# RANSE-CFD Simulation of Rigid Multiple Sails

Patrick Queutey, Emmanuel Guilmineau, Jeroen Wackers, Michel Visonneau

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Patrick Queutey, Emmanuel Guilmineau, Jeroen Wackers, Michel Visonneau. RANSE-CFD Simulation of Rigid Multiple Sails. 5th High Performance Yacht Design Conference, HPYD5, Mar 2015, Auckland, New Zealand. hal-01202507

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# RANS AND DES CFD SIMULATION OF RIGID MUTIPLE SAILS

Patrick Queutey<fnref n="1" />, patrick.queutey@ec-nantes.fr, Emmanuel Guilmineau<fnref n="1" />, emmanuel.guilmineau@ec-nantes.fr, Jeroen Wackers<fnref n="1" />, jeroen.wackers@ec-nantes.fr, Michel Visonneau<fnref n="1" />, michel.visonneau@ec-nantes.fr.

**Abstract.** The numerical simulation of the flow around sails addressed here forms part of the challenging objective of the full-scale simulation with the help of a single tool of a complete high performance sailing boat including hull, appendages (foils, rudders), sails and masts. Parallel to sailing boats design, sail is also a topical subject as a promising solution for auxiliary zero-emission propulsion system for marine vehicles. The numerical simulations are conducted with ISIS-CFD, the unstructured Reynolds-averaged Navier-Stokes solver developed at the LHEEA Laboratory. This flow solver is aimed at the simulation of realistic flow problems in all branches of marine hydrodynamics. The case studied still in progress concerns multiple sails with a genoa and a mainsail in upwind condition as experimented in the University of Auckland's Twisted Flow Wind Tunnel. Forces and pressure distributions in different sections are available at various trim angles to find the optimum. The focus of the present study is to compare CFD with aforementioned EFD (Experimental Fluid Dynamics) and to address opened questions in order to find best practices in general for reliable computation of rigid sails. One and two equations turbulence modelling have been used and compared simulations: the Spalart-Allmaras model, the isotropic $k-\omega$ SST model of Menter and our non-isotropic EARSM model. DES (Detached Eddy Simulation) approach based on the $k-\omega$ model has also been considered as hybrid RANS-LES modelling in the context of unstructured finite-volume grids.

## 1. INTRODUCTION

Improvement of steering efficiency for sailing boat includes both hydrodynamics and aerodynamics improvement of the boat. Considering latest racing sail yachts, the research is to provide a better understanding about interactions between the hull, the appendages, the sails, the wind and the air and water interface and the motion of the boat. A better understanding is a precondition to ensure the success of the design process. Along with this racing boat design for which the wind is a key driving force, sail is also a topical subject as a promising solution for auxiliary zero-emission propulsion system for marine vehicles in general.

Both experimental fluid dynamics (EFD) and computational fluid dynamics (CFD) are the usual tools to investigate the flow field and forces. However the difficulty for wind tunnel testing is to consider real scale system and therefore extrapolation to full scale can be questionable. For its part, advanced CFD tools are now more and more able to address the system complexity and interactions in this field as the computational resources increases.

The present study is limited to the computation of sails only in upwind conditions. The viscous flow solver ISIS-CFD used to this purpose is aimed at the simulation of realistic flow problems in all branches of marine hydrodynamics. Unlike ship resistance and propulsion, reliable sails experimental data is scarce. This is why the present study, as a first exercise with the solver to deal with sails, focuses on upwind conditions. In this case the flow is mostly attached and therefore can be addressed more easily with CFD within different level of approximation from thin airfoil theory to most advanced CFD tools. Reader may consider [1] for a comprehensive view of the recent work carried out on this subject. The case of downwind sail is challenging as it implies massive separations and has been less investigated

numerically. Recent study about downwind sail has been done with the considered viscous flow solver but coupled with an original finite element code to model the sail in the context of the fluid/structure interaction [2]. The considered flow solver has been extensively validated and is widely used for ship hydrodynamics involving Reynolds number between $10^6$ for model scale and $10^9$ in full scale condition. The considered upwind and rigid sails condition addresses very thin surfaces with relatively low Reynolds numbers (in the order of $10^5$ - $10^9$). Even if the flow is mainly driven by the pressure in this case, observed onset of separation and progression of vortical structures will be therefore strongly dependant on the turbulence modelling retained and to the still challenging laminar-to-turbulent transition phenomena. The case studied, still in progress, concerns multiple sails with a genoa and a mainsail in upwind condition as experimented in the University of Auckland's Twisted Flow Wind Tunnel [3].

