Proceedings of the ASME/JSME th Thermal Engineering Joint Conference LARGE EDDY SIMULATION OF FILM COOLING WITH SWIRLING COOLANT FLOW

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1 Proceedigs of the ASME/JSME th Thermal Egieerig Joit Coferece AJTEC2011 March 13-17, 2011, Hoolulu, Hawaii, USA Proceedigs of the ASME/JSME th Thermal Egieerig Joit Coferece AJTEC2011 March 13-17, 2011, Hoolulu, Hawaii, USA AJTEC AJTEC LARGE EDDY SIMULATION OF FILM COOLING WITH SWIRLING COOLANT FLOW Yutaa Oda Osaa Uiversity Suita, Osaa, Japa Keichiro Taeishi Osaa Uiversity Suita, Osaa, Japa Dai Shimizu Osaa Uiversity Suita, Osaa, Japa ABSTRACT LES (Large Eddy Simulatio) of a film coolig with a swirlig coolat jet has performed for a circular hole at the blowig ratios of M = 0.5 ad 1.0. For the LES of film coolig flows, a film-hole model based o a RFG (Radom Flow Geeratio) techique was proposed to simulate turbulet fluctuatig flows at the exit plae of film coolig hole as a boudary model. As a result, film coolig with a swirlig coolat jet is cofirmed to be effective to reduce et heat trasfer from the hot gas to the wall at give uiform temperature coditios by about 6% ad 12% at the blowig ratio of M = 0.5 ad 1.0, respectively, compared to oswirlig cases. I a swirlig film coolat jet case at M = 1.0, peetratio of coolat jet is suppressed. It seems that oe of the two jet core regios is pressed agaist the bottom wall by the primary swirl of the coolat jet itself, ad this seems to prevet the detachmet of the film coolat from the wall. I additio, the proposed film-hole model for LES was validated by the compariso of predicted ceter-lie film effectiveess with a ow experimetal result. INTRODUCTION Gas turbies are used for aircraft propulsio ad ladbased power geeratio. Developmets i turbie coolig techology play a critical role i icreasig the thermal efficiecy ad power output of advaced gas turbies. Gas turbie s vaes ad blades are cooled exterally by film coolig. It is achieved by ijectig relatively cooler air (film coolat) from the iteral coolat passages out of the blade surface i order to form a protective layer betwee the blade surface ad hot gas-path flow. The iteractio betwee the film coolat ad maistream forms a shear layer, where the mixig of them occurs ad leads to the decay of the film coolig performace alog a blade surface. It is importat for film coolig to improve the coolig efficiecy with a allowable coolat flow rate, because the excess use of the coolat ca result i the decrease of thermal efficiecy of gas turbies. Thus, it is required for ew film coolig techiques to achieve wider ad loger coverage of the coolat with a miimum coolat flow rate. Whe simplest circular holes are employed, it is ow that the film coolat ofte peetrates ito maistream ad geerates a pair of idey-shaped vortices by the iteractio betwee maistream ad film coolig jet. The dowwash of the vortices etrais the hot maistream below the film coolat jet, ad drastically decreases the film coolig effectiveess o turbie blade surfaces. Thus, shaped film coolig has bee oe of the most attractive ivetios by icorporatio of the exit shapig to the film holes, which results i lower mometum coolat ijectio jets with greater surface coverage. There have bee so may studies o film coolig. A review paper by Goldstei [1] summarized early wors i this area ad Bogard ad Thole [2] reviewed latest oe. Early ivestigatios o film coolig were flows blowig through iclied discrete holes icludig Erise ad Goldstei [3] ad Bersdorf et al. [4]. The efforts to improve film coolig efficiecy by adoptig film coolig holes with expaded exits have bee made experimetally by Goldstei ad Ecert [5], Bell et al. [6], Taeishi ad Aoi. [7] ad Yu et al. [8]. Excellet summary paper o shaped film coolig was published by Baer [9]. Several ew ideas to cotrol ati-idey vortex structure are preseted. Kusterer et al. [10] ivestigated two film coolig arragemet with differet compoud agles, ad Heidma [11] proposed additioal coolig air jets i a circular film coolig hole to cotrol ad to crash