Adjoint Optimization for Vehicle External Aerodynamics

Transcription

1 1109 Adont Optmzaton for Vehcle External Aerodynamcs Georgos K. Karpouzas 1) Evangelos M. Papoutss-Kachagas 2) Thomas Schumacher 1) Eugene de Vllers 1) Kyrakos C. Gannakoglou 2) Carsten Othmer 3) 1) Engys Ltd., Studo 20, RVPB, John Archer Way, London, SW18 3SX, U.K. (E-mal: 2) Natonal Techncal Unversty of Athens, School of Mechancal Engneerng, Parallel CFD & Optmzaton Unt, P.O. Box 64069, Athens, GREECE 3) Volkswagen AG, Group Research, Letter Box 1777, K-EFFG/V, D Wolfsburg ABSTRACT: Adont optmzaton s an exctng and fast growng feld that has many applcatons n the automotve ndustry. We focus on the usage of adont for the optmzaton of aerodynamc performance. Whle adont methods have come to the attenton of manstream CFD through ncluson n promnent commercal codes, most of the avalable tools are severely lmted, precludng productve use n ths feld. We detal a methodology that s based on the contnuous adont method and s mplemented n an Open Source framework. Whle more mathematcally demandng n terms of ts dervaton, the contnuous adont method requres orders of magntude fewer resources wthout sacrfcng sgnfcant accuracy. In ths paper contnuous adont methods are used for calculatng gradents of aerodynamc obectve functons (drag, lft, moments etc.) n applcatons wth a huge number of desgn varables. Methodologes that accept ether steady-state RANS (1)(2)(3) or tme averaged DES (4) as prmal flow nput are outlned and extensons to mprove the accuracy of prevously publshed methods are detaled. Fnally a novel methodology, based on volumetrc B-splnes to translate the surface senstvtes produced by the adont nto optmzed shapes, s ntroduced and showcased. KEY WORDS: Heat Flud, Aerodynamc Performance, Optmzaton, Detached Eddy Smulaton, Adont (D1) 1. INTRODUCTION Computatonal Flud Dynamcs (CFD) s central to large portons of automotve desgn. Not only s t used promnently for the predcton of external aerodynamc performance, but t also sees extensve use n a dverse set of applcatons ncludng (but not lmted too) HVAC (heatng ventlaton and coolng), combuston, exhausts, after treatment, ar ntakes, thermal management, head-lghts, ar bags, aero-acoustcs, fuel supply, and the desgn of pumps/fans/blowers. Much of the desgn process attached to these components and systems s stll dependent on manual teratons between desgner and computatonal analysts. Even n nstances where automated stochastc optmzaton loops are n place, these are severely constrcted by the fact that the costs are proportonal to the number of parameters to be optmzed. Ths places a lmt on the degrees of freedom avalable to the optmzaton process and constrans the degree of optmzaton that can be acheved wthn the allowable parameter space. Further, the conceptually smple step of parameterzng the nput CAD necessary for such a process can be a stumblng block n and of tself, especally consderng the complexty of many of the components. One of the fastest growng felds n CFD research s adont optmzaton. It s based on the Adont method, whch allows for very effcent calculaton of senstvtes of the obectve functon wth respect to desgn varables. In fact, the computatonal effort n typcal adont systems s dependent only on the number of obectves (drag, lft, etc.) rather than the number of desgn varables (surface node dsplacement). Ths makes adont methods deal for optmzng problems wth large numbers of varables and/or large desgn spaces. In the context of the adont method, there are two man varants: dscrete adont and contnuous adont. In the dscrete approach, the dscretzaton of the partal dfferental equatons happens before the adont dfferentaton. Ths can be done manually or va algorthmc dfferentaton tools such a TAPENADE (9). In the contnuous approach, the adont equatons are formulated by dfferentatng the partal dfferental equatons representng the flow (prmal problem) drectly. These adont equatons are then dscretzed and solved. The two 2015 JSAE Annual Congress on May, 20 to 22 Copyrght 2015 JSAE

