International Journal of Heat and Fluid Flow

Transcription

1 International Journal of Heat and Fluid Flow 30 (2009) 29 4 Content lit available at ScienceDirect International Journal of Heat and Fluid Flow journal homepage: Development and aement of a coupled trategy for conjugate heat tranfer with Large Eddy Simulation: Application to a cooled turbine blade F. Duchaine a, *, A. Corpron b, L. Pon b, V. Moureau b,c, F. Nicoud d, T. Poinot e a CERFACS, 42 av. Corioli, Touloue Cedex 0, France b Turbomeca (Safran Group), BP7, 64 5 Borde Cedex, France c CORIA, Site univeritaire du Madrillet, BP8, Saint Etienne du Rouvray Cedex, France d Unviervité Montpellier II, Place Bataillon, Montpellier Cedex 5, France e IMFT, Avenue Camille Soula, Touloue Cedex, France article info abtract Article hitory: Received 22 May 2009 Received in revied form 29 July 2009 Accepted 29 July 2009 Available online 3 September 2009 Keyword: Conjugate heat tranfer Large Eddy Simulation Code coupling Stability analyi Although Large Eddy Simulation (LES) i identified today a the mot promiing method for turbulent flow problem, few application of LES coupled to heat tranfer olver in olid have been publihed. Thi paper decribe a coupling trategy of a LES olver and a heat tranfer code within olid on parallel architecture. The numerical method ued in both olver are briefly recalled before dicuing the coupling trategy in term of phyical quantitie to exchange (fluxe and temperature), tability and parallel efficiency. The tability tudy i performed uing an amplification matrix analyi on a one-dimenional cae and allow the determination and optimization of coupling parameter. The coupled tool i then applied to a cooled turbine blade model where reult demontrate both the efficiency of the parallel implementation and the quality of the reult. Coupled and non-coupled imulation are compared to experimental reult and dicued in term of cooling efficiency and flow tructure. Ó 2009 Elevier Inc. All right reerved.. Introduction Determination of heat load, a wall temperature and heat fluxe, i a key iue in combution (Lakhminarayana, 996; Lefebvre, 999; Schiele and Wittig, 2000; Dunn, 200; Bunker, 2007): the interaction of hot gae and reacting flow with colder wall i an important phenomenon in combution chamber and a main deign contraint in ga turbine. After combution, the interaction of the hot burnt gae with the high preure tator and the firt turbine blade condition the temperature and preure level reached in the combutor, and therefore the engine efficiency. Numerical imulation of the thermal interaction between fluid flow and olid offer new deign path to diminih development cot through important reduction of the number of experimental tet. When a Computational Fluid Dynamic (CFD) olver i coupled to a heat tranfer olver, the accuracy of the coupled tool i generally controlled by the fluid code. Conventional CFD technique ue Reynold Averaged Navier Stoke (RANS) method. Such approache cannot capture all complex effect in turbomachinery flow and looking for more precie flow olver i a uual objective * Correponding author. Tel.: +33 (0) ; fax: +33 (0) addre: florent.duchaine@cerfac.fr (F. Duchaine). in thi field. Direct Numerical Simulation (DNS) method cannot offer uch an alternative olution becaue of their computational cot. Recent progree in Large Eddy Simulation (LES) (Sagaut, 2000; Maheh et al., 2004; Poinot et al., 2005) and the continuouly increaing computer power offered by the newly developed parallel computer architecture, allow to accurately predict turbulent flow in complex geometrie (Acharya et al., 200; Azzi et al., 2002; Rozati, 2007; Boudier et al., 2007). A LES i till a computationally expenive method, the aim of thi paper i to develop and ae a uitable trategy baed on LES to efficiently converge to teady thermal tate. There are two baic approache to olve Conjugate Heat Tranfer (CHT) problem. The firt one i a direct coupling where the different field are olved imultaneouly in a large ytem of equation by a monolithic olver (Kao and Liou, 997; Han et al., 200; Rahman et al., 2005; Luo and Razinky, 2007; Ganean et al., 2007). The econd approach conit in olving each et of field equation eparately with dedicated olver that exchange boundary condition (Heelhau et al., 995; Sondak and Dorney, 2000; Papanicolaou et al., 200; Garg, 2002; Bohn et al., 2005). Thi olution ha the advantage of uing exiting tate-of-the-art code to olve fluid and olid equation and of being able to exchange one olver with another eaily (Alono et al., 2006). The main drawback of thi coupling methodology i that an adapted CHT framework i requeted for the imulation epecially on parallel machine. The performance of uch a coupling framework are linked to () the X/$ - ee front matter Ó 2009 Elevier Inc. All right reerved. doi:0.06/j.ijheatfluidflow

2 30 F. Duchaine et al. / International Journal of Heat and Fluid Flow 30 (2009) 29 4 trategy to couple the olver in an accurate and table fahion a well a (2) the exchange of information between the olver in an efficient and calable fahion when uing a large number of proceor Alono et al., Thi paper (Alono et al., 2006) invetigate important iue for fully parallel and coupled CHT baed on LES for flow model: The boundary condition applied to the fluid and olid code, including the variable hared by the code, are critical for the accuracy and tability of the computation, In ga turbine application, the time cale of the flow and of the olid are generally very different. A a conequence, the frequency of exchange between the code and the ynchronization of the olver influence the tability a well a the retitution time of the computation. The document i organized a follow. The fluid and olid olver are preented in Section 2. Section 3 i dedicated to the CHT framework. The coupling methodology (boundary condition and ynchronization of the olver) i decribed in Section 3.. The tability tudy (Section 3.2) i performed on a one-dimenional problem uing an amplification matrix analyi. The trategy i validated (Section 4) through comparion of preure and temperature field on the experimental film-cooled blade. After a hort decription of the configuration (Section 4.) and of olid and fluid dicretization (Section 4.2), an adiabatic LES i dicued (Section 4.3). Thermal reult given by the CHT methodology are preented in Section 4.4 which alo decribe the main flow tructure controlling heat tranfer. Finally, Section 4.5 propoe efficiency analye of the coupled trategy. 2. Numerical approach 2.. Governing equation for flow LES model LES of reacting flow involve the patial Favre filtering operation that reduce for patially, temporally invariant and localied filter function (Vreman et al., 994) to: fðx; gtþ ¼ qðx; tþ Z þ qðx 0 ; tþf ðx 0 ; tþgðx 0 xþdx 0 where G denote the filter function. In the mathematical decription of compreible turbulent flow the primary variable are the volumic ma fraction qðx; tþ, the velocity vector u i ðx; tþ and the total energy Eðx; tþ e þ =2u i u i. The fluid follow the ideal ga law, p ¼ qrt and e ¼ R T C 0 pdt p=q, where e i the enible energy, T the temperature, C p the fluid heat capacity at contant preure and r i the mixture ga contant. The LES olver take into account change of heat capacity with temperature uing tabulated value of heat capacitie. The vicou tre tenor and the heat diffuion vector ue claical gradient approache. The fluid vicoity follow Sutherland law and the heat diffuion coefficient follow Fourier law. The application of the filtering operation to the intantaneou et of compreible Navier Stoke tranport equation yield the LES tranport equation (Poinot et al., 2005) which contain ocalled Sub-Grid Scale (SGS) quantitie that need modelling (Sagaut, 2000; Ferziger, 977). The unreolved SGS tre tenor t ij i modelled uing the Bouineq aumption (Smagorinky, 963; Pope, 