the idey type vortex. Kuya et al. [12] studied the effect of swirled film coolig air o film coolig effectiveess by usig a twisted tape i a circular coolig hole ad foud the improvemet of film coolig effectiveess with swirlig coolat flow. But, there was o descriptio ad experimetal results to uderstad the mechaism of the film coolig with swirlig flow. Recetly, Taeishi, et al. [13] has iveted a ew film coolig techique, i which some swirlig motio was added to the coolat flow iside the guide chael with a simpler ad realistic method tha that with a twisted tape. Their PSP (Pressure Sesitive 1 Copyright 2011 by ASME

2 FIGURE 1. WIND TUNNEL AND CLOSE-UP OF TEST SECTION EQUIPPED WITH A CIRCULER FILM HOLE, GUIDE CHANNEL, AND PLENUM WITH TWO SLUNT JETS TO PRODUCE SWIRL MOTION OF FILM COOLANT Pait), LIF ad PIV measuremets of the film coolig effectiveess ad flow fields have demostrated that this ew film coolig method ca improve the coolig efficiecy both i circular ad shaped film coolig holes, by prevetig the peetratio of the coolat i circular holes ad by achievig the effective diffuse of the coolat at the hole exit i shaped holes. I this study, large eddy simulatio was performed to examie the detailed iteractio mechaism betwee the hot maistream ad the swirlig coolat flows over the vae s surface. Especially, the effect of the swirlig motio i the coolat o the covective heat trasfer coefficiet was examied uder the uiform wall temperature coditio, which was ot cosidered i the previous experimets [13]. To the distace dowstream the film coolig hole, where the coolat temperature is still less tha that of wall, ehaced covective heat trasfer by the swirlig is cosidered to be preferable, while it will become uprofitable after the coolat temperature reaches the wall temperature. The effectiveess of our ew film coolig techique will be discussed i view of film coolig effectiveess ad covective heat trasfer rate, which are both importat i the real gas turbies. FILM COOLING WITH A SWIRL OF COOLANT JET As show i Fig. 1, experimet by Taeishi, et al. [13] was coducted usig a scale-up model of a film coolig hole istalled o the bottom surface of a low-speed wid tuel. The test sectio is 300 mm wide, 300 mm height, ad 1950 mm log. A film coolig hole is located 950 mm dowstream from the exit of the cotractio sectio. The geometry of circular film coolig hole is similar as that used by Taeishi ad Aoi [7]. The guide chael to the exit of film coolig hole was iclied at 30º toward the mai flow directio. The diameter of the guide chael, d, was 5 mm. Swirlig motio of film coolat was iduced iside a hexagoal pleum by two slat jets, which are iclied at degree toward the vertical directio ad istalled i a staggered positio as show i Fig. 1. The two jets geerate swirlig flows iside the pleum, ad this swirlig flow eters ito a guide chael eepig the agular mometum util the exit of film coolig hole. The slat agle of the jets was chaged as = 0º, 10º, 20º, 30º i their wid tuel tests. The experimetal coditios are show i Tab. 1. The hexagoal structure of pleum was desiged with a cocept to juxtapose them without void space, because the two jets also act as impigig jets to cool the iteral surface of the edwall. By this structure, the iteral pressure of the pleum ca be locally adjustable to eep a optimal coolat flow rate uder differet exteral pressure coditios, which depeds o the edwall locatio i real gas turbies. I the experimets, spatial distributios of film coolig effectiveess were measured o the bottom wall (y/d = 0) by PSP ad at some cross sectios (x/d = 0, 2, 4 ad z/d = 0) by TABLE 1. CONDITIONS IN EXPERIMENTS AND LES Experimet [13] LES Maistream velocity, U 20 m/s Turbulet itesity 0.36% Boudary layer thicess, 25 mm Film hole diameter, d 5 mm Blowig ratio, M = c u c / u 0.5, 1.0, 1.5, , 1.0 Slat agle of the two jets, 0º, 10º, 20º, 30º 0º, 30º LIF. The film coolig effectiveess ca be defied as follows, based o heat ad mass trasfer aalogy. C C) ( C C ) ( T T ) ( T T ) (1) ( c c where C is cocetratio of oxyge ad acetoe i PSP ad LIF, respectively. PIV measuremet of velocity fields was also coducted at x/d = 0, 2, 4 ad z/d = 0. The detail of experimetal procedure was show i the referece [13]. LARGE EDDY SIMULATIONS I this study, LES (Large Eddy Simulatio) was performed to simulate film coolig flows with a swirlig coolat jet i the 2 Copyright 2011 by ASME