2 approaches perform smlarly when appled to smple canoncal test cases: the calculaton of the senstvty dervatves s fast, the procedure converges rapdly and the whole process s relatvely straght-forward. However, n ndustral scale applcatons the soluton of the adont problem becomes sgnfcantly more challengng. The dscrete adont can theoretcally provde the exact gradent w.r.t. the desgn varables for any obectve specfed, but t requres large amount of memory and computatonal cost. More precsely, all the ntermedate states durng the dscrete calculaton have to be stored n the memory. In dscrete termnology these ntermedate states are referred to as the tape. Technques such as revolve (check-pontng) have been developed to reduce the memory requrements, but ths sgnfcantly ncreases the computatonal cost of the method. The net effect s that the cost of dscrete adont wll typcally be an order of magntude or more n excess of the prmal soluton, and can often place unmanageable burdens on the compute nfrastructure n terms of memory requrements. In the contnuous adont method on the other hand, the bottle-neck les n the analytcal dfferentaton of the prmal flow equatons, whch can be complcated and tme-consumng. Ths amount of effort wll depend on the complexty of the prmal equaton system, but the full dervaton only has to be performed once for each unque equaton set. The memory requrements and computatonal cost s however smlar to the soluton of the prmal equatons. Ths makes the contnuous approach deal for ndustral scale applcatons wth ntermedate to large computatonal meshes. Further, the dervaton process that produces the contnuous adont equatons and the famlarty of the resultng equatons and algorthms promotes a deeper understandng of the soluton system. Ths n turn can be of sgnfcant beneft n the development of effcent adont solvers, as wll be shown n ths publcaton. 2. METHODOLOGY 2.1. Contnuous Adont In ths paper, we demonstrate the use of the contnuous adont method for effcent shape optmzaton of vehcle external aerodynamc problems. Whle transent adont formulatons are possble, they are much more complex and costly to mplement and mantan. We thus ntally restrct ourselves to steady state: the prmal flow RANS (Reynolds- Averaged-Naver-Stokes) equatons are: R p = v = 0 R v = v v + p [(ν + ν t ) ( v + v )] = 0 R z = Convecton + Dffuson + Producton + Dspaton = 0 ( 1 ) ( 2 ) ( 3 ) Where v s the prmal velocty, p s the prmal pressure, and t are the knematc and turbulent knematc vscosty, respectvely. R z s consdered to be an arbtrary turbulence model wth z representng the multcomponent turbulence vector. Now n order to derve the adont, let us start by defnng an obectve functon F. The obectve can be defned as a combnaton of surface and volume ntegrals. and R v. F = F s S ds + F Ω Ω dω ( 4 ) F s then augmented (extended) by the state equatons, R p F aug = F + Ω qr p dω + u R v dω ( 5 ) Ω Here q and u are the adont varables and due to the way they enter the soluton algorthm can be nterpreted as adont pressure and adont velocty respectvely. In ths example dervaton the turbulent knematc vscosty ( ν t ) s assumed constant wth respect to changes n the desgn varables (frozen turbulence assumpton). Ths assumpton can have an effect on senstvty, but n many nstances the reduced complexty that results makes the assumpton ustfable. The morphng cases n secton 3, however nclude the adont to the turbulence model equatons. Dfferentatng the augmented cost functon, F aug, (see (1) for detals) produces the adont equatons for ncompressble flow wth frozen turbulence: R u Ω R Ω q = u F p = 0 = v u + u v + q [(ν + ν t ) ( u + u )] + F v = 0 ( 6 ) ( 7 ) The adont equatons are very smlar to the prmal equatons (eqs. (1-3)). They both have convecton, dffuson, a

