation turbulence models. Assuming incompressible flow this yields,
( )
( ) ( )( ) Ω⋅+⋅∇+∇++
⋅⎟⎠⎞
⎜⎝⎛ +−=⋅+Ω
∫∫
∫∫∫
Ω
Ω
ddS
dSkpdSddtd
S
TT
SS
bnuu
nnuuu
νν
ρρ
321
(2)
∫ ⋅S
dSdtd nu (3)
The turbulence model used in the presented approach is the Shear Stress Transport (SST) model. It calculates the turbulent viscosity νT from the turbulent kinetic energy k and the specific turbulent dissipation ω:
( )1
1 2max ,Ta ka F
νω
=Ω
(4)
In the present case two different fluids (water and air) have to be taken into account in the simulation. Therefore an additional conservation equation has to be introduced to capture the free surface interface and its deformation due to the yachts wave pattern. Since this fluids are not expected to mix, a homogenous multiphase model based on a Volume-of-Fluid (VOF) approach is applied, which assumes that the two phases share a common velocity and pressure field. Effectively the method treats both phase in the computational domain as one fluid with variable properties. The additional transport equation is solved for the VOF-fraction c in every cell, with values between 0 and 1 indicating a cell
which is filled with both fluids. The free surface interface is assumed to be represented by a value of c=0.5.
∫∫ =⋅+ΩΩ
0dSccddtd nu
(5) The density ρ and molecular viscosity μ are calculated from volume fraction c and the fluid properties as shown below. If a cell is filled with both fluids, they are assumed to share the same velocity and pressure.
( )cc −+= 121 ρρρ (6) ( )cc −+= 121 μμμ (7)
3.2 RIGID BODY MOTION To take into account the effects of hydro- and aerodynamic forces acting on the yacht, RVPP makes use of a 6-degree-of-freedom (DOF) body motion module which is embedded into the global RANSE iteration. The translation and rotation resulting from the forces acting on the body are determined by integrating the equation of linear and angular momentum. The equation of linear momentum may be written as:
Fv=
dtdm (8)
Here m stands for the mass of the investigated body, v is the linear velocity of the centre of mass and F is the resultant force. The contributions of external and internal forces to the resulting force F is listed below:
ExtHydro FgFF ++= m (9) Where g denotes the gravity vector which is positive in downward direction and Fext may be any kind of external force applied. Typical examples for this application are the sail force and the additional rudder force vector. The flow force FHydro is the resultant force of the flow field acting on the body. It is determined from the RANS equations by integrating viscous wall shear stresses and pressure field over the body’s boundary faces.
( )∑ +−=i
iiii Sp τnFHydro (10)
Here pi is the pressure acting on the face of a control volume whilst ni is the normal vector of the individual control volume face. The viscous stresses are denoted τi and the surface of the control volume face is iS . In general, the equation of the angular momentum may be written as follows:
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with I representing the tensor of the moment of inertia of the investigated body, ω the angular velocity of the rigid body and M the resultant moment acting on the body. The resultant moment M can be summarized as follows:
HydroExt MMM += (12) Here MExt represent the trimming moment due to external forces which may be expressed as:
( ) ExtGCEExt FxxM ×−= (13) with xCE representing the vector to the centre of effort of the external force and xg being the location of the centre of gravity. The dynamic contribution of the flow force to the fluid flow moment MHydro may be expressed as stated below. Here xi stands for the control volume face centre vectors.
( ) ( ) iii
Sp iiGiHydro τnxxM +−×−= ∑ (14)
The translation and rotation of the body is determined by integrating the equation of linear and angular momentum. Since the whole computational grid is kept rigidly attached to the floating body, the resulting displacements and rotations of the body are resolved by moving the complete grid. This single-grid strategy has proved to be very robust compared to mesh deformation techniques, with the only additional effort needed to keep the RANSE solution valid being the correction of flow variables for grid movement 3.3 AERODYNAMIC FORCES The aerodynamic model is responsible for the calculation of aerodynamic forces, being more precise the aerodynamic force vector. The calculation of the unsteady aerodynamic force vector is based on a HAZEN-like sail force model [7]. It is implemented as a direct two-way coupling with the flow solver and coded in JAVA. As an initial input before the beginning of the calculation procedure, the user has to provide tables with permutations of True Wind Angle (TWA) and True Wind Speed (TWS) as well as data about the sail plan of the yacht and aerodynamic data of the individual sails in form of lift and drag coefficients as functions of the Apparent Wind Angle (AWA).
