NUMERICAL BASIS OF CAD-EMBEDDED CFD

Transcription

1 NUMERICAL BASIS OF CAD-EMBEDDED CFD Dr. A. Sobachkn, Dr. G. Dmnov, (Mentor Graphcs Corporaton, Mechancal Analyss Dvson, Rssa) Dr. A. Sobachkn, Engneerng Manager THEME CAD CAE Integraton: Meshng & Integraton of Analyss nto the Desgn Process SUMMARY FloEFD s a new class of CFD (Comptatonal Fld Dynamcs) analyss software (called Concrrent CFD) that s flly embedded n the mechancal desgn envronment, for all general engneerng applcatons. FloEFD was developed by Mentor Graphcs Mechancal Analyss Dvson, whch s one of the top three CFD vendors n the world today and the leader n mltcadembedded CFD. All CFD software ncldes a representaton of the Naver-Stokes eqatons, trblence models and models for physcal phenomena. Snce the early 1980s CFD codes have grown n complety, partclarly n physcal modellng, bt wth less emphass on dealng wth geometrc complety. In parallel, mechancal CAD systems have become the backbone of the prodct creaton process n almost all ndstry sectors, allowng very comple geometres to be constrcted wth relatve ease. In 1999, SoldWorks ntrodced the frst verson of FloWorks, provdng for the frst tme a CFD smlaton capablty nsde a MCAD system, drectly sng natve CAD geometry wthot modfcaton as the startng pont for the CFD process. Snce then a nmber of CAD-embedded and CAD-assocated tools have appeared. These tools se dfferent nmercal technologes to tradtonal CFD rangng from mesh generaton to dfferencng schemes and wall treatment, yet not mch has been pblshed abot ther nner workngs. Ths paper takes an n-depth look nder the hood at the nmercal bass for one sch tool FloEFD. The dea s nderpnned by the choce of meshng technology n FloEFD and the mpact that choosng a Cartesan-based mesh has on the way the geometry s handled, n partclar sold-fld and sold-sold nterfaces, the wall treatment sed to captre bondary layer evolton, and calclaton of skn frcton and heat fles. A specfc challenge s the treatment of thn walls and mltlayer shells.

2 NUMERICAL BASIS OF CAD-EMBEDDED CFD Fnally, we show how the rectlnear mesh and bondary layer models have been etended by a set of physcal models coverng: real gases; spersonc and hypersonc flows; gas/gas premed and non-premed combston; bolng; cavtaton and condensaton processes. Radaton models that accont for spectral characterstcs wll also be brefly presented. KEYWORDS CAE, CFD, EFD, FloEFD, CAD-embedded, mesh, meshng technology, nmercal schemes, solver technology, engneerng analyss, engneerng fld dynamcs, mltphyscs.

3 1: INTRODUCTION In modern desgn practce, prodct lfecycle management concepts (PLM) are wdely deployed by engneers n many ndstres as the means by whch 3D manfactred prodct data are sed and mantaned consstently drng an entre prodct s lfecycle and across all ts desgn changes. The bass of a PLM concept s the avalablty of hgh-qalty, complete, detaled, and accrate 3D prodct model data wthn a mechancal CAD system as the central element. 3D prodct model data are therefore both the fondaton and startng pont for all vrtal prototypng and physcal smlatons today. The se of fld flow smlatons sng Comptatonal Fld Dynamcs (CFD) n sch a CADembedded contet s obvosly very attractve, as t can not only accelerate the desgn process, bt make these processes more predctable and relable, aganst a backgrond of ncreasng desgn complety and dependence on eternal development partners. It s essental to note that all major CAD systems were created some tme ago and were optmzed as a desgn tools. Only later was the necessty of embedded CAE (and n partclar CFD) recognzed. Moreover, CAE and CFD tools already have a long hstory drng whch they have been optmzed for ther respectve tasks. Therefore t was logcal that for some perod CFD contned as an ndependent development, and nteracton wth CAD was lmted by smple data echange. Nevertheless from the standpont of sng CFD drng desgn, and as a reqrement of all PLM roadmaps the need to flly embed CFD wthn CAD becomes more and more pressng. At the end of the 1990s the frst flly-embedded CFD prodct, FloWorks, was developed as an add-n for SoldWorks. Later ths prodct became the startng pont for the Mentor Graphcs FloEFD ste of prodcts for dfferent CAD systems based on an Engneerng Fld Dynamcs (EFD) approach. The solver and mesher s sed not only for FloEFD, bt has been re-packaged as an enablng technology for a new stand-alone prodct, FloTHERM XT, dedcated to electroncs coolng applcatons. The EFD approach s based on man prncples: Drect se of natve CAD as the sorce of geometry nformaton; Combnaton of fll 3D CFD modellng wth smpler engneerng methods n the cases where the mesh resolton s nsffcent for fll 3D smlaton. Snce the EFD technology has to operate wthn dfferent CAD systems t was developed as a nversal CAD/CFD platform that ncorporates a nmber of technologes: CAD data management; Mesh generaton; Several CFD solvers; Engneerng Modellng Technologes; and Reslts processng