3 modes, i.e. the sum of sie ad cosies with radom phases ad amplitude. The first step i recostructio of fluctuatig velocity field is to fid a orthogoal trasformatio tesor a ij that would diagoalize a give Reyolds stress tesor r ij. a mi a j r ij = m c 2 () (2) a i a j = ij (3) where c () = {c 1, c 2, c 3 } are the square root of eigevalues of Reyolds stress tesor, ad thus they play the role of turbulet fluctuatig velocities i the pricipal axis coordiates produced by trasformatio tesor a ij. The, a itermediate velocity v i are costructed as follows: FIGURE 2. COMPUTATIONAL DOMAIN FOR PRELIMINARY 3-D RANS SIMULATIONS TO OBTAIN TURBULENCE STATISTICS AT THE EXIT OF FILM COOLING HOLE [18] above-metioed experimets. For the simulatio of film coolig flows, it is regarded as ecessary to iclude the whole structures of the test sectio i the computatioal domai, that is, a film hole, a guide chael, ad a pleum sectios should be icluded i the preset case as show i Fig. 2. This is because the iteral flow i the pleum ad the guide chael determies the velocity distributio iside the film coolig hole, i.e., the velocity profile at the exit plae of film hole, which gives a sigificat effect o the exteral flows where the mixig of maistream ad film coolat jet occurs. Thus, a reliable approach for LES of film coolig flows geerally icludes the whole structure i the computatioal domai. Ustructured or multi-bloc structured grid ca be applied to this id of complex geometry. I this study, however, aother method is proposed to facilitate LES of film coolig flows with o sigificat sacrifices of predictio capability of the relevat turbulet flows. I this method, oly the mai flow regio above the exit plae of film coolig hole is icluded i the computatioal domai. The film coolat jet ejected from the coolig hole is modeled by a boudary model (what we call a film-hole model for LES) to give a iflow boudary coditio, which is based o RFG (Radom Flow Geeratio) method by Smirov, et al. [14] to geerate realistic fluctuatig velocities of turbulet flows. The RFG procedure of Smirov, et al. is a modified versio of Kraicha s method [15], ad ivolves scalig ad orthogoal trasformatio operatios applied to a cotiuous flow-field geerated as a superpositio of radom Fourier N p j j i cos( ˆ j xˆ tˆ) q i si( ˆ j xˆ tˆ) 2 vi ( x, t) N 1 xˆ j 2x j L, tˆ 2t, V L, ˆ j jv c( j) (5) i p i i ij j d, q i ij j (4) d (6),, N(0,1), j N(0,1/2) (7) where L, ad V are the legth, time ad velocity-scales of turbulece, ij is the permutatio tesor used i vector product operatio ad N(M, ) meas a ormally distributed radom variable with mea M ad stadard deviatio. Numbers j, represet a sample of wave-umber vectors ad frequecies of the modeled turbulece spectrum below. 1/ 2 4 E( ) 16(2 ) exp( 2 ) (8) Fial fluctuatig velocities will be obtaied by applyig a scalig ad orthogoal trasformatio to the itermediate velocity field v i after the scalig by a factor of c (i). w i = c (i) v (i) (9) u i = a i w (10) Iflow boudary coditios of LES with RFG procedure require r ij, ad V as iput data i additio to averaged velocity U i at grid poits of the boudary. These iputs ca be obtaied or estimated by experimets ad prelimiary simulatios usig RANS, LES, ad DNS. I egieerig-orieted problems lie film coolig flows i gas turbies, RANS simulatios are easily available for this purpose. It is worth otig that the RFG procedures [15] or its simplified versio by Batte, et al. [16] also require Reyolds stress r ij to be realizable i a sese that c 2 () must be positive (or zero) i orthogoal trasformatio by Eq. (2), or i Cholesy decompositio of r ij i the Batte s method. However, realizability of Reyolds stress is ot always satisfied i RANS simulatios, especially i complex turbulet flows at the exit regio of film coolig holes. 2 3 Copyright 2011 by ASME

