THE OVERLAPPING GRID TECHNIQUE FOR THE TIME ACCURATE SIMULATION OF ROTORCRAFT FLOWS. Thorsten Schwarz

Transcription

1 THE OVERLAPPING GRID TECHNIQUE FOR THE TIME ACCURATE SIMULATION OF ROTORCRAFT FLOWS Thosten Schwaz Geman Aeospace Cente (DLR) in the Helmholtz-Association Institute fo Aeodynamics and Flow Technology Lilienthalplatz 7, D Baunschweig, Gemany Abstact This pape pesents the implementation of the ovelapping gid technique into DLR s stuctued flow solve FLOWe. The hole cutting pocedue and the seach methods ae descibed. Tilinea intepolation is used to tansfe flow data between gids. Fo data intepolation close to solid sufaces, a pojection algoithm is applied which coects discetization effects. The appoach used to pescibe igid body motions fo unsteady flow simulations allows to elate the motion of any body to any othe body. Unsteady simulations also equie to conside the hole motion duing the definition of the intepolation points. Fo the integation of foces on gids with mesh ovelap on body sufaces a unique suface is geneated. Backgound gids ae ceated with a Catesian gid geneato, which allows fo cubic and anisotopic cells. Seveal examples of applications demonstate the geneality of the implementation of the Chimea technique. Intoduction The numeical solution of the Navie-Stokes equations fo helicopte type applications is a demanding task: Fist of all, the flow solve must be able to account fo the moving pats of the helicopte, e.g. the main and tail otos, see Figue 1. The second difficulty is to ceate the computational gids, paticulaly if block stuctued solves ae used and the configuation has a complex shape. Finally, the long un time of unsteady flow simulations equies efficient solution algoithms in ode to minimize the execution time. Nomenclatue Δa, Δb, Δc d 1, d IBLANK x 1 Kx 4 x spacings of cuboidal cell ange of weighting function Chimea tag aay vetex coodinates of tetahedon coodinates of intepolation point P x P* coodinates of vitual intepolation point w weighting function W vecto of consevative vaiables Δ W change of consevative vaiables pe time step Δx, Δy, Δz spacings of Catesian cell γ, γ γ intepolation coefficients 1, 3 α, β auxiliay vaiables ε pojection vecto ϕ,θ spheical coodinates Figue 1: BO 105 Helicopte One appoach to educe the effot fo a flow simulation is to use the so called Chimea o ovelapping gid appoach (ef. [1]). This method allows to geneate the computational meshes fo the otos and the fuselage independently. In a subsequent step, the gids ae embedded into each othe with an abitay ovelap, see the D example in Figue. Gids associated with moving bodies move with the bodies without stetching o distoting the gids. If some gid points of one mesh fall within a solid body, these points ae blanked and excluded fom the flow computation. The blanked egions of the gid ae often called hole. The communication among the gids is usually established by intepolation techniques. 86.1

2 computed eithe with a cental scheme o with vaious upwind schemes. Tubulence is modeled by seveal 0-, 1-, - o 7-equation models, e.g. Spalat- Almaas, kω, kω-sst, EARSM o RSM. Fo steady flow simulations the time integation of the main equations is advanced with a five stage Runge-Kutta method with multigid acceleation. Fo the tubulence equations, an implicit DDADI method is used. Unsteady flow simulations ae pefomed with the implicit dual time stepping fomulation. Fo high pefomance computing, FLOWe is paallelized based on MPI and is optimized fo vecto computes. Figue : Ovelapping gid system The ovelapping gid technique also allows to simplify the gid geneation fo complex geometies. This is achieved by beaking down the geomety into simple shaped components, fo which individual gids can easily be ceated. The Chimea technique has now been used fo otocaft applications fo some time. It has been implemented in many flow solves used in industy, fo example Begga (ef. [17]), OVERFLOW (ef. [5]), CFD-Fastan (ef. [1]), elsa (ef. [8]) and FLOWe (ef. [11]). Best pactice expeiences have been summaized in ef. [6]. In the following, the Chimea capabilities of the block stuctued flow solve FLOWe will be descibed in detail. FLOWe is developed by the Geman eseach cente DLR with contibutions fom univesities and aeospace industy. The extension of FLOWe fo helicoptes like configuation has been suppoted duing the last six yeas by the Fench-Geman coopeative poject Complete Helicopte AdvaNced Computational Envionment (CHANCE) (ef. [16]). In this context, the implementation of the Chimea technique in FLOWe was widely extended. Stating with a basic Chimeascheme six yeas ago, FLOWe has now many capabilities to handle moving gids and to simplify gid geneation. The method has been veified and validated fo a wide ange of applications and much expeience in its use has been gained. Flow solve The flow solve FLOWe (ef. [11]) solves the Reynolds aveaged Navie-Stokes equations with a second ode accuate finite volume discetization on stuctued, multi-block gids. The fluxes can be Hole cutting Chimea technique The fist step in a Chimea calculation is the blanking of gid points, which ae inside solid bodies. Fo this pupose, the use geneates one o moe auxiliay gids, which totally include the solid body, see Figue 3. Now all cell midpoints of the computational gids ovelaying the solid body ae checked, if they ae inside the auxiliay mesh. Any cell being inside the auxiliay gid is flagged and is excluded fom the flow computation. Figue 3: Auxiliay gid (thick lines) with two cells fo hole cutting No gid hieachy is used to blank cells. Instead, any auxiliay gid can cut holes in any gid which does not contain the solid body enclosed by the auxiliay gid. Although the pesented hole cutting method is non automatic, the effot fo the use is usually small, since the auxiliay gids can be coase and they do not have to fulfill any quality equiements. The advantage of the chosen appoach is its vey simple implementation and its high execution speed. Futhemoe it allows the use to contol the exact geomety of the hole. An example of a set of 86.