4 NUMERICAL BASIS OF CAD-EMBEDDED CFD The CAD/CFD platform forms the brdge between CAD system and CADembedded CFD prodcts, lke FloEFD, or alternatvely provdes an API for vertcally-specalzed CFD prodcts lke FloTHERM XT to make se of all the relevant fnctons of a sold modellng engne (see Fg. 1): CAD 1 CAD CAD 3 CAD 4 Unversal CAD/CFD EFD Technology Platform FloEFD nversal CFD prodcts FloTHERM XT Fgre 1: Unversal EFD Platform Technology as a brdge between CAD and CFD. : EFD BOUNDARY TREATMENT CAD descrbes the sold model, whereas CFD s prmarly concerned wth the flow space (the solton doman mns the sold model). Hstorcally, for tradtonal CFD codes, the fld space s created by Boolean sbtracton of the sold model wthn the CAD system, and ths nverse sold passed to the CFD tool for meshng. Mesh generators n tradtonal CFD are sally based on body-ftted algorthms. The detaled revews of basc types of mesh geometres are presented n several pblcatons (e.g. Weatherll & Hassan, 1994, Flpak, 1996 and Parry & Tatchell, 008). In these works t s shown that body-ftted meshes have been wdely sed for solvng ndstral problems. As a rle, for complcated geometres nstrctred meshes are sed, formed by constrctng rreglarly dstrbted nodes (see Fg. a). Where the geometres beng meshed are less comple t s often possble to se strctred meshes (see Fg. b), and these two meshng strateges can be combned, wth strctred meshes n some sb-regons, e.g. close to walls, and nstrctred meshes everywhere else (see Fg. c). Sch meshes may be called partally strctred or partally nstrctred. CAD systems were orgnally developed solely wth desgn n mnd, and not nmercal smlaton. A characterstc of body-ftted meshes s that they are hghly senstvty to the qalty (for smlaton prposes, not necessarly for desgn) of the CAD geometry. Usally sch meshes are generated begnnng from nodes generaton at sold srface. Then the srface s meshed by means of Delanay tranglaton. After that, based on the srface tranglaton, the space mesh s generated. Often t s a mesh wth tetrahedral elements that meet

5 Delanay crteron (e.g. Delanay, 1934, Lawson, 1977, Watson 1981, Baker, 1989 and Weatherll & Hassan, 1994). In many cases, defects n the srface representaton reqre ser nterventon to resolve the ambgtes to heal the defects n the CAD geometry. In addton, n some statons over-refnement of the srface can reslt n an ecessve nmber of small trangles. Ths can happen n areas that are not sgnfcant n terms of flow smlaton as the meshng algorthm responds to geometry featres (small rad, small spkes, materal jonts etc.) reqrng the ser to take remedal acton. (a) (b) (c) (d) Fgre : Unstrctred body ftted mesh (a), strctred body-fnned mesh (b), combnaton of strctred Cartesan mesh and non-strctred body-ftted mesh near the wall (c) and strctred Cartesan mmersed-body mesh (d) The alternatve approach s to se an mmersed-body mesh as t shown n Fg. d. In ths approach the creaton of the mesh starts ndependently from geometry tself and the cells can arbtrarly ntersect the bondary between sold and fld. Ths makes t possble to se a Cartesan-based mesh, whch n the general case cannot be body-ftted. Sch a mesh can be defned as a set of cbods (rectanglar cells), whch are adjacent to each other and to the eternal bondary of the comptatonal doman, orentated along the Cartesan coordnates. Cbods ntersected by the srface ( ct-cells ) are treated n a specal way, descrbed later, accordng to the bondary condtons defned on the srface. It s necessary to pont ot that the mmersed body mesh approach