4 Therefore, i this study, Durbi s costrait [17] o timescale of turbulece,, was applied to esure the realizability of Reyolds stress r ij as iput for the above RFG procedure. Thus, r ij is estimated at the film-hole exit by the followig equatios. r ij = 2 t S ij + (2/3) ij (11) t = C V) mi,, V = 1/2 (13) 2 2 3V C 8 S ij where S ij, ad are the strai rate tesor, turbulece ietic eergy ad turbulece dissipatio rate, respectively, ad C is a model costat beig Cosequetly, the proposed filmhole model for LES requires S ij, ad as iput data. This provides flexibility i the choice of RANS models or methods of data acquisitio i experimets. Thus, i this study, iput data at the film-hole exit were obtaied from a prelimiary 3-D RANS aalysis with a - realizable model [18], which icludes all structure of the test sectio as show i Fig. 2. For the ilet coditio of maistream domai, the RFG procedure was also used to simulate turbulet boudary layer flows i wid tuel tests. Based o the boudary layer thicess measured by the Pitot tube i the wid tuel experimets, the iput data are extracted from the computed plae where the boudary layer thicess reaches 20 mm i 2-D RANS simulatio of a parallel plate chael. The umber of modes was set at N = 200 to esure the resultig statistics is idepedet of N [19]. I the above umerical procedure, followig filtered coservatio equatios of mass, mometum ad eergy were solved i the geeral coordiate system. 1 JU 0 J u i 1 JU ui P l ui t J l x i J 1 2 ej Dij J x j (14) (15) T 1 JU T l T 1 T l ej (16) t J J J x j x j l l J xm xm, 3 J, e e PrSGS l l 1 u i u j D ij 2 x l l j xi Sub-grid scale (SGS) stress was based o the eddy viscocity cocept ad the SGS eddy viscosity e was give by Mixed- Time-Scale (MTS) model by Iagai, et al. [20] as follows. (17) e CMTS ests CT S es D ij T (18) es u u 2 (19) ˆ The model parameters, C MTS ad C T, are set to 0.05 ad 10. The otatio, ( ˆ ), deotes the filterig operator, for which the Simpso rule is adopted. is a grid filter width. For temperature fields, SGS heat flux was modeled usig the costat SGS Pradtl umber of 0.5. Note that iematic pressure P i Eq. (15) is defied as P/ + ii /3, icludig the diagoal compoets of the residual stress. The goverig equatios are solved with a fiite differece method o a collocated grid system. Spatial derivatives are basically approximated by a coservative secod-order cetral differeces except for the covective terms i Eqs. (15) ad (16), to which Roe s superbee flux limiter [21] was applied. For time itegratio, a fractioal step method was used with the secod-order Adams-Bashforth method. The dimesios of a simple rectagular domai of the preset LES are 10 < x/d < 40, 0 < y/d < 15, ad 12 < z/d < 12 i stream-wise, height-wise, ad spa-wise directios, respectively, where the coordiate origi is located at the dowstream ed of film coolig hole. A orthogoal structured grid was employed, ad the umbers of grid poits were i x, y ad z directios, respectively. Time step was set at t = sec. At the grid poits iside the film coolig hole, bi-liear iterpolatio of required iput for RFG was employed betwee the body-fitted grids i 3-D RANS ad the orthogoal grids i LES. For other boudaries, a periodic coditio was employed i spawise (z) directio. No-slip coditio is applied o the wall at y = 0, with a Neuma coditio for pressure. The symmetric coditio was applied at y/d = 15. At the outflow plae at x/d = 40, the covective outflow coditio was applied to all variables icludig P. U for = u, v, w or T (20) t x P P P P U U (21) t x L where the secod term i the r.h.s. of Eq. (21) was added to set a far-dowstream P (= 0) at a distace of L (= 5 m) from the outflow plae [22]. For thermal boudary coditios, maistream temperature T ad film coolat temperature T c were give uiformly as 330 ad 300 K ( = 0 ad 1), respectively. At the bottom wall, thermal isulatig coditios was applied for the adiabatic wall case, ad wall temperature T w was set uiformly at 312 K ( = 4 Copyright 2011 by ASME