3 gradent of pressure and (possbly) a source term. The man dfference s the addtonal term ( u v ), whch appears n the adont momentum equatons. Ths term s referred to as the Adont Transpose Convecton (ATC). After solvng the adont equatons, the surface senstvtes of the obectve functon wth respect to the surface normal moton of the surface nodes (desgn varables) can be calculated wth the followng expresson: δf aug δb = [(ν + ν t ) ( u + u v x k ) qn ] ds ( 8 ) x k b m S w In shape optmzaton problems, the surface senstvtes are used as an nput to a deformaton tool, whch morphs the computatonal doman. Ths process s typcally teratve and there are many dfferent methods that can be used to acheve the shape modfcaton. These range from two-way couplng of the adont problem to parameterzed CAD to drect free form deformaton of the surface nodes Verfcaton In order to verfy the basc methodology, we apply a naïve morphng operator to a prevously publshed model vehcle the DrvAer Estate (5). The obectve functon n ths case s drag mnmzaton and the prmal s a steady state RANS usng the Spalart-Allmaras turbulence model. Fg. 1: DrvAer Estate showng the orgnal model wth adont surface senstvtes (blue = push n to reduce drag and red = pull out) and the morphed geometry. Wheels are omtted for clarty. We apply a smple hyperbolc tangent flter to the adont surface senstvtes that lmts the maxmum sngle-step dsplacement to 2mm. Fgure 1 dsplays the surface senstvtes generated for the case along wth the result of the morphng operaton. The morphed geometry was re-meshed and drag coeffcent was found to reduce from C D = to (~8%). The dfference between the two geometres s mnmal and dffcult to dentfy from the mage. In ths context, the large mprovement acheved n the obectve wth such a small modfcaton s all the more surprsng. Unfortunately, morphng wthout constrants wll not n general result n a manufacturable desgn, whch means ths approach has lmted utlty as an actual desgn tool. It does however showcase the effectveness of the adont method n the context of a realstc vehcle geometry. Further and more rgorous valdaton of the method can be found n (1) (2) Lnearzed ATC The ATC term dentfed n sec. 2.1 s the man source of dffculty when attemptng to solve the contnuous adont equatons wth tradtonal segregated algorthms such as SIMPLE (Sem-Implct Method for Pressure Lnked Equatons). The ATC cross couples the components of the adont velocty, whch means t cannot be mplemented mplctly n a segregated algorthm. The contrbuton thus has to be lagged, makng t fully explct. Ths results n weak couplng between the adont pressure and velocty, whch n combnaton wth mperfect cell qualty or hgh surface normal gradents can lead to gradual selfrenforcng dvergence of the soluton. In aerodynamc calculaton, these condtons typcally occur near the wall. The general practce n such cases s to lmt the contrbuton of the ATC n the near-wall cells and to employ frst order convecton for the mplct part of the adont convecton. The addtonal numercal dsspaton ntroduced by the use of the upwnd scheme and the excson of the strong source regons s typcally enough to stablze the calculaton. The obvous drawback however s that the upwnd scheme s less accurate than the second order schemes typcally used for RANS prmal calculatons and secondly that by maskng the near-wall contrbutons to the ATC, we are removng some of the largest source terms from the equaton. A method that preserves second order accuracy whle mantanng stablty s thus hghly desrable. The obvous long term soluton s to mplement the prmal and adont equatons n a block coupled framework that allows

4 mplct mplementaton of the full equaton set. In the current context an approxmate approach based on the selectve maskng of nstablty nducng flow regons has been developed. A lnear surrogate model s constructed for the ATC contrbuton to the matrx. The man purpose of ths model s to dentfy the cells n whch the ATC would gve negatve contrbutons n the dagonal of the matrx (left hand sde) f t was mplct. ATC = u v A = ATC u u 2 ( 9 ) ( 10 ) A s the proected dagonal contrbuton for an mplct ATC term. If A s negatve, the ATC wll reduce the matrx dagonal domnance and make the soluton more unstable. As a result, the system wll become ll-posed and potentally dverge. Usng ths ndcator, the ATC contrbuton can be damped on a cell-by-cell bass so that dagonal domnance of the matrx, and by nference stablty, s guaranteed. Ths approach results n a mnmal reducton