UNSTEADY NUMERICAL SIMULATIONS OF DOWNWIND SAILS
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1 UNSTEADY NUMERICAL SIMULATIONS OF DOWNWIND SAILS M. Durand, Company K-Epsilon, Ecole Cenrale de Nanes, France F. Hauville, P. Bo, and B. Augier, Research Insiue of he French Naval Academy, France Y. Roux, Company K-Epsilon, France A. Leroyer, and M. Visonneau, Ecole Cenrale de Nanes, France SUMMARY Modelling he wind, sail and rig ineracions on a sailing yach is a complex subjec, because he qualiy of simulaion depends on he accuracy of boh srucural and fluid simulaions which srongly inerac. Moreover, he sails are submied o highly unseady oscillaions due o waves, wind variaions, course changes or rimming for example, bu someimes also due o he unseadiness of he flow iself (vorex shedding, ). The problem for downwind sails is even more complex because he flow is ofen deached from he sails, and he sails are subjec o large shape changes. A specific dynamic coupling has been developed beween a RANSE code from Ecole Cenrale de Nanes for he aerodynamics (ISIS-CFD) and a FEM code from K-Epsilon for he srucure (ARA) specialized o simulae he aeroelasic problem of yach sails and rig. In his paper, he paricular issues of coupling, remeshing and ransfer of forces from one code o he oher are deailed. An experimenal comparison is made on a well conrolled es case wih an original experimen developed by IRENav Ecole Navale, consising in a square of spinnaker fabric mouned on wo carbon baens which are moved in a forced oscillaion. The good agreemen of numerical resuls wih experimenal resuls permis o be confiden o go ahead and invesigae a full example of applicaion on a racing yach spinnaker. 1. INTRODUCTION Unseady compuaions of a sail-like membrane using a Navier-Sokes solver is really no rivial, since i requires a srong coupling beween he fluid equaions and he equaions modelling he sail behaviour. In he presen case, he Arbirary Lagrangian Eulerian (ALE) formulaion enables o reach accurae soluions, provided ha he force ransfer is cauiously carried ou. Besides, i is essenial o dispose of robus, fas and efficien volume grid deformaion echniques o keep simulaions wih moderae CPU ime. Up o now, his remains a challenging ask. This paper aims a describing he differen mehodologies developed o reach such a fluid/srucure coupling. Firs resuls reproducing an experimenal se up (a square of spinnaker fabric mouned on wo carbon baens which are moved in a forced oscillaion) are also presened. 2. EXPERIMENTAL SET UP The experimenal sysem consiss in a recangular piece of 11 by 85mm of spinnaker sailcloh mouned on wo cylindrical carbon baens which are moved in a forced periodic oscillaion wih no exernal wind. Figure 1 presens he principal dimensions of he se up. The se up is placed in a large room, so he swiveling sail is locaed 6m from he floor and he wall, in order o avoid any confinemen phenomenon. Only he srucure moion generaes a flow which affecs he srucure back. This simplified experimen is a good es case for he model because i reproduces mos of he relevan physical phenomenon o be modeled in he aero elasic problem of yach sails fluid srucure ineracion: srucural deformaion wih large displacemens, elasic flexion Furhermore inpus are compleely under conrol, conrarily o he case of real sailing. Figure 1. Principal dimensions of he swiveling sail se up. The swiveling moion consiss in an oscillaion around he verical reference posiion wih ampliude of 2 degrees. The verical posiion is he angular posiion and is he sail posiion a res. The sailcloh used is 45g/m² nylon. Is mechanical characerisics have been verified wih a racion es bed in he principal direcions -warp, filling- and are given in able 1. Tracion ess made on a 5mm wide spinnaker sailcloh sripes wih he LBMS-MMA of Bres have shown visco-elasic behavior bu requires developing a dedicaed racion es procedure. A PhD suden supervised by G. Bless in Bres is currenly working on his subjec. Characerisics of he carbon baens have been measured and are shown in able 1.