## 2. NUMERICAL METHOD

Simulations have been performed with our in-house ISIS-CFD flow solver, available as a part of the FINE™/Marine computing suite to solve the incompressible unsteady Reynolds-averaged Navier-Stokes (RANS). The solver is fully implicit, based on the finite volume method to build the spatial discretisation of the transport equations. Surface and volume integrals are evaluated according to second-order accurate approximations and the unstructured discretisation is face-based. Time derivatives are evaluated using three-level Euler second-order accurate approximations. While all unknown state variables are cell-centred, the systems of equations used in the implicit time stepping procedure are constructed face by face. Fluxes are computed in a loop over the faces and the contribution of each face is then added to the two cells

<footnote n="1">¹ Ecole Centrale Nantes, LHEEA - CNRS, France</footnote>
next to the face. This technique poses no specific requirements on the topology of the cells. Therefore, the grids can be completely unstructured; cells with an arbitrary number of arbitrarily-shaped faces are accepted.

Pressure-velocity coupling is obtained through a Rhie & Chow SIMPLE type method: in each time step, the velocity updates come from the momentum equations and the pressure is given by the mass conservation law, transformed into a pressure equation. In the case of turbulent flows, transport equations for the variables in the turbulence model are added to the discretisation. Free-surface flow is simulated with a multi-phase flow approach: the water surface is captured with a conservation equation for the volume fraction of water, discretised with specific compressive discretisation schemes, see [4].

The method features sophisticated turbulence models: apart from classical one equation and two-equation $k-\epsilon$ and $k-\omega$ models [5], the anisotropic two-equation Explicit Algebraic Reynolds Stress Model (EARSM) [6], as well as hybrid RANS-LES(Large-Eddy Simulation) [7,8]. The technique included for the 6 degree of freedom simulation of ship motion is described by [9]. Time-integration of Newton's laws for the ship motion is combined with analytical weighted or elastic analogy grid deformation to adapt the fluid mesh to the moving ship.

Parallelization is based on domain decomposition. The grid is divided into different partitions; these partitions contain the cells. The interface faces on the boundaries between the partitions are shared between the partitions; information on these faces is exchanged with the MPI (Message Passing Interface) protocol. This method works with the sliding grid approach and the different subdomains can be distributed arbitrarily over the processors.

### 3. MODEL TEST CASE

The case retained corresponds to the test setup used in the wind tunnel of Yacht Research Unit (YRU), University of Auckland [3]. It consists in a test plate with AC33 America's Cup class sails (mainsail and genoa) suspended above, Figure 1. These sails are built at 1/15th-scale. The corresponding data presented in [1,3] are measurements of pressures from pressure transducers and build into the sails along four horizontal sections of each sail, Figure 2 and Table 1. The tables of the pressure coefficients as well as IGES files of the sail geometries have been downloaded from [10]. These IGES files correspond to sails of zero thickness whereas the rigid sails in the wind tunnel were less than 4mm thick and chamfered at about 20° on the windward side. In the simulations presented here the sails have been used as they are from the IGES definitions due to the difficulty in

producing a suitable CAD model with finite thickness and correct chamfer.