5 0.6) for the case to examie et heat trasfer from the bottom wall. Periodic coditio was employed i z directio. RESULTS AND DISCUSSION Validatio of Proposed Film Hole Model for LES Figure 3 shows the compariso of time-mea film coolig effectiveess o the ceter-lie (z/d = 0) betwee the preset LES with a film-hole model with a RFG procedure ad the experimet by Goldstei [1] for a circular hole at M = 0.5 ad = 0º. The predicted film effectiveess by LES shows a excellet agreemet with the experimetal results at ay locatios, though there is a slight differece i the agle of the film coolat jet; the agle is 30º i LES ad 35º i experimet. Figures 4 (a) to (d) show the compariso of time-mea film coolig effectiveess distributios betwee the preset LES ad PSP (Pressure Sesitive Pait) measuremet by Taeishi, et al. [13], for a circular hole at M = 0.5 ad 1.0 at = 0º. As observed by the PSP experimets, LES predicts the effect of blowig ratio M o film coolig effectiveess correctly, i.e., the film effectiveess is decreased with a icrease of the blowig ratio from 0.5 to 1.0. As show i Fig. 4 (d) for experimet at M = 1.0, the iitial decrease of film effectiveess followed by the recovery at dowstream was caused by the detachmet of film coolat jet from the wall by the peetratio ito the maistream, which is the followed by the reattachmet to the wall. Though the preset LES does ot predict the iitial decrease i M = 1.0 clearly, the effect of Film Effectiveess, LES Goldstei x/d FIGURE 3. VALIDATION OF A FILM-HOLE MODEL FOR LARGE EDDY SIMULATIONS blowig ratio o the spa-wise width of the coolat distributio is predicted i good agreemet both i M = 0.5 ad 1.0. Figures 4 (e), (f), ad (g) show the cross-sectioal profiles of time-mea film coolig effectiveess for M = 1.0 predicted by RANS with - realizable model [18], the preset LES, ad that measured by LIF (Laser Iduced Fluorescece) usig a acetoe vapor mixed with a film coolat jet [13], respectively. The preset LES clearly predicts a well-ow idey-shape distributio of the film coolig effectiveess formed by a pair of couter-rotatig vortices, while - realizable model caot predict due to the excess diffusio of the coolat. It is worth FIGURE 4. COMPARISON OF FILM COOLING EFFECTIVENESS BETWEEN LES AND EXPERIMENTS 5 Copyright 2011 by ASME

6 FIGURE 5. EFFECT OF SWIRLING FILM COOLANT JET ON THE FILM EFFECTIVENESS otig that the preset LES uses the time-mea velocities ad turbulece statistics, which were obtaied by the prelimiary RANS aalysis with the - realizable model [18], as iputs for RFG procedure of the film-hole model. That is, the preset LES ad RANS aalyses, show i Figs. 2 (f) ad (e) respectively, were performed based o the same flow iformatio at the exit plae of a film coolig hole. Thus, this implies that the preset LES with a combiatio of the proposed film-hole model ad a simple computatioal domai ca provide better predictio of film-coolig flows tha a RANS aalysis, which uses a complex domai icludig the whole structure of film hole, guide chael ad pleum. The compariso betwee LES ad experimets with PSP ad LIF also implies that LES shows less diffusive advectio of film coolat dowstream. Oe possible explaatio for this is that the turbulece itesity i the turbulet boudary layer of the maistream is uderestimated by the preset LES, because the iflow boudary coditio of maistream domai also uses the same RFG procedure as that for the film-hole exit. It is ow that fluctuatig velocities geerated by RFG techiques experiece a iitial decay of turbulece just dowstream of the iflow plae, ad it requires a log distace to recover the target turbulece statistics. I future wors, a id of rescale ad recyclig method to simulate spatially developig turbulet boudary layer flows should be applied at the ilet plae for the direct compariso with the wid tuel test. Effect of Swirlig Coolat o Film Effectiveess Figures 5 (a) ad (b) show the effect of swirlig film coolat jet o time-mea profile of film coolig effectiveess predicted by the preset LES for M = 0.5 ad 1.0, respectively, at = 30º. The correspodig experimetal results by PSP are also show i Figs. 5 (c) ad (d) for compariso. By addig a swirlig motio to the film coolat jet, the iitial disappearace of film effectiveess just dowstream the film-hole is ot observed at M = 1.0 both i LES ad PSP results. This implies that the peetratio of the film coolig jet ito the maistream was suppressed strogly by swirlig motio of the film coolig jet. The swirlig of coolat jet also has a effect to spread the 6 Copyright 2011 by ASME

