EXPERIMENTAL AND NUMERICAL ANALYSIS OF SUPERSONIC BLADE PROFILES DEVELOPED FOR HIGHLY LOADED IMPULSE TYPE STEAM TURBINE STAGES

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1 Pper ID: ETC Proeedings of 12th Europen Conferene on Turomhinery Fluid dynmis & Thermodynmis ETC12, April 3-7, 2017; Stokholm, Sweden EXPERIMENTAL AND NUMERICAL ANALYSIS OF SUPERSONIC BLADE PROFILES DEVELOPED FOR HIGHLY LOADED IMPULSE TYPE STEAM TURBINE STAGES R. Ghio - C. Rffeli - A. Sttini Mrine Systems nd Components Business Unit, Finntieri S.p.A., Genov, Itly rirdo.ghio@finntieri.it V. Dossen - A. Fusetti - A. Spinelli - C. Osnghi - F. Cozzi Politenio di Milno, Diprtimento di Energi, Vi Lmrushini 4, Milno, Itly vinenzo.dossen@polimi.it ABSTRACT The pper desries the results of numeril nd experimentl reserh progrm ddressing the erodynmi investigtion on the performne of lde profiles speifilly developed for pplition in highly loded impulse type turine stges. The industril requirements driving towrd the doption of highly loded stge solutions re presented, long with n estimtion of the profiles operting prmeters. Two sttor vnes nd one rotor lde profile hve een developed nd extensively tested y mens of flow field mesurements nd shlieren visuliztion in trnsoni low-down wind tunnel for liner sdes. Experimentl results for the relevnt operting onditions re presented, providing vlidtion dt for the CFD model used for lde design nd evidening tht the min gols of the design optimiztion proedure hve een hieved. KEYWORDS Supersoni Turine, Shok Visuliztion, Supersoni Impulse Stge, Turine Csdes NOMENCLATURE hord h lde height s pith o pssge throt x xil diretion xil hord M Mh numer Re Reynolds numer N numer of ldes PS pressure side SS sution side U turine peripherl veloity C solute flow veloity Greeks ν kinemti visosity α flow ngle ζ kineti energy loss oeffiient (= VV 2,iiii 2 VV2 2 VV2 ) 2,iiii Susripts nd supersripts 2 sde outlet is isentropi T turulent mix mixed out OPEN ACCESS Downloded from 1 Copyright y the Authors

2 INTRODUCTION In the mrket segment of smll nd medium stem turine size for industril, oil&gs nd mrine pplitions, requirements in terms of ost effetiveness nd need for lightweight instlltions drive the development of ompt mhine solutions with inresed lod per stge. As onsequene of the high required stge lod, for impulse type mhines suh s those mnuftured y Finntieri S.p.A., the sttor lde hnnel will e operting in high expnsion rtio onditions, resulting in trnsoni/supersoni flow regime in oth nozzles nd ldes nd lose to tngentil reltive flow t rotor inlet. These spets require the development of non-onventionl erodynmi profiles for oth sttionry nd moving ldes. In the industril stem turine field, hrdly ny literture referene n e found deling with the kind of optimiztion of onern to the present work, nmely highly loded impulse type turine stges. A relevnt work for industril stem turine pplitions ws pulished y Rshid et l. (2007), minly deling with performne predition vriility of veloity ompounded highly loded Curtis stges, therefore foused on the supersoni erodynmi intertion etween nozzle nd rotor. Conversely, other studies re ville in the stem turine literture where the methodologil spets nd phenomen re similr to the present work, ut the pplition dels with nlysis nd design of supersoni lde profiles used in lst stges of lrge output stem turines, see for instne the work of Váhová et l. (2015). Atully, the topi of inresed stge loding driven y the dvntges of lower stge ount, nd of the relted lde profiles design nd optimiztion, is often found in erospe pplition, for exmple in the works of Wolf et l. (2010) nd Sonod et l. (2006), deling however with retion type stges optimiztion. The hllenging design gol is therefore to meet the mrket requirements s desried ove, ensuring ompetitive level of effiieny for turines with highly loded impulse type stges. This n e otined y mens of hieving lde profiles effiieny level in the supersoni design regime omprle to tht ttined with onventionl lde design in susoni rnge, still providing ompetitive performne in the off-design onditions. For this purpose, two new onvergentdivergent nozzle profiles nd rotor lde profile hve een speifilly designed nd optimized y mens of two-dimensionl CFD tools, nd their performne tested nd ompred with experimentl dt tken t the Lortorio di Fluidodinmi delle Mhine (LFM) of Politenio di Milno. AERODYNAMIC DESIGN PARAMETERS DEFINITION In order to define the expeted rnge