n the ATC source term and allows the use of second order schemes for the adont convecton term. Wthout ths targeted dampng a strong much more global dampng of the ATC s requred to ensure stable second order operaton. Fgure 2 shows a comparson of drag mnmzaton surface senstvtes for second order convecton wth lnearzed ATC and frst order convecton wth global near-wall dampng for the DrvAer Sedan model (5). There are clear qualtatve and quanttatve dfferences. The second order method produces smoother felds wth much more detaled small features. The overall trends are smlar (as expected), but there are clear regonal dfferences n the rear spoler and front bonnet regons, whch mples the use of near-wall ATC dampng plus frst order upwnd for the adont convecton can lead to suboptmal desgns Tme Averaged DES Adont The steady state RANS adont approach has shown very postve results over a large range of applcatons (1)(4)(7). The method however suffers from a shortcomng that s nherent to the underlyng prmal RANS equatons n that many problems are not accurately descrbed by ths approach. Thus, any method that reles on RANS to generate senstvtes (adont or stochastc) wll suffer from the same naccuraces. The DES (Detached Eddy Smulaton) method s an approach that drectly resolves most of the mportant scales of moton rather than approxmatng these scales wth a turbulence model. Due to the reduced modellng dependence, t can be much more accurate and consstently accurate than any RANS based method (10). The method s however nherently transent and as mentoned prevously, transent adont s much more costly and cumbersome to evaluate than the steady equvalent. If we are however, only nterested n the tme averaged aerodynamc propertes of the vehcle,.e. the mean drag, then an nterestng possblty presents tself: to formulate a steady adont for the tme averaged transent prmal flow. To derve such an adont let us start from the basc LES/DES equatons for an ncompressble flow. In what follows, we neglect the contnuty equaton, snce t s tme averaged form s dentcal to ts nstantaneous form. The turbulence quanttes are assumed frozen to smplfy the dervaton (ths mght not be the case for actual smulatons). The focus s then on the standard LES/DES momentum equaton: v t + v v + p [(ν + ν SGS ) ( v + v )] = 0 ( 11 ) The over-bar denotes a spatal flterng operaton and ν SGS represents the sub-grd scale turbulence vscosty, whch s typcally much smaller than a RANS based turbulence vscosty. In order to recover a steady flow feld, we apply a tme averagng operator to eq. (15) denoted by the claret (^). The tme averaged DES equaton results: v t + v v + p [(ν + ν x SGS ) ( v + v )] = 0 ( 12 ) Fg. 2: Comparson of surface drag senstvtes for second order LUD plus adaptve lnearsed ATC (top) and frst order UD wth fxed near-al blendng (bottom). DrvAer sedan model (5).

5 Assumng the dfference operators are constant n tme, the flow s statstcally steady and the averagng s long enough, several smplfcatons can be made: v p p 0, = ( 13 ) t v v = v v T ( 14 ) tme averaged DES adont usng the Spalart-Allmaras model to calculate the turbulent vscosty. Note the smlarty between RANS- and DES-based drag senstvtes for the largest part of the car roof and the dramatc dfference at the rear part. Whle the RANS computaton msses the favorable effect of a rear spoler, t s clearly present n the DES results. Tests wth a varable spoler on the actual vehcle have corroborated the DES senstvty result. T = v v v ( 15 ) For the vscous term we assume that: ν SGS ( v + v ) ν x SGS ( v + v ) ( 16 ) and collect the dfferent nto the resolved Reynolds stress tensor T. Substtutng eqs. (13-16) back nto (12), the tme averaged DES momentum equaton becomes: v R v v = p [(ν + ν x SGS ) ( v + v ) + Τ ] = 0 ( 17 ) All the tme averaged quanttes, v, p, νsgs and Τ can be calculated durng the prmal run. The averaged resolved Reynolds stress Τ s not however dfferentable, so n order to nclude ts effect n the adont, we need to defne a more mplct approxmaton. Takng a cue from RANS and as a frst approxmaton, we formulate the stress as