3 auxiliay gids fo a complex configuation is shown in Figue 4. Figue 4: Set of seven auxiliay gids enclosing a helicopte fuselage Seach and intepolation Communication between the ovelapping gids is established by intepolating data fom ovelapping gids. In ode to set up the intepolation, at fist the intepolation cells have to be identified. This is accomplished by checking fo each cell, if the spatial discetization opeato accesses cells inside holes o non existent cells at the oute gid bounday. In FLOWe two layes of intepolation cells ae equied at oute gid boundaies and at the hole finge, see Figue 5. Figue 5: Intepolation points Now a Chimea tag aay IBLANK is set up, which indicates the status of a cell. It is: IBLANK = 0 IBLANK = 1 : hole cell o intepolated cell (excluded fom flow computation) : valid cell Following the definition of the Chimea tag aay, a seach is stated to find appopiate dono cells fo the intepolation cells. Since the flow vaiables ae given at the centes of the cells, the seach must be pefomed fo the dual meshes that connect the coodinates of the cell centes. In FLOWe the seach on geneal type meshes is pefomed with an Altenating Digital Tee method (ADT) (ef. []). The ADT method uses a tee like data stuctue to stoe the boxes given by the minimum and maximum coodinates of the dual gid cells. Duing the seach pocess, all boxes enclosing the intepolation point ae identified with log (N) opeations, whee N is the total numbe of gid points. In a subsequent step, each cell associated with a etieved box is checked if it includes the intepolation point. To this end, the cell is subdivided into six tetaheda and the linea system of equations γ 1 = x 1 x ( x x ) + γ ( x x ) + γ ( P x 4 x is solved fo the unknown coefficients γ 1, γ, γ 3, whee x 1 Kx4 ae the vetex coodinates of the tetahedon and x P denotes the coodinates of the intepolation point. If the conditions γ 1, γ, γ 3 0, γ 1 + γ + γ 3 1 ae tue, then the intepolation point is inside the tetahedon. Additionally it is tested, if the cells at the vetices of the tetahedon ae not blanked (IBLANK=1). If all checks ae successful, the cell is a valid dono cell and the flow values at the vetices of the tetahedon ae used fo the tilinea intepolation of flow data with the intepolation coefficients γ 1, γ, γ 3. A Chimea gid system often consists of moe than two ovelapping gids. In this case, FLOWe seaches all gids fo dono cells without pefeing one gid to anothe. If moe than one cell including the intepolation point is found, the cell with the smallest volume is chosen to be the dono cell. This choice is based on the assumption, that the discetization eo of the Navie-Stokes equations is smallest on the finest gid and thus the intepolated flow data will be most accuate. In many applications the ADT seach algoithm and the intepolation method have been poven to be vey obust even fo gids of bad quality. Backgound gids fo Chimea computations ae often Catesian with an equidistant o non 1 ) 86.3