6 NUMERICAL BASIS OF CAD-EMBEDDED CFD can be mplemented for tetrahedral and other types of the elements (see Löhner et al., 004), bt n terms of appromaton accracy and ease of mplementaton, Cartesan meshes are strongly preferred. Advantages of Cartesan meshes can be smmarzed as follows: Smplcty, speed and robstness of the mesh generaton algorthm especally when dealng wth natve CAD data; Mnmzaton of Local Trncaton Errors (Mentor Graphcs, 011a); and Robstness of the dfferental scheme. The EFD technology s based pon the se of Cartesan-based meshes and Meshng Technology s one of the key elements of the CAD/CFD brdge for CAD-embedded CFD. As a reslt of sng Cartesan-based meshes we have cells whch are located flly n sold bodes (sold cells), n the fld (fld cells) and cells ntersected the mmersed bondary (whch we term partal cells ). In the smplest case the partal cell conssts from control volmes (CV): a fld CV and a sold CV (see Fg 3). Fgre 3: Partal cell n the smplest case and wth control volmes (CV) nsde. Each CV s then flly sold or flly fld. For each CV all necessary geometrcal parameters sch as volme and the coordnates of cell centre are calclated. The areas and normal vector drecton are calclated for the faces that bonds the CV. All these data are taken drectly from the natve CAD model. Moreover, the drect se of the natve CAD model allows all aspects of the geometry wthn the partal cell to be specfed (e.g. sold edges) see Fg. 4. Here the CAD/CFD brdge technology takes nto accont the ponts C 1 C on the sold edge n order to descrbe n mesh representaton the facets: A 1 - C 1 -C -A and B 1- C 1 -C -B whch correspond eactly to the facets n the CAD model.

7 Fgre 4: Representaton of CAD geometry (left) n the partal cell (rght) n case of facets and sold edge nsde one cell. Sch technology allows good resolton of geometry featres even n case of relatvely coarse meshes (see Fg. 5). Fgre 5: Mesh representaton of CAD geometry wth resolton of sold edges wthn partal cells. Wthn one sngle cell t s possble to have an arbtrary nmber of CVs: 3 n case of one thn wall or more, as shown n Fg. 6. Fld 1 Fld 1 Fld Fld Fgre 6: Partal cell wth 3 control volmes (fld-sold-fld) n case of thn sold wall and partal cell wth 7 control volmes n case of thn sold wall havng nsde 5 layers wth dfferent materal propertes.

8 NUMERICAL BASIS OF CAD-EMBEDDED CFD Mltple layers of CVs are essental not only for fld flow modellng bt for heat transfer phenomena, ncldng the contact resstances and Jole heatng calclatons wthn a sold body (a flly-copled mltphyscs applcaton). The sold and fld CVs can be alternated many tmes wthn each cell as presented n Fg. 7. Fgre 7: Mltple control volmes (sold-fld-sold-fld-.. etc.) for partal cells. Mesh generaton s started by dvdng the rectanglar comptatonal doman nto a set of rectanglar cells (cbods) formed by ntersecton of planes parallel to the aes of coordnate system. The mesh can be refned (by splttng each cbod nto 8 geometrcally-smlar cbods) sng varos adaptaton crtera that can be defned for each sold body (crvatre, narrow channels, small featres, etc.) and atomatcally accordng to gradents n the solton. Fgre 8: EFD mesh after refnement.

9 De to refnement, cells havng dfferent refnement level are formed, t s essental to note that the dfference n refnement level for neghborng cells n the EFD technology s not more then 1, as shown n Fg. 8. These refnement procedres are essental to resolve featres of the CAD geometry lke srfaces wth small crvatre, small featres, narrow channels, etc. Moreover, the se of sch mesh generaton technology allows the mplementaton of effcent and robst atomatc tools for meshng. The npt data reqred can be only the sze of the geometrc object (whch can be taken from CAD atomatcally), the sze of the smallest featre to be resolved and some general nformaton abot the task (nternal or eternal flow, choce of physcal models to be sed, etc.). It s also possble to actvate addtonal refnement of the mesh drng the calclaton, wth the goal of better adaptaton of the mesh to snglartes n the solton lke shock waves. 3: PHYSICAL MODELS In general the Cartesan mesh approach sed n FloEFD allows to be performed conjgate mltphyscs calclatons, sng one comptaton mesh havng fld cells, sold cells and (mlt-cv) partal cells: Fld flow analyss for fld regons; Heat transfer and drect electrcal crrent calclaton n sold regons. Fld flow analyss and thermal condcton can also be treated separately. In addton, all these calclatons can be copled wth dfferent radaton models. For all these physcal phenomena the natve CAD geometry remans the sorce of ntal geometrc nformaton. 1. Fld regons In fld regons FloEFD solves the Naver-Stokes eqatons, whch are formlatons of mass, momentm and energy conservaton laws: ρ ( ρ ) = 0 t ( ρ ) P ( ρ j ) t j ρ H ρ H = j t H = h = R ( ( τ τ ) q ) j j j ( τ τ ) S j R j p R τ j t j ρε S Q H (1) () (3)

