RANS BASED VPP METHOD FOR MEGA-YACHTS

Transcription

1 RANS BASED VPP METHOD FOR MEGA-YACHTS Tyler Doyle 1, Bradford Knight 2, Abstract. Velocity prediction programs (VPPs) are valuable design tools that allow designers to parametrically study yacht performance. The three main components of a VPP are an aerodynamic force model, a hydrodynamic force model and an algorithm to balance the forces. VPP force models can be derived from many sources such as model testing, empirical or analytic formulations, computational fluid dynamics (CFD) or often a combination of these. This paper describes an approach to VPP force modeling based on Reynolds Averaged Navier Stokes (RANS) CFD. RANS CFD captures turbulent flow effects important for sailing such as separation, viscous drag and wakes. The aerodynamic forces are calculated using steady state RANS and the hydrodynamic forces are calculated using free surface RANS Volume of Fluid (VOF) with OpenFOAM. VOF simulations are computationally expensive and many data points are needed for the VPP force models. A cost effective approach to running VOF simulations using OpenFOAM and cloud computing is described. This approach allows the method to be used on a wide range of projects and not only those with large R&D budgets such as the America s Cup and Volvo campaigns. The force models are derived by direct interpolation of CFD data using both structured and unstructured data point sampling. As a test case the method is applied to analyze three keel options for a 125 mega-yacht as well as make comparisons to flat water sailing performance. Modelling turbulent flow effects is especially important for mega-yachts because they have many drag producing design features. NOMENCLATURE α Angle of attack γ Leeway angle ε hydro Hydrodynamic efficiency ϕ Heel angle θ Rudder angle AWA Apparent Wind Angle AWS Apparent Wind Speed BS Boat Speed CFD Computational Fluid Dynamics FX air Aerodynamic drive force (axial direction) FY air Aerodynamic heel force (side direction) FZ air Aerodynamic vertical force FX hydro Hydrodynamic drag force (axial direction) FY hydro Hydrodynamic side force FZ hydro Hydrodynamic vertical force MX air Moment about boat direction MZ air Moment about vertical direction MX hydro Moment about boat direction MZ hydro Moment about vertical direction RANS Reynolds Averaged Navier Stokes TWA True wind angle TWS True wind Speed VMG Velocity made good VOF Volume of Fluid 1. INTRODUCTION Yacht designers use Velocity Prediction Programs (VPP) to evaluate sailboat designs. A VPP is an algorithm that balances hydrodynamic and aerodynamic forces calculated or measured from models to determine sailing conditions for given wind conditions. This paper depicts the process of generating a VPP for a mega-yacht using a Computational Fluid Dynamics (CFD) based VPP. Reynolds Averaged Navier Stokes (RANS) CFD is used, which captures important turbulent flow phenomena such as separation and viscous drag. Modern computers and state of the art CFD techniques allow for fully computergenerated VPPs for mega-yachts. Even though megayachts are high budget projects, they do not always have high R&D budgets. RANS CFD can be used as a less expensive method than full tank testing, especially when only select points of sail are analysed. [1] VPPs are not new to the yachting industry; however, only recently have modern computers enabled accurate and cost effective computationally driven solutions. Van Oossanen depicts a VPP to accurately calculate the speed for the 12M Australia II in his 1993 paper. In 1993 the best way to calculate sailboat speed was to use a tow tank to characterize hydrodynamic forces and to use either the full sized sails, sail force coefficients, or a wind tunnel to determine the aerodynamic forces. Computers twenty years ago were just becoming powerful enough to run panel codes but were not powerful enough to solely determine the velocity of a sailboat. [2] Computers ten years ago were advanced enough to perform RANS CFD analysis on sails. Generally sails were analysed in 2D and final results were analysed in 3D due to computational complexity. [3] With modern computers, 3D upwind sail RANS CFD calculations take less than an hour on a standard work station. Despite advances in computers that allow for rapid aerodynamic analysis, creating a computationally based VPP is still time-intensive. RANS CFD is a great tool to evaluate fine geometry changes or to minimize error when small design changes are to be evaluated, however due to the high complexity of the analysis it is not appropriate for all projects. This paper will depict a method using RANS CFD to determine aerodynamic and hydrodynamic forces, and balance these forces to determine the sailing conditions 1 President, Doyle CFD 2 Engineer, Doyle CFD 267