During the simulation, the flow code is called by the sail force calculation routine at the beginning of every time-step and receives the yachts current linear and angular velocity components as well as its orientation in space as input data. From these the sail force vector FAero is calculated in the following manner: First, the apparent wind vector AW is calculated as a function of true wind conditions, boat speed and heel angle.
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡++
++=
0cossin
cosyy
xxusuTWATWS
usuTWATWSφAW (15)
Here, the vector us has been added in the equation to account for changes in AW due to rotating motions of the boat, namely pitch and roll. Thus, us is defined as the angular velocity of the boat ωB times the vertical centre of effort of the sails, zceAero, see (16).
AerozceBωus = (16) Using AW as calculated above, one can easily derive AWA (17) and AWS (18) by applying basic vector calculus.
x
y
AWAW
aAWA tan= (17)
22
yx AWAWAWS += (18)
RVPP uses a modification of the sail force calculation method that has been implemented in the IMS velocity prediction program. It is based on individual sail force coefficients for mainsails, jibs and spinnakers, derived from wind tunnel tests. Whilst the individual sail force data for RVPP may come from any source, the procedure has been adapted because of its versatile usable approach. From the individual sail coefficients aggregate lift and drag coefficients cLtotal and cDtotal for a sail set are calculated from:
222*2 reefflatcCEreefcc LDTotalD += (19)
LTotalL creefflatc 2= (20) Here cD and cL are weighted sums of the drag and lift coefficient of all sails in the sail set while CE* is an efficiency coefficient, taking into account the quadratic parasite profile drag and the effective span of the sail set. reef and flat are trimming parameters for the sail to obtain maximum boat velocity via depowering the sail or reducing sail area. flat is a linear reduction of lift and a
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squared reduction of induced and parasitic drag at constant span, corresponding to a sail chord or traveller angle trimming action of the sailors. reef is a factor taking into account a reduction of sail luff length as the name implies, with corresponding impact on lift, drag and effective span. Whilst theoretically available, the factor reef is usually omitted in the current version of RVPP. This mainly owed to the fact that the development of RVPP aims towards racing yacht for which reefing most often is not an option. For details of the IMS method see Claughton [4] or the IMS documentation from the Offshore Racing Council. By using the aggregate sail coefficients as calculated in (19) and (20) one can calculate the sail force FS as shown in (21):
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡−−
⋅=
0sincoscossin
21 2
AWAcAWAcAWAcAWAc
AWSA
DTotalLTotal
DTotalLTotal
SailsAirρSF
(21)
Experience gained from seakeeping investigations showed that the added air mass of sails contributes significantly to the moment of inertia of a sailing yacht, especially around the longitudinal axis. For details see Graf [5]. Therefore an additional added mass force FSA due to the movement of the sails in the surrounding air is taken into account:
BS ωF SailsAirMA Ac ρπ4
−= (22)
This leads to the final definition of the sail force vector as shown below.
SASAero FFF += (23) After transformation from the coordinate system planar to the water surface to a boat-fixed coordinate system, the sail force vector FAero is applied to the boat at the position of aerodynamic longitudinal and vertical centre of efficiency. At the current state of the program the centre of efficiency CEAero is approximated to be at the geometrical centre of the sails. Since this approximation does not coincide with the physical position of CEAero, a better approximation is currently under development. 3.4 OPTIMIZER To reflect the efforts of the sailors in order to trim the sails for optimum boat speed an optimizer has to be applied on the trim parameter flat. The optimizer applied here is a custom modification of Brent’s Method, combining a bracket search with a parabolic search algorithm.