4 equidistant distibution of gid points. Fo these types of meshes FLOWe offes a specialized seach pocedue which is much faste than the ADT method. While fo equidistant meshes the i,j,kindices of the dono cell can be diectly computed based on the cell spacing, fo non equidistant gids the indices ae detemined by applying a bisection method in one index-diection afte the othe. Sometimes the computation of intepolation coefficients is not possible, since the gid ovelap is not sufficient o because pats of the ovelapping gids ae blanked. This situation equies to impove the gids. But fo lage gid systems with many ovelapping gids aound a complicated configuation the optimization of the gids may be vey time consuming. Theefoe a method is available in FLOWe to enable a flow computation even if a non sufficient ovelap exists: Afte the computation of intepolation coefficients has failed fo a cell, all ovelapping gids ae seached fo the cell with the smallest distance to the intepolation point. The flow data of this cell ae subsequently used to update the intepolation cell data duing the flow simulation. The descibed method educes the accuacy of the flow solution locally. Thus the numbe of cells which equies its application should be kept to a minimum. Fo unsteady flow simulations including igid body motion an extension of the hole cutting pocedue is equied to avoid an invalid update of flow data close to holes, see section Gids in elative motion. Fo the modifications of the multigid method the following appoach has been chosen. Duing the hole cutting pocedue, all cells of coase meshes ae flagged, if the estiction o polongation opeatos access cells inside the holes on the next fine gid. Intepolation of flow data fom an ovelapping gid is only pefomed on the finest gid, wheeas fo coase gids the data at hole finges and oute gid boundaies ae intepolated fom the next fine level of the same gid. The IBLANK values ae set analogous to the finest gid, whee IBLANK=0 indicates hole cells o intepolated cells. Duing the flow simulation the focing function and the esiduals computed on the coase gid levels ae multiplied with IBLANK in ode to avoid an update of the coase gid data. A modification of the fine gid data is pevented by multiplying the coase gid coections befoe and afte the polongation with the IBLANK values of the coase and fine gid espectively. Othe possibilities to adapt the multigid technique fo Chimea computations have been published in ef. [9]. The method implemented in FLOWe has been chosen, because the autho believes it to be the most obust one. Gid ovelap on body sufaces In many cases the Chimea gids ovelap on body sufaces. One example is pesented in Figue 6 showing the junction of a wing and a body, whee the wing and the body ae discetized with diffeent gids. Flow simulation Little extension to the flow solve is necessay to enable computations on ovelapping gids. In the case of a puely explicit solve, any spatial o tempoal discetization opeato emains unchanged. Only the update of the consevative vaiables W in the blanked egions must be suppessed by multiplying the change of the consevative vaiables pe time step Δ W with the tag aay IBLANK W t+1 = W t + IBLANK ΔW. The adaptation of the implicit esidual smoothing is accomplished by multiplying the esidual befoe and afte the smoothing with IBLANK. The implicit teatment of the tubulence equation with the DDADI algoithm is adjusted accodingly by multiplying the intemediate and final esults with IBLANK. Figue 6: Gids with ovelap on body suface A gid ovelap on body sufaces equies a modification in the computation of intepolation coefficients, since the standad intepolation descibed in section Seach and intepolation may yield inaccuate esults. The eason is sketched in 86.4

5 Figue 7. Due to the diffeent discetization of a cuved analytic suface in the two ovelapping gids, the distance of a point P to the discete suface epesentations is unequal, δ1 δ. Theefoe all intepolation points close to a cuved suface will intepolate flow data fom locations with diffeent wall distance than expected. This may fo example cause poblems when tansfeing data within bounday layes. Sometimes an intepolation point may even be outside of the ovelapping gid making an intepolation impossible. intepolation point x P giving the coodinates x P* of a vitual intepolation point P* x P* = w ε + x P, see Figue 8, bottom. The weighting function is used to apply a full coection close to the suface and to educe the coection with inceasing distance fom the suface d w = 1 x x P d d1 0 P* if if if 0 x x < d d1 xp xp* < d, d x x P P P* P* 1 whee d = 10 ε, = 30 ε 1 d Figue 7: Non unique wall distance in ovelap egion fo point P In ode to cicumvent the descibed poblem a coection method was developed. The pocedue stats by seaching the gid containing the intepolation point P fo the point P S on the suface, which is closest to point P, see Figue 8, top. The point P S is pojected onto the discete suface epesentation of the ovelapping gid. The pojection vecto is denoted with ε. gives good esults. The coodinates of the vitual intepolation point ae now used to seach a dono cell and to compute the intepolation coefficients. The pesented algoithm ensues an identical wall distance of the intepolation point and the * 1 δ intepolated data, δ =, see Figue 8, bottom. If the intepolation point P is ovelapped by moe than one gid, the coection method is to be applied fo each dono gid, since in geneal the pojection vecto ε will be diffeent. Slightly diffeent coection methods ae known fom liteatue, see ef. [19] and ef. [6]. But instead of intoducing vitual intepolation points, the algoithms tempoaily modify the gid coodinates befoe the computation of intepolation coefficients. As a consequence, a coect calculation of the intepolation coefficients is not possible if moe than two gids ovelap on the body suface, because the coodinates can only be adjusted to match with one ovelapping gid. This difficulty is avoided by the intoduction of the vitual taget point, since its coodinates ae computed fo each dono gid independently. Gids in elative motion Figue 8: Coection of computation of intepolation coefficients, top: pojection of wall point P w on suface of othe gid, bottom: intoduction of vitual intepolation point P* The pojection vecto is now multiplied with a scaling function and added to the coodinates of the The ovelapping gid technique allows to move the gids elatively to each othe without affecting the gid s quality. It is theefoe an appopiate method fo the simulation of bodies in elative motion. This equies to update the integid communication each time the gids have been shifted to a new position. Theefoe, the hole cutting pocedue and the 86.5