2 for a given wind condition of a mega-yacht. Sailing conditions are illustrated for downwind and upwind sailing angles. The complete VPP method is shown for an upwind case. A case study depicting a keel modification is also discussed, which describes how RANS can be used to improve designs for mega-yachts. 2. RATIONALE FOR RANS BASED VPP FOR MEGA-YACHTS RANS based VPP force modelling is appropriate when turbulence and flow interaction is important. Megayachts have relatively larger drag and more interacting geometry than a typical sail boat. The potential gain in accuracy for full RANS CFD takes more time than panel code CFD, both computationally and in man-hours. Dense computational meshes are required to accurately capture the turbulent flow fields. With modern workstations, RANS CFD can take as little as thirty minutes for upwind sail analysis, but can take days to reach a converged VOF solution. Recent America s Cup and Volvo campaigns have utilized RANS CFD to optimize designs. These elite racing programs have applied it to obtain a competitive edge, but only in recent years has this technology been applied to mega-yachts. Due to the sheer expense of mega-yachts, a comparably small price for an engineering confirmation of performance is often logical. Mega-yachts are no longer a vessel for pure pleasure sailing. With the emergence of mega-yacht regattas these boats need to be capable of handling race conditions, most important of which is being able to sail upwind at a reasonable angle. [4] The sailing requirements of these yachts require modern engineering and optimization to truly make them super yachts. RANS CFD can be used to create a full VPP or examine specific points of sail of interest to a designer. This level of analysis can fit into mega-yacht programs without the need to develop a tow-tank or wind tunnel model. The reduced size required for a model of a mega-yacht to fit in a tow tank often results in an inability to test and pinpoint effects of small changes. RANS can accurately capture the water line and wave effects like a towed model, but does not require the results to be scaled. Unlike panel codes, RANS CFD can pinpoint turbulent flow effects and interactions caused by small changes to the geometry like sail trim, sail shape, rig, hull, or appendage modifications. Many panel codes have been validated to give reasonable force predictions, but frequently the force distribution is not accurate. [5] More importantly, panel codes do not directly include geometry such as the superstructure or masts which create added drag. The geometry in a complete RANS CFD model calculates drag which is not included in conventional mega-yacht VPPs. Since RANS is able to capture turbulent effects and calculates the flow for the entire field, post processing RANS CFD provides a distinct advantage for custom projects like mega-yachts by allowing yacht designers to understand how the yacht functions as a whole, instead of just the sum of the parts Figure 1: Velocity plane illustrating separation, pressure contours on surfaces, and streamlines depicting turbulent flow for a downwind aerodynamic case Figure 2: Turbulent flow around hull and appendages, with streamlines and cut planes. Figure 1 illustrates turbulent flow around the mast, rigging, and spinnaker for a downwind sail set. This depicts how RANS CFD calculates separation around the sails, especially around the spinnaker. Streamlines in the figure also illustrate the tip vortex off of the head of the mizzen sail. These effects would only be noticeable on a large scale model in a wind tunnel. Figure 1 also illustrates how the flow around each sail is influenced by the other sails; the forward sails allow the aft sails to be eased further than they would be on their own. Figure 2 illustrates turbulent flow around the hull, wing keel, folded propeller, skeg, and rudder of a 125 foot mega-yacht. The hull and appendages are depicted by contours of dynamic pressure and the flow field is illustrated with cut planes of velocity and streamlines. This image depicts the flow field and wakes for visualization purposes, alongside numerical solutions. Streamlines show how the lift around the wing keel induces strong tip vortices. The ambient velocity is shown in orange, where low velocity is shown in darker colors. The top clip plane about the rudder shows separation towards the trailing edge of the rudder. Low velocity regions are shown by the clip plane behind the wing keel in the bottom most cut plane, which is set to partial transparency to illustrate the full geometry. The middle cut plane shows the flow across the keel, folded propeller and rudder. The wake from the keel and propeller travels downstream and intersects with the 268