10 NUMERICAL BASIS OF CAD-EMBEDDED CFD For calclaton of hgh speed compressble flows and flows wth shock waves the followng energy eqaton s sed: ( ) ) ( e E Q S q = p E t E H j R j R j j j = ρε τ τ τ ρ ρ ρ (4) These eqatons are spplemented by fld state eqatons defnng the natre of the fld, and by emprcal dependences of fld densty, vscosty and thermal condctvty on temperatre. Inelastc non-newtonan flds are consdered by ntrodcng a dependency whereby ther dynamc vscosty s dependent on flow shear rate and temperatre. Specal models are sed for the descrpton of real gases, volme condensaton and vaporzaton, cavtaton, combston as well as for poros meda. FloEFD s able to consder both lamnar and trblent flows. Lamnar flows occr at low vales of the Reynolds nmber, whch s defned as the prodct of representatve scales of velocty and length dvded by the knematc vscosty. When the Reynolds nmber eceeds a certan crtcal vale the flow transtons smoothly to trblent. To predct trblent flows, the Favre-averaged Naver- Stokes eqatons are sed, where tme-averaged effects of the flow trblence on the flow parameters are consdered, whereas the large-scale, tme-dependent phenomena are taken nto accont drectly. Throgh ths procedre, etra terms known as the Reynolds stresses appear n the eqatons for whch addtonal nformaton mst be provded. To close ths system of eqatons, FloEFD employs transport eqatons for the trblent knetc energy and ts dsspaton rate, sng the k-ε model. The modfed k-ε trblence model wth dampng fnctons proposed by Lam and Bremhorst (1981) descrbes lamnar, trblent, and transtonal flows of homogeneos flds consstng of the followng trblence conservaton laws: B t j R j k t P k = k t k ρε τ σ ρ ρ, (5) k C f P C f k C = t B t B j R j t 1 1 ρε τ ε ε σ ρε ρε ε ε ε (6) j s j τ =, j j t R j k s δ ρ τ 3 =, k k j j j j s = δ 3, (7)

11 P B g = σ B 1 ρ, (8) ρ where C = 0. 09, C = 1. ε1 44, C = 1. ε 9, σ k = 1, σ ε = 1. 3, σ B =0.9, C B = 1 f P B > 0, C B = 0 f P B < 0, the trblent vscosty s determned from: C ρk t = f ε, (9) Lam and Bremhorst s dampng fncton f s determned from: f 0.05R 0. 5 ( ) y 1 e 1 Rt = Where:, (10) ρ k y R y =, (11) ρk R t = ε, (1) y s the dstance from pont to the wall and Lam and Bremhorst s dampng fnctons f 1 and f are determned from: 0.05 f 1 = 1, f 3 f 1 e R t =. (13) Lam and Bremhost s dampng fnctons f, f 1, f decrease trblent vscosty and trblence energy and ncrease the trblence dsspaton rate when the Reynolds nmber R y based on the average velocty of flctatons and dstance from the wall becomes too small. When f = 1, f 1 = 1, f = 1 the approach reverts back to the orgnal k-ε model. The heat fl s defned by: q t h =, = 1,,3 Pr σ c (14) Here the constant σ c =0.9, Pr the Prandtl Nmber, and h s the thermal enthalpy. A partclar comptatonal task s fnally specfed by the defnton of ts geometry, bondary and ntal condtons. All data for sch condtons are defned drectly on the natve CAD model.

12 NUMERICAL BASIS OF CAD-EMBEDDED CFD. Sold regons FloEFD calclates two knds of physcal phenomena wthn sold regons: heat condcton and drect electrcal crrent, wth the resltng Jole heatng beng a sorce of heat n the energy eqaton. Heat transfer n solds and flds wth energy echange between them (conjgate heat transfer) s an essental and mplct element of CADembedded CFD software. Heat transfer n flds s descrbed by the energy eqaton (3-4) where the heat fl s defned by (14). The phenomenon of heat condcton n sold meda s descrbed by the followng eqaton: ρe t = T λ Q H (15) where e s the specfc nternal energy, e = c T, c s specfc heat, Q H s specfc heat release (or absorpton) rate per nt volme, and λ are the egenvales of the thermal condctvty tensor. It s spposed that the heat condctvty tensor s dagonal n the consdered coordnate system. For an sotropc medm λ 1 = λ = λ 3 = λ. In presence of electrc crrent, Q H may nclde the specfc Jole heat release Q J. It s defned as Q J = r j, where r s the electrcal resstvty and j s the electrc crrent densty. The electrc crrent densty vector: 1 ϕ 1 ϕ 1 ϕ =,, (16) r11 1 r r33 3 s determned va the electrc potental ϕ[v] from the steady-state Laplace eqaton: 1 r ϕ = 0 (17) Here r s the temperatre-dependent electrcal resstvty n the -th coordnate drecton. The Laplace eqaton s solved nmercally n sb-domans that contan electrcally condctve materals. Delectrc solds and fld areas nsde sch sb-domans are atomatcally eclded. The total electrc crrent over a srface I[A] or electrc potental φ[v] may be specfed by the ser as a bondary condton for the problem.