6 calculation of intepolation coefficients must be executed epeatedly. Unsteady flow simulations equie an extension of the method used to identify intepolation points. Wheeas in section Seach and intepolation only the spatial discetization opeato was checked if it accesses hole cells, fo unsteady flow computations also the tempoal discetization opeato must be taken into account. Othewise the coect calculation of the flow data cannot be guaanteed in case of holes with vaying positions. Such a situation is depicted in Figue 9, top, showing a one dimensional gid with a hole moving two cells to the ight at each time step. The spatial discetization opeato is assumed to have a width of five cells. Thus two layes of intepolation cells ae necessay at the hole finge. If now a time discetization opeato is used, which equies valid data on two pevious time steps, a valid update of some cells in the wake of the hole is not possible. a blade can best be defined elatively to the oto hub. Accoding to these elations, a tee like data stuctue is used in FLOWe to specify igid body motions, see Figue 10. This allows to define a complex body movement by a seies of simple tansfomations. In FLOWe each tansfomation may include a tanslation in any diection and a otation aound an abitay axis. The time dependent tanslation and otation ae specified by polynomial and Fouie seies. inetial fame blade 1 blade blade n blade 1 hinge flap hinge lead/lag main oto fuselage motion specification tail oto blade hinge pitch Figue 10: Tee like data stuctue fo the definition of igid body motions fo helicopte Afte the use has defined the motion elations each of the ovelapping gids is linked to any of the specified tansfomations. Duing a subsequent flow computation the tansfomations ae used to position the gids in space and to tansfom vectoial quantities when they ae tansfeed between the gids. Calculation of global foces Figue 9: One dimensional gid with a moving hole, top: invalid update of flow data, bottom: extension of hole finge enables coect flow simulation, : cell with IBLANK = 1, : intepolated cell, : hole cell In ode to solve this poblem, all cells whose time discetization opeato accesses hole cells ae added to the list of intepolation cells. This esults in an extended hole finge in the wake of the hole, see Figue 9, bottom. The motion of a igid body is eithe defined based on the inetial fame of efeence o elatively to anothe moving geomety. Fo example, the fuselage of a helicopte moves elatively to the inetial fame, wheeas the otational velocity of the oto shaft is constant elative to the fuselage while the flapping of The standad pocedue to calculate global foces like lift and dag is to sum up the pessue and fiction foces of all cells on the body suface. This appoach fails in case of a gid ovelap on body sufaces, since the foces in the aea of the gid ovelap ae counted twice. Theefoe a method is to be used, which geneates a unique suface befoe integating the foces. In FLOWe this is accomplished by a postpocessing tool which emoves the ovelap and fills the esulting gap with tiangles, see Figue 11. The pocedue can be subdivided into the following steps. At fist, a citeion has to be defined which one of two ovelapping cells has to be emoved. To this end, each cell is assigned a pioity. Cells at Chimea gid boundaies and at hole finges ae set to pioity one. This is the lowest pioity. All othe 86.6

7 cells get a pioity, that is inceased by one compaed to thei neighboing cells. Theefoe the pioity of the cells is inceasing with inceasing distance to Chimea boundaies. In the next step, each cell of the suface gid is checked on ovelaps with anothe cell. If this is tue, the cell with the lowe pioity is emoved. Afte the execution of this step fo all cells, the ovelap of the suface gid is emoved. Due to the pioity tagging, the esulting gap is placed appoximately in the middle between the Chimea gid and hole boundaies. gids and to iteatively wap them with coase Catesian meshes. This pocedue is epeated until the complete computational domain is coveed by the backgound gid, see Figue 1. The diffeent cell size of neighboing blocks esults in patched gid intefaces with hanging gid nodes. This type of backgound gid has aleady been pesented in ef. [1]. Instead of using gids with patched intefaces, the Catesian gid blocks may also ovelap each othe, see ef. [3]. But this appoach does not ensue the flux consevation inside the backgound gid, which may esult in highe numeical eos in the computed flow. Theefoe the fist-mentioned appoach is used. Figue 11: Geneation of a unique suface fo the calculation of global foces In the last step the gap is filled with tiangles by using a Delauny tiangulation method. In contast to othe tiangulation methods (e.g. ef. [4]), that always connect points of one side of the gap with points of the othe side, the Delauny tiangulation can build a tiangle with any points at the gap bode. Thus a special teatment at banches of the gap is not equied. Additionally, the quality of the tiangulation with espect to tiangle distosion and stetching is bette. Figue 1: Catesian backgound gid In addition to the methods known fom liteatue, the Catesian gid geneato used in this wok does not only allow to ceate gids with cubic cells but also with anisotopic cells, see Figue 13. This inceases the similaity of the cell geometies of the component and backgound gids. Hence intepolation eos ae educed. In addition, anisotopic cells may also help to ensue a sufficient ovelap between the gids if the component gid extends only little into the fa field diection. Catesian backgound gids The component gids aound a configuation extend often only a shot distance into the computational domain. They must theefoe be embedded into a backgound gid. While its manual ceation is time consuming, it may instead be ceated automatically. The appoach followed with FLOWe is to place one laye of fine Catesian gids aound the component 86.7