3 rudder. Scale models, panel codes, and even real world measurements often pose difficulty in combining measured forces with flow field data; whereas RANS provides both qualitative and quantitative results. 3. METHOD The three main components of a VPP are the aerodynamic force model, the hydrodynamic force model and an algorithm to balance the forces. In this method both the aerodynamic and hydrodynamic force models are derived from RANS CFD data. The aerodynamic forces are calculated using steady state RANS and the hydrodynamic forces are calculated using free surface RANS Volume of Fluid (VOF). The VPP hydrodynamic force functions are defined by directly interpolating the CFD data points whereas the aerodynamic force functions are defined by interpolating force coefficients calculated from the CFD data. Once the force models have been created, the aerodynamic and hydrodynamic forces are balanced to determine the speed, yaw, heel, and rudder angle of the yacht for different wind conditions using a VPP program we developed. 3.1 OpenFOAM: Open Source CFD software The results in this paper are calculated using OpenFOAM, which is a Linux based open source software. The fact that OpenFOAM is open source, allows for affordable RANS CFD calculations since the software does not need to be purchased or leased and a premium does not need to be paid to run cases in parallel. Furthermore, OpenFOAM can be installed and run on cloud computers, which allows for computer expenses only when demanded. Since OpenFOAM is open source it is possible to modify the solver which allows users to customize the program to suit their needs without having to develop a CFD program from scratch. Despite some of the advantages of open source CFD, it requires development time to validate and develop models. However, these computational advantages enable affordable VPPs based purely on RANS CFD. Many commercial CFD programs require a license fee for each node that the program is run on including each core that is used. This can limit small companies to only being able to afford running CFD on select work stations. Since each data point takes a long time to solve with VOF CFD, it is critical to be able to run multiple data points at once. With cloud computing, even small companies are able to take advantage of the open-source software and run these computationally expensive cases, without the need for maintaining an in-house supercomputer. The combination of open-source software and cloud computing allows increased access to RANS based VPPs for sailing programs for which cost factors would have previously limited such application. 3.2 Aerodynamic RANS CFD Steady-state RANS CFD is used to calculate the forces and moments on the sails, rig, superstructure and equipment. The SimpleFOAM solver in OpenFOAM was used for these calculations.. For each point of sail, data points that range from eased to over-trimmed are analysed, through a variety of AWA and heel angles so that the results can be matched to the hydrodynamic data. Figure 3: Aerodynamic mesh Correctly refined aerodynamic meshes with sails only range from two to three million cells. These coarse meshes are used to preliminarily trim sails independently of the other structures of the vessel. Once sails are preliminarily trimmed, the masts, booms, radar domes and hull are added which raises the cell count to approximately 10 million cells. Downwind sail meshes are larger at 13 million cells due to larger sail areas. Figure 3 depicts the mesh around a fully meshed downwind aerodynamic CFD case. These meshes are generated with SnappyHexMesh, the default mesher for OpenFOAM. A grid resolution study was performed for a similar mesh for upwind. The grid resolution study compared a base case with 9.8 million cells, a high resolution mesh with 35 million cells, and a low resolution mesh with 6.4 million cells. There is a refinement box around the sails that was increased for the fine resolution mesh. For the fine mesh an extra refinement was added to the surfaces and for the coarse mesh a surface refinement was removed but the refinement box was not changed. In 20 knots AWS the y+ ranges from an average of about 400 for the base case, to 200 for the fine mesh, to 700 for the low resolution mesh. The high resolution mesh produced 3.5 percent more drive force and 2.2 percent more heel force than the base case; the low resolution mesh produced 5.6 percent less drive force and 1.5 percent less heel force than the base case. The kω-sst turbulence model was used with wall functions. The upstream boundary condition was assigned a velocity inlet, downstream was assigned as a pressure outlet, the top and bottom were prescribed as slip walls. The domain was sized so that there were nearly 30 LWL downstream in the in the heading direction, 17 LWL in the leeward 269

4 direction, 9 LWL upstream in both the heading direction and to windward, and 13 mast heights in the vertical direction. Figure 5: Components of heel and 20 knots AWS, 36 degrees AWA, 19 degrees heel Figure 4: Velocity contours around sails and rig for a loose trimmed upwind case Upwind cases have little separation and are thus computationally faster than downwind and reaching cases, which have to be solved for a more complicated flow field with eddies and other turbulent flow effects. RANS CFD not only accurately calculates forces for different sail and rig shapes, but it also can depict the turbulent flow field so that problem areas of the geometry can be analysed and improved. For upwind cases, RANS CFD shows the turbulent flow around the rig, sails, and even the hull. RANS