13 A srface between two electrcally-condctve solds n the sb-doman s ether consdered zero-resstance (the defalt) or the ser can specfy an electrcal contact resstance on t. The resstance vale s ether gven eplctly or calclated drectly from the gven materal and ts thckness. A contact resstance specfed on a srface mples that the crrent passng throgh t prodces the correspondng Jole heatng, whch gves rse to a srface heat sorce, as follows. If a sold conssts of several sold materals attached to each other, then the thermal contact resstances between them are taken nto accont when calclatng the heat condcton. As a reslt, a sold temperatre step appears on the contact srfaces. A very thn layer of another materal between solds or on a sold n contact wth fld can be taken nto accont when calclatng the heat condcton n solds n the same manner (.e. as a thermal contact resstance), bt s specfed va the materal s thermal condctvty and the layer thckness. The energy echange between the fld and sold meda s calclated va the heat fl n the drecton normal to the sold/fld nterface takng nto accont the sold srface temperatre and the fld bondary layer characterstcs, and radaton heat echange f necessary. 3. Radaton between sold srfaces and n transparent solds Radaton s a comple phenomena and therefore there are a lot of smplfed models of radaton. All of them have advantages, dsadvantages and lmtatons. FloEFD ncldes models: 1) Ray Tracng, also known as DTRM (Dscrete Transfer Radaton Model). ) Dscrete Ordnates (or DO). For the Ray Tracng model the heat radaton from sold srfaces, both the emtted and reflected, s assmed dffse (ecept for symmetry and mrror radatve srface types),.e. they obey Lambert s law, accordng to whch the radaton ntensty per nt area and per nt sold angle s the same n all drectons. Solar radaton s absorbed and reflected by srfaces ndependently from thermal radaton. Thermal radaton passes throgh a sold specfed as radaton transparent wthot any absorpton. A sold can be specfed as transparent to the solar radaton only, or transparent to the thermal radaton from all sorces ecept the solar radaton, or transparent to both types of radaton: thermal and solar. Refracton can also be taken nto accont for ths opton. Flds nether emt nor absorb thermal radaton (.e. they are transparent to the thermal radaton), so the thermal radaton affects sold srfaces only. Radatve sold srfaces not specfed as a blackbody or whte body are assmed to be an deal gray body,.e. havng a contnos emssve power spectrm smlar to that of a blackbody, so ther monochromatc

14 NUMERICAL BASIS OF CAD-EMBEDDED CFD emssvty s ndependent of the emsson wavelength. For certan materals wth certan srface condtons, the gray body emssvty can depend on the srface temperatre. Spectrm dependency sn t taken nto accont n the Ray Tracng model. The Dscrete Ordnates model s more complcated. Here the whole 4π drectonal doman at any locaton wthn the comptatonal doman s dscretzed nto the specfed nmber of eqal sold angles. Radaton governng eqaton can be wrtten as follows: di ( s, r ) σ s = κ σ I s r n I r Φ s s I s s, κ b,, r d ds 4π ( ) ( ) ( ) ( ) ( ) Ω Ω = 4π (18) Radaton absorptve (sem-transparent) solds absorb and emt thermal radaton n accordance wth the specfed sold materal s absorpton coeffcent. Scatterng s not consdered. Srfaces of opaqe solds absorb the ncdent thermal radaton n accordance wth ther specfed emssvty coeffcents, the rest of the ncdent radaton s reflected speclarly or dffsvely, or both speclarly and dffsvely, n accordance wth the specfed speclarty coeffcent. Radaton s refracted n accordance wth the specfed refracton ndces of the sold and adjacent medm (another radaton absorptve sold, or a transparent sold or fld, the refracton nde of whch s always consdered as eqal to 1). The radaton spectrm s consdered as consstng of several bands, the edges of whch are specfed by the ser. Propertes of radaton sorces, srfaces and materals are consdered constant wthn each band. As the reslt of radaton calclatons the approprate heat fles are takng nto accont n partal cells for mmersed fld-sold bondares or n sold cells nsde the sem-transparent sold bodes. 4: BOUNDARY LAYER TREATMENT Non body-ftted Cartesan meshes appear optmal for managng the natve CAD data, and so form the bass for the CAD/CFD brdge. The man sse for Cartesan mmersed-body meshes s the resolton of bondary layers on coarse meshes. For ths the EFD technology ncorporates an orgnal approach descrbed below, and the combnaton of ths approach wth the EFD Cartesan mesh technology forms a major part of EFD CAD/CFD brdge. Consderaton of the near-wall cells shows that for arbtrary natve CAD geometry the mesh between the sold/fld bondary can be too coarse for the accrate solton of Naver-Stokes eqatons wthn the hgh-gradent