2000; Chaaing et al., 2000): ij t 3 kk t d ij ¼ 2qm t e Sij with e S ij ¼ i i k d ij ðþ ð2þ In Eq. (2), e S ij i the reolved train rate tenor and m t i the SGS turbulent vicoity. The Wall Adapting Linear Eddy (WALE) model (Nicoud and Ducro, 999) i choen to model the SGS vicoity: m t ¼ðC w DÞ 2 ð d ij d ij Þ3=2 ð e S ij e Sij Þ 5=2 þð d ij d ij Þ5=4 with d ij ¼ 2 fg 2 2 ij þ fg ji þ 3 fg 2 kk d ij In Eq. (3), D denote the filter characteritic length (approximated by the cubic-root of the cell volume), C w i a model contant equal to 0.5 and fg ij i the reolved velocity gradient. The SGS energy flux q i t i modelled uing a SGS turbulent heat conductivity obtained from m t by k t ¼ qm t C p =Pr t, where Pr t ¼ 0:7 i a contant turbulent Prandtl number: q T i ¼ k e t i In Eq. (4), T e i the Favre filtered temperature which atifie the modified filtered tate equation p ¼ qr T e (Moin et al., 99; Erlebacher et al., 992; Ducro et al., 996; Comte, 996). Although the performance of the cloure could be improved through the ue of a dynamic formulation (Moin et al., 99; Lilly, 992; Germano et al., 992; Ghoal and Moin, 995; Meneveau et al., 996) Eq. (2) (4) are conidered ufficient to addre the preent preliminary invetigation. The WALE ubgrid model i ued in conjunction with no-lip wall condition. Thi model i deigned to provide correct level of turbulent vicoity down to the wall and no wall model i required. Total preure and total temperature with velocity angle are impoed uing the Navier Stoke Characteritic Boundary Condition (NSCBC) formalim (Poinot and Lele, 992) at the inlet of the fluid domain. Static preure are enforced at outlet boundarie in characteritic NSCBC form Governing equation for olid heat tranfer model Heat tranfer in olid domain i decribed by the energy tþ q C i where T i the temperature, q the denity, C i the heat capacity and q the conduction heat flux. The heat diffuion follow Fourier q i ¼ k i where k i the heat conductivity of the medium. The olid olver take into account local change of heat capacity and conductivity with temperature Numerical cheme The parallel LES code (Schönfeld et al., 999; Moureau et al., 2005; Mendez and Nicoud, 2008; Roux et al., 2008) olve the full compreible Navier Stoke equation uing a cell-vertex/finite element approximation and Taylor-Galerkin weighted reidual central ditribution cheme (Donea and Huerta, 2003). Thi explicit cheme, which provide third-order accuracy on hybrid mehe, i particularly adequate for low-diipation requirement of LES application (Colin and Rudgyard, 2000). Boundary condition are handled with the NSCBC formulation (Poinot et al., 2005; Moureau et al., 2005). The parallel conduction olver i baed on the ame data tructure and ue an explicit cheme for time advancement. ð3þ

3 F. Duchaine et al. / International Journal of Heat and Fluid Flow 30 (2009) Conjugate heat tranfer During thi work, only a thermal teady tate olution within the blade tructure wa ought for. Since the two olver are explicit and time dependent, the coupling trategy between the olver require a pecific approach dicued in Section 3.. The tability of the approach i tudied in Section 3.2 by determining tability limit in a implified D cae. 3.. Coupling trategie The reolution of CHT problem on maively parallel machine involve two main iue: The boundary condition applied to the fluid and olid code control the preciion and tability of the computation (Section 3..). The frequency of exchange between the code and the ynchronization of the olver influence the tability a well a the retitution time of the computation (Section 3..2) Boundary condition At a fluid/olid interface C f, heat flux and temperature are continuou: ( / I f ¼ / I ; I 2 C f ð7þ T I f ¼ T I with ð/ I f ; /I Þ the fluid and olid heat fluxe at the interface point I and ðt I f ; TI Þ the fluid and olid temperature at the ame location. Thu, natural variable to hare between the code are / and T at the interface. However, it i uually not efficient to directly impoe / or T on either one of the olver. Typical trategie to treat CHT problem (Sondak and Dorney, 2000; Bohn et al., 2005) conit in chooing an adequate compoition of variable / I and TI coming from the olid computation a boundary condition for the fluid domain. The flow olution i computed with thi et of boundary condition during n f iteration of the fluid olver. Similarly, an adequate compoition of variable / I f and T I f coming from the fluid computation i impoed a boundary condition for the olid domain during n iteration of the thermal code. To reach a thermal teady tate, thee tep are repeated until convergence of boundary variable / I and T I. The olution retained here i to write the continuity of heat flux and temperature acro the interface C f (Eq. (7)) in the following form (Chemin et al., 2006): ( T I f ¼ T I / I f þ hti f ¼ / I þ ð8þ hti where h i a poitive numerical coupling relaxation parameter (CRP) which ha the dimenion of a convection coefficient. A recommended by previou tudie to improve the tability of the coupled cheme (Gile, 997; Chemin et al., 2006; Radenac et al., 2006; Roe et al., 2008), the temperature from the olid i impoed to the fluid domain with a Dirichlet condition: T I;n f ¼ T I ; with n ¼ ; n f ð9þ / I;n The reulting mixed boundary condition for the tructure i: ¼ / I f þ hðti f TI;n Þ; with n ¼ ; n ð0þ and T I;n Both / I;n of the mixed formulation (Eq. (0)) converge to teady tate between two ucceive update of / I f and T I f. The tability of the mixed condition for the olid domain ued in conjunction with Dirichlet boundary temperature for the fluid depend on the value of the CRP h and on update frequency. Section 3..2 give argument concerning update frequencie adopted within thi tudy and Section 3.2 propoe a tability analyi of the coupled trategy baed on a implified configuration Synchronization of the olver In a ga turbine, a blade ubmitted to the hot tream exiting from a combution chamber ha a characteritic time cale, baed on a reference length and thermal diffuivity, of the order of a few econd, while the flow-through time along the blade f i le than m. Hence, the convergence to a thermal teady tate of the conjugate ytem i controlled by the olid. Let u conider that between two update of the boundary value, the flow i advanced in time of a quantity a f f and the olid i advanced of a time a where a f and a are two non-dimenional contant. Then, two limit cae are of interet: () a ¼ a f enure that both olid and fluid converge to teady tate at the ame rate and (2) a f f ¼ a enure that the two olver are ynchronized in phyical time. Thi lat cae i needed for fully coupled unteady computation. A for the preent application only the teady tate temperature field in the olid i requeted, cae () a ¼ a ¼ a f i ued. In the following, a i called the coupling ynchronization time parameter (CSTP). The number of iteration of the fluid and olid olver, repectively, n f and n, are linked to fluid and olid time tep Dt f and Dt by: n f ¼ a f =Dt f n ¼ a =Dt ðþ On a parallel machine, code for the fluid and for the tructure may be run together or equentially. Fig. how how heat fluxe and temperature are exchanged in a mode called Sequential Coupling Strategy (SCS) (Duchaine et al., 2008) or taggered olution procedure (Felippa et al., 200): at ynchronization n cpl of the olver (the ubcript cpl refer to CouPLing quantitie), after a phyical time a f the fluid olver provide fluxe and temperature to the olid olver which then tart and give back temperature (phyical duration a ). In SCS, the code are loaded into the parallel machine equentially and each olver ue all available proceor ðpþ. Mot exiting application that ue SCS are baed on teady tate code (i.e. RANS olver for the fluid) (Divo et al., 2002; Heidmann et al., 2003; Mercier and Tee, 2006; Vertraete et al., 2007). Another olution i Parallel Coupling Strategy (PCS) (Duchaine et al., 2008), or parallel taggered procedure (Felippa et al., 200), where both olver run together uing information obtained from the other olver at the previou coupling iteration (Fig. 2). PCS i employed to tudy tranient or unteady phenomena (Montenay Fluid run # n cpl BC: T ncpl - Duration: f (T ncpl f, f ncpl ) Fluid run # n cpl + BC: T ncpl Duration: f (T ncpl + f, f ncpl + ) T ncpl T ncpl + Fig.. Sequential coupling trategy SCS. Solid run # n cpl BC: (T ncpl - f, f ncpl - ) Duration: Solid run # n cpl + BC: (T f ncpl, f ncpl ) Duration:

4 32 F. Duchaine et al. / International Journal of Heat and Fluid Flow 30 (2009) 29 4 Fluid run # n cpl BC: T ncpl - Duration: f Fluid run # n cpl + BC: T ncpl Duration: Fluid run # n cpl +2 BC: T ncpl + Duration: f f (T f ncpl, f ncpl ) (T f ncpl +, f ncpl + ) (T f ncpl +2, f ncpl +2 ) et al., 2000; Hegab et al., 200; do Santo et al., 2008; Duchaine et al., 2008). In the cae of PCS, the two olver mut hare the P ¼ P þ P f proceor. To firt order, enuring load balancing require that the P and P f proceor dedicated to the olid and the fluid, repectively, mut be uch that: P f P ¼ þ T =T f ð2þ where T and T f are the execution time of the olid and fluid olver on one proceor to compute phyical time a and a f, repectively. Perfect caling for both olver i aumed in Eq. (2). Efficient implementation of PCS require a oftware to manage the parallel execution of the olver a well a the data exchange during their execution. In order to inure the performance of the PCS, a code coupler, initially developed for ocean atmophere coupling (Lagarde et al., 200; Bui et al., 2005), ha been ued here. Both SCS and PCS have been teted: to deal with a fully non tationary coupled problem with ynchronization in phyical time ða f f ¼ a Þ, PCS i recommended (Hegab et al., 200). However, when tudying the convergence to a teady thermal tate where a ¼ a f ¼ a, the choice of the method i open and will be addreed in Section Stability of the coupling methodology Solid run # n cpl BC: (T ncpl - f, f ncpl - ) Duration: Solid run # n cpl + Solid run # n cpl +2 The coupling methodology ued to reach a teady thermal tate i compoed of the following et of boundary condition: 8 < Fluid ðdirichletþ : T I;i f f ¼ T I ; i f ¼ ; n f ð3þ : Solid ðmixedþ : / I;i ¼ / I f þ hðti f TI;i Þ; i ¼ ; n Boundary condition of Eq. (3) are applied to fluid and olid domain during the n f and n iteration of the olver between two conecutive update. In Eq. (3), the coupling relaxation parameter h and the coupling ynchronization time parameter a are adjutable. The other free parameter i the mode of ynchronization: SCS or PCS. Before applying the CHT methodology to a full configuration, it i intereting to tudy it tability in term of h and a. Thi i done here in a implified D cae with the PCS. T ncpl T ncpl + T ncpl +2 Fig. 2. Parallel coupling trategy PCS. BC: (T f ncpl, f ncpl ) Duration: BC: (T ncpl + f, f ncpl + ) Duration: Decription of the implified conjugate heat tranfer problem In coupled imulation, mode which are normal to the interface between the fluid and the olid can become untable. Hence, the tability of the PCS with Dirichlet/mixed et of boundary condition i analyzed here with a D purely thermal diffuion problem P SCHT (Simplified conjugate heat tranfer problem). A mentioned by Gile (Gile, 997), ince there i no velocity component normal to the olid boundarie, it i appropriate in a D model to omit convection term. Stability for problem P SCHT i a neceary condition for real application but may not be ufficient. Neverthele, undertanding D intabilitie clearly give inight into the potential intabilitie in 2D and 3D complex computation. The problem P SCHT i a ytem compoed of two domain with contant propertie. Domain # ha the thermal propertie (thermal conductivity, heat capacity and denity) of plexigla (Table ) while domain #2 ha the thermal propertie of air at 328 K (Table 2). The interface between the domain at x ¼ 0 i noted C. Dirichlet condition on temperature are impoed at x ¼ b ðb < 0Þ and x ¼ b 2 ðb 2 > 0Þ. To olve the problem P SCHT, the heat diffuion equation i conidered in both q i 2 T i ðxþ i C i ¼ k i ; i ¼ ; 2 with the boundary and continuity condition: 8 T ðx ¼ b Þ¼T b >< T 2 ðx ¼ b 2 Þ¼T b2 / ðx ¼ 0Þ ¼/ 2 ðx ¼ 0Þ >: T ðx ¼ 0Þ ¼T 2 ðx ¼ 0Þ ð5þ For the ake of implicity, Eq. (4) i dicretized uing a forward Euler time differencing and a claical econd-order central difference cheme on uniform grid in each domain: T nþ i;j ¼ T n i;j þ F iðt n i;jþ 2Tn i;j þ Tn i;j Þ; i ¼ ; 2 ð6þ where F i ¼ k idt i ; Dt q i C i Dx 2 i and Dx i are the Fourier number, the time tep i and the meh ize of domain i, repectively. For a periodic domain with uniform thermo-phyical propertie, the tability of the dicretization given by Eq. (6) i enured when F i 6 0:5 (Burnett, 98). In Eq. (6), T n i;j i given by: T n i;j ¼ T ðb þ jdx ; ndt Þ j ¼ ; N n ¼ ; n ðolidþ ð7þ T 2 ðjdx 2 ; ndt 2 Þ j ¼ ; N 2 n ¼ ; n 2 ðfluidþ where N and N 2 are the number of meh point of domain # and #2, repectively. Previou work dealing with numerical tability of coupled thermal computation (Gile, 997; Chemin et al., 2006; Radenac et al., 2006; Roe et al., 2008) were done with the very retrictive condition n ¼ n 2 ¼ and Dt ¼ Dt 2. In thi tudy, the coupled olver conerve their own time tep baed on tand-alone numerical tability. Moreover, the olver can integrate Eq. (6) with different number iteration n and n 2 between two update. To mimic the condition of the blade heat tranfer problem, the patial and time dicretization Dx i and Dt i are imilar to thoe of the Table Thermal characteritic of plexigla. Thermal conductivity k 0:84 W m K Heat capacity C 450 J kg K Denity q 90 kg m 3 Thermal diffuivity D : m 2 Table 2 Thermal characteritic of air at 328 K. Thermal conductivity k 2:6 0 2 Wm K Heat capacity C p 05 J kg K Denity q 0:266 kg m 3 Thermal diffuivity D f 9: m 2

5 F. Duchaine et al. / International Journal of Heat and Fluid Flow 30 (2009) computation with heat conduction olver for domain # and the LES code for domain #2. The dicretized heat flux ued for boundary condition are approximated with firt-order difference. After the ynchronization number n cpl in PCS (Fig. 2), the boundary condition applied to domain # and #2 during n and n 2 iteration, repectively are: 8 T i ;n cpl ; ¼ T b / i ;n cpl ;N ¼ / n cpl 2; þ hðt n 2;n cpl 2; T i ;n cpl >< ;N Þ T i 2;n cpl 2; ¼ T n ;n cpl ð8þ ;N T i 2;n cpl 2; ¼ T b2 >: with i ¼ ; n and i 2 ¼ ; n 2 where / n cpl 2; i the mean value of the heat flux / i 2;n cpl 2; at the interface in domain #2 over the n 2 iteration. Thi mean heat flux i introduced in the mixed condition due to the ue of a LES olver, intrinically non tationary, for target application Stability of the olid dicretization Before tudying the coupled problem P SCHT, let u conider only domain # to analyze the effect of the mixed boundary condition (Eq. (3)) on tability. Domain # i dicretized with Eq. (6). The mixed boundary condition i applied at x ¼ 0 and a Dirichlet condition on temperature at x ¼ b : 8 T i >< ; ¼ T b / i ;N ¼ / b þ hðt b T i ;N Þ ð9þ >: with i ¼ ; n In Eq. (9) / b ; T b and T b are contant heat flux and temperature. The vector of unknown U i introduced a: U ¼ ½T ; T ;N T b / b Š t ð20þ The contant T b and / b are introduced in the vector U at thi level of the tudy in order to prepare the notation ued during the analyi of the coupled problem P SCHT. The olution at time i Dt and ði þ ÞDt are linked by: U i þ ¼ M ðf ; hþu i ð2þ In Eq. (2), M ðf ; hþ i the dicretization operator of Eq. (6) augmented by boundary condition Eq. (9): 2 3 F 2F F.. M ðf ; hþ ¼. F F ð þ DÞ F D F D 6 h ð22þ where D i a Biot like number baed on the meh ize in domain Dx, the conductivity k and the coupling relaxation parameter h ued in Eq. (8): D ¼ hdx ð23þ k The value of the pectral radiu