<figure><img src="image_2.png" /><figcaption>Figure 1: YRU wind tunnel with sails [1]</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2: Locations of the 8 test sections with pressure measurements. The genoa on the left and the mainsail is on the right.</figcaption></figure>

<table><caption>Table 1: Y-Vertical positions (in m) of the pressure taps. The bottom of the genoa bottom is located at Y=0m</caption><thead><tr><th>Sections</th><th>Sec1</th><th>Sec2</th><th>Sec3</th><th>Sec4</th></tr></thead><tbody><tr><td>Genoa</td><td>Y=0.3</td><td>Y=0.7</td><td>Y=1.1</td><td>Y=1.5</td></tr><tr><td>Mainsail</td><td>Y=0.583</td><td>Y=0.983</td><td>Y=1.383</td><td>Y=1.983</td></tr></tbody></table>

From the experiments, varying the sheet angle, four genoa (G#) trims and four mainsail (M#) trims are available resulting in 16 test conditions. The yaw angle
between the upcoming free stream and the line through
the tacks of the sails is 19°. Among these 16 conditions,
it was found that the optimum configuration from the
point of view of the driving forces was the G3M2
configuration. The main particulars of the sails are a
distance between the bottom of the genoa (root of the
plate) and the top of the mainsail of 2.24 m, the
maximum width of the mainsail is 0.65 m, and 0.70 m
for the genoa. The area of the two sails is S = 1.8 m².

As a first CFD about rigid sails, the present study retains
the G2M3 configuration. Based on a mean chord
c=0.49m, a fluid density of 1 kg/m³, a dynamic viscosity
of the fluid of 1.515x10⁻⁵ Pa.s, and a reference velocity
Uref = 7.11 m/s, the Reynolds number Re is 2.3x10⁵ to
follow the test conditions in [1]. The free-stream
turbulence intensity in the tunnel test was about 3%.

4. NUMERICAL SETTINGS

This section is devoted to the description of the
numerical settings retained to compute the flow around
the rigid sails. The choice of the computational domain,
boundary conditions and grid generation is first presented
followed by a grid convergence analysis to evaluate the
numerical uncertainty. This assessment was done on the
basis of the EARSM turbulence model only. Simulations
have been performed on the national research IBM
x3750 cluster (2.7 GHz 8 cores quad-processors).

4.1. Computational domain

The size of the computational domain is [-5 m, 10 m] x [-0 m, 2.9 m] x [-5 m, 5 m] in X, Y and Z directions respectively. Y = 0 corresponds to the additional plate and X = 0 is closed to the tack of the main sail. The mesh is generated by the unstructured automatic mesh generator Hexpress™ This software generates meshes containing only hexahedral cells except in specific case of zero-thickness surfaces where prismatic cells are generated close to limiting curves of these sheets. Figure 3 illustrates the computational domain with highlight of the sails and of the plate The sails have been rotated with the prescribe 19° yaw angle.

<figure><img src="image_4.png" /><figcaption>Figure 3: Computational domain.</figcaption></figure>

Concerning the boundary conditions (BC's), a uniform
velocity Uref aligned with the X-axis is prescribed at the
inlet plane. The same boundary condition applies on the
sides. At the outlet pressure is prescribed to zero. On the
top, a slip boundary condition is used to approximate the
roof of the wind tunnel. A slip boundary condition is
applied on all the bottom plane Y = 0 to simplify the grid
convergence study but a no-slip condition will be used on
a part of it to improve the tunnel test condition with the
presence of the plate, see Figure [3]. No-slip boundary
condition applies on both sides of zero thickness sails.

In experiments, the inlet flow is untwisted and tests were
performed outside the tunnel boundary layer.

This computational domain does not respect the
complexity of the real wind tunnel configuration as
partially shown in Figure 1 and fully described in [3]. As
performed in [1] with the help of structured grids, a more
appropriate and possible numerical approach to better
reproduce EFD from CFD in this case would be to
consider a simulation into two steps: the first one with
most of the complexity of the tunnel walls (no-slip)
including the sails (frictionless BC's) to investigate the
blockage effects, and the second one, the "sails model",
with a simplified tunnel that focuses on the sails (no-slip)
with the inlet prescribed from the "blockage model" of
the first step. However, the use of structured grids makes
things easier for that, mainly for interpolating the inlet
BC's of the "sails model" from the "blockage model". In
our case it is not possible to easily interpolate between
unstructured grids even in prescribed planes since non-
matching grid points cannot be guaranteed.