15 bondary layer. Therefore, n order to calclate skn frcton and heat fl at the wall, the Prandtl approach for bondary layers s sed. The key dea of ths approach has some smlarty wth the wall fncton approach tradtonally sed n CFD. The wall treatment that forms part of the EFD platform technology ses a novel and orgnal Two-Scale Wall Fncton (SWF) approach (Mentor Graphcs, 011b) that conssts of two methods for coplng the bondary layer calclaton wth the solton of the blk flow: 1) A thn bondary layer treatment that s sed when the nmber of cells across the bondary layer s not enogh for drect, or even smplfed, determnaton of the flow and thermal profles; and ) A thck bondary layer approach when the nmber of cells across the bondary layer eceeds that reqred to accrately resolve the bondary layer. 3) In ntermedate cases, a complaton of the two above approaches s sed, ensrng a smooth transton between the two models as the mesh s refned, or as the bondary layer thckens along a srface. thn bondary layer thck bondary layer ntermedate bondary layer Fgre 9: Mach Nmber flow feld wth thn, ntermedate and thck vscos bondary layer. Verfcatons of the EFD technology bondary layer treatment were done by Balakne et al. (004). These treatments are dscssed below. 1. The Thn-Bondary-Layer approach In the thn-bondary-layer approach the Prandtl bondary layer eqatons already ntegrated along the normal to the wall (.e. along the normal to body srface ordnate) from 0 (at the wall) to the bondary layer thckness δ are solved along fld streamlnes coverng the walls. If the bondary layer s

16 NUMERICAL BASIS OF CAD-EMBEDDED CFD lamnar, these eqatons are solved wth a method of sccessve appromatons based on the Shvetz tral fnctons technology (Gnzbrg, 1970). If the bondary layer s trblent or transtonal, a generalzaton of ths method employng the Van Drest hypothess abot the mng length n trblent bondary layers s sed (Van Drest, 1956). The nflence of roghness, consdered as the eqvalent sand gran roghness, and the eternal flow s trblence on the bondary layer are modeled throgh sem-emprcal coeffcents correctng the wall shear stress and the heat fl from the fld to the wall. Fld compressblty, trblence knetc energy dsspaton, and varos body forces are also taken nto accont throgh correspondng emprcal and sem-emprcal models. From the bondary layer calclaton FloEFD obtans the bondary layer thckness δ, the wall shear stressτ e w, and the heat fl from the fld to the e wall q w, whch are sed as bondary condtons for the Naver-Stokes eqatons: e τ w = τ w, e q w = q w, (19) Bondary condtons for k and ε are determned from the condton of trblence eqlbrm n the near-wall comptatonal mesh cell: k y = 0, C k ε =. (0) κy. The Thck-Bondary-Layer approach When the nmber of cells across the bondary layer s sffcent (more than ~10) the smlaton of lamnar bondary layers s done va Naver-Stokes eqatons as part of the core flow calclaton. For trblent bondary layers a modfcaton of the well-known wall fncton approach s sed. However, nstead of the classcal approach where the logarthmc velocty profle s sed, the EFD technology ses the fll profle proposed by Van Drest (1956): = y 0 1 dη 1 4 κ η 1 ep η A v (1) where κ = s the Karman constant, A v = 6 s the Van Drest coeffcent. All other assmptons are smlar ones to the classcal wall fncton approach.