2 Table 1: Sailcloh and carbon baens mechanical specificaion As shown in figure 1, he carbon baens are insered in pockes along he verical boundaries of he sailcloh and he op ends of he baens are clamped on a rigid horizonal aluminum cylinder which is mainained by wo pivos and swiveled by a permanen magne harmonic drive CC moor FHA-25B. The angular velociy and posiion are conrolled boh by a Baldor MinDrive conroller which commands he moor wih high precision. The forced oscillaion is characerized by he period, ampliude, roaional velociy and acceleraion duraion. These parameers are recorded, as shown in figure 3, and are used as inpu daa o play he same moion wih he model. Figure 3: picures of he ligh shee for a 2 oscillaion ampliude sho by he camera from below. Exracion and calibraion of he sripes. Furher work is under developmen o measure direcly he 3D shape of he srucure by means of sereovision using wo high speed cameras. 3. NUMERICAL METHOD To invesigae numerically aero-elasic problems ha can be found wih sails, wo codes have been coupled: he ISIS-CFD flow solver and he ARA solver dedicaed o model he srucural pars of a sail boa. 3.1 THE RANSE SOLVER: ISIS-CFD Figure 2. CC moor recorded parameers The scene is filmed wih a high speed camera Phoron fascam SA3 a 25 fps o deermine he shape of he moving srucure along ime. To easily measure he srucure shape, he scene was illuminaed wih a horizonal ligh shee and filmed from below a shown in figure 1, along he average orienaion of he oscillaing sailcloh. This way, he inersecion of he sailcloh and he ligh shee is exraced from he images. Thus he shape of he srucure a a given heigh can be exraced. Calibraion is made for each posiion. Figure 3 shows picures of he ligh shee sho by he fas camera from below and he resuls afer calibraion obained afer image processing wih Malab. The posiion given by he moor conroller is used o rig he video acquisiion. The ligh shee is successively placed a differen heighs o deermine he 3D shape of he srucure over an oscillaion period. To ensure an esablished periodic regime, he firs five oscillaion cycles are no considered. The experimenal resuls are compared o he numerical ones for which all he inpus are he conrolled parameers of he experimen: mechanical characerisics of he srucure and kinemaic parameers of he forced oscillaion. The ISIS-CFD flow solver, developed by he EMN (Equipe Modélisaion Numérique) of he Fluid Mechanics Laboraory of Ecole Cenrale de Nanes, uses he incompressible unseady Reynolds-averaged Navier Sokes equaions (URANSE). The solver is based on a finie-volume mehod o build he spaial discreizaion of he ranspor equaions. The face-based mehod is generalized o unsrucured meshes for which nonoverlapping conrol volumes are bounded by an arbirary number of consiuive faces. A cenered scheme is used for he diffusion erms, whereas for he convecive fluxes, he Gamma Differencing Scheme is used (GDS) [1] hrough a Normalized Variable Diagram (NVD) analysis, his scheme enforces local monooniciy and convecion boundedness crieria. The velociy field is obained from he momenum conservaion equaions and he pressure field is exraced from he mass conservaion consrain, or coninuiy equaion, ransformed ino a pressure-equaion. These non-linear and coupled equaions are solved by a segregaed SIMPLE-like algorihm. A second-order accurae hree-level fully implici ime discreizaion is used and surface and volume inegrals are evaluaed using second-order accurae approximaion. In he case of urbulen flows, addiional ranspor equaions for he modeled variables are discreized and solved using he same principles.