qðm ðf ; hþþ of the operator M ðf ; hþ determine the tability of the dicretization (Hirch, 988; Allaire and Craig, 2007). Indeed, a requirement for a table numerical cheme i: qðm ðf ; hþþ 6 ð24þ When the dimenion of matrix M ðf ; hþ i ufficiently mall (i.e. when the number of dicretization node N i mall), the eigen value of M can be expreed analytically. For N ¼ 4, the condition of tability (Eq. (24)) give a bounded region of tability for D: D 6 F3 2F2 þ 20F 8 3F 3 þ 8F2 4F ð25þ The tability limit of D i a function of the Fourier number F : above F ¼ 0:5, the cheme i alway untable a expected for an explicit formulation. When F goe to 0 (Dt tend to 0), the upper limit D u of D i : the cheme become unconditionally table. On the interval F 2Š0; 0:5Š, the u =@F i negative. The ue of larger time tep (increaing F ) reduce the range of D leading a table cheme. Decreaing D alo ha a poitive effect on convergence (ee Section 4.5) o that the optimum point for CHT in thi cae i F ¼ 0:5 and D ¼ 2:33. Fig. 3 compare the analytical evolution of D u given by Eq. (25) for F 2Š0; 0:5Š and numerical olution obtained with a dicrete procedure. The dicrete procedure i validated with the cae N ¼ 4(Fig. 3) and ued to meaure the enibility of the tability domain to N. Reult how that the curve D u ðf Þ weakly depend on the number of node N : the cae N ¼ 5 lead to the ame tability limit a N ¼ 4. When the number of node N increae, the optimal point for convergence peed goe to F ¼ 0:5 and D Stability analyi of the coupled dicretization Now that the tability of domain # with a mixed boundary condition ha been tudied, the tability of the coupled problem P SCHT i invetigated. Between the ynchronization n cpl and n cpl þ, olution U and U 2 of domain # and #2 are advanced in time uing dicretization operator M ðf ; hþ and M 2 ðf 2 Þ imilar to the definition given in Eq. (22): 8 >< >: U n cpl þ ¼ Qn M n¼ U n cplþ 2 ¼ Qn 2 M 2 n¼ U n cpl ¼ M n Un cpl U n cpl 2 ¼ M n 2 2 Un cpl 2 ð26þ where the number of iteration n and n 2 between two ynchronization event are linked to time-tep of domain # and #2: n ¼ a =Dt n 2 ¼ a 2 =Dt 2 ð27þ The characteritic time cale and 2 in Eq. (27) are choen in order to mimic the behavior of CHT of the turbine vane given in Table 5. Thu, ¼ q C b 2 k i a diffuion time in domain # while 2 i a convection time taken in the condition of the blade imulation. For the ame reaon, the time-tep Dt i obtained with a Fourier D u 00 Stable Untable F Fig. 3. Upper limit of tability D u for the dicretiation Eq. (22) a a function of Fourier Number F :, analytical olution for N ¼ 4; d, computed numerically with N ¼ 4;, computed numerically with N ¼ 5.

6 34 F. Duchaine et al. / International Journal of Heat and Fluid Flow 30 (2009) 29 4 number F equal to 0.5 while Dt 2 i of the order of the time-tep in LES computation, viz. F 2 << 0:5 (the CFL tability limit aociated to acoutic wave i uually much more retrictive than diffuion in compreible LES). Baed on Eq. (26), the dicretization of the whole ytem can be expreed a: U n cplþ ¼ Mða; hþu n cpl ð28þ where U i a compoition of the nodal temperature in the domain and heat fluxe at the interface. The value of the pectral radiu qðmða; hþþ of the operator Mða; hþ determine the tability of the dicretization (Hirch, 988; Allaire and Craig, 2007). Fig. 4 give the tability map of the operator Mða; hþ for a in ½0:00; 3Š and D ¼ hdx =k from 0 (Neumann boundary condition) to 2.3. Above a threhold D ¼ D m, the mixed condition i table. A hown on Fig. 4, D m i a function of a: if the CSTP i ufficiently mall ða < 0:02Þ, the Neumann condition i table. Then, until a ¼ 0:5, the value of D that enure numerical tability increae with a. Beyond thi point, D m remain approximatively contant when the CSTP increae. The tability domain i alo limited by an upper bound D M (Fig. 4). The limit of D M when a increae i D u 2 obtained during the tability analyi of domain # alone. A a ummary, the tability analye performed for a imple D problem have pointed out a tability domain in term of ða; DÞ where a tand for the frequency between two ucceive update of the coupled boundary condition and D ¼ hdx =k where h i a coupling relaxation factor defined in the mixed boundary condition (Eq. (3)). For a given value of the coupling ynchronization time parameter a, a range of h allow numerical tability of the coupled cheme. Thi range of CRP i bounded by an upper limit determined by the olid dicretization wherea the lower bound i linked to the coupling cheme. An important information not acceible from thee analye till mie: ince the aim of the film-cooled turbine vane imulation i to find a tationary thermal tate of the blade in a reduced computational time, it i crucial to undertand the effect of the CSTP a and of the CRP h on convergence. Section 4.5 preent enitivity analye obtained on the blade configuration when varying a and h. 0 Untable Stable 4. Application of the coupled trategy to the T20D blade Thi ection preent the application of the conjugate heat tranfer (CHT) trategy to the T20D blade. After decribing the configuration, an adiabatic computation i analyzed. It how the potential of the LES to predict accurately complex turbomachinery flow. Then, CHT reult are preented. Finally the performance of the CHT methodology i dicued. 4.. Decription of the T20D blade The T20 cacade were deigned by Roll Royce Deutchland for the European project AITEB (Haelbach and Schiffer, 2007) (Aerothermal Invetigation on Turbine Endwall and Blade). The experiment were conducted in the High-peed Cacade Wind Tunnel of the Intitute of Jet Propulion (Sturm et al., 985; Homeier et al., 2005; Gome et al., 2009). The highly-loaded high-preure turbine airfoil of the T20 cacade wa deigned in order to have a large eparation on the preure ide. Therefore the profile preent a trong concave curvature on the preure ide tarting hortly after the leading edge. Together with the high pitch to chord ratio relatively trong advere preure gradient are preent on the preure ide reulting in flow eparation. Typically for high-preure turbine blade, a high change of direction i impoed on the flow. The blade i deigned for high exit Mach number. The aerodynamical and geometrical data at deign condition are lited in Table 3. The film cooling device of the T20D blade i compoed of three jet row located on the preure ide in the region of the main flow eparation (Fig. 5). The firt row of jet i placed near the tagnation point and ha cylindrical hole with compound angle againt the main tream. Thi firt row i located to protect the leading edge region which ha the highet heat tranfer rate over the entire airfoil (Han et al., 2000). The econd jet row contain fan-haped hole with zero compound angle located at approximately 20% of the axial chord length. The econd row i uppoed to re-energize the boundary layer of the main tream and therefore reduce the flow eparation. A third row of cylindrical hole i placed at approximately 35% of the axial chord. Thi lat row lightly diminihe the eparation bubble on the preure ide. The temperature difference between the maintream ðt t ¼ 333:5 KÞ and cooling ðt t c ¼ 303:5 KÞ flow i limited to 30 K to facilitate meaurement. The blade i made of plexigla with a low conductivity of 0:84 W m K that make the CHT problem difficult to treat. Experimental reult include preure data on the blade uction and preure ide a well a temperature meaurement on the preure ide (Gome et al., 2009) Computational domain D Untable The computational domain for the fluid and the tructure contain one panwie pitch of the film cooling hole pattern corre- Table 3 Experimental etting for T20D blade α Fig. 4. Stability map in the ða; DÞ pace of the implified conjugate heat tranfer problem P SCHT (Eq. (6) and (8)):, lower tability limit D m; upper tability limit D M. a i the coupling ynchronization time parameter (Eq. (27)) and D i a function of the coupling relaxation parameter h (Eq. (23)). Poition of ome computation done on T20D blade (Section 4): point ða ; h 2Þ h; point ða 2; h Þ ; point ða 2; h 2Þ}and point ða 2; h 3Þ4. The parameter ða i; h jþ are given in Table 6. Blade height to chord ratio.5 Pitch to chord ratio.007 Turning Db 20 Inlet angle b 38 Inlet Mach number Ma Outlet Mach number Ma Outlet Reynold number Re 2 390,000 Inlet total preure P t 26737:0 Pa Inlet total temperature T t 333:5 K Cooling total preure P t c 2943:3Pa Cooling total temperature T t c 303:5 K Outlet tatic preure P Pa