8 subsequent flow computation. They can theefoe be emoved fom the gid without affecting the flow solution. This minimizes the numbe of gid cells. Afte the adaptation pocess is finished the gid consists of a lage numbe of gid blocks of size n n n cells. The numbe of gid blocks is now educed by meging gid blocks with the same cell spacing. To this end the method of the weakest descent (ef. [18]) is used. The algoithm ties to maximize the numbe of meging steps in ode to minimize the numbe of the esulting gid blocks. At the end of this step, the gid coodinates and the infomation on the patched gid intefaces ae witten to disk. Figue 13: Catesian backgound gid with anisotopic cells A desciption of the numeical teatment of the hanging gid nodes in FLOWe can be found in ef. [0]. Geneation of Catesian gids The ceation of the Catesian gid stats with a vey coase mesh of n n n cells, which coves the entie computational domain. n is usually taken to be 4, 8 o 1. The initial gid is iteatively efined and subdivided into subblocks of size n n n, until the gid blocks have appoximately the same cell spacing as the ovelapped cells of the component gid. As long as a gid is patitioned into eight fine gids, the gid cells ae cubic. A subdivision of a gid into one o two index diections yields a gid with anisotopic cells. The numbe of efinements and the efinement diections ae calculated with a senso function that analyses the geomety of evey cell of the component gid. Details of the senso function will be epoted in the subsequent paagaph Adaptation senso. Duing the fist adaptation cycle, the gids ae efined without consideing the cell spacing of neighboing blocks. Theefoe the gids ae efined futhe until the efinement is not lage than by a facto of two. In ode to limit the use of gid blocks with anisotopic cells, the index diection with the lagest spacing is coasened only, if the cell is aleady cubic. Duing the gid geneation pocedue the gid data ae stoed in an Altenating Digital Tee (ADT) data stuctue (ef. []). This method allows to keep gid blocks with an abitay numbe of cells whee the cells can be eithe cubic o anisotopic. In the tee, the minimum coodinates of the gid blocks, the numbe of cells in each index diection and the efinement level in each index diection ae saved. Theefoe only nine vaiables ae stoed pe gid block esulting in small memoy consumption. The actual gid coodinates and the infomation on the gid bounday conditions ae only computed duing the final data output. Adaptation senso The adaptation of the backgound gid to the component gids equies to use a senso function which calculates fo each of the abitaily shaped cells the dimensions of a simila Catesian gid cell. The senso used hee equies thee steps. At fist each cell is tansfomed into a paallelepiped, whee the edges of the paallelepiped ae set identical to the length and diection of the lines, which connect the mid points of opposite faces of the cell, see Figue 14a, b. The paallelepiped is next tansfomed into a cuboid. This is accomplished by shifting the longest edges paallel to each othe, until they ae pependicula to the second longest edges. The lagest cell faces ae now shifted paallel to each othe until all edges ae pependicula to each othe, see Figue 14c. Both opeations do not change the volume of the paallelepiped (Cavaliei s pinciple). Some blocks of the backgound gid may be entiely inside the auxiliay gids used fo the hole cutting. Fo these gids all cells would be blanked in a 86.8