4. IMPLEMENTATION The theoretical method as described in the previous chapter is implemented in the commercial RANSE code Star-CCM+5.02, which has been used for the investigation presented here. Star-CCM+ solves mass- and momentum transport equations using a finite volume approach with polyhedral grid cells, Cartesian velocity components and a cell centred flow variable arrangement. For wall boundary conditions the SST turbulence model uses a wall treatment scheme, where low Reynolds number modelling of turbulence is used near a wall if the local dimensionless wall distance y+ falls below the limits of the logarithmic wall functions. Motions of the rigid body are accounted for using the DFBI-Solver which calculates 6-DOF Motion of a rigid body. Translations and rotations of the yacht are resolved by moving the whole computational grid. The equations of motion are solved for in 5-DOF with the yaw rotation being kept fixed. Star-CCM+ is based on a client-server architecture with a lightweight client based on a JAVA-Interface and a C++ Server. It is fully parallelized using a domain decomposition approach and the SPMD (Single Program Multiple Data) approach to run on a network of individual machines. MPI (Message Passing Interface) is used as the underlying messaging and synchronization mechanism. At YRU-Kiel Star-CCM+ runs on a 98-node Linux cluster. However, for a typical run only 48 processors have been available for this study. For the study presented here, a typical computational grid consists of approx. 2 million hexahedral grid cells. A typical run time for an individual run (one optimal boat speed for a specific TWA and TWS combination) on 48 processors is approx. 8 h to achieve an imbalance of body forces of less than 10 N. 5. BENCHMARK DESIGN For the following investigation a generic benchmark design has been created. Choice fell on a GP26 level class racer because this design being based on a box rule which makes the choices of principal dimensions, sail plan etc. pp. much easier. Another reason for this choice is that this boat type can be regarded as modern but conventional, meaning that it has no canting keel, wing mast or something alike. This makes it easier to compare the results with VPP data gained by using hydrodynamic data from a regression of systematic hull variations. The lines plan of the GP26 design is shown in Figure 1. The authors are not claiming to have come up with a particular good design, the design being just a basis for testing of the method.
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Figure 1: Lines plan of the GP26 design Calculation of centre of gravity and mass moment of inertia have been carried out using estimations of the weight of keel, bulb, rig, accommodation and panel weight of the canoe body along with specifications of the class rule. The resulting principal dimensions and boat characteristics are shown in Table 1. Here the weight of the boat reflects not the measurement weight but the sailing weight including crew and spare sails.
Table 1: Principal dimensions and boat characteristics Table 2 shows the characteristics of the sail plan for upwind and downwind sail set. The rig has an adjustable backstay, but no checkstay, the main sail has full battens and the asymmetric spinnaker is tacked on centreline. These rig characteristics are reflected in the aerodynamic coefficients of the sails.
Table 2: Sail Plan used for the simulation 6. SETUP Starting point of the setup is the yacht in its initial sailing trim including crew and effects according to Table 1. This corresponds to a displacement of 1485.2kg and a CG of (3.609m, 0.0m,-0.181m) measured from aft and at height of CWL.
Figure 4: CAD Model of the investigated design The geometry is blocked with a hexahedral volume grid. The grid consists of a body fitted O-Grid around yacht and appendages which then eradiates in the far field. Note that grid resolution is spread in radial direction around the initial water plane for a better capturing of the free surface when the boat is sailing in heeled conditions (Figure 5). The simulation environment around the yacht body extends 1 boat length L to front and sides of the test case and 2L in the wakefield. The box extends 0.5L above the hull and 1L below. The computational domain consists of approximately 2 million grid cells, with refinements in
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the vicinity of the water surface and of the boundary layer on the yacht surface.
Figure 5: Blocking of the computational grid The box walls are set as velocity Inlet whilst the yacht hull and appendages are treated as hydrodynamic smooth no-slip walls. The fluid properties are that of seawater according to ITTC with a dynamic viscosity ν of 1.219e-3 [Pa s] and a density ρ of 1026 kg m-3. Free stream turbulence intensity level has been set to 1%. 7. FIRST RESULTS In the following some of the first results obtained with RVPP are shown. Boat speed has been calculated at a TWS of 5m/s. TWAs considered for the upwind sail set range from 30° - 100°, the TWAs for the downwind sail set are varying from 90° - 180°.
Figure 6: History Plot of Fx
Figure 6 shows a history plot of the longitudinal-component of the force acting on the sailboat. The dotted line shows the fluid and gravity force whilst the solid line depicts the total force, including the external force from the sails. The plot is divided into five phases, marked by the dotted lines. Phase I is a start-up phase in which the simulation is allowed to converge from its initial values to a stable solution without rigid body motion. Phase II marks the beginning of the rigid body motion, which is at first conducted with steady sail forces similar to the approach in a towing tank. Note that the solid line reaches the abscissa, marking the equilibrium of forces. Next unsteady sail forces are introduced (Phase III – V) and allowed to reach convergence to sailing equilibrium. When convergence is reached, the optimizer starts to change the flat factor, trying to optimize boat speed. This procedure is conducted for at least three flat factors.