7 F. Duchaine et al. / International Journal of Heat and Fluid Flow 30 (2009) the hole i a reult of the imulation. The kin mehe are the ame for the fluid and the olid o that no interpolation error i introduced at thi level when CHT i imulated. The computational domain for both fluid and olid part are conidered fine enough to ae the coupling methodology in a reaonable time Adiabatic computation of the T20D blade Fig. 5. Fluid computational domain. ponding to 8 mm along the z-axi (Fig. 5), with periodicity enforced on each ide. Thi implification neglect end-wall effect but retain the three-dimenionality of the flow and greatly reduce the number of tetrahedral cell required to model the blade: about 6.5 million cell for the fluid and 600,000 for the olid. For the fluid region, periodicity condition i alo aumed in the y- direction. Specific care i devoted to the tetrahedral cell iotropy in the wall region; the maximum value of grid pacing on the blade urface expreed in wall unit are about dx þ dy þ dz þ 40. In the dilution zone, grid pacing are maller than 5 wall unit. Such reolution are fine enough to capture major aerodynamic event at the wall reaonably well. The ize of one panwie pitch of hole pattern allow thee grid pacing with a moderate number of cell. A hown in Fig. 5, the three film-cooling hole and the plenum ued to inject the cooling air are alo included in the fluid domain. Hence, the ditribution of ma flow rate within The decription of the LES reult with adiabatic wall condition jutifie the ue of LES for CHT. The main flow tructure are firt emphaized before comparing computational reult and experimental data. Fig. 6 depict an intantaneou naphot of vorticity (left) and a field of mixture fraction howing the path of cooling air in the main tream (right). The LES predict an intene turbulence intenity and mixing in the region of the three jet. Downtream from the jet, the trong acceleration on the preure ide relaminarize the flow and force the cooling air againt the blade urface. At the beginning of the uction ide, the boundary layer i rather laminar. Then, the flow accelerate up to uperonic velocitie. A weak hock appear at a reduced abcia of about 0.75 and detabilize the boundary layer. Vortex hedding develop behind the blade. Fig. 7 how that jet, directly expoed to the main tream, mixe rapidly with hot gae. Protected by the concave hape of the blade and by the firt jet, the cooling air of the econd hole penetrate more into the flow until it mixe with the third jet. Jet 3 i aligned with the main tream and remain coherent until it impact the blade in a region between reduced abcia of The adiabatic LES reult are compared to the experiment in term of preure profile on the blade (Fig. 8) and of temperature profile on the preure ide (Fig. 9). Preure field are diplayed in term of ientropic Mach number M i ðxþ computed by: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 u 2 Ma i ðxþ ¼t 4 c P t P t w ðxþ!c c 3 5 ð29þ Fig. 6. Intantaneou naphot of (a) vorticity and (b) ditribution of cooling air within a cutting plane at contant z paing thought jet 2. The dahed line on (a) repreent the approximate poition of the hock at 75% of the axial chord.

8 36 F. Duchaine et al. / International Journal of Heat and Fluid Flow 30 (2009) 29 4 uction ide i not perfectly captured, the overall agreement between LES and experimental reult i fair. Table 4 compare numerical and experimental value of the total ma flow rate of air Q ¼ P j Q j pae through the three hole a well a of the blowing ratio M i of the jet. Proper decription of the ma flow rate and blowing ratio of each jet are crucial to predict heat tranfer with a good accuracy. LES give a good approximation of the total ma flow rate acro the hole. The numerical imulation alo give the ditribution of air among the three jet, not available experimentally. Since the total coolant preure i the ame for all three coolant row, the ma flow rate i almot equally ditributed between the hole. Blowing ratio are expreed in term of velocity U and denity q a: M j ¼ q j U j q U ; j ¼ ; 2; 3 ð30þ Fig. 7. Intantaneou iourface of temperature T ¼ 38 K: (a) z view and (b) y view. Ientropic Mach number Reduced abcia Fig. 8. Time-averaged ientropic Mach number (Eq. (29)) along the blade at preure probe location a a function of reduced abcia: d, adiabatic LES; h, experiment. where c i the ientropic coefficient, P t and Pt wðxþ are the total preure of the maintream and at the wall at location x. Fig. 8 diplay a time-averaged ditribution of ientropic Mach number obtained by LES and experimentally at tatic preure tap location. The flow trongly accelerate on the uction ide up to uperonic condition ðma i ðxþ > Þ and feature a weak hock at about 75% of the axial chord. On the preure ide, the flow i expoed to trong advere preure gradient hortly downtream of the tagnation point. The flow eparate at a reduced abcia of about 0.2 (poition of the econd jet) reattaching at about 0.45, after the third jet. After reattachment, the flow i trongly accelerated leading to value for the acceleration parameter that are beyond common relaminarization limit (Mayle, 99). Although the hock poition on the where j refer to jet quantitie and to local main tream value. Equal coolant ma flow Q j ¼ q j U j per hole i aumed for the determination of experimental blowing ratio of Table 4 and the LES validate thi hypothei. The agreement between experimental and numerical blowing ratio i rather good (Table 4). Wall temperature T t wðxþ are preented in Fig. 9 in term of cooling efficiency defined by: HðxÞ ¼ Tt Tt w ðxþ T t Tt c ð3þ where T t and Tt c are the total temperature at the inlet of the maintream and plenum, repectively. Time and panwie averaged cooling efficiencie for adiabatic LES and RANS computation a well a experimental reult are plotted a function of relative axial chord on Fig. 9. The RANS computation i done with Fluent uing a k x=sst turbulence model (Menter et al., 993). A expected, in the region of the jet (reduced abcia up to 0.45) the cooling efficiencie obtained with the adiabatic imulation are lower than the experimental value: adiabatic temperature field over-predict the real one. Downtream of the impact of the jet on the blade, the adiabatic LES fit the experimental level of H wherea the RANS computation over-etimate it. In the experience, the film of colder air that form after the interaction between the jet and the urface of the blade maintain the wall temperature cloe to adiabatic one. Hence, the LES capture fairly well the air ma flow through the jet a well a the mixing of the cooling air with the main tream. That i not the cae for the RANS imulation. Indeed, even if the RANS computation reproduce the real air ma flow rate ejected by the hole, the imulation doe not decribe mixing correctly. A a reult, the jet remain coherent on a too long ditance without mixing with the hot tream and too much cold air impact the blade urface. Both LES and RANS imulation exhibit a non-phyical peak of H near the trailing edge. Thi peak i due to an over-expanion near the trailing edge which doe not appear in the experiment. The round trailing edge of the T20D blade profile and a lack of reolution in thi region where there i a very trong acceleration of the flow caue thi difficulty in the computation (Denton et al., 999; Mei et al., 2005). From thee reult, LES appear to be a good candidate to treat CHT problem in complex turbomachinery flow Coupled computation of the T20D blade Thi ub-ection preent a fully coupled imulation of the T20D blade obtained with a two-tep methodology:

9 F. Duchaine et al. / International Journal of Heat and Fluid Flow 30 (2009) Cooling efficiency Reduced abcia Fig. 9. Time and panwie averaged cooling efficiency (Eq. (3)) veru abcia on the preure ide a a function reduced abcia: d, experiment from UNIBW; adiabatic LES; adiabatic RANS; coupled LES. Table 4 Ma flow rate of air through the three jet Q j and blowing ratio (Eq. (30)) of each jet M j of the T20D blade. Q ðg Þ Q 2 ðg Þ Q 3 ðg Þ Q ¼ P j Q j ðg Þ M M 2 M 3 Experiment LES Initialization of the coupled calculation that include: a converged adiabatic fluid imulation (preented in Section 4.3), a converged olid computation with impoed boundary temperature given by the adiabatic fluid olution, 2. Coupled imulation with a parallel coupling trategy (PCS on Fig. 2). The maximum value of the Biot meh number D ¼ hdx =k that give a table mixed condition for the olid dicretization of the blade (Eq. (3)) with a Fourier number of 0.5 i D u :8. The olid meh ize Dx ued to compute D u correpond to the dicretization ize at the fluid/olid interface (i.e. min Dx for the olid in Table 5). The conductivity of the olid media i given in Table. Iti intereting to note that the value D u 2 highlighted in Section 3.2 for D imple problem i a good approximation for the complex 3D problem. A a reult, the value of the coupling ynchronization time parameter a and of the coupling relaxation parameter h ued for the CHT imulation are choen o that the point ða; hþ belong to the tability domain of the imple D problem P SCHT (Fig. 4) preented in Section 3. Thee coupling parameter correpond to ða ; h 2 Þ in Table 6. Table 5 Minimum length, time-tep and characteritic time of fluid and olid dicretization for the T20D blade. Fluid Solid min Dx : m :4 0 4 m Dt 9: : : :6 The coupled imulation wa performed on 32 proceor of an IBM JS2. The ynchronization in CPU time (Eq. (2)) wa reached with 30 proceor allocated to the fluid olver and two for the olid one. The converged tate i obtained in 0 characteritic olid time cale (Fig. ) and require about 4800 CPU h. A a previou tudy on thi configuration ha hown that the preure ditribution over the blade i not affected by the coupling (Duchaine et al., 2008), the analyi focue on thermal apect. At the converged tate, the net heat flux through the blade reache zero (i.e. the mean temperature of the blade i tabilized, Fig. ). Fig. 9 how meaurement, adiabatic and coupled reult of the cooling efficiency HðxÞ panwie and time averaged along preure ide. A mentioned previouly, the adiabatic temperature field (olid line) over-predict the real one. The main contribution of conduction throughout the blade i to reduce the wall temperature on the preure ide and thu to increae HðxÞ (dot dahed line). The global form of the reduced temperature from the coupled imulation matche the experimental data correctly. Difference in the level are explained by the inufficient wall reolution ued for the LES computation a well a to the experimental difficultie and uncertaintie for temperature meaurement and proceing (i.e. panwie average). The trong acceleration caued by the blade induce large thermal gradient not-well reolved by the imulation that lead to an underetimation of the thermal fluxe a well a to non-phyical value of cooling efficiency at the trailing edge. Table 6 Value of the coupling ynchronization time parameter and coupling relaxation parameter ued in Section 4. a ¼ 0: a 2 ¼ 0:85 a 3 ¼ 5:00 h ¼ 50 h 2 ¼ 00 h 3 ¼ 200

10 38 F. Duchaine et al. / International Journal of Heat and Fluid Flow 30 (2009) 29 4 Fig. 0 compare experimental and numerical cooling efficiency field on a 2D plot of the preure ide. The computation matche the experimental viualization. Fig. 0 evidence the thermal effect of the cooling jet on the vane. Jet i folded back againt the urface by the main tream but detache rapidly and mixe with the hot gae due to the curvature of the blade. Downtream of the econd hole, a treak with higher efficiency and a pot with enhanced cooling cloe to the ejection location indicate a partially attached jet. A treak with a lower urface temperature i alo viible downtream of the third jet. Jet 3 eem to be the mot active in the cooling proce: it protect the blade from the hot tream until a reduced abcia of 0.5 and it impact the vane at reduced abcia between 0.5 and 0.6. The curvature of the preure ide induce a lack film coverage: the concave hape of the urface pread the cooling air laterally along the panwie direction, a explained by Schwarz and Goldtein (Schwarz and Goldtein, 989). Temperature [K] Reduced time 4.5. Efficiency analye of the coupled trategy Thi lat ub-ection analyze the efficiency of the coupling methodology with regard to the adjutable parameter ued in the boundary condition, the coupling ynchronization time parameter a and the coupling relaxation parameter h: 8 < : Fluid ðdirichletþ : T I;i f f ¼ T I ; i f ¼ ; n f Solid ðmixedþ : / I;i ¼ / I f þ hðti f TI;i Þ; i ¼ ; n ð32þ The number of iteration of fluid ðn f Þ and olid ðn Þ olver between two conecutive update of boundary condition are: n f ¼ a f =Dt f n ¼ a =Dt ð33þ In Eq. (33), Dt f and Dt are the time-tep of the fluid and olid olver, repectively. f and are characteritic time of the flow and olid phenomena. The different value ued for the CSTP a k and CRP h k in thi ection are ummarized in Table 6. A the implementation of SCS i impler than PCS, SCS i preferred for efficiency analye. A the formulation for SCS and PCS are different, it i ueful to check whether the implementation of thee trategie give the ame reult: Fig. compare SCSða ; h 2 Þ and PCSða ; h 2 Þ and how that both trategie converge to the ame thermal tate at the ame rate. A a reference for computational Fig.. Evolution of the mean temperature in the blade a a function of reduced olid time t = for SCSða ; h 2Þ and PCSða ; h 2Þ. The parameter ða ; h 2Þ are given in Table 6. A a reference for retitution time, one olid characteritic time require almot a total of 295 CPU h for the LES and the heat conduction olver on a SGI Altix ICE8200. cot and retitution time, one olid characteritic time require almot a total of 295 CPU h for the LES and the heat conduction olver on a SGI Altix ICE8200. To evaluate the impact of h in Eq. (32) on retitution time for the T20D CHT problem, three computation with SCS are compared: SCSða 2 ; h Þ, SCSða 2 ; h 2 Þ and SCSða 2 ; h 3 Þ (Table 6). Fig. 2a depict the evolution of the mean temperature in the blade a a function of reduced olid time t = for thee imulation. The retained value h, h 2 and h 3 with a 2 give table coupled cheme that converge to the ame thermal teady tate. Fig. 4 how that the prediction from the D problem P SCHT are not directly applicable to the complex 3D CHT cae: following the D analyi, the point ða 2 ; h 2 Þ and ða 2 ; h 3 Þ are table while the point ða 2 ; h Þ i not table. The convergence rate i influenced by the choice of the CRP: imulation converge fater for lower value of h (Fig. 2a). Indeed from h 3 to h the CPU time needed to reach a teady tate i divided by approximatively 2.5. A done for the CRP h, three computation with SCS are then compared to evaluate the effect of the CSTP a in Eq. (33) on convergence: SCSða ; h 2 Þ, SCSða 2 ; h 2 Þ and SCSða 3 ; h 2 Þ (Table 6). Fig. 2b how the evolution of the mean temperature in the blade a a function of reduced olid time t = for thee imulation. The Fig. 0. 2D plot of time averaged cooling efficiency on the preure ide: comparion of experimental reult and coupled imulation. The cale of H correpond only to the LES field.