17 5: NUMERICAL METHODS AND COMPUTATIONAL EXAMPLES The fld regon represents the man comptatonal challenge from the pont of vew of algorthmc complety and of calclaton overhead. Usng arbtrary CAD as a sorce of geometrc nformaton, t s essental to pay specfc attenton to the robstness and effcency of the nmercal methods sed. FloEFD ses 3 dfferent types of solver and related nmercal algorthms for modelng fld flows. The frst solver s optmal for ncompressble flows and flows wth Mach Nmbers less than 3.0. Tme-mplct appromatons of the contnty and convecton/dffson eqatons (for momentm, temperatre, etc.) are sed together wth an operator-splttng technqe (see Glownsk and Tallec, 1989, Marchk,198, Samarsk, 1989, Patankar, 1980). Ths technqe s sed to effcently resolve the problem of pressre-velocty decoplng. Followng a SIMPLE-lke approach (Patankar, 1980), an ellptc type dscrete pressre eqaton s derved by algebrac transformatons of the orgnallyderved dscrete eqatons for mass and momentm, takng nto accont the bondary condtons for velocty. To solve the asymmetrc systems of lnear eqatons that arse from appromatons of momentm, temperatre and speces eqatons, a precondtoned generalzed conjgate gradent method from Saad (1996) s sed. Incomplete LU factorzaton s sed for precondtonng. To solve the symmetrc algebrac problem for pressre-correcton, an orgnal doble-precondtoned teratve procedre s sed. It s based on a specallydeveloped mltgrd method from Hackbsch (1985). The eample below s based on the se of ths frst type of solver. Ths s an eternal flow arond a F-16 fghter (Mach Nmber eqals 0.6 and 0.85). The geometry s a natve CAD model of the arplane wth eternal tanks and armaments. Flow nto the ntake and ehast from the engne s nozzle are both takng nto accont. Calclatons were performed wth appromately 00,000 cells, showng the effcency of EFD technology. Calclaton reslts are compared wth the test data from Ngyen, Lat T. et al. (1979).

18 NUMERICAL BASIS OF CAD-EMBEDDED CFD Fgre 10: Fghter Arplane F-16 calclaton. Ths solver s etended by the broad set of physcal models avalable for FloEFD lke gravtaton, radaton, real propertes of varos fld meda, combston, phase transfer, etc. Presented below are some eamples that llstrate some of these capabltes. The frst eample shows the modelng of the combston processes n vorte combstor shown n Fg 11. BERL Combstor BERL Combstor Aal Velocty [m/s] Temperatre of Fld [K] X= X= Poston [m] Fg. 11: Vorte combstor (natral gas/ar) Poston [m] Here calclaton eamples are compared wth epermental data from Sayre et al. (1994). Ths eample also shows the effcency of the technology for cases havng geometry wth dfferng characterstc dmensons.

19 Use of the EFD technology platform as a CAD/CFD brdge brngs addtonal benefts for the resolton of specfc flows n dedcated elements of comple models where the nmber of cells s not enogh for fll 3D modelng. Havng drect access to the natve CAD data, the EFD technology platform can recognze that some geometry can form flow passages akn to ppes or thn channels, becase ths nformaton ests n the CAD system. In sch cases, analytcal or emprcal data s sed to replace the 3D Naver Stokes eqaton modelng wthn sch flow passages. In Fg. 1 sch an approach s presented for the flow wthn a pn fn heatsnk. t=0 Heat sorce 10 W Fgre 1: FloEFD calclaton sng Thn channel technology. Here the abovementoned thn channel technology s sed, where the nmber of cells across the channel was 1-. FloEFD calclaton reslts for a very coarse mesh (3,900 cells n a total) and a relatvely fne mesh (180,000 cells n a total) wth comparson aganst epermental data from Jonsson and Palm, (1998) are presented n Table 1. Table 1. FloEFD calclaton reslts sng Thn channel approach (3,900 cells), fll 3D approach (180,00) cells and ts dfference wth eperment. Calclaton of an ar condtonng devce contanng Freon R as the workng fld shows the benefts of the same approach for a far more complcated model (see Fg 13).

20 NUMERICAL BASIS OF CAD-EMBEDDED CFD Freon R, m=5.4 g/s; t=5 C Ar, V=.5 m/s; t=30 C Ar at otlet t=18 C Freon R at otlet t=7 C, gas Fgre 13: Ar condton operaton smlaton In ths case, heat echange n the sold and phase echange processes n the Freon are both taken nto accont. The second solver s optmal for Hgh Mach nmber tasks wth shock waves and other related phenomena. Ths eplct nmercal solver (see Gavrlok et al., 1993) s based on modfcaton of Godnov method (see Samarsc, 1989). Ths solver s also sed n FloEFD for modelng of hypersonc flows of ar wth Mach Nmber p to 30, by takng nto accont the phenomena of ar onzaton and dssocaton. In Fg. 14, the calclaton eample presented shows the flow arond a blnt-nosed cylnder and comparson of calclaton reslts wth the epermental data of Gatonde and Shang, M =16.34; T =5 K; P =8.95 Pa Tw=94 K Eperment EFD 9. qw, 10 5 W/m Fgre 14: Hypersonc flow arond blnt - nose cylnder angle, deg. The thrd recently-proposed solver n FloEFD s sed for the calclaton of flows n lqds wth cavtaton, sng a nmercal approach that s essentally