9 and the inetial fame is identical, the spacing in this diection is unchanged. a) b) c) Figue 14: Tansfomation of a hexahedal (a) to a paallelepiped (b) and to a cuboid (c) Fo the thid tansfomation, a local coodinate system (a,b,c) is intoduced, which is aligned with thee edges of the cuboid. The length of the edges will be denoted by Δa, Δb, Δc. The oigin of the coodinate system is now shifted to the oigin of the inetial coodinate system (x,y,z). Then, the axis diections of the inetial fame ae calculated in spheical coodinates of the local fame. This gives the angles (ϕ x,θ x ), (ϕ y,θ y ), (ϕ z,θ z ), see Figue 15. By using the adaptation senso outlined above, the Catesian backgound gid will have the same gid esolution as the undelying component gid and a simila cell stetching. In Figue 1, the shape of the computed Catesian cell is plotted fo a otated cuboid. Figue 16: Shape of Catesian cell (gey) fo otated cuboidal cell with stetching 1:4 Examples of applications In the famewok of the CHANCE poject, the Chimea technique has been validated fo vaious types of helicopte applications. Thee test cases will be exemplified in the following. Isolated oto in fowad flight Figue 15: Tansfomation elations The angles ae used to compute the senso function: α x ( 1 β x ) (1 α x )( 1 β x ) βx Δx = Δa Δb Δc with α x = cos ( ϕ x ), β x = cos ( Θ x ), α y ( 1 β y ) (1 α y )( 1 β y ) β y Δy = Δa Δb Δc with α y = cos ( ϕ y ), β y = cos ( Θ y ), α z ( 1 β z ) (1 α z )( 1 β z ) β z Δz = Δa Δb Δc with α z = cos ( ϕ z ), β z = cos ( Θ z ), whee Δx, Δy, Δz ae the spacings of the Catesian cell in x-, y-, z-coodinate diection. The senso function has been chosen fo thee easons: 1) the volume of the oiginal cuboid is peseved, ) the spacings of the Catesian cell ae identical to those of the cuboid, if the inetial and the local fame ae identical, 3) if one axis of the local In ef. [15] the aeodynamics of the ONERA 7A oto in fowad flight including elastic blade defomation and tim has been investigated by embedding individual meshes fo the blades into a backgound gid (3. million gid points in the whole gid system), see Figue 17. In Figue 18 the distibution of the nomal foce and the pitching moment close to the blade tip computed with two diffeent methods is shown in compaison with expeimental data. The fist calculation (S4 no coupl.) was pefomed with the DLR oto simulation code S4. In S4 the aeodynamics of the oto is calculated by using the blade element theoy based on measued aifoil tables including unsteady and Mach effects, a dynamic stall model, vaying velocity effects and a pescibed wake model. Fo the second simulation (FLOWe/S4) the FLOWe code was applied. In both calculations the elastic blade defomation is simulated with the stuctual dynamics module of the S4 code. The compaison of the timmed simulations pesented in Figue 18 shows the significantly impoved esults when using the Navie-Stokes solve. 86.9

10 suface pessue distibution and the suface fiction lines ae shown. The lage flow sepaation at the boot of the fuselage is clealy captued. Figue 19: Chimea gid fo EC 145 helicopte fuselage with actuato discs fo main and tail oto, evey fouth gid line plotted (ef. [1], with pemission) Figue 17: Ovelapping gids fo isolated oto in fowad flight including elastic blade defomation (ef. [15], with pemission) Figue 0: Suface pessue distibution and suface fiction lines on fuselage of EC 145 helicopte (ef. [1], with pemission) Complete helicopte Figue 18: Nomal foces (top) and pitching moment (bottom) fo one evolution of 7A main oto (ef. [15], with pemission) Actuato disc modelling The time aveaged effects of the main and tail oto on the fuselage of an EC 145 helicopte have been analyzed in ef. [1]. This was achieved by embedding gids fo the actuato discs of main and tail oto into an existing mesh fo a helicopte fuselage, see Figue 19. In Figue 0 the computed The simulation of an almost complete helicopte configuation is epoted in ef. [10], whee the unsteady flow aound a BO 105 wind tunnel model including main and tail oto, skids and wind tunnel suppot stut was computed. The authos geneated twelve ovelapping gids fo the components of the configuation and embedded the component gids into an automatically ceated Catesian backgound gid, see Figue 1. One esult obtained duing the simulation is the pessue distibution at the symmety plane of the fuselage, see Figue. The ageement between expeimental and computational esults is good. Unsteady pessue distibutions on the fin fo a half evolution of the main oto o

11 evolutions of the tail oto, espectively, ae plotted in Figue 3. Although some offset can be obseved in the c p -values, the unsteady vaiations of the pessue ae well captued. Figue : computed pessue distibution compaed to expeimental data in symmety plane fo unsteady simulation of BO 105 (ef. [10]) Figue 1: Chimea gid system fo the time accuate simulation of the flow aound a BO 105 wind tunnel model, evey second gid line plotted, top: component gids without mesh fo fuselage, bottom: cut at symmety plane (ef. [10]) Figue 3: unsteady pessue distibution on tail fin at 50% adius (top) and at the oute adius (bottom) of the tail oto of BO 105 helicopte, ed: CFD, black: expeiment (ef. [10]) Applications by industy The Chimea technique in FLOWe has also been successfully applied by industial customes. Euocopte Gemany (ECD) has investigated the fuselage aeodynamics of the EC145 helicopte including the time aveaged influence of the main oto by embedding a sepaate gid fo the actuato disc into the fuselage gid (ef. 13). The gid system was used to compute polas fo the helicopte. Aibus Gemany has used the Chimea technique to embed individual gids fo aileons and spoiles into an existing gid fo a wing-body aiplane configuation (ef. [14]). The computational esults 86.11