11 F. Duchaine et al. / International Journal of Heat and Fluid Flow 30 (2009) a 38 b 38 Temperature [K] Temperature [K] Reduced time Reduced time Fig. 2. Evolution of the mean temperature in the blade a a function of reduced olid time t = for (a) SCSða 2; h Þ, SCSða 2; h 2Þ and SCSða 2; h 3Þ ; and for (b) SCSða ; h 2Þ, SCSða 2; h 2Þ and SCSða 3; h 2Þ. The parameter ða i; h jþ are given in Table 6. A a reference for retitution time, one olid characteritic time require almot a total of 295 CPU h for the LES and the heat conduction olver on a SGI Altix ICE8200. numerical cheme obtained with a ; a 2 and a 3 combined with h 2 are table and converge to the ame thermal teady tate. Fig. 2b how that the choice of the CSTP directly affect the convergence rate of the coupled imulation. Small value of a enhance the retitution time of the computation: high update frequencie of interface variable allow the computation to follow the teepet decent to converged tate. To conclude, good convergence rate are obtained for mall value of both the CSTP a and CRP h within the tability domain. When a i ufficiently mall, SCS become inefficient compared to PCS. Indeed, below a certain value of the CSTP, the computational time due to the reolution of fluid and olid equation i maller than the management time due to launching of the code a well a initialization and finalization of the computation (reading of mehe and initial olution, writing of final olution...). PCS allow to avoid thee retart tep and i therefore recommended. It i alo important to note that when the CSTP a become too mall (i.e. decreaing the number of iteration of the olver), the execution time of the fluid and olid olver between two ucceive update of boundary condition can become lower than the time requeted to data exchange. Such a configuration i not acceptable for the efficiency of the method and a balance i needed to fix the CSTP. 5. Concluion The thermal load on ga turbine component control life-time of the ytem. Numerical prediction of conjugate heat tranfer raie problem which make the imulation difficult to compute: the flow are very complex: three-dimenional unteady turbulent effect, mixing of flow with different propertie, high peed with compreibility effect (with large variation of Mach number up to uperonic condition), ditinct phyic mut be coupled with very different length and time cale, the ize of the computation require parallel computation to reduce retitution time. In the preent tudy, a coupling trategy for conjugate heat tranfer with Large Eddy Simulation (LES) i propoed and applied to a film-cooled turbine vane experimentally teted at the Intitute of Jet Propulion. The methodology i baed on a partitioned approach: a LES olver exchange information with a heat tranfer code within olid via a upervior. It i hown that the LES olver i well adapted to capture the flow that develop around the filmcooled turbine blade. The coupling methodology i firt aeed in term of tability and efficiency. At the fluid/olid interface, a mixed condition on wall temperature and heat fluxe i written baed on a coupling relaxation parameter h. A tability analyi on a implified onedimenional problem allow the determination and optimization of coupling parameter. Two parameter control both the tability and cot of the coupled imulation: the meh Biot number of the olid domain D ¼ hdx =k (where Dx and k are, repectively, the olid dicretization and the olid conductivity) and the coupling ynchronization time parameter a which defined the time between two coupling event. The coupled tool i ported on maively parallel architecture and applied to an experimental film-cooled turbine vane. Reult demontrate both the efficiency of the parallel implementation and the quality of the reult. Thermal convergence of the blade i accelerated by high frequencie of exchange between the code (mall value of the coupling ynchronization time parameter a). Coupled and non-coupled imulation are compared to experimental reult and dicued in term of cooling efficiency and flow tructure. The comparion between adiabatic LES and meaurement i good for the ientropic Mach number along the blade. Reaonable aerodynamic prediction are a neceary condition to reproduce the blade kin temperature field. A the LES computation give a correct air flow ditribution within the cooling ytem and reproduce the mixing between the hot tream and the cooling flow, the trend of computed cooling efficiency agree reaonably well with experimental data. Dicrepancie in the level are mainly due to a lack of reolution in the fluid flow near the wall. Finally, the coupled imulation i ued to decribe the role of the three row of cooling jet in heat tranfer. Further tudie will concern the analyze of meh reolution a well a the ue of thermal wall model to enhance thermal prediction. The effect of the number of panwie pitch of the film cooling hole pattern including jet to jet interaction will alo be invetigated.

12 40 F. Duchaine et al. / International Journal of Heat and Fluid Flow 30 (2009) 29 4 Acknowledgement A large part of numerical imulation have been conducted on the computer of the French National Computing Center (CINES) in Montpellier. Part of thi work wa performed at the 2008 Stanford CTR Summer Program. The help of R. Gome from the Univerity of the Federal Armed Force Munich and of the AITEB- and AITEB-2 conortium who provided experimental reult i gratefully acknowledged. Dr. N. Lamarque i gratefully acknowledged for the variou dicuion on numeric. Reference Acharya, S., Tyagi, M., Hoda, A., 200. Flow and heat tranfer prediction for film cooling, heat tranfer in ga turbine ytem. Annal. NY Acad. Sci. 934, Allaire, G., Craig, A., Numerical Analyi and Optimization: An Introduction to Mathematical Modelling and Numerical Simulation. Oxford Univerity Pre. Alono, J.J., Hahn, S., Ham, F., Herrmann, M., Iaccarino, G., Kalitzin, G., LeGreley, P., Matton, K., Medic, G., Moin, P., Pitch, H., Schlüter, J., Svard, M., der Weide, E., You, D., Wu, X., CHIMPS: a high-performance calable module for multiphyic imulation. In: 42nd AIAA/ASME/SAE/ASEE Joint Propulion Conference & Exhibit, AIAA-Paper Azzi, A., Lakehal, D., Perpective in modeling film cooling of turbine blade by trancending conventional two-equation turbulence model. J. Turbomach. 24, Bohn, D., Ren, J., Kuterer, K., Sytematic invetigation on conjugate heat tranfer rate of film cooling configuration. Int. J. Rotating Mach (3), Boudier, G., Gicquel, L.Y.M., Poinot, T., Biière, D., Bérat, C., Comparion of LES, RANS and experiment in an aeronautical ga turbine combution chamber. Proc. Combut. Int. 3, Bui, S., Piacentini, A., Déclat, D., PALM: a computational framework for aembling high performance computing application. Concurr. Comput. 8 (2), Bunker, R.S., Ga turbine heat tranfer: ten remaining hot ga path challenge. J. Turbomach. 29, Burnett, D.S., 98. Finite Element Analyi. Addion-Weley. Chaaing, P., Turbulence en mécanique de fluide, Analye du phénomène en vue de a modéliation à l uage de l ingénieur, Cépaduè-édition, Touloue, France. Chemin, S., Étude de Interaction Thermique Fluide-Structure par un Couplage de Code de Calcul. Ph.D. Thei, Univerité de Reim Champagne- Ardenne. Colin, O., Rudgyard, M., Development of high-order Taylor Galerkin cheme for unteady calculation. J. Comput. Phy. 62 (2), Comte, P., 996. New Tool in Turbulence Modelling. Vortice in Incompreible LES and Non-Trivial Geometrie, Howpublihed Springer-Verlag, France (Notecoure of Ecole de Phyique de Houche). Denton J., Dawe W.N., 999. Computational fluid dynamic for turbomachinery deign. In: Proceeding of the Intitution of Mechanical Engineer, M.E. Publication, London, United Kingdom. Part C, Journal of Mechanical Engineering Science 23 (2), doi:0.243/ issn Divo, E., Steinthoron, E., Kaab, A., Bialecki, An iterative BEM/FVM protocol for teady-tate multi-dimenional conjugate heat tranfer in compreible flow. Eng. Anal. Bound. Elemen. 