CFD can be used to determine the optimal trim, twist, and camber for sail shapes by capturing even minor separation around the mast or towards the leach on upwind sails. Furthermore, effects of the turbulent wake and its interaction with other sails can be seen. More profound separation is seen with reaching and downwind sails. Figure 4 depicts turbulent flow around the yacht sailing upwind. Flow separation can be seen around the spreaders, towards the leech of jib and mizzen, behind the cabin, on the leeward side of the hull, around the mast, and around the radar. Figure 5 depicts each components percentage of total heel and drive force. This shows that the genoa produces the most force of any component, but more importantly that added geometries like the hull, masts (with radar domes and spreaders included) and booms add to nearly 20 percent of the total heel force. 3.3 Hydrodynamic VOF CFD The OpenFOAM solver, LTSInterFOAM, is used for the RANS VOF calculations. VOF calculations are performed for an array of data points that specify boat speed, rudder angle, yaw angle, and heel angle. Meshes for hydrodynamic VOF CFD must be very fine especially around the waterline and surface. These meshes are also generated with SnappyHexMesh. The large cell count in the mesh translates to long computation times, generally about 140 hours to complete on a node with 2 Xeon processors (16 real cores) and 60 GB of RAM. The CFD solver scales well with clustering nodes together with infiniband interconnects, but the mesher does not. [6] VOF meshes that this paper describes are over thirty million cells. The geometry included in this geometry includes the hull, keel, skeg, and rudder. For one speed (9 kts) the propeller was included and used as a corrector for the other speeds. The propeller on this yacht is folded while the yacht sails, so this was the configuration used for the CFD. The primary cells are hexahedral cells, but to properly model the turbulent flow around the hull, prism layers are used. Mesh refinements are used around the hull, appendages, and the waterline to properly capture the turbulent flow effects and the waterline. Figure 6 depicts the VOF mesh around the base hull. Domain and grid studies were performed to evaluate the sensitivity to mesh count. A 23 million cell mesh count provided reasonable results, however, convergence and solver robustness varied between cases due to waves interfering with symmetry planes. The lack of robustness led to many failed or unconverged data points that needed rerunning. One issue that led to divergence and incorrect solutions was numerical ventilation, where the CFD calculated air bubbles beneath the waterline. By increasing the domain and further numerically controlling the convergence, the numerical ventilation was corrected. It was found that increasing the domain by 50 % in the flow direction and doubling the area on the sides improved convergence and robustness. Scaling up the mesh domain resulted in a total mesh count of about 33 million cells. The domain that provided both robustness and an efficient computation rate had a 3 LWL upstream, 6 LWL downstream, and 2.5 LWL on 270

5 either side. For the purposes of this report, there was not time to complete a full grid dependence study with fine meshes. Adding more prism layers and surface refinements led to numerical ventilation, which actually provided less accurate results. Due to time restraints further mesh development was not possible. Comparing the viscous drag of the keel to the empirical calculation using Delft coefficients, the CFD viscous drag in this model is underestimated by about 10%. Since the Delft coefficients examine the parameter of the keel and the keel has 100% wetted surface area the Delft viscous drag prediction should be accurate, especially at 0 degrees heel and yaw. Furthermore, the keel by itself was analysed in SimpleFOAM with a y+ average of 170, and this also showed 10% more viscous drag than the full VOF model. Figure 6: Hydrodynamic Mesh Similar to the aerodynamic simulations, the turbulence model used was kω-sst with wall functions. Each surface of the yacht analysed was prescribed as a non-slip wall, the sides and bottom were assigned as a symmetry plane, the inlet was a velocity inlet, the outlet was specified with the zero-gradient condition, and the top was an inlet-outlet where ambient pressure was assigned. After the geometry has been meshed, the array of hull conditions is analysed. The CFD is performed at fixed sink and trim with zero degrees of freedom to simplify the solutions; however, the cases are analysed at two different displacements over a small range and linear interpolation is used to match sailing displacement. By analyzing the geometry with fixed trim and pitch, the complexity of each simulation is reduced, but more data points are analysed and more interpolation is done for each set of sailing variables. Generally the first step for a new project is to analyse it upright with no rudder angle to create an upright drag curve and check that