3 An ALE formulaion enables o deal wih moving and deformable bodies [2]. The grid displacemen velociy fluxes are compued o ensures he discree space conservaion law o be exacly saisfied (see [3]) Free surface flows can also be compued hrough an inerface capuring mehod. [4] This solver has been validaed in numerous validaion es cases in naval hydrodynamics [5] and European projecs (EFFORT, Virue...). The funcionnaliies, especially concerning he body moions (and he free surface for o deal wih a complee sailing boa), make his solver suiable o invesigae sailing problems THE STRUCTURAL SOFTWARE: ARA ARA is a srucural mechanics code developed by he company K-Epsilon. This code is able o model a complee sailboa rig in order o predic forces, ensile and shape of sails according o he loading [6, 7, 8] 3.2(a) Marix of Properies The marix of properies for a given fabric relaes srain o sress. Is properies are derived from science of maerial or ensile ess: 3.2(b) σ [ C]ε = (8) Wrinkling Analysis Such a model assumes ha membranes are siff boh in ension and in compression. However, for a fabric ha does no have bending resisance, any ype of compression resuls in fabric wrinkling. Following double crieria on he main ensiles and heir corresponding deformaions: Tau Sae, where σ min > : sail compleely in ension Wrinkled Sae, caseε max > & σ min : ension in one direcion only slack sae : sail compleely in compression When wrinkles are foreseen, he direcion of folds (n) and he amoun of wrinkles (γ) are calculaed, he relaionship sress-srain becomes: σ * = [ C]( ε + γ n) (9) A marix of equivalen behaviour will be used o deermine he angen siffness: σ * [ C ]( ε + γ n) = [ C*]. ε = (1) 3.2(c) Finie Elemens: Spaial Inegraion The nonlinear finie elemen formulaion is esablished by he use of he virual work equaion. δ R h ( σ * δε ) ds (11) = S Where h is he membrane hickness, S is area of he elemen and δ is variaion due o virual displacemen. Inegraion of he above equaion resuls in a marix of forces a each node of he domain as well as [K] angen marix ha links he variaion of forces o he variaion of displacemen. The elemen seleced for his research is he CST riangle. Despie is simpliciy, his choice has proven o give a good raio of accuracy o compuing power. 3.2(d) Oher elemens and links In order o represen our experimenal oscillaing flag a model of beam elemens and a sliding model for linking elemens from ARA are used o simulae baens and he sliding of he cloh on baens. 3.2(e) Srucural Dynamic Scheme The Newmark-Bossak Ineracion scheme (emporal discreizaion) is based on a predicion-correcion ieraive mehod. The predicion is done by assuming ha he acceleraion remains consan. This assumpion does no affec he final resul. x = x x +Δ +Δ = x + x. ( 1 γ ). Δ + x +Δ. γ. Δ 1 2 x = x + x. Δ + +Δ x. β. Δ + x 2 The general equaion o solve expresses as: F + F = R ; R +Δ. βδ (12) in ernal exernal (13) In which he inernal forces can be divided ino 3 componens: ( F F + F ) + F R + (14) inerial damping siffness exernal = Deriving hese as a funcion of posiion, speed and acceleraion resuls in a Newon-ype scheme: [ M ]. u + [ C]. u + [ K ]. u = R (15) The Newmark scheme pus posiion, speed and acceleraion in he following relaion: K *. u = (16a) [ ] R 2
4 and: 1 βδ γ βδ [ K ] = [ M ]. + [ C]. + [ K] * 2 n n 1 n 1 n n 1 n γ x = x + u., x. 2 = x + u β. Δ β. Δ n n 1 n (16b) (17a) x = x + u (17b) up o convergence in he srucural par ISIS-CFD/ARA COUPLING In 22, he company K-Epsilon developed and coupled he srucural code ARA wih he aerodynamic code AVANTI (Unseady Vorex Laice Mehod sofware) [6, 7, 8]. The less CPU ime of he UVLM sofware has enabled us o develop and validae specific algorihms for FSI on membrain (sofware ARAVANTI). Boh he algorihms and he philosophy of he coupling of ARAVANTI were applied o he URANSE code ISIS CFD and ARA. 3.3(a) Fluid/Srucure coupling second one, denoed here he FSI loop, aims a solving he non-lineariy s of he fluid problem (i correspond o he non-linear loop when dealing wih non-fsi compuaions). In he case of FSI compuaion, he dashed box in Fig.4 is added. In paricular, i includes he resoluion of he srucure problem (srucure loop). Thus, a each new FSI ieraion (where he ime is fixed), he srucure problem is solved unil convergence on he geomeric non-lineariies using he curren fluid loads. I can be done a each FSI ieraion, since he CPU ime of he srucure resoluion is negligible compared o ha of he fluid resoluion. The geomery