7 FIGURE 6. FILM EFFECTIVENESS AT x/d = 0, 2, AND 4 IN SWIRLING FILM COOLANT CASES film coolat wider i spa-wise directio ad eep higher film effectiveess loger i stream-wise directio tha o-swirlig cases at the both blowig ratios of M = 0.5 ad 1.0. Compariso of Figs. 4 ad Figs. 5 idicates that the preset LES ca predict the overall feature of the swirlig effect of film coolat jet, though LES results remai to show less diffusive advectio of film effectiveess i the stream-wise directio. Figures 5 (e) ad (f) show the distributios of film coolig effectiveess, which are spatially averaged over -3 < z/d < 3, for circular hole at M = 0.5 ad 1.0, respectively, at = 0º ad 30º. The preset LES teds to overestimate the spa-wise averaged effectiveess i etire regios for the same reaso metioed earlier. That is, the uphysical decay of turbulece i the turbulet boudary layer at the iflow plae of the maistream regio occurs due to the curret RFG procedure, ad it results i uderestimatio of turbulet mixig at the exit regio of film-hole, where the iteractio of the film coolat jet ad turbulet boudary layer plays a ey role i determiig the iitial spatial distributio of film coolat jet, as show later i Fig. 6. Aother reaso may exist i a prelimiary RANS aalysis usig - realizable model, which gives time-mea velocities ad turbulece statistics as iputs for the curret RFG procedure at the exit plae of film-hole, because liear eddy viscosity models ted to fail time-mea velocity profiles of complex flows, such as flow separatio, reattachmet ad swirl, existig i a guide chael ad pleum of the curret flow cofiguratio. Sice the precise predictio of time-mea flows ad turbulet statistics are quite importat for the curret film-hole model, state-of-the-art o-liear eddy viscosity or secod momet closure models should be applied for prelimiary simulatios i future wors. However, except for the overestimatio of film effectiveess especially for the swirlig jet cases, the curret LES shows a similar tedecy as PSP experimets i predictig the effect of swirlig coolat o film coolig flows. Figure 6 shows the spatial distributios of time-mea film coolig effectiveess at x/d = 0, 2, ad 4 obtaied by LES ad PSP measuremet. Compariso of Fig. 6 ad Fig. 4 clearly shows that the peetratio of the coolat jet at M = 1.0 is suppressed by swirlig motio of the film coolig jet. It seems that oe of the two jet core regios, which are formed by a secodary swirlig flow iduced by the primary swirlig motio of the coolat jet (or by the axial velocity of strogly ejected jet at M = 1.0), is pressed agaist the bottom wall by the primary swirl of the coolat jet itself. This mechaism seems to prevet the detachmet of the film coolat from the wall ad eep relatively higher film effectiveess dowstream. At M = 0.5, the secodary swirlig flow is ot so itese as to roll up the film coolat from the wall ad primary swirl i the jet itself press the coolat agaist the wall. As metioed earlier, at x/d = 0 just dowstream of the film-hole exit, film coolat jets i PSP experimets show more diffusive profiles tha those i LES probably due to the itesive iteractio with the upstream turbulet boudary layer. The uderestimatio of turbulet itesity i turbulet boudary layer seems to affect ot oly the iitial mixig but also mixig at the dowstream regio, where LES also show less diffusive behavior of coolat jets. 7 Copyright 2011 by ASME