CFD results match empirical results like Delft Coefficients across a range of boat speeds. [7] This is used to confirm that the model setup is correct and does not deviate from theoretical limits. Since there should be very little separation, conventional methods should provide reasonable results and can be used to check the base setup. After a preliminary upright drag curve is created, yaw, heel, and rudder angle are introduced. These changes produce more turbulent effects like flow separation around appendages. For each point of sail a range of displacements, rudder angles, heel angles, yaw angles, and boat speeds are examined.. RANS VOF CFD calculates forces caused by viscous effects, wave making forces, and turbulent flow around appendages. Beyond calculating these forces the flow fields can be analysed to depict negative flow characteristics like separation around appendages or sever tip vortices. Furthermore, RANS CFD depicts the interaction of wakes on downstream objects, such as how separation around a keel or propeller can reduce rudder efficiency. 3.4 VPP Method The VPP program predicts sailing performance by balancing the aerodynamic and hydrodynamic forces for a given TWS and TWA. This VPP system balances four degrees of freedom Fx, Fy, Mx and Mz by adjusting four state variables BS, γ, ϕ, θ. Forces are represented in the program as multi-dimensional response surfaces. The response surfaces are implemented in the program as cubic splines. To create the cubic spline surfaces, the program reads force data as structured grid data. One method for creating the structured input data is to systematically adjust each independent variable. This structured data sampling often leads to points being calculated that are not near expected sailing conditions. Another approach to generating the data is to use an unstructured interpolation scheme such as kriging or neural network based sampling to cluster data points around sailing states that are of interest. The unstructured response surfaces can be converted to structured data sets for the program. The method in this paper uses a structured data point sampling for the aerodynamic data points and use unstructured sampling for the hydrodynamic data points. The VPP solution procedure follows the development by Korpus [8]. The VPP program is implemented as a simple object oriented Java program. Classes are defined to store force and state data so that the loop structure of the program is easily readable. The program runs through three nested loops. The two outer loops run the desired range of true wind speeds and true wind angles while the inner loop solves for the state variables that give equilibrium between the aerodynamic and hydrodynamic forces. The inner loop uses Newton-Rhapson iteration to solve the system of four nonlinear force balance equations. 271

6 For a given TWS and TWA the above set of nonlinear equations is solved for the state variables BS, γ, ϕ, θ that give a balance between the aerodynamic and hydrodynamic forces using Newton-Raphson iteration. The iteration scheme works by updating the state vector with a perturbation vector at each step. The perturbation vector at state n is given by Equation 3. Derivatives are calculated with finite differences. The state vector at state n+1 is given by Equation 4. = (3) (4) Figure 7: Global Coordinate System The VPP system uses four degrees of freedom to represent the state of the yacht: BS, γ, ϕ, θ. The aerodynamic forces are defined as functions of AWA, AWS and ϕ, however, for each sailing state the program calculates AWA and AWS from TWS, TWA and BS so that both the aerodynamic and hydrodynamic forces are internally defined as functions of BS, γ, ϕ, θ. To account for the different definitions of the x-axis and y-axis between aerodynamic and hydrodynamic, the aerodynamic force routine projects the aerodynamic forces which are defined relative to the centreline of the yacht onto the hydrodynamic force coordinate system defined by the direction of the boat. The coordinate systems used for the aerodynamic and hydrodynamic simulations are shown in Figure 7. The set of nonlinear force equations that the program calculates is represented below. Surface plots representing the force functions can be displayed by the program to check how smooth the input force data is. Equation 1 illustrates that, functions f1-f6 and f8 are derived from RANS data while f7 is defined by the boats righting moment curve. Equation 2 depicts the conditions for the boat to balance. FX air = f1(aws, AWA, ϕ) FY air = f2(aws, AWA, ϕ) MX air = f3(aws, AWA, ϕ) MZ air = f4(aws, AWA, ϕ) (1) FX hydro = f5(bs, γ, ϕ, θ) FY hydro = f6(bs, γ, ϕ, θ) MX hydro = f7(ϕ) MZ hydro = f8(bs, γ, ϕ, θ) (2) The iterations continue until the state variables are no longer changing. The program terminates the loop when the norm of the force vector residual drops below the convergence criteria. For well-defined aero and hydro sets the iteration schemes converges within 10 iterations. 