12 showed good ageement with wind tunnel expeiments. Pefomance Unsteady flow simulations ae often vey time consuming. Theefoe efficient solution algoithms and thei paallelized and vectoized implementation ae equied to minimize the execution time. In ode to demonstate the pefomance of FLOWe, the time needed fo one physical time step of a flow simulation was measued. The test case chosen was the configuation pesented in section Complete helicopte. This test case consists of 11.8 million gid cells and 480 gid blocks. The time integation was pefomed with the dual time stepping method which equied 50 iteations of the flow solve to convege the flow equations at each physical time step. Convegence was acceleated by implicit esidual smoothing and thee levels multigid. Tubulence was modeled with the kω-tubulence model. The time consumption of the FLOWe flow solve on a NEC SX8 vecto compute and fo a PC- Cluste with INTEL Xeon Pocessos with 3.06 GHz is pesented in the following table: NEC SX8 No. of pocs execution time hole cutting & seach execution time flow solve s 50 * s s 50 * s s 50 * 9.03 s s 50 * 5.47 s PC s 50 * 7.6 s A flow simulation with less then eight pocessos on the PC Cluste was not possible due to memoy limitations. The total time consumption fo one physical time step is the sum of the time needed fo the hole cutting and seach pocedues at the beginning of a physical time step and the time equied fo 50 iteations of the flow solve to convege the flow equations. Accoding to the table the Chimea algoithms equie on the vecto compute less then 15% of the total CPU time and on the scala compute less than %. This shows that the Chimea outines have only a mino impact on the total CPU time. The elatively high time consumption of the Chimea algoithms on the NEC SX8 is due to the ADT seach method, which is not vectoized because of its ecusive algoithm. The speed up time consumption one pocesso speed up = time consumption n pocessos fo the NEC SX8 is shown in the following table: NEC SX8 No. of pocs speed up hole cutting & seach speed up flow solve The theoetical speed up of 8.0 fo a computation on eight pocessos is not eached by the Chimea algoithms. This is due to the load balancing algoithm which is optimized fo the flow solve and does not take into account the time consumption of the hole cutting and seach pocedues. A good speed up is obtained fo the flow solve up to fou pocessos. With inceasing numbe of pocessos, the time needed to solve the flow equations is educed wheeas the time needed fo intepocesso communication is almost constant. This explains the non optimum speed up when using eight pocessos of the NEC SX8. Summay In this pape the implementation of the Chimea technique in DLR s stuctued flow solve FLOWe is pesented. The hole cutting algoithm uses auxiliay gids to blank all cells which ae in its inteio. An ADT-seach algoithm o a specialized method fo Catesian gids is used to find appopiate dono cells fo the tilinea intepolation of flow data. If the gids ovelap on a body suface, vitual intepolation points ae intoduced. They enable an accuate calculation of intepolation coefficients nea sufaces despite the diffeent suface discetizations. No gid hieachy is used duing hole cutting and data intepolation. Instead any solid body can cut holes in any gid and all meshes ae seached fo dono cells. Fo unsteady flow simulations the motion of gids ae defined with a hieachical data stuctue. This allows to define complex motions by a sequence of simple tansfomations. A valid update of flow data on moving gids is ensued by intepolating data fo all cells, fo which the discetization opeato accesses hole cells eithe in spatial o in tempoal diection. Chimea flow simulations in geneal do not equie a specialized postpocessing. One exception is the calculation of foces and moments which must be 86.1