4.2 Grid convergence analysis

A grid dependency study has been performed with the
help of three systematically refined grids, namely Grid1,
Grid2 and Grid3. The case has been simplified by
considering the entire bottom plane Y = 0 as a
frictionless wall (slip BC). A refinement box with
explicit refinement criterion is added all around the sails
whose extension is [-0.75 m, 1.5 m] x [0 m, 2.5 m] x [-
0.4 m, 0.4 m] in X, Y and Z directions respectively.

The number of cells is indicated in the second column of Table 2. For all the grids, the non-linear EARSM turbulence model is used with a target Y⁺ value of 0.3 on the sails prescribed into the mesh generator. As an example, with grid Grid3, after the run, the computed average value of Y⁺ on the sails is about 0.17 with a maximum value of 0.97. The target cell size in the refinement box is 0.0313 m for grid Grid1, 0.0188m for Grid2 and 0.0150 m for Grid3. It is underlined the difficulty to assume a perfect scale on the grid size based upon a systematically refined characteristic grid size in case of unstructured grids.

Figures 4 shows the surface mesh and Figure 5 is a cut at
an arbitrary Y section corresponding to grid Grid3 with
visible enhancement of the grid density at the vicinity of
the leading and trailing curves of the sails. With Grid3,
the mainsail has 270k cells faces on its surfaces and the
genoa has 219k cells and inside the refinement box the isotropic grid resolution is around 6 mm (target was 15 mm). On these sail surfaces the characteristic length scale of the grid is 5.5 mm with improved resolution divided by two near the edges.

<figure><img src="image_5.png" /><figcaption>Figure 4: Surface mesh</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 5: Y-section showing the volume mesh</figcaption></figure>

Aerodynamic forces are presented in term of dimensionless coefficients with normalization by $ρU_{ref}^2S/2$. These forces (both pressure and friction) are integrated all over the sails and projected along the direction of the incoming flow (wind) to give the drag coefficient $C_D$ and normal to it for the lift coefficient $C_L$. 10,000 iterations are used in all cases and the value of the forces are averaged during the last 5000 non-linear iterations. On grid Grid3, Table 3 and Table 4, the standard deviation of the drag coefficient is $2.6x10^{-4}$ and $7.9x10^{-4}$ for the lift coefficient with denotes a relatively well established steady flow. Concerning the CPU cost, with 64 partitions for grid Grid3, the 10,000 non-linear iterations are achieved within 20 hours.

For the considered case of upwind sail aerodynamics, we find that the convergence property is very sensitive on the loads since these loads, both drag and lift, are highly dominated by the pressure and also strongly dependent on flow separation. Tables 3 and 4 again provide details about the contributions of the pressure and of the friction to the forces and for each sail. The square of the lift coefficient is also reported as it is related to the induced

drag coefficient (additional resistance force induced by the lift) in the thin airfoil theory. If the mainsail largely contributes to the drag (83%), the lift is divided equally between the genoa and the mainsail

<table><caption>Table 2: Grid convergence summary on forces, lift ($C_L$) and drag ($C_D$)</caption><thead><tr><th>Grid</th><th>Number of cells</th><th>C<sub>D</sub></th><th>C<sub>L</sub></th><th>C<sub>L</sub><sup>2</sup></th></tr></thead><tbody><tr><td>Grid1</td><td>4.76M</td><td>0.15381</td><td>1.23965</td><td>1.53673</td></tr><tr><td>Grid2</td><td>8.64M</td><td>0.15282</td><td>1.23181</td><td>1.51736</td></tr><tr><td>Grid3</td><td>14M</td><td>0.15232</td><td>1.23067</td><td>1.51454</td></tr></tbody></table>

Richardson extrapolation fails on the lift and gives a drag coefficient of 0.151 with an observed order of convergence of 2.6. With such a high observed order of convergence, extrapolation with assumed second order of accuracy is considered to be more reliable. Such an extrapolation gives a drag coefficient of 0.1509 and a value of 1.221 for the lift. Based on this analysis, we can conclude that numerical discretisation error is about 1%.