the product of the stran wth some turbulent vscosty, ν t, plus a resdual stress. ν SGS ( v + v ) + Τ = ν t ( v + v ) + Q ( 18 ) Where Q, s the uncorrelated resdual stress assumed to be ndependent of the mean flow and desgn varables (frozen assumpton). There s a degree of freedom n choosng ν t as any resdual wll smply be absorbed ntoq. However, choosng a model that mnmzes Q n the context of the formalsm wll lead to a more mplct and therefore accurate adont. The easest approach s to fnd ν t by smply solvng a standard RANS model wth the tme averaged prmal velocty v, as nput. The adont equatons for the tme averaged DES prmal are dentcal to those for the steady RANS prmal, other than that tme averaged nputs are used. Fgure (3) shows a comparson between the surface senstvtes on an Aud A7 of a RANS steady state adont and a Fg. 3: RANS vs. approxmate DES senstvtes for Aud A7. The actual shape of the actve spoler n the current Aud A7 s shown n the bottom of the mage Tensoral Vscosty Usng a scalar vscosty calculated va a RANS turbulence model mght be straght forward, but t completely neglects the avalablty of the tme averaged resolved Reynolds stress (T ). In order to reduce the magntude of the resdual stress, Q,. we can nstead derve a tensoral vscosty. Choosng a tensor coeffcent provdes more degrees of freedom when tryng to approxmate T, snce we do not have to assume sotropy nor algnment of the stress and stran rate. The proposed method uses

6 the same relaton as eq. (18) but nstead of a scalar vscosty (ν t ) we calculate a tensoral vscosty (N) from the averaged stran ( S ), averaged SGS stresses ( B ) and averaged resolved Reynolds stresses (T ). The necessary averaged quanttes are calculated wth the followng formulas: n+1 n B = ab + (1 a)b ( 19 ) N d = E d /S d ( 26 ) For degenerate entres heurstcs are used to fnd an approxmate value for the correspondng dagonal element to produce N and S s made sphercal usng the mean of the fnte dagonal entres. The resultng stress tensor s calculated. S n+1 = as n + (1 a)s T n+1 = a(t n + v n v n ) + (1 a)v v ( 20 ) E = N k S k ( 27 ) The E and the S k are transformed usng the egenvectors g and λ, respectvely. v n+1 v n+1 ( 21 ) E = g 1 E g T 1 ( 28 ) a = t Δt t S = λ 1 S λ T 1 ( 29 ) Where t s the current tme and Δt s the tme step. The total mean stress, E, can be found from: The new tensoral vscosty s calculated by nvertng the S k tensor. E = B + T = N k S k + Q ( 22 ) N = E S 1 ( 30 ) We stll need to account for a resdual stress Q, snce t entrely possble for a mean stress to exst n the absence of mean stran. We seek a value of N such that Q, s mnmzed whle avodng sngulartes. If the stran S s nvertble (.e. S 1 exsts), whch s the case for the maorty of the mesh elements, then N s can be calculated drectly. N = E S 1 ( 23 ) The resultng tensoral vscosty can be used drectly n the adont equatons. Fgure (4) shows a comparson of the vscosty generated by the new scheme wth that from the Spalart- Allmaras RANS equaton. Pronounced dfferences can be observed. The effects on the adont senstvtes are sgnfcant, but do not change the general character of the results. The valdaton of the new method wll be detaled n future publcatons. The process becomes more problematc f S s one or two dmensonal or S and E are uncorrelated. In such elements, a tensor component analyss s appled n order to nvert the S tensor wth mnmum amount of modfcaton. The transformaton analyss s based on the fact that the mean stran s a symmetrc tensor. Symmetrc tensors are dagonalzable and they have orthogonal egenvectors. E = ge g T S = λs λ T ( 24 ) ( 25 ) Fg. 4: Comparson of tensoral vscosty magntude (top) wth RANS vscosty for a tme averaged DES flow feld (bottom). Ahmed body 35 rear slant. After makng S dagonal, the elements wth 1D and 2D strans wll have zero or near-zero entres n one or more postons on the dagonal. In the locatons that the dagonal of S s not zero or very small, the dagonal of N s calculated. 3. MORPHING Ths secton presents the couplng of the contnuous adont method wth a morphng tool for shape optmzaton n car aerodynamcs.