21 new for CFD (see Aleandkova et al., 011). The phenomena of cavtaton presents a lot of nmercal dffcltes concerned wth varatons of densty, speed of sond and tme scale. The speed of sond may drop from thosands of meters per second n lqd flow to order ten or less n vaporzed flow. Ths can lead to spersonc flows wth hgh Mach nmbers, sometmes wth shocks., Cavtaton problems are thereby characterzed by wde range of Mach nmber from near zero to several tens wthn a sngle calclaton doman. Therefore, when constrctng a nmercal method to smlate cavtatng flows, t s mportant to take nto accont the fact that regons of ncompressble flow and hghly compressble flow coest n the calclaton doman. To date there are two man approaches to calclatng sch all-speed compressble flows. The frst one employs the densty-based methods orgnally developed to smlate speed compressble flows. These methods are adapted for low Mach nmber cases by ntrodcng artfcal compressblty or sng some precondtonng technqes (Knz et al., 000, Lee et al., 006, 007). The second approach tlzes the pressre-based methods orgnally developed for ncompressble flows. Usally these are the SIMPLE-famly of dfferencng schemes (or pressre-correcton methods) and adapted for the cases nvolvng compressble flows at hgh speed (van der Hel et al., 000). FloEFD s approach dffers from both of the above. At frst glance the dea to apply the pressre-based n regons of ncompressble flow and the denstybased approach n regons of spersonc compressble flow looks qte natral. Bt t s not obvos how to cople these approaches. We propose a way of combnng the approaches that s based on the followng smple key dea. Employng the fnte-volme method, we sggest mng the fles and pressre appromatons that correspond to pressre-based and denstybased approaches on the faces of control volmes. After that, these med appromatons are sbsttted n a SIMPLE-type dfferencng scheme. Managng the mng weght between the fles and pressre appromaton, we can obtan ether the orgnal SIMPLE-type sem-mplct splttng scheme or the eplct densty-based scheme or a mtre of these approaches H, m 36 Test data 34 calclaton reslts wth EFD NPSH, m Fgre 15. Calclaton of cavtaton n centrfgal pmp.

22 NUMERICAL BASIS OF CAD-EMBEDDED CFD Fgre 15 shows an eample of flow n a centrfgal pmp, wth cavtaton captred sng ths hybrd solver. The FloEFD calclaton reslts are compared wth epermental data by Hofman et al. (001). 6: CONCLUSIONS Trends n the worldwde CAE market clearly shows steady growth n the market share of CFD calclatons n the solton of p-to-date desgn problems. Wthn ths market, FloEFD s an nnovatve eample of the adaptaton of p-to-date CAE technology (namely fld dynamcs and heat transfer) for the everyday needs of desgn engneers. EFD (Engneerng Fld Dynamcs) Technology has been developed as a nversal CAD/CFD platform, whch conssts the followng technologes: managng wth CAD data, Cartesan-based mesh generator, a set of CFD solvers, Engneerng Modellng Technologes, and reslt processng. Sch platform becomes a complete brdge between CAD and CFD. EFD Technology s based on the followng key prncples: Cartesan-based meshng technology, drectly dealng wth arbtrary comple natve CAD geometry; Bondary Layer treatment technology that allows fld flow calclatons to performed on relatvely coarse Cartesan-based meshes. Ths technology s based on a flly scalable wall fncton approach to defne skn frcton and heat flows at sold walls; and Engneerng Models, employed when the comptatonal mesh s not fne enogh for fll 3D modellng. The paper presents calclaton eamples sng all 3 types of CFD solvers sed n FloEFD: an mplct solver for ncompressble and low compressble flows; an eplct solver for hgh Mach Nmber and hypersonc flows; and hybrd solver for lqd flows wth cavtaton, ths demonstratng both the hgh smlaton effcency and the hgh accracy of the EFD technology. Ths combnaton of good performance for relatvely coarse meshes, CADembedded capablty, and a hgh level of atomaton and sablty regardng the model set p, meshng and solton make FloEFD an effectve CFD tool for analyss n spport of engneerng desgn.

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