<table><caption>Table 3: Contributions of pressure and friction to the drag ($C_D$) and for each sail with grid Grid3</caption><thead><tr><th>C<sub>D</sub></th><th>Genoa</th><th>Mainsail</th><th>Total</th></tr></thead><tbody><tr><th>Pressure</th><td>0.02294</td><td>0.12225</td><td>0.14519</td></tr><tr><th>Friction</th><td>0.00250</td><td>0.00463</td><td>0.00713</td></tr><tr><th>Total</th><td>0.02543</td><td>0.12689</td><td>0.15232<br>Std=2.6x10<sup>-4</sup></td></tr></tbody></table>

<table><caption>Table 4: Contributions of pressure and friction to the lift ($C_L$) and for each sail with grid Grid3</caption><thead><tr><th>C<sub>L</sub></th><th>Genoa</th><th>Mainsail</th><th>Total</th></tr></thead><tbody><tr><th>Pressure</th><td>0.61132</td><td>0.62085</td><td>1.23217</td></tr><tr><th>Friction</th><td>-2.73x10<sup>-4</sup></td><td>-1.23x10<sup>-3</sup></td><td>-1.51x10<sup>-3</sup></td></tr><tr><th>Total</th><td>0.61105</td><td>0.61962</td><td>1.23067<br>Std=7.9x10<sup>-4</sup></td></tr></tbody></table>

Thereafter, the settings of the finest grid Grid3 are retained for the working grid used to evaluate and compare the influence of turbulence modeling on the flow field and on the forces.

## 5. NUMERICAL RESULTS

This section compares the numerical simulations obtained with different turbulence modelling, from the one equation Spalart-Allmaras to a DES approach as hybrid RANS-LES modelling. To this purpose the computational domain is the same as previously described with addition of the plate with a no-slip boundary condition. The grid generated is based on grid Grid3 settings and the size increases to 20M due to the added cells to resolve the plate wall. Comparison with experiments concerns the pressure distribution of the pressure coefficient defined as $C_p = 2(p-p_\infty)/(ρU_{ref}^2)$ where p is the pressure, $p_\infty$ the undisturbed upstream pressure and $U_{ref}$ the uniform inflow velocity.
Simulations have been carried out in the same manner as the convergence analysis with the EARSM model except for the DES simulation. In this case, the simulation is run unsteady with a constant time step of 0.00035 seconds which corresponds to the characteristic timescale ($U_{ref}/c$ = 0.0689s) divided by 200. Slightly more than 14000 time steps have been computed corresponding to a physical duration of 5 seconds. The averaging process to compute the mean flow features starts after $t = 2.2$ s, corresponds to a duration of 2.8 s or 40 times the characteristic timescale. Such a choice has been retained according to settings used for studies involving DES modelling of the flow around bluff bodies [7,8]. The CPU cost represents 116h using 128 processors, 8 times more expensive than the steady simulation with the EARSM model on the same grid and same number of partitions.

## 5.1. Forces

The lift and drag coefficients, relatively to the undisturbed flow direction at inlet, are listed in Tables 5 and 6 below depending on the turbulence modelling and with separate contribution of the two sails.