Figure 7: wave pattern of the boat at TWA 140° The polar plot in Figure 8 shows first results of the simulation at a TWS of 5m/s. The solid lines show the results using RVPP whilst the dotted lines have been calculated using AVPP, YRU-Kiel’s in-house conventional VPP. The results from AVPP have been calculated using the regressions of the Delft Systematic Yacht Hull Series (Keuning [6]) for the bare hull resistance. Coefficients modelling the influence of lift are also derived on empirical regressions with some extensions derived from linear lifting surface theory. For more details of the method behind AVPP see Graf [1]. One can see that the results from RVPP are reasonable close to the results from conventional VPP. Naturally one has to expect differences, since the VPP result has been achieved using empirical formulations, whilst the results using RVPP take into account all features of the geometry and do not interpolate hydrodynamic flow forces but rather predict them for the actual sailing state.
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Generally said, for sailing states which are fully powered up (broad reach) the velocity potential predicted by RVPP is a little bit higher than that predicted by AVPP. In return, AVPP predicts slightly higher velocities in sailing states which are characterized by less sail forces, e.g. TWA’s greater than 150°. Consequently, RVPP shows the characteristically hollow of the downwind polar to be more distinctive, clearly urging to avoid a dead run.
Figure 8: Velocity Polar plot For Upwind conditions, one can see a similar pattern. The boat speed predicted by RVPP is a little bit higher than the results gained from the conventional VPP. This holds especially true for courses where the boat sails on a beam reach. This is an analogy to the downwind results where the differences in boat speed were also biggest at the sailing point where the heeling moment acting on the boat was highest. An important topic when comparing velocity polar plots is the Velocity Made Good, VMG, as a measurement of
the boat speed in terms of making way to windward or leeward. The common formulation for VMG is:
( )β−⋅= TWAVMG cosBu (24) With boat speed uB, leeway angle ß and true wind angle TWA. Figure 9 shows VMG in m/s for upwind and downwind polar lines for both VPP methods. As a convention, TWA < 90° is considered positive whilst TWA > 90° is negative. One can see that upwind VMG is almost equal for both methods, with a little amount of higher VMG values calculated by RVPP for TWA <60°. Maximum VMG upwind is 2.31m/s at a boat speed of 2.94m/s and a TWA of 37.9° for the results gained from AVPP. The corresponding values calculated by RVPP are a VMG of 2.41m/s at a boat speed of 3.13m/s and a TWA of 39.6°. This results in difference in VMG 0.1m/s between the two methods.
Figure 9: VMG Downwind VMG shows almost the same top VMG speed but at different TWA. This is reflected in the VMG max values, with maximum VMG downwind as calculated by AVPP being 2.85m/s at a TWA of 146.2° and a boat speed of 3.43m/s. Downwind results calculated by RVPP give a VMG of 2.86m/s at a boat speed of 3.71m/s and a TWA of 140.4°. This gives a rather small overall difference in VMG of 0.01m/s between the two methods. Whilst the results presented above are quite satisfactory for the first results of a method being in an early development phase, there a currently some unsolved problems present.
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A visual analysis of the present simulation results showed that RVPP currently suffers from a problem regarding the smooth resolution of the free surface for heel angles greater than 15°. A typical example of this problem is shown in Figure 10. Here one can clearly see the wave pattern of the free surface on starboard side is crossed by stripes. The resolution on port side on the contrary is quite satisfactory.
Figure 10: Resolution of free surface at larger heel angles Figure 11 shows an x-normal plane of the grid with the free water surface included. One can see that the grid pattern on the port side almost follows the free surface contour, while on starboard side the grid cells are intersected in an inappropriate angle. From this picture one can conclude that the difficulties encountered with the free surface resolution are related to grid resolution and are most likely interpolation errors.