of the design prmeters for the ldes irfoil, representtive pplition onsisting of stem turine genertor for wste het reovery on ruise ship hs een onsidered. The stem turine genertor is prt of omined yle with Diesel min engines nd produes eletril energy through the reovery of exess stem not used y the ship servies. Different wste het reovery plnt onfigurtions were nlyzed, sed on therml lods nd stem onsumption dt supplied y the ship-owner. Hving defined the stem turine oundry onditions, referene onventionl design hs een developed with the ssumption tht the stges operte t the optiml isentropi veloity rtio U/C for impulse type stges. Speifilly, the resulting mhine onsists of 6 stges with sttor profiles operting in the high susoni or trnsoni regime nd with susoni inlet reltive veloity for rotor profiles, llowing the lding to e omposed of profiles designed with onventionl erodynmi riteri. With the gol to deliver lightweight nd ompt mhine, s required y the pplition, different lyout onepts with deresed numer of stges were lso nlyzed with the effort to hieve the low ost trget. It ws found tht deresing the numer of stges up to 4 rther thn the 6 of the onventionlly loded referene solution resulted in rotor inlet reltive Mh numer pprohing 1.0 nd in nozzle exit Mh numer peking t mximum vlues of 1.5 for the two intermedite stges. Moreover, the rotor inlet reltive flow ngle ws redued to pproximtely 20, while the inter-stge solute flow ngle inresed to 127 (see top left of Figure 1 for ngle referene diretion). All these spets re 2

3 AXIAL + TANGENTIAL S11 CD1, CD Figure 1: Chnnel geometry: onventionl trnsoni nozzle S11; onvergent-divergent supersoni nozzles CD1 nd CD2; rotor impulse profile onsequenes of the inresed stges lod, s indited y the isentropi veloity rtio eing redued to pprox. U/C0=0.28. The lde design effort ws susequently undertken, with different design philosophies dopted for the sttionry nd for the moving ldes setions. Two sttionry lde setions were designed for the sme expeted outlet Mh numer rnge: the CD1 profile ws designed for purely xil inlet flow, typil of the turine first nozzle, while the CD2 profile ws designed for nominl inlet ngle of 130 typil of n intermedite high loded turine stge. The design Mh numer for the nozzles ws set in the rnge , slightly lower thn the mximum expeted Mh regime for the desried pplition, hoosing proper exit to throt re rtio; this ensures voiding high losses in nozzle profiles t off-design opertion. Prtiulr re hs een devoted to the design of the rer portion of the nozzle in order to void disontinuous urvture in the supersoni prt of the nozzle geometry. In the present pper, the mesured performnes of the new geometries re presented nd ompred to those of the referene trnsoni profile (S11), ommonly dopted for pplitions with onventionl U/C The impulse type moving lde profile design minly ddressed the leding edge portion, where high flow veloities rise due to elertion on the sution side, nd where, in se of rotor inlet reltive Mh numer pprohing 1.0, poket of supersoni flow nd ssoited shoks our, using redution of onventionl profile performne. The lde profile ws therefore modified in suh wy to minimize the strength of the sution side shok in order to mke it more tolernt to low vlues of inlet flow ngle y mens of redution in sution side urvture nd inlet metl ngle. The resulting moving lde geometry (0747) llows reduing losses ompred to onventionl design profiles in the high susoni/trnsoni operting rnge. Skethes of the onventionl profile S11 together with the two onvergent divergent nozzles (CD1 nd CD2) nd the new rotor profile (0747) re reported in Figure 1, long with the referene diretion used for solute nd reltive flow ngle definition. EXPERIMENTAL SETUP AND TEST MATRIX The mesurements mpign ws rried out in the trnsoni wind tunnel for liner sdes of the Lortorio di Fluidodinmi delle Mhine t the Politenio di Milno. This is low down fility fed y 6000 kg of pressurized stoked ir. The mximum sizes of the test setion re 80 mm height nd 470 mm width. The sttor sdes were omposed y 8 ldes, using sle ftor of 2:1 ompred with the originl size of the profiles. For the rotor nlysis, sle ftor of 2:1 resulting in n spet rtio of 2 ws used in order to void the presene of seondry flows in the mesurement zone t mid spn, due to the lrge defletion imposed ( 140 ) to the flow. Consequently, the rotor sde ws omposed of 12 ldes. A movle tilord pled downstrem of the sde ensures the periodiity ondition. 3