and kinemaics of he configuraion are hen updaed. In paricular, an adjusmen of he fluid mesh is carried ou o recover a body-fied mesh. A ha ime, he core of he fluid solver is called o obain a new evaluaion of he curren flow (inducing new values of fluid loads for he srucure). A new non-linear ieraion can hus resar. This coupling process (FSI loop) is repeaed unil convergence of he fluid flow. Then, a new ime sep can go on. Even if fluid/srucure exchanges are performed during he resoluion of he fluid wihin he same ime sep special aenion has o be paid for he evaluaion of [K*] o reach a sable coupling (see eq. 16), since fluid/sail ineracion is very srong. In fac, if Fex (i.e. Fluid forces) is considered as a consan (independen of x and is derivaives), as i is classically done for weaker FSI problems (in his case, [M], [C] and [K] only depend on he srucure properies), divergen oscillaions quicky appear. To ensure sabiliy, a specific approximaion of [K*] aken ino accoun he dependancy of Fex ono x is required. More precisely, an approximaion of he ineria marix of he fluid denoed [M_fluid] (which is he predominan fluid erm for such a problem) has o be inegraed ino [K*] in addiion o he conribuion of he srucure. This marix [M_fluid] is compued using an invisid flow solver (inegraed aside he ARA solver). 3.3(b) Grid deformaion echniques Ad-hoc deformaion echniques have hus been developed o keep a body-fied mesh during is moion. Figure 4: implici coupling diagram An implici/ieraive algorihm (see Fig.4) is used o coordinae he daa exchanges beween he fluid and srucure solvers and obain a sable coupling. This algorihm is srucured ino hree hierarchical loops. The highes level corresponds o he emporal loop. The One is based on a pseudo-srucure approach o build a consisen and robus unsrucured grid deformaion sraegy. The fluid domain is considered as a linear elasic solid srucure obeying srucural equaions which are linearised and used even in he case of large deformaions. The non-uniform local orhoropic behaviour enables o conrol he qualiy of he mesh and o enhance he robusness. This mehod is only used once per ime sep when he deformaions are significan. Inside he FSI loop, an analyical weighing echnique has been developed o adjus he new shape of he
5 srucure o he fluid domain and hen recover a bodyfied mesh wih an insignifican CPU ime. I is based as an exension of weighing echniques implemened for rigid bodies and beam-like bodies. The idea is o diffuse he rigid moion of each fluid face belonging o he bodies inside he fluid domain, layer by layer. The noion of layer is defined during he iniializaion of he simulaion using a crieria based on he shorer way o reach he face. Then, he compued displacemen of each node is damped using a weighing coefficien which decreases up o zero when going far away from he body. 3.3(c) Force ransfer Even if boh srucure and fluid meshes are generaed from he same geomery, an exrusion of he geomeric definiion of he surface is needed o obain a suiable boundary for he fluid mesh, whereas only a 3-D surface is required for he srucure mesh. Furhermore, he meshing procedure is no idenical for boh, so as o he locaion of he variables (srucure variables are locaed a he nodes, whereas fluid variables are cell-cenered). A redisribuion of he fluid force applied on each fluid face is hen needed. This is done hrough a conservaive way. The firs sep concerns he spliing of fluid faces which cu srucure faces. Fluid forces are hus weighed according o heir respecive area. Nex, he disribuion of forces are broadcased owards he nodes of he considered srucure elemen: his sep is done by wriing he force and momenum balances (see Fig.5) Figure 6: comparison video / compuaions Figure 7 shows comparisons of he experimenal ligh shee (blue line) wih he compuaion of inersecion beween consan plane and cloh (orange line). This resul shows a really good accordance during all he moion of he cloh. Figure 5 : force ransfer procedure 4. RESULTS Here comparisons beween video from IREnav and compuaions of he same benchmark are presened. The figure 6 shows wo paricular evens: when cloh of he edge is no in a au sae wih an angular shape, and when cloh is in a au sae wih a curvaure edge. For boh evens, he shape looks similar, in paricular simulaions manages o capure he inflexion near he edge. Figure 7: comparison experimenal (blue) / compuaion (orange) of a secion of he cloh