8 FIGURE 7. TIME-MEAN NUSSELT NUMBER DISTRIBUTIONS Effect of Swirlig Coolat o Net Heat Trasfer The objective of film coolig i gas turbies is to reduce covective heat flux as heat iput from the hot maistream to the surface of vae ad blades. Thus, the effectiveess of ewly proposed film coolig techiques should be evaluated i view of et heat trasfer to the vae surfaces, because secodary flows itroduced by ew film coolig techique may ehace covective heat trasfer ufavorably. I the preset case with a swirlig coolat jet, the primary swirlig flow (i the jet itself) ad the secodary swirlig flows may ehace covective heat trasfer o the wall. Of course, at the iitial stage of film coolig util some distace from the film-hole exit, the coolat temperature is lower tha the wall temperature, ad thus the directio of heat flow is from the wall to the coolat. I this case, the ehaced covective heat trasfer has geerally o problem. However, after the film coolat temperature exceeds the wall temperature, the directio of heat flow chages to be from the coolat to the wall ad the ehaced heat trasfer is ufavorable. Therefore, i this sectio, et heat trasfer is examied by LES assumig a uiform wall temperature of the vae surface. The selected uiform temperatures of the mai stream, wall, ad film coolat correspods to 1800 K, 1260 K, ad 900 K, respectively, as a rough example. Figure 7 shows time-mea local Nusselt umber defied as follows. Nu d = hd/ = q w d/(t T w ) (22) I the above defiitio, time-mea local heat flux q w is defied to be positive whe a time-mea heat flow is from the gas to the wall, ad vice versa. I a overall view, Nusselt umber is decreased dowstream the film-hole by a film coolat jet, ad relatively higher Nusselt umber regios exist at the outer edge of the lower Nusselt umber regios due to the secodary flows Nud M = 1.0, = 0 o M = 1.0, = 30 o M = 0.5, = 0 o M = 0.5, = 30 o Spawise-averaged Nud at -3 < z/d < x/d FIGURE 8. SPAN-WISE AVERAGED TIME-MEAN NUSSELT NUMBER DISTRIBUTIONS iduced by the film coolat jet. No-swirlig cases show symmetric distributios ad two bads of egative Nusselt umber regios exist just dowstream the hole for M = 0.5, which merges ito oe egative regio. This is caused by a pair of idey-shape vortices. At M = 1.0 at = 0º, o egative Nu regio exists dowstream the hole due to the peetratio ad detachmet of the film coolat jet. The strog ejectio of the coolat jet iduces strog secodary swirlig flows at the both sides of the film-hole, ad they are resposible for high positive Nu regios ear the film-hole. O the other had, swirlig flow cases show asymmetric Nu distributios. Negative Nu regios are caused by the primary swirlig flow of the coolat jet itself, while positive Nu regios are due to the secodary swirlig flow of exteral hot gas iduced by the coolat jet. Iterestigly, egative Nu area is larger i swirlig 8 Copyright 2011 by ASME

9 jet cases thas to the wider ad loger area of high film effevtiveess. Figure 8 shows the spa-wise averaged Nu over 3 < z/d < 3 for all cases. As expected from Fig. 5, the o-swirlig film coolat jet at M = 1.0 shows the highest Nu distributio i the etire regio, while it is fairly reduced by addig a swirlig motio to the coolat jet. At M = 0.5, the swirlig film coolat jet ca reduce the et heat trasfer to the wall aroud 1 < x/d < 19. I swirlig coolat jet cases, the total spatial averages of Nu i the area of iterest, 3 < x/d < 35 ad 3 < z/d < 3, are 93.8% ad 88.3% of o-swirlig cases for M = 0.5 ad 1.0, respectively. As a cosequece, it is cocluded that film coolig with a swirlig coolat jet is proved to be effective to reduce et heat trasfer from the hot maistream to the vae surface for a circular film coolig hole at the blowig ratio of M = 0.5 ad 1.0. CONCLUSIONS I this study, large eddy simulatio of a film coolig with a swirlig coolat jet has performed for a circular hole at M = 0.5 ad 1.0. For the LES of film coolig flows, a film-hole model based o a RFG (Radom Flow Geeratio) techique was also proposed to simulate turbulet fluctuatig flows at the exit plae of film coolig hole as a boudary model. The film-hole model facilitates the LES of complex film coolig flows, which should cotai multiple film coolig holes o the edwall ad vae surfaces to simulate realistic film coolig flows uder the ifluece of complex turbie cascade flows i real gas turbies. By the LES applyig the proposed film-hole model to film coolig flows with a swirlig coolat jet, the followig coclusios are obtaied. 