4 The flow field downstrem of the sde ws tngentilly trversed y miniturized 5 hole proe (hed of 1.8 mm) pre-ligned with the expeted verge flow ngle t distne of 33% of the lde xil hord. The 5 hole proe ws lirted in referene Mh numer rnging from 0.3 to 2.35, on yw nd pith ngle rnge of ±20. For the supersoni ses, totl pressure orretion orresponding to tht of the norml shok t the relevnt Mh hs een onsidered during lirtion. The 5 hole proe unertinty ssoited to the lol vlue of ζ is , while ±0.25 is the unertinty in the flow ngle mesurement. The dt reported ove, sed on onfidene level of 95%, re not vlid when the proe hed is rossed y shok. Under this ondition, the pressure grdient evluted on the proe hed dimeter my eome drmtilly high, nd the results otined y the lirtion performed under uniform flow onditions re not representtive ny more. Therefore, the pressure differene ross the proe hed is interpreted s high yw ngle nd, onsequently, relevnt error in the lol flow ngle nd stti pressure my e introdued. This effet is lerly visile in the trversing results performed t high Mh numer (Figures 6 nd 10), where the mesurement points neighouring the shok show relevnt disontinuities in flow ngle nd Mh numer distriutions. It should e underlined tht this is only lol effet, prtly influening the pithwise verged dt. More detils out the experimentl fility nd the mesurement tehnique n e found in Dossen et l. (1996, 1999) nd D Ippolito et l.(2011). The mesurement grid downstrem of the three sttor sdes ws defined y 71 points eqully sped y 1.5 mm; 53 points sped y 1 mm defined the mesurement grid dopted for the rotor sde. In ll the ses nd for every expnsion rtio, minimum of two lde pssges ws overed in order to verify the estlishment of proper periodiity ondition s resulting from the position of the downstrem tilord. The referene upstrem flow ws provided y three hole proe, positioned pproximtely one xil hord from the profile leding edge. A flow turulene intensity lower thn 1% ws mesured t the sde inlet y mens of hot wire nemometry. With referene to the three sttor profiles, wide rnge of expnsion rtios (M2is= ) ws nlyzed y mens of pproximtely tests for every onsidered inidene ngle. For the rotor sde, the rnge of M2is= ws explored y pproximtely 8 tests for every inidene ngle. A summry of the experimentl test grid, together with the min hrteristis of the four sdes, re reported in Tle 1. A totl numer of pproximtely 40 pressure tps mhined on the pressure side nd sution side of two djent ldes llowed to otin the distriution of isentropi Mh numer on the mid spn setion of the lde hnnel. 25 pressure tps, loted on the endwll plte in orrespondene to the trversing setion, give the referene stti pressure for the tests. Csde Nominl inlet Inidene ngle M designtion flow ngle (α) 2is Re 10 6 h/ s/ N S tests in the CD1 90 0, +30, rnge CD , 0, tests in the rnge , +1, Tle 1: Summry of erodynmi tests performed in the LFM low-down wind tunnel nd min sdes hrteristis. A doule pssge shlieren system hs een dopted to visulize shoks in the test setion. In this onfigurtion, the emitting nd the reeiving optil omponents lie on the sme optil enh, llowing n esy lignment with respet to onventionl Z-type set-up. The light emitted y 1.12 W lue LED is foused nd then ollimted y spheril mirror (150 mm dimeter). The ollimted light rys trverse the test setion twie: the light em is refleted k to the sme spheril mirror y the mirror-polished sde endwll. The knife orienttion is suh tht positive density grdients (ompression wves nd shoks) pper s drker regions, while expnsion wves pper righter. 4

5 NUMERICAL SETUP The omputtions were rried out y mens of the ommeril suite of odes FINE/Turo v9.1-2, oth for the lde profiles development tivity nd for the numeril nlyses performed with the purpose to ompre CFD results with detiled experimentl dt. The design phse omputtions were run with defult setup prmeters suggested y the odes, resulting in stle omputtions with good onvergene ehvior, whih llowed for fst development work. However, when the detils of the flow field were nlyzed for omprison with test dt, it ws found tht this hoie produed results hrterized y some inonsisteny, suh s lol negtive levels of loss nd exessive diffusion for wke predition. This kind of results ws lso reported in Wolf et l. (2010), where the sme ode ws pplied to simulte very similr operting ondition. Therefore, in order to improve the physil onsisteny of the numeril results, CFD dt hve een