26 (5), Donea, J., Huerta, A., Finite Element Method for Flow Problem. John Wiley & Son Inc., New York. do Santo, R.G., Lecanu, M., Ducruix, S., Gicquel, O., Iacona, E., Veynante, D., Coupled large eddy imulation of turbulent combution and radiative heat tranfer. Combut. Flame 52 (3), Duchaine, F., Mendez, S., Nicoud, F., Corpron, A., Moureau, V., Poinot, T., Coupling heat tranfer olver and large eddy imulation for combution application. In: Center for Turbulence, Center for Turbulence Reearch, NASA Ame/Stanford Univ., pp Ducro, F., Comte, P., Leieur, M., 996. Large-eddy imulation of tranition to turbulence in a boundary layer developing patially over a flat plate. J. Fluid Mech. 326, 36. Dunn, M.G., 200. Convective heat tranfer and aerodynamic in axial flow turbine. J. Turbomach. 23, Erlebacher, G., Huaini, M.Y., Speziale, C.G., Zang, T.A., 992. Toward the large-eddy imulation of compreible turbulent flow. J. Fluid Mech. 238, Felippa, C.A., Park, K.C., Farhat, C., 200. Partitioned analyi of coupled mechanical ytem. Comput. Method Appl. Mech. Eng. 90 (24 25), Ferziger, J.H., 977. Large eddy imulation of turbulent flow. AIAA J. 5 (9), Ganean, V., Non-reacting and reacting flow analyi in an aero-engine ga turbine combutor uing CFD. In: SAE 2007 World Congre, , Detroit, Michigan, USA. Garg, V.K., Heat tranfer reearch on ga turbine airfoil at NASA GRC. Int. J. Heat Fluid Flow 23 (2), Germano, M., 992. Turbulence: the filtering approach. J. Fluid Mech. 238, Ghoal, S., Moin, P., 995. The baic equation for the large eddy imulation of turbulent flow in complex geometry. J. Comput. Phy. 8, Gile, M.B., 997. Stability analyi of numerical interface condition in fluidtructure thermal analyi. Int. J. Numer. Meth. Fluid 25 (4), Gome, R.A., Niehui, R., Film cooling effectivene meaurement with periodic unteady inflow on highly loaded blade with main flow eparation. In: Proceeding of ASME Turbo Expo 2009: Power for Sea, Land and Air, Orlando, Florida, USA. Han, J.C., Dutta, S., Ekkad, S.V., Ga Turbine Heat Tranfer and Cooling Technology. Taylor & Franci, New York, NY, USA. Han, Z.X., Denni, B., Dulikravich, G., 200. Simultaneou prediction of external flow-field and temperature in internally cooled 3-D turbine blode material. Int. J. Turbo Jet-Eng. 8, Haelbach, F., Schiffer, P., AITEB an european reearch project on aerothermodynamic of turbine endwall and blade. Int. J. Therm. Sci. 3 (2), Hegab, A., Jackon, T.L., Buckmater, J., Stewart, D.S., 200. Nonteady burning of periodic andwich propellant with complete coupling between the olid and ga phae. Combut. Flame 25 ( 2), Heidmann, J.D., Kaab, A.J., Divo, E.A., Rodriguez, F., Steinthoron E., Conjugate heat tranfer effect on a realitic film-cooled turbine blade. In: Proceeding of ASME Turbo Expo 2003, ASME Paper GT , Atlanta, Georgia, USA. Heelhau, A., Vogel, D.T., 995. Numerical imulation of turbine blade cooling with repect to blade heat conduction and inlet temperature profile. In: ASME, SAE, and ASEE, Joint Propulion Conference and Exhibit, 3t, AIAA , San Diego, CA, USA. Hirch, C., 988. Numerical Computation of Internal and External Flow, vol.. John Wiley, New York. Homeier, L., Haelbach, F., Film cooling of highly loaded blade. In: XVIII International Sympoium on Air Breathing Engine (ISABE), AIAA , Munich, Germany. Kao, K.H., Liou, M.S., 997. Application of chimera/untructured hybrid grid for conjugate heat tranfer. AIAA J. 35 (9), Lagarde, T., Piacentini, A., Thual, O., 200. A new repreentation of data-aimilation method: the PALM flow-charting approach. Q.J.R. Meteorol. Soc. 27 (57), Lakhminarayana, B., 996. Fluid Dynamic and Heat Tranfer of Turbomachinery. John Wiley & Son, Inc., New York, NY, USA. Lefebvre, A.H., 999. Ga Turbine Combution. Taylor & Franci, Berlin. Lilly, D.K., 992. A propoed modification of the germano ub-grid cloure method. Phy. Fluid 4 (3), Luo, J., Razinky, E.H., Conjugate heat tranfer analyi of a cooled turbine vane uing the V2F turbulence model. J. Turbomach. 29 (4), Maheh, K., Contantinecu, G., Moin, P., A numerical method for large-eddy imulation in complex geometrie. J. Comput. Phy. 97 (), ISSN in Mayle, R.E., 99. The role of laminar turbulent tranition in ga turbine engine. J. Turbomach. 3, Mei, Y., Guha, A., Implicit numerical imulation of tranonic flow through turbine cacade on untructured grid. In: Publihing, P.E. (Ed.), Proc. Int. Mech. Eng. Part A: J. Power Energy, vol. 29. Bury St. Edmund, United Kingdom, pp Mendez, S., Nicoud, F., Large-eddy imulation of a bi-periodic turbulent flow with effuion. J. Fluid Mech. 598, Meneveau, C., Lund, T., Cabot, W., 996. A lagrangian dynamic ubgrid-cale model of turbulence. J. Fluid Mech. 39, 353. Menter, F.R., 993. Zonal two equation k w turbulence model for aerodynamic flow. In: Fluid Dynamic, Plamadynamic, and Laer Conference, 23rd, AIAA , Orlando, FL, USA. Mercier, E., Tee, L., Savary, N., D full predictive thermal chain for ga turbine. In: 25th International Congre of the Aeronautical Science, Hamburg, Germany. Moin, P., Squire, K.D., Cabot, W., Lee, S., 99. A dynamic ubgrid-cale model for compreible turbulence and calar tranport. Phy. Fluid A 3 (), doi:0.063/ Montenay, A., Paté, L., Duboué, J.M., Conjugate heat tranfer analyi of an engine internal cavity. In: Proceeding of ASME Turbo Expo 2000, ASME Paper 2000-GT-282, Munich, Germany. Moureau, V., Lartigue, G., Sommerer, Y., Angelberger, C., Colin, O., Poinot, T., Numerical method for unteady compreible multi-component reacting flow on fixed and moving grid. J. Comput. Phy. 202 (2), doi:0.06/ j.jcp Nicoud, F., Ducro, F., 999. Subgrid-cale tre modelling baed on the quare of the velocity, gradient. Flow Turb. Combut. 62 (3), doi:0.023/ A: Papanicolaou, E., Giebert, D., Koch, R., Schulz, A., 200. A conervation-baed dicretization approach for conjugate heat tranfer calculation in hot-ga ducting turbomachinery component. Int. J. Heat Ma Tranfer 44 (8), Poinot, T., Lele, S., 992. Boundary condition for direct imulation of compreible vicou flow. J. Comput. Phy. 0 (), doi:0.06/ (92) Poinot, T., Veynante, D., Theoretical and Numerical Combution, econd ed. R.T. Edward. Pope, S.B., Turbulent Flow. Cambridge Univerity Pre.

13 F. Duchaine et al. / International Journal of Heat and Fluid Flow 30 (2009) Radenac, E., Développement et validation d une méthode numérique pour le couplage fluide tructure en aérothermique intationnaire. Ph.D. Thei, Univerité Paul Sabatier Touloue. Rahman, F., Vier, J.A., Morri, R.M., Capturing udden increae in heat tranfer on the uction ide of a turbine blade uing a Navier Stoke olver. J. Turbomach. 27 (3), Roe, B., Jaiman, R., Haelbacher, A., Geubelle, P.H., Combined interface boundary condition method for coupled thermal imulation. Int. J. Numer. Meth. Fluid 57 (3), Roux, A., Gicquel, L.Y.M., Sommerer, Y., Poinot, T.J., Large eddy imulation of mean and ocillating flow in a ide-dump ramjet combutor. Combut. Flame 52 ( 2), Rozati, A., Large Eddy Simulation of Leading Edge Film Cooling: Flow Phyic, Heat Tranfer, and Synga Ah Depoition. Ph.D. Thei, Virginia Polytechnic Intitute and State Univerity. Sagaut, P., Large Eddy Simulation for Compreible Flow. Scientific Computation Serie. Springer-Verlag. Schiele, R., Wittig, S., Ga turbine heat tranfer: pat and future challenge. J. Prop. Power 6 (4), Schönfeld, T., Poinot, T., 999. Influence of boundary condition in LES of premixed combution intabilitie. In: Center for Turbulence Reearch, Center for Turbulence Reearch, NASA Ame/Stanford Univ., pp Schwarz, S.G., Goldtein, R.J., 989. The two-dimenional behavior of film cooling jet on concave urface. J. Turbomach., Smagorinky, J., 963. General circulation experiment with the primitive equation:. The baic experiment. Mon. Weather Rev. 9, Sondak, D.L., Dorney, D.J., Simulation of coupled unteady flow and heat conduction in turbine tage. J. Prop. Power 6 (6), Sturm, W., Fottner, L., 985. The high-peed cacade wind-tunnel of the German armed force Univerity Munich. In: 8th Sympoium on Meauring Technique for Tranonic and Superonic Flow in Cacade and Turbomachine, Genova, Italy. Vertraete, T., Alalihi, Z., den Braembuche, R.A.V., Numerical tudy of the heat tranfer in micro ga turbine. J. Turbomach. 29 (4), Vreman, B., Geurt, B., Kuerten, H.H., 994. On the formulation of the dynamic mixed ubgrid-cale model. Phy. Fluid 6 (2),