7 3.1. Morphng Methodology All cases that follow use a mesh parameterzaton and dsplacement strategy based on volumetrc B-splnes, whch can be seen as a Free Form Deformaton (FFD) method, and ts couplng wth the contnuous adont solver. The method uses a set of control ponts n 3D space, n the form of a structured control grd, fg(5). CFD mesh ponts resdng nsde the boundares of the control grd are dsplaced followng the dsplacement of the control grd ponts. The use of ths software n aerodynamc shape optmzaton s twofold: (a) for the parameterzaton of the surface of an aerodynamc body by defnng arbtrary control ponts n 3D space, to be used as the desgn varables and (b) for the dsplacement of the surface and volume nodes of the CFD mesh wthn each optmzaton cycle. The method exhbts great potental snce the cost of each mesh dsplacement s extremely small, the mnmum degree of surface contnuty can be defned a-pror and the setup of each case s not cumbersome. The verson of the contnuous adont solver employed for the morphng does not neglect varatons n turbulent vscosty: both the mean flow and turbulence equatons are dfferentated. The dfferentaton has been performed for the most wdely used turbulence models (Spalart Allmaras (1), k-ϵ (2) and k-ω SST (3) models). Whle t s case dependent, the omsson of the turbulence adont can result n ncorrect or even ncorrectly sgned senstvtes. Ths wll n turn result n an erroneous optmzaton outcome (4). The steps of the shape optmzaton algorthm are lsted below: (a) Defne the control grd to enclose the part of the geometry to be optmzed. The desgner may choose to ncrease the control ponts number or lower the bass functons degree, leadng to more localzed (but less smooth) geometry changes. (b) Locate the CFD mesh ponts that resde wthn the boundares of the control grd. (c) Compute the parametrc coordnates of the ponts found n the prevous step. The computatonal cost of ths step ncreases wth the number of control ponts and the number of the mesh ponts to be parameterzed. (d) Solve the flow equatons. (e) Compute the obectve functon value and apply the termnaton crteron. (f) Solve the adont equatons. (g) Compute the obectve functon gradent w.r.t the boundary CFD mesh nodes to be dsplaced, δf/δx m, where x m are the coordnates of the surface nodal ponts. (h) () () (k) Proect the surface senstvtes to control ponts, n order to compute the control ponts senstvtes, by applyng the chan rule δf = δf δx m ( 31 ) δb l δx m δb l where b l are the control pont coordnates. Update the control pont postons. Compute the new surface and volume mesh ponts postons through the volumetrc B-splnes equatons, usng the already computed parametrc coordnates assocated wth each one of them. Move to step (d). Three test cases are presented. Fg. 5: Boundary of control box and control ponts coloured based on ther z coordnate, for the ntal (left) and optmzed (rght) geometres Sde Mrror Morphng The frst case s the optmzaton of a sde-mrror of a passenger car, wth mrror-nduced drag mnmzaton beng the target obectve. The Spalart-Allmaras turbulence model wth wall functons and ts adont solver (4), were used. The startng and fnal mrror geometres are shown n fg.(5). The mrrornduced drag s reduced by ~7%. Fg. 6: Intal (left) and optmzed (rght) rear parts of the DrvAer geometry, targetng mn. drag force. The boundares of the control box are panted n black. Car surface colored by pressure and symmetry plane by velocty magntude.