6 5. CONCLUSIONS Numerical mehodologies which have been described make possible o deal wih simulaion involving unseady configuraion around sails using a RANSE solver based on an ALE formulaion: he implici/ieraive coupling associaed wih an evaluaion of he surface added mass of he surrounding fluid makes he fluid/srucure sable, he grid deformaion echniques implemened ino he fluid solver enable o recover a bodyfied mesh each ime i is needed wihou increasing oo much he cpu ime compared o a classical CFD compuaion (indeed, inside he FSI loop, he analyical weighing regridding has negligeable cpu ime) he conservaive force ransfer ensures an accurae procedure Resuls on an experimenal se up carried ou in laboraory confirm robusness of he whole procedure. More deailed validaions are planned wih his case: Comparisons of 3D shape when he new experimenal pos-reamen is available so as comparison of global fluid force. Compuaions dealing wih realisic configuraions (like in Fig 8 which shows a configuraion around a racing yach spinnaker) are now in progress oo. Comparisons wih differen experimenal daa, especially daa coming from in-siu measuremens (insrumened J8 sailing boa) are also planned. 2. LEROYER, A. and VISONNEAU, M., Numerical mehods for RANSE simulaions of a self-propelled fish-like body, J. Fluid & Srucures, Vol. 2, No. 3, pp , LEROER, A. and BARRE, S. and KOBUS, J.M. and VISONNEAU, M. Experimenal and numerical invesigaions of flow around an oar blade, Journal of Marine Science and Technology, volume 13,1-15, QUEUTEY, P. and VISONNEAU, M., An inerface capuring mehod for free-surface hydrodynamic flows, Compuers & Fluids, Vol. 36, No. 9, pp , GUILMINEAU, E. and QUEUTEY, P. and VISONNEAU, M. and LEROYER, A. and DENG, G. RANS simulaion of a US Navy frigae wih PMM moions, Workshop on Verificaion and Validaion of Ship Manoeuvering, Simulaion Mehods, SIMMAN 28, Copenhagen, Avril Durand, M., Hauville, F., Mounoury, S. and Roux, Y., Comparaison des résulas d un modèle aéroélasique appliqué à la déformaion d un gréemen avec des mesures en soufflerie e in siu - In 11èmes Journées de l'hydrodynamique, Bres, ENSIETA, 3-5 Avril, 27, pp Y.Roux, M. Durand, A. Leroyer, P. Queuey, M. Visonneau, J Raymond, J. M. Fino, F. Hauville, A. Purwano. Srongly coupled VPP and CFD RANSE code for sailing yach performance predicion. High Performance Yach Design Conference, Auckland, December 28, pp Hauville, F., Durand, M., and Roux, Y., 27, Modèle aéroélasique appliqué à la déformaion d un gréemen. European Journal of Environmenal and Civil Engineering, 28, Vol. 12, No 5, pp AUTHORS BIOGRAPHIES Mahieu Durand is Researcher Suden wihin he K- Epsilon company since 28 and preparing his PhD wih Ecole Cenrale de Nanes and IRENav. His work deals wih numerical FSI modelling. He is also a op 1 mach racer sailor. Figure 8 : resul of a complee IFS on a spinnaker 6. REFERENCES 1. JASAK, H. and WELLER, H.G. and GOSMAN A.D., High resoluion NVD differencing scheme for arbirarily unsrucured meshes, Inernaional Journal for Numerical Mehods in Fluids, Vol 31, pp ,1999 Frederic Hauville and Parick Bo are associae professors a IRENav, specialised in fluid mechanics. They are sudying Fluid Srucure Ineracion and marine renewable energy. They have been working on FSI of sails for many years and sared o develop measuremens on sailing yachs in 2. Benoî Augier is PhD suden in he Research Insiue of he French Naval Academy (IRENav). He is sudying he Fluid Srucure Ineracion on sof surfaces wih a srong
7 applicaion o sails. He is paricularly in charge of he experimenal work. Yann Roux holds he curren posiion of C.E.O. a he company K-Epsilon and is he main founder. In parnership wih he laboraory Ecole Cenrale de Nanes and IRENav, he develops sofware and cusomised ools and provides sudies and service in unseady hydrodynamic and aerodynamic compuaion. Alban Leroyer is Assisan Professor a he Fluid Mechanics and Energeics Deparmen of ECN since 25. He is carrying ou is research wihin he CFD deparmen of he ECN Fluid Mechanics laboraory. His research opics include Naval Hydrodynamics, Fluid- Srucure Ineracion and Bio-Hydrodynamics. Michel Visonneau is Research Direcor wihin CNRS since 26. He is currenly he head of he CFD deparmen of he Fluid Mechanics Laboraory (ECN) in His main research opics are Compuaional Fluid Dynamics (CFD), Ship Hydrodynamics and Turbulence Modeling for high Re flows. He has been seleced as 3h Georg Weinblum Memorial Lecurer (27-28).
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