<table><caption>Table 5: Drag coefficient</caption><thead><tr><th>C<sub>D</sub></th><th>Genoa</th><th>Mainsail</th><th>Total</th></tr></thead><tbody><tr><td>SA</td><td>0.01631</td><td>0.12738</td><td>0.14387</td></tr><tr><td>K-ω SST</td><td>0.01992</td><td>0.12079</td><td>0.14700</td></tr><tr><td>EARSM</td><td>0.02530</td><td>0.12695</td><td>0.15225</td></tr><tr><td>DES</td><td>0.02826</td><td>0.12437</td><td>0.15263</td></tr></tbody></table>

<table><caption>Table 6: Lift coefficient</caption><thead><tr><th>C<sub>L</sub></th><th>Genoa</th><th>Mainsail</th><th>Total</th></tr></thead><tbody><tr><td>SA</td><td>0.66271</td><td>0.62610</td><td>1.28881</td></tr><tr><td>K-ω SST</td><td>0.64574</td><td>0.62941</td><td>1.27515</td></tr><tr><td>EARSM</td><td>0.61033</td><td>0.61792</td><td>1.22827</td></tr><tr><td>DES</td><td>0.64283</td><td>0.64887</td><td>1.29171</td></tr></tbody></table>

Regardless of the turbulence model, the first observation from these tables is that the mainsail is the major contributor to the drag (more than 80%) and that the lift is equally divided between the two sails. The second point is that the loads are strongly dominated by the pressure which represents around 95% of the drag and the essential of the lift.

The last point concerns the dispersion of the predicted coefficients depending on the turbulence model. The larger dispersion is the drag from genoa which is about 50% but only 5% for the mainsail. As a consequence, since the mainsail is the main contributor to the drag, the dispersion of the total drag is only 6%. The dispersion of the results for the total lift coefficient is only 5%, in the same order of magnitude as the drag coefficient, with higher dispersion of 8% for the genoa than for the mainsail with 5%.

The computed values from [1] with the k-ω SST model on the G2M3 configuration with a blockage model are estimated to be $C_D = 0.144$ and $C_L = 1.22$ which are

between the results obtained with the EARSM and the k-ω SST models employed in the present study. The influence of the additional bottom plate is very weak, much lower than the estimated error of discretisation, and of modelling, since the relative differences between the two cases (see Tables 3 and 4 for the case with frictionless plate) are less than 0.05% for the drag and less than 0.2% for the lift.

Sensitivity to the incoming flow changes in incidence has been investigated is a very simple way by changing the prescribed velocity components at the inlet and on the sides with variations of ±0.25°. Such a small absolute value has been retained after noting that, from numerical results of [1], the maximum upwash angle in the jet section of the tunnel was found to be 0.25°. The results are summarized in Table 7 for the drag coefficient and in Table 8 for the lift coefficient.

<table><caption>Table 7: Drag sensitivity to incidence (EARSM)</caption><thead><tr><th>Variation</th><th>Genoa</th><th>Mainsail</th><th>Total</th></tr></thead><tbody><tr><td>-0.25°</td><td>0.02555</td><td>0.12831</td><td>0.15386</td></tr><tr><td>0°</td><td>0.02530</td><td>0.12695</td><td>0.15225</td></tr><tr><td>+0.25°</td><td>0.02477</td><td>0.12606</td><td>0.15083</td></tr></tbody></table>

<table><caption>Table 8: Lift sensitivity to incidence (EARSM)</caption><thead><tr><th>Variation</th><th>Genoa</th><th>Mainsail</th><th>Total</th></tr></thead><tbody><tr><td>-0.25°</td><td>0.60390</td><td>0.62664</td><td>1.23054</td></tr><tr><td>0°</td><td>0.61033</td><td>0.61792</td><td>1.22827</td></tr><tr><td>+0.25°</td><td>0.61442</td><td>0.61005</td><td>1.22447</td></tr></tbody></table>

The main conclusion is that both the lift and drag coefficients decreases as the incidence increases. Variation of drag is about 1% and about 0.5% for the lift to be compared to the variation of the flow incidence of 2.6%. Variations are in the same order of the uncertainty but if the downward trend is correct this would indicate that the considered configuration of the sails is closed to condition of stall.