13 adapted if a gid ovelap exists on body sufaces. In ode to ceate a unique suface fo the integation of foces and moments a tool was developed which emoves the gid ovelap and fills the esulting gap with tiangles. The decomposition of the computational domain into seveal independently ceated gids offes the possibility to ceate the backgound mesh automatically. To this end a Catesian mesh geneato is used which adapts an initially vey coase mesh to the cell size of the component gids. The esulting mesh has cubic and anisotopic cells which minimizes intepolation eos and may educe the equied ovelap width. The spacings of the Catesian cells ae computed with a novel adaptation senso. The implementation of the Chimea technique in FLOWe has been validated fo seveal helicopte applications. It has been shown that ovelapping gids can be used to simplify gid geneation and to simulate the flow aound bodies in elative motion. Pefomance measuements on a PC-Cluste and a paallel vecto compute show that the hole cutting and seach pocedues have a mino impact on the total CPU time consumption. Refeences [1] BENEK, J.; STEGER, J. L.; DOUGHERTY, F. C.: A Flexible Gid Embedding Technique with Application to the Eule Equations. AIAA Pape , 1983 [] BONET, J.; PERAIRE, J.: An Altenating Digital Tee (ADT) Algoithm fo 3D Geometic Seaching and Intesection poblems. In: Intenational Jounal fo Numeical Methods in Engineeing, Vol. 31, 1991, pp [3] BLAYLOCK, T. A.; ONSLOW, S. H.; ALBONE, C. M.: Mesh Geneation and Flow Solution fo Complex Configuations using the FAME System. In: Poceedings of the 1993 Euopean Foum on Recent Developments and Applications in Aeonautical CFD, Royal Aeonautical Sosiety, Bistol, England, Septembe, 1993, pp [4] CHAN, W. M.; BUNING, P. G.: Zippe gids fo Foce and Moment Computation on Oveset Gids. AIAA Pape , 1995 [5] CHAN, W. M.; MEAKIN, R. L.; POTSDAM, M. A.: CHSSI Softwae fo Geometically Complex Unsteady Aeodynamic Applications. AIAA Pape , 001 [6] CHAN, W.; GOMEZ III, R. J.; ROGERS, S. E.; BUNING, P. G.: Best Pactices in Oveset Gid Geneation. AIAA Pape , 001 [7] D ALASCIO, A.; BERTHE, A.; LE CHUITON, F.: Application of CFD to the Fuselage Aeodynamics of the EC145 Helicopte. Pediction of Unsteady Phenomena and of the Time Aveaged Influence of the Main Roto. In: Poceedings of the 9 th Euopean Rotocaft Foum, Pape 39, Fiedichshafen, Gemany, Septembe 16-18, 003 [8] JEANFAVRE, G.; BENOIT, C.; LE PAPE, M.-C.: Impovement of the Robustness of the Chimea Method. AIAA Pape , 00 [9] JUVIGNY, X.; CANNONE, E.; BENOIT, C.: Multigid Algoithms fo the Chimea Method. AHS Pape , 004 [10] KHIER,W.; SCHWARZ, T.: Time-accuate simulation of the flow aound the complete BO 105 wind tunnel model. In: Poceedings of the 31 st Euopean Rotocaft Foum, Pape 87, Floence, Italy, Septembe 13 15, 005 [11] KROLL, N.; ROSSOW, C.-C.; BECKER, K.; THIELE, F.: The MEGAFLOW Poject. In: Aeospace Science and Technology, Vol. 4, 00, pp [1] LE CHUITON, F.: Chimea Simulation of a complete helicopte with otos as actuato discs. 14 th Symposium of STAB, Bemen, Gemany, Novembe , 004, to appea in: Notes in Numeical Fluid Mechanics and Multidisciplinay Design, Spinge, 005 [13] MEAKIN, R. L.: An efficient means of Adaptive Refinement within Systems of Oveset Gids. AIAA Pape 95-17, 1995 [14] MERTINS, R.; ELSHOLZ, E.; COLAK, B.; BARAKAT, S.: 3D Viscous Flow Analysis on Wing-Body- Aileon-Spoile Configuations. In: Poceedings of the Deutsche Luft- und Raumfahtkongess 003, Pape DGLR , Munich, Gemany, Novembe 17-0, 003 [15] PAHLKE, K.; VAN DER WALL, B.: Chimea Simulations of Multibladed Rotos in High-Speed Fowad Flight with weak fluid-stuctue coupling. In: Aeospace Science and Technology, Vol. 9, No. 5, 005, pp [16] PAHLKE,K.; COSTES, M.; D ALASCIO, A.; CASTELLIN, C.; ALTMIKUS, A.: The 6-yea Fench- Geman CHANCE Poject. In: Poceedings of 86.13

14 the 31 st Euopean Rotocaft Foum, Pape 69, Floence, Italy, Spetembe 15-17, 005 [17] PREWITT, N. C.; BELK, D. M.; MAPLE, R. C.: Multiple Body Tajectoy Calculations Using the Begga Code. In: Jounal of Aicaft, Vol. 36, No. 5, 1999, pp [18] RIGBY, D. L.: Method of the Weakest Descent fo Automatic Block Meging. In: Poceedings of the 15 th Intenational Confeence on Numeical Methods in Fluid Dynamics, Monteey, Califonia, USA, June 1996 [19] SCHWARZ, T.: Development of a Wall Teatment fo Navie-Stokes Computations using the Oveset-Gid Technique. In: Poceedings of the 6 th Euopean Rotocaft Foum, The Hague, The Nethelands [0] SCHWARZ, T.: Enhancement of a Navie-Stokes Flow Solve fo Patched Gids with Non- Coincident Gid Nodes. In: Notes on Numeical Fluid Mechanics, Vol. 77, Spinge, 00, pp [1] WANG, Z. J.; PARTHASARATHY, V.: A Fully Automated Chimea Methodology fo Multiple Moving Body Poblems. In: Intenational Jounal fo Numeical Methods in Fluids, Vol. 33, 000, pp