8 3.3. Vehcle Rear Spoler Morphng The second case deals wth the drag mnmzaton of the fastback confguraton of the DrvAer car geometry (5). The morphng box was placed around the rear part of the car only, targetng the formaton of a rear spoler. Agan, the Spalart-Allmaras turbulence model wth wall functons s employed. Fg.(2) shows the comparson between the baselne and the optmzed rear part of the car. The spoler reduces the drag by 0.2% S-Bend Duct Morphng The thrd case demonstrates the reducton of total pressure losses n an S-bend duct used n the HVAC system of a passenger car (an EU ITN AboutFlow test case). Here the flow s lamnar and the optmzaton has led to a reducton n total pressure losses by more than 60%, (fg.(7)). Fg. 7: Total pressure losses for the ntal (top-left) and optmzed (top-rght) ducts. Flow from rght to left. The large mesh dsplacements (up to 64% of the nlet dameter, bottom) can be effcently handled by the morphng tool. 4. CONCLUSION We have ntroduced a set of methods and tools for applyng adont-based optmzaton methods to vehcle external aerodynamcs. Whle not unque n concept t s the frst such method wth suffcently robust and effcent algorthms to allow t to be confdently appled wthn the context of exstng vehcle smulaton workflows. Specfcally, the nature of the method allows t to be used n conuncton wth geometres and grds of ndustral scale and complexty. The ntroducton of the tme averaged DES adont approach allows the use of the type of hgh accuracy prmal nput that s requred for relable and dependable aerodynamc predcton and optmzaton. The adont solvers, when coupled wth approprate free form deformaton methods, result n powerful automatc optmzaton methods able to radcally mprove vehcle aerodynamc characterstcs at a fracton of the cost of equvalent stochastc methods. REFERENCES (1) A.S. Zymars, D.I. Papadmtrou, K.C. Gannakoglou, C. Othmer: Contnuous Adont Approach to the Spalart--Allmaras Turbulence Model for Incompressble Flows, Computers & Fluds, 38, p , (2009). (2) E.M. Papoutss-Kachagas, A.S. Zymars, I.S. Kavvadas, D.I. Papadmtrou, K.C Gannakoglou: The Contnuous Adont Approach to the k-ε Turbulence Model for Shape Optmzaton and Optmal Actve Control of Turbulent Flows, Engneerng Optmzaton, Vol. 47(3), p , (2015). (3) I.S.Kavvadas, E.M. Papoutss-Kachagas, G. Dmtrakopoulos, K.C. Gannakoglou: The Contnuous Adont Approach to the k-ω Turbulence Model wth applcatons n shape optmzaton, Engneerng Optmzaton, to appear, (4) E.M. Papoutss-Kachagas, K.C. Gannakoglou: Contnuous Adont Methods for Turbulent Flows, Appled to Shape and Topology Optmzaton: Industral Applcatons, Archves of Computatonal Methods n Engneerng, p. 1-45, (5) A. Heft, T. Indnger, N. Adams: Introducton of a New Realstc Generc Car Model for Aerodynamc Investgatons, SAE 2012 World Congress, Aprl 23-26, 2012, Detrot, Mchgan, USA, Paper (6) G.K Karpouzas, E. de Vllers Level-set based topology optmzaton usng the contnuous adont method. An Internatonal Conference on Engneerng and Appled Scences Optmzaton. OPT-I 2014 (7) I.S. Kavvadas, G.K. Karpouzas, E.M. Papoutss-Kachagas, D.I. Papadmtrou, K.C. Gannakoglou Optmal Flow Control and Topology Optmzaton Usng the Contnuous Adont Method n Unsteady Flows. Advances n Evolutonary and Determnstc Methods for Desgn, Optmzaton and Control n Engneerng and Scences Computatonal Methods n Appled Scences Volume 36, 2015, pp (8) P.R Spalart, W.-H. Jou, M. Strelets, S.R. Allmaras, Comments on the feasblty of LES for wngs, and on a hybrd RANS/LES approach. In: Lu, C., Lu, Z. (Eds.), Advances n LES/DNS, Frst AFOSR Internatonal Conference on DNS/LES. Greyden Press, Lousana Tech Unversty (9) L. Hascoet, L. and V. Pascual TAPENADE 2.1 user's gude. INRIA. (10) E. de Vllers, A. Lock, P. Gerema, Todd Johansen: ELEMENTS, A New Aerodynamcs Analyss Software Aerodynamcs, UHTM, HVAC and Cabn Comfort, Solng and Water Management.