## 5.2. Flow field

Figure 6 illustrates the main characteristics of the flow field from various computed data interpolated in section 2 of the genoa with the EARSM model. In this figure, the total pressure coefficient defined as $C_{pt}=C_p+||U||^2/(ρU_{ref}^2)$ where $U$ is the velocity vector. Value different from 1 indicates region where the viscous effects are expected to be significant (wakes and boundary layers). The streamlines are plotted according to the secondary components (U,W) of the velocity field in that section. A noticeable recirculation zone takes place above part of the genoa but with little interaction on the mainsail as shown with the $C_{pt}$ coefficient distribution. In the same section, regardless of 3D effects, the distribution of the pressure coefficient is representative of the flow features observed in the aerodynamics of multiple airfoils of modern wing. As in the case of high-lift devices of
modern wings, the trailing edge of the genoa operates in a region of low pressure induced by the suction side of the mainsail (see $C_p$ in Figure 8) then providing extra lift as the suction peak increases. However for thick airfoil the effect of the flap is to move the stagnation point of the main wing farther downstream of the leading edge on the pressure side whereas it stays closed to the leading edge of the zero thickness geometries considered here. Figure 7 contains representations of the computed flow toward the top of the mainsail (section 4) in a way similar to Figure 6 with EARSM too. Here the mainsail is alone in front of the incoming flow with incidence, flow separation takes place all over the leeward side and high lift benefit due to the genoa is lost. Additional explanation given in [1] is that the onset of separation observed on top of the mainsail could be attributed to the tip vortex from the genoa.

To go further with 3D analysis, the visualisation of iso-surfaces of the second invariant $Q$ is useful to detect the onset and progression of vortical structures. Figure 8 shows instantaneous and time-averaged views of the dimensionless invariant iso-surface $Q*=50$. Although not shown, the (averaged) structures illustrated by mean of $Q*$ with other turbulence modelling are similar but with less extension downstream to those obtained with DES. The instantaneous view from the suction side is interesting as it outlines the onset of separated flow regions: important tack separation on the suction side of the genoa, same tack separation on the mainsail, and separation on top of the mainsail (see previous comment). The strongest and well established structures are related to tip vortex separations at the top and bottom of the mainsail. The bottom separation of the mainsail is strong enough to promote a separation of the boundary layer downstream on the plate. It is interesting to note the weak intensity of the genoa tip vortex so that this vortex may be not responsible alone of the separated flow on the mainsail.

### 5.3. Pressure coefficient

The pressure coefficient distribution is presented in Figure 9 to Figure 12 on the suction side of the sails for the various turbulence models. The plot of significant limiting streamlines is also added. Figure 10 presents the time-averaged computed results obtained with the simulation involving DES model.

First impression is the three-dimensionality of the flow for the genoa and the top of the mainsail contrary to what is observed on the windward side (not shown). These views have also to be connected with the vortical structures shown in the previous section. The area affected by the separation from the tack of the genoa is more or less the same for the two models. This is also the case for the separated area observed toward the top of the mainsail. Lowest pressure coefficients are located at the vicinity of the leading edge of the genoa. Flow separation is also noticed all along the leading edge of the mainsail

to be attributed to laminar flow separation. This would require further analysis.

The available pressure coefficient presented in [1] and [3] were measured with an uncertainty of ±0.23 on the suction side and of ±0.08 on the pressure side. Thus the experimental uncertainty is in the order of 12 to 16% considering a pressure coefficient of -2 on the suction side and of 0.5 on the pressure side.

<figure><img src="image_7.png" /><figcaption>Figure 6: Streamlines (top), total pressure (middle) and pressure (bottom) coefficient distributions in section 2 of the genoa (EARSM)</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 7:** Streamlines (top), pressure (middle) and total pressure (bottom) coefficient distributions in section 4 of the mainsail (EARSM)</figcaption></figure>

The results of the distributions of the pressure coefficient depending on the turbulence modeling are presented in Figure 13 for the sections of the genoa and in Figure 14 for the sections of the mainsail (see Figure 2 and Table 1 for locations). On this figures, the pressure side is below the suction side. x/C represents the x coordinate normalized by the chord of the considered section.