1. Film coolig with a swirlig coolat jet is cofirmed to be effective to reduce et heat trasfer from the hot gas to the wall at give uiform temperature coditios by about 6% ad 12% at the blowig ratio of M = 0.5 ad 1.0, respectively, compared to oswirlig cases. 2. I a swirlig film coolat jet case at M = 1.0, peetratio of coolat jet is suppressed. It seems that oe of the two jet core regios is pressed agaist the bottom wall by the primary swirl of the coolat jet itself, ad this seems to prevet the detachmet of the film coolat from the wall. 3. The proposed film-hole model for LES was validated by the compariso of predicted ceter-lie temperature with a ow experimetal result. REFERENCES [1] Goldstei, R. J., 1971, Film coolig, Advaces i Heat Trasfer, 7, pp [2] Bogard, D. G. ad Thole, K. A., 2006, Gas turbie film coolig, J. of Propulsio ad Power, 22, pp [3] Erise, V, L. ad Goldstei, R. J., 1974, Heat trasfer ad film coolig followig ijectio through iclied circular tubes, J. of Heat Trasfer, 96, pp [4] Bersdorf, S., Rose, M. G. ad Abhari, R. S., 2005, Modelig of film coolig - Part I: Experimetal study of flow structure, ASME Paper No. GT [5] Goldstei, R. J. ad Ecert, E. R. G., 1994, Effect of hole geometry ad desity o three-dimesioal film coolig, It. J. Heat ad Mass Trasfer, 17, pp [6] Bell, C. M., Hamaawa, H. ad Ligrai, P. M., 2000, Film coolig from shaped holes, J. of Turbomachiery, 122, pp [7] Taeishi, K., ad Aoi, S., 2001, Cotributio of heat trasfer to turbie blades ad vaes for high temperature idustrial gas turbies: Part 1, Film coolig, A. N. Y. Acad. Sci., 934, pp [8] Yu, Y, Ye, C. -H. Shi, T. I. -P. ad Chyu, M. K., 2000, Film coolig effectiveess ad heat trasfer coefficiet distributio aroud diffusio shaped holes, J. of Heat Trasfer, 124, pp [9] Buer, R. S., 2005, A review of shaped hole turbie filmcoolig techology, J. of Heat Trasfer, 127, pp [10] Kusterer, K., et al., 2009, A parametric study o the ifluece of the lateral ejectio agle of double-jet holes o the film coolig effectiveess for high blowig ratios, ASME Paper GT [11] Heidma, J. D. ad Ead, S., 2007, A ovel ati-votex turbie film- coolig hole cocept, ASME paper, GT [12] Kuya, Y., Nutadusit, C., Ishida, H., Momose, K. ad Kimoto, H., 2004, A applicatio of swirlig jet to film coolig, Proc. JSME Thermal Egieerig Coferece, Sedai, No (i Japaese) [13] Taeishi, K., Oda, Y., Egawa, Y., Kitamura, T., 2010, Film coolig with swirlig coolat flow, WIT Tras. o Egieerig Scieces, 68, pp [14] Smirov, A., Shi, S. ad Celi, I., 2001, Radom flow geeratio techique for large eddy simulatios ad particle-dyamics modelig, ASME J. of Fluids Egieerig, 123, pp [15] Kraicha, R.H., 1970, Diffusio by a radom velocity field, Physics of Fluids, 13 (1), pp [16] Batte, P., Goldberg, U. ad Charavarthy, S., 2004, Iterfacig statistical turbulece closures with large-eddy simulatio, AIAA Joural, 42, pp [17] Durbi, P.A., 1996, "O the -3 stagatio poit aomaly", It. J. Heat ad Fluid Flow, 17, pp [18] Shimizu, D, Taeishi, K., Oda, Y. ad Egawa, Y., 2010, "Numerical simulatio of film coolig with swirlig coolat 9 Copyright 2011 by ASME

10 air", Proc. It. Sympo. o Traport Pheomea, Kaohsiug, Taiwa, CD-ROM. (to appear) [19] Keatig, A., De Prisco, G. ad Piomelli, U., 2006, "Iterface coditios for hybrid RANS/LES calculatios", It. J. Heat ad Fluid Flow, 27, pp [20] Iagai, M., Kodoh, T. ad Nagao, Y., 2005, A Mixed- Time-Scale SGS model with fixed model-paramters for practical LES, Tras. ASME Joural of Fluids Egieerig, 127, pp [21] Roe, P.L., 1986, "Characteristic-based schemes for the Euler equatios", A. Rev. Fluid Mech., 18, pp [22] Oita, K. ad Kajishima, T., 2000, "Numerical ivestigatio of usteady cavitatig flow aroud a rectagular prism", Proc. JSME-KSME Thermal Egieerig Coferece, 2, pp Copyright 2011 by ASME