Figure 11: Free surface intersection of grid cells The problem seems to be grounded in the use of a single grid strategy with a moving computational domain. This strategy arises the need to produce a grid which is sufficient to resolve the free surface for heel angles of +/- 30° around the boat’s CWL. Possible solutions to this problem can be divided in those which keep up the strategy of single moving grid and those who do not. For the first a better alignment of the grid lines with the expected heel angles seems to be a good idea, but produces complicated grid topologies. Another idea which will probably give the expected
results is a refinement of the grid in the far field. This is not very desirable because it increases the computational effort. Another possible grid strategy could be to deform the grid around the boat instead of moving the whole grid. This method has been used before by the authors with another CFD package and was abandoned since it was neither very flexible nor reliable since it tended to produced negative Jacobian of the CV’s. An additional strategy could be to use overlapping grids with an orthogonal grid for the far field and a box around the yacht which could be resolved with a fine polyhedral grid. In the authors opinion this would be the most flexible and elegant solution, alas it is not available in the current Version STAR-CCM+. This leads to the conclusion that until overlapping grid technique is available; the other mentioned solution approaches have to be tried out. 8. DISCUSSION The paper presented here shows a new method to predict the performance of sailing vessels. It proposes to directly include the prediction of velocity into the simulation of the boat hydrodynamics by applying the sail forces via a dynamic sail force vector. First results show that the method is generally feasible. As an example, a GP26 boat design was investigated with RVPP. The results gained have been compared with data from a conventional VPP method. The advantages of the method include lesser number of simulations necessary to calculate a velocity polar plot and therefore a smaller computational effort as well as an increase in accuracy in the consideration of the hydrodynamics. A disadvantage is that the calculated performance prediction is valid only for a specific sail set. If the performance of others sail sets shall be investigated, the calculation procedure has to be redone. A further possible disadvantage is that the method does not allow the direct comparison of resistance curve and lift slope, thus eventually impending the detection of cause and effect of geometrical changes on boat performance. Since the method is still in its development phase it is naturally not flawless. The major problem in the current approach is vested in the need to accurately resolve the free surface in heel angles of +/- 30° around the boat’s CWL. Possible solutions to this include grid refinement, grid morphing and overlapping grids. Further objectives include the implementation of yaw balance, which has to be based around an improved formulation to predict the LCE of the sails.
The Second International Conference on Innovation in High Performance Sailing Yachts, Lorient, France
Another desirable feature is to include the dynamic pitch an roll moment applied by movement of the crew or other types of ballast. As a final and most important step, the method has to be validated. It is planned to do so against VPP results gained from processing of high quality towing tank data. 9. REFERENCES 1. GRAF, K. and BÖHM, C.: A New Velocity
Prediction Method for Post-Processing of Towing Tank Test Results, Proc. 17th Chesapeake Sailing Yacht Symposium, Annapolis, Maryland, March 2005
2. FERZIGER, J.H. and PERIC, M.: Computational Methods for Fluid Dynamics, Springer, New York 2002
3. BÖHM, C. and GRAF, K.: Validation of RANSE simulations of a fully appended ACCV5 design using towing tank data Proceedings of the INNOV'Sail08, Lorient, France, April 2008
4. CLAUGHTON, A., WELLICOME, AND SHENOI: Sailing Yacht Design / Theory, Addison Wesley Longman Limited, Essex, GB, 1998
5. GRAF, K., PELZ. M., BERTRAM, V. AND SÖDING, H.: Added Resistance in Seaways and its Impact on Yacht Performance, Proc. 18th Chesapeake Sailing Yacht Symposium, Annapolis, Maryland, March 2007
6. KEUNING, J. A.: Regression of the Delft Systematic Yacht Hull Series, Proceedings of the 15th Intl. HISWA Symposium, Amsterdam/NL, 1998
7. HAZEN, G.S.: A model of sail aerodynamics for diverse rig types, Proceedings of the New England Sailing Yacht Symposium, 1980
10. AUTHORS BIOGRAPHY Christoph Böhm holds a diploma degree in naval architecture from the University of Applied Sciences Kiel. He is currently working as a flow scientist at the Yacht Research Unit Kiel. He is specialized on RANSE simulations of sailing yacht appendages and hulls as well as subsequent VPP integration. He is currently working towards his PhD thesis at TU Delft. Kai Graf is professor for ship hydrodynamics at the University of Applied Sciences Kiel and senior scientist of the Yacht Research Unit Kiel. Kai is working on sailing yacht aero- and hydrodynamics since 1998, being specialized on numerical simulation methods.