<figure><img src="image_9.png" /><figcaption>**Figure 8:** Instantaneous (top) and time-averaged (bottom) iso-surface (Q*=50) of the second invariant coloured by the helicity. View from suction side with DES simulation.</figcaption></figure>

On the genoa, sections 2 to 4 and before x/C = 0.05 the behavior of the pressure coefficient with a noticeable minimum (of -Cp) denotes the occurrence at the vicinity of the leading edge of a separation then a reattachment with flow acceleration. This is the case for all turbulence models with a more or less pronounced intensity. The separation toward the leading edge of the genoa is more visible with the DES simulation as the pressure plateau on the suction side is more pronounced in comparison to the other models. Concerning the behavior of the pressure coefficient on the suction side of the mainsail, the behavior is similar near the leading edge, before x/C = 0.1 approximately: a leading edge separation then a flow acceleration also induced by the high lift effect due to the presence of the genoa trailing edge over it (see Figure 6). This is the case for the three lower sections. The upper section of the mainsail is characterized by a massive separation on the suction side. Concerning the pressure side on both sails agreement with measure coefficient is fine except in the leading edge regions. Without further explanation, the difference between EFD and CFD could be attributed to the fact that the numerical model has a zero-thickness so that the stagnation point is not correctly predicted. This difference can also be issued to the uncertainty of the measurements.
<figure><img src="image_10.png" /><figcaption>Figure 9: Wall pressure coefficient and wall limiting streamlines on the suction side, EARSM simulation</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 11: Wall pressure coefficient and wall limiting streamlines on the suction side, k-ω SST simulation</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 10: Time-averaged wall pressure coefficient and wall limiting streamlines on the suction side, DES simulation</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Figure 12: Wall pressure coefficient and wall limiting streamlines on the suction side, Spalart-Allmaras simulation</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Figure 13: Cp distribution on the sections of the genoa.
From section 1 (bottom) to section 4 (top)</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Figure 14: Cp distribution on the sections of the mainsail.
From section 1 (bottom) to section 4 (top)</figcaption></figure>
# 6. CONCLUSIONS

Numerical simulations of the flow around two rigid sails in upwind condition have been investigated. The test case selected has been experimented in wind tunnel at the University of Auckland and the geometry of the sails as well as measured pressure distributions are available as a database to validate numerical simulations.

The numerical model used to represent the sails consists in zero-thickness surfaces. The reason is the fact that it was difficult to generate a suitable CAD model with finite thickness and correct chamfer as it was tested in the tunnel. The other source of uncertainty lies in the complexity of the arrangement of the sails in the tunnel and in the complexity of the tunnel itself.

The ISIS-CFD flow solver was used with various turbulence models to simulate the flow around a specific configuration. Among sixteen measured configurations, that specific configuration was considered to be the optimum from the point of view of the better resulting driving force.

Grid convergence analysis has been done and the Richardson extrapolation indicates a numerical discretisation error about 1%. The difficulty to assume a perfect scale between the systematically refined unstructured grids was underlined so that successful Richardson extrapolation is tedious.

A 20M cells fine grid was retained in order to expect better description of the overall flow field. Based upon numerical experience about bluff body flows, DES simulation was also conducted in conjunction with steady simulation from classical isotropic k-ω and non-isotropic EARSM models. Considering the forces, it is hard to conclude about the better turbulence model to use since the deviation of the forces is about 5% between the models. Moreover, such a deviation corresponds more or less to the maximum error observed from numerous numerical simulations performed in ship resistance with the flow solver. A DES simulation at least in this case, brings up understanding of the flow physics of the vortical structures but it still remains too expensive to use in early stage of a design process.

It is expected that additional numerical studies will eventually be conducted for the other available genoa and mainsail conditions of trim for better assessment of the flow solver to predict the optimum configuration.

# Acknowledgements

This work was granted access to the HPC resources of IDRIS under the allocations 2014-2a0129 and 2014-2a1308 made by GENCI (Grand Equipement National de Calcul Intensif).

Authors are also grateful to I.M. Viola, University of Edinburgh, and P. Bot, Institut de Recherche de l'Ecole Navale de Brest, for their advices and discussions.

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