4. AXIA DOWNWIND ANALYSIS This section describes the method for the downwind analysis of Axia, a 125 foot ketch with a wing keel and a skeg rudder. The first step for the hydrodynamic analysis is to create an upright drag curve and validate it with the Delft Polynomials. The mesh for this case is 33 million cells, similar to Figure 5 above. Figure 8 illustrates the upright CFD compared to Delft polynomials. [7] The CFD frictional drag is 10% less than predicted by Delft. It is believed that the higher than ideal y+ values used in this study account for this difference. The mesh resolution study performed on the keel agrees with this conclusion. The pressure drag is well predicted at lower Froude numbers with speed up to 12 knots but for higher Froude numbers the pressure drag is over predicted with the CFD. To illustrate the VPP method for downwind conditions, a sailing state of 9.5 kts AWS, 10 kts BS, and 91 AWA is used. The sails used for this case are an A3 spinnaker, main sail, a staysail, and mizzen sail. To properly create the sail geometries, images of the flying shapes are used to correlate sail stripes with known points on the geometry. Flying shape images for the downwind cases were not available for this data set. Sail shapes were created by deforming design moulded shapes to match pictures taken from off the boat. Figure 9 depicts the pressures on the yacht and the waterline as viewed from the side. These aerodynamic forces can be coupled with the upright and low heel hydrodynamic data to determine how the yacht will sail downwind. 272

7 shapes were based on how the sails are trimmed according to the crew. When sailing upwind, the sails are trimmed so that the sail conforms to the spreaders. This shape is eased and twist is added for loose configurations. Figure 8: Upright CFD drag compared to Delft Polynomials Figure 10: Aerodynamic Force Coefficients Figure 9: Downwind pressures on yacht and elevation plots of waterline 5. AXIA UPWIND COMPARISON To evaluate the accuracy of the system an upwind VPP analysis was run to compare with sailing data taken at a regatta in 2013 on the yacht Axia. Only a narrow range of TWS and TWA data was available so the RANS data sets were clustered around these points. 5.1 Aerodynamic data The upwind sail plan consisting of the mizzen, main and genoa along with the mast, hull and deck was simulated across a range of apparent wind angles from 26 to 38 degrees and a range of heels from 12 degrees to 24 degrees. A total of 16 heel and AWA combinations were simulated at two sheeting configurations each. The data points were sampled in a structured way allowing for direct interpolation by the VPP force routine. The aerodynamic forces are assumed to scale with dynamic pressure, as is commonly done in wind tunnel testing. This allows the aerodynamic simulations to be run at only one apparent wind speed. Force coefficients of driving force, heeling force, heeling moment and yaw moment are input to the VPP. It is important to use sail shapes that accurately represent the real flying shapes so that the forces are properly calculated. Because the yacht did not have pictures of the sails for the data that this paper compares to, the sail For each data point run, the sail plan was run with a tight and loose sheeting configuration representing the range of possible trims at a given apparent wind angle. The aerodynamic force coefficients were then selected across a range of tight to loose trim. The force coefficients changed as much as 20% going from tight to loose trim in some conditions. The final data set used in the VPP analysis used only the tight trimmed condition. In the analysed conditions, Axia only has enough winch power to trim the genoa in tightly during a tack thus the sail is usually trimmed tightly out of a tack and left. Both the main and the mizzen are generally trimmed as tight as possible in this condition to avoid back-winding. The aerodynamic force coefficients used in the analysis are in Figure 10. The heeling moment coefficient uses the mast height for the non-dimensional moment arm while the yaw moment used the water line length. The x- axis is the heel angle, the y-axis is the apparent wind angle and the z-axis is the force coefficient. The forces flatten out a higher apparent wind angles because the sails are over trimmed in this condition and the flow is separated. 5.2 Hydrodynamic Data The hydrodynamic data does not scale with the boats velocity because of non-linear wave making forces so the hydrodynamic data needs to be given as a function of boat speed, yaw angle, heel angle and rudder angle. The hydrodynamic data is clustered around the expected sailing state in 18 knots of true wind speed with the heel ranging from 14 to 26 degrees, yaw ranging from 3 to 11 degrees and boat speed ranging from 6 to 12 knots. A total of 27 data points were calculated for the upwind comparison. This number of data points is not enough to accurately capture the speed, heel and yaw dependence across all sailing conditions but is believed to be enough to capture the performance in the small window of 273

8 conditions we compare to. Kriging interpolation is used to build the hydrodynamic response surfaces from the unstructured set of sampled data. Figure 12: VPP Results. Figure 11: Hydrodynamic Response Surfaces at BS=9 knots An example of the hydrodynamic response surfaces at 9 knots boat speed is shown in Figure 11. All forces are in N and moment in N-m. The x-axis is yaw angle and the y-axis is heel angle. The righting-moment is defined only as a function of heel angle. The righting-moment curve takes into account the 35 crew Axia has on the rail while racing upwind in these conditions. The effect of the rudder is included as a correction to the hydrodynamic forces. For each yaw angle the RANS geometry is defined with a pre-set rudder angle that is thought to be close to that needed to maintain a steady course. The rudder angle variable that the program solves for is added to the pre-set rudder angle to give the total rudder angle at a given state. Rudder correction coefficients are obtained from a set of CFD simulations with varying rudder angles. 5.3 VPP Predictions Compared With Sailing Data The VPP analysis was first run with the raw interpolation data from the RANS calculations. The results obtained overestimate heel angle by roughly 15%. Because the righting moment is only a function of the heel angle it is concluded that the aerodynamic heel moment is over predicted. The aerodynamic heel moment may be overpredicted because the true sail flying shapes were more eased and twisted than the sail shapes used in this analysis For the purpose of testing the system it was assumed that the sails needed to be eased and twisted more than had been originally assumed. Therefore aerodynamic force coefficients must be adjusted accordingly. For a more accurate comparison, sail flying shapes must be recorded along with the sailing data. With this change the VPP heel angles match better across the range of conditions that were studied, but the boat speed is too high. The hydrodynamic resistance used in the force model assumes flat water and ideal hull geometry. In reality the hull and appendages are not perfect and there are some wave effects that will add drag to the sailing data. It is found that by increasing the hydrodynamic resistance by 10%, the boat speed, heel, yaw and rudder angles predicted by the VPP match the sailing data reasonably. The VPP predictions are shown in Figure 12. In all of the charts, the sailing data is shown in blue and the VPP in red. The sailing data is noisy even after being time averaged but the trends seen in the sailing data are similar to those seen in the VPP predictions 6. DEMONSTRATION OF DESIGN CHANGES RANS CFD is useful to evaluate effects of small design changes because the high resolution grids used pick up small geometry changes. This section analyses the effects and performance changes caused by modifying the wing keel of Axia to two versions of a fin keel. VOF simulations were re-run for the upwind cases for speeds between 8 and 10 kts with the new keel geometries. Figure 14 shows that Keel B has the same profile shape as keel A except towards the tip it has an elliptical shape and therefore less area. Keel B has an area of 33.6 m 2, and keel A has an area of 37 m 2. The base wing keel has the smallest area, with 32 m 2. Efficiency is a common metric for keel performance, which is the ratio of side force to resistance. For the purposes of this report, efficiency is evaluated as the total hydrodynamic force on the hull, instead of just the forces on the keel. A keel study could be performed solely on the keels to determine the efficiency of the keels alone; but this would not incorporate effects with the hull. 274

9 Figure 14: Keel Comparison of Yaw, Boat Speed, and VMG vs True Wind Conditions and Efficiency vs Yaw Figure 13: Comparison of flow around keels A and B The keel geometries are shown in Figure 13. There are two cut planes shown, with plane one at the top and plane two towards the tips of the keels. The cut planes show velocity contours, with red being high velocity and blue is low velocity. The keel root sections are very similar between the two keels since they have the same shape. It is notable that the wake off of the keel lines up with the flow of the rudder. This wake interaction is something that RANS can be used to determine the magnitude of the effects of this interaction. Towards the tips of the keel, Keel A has separation towards the trailing edge, but keel B due to the smaller shape does not. The tapered section of Keel B reduces the tip vortex and makes the shape more efficient. Comparing the forces obtained at fixed heel and yaw angles between the two new keel options, shows that keel B is 12% more efficient. When all of the forces are taken into account in the VPP this 12% efficiency gain translates to 2% better VMG. Both keels A & B are an improvement over the original keel mainly because their increase in side force allows the boat to sail at lower yaw angles. The VMG of keels A & B peaks at lower apparent wind angles than the original keel allowing the boat to sail closer to the wind while maintaining good speed. Figure 14 shows plots of yaw angle, boat speed and velocity made good at 17 knots of true wind speed. The differences between the new keels and the original keel are greatest when the boat is heading the closest to the wind, thereby requiring the most side force from the keel. 7. VALIDATING OBSERVED RESULTS The data presented in this paper is meant to illustrate the procedure of creating a RANS based VPP. To validate the CFD based VPP predictions with real-mega yacht performance more and higher resolution sailing data is needed; this data needs to correlate to flying shapes at the same time as boat speed, heel, yaw, rudder angle, and wind conditions. Furthermore, the sea state must be measured. 8. CONCLUSIONS This paper has demonstrated a method for creating a VPP for a mega-yacht using purely RANS CFD based force modelling. The case study that was used was a 125 foot mega-yacht ketch with a wing keel. Comparisons were made between VPP predictions and flat water sailing data. It was found that some corrections were needed to the raw interpolated data to have the VPP predictions match the sailing data. Limited performance and sailing parameter data was available to compare with. A proper validation that more accurately takes into account all important variables needs to be performed to determine the accuracy of the method. The paper also discussed a keel modification study. This illustrated that RANS CFD not only calculates aerodynamic and hydrodynamic forces, but also depicts the turbulent flow field around the hull, appendages, and sails which gives physical insight to the balance of forces and potential issues with the design. The aerodynamic forces were calculated using steady state RANS, the hydrodynamic forces were calculated using free surface RANS Volume of Fluid (VOF) and a program was described for calculating the balance between the aerodynamic and hydrodynamic forces. RANS VOF hydrodynamic calculations are computationally intensive and an efficient CFD system is needed to use them effectively for VPP force modeling. A method based on OpenFOAM and cloud computing 275

10 was discussed that is both computationally and cost efficient. There are a number of ways that RANS force data can be used to create VPP force models. This paper described a method that directly interpolates the force data to create the force model. Two types of interpolation were used. The aerodynamic data is sampled in a structured fashion and interpolated using cubic splines. To attempt to cluster the hydrodynamic data around known sailing points and avoid unnecessary calculations unstructured data sampling was used for the hydrodynamic data points and interpolated using kriging. Another method for using RANS force data in VPP s is to use the data to calibrate empirical or analytic calculations. Many empirical models have coefficients that relate to geometry such as keels and rudders. These coefficients are often calculated using only limited information on the true geometry. RANS data can be used to calibrate these coefficients to the true geometry. This method may be able to use fewer RANS data points because the response of the yacht is not defined by the RANS data alone. The drawback to this approach is that nonlinearities in the RANS data may be hard to capture with empirical models. Recently we have completed another mega-yacht study using this approach and feel that there may be some projects where this approach is more appropriate. PRACE-1IP WP7 Whitepaper Keuning, J A & Sonnenberg, U B. Approximation of the Hydrodynamic Forces on a Sailing Yacht based on the Delft Systematic Yacht Hull Series, The International HISWA Symposium on Yacht Design and Yacht Construction, HISWA, 1998, Amsterdam, Netherlands. 8. Korpus, R. Performance Prediction without Empiricism: A RANS-Based VPP and Design Optimization Capability, 18 th Chesapeake Sailing Yacht Symposium, 2007, Annapolis, MD. Acknowledgements The authors would like to thank Robbie Doyle for his insights on mega-yachts, Thomas Degremont for assembling the sailing data of Axia, and Will Whitman for preparing the CAD models. References 1. Azcueta, R & Rousselon, N. (2009), CFD Applied to Super and Mega Yacht Design, Design, Construction and Operation of Super and Mega Yachts Conference, Royal Institution of Naval Architects, April 2009, Genova, Italy. 2. van Oossanen, Peter. (1993), Predicting the Speed of Sailing Yachts, Sname Transactions,Vol. 101, 1993, Doyle, T, Gerritsen, M, & Iaccarino, G. (2002) Optimization of Yard Sectional Shape and Configuration for a Modern Clipper Ship, The International HISWA Symposium on Yacht Design and Yacht Construction, HISWA, 2002, Amsterdam, Netherlands. 4. Doyle, T. (2012), Megayachts and Mega-Loads, SNAME MT Magazine, April Korpus, R. Reynolds-Averaged Navier-Stokes in an Integrated Design Environment, Madrid Diseno de Yates, Madrid, Culpo, M. Current Bottlenecks in the Scalability of OpenFOAM on Massively Parallel Clusters, 276