otined with n improved numeril setup, resulting from sensitivity nlysis to grid size nd shpe. The finl grid differs from the defult one for the inresed numer of grid points nd for the lignment with the wke diretion. Furthermore, seond order upwind sptil disretiztion sheme ws seleted. It ws found tht the mentioned hnges profiiently improved the detiled flow field predition when ompred to test dt, even if showing higher levels of glol residul (the differene to the defult set up is pproximtely 3 orders of mgnitude, depending on the se), euse the omputtions were less stle due to the seleted numeril sheme. Nevertheless, the mss flow rte error is negligile in ll ses (reltive mss flow error lower thn 0.025%), inditing tht the overll solution is tully stle nd tht the high residul vlues represent some lolized smll instility in the flow field. All the profiles were studied in 2D plnr sde onfigurtion, with two lde-to-lde mesh lyers in spnwise diretion, where symmetry ondition ws pplied to enfore two dimensionl flow. The multi-lok mesh topology ws provided for ll ses y the Autogrid5 defult O4H templte with upstrem nd downstrem loks, with n ngle ontrol for wke lignment pplied for the sttor lde profiles. As n exmple, Figure 2 shows the multi-lok omputtionl domin nd the grid topology dopted for the S11 referene nozzle omputtions. The min overll grid qulity prmeters re reported in Tle 2. Figure 2: Multi-lok omputtionl domin with downstrem wke lignment: O-grid lok round the profile; 4 H-grid loks surrounding the O-grid; upstrem nd downstrem H-grid loks. S11 CD1 CD Points numer per lyer Minimum skewness ngle Mximum expnsion rtio Tle 2: Min omputtionl grid prmeters for the four ses. 5

6 Stedy stte fully turulent RANS were solved with the provided seond order upwind disretiztion sheme, using the Splrt-Allmrs model for turulene modeling nd ir ssumed to e perfet gs s working fluid. Given the different lde setions geometries nd the wide rnge of operting pressure rtio, the y+ prmeter shows different vlues depending on the se, ut the verge y+ vlue of points losest to the lde surfe is lwys lower thn 10 for ll presented ses. The inlet oundry onditions were presried y onstnt totl pressure, totl temperture nd inlet flow ngle, while n verge vlue of stti pressure is pplied t the outlet region. The turulent visosity imposed t inlet orresponds to turulent to moleulr visosity rtio νt/ν = 2. Inlet nd outlet oundry regions were loted pproximtely 1 xil hord upstrem nd 1.5 xil hord downstrem of the lde for ll the nlyzed lde geometries. ANALYSIS OF RESULTS Experimentl tests hve een initilly rried out on purely onvergent trnsoni sttor profile (S11). This first experimentl dt set hs een used for the definition nd the vlidtion of the est omputtionl setup nd numeril sheme. Then, the sme numeril pproh hs een pplied to the susequent nlyses of the two new onvergent-divergent sttor profiles (CD1 nd CD2) nd of the rotor profile (0747). Further on, experimentl tests hve een performed on oth onvergentdivergent vnes nd on the rotor lde. The rod test mtrix, inluding wide rnge of expnsion rtios nd inidene ngles for every onsidered profile, hs een summrized in Tle 1, where the min sdes geometril prmeters re lso reported. The pithwise distriution of the lol kineti energy loss oeffiient (ζ) nd outlet flow ngle (α2) t distne equl to 33% of the xil hord from the triling edge support the nlysis nd the omprison of numeril to experimentl dt; the surfe isentropi Mh numer distriutions will lso e presented for the sme purpose. Furthermore, only for trnsoni nd supersoni outlet onditions, shlieren pitures nd ontours of the projeted density grdient mgnitude re lso proposed, ompred nd disussed. To ensure proper resolution of density grdients, the projetion diretion ws set to the estimted stremwise diretion -given y the rsin(o/s)- for the nozzles, nd to the tngentil diretion for the rotor lde. For the ske of revity, only results of some seleted ses (susoni, trnsoni nd supersoni) onerning the nominl inidene for S11 nd CD2 vnes will e here presented, followed y two representtive ses for the 0747 rotor profile t the most severe inidene ondition. Figure 3: S11 t M2,is=0.83: pithwise distriution of ζ () nd flow ngle () t x/= Isentropi Mh numer distriution on lde surfes (). S11: onvergent trnsoni sttor profile (referene) The experimentl nd numeril results otined t three outlet isentropi Mh numers (i.e., M2is=0.83, 1.19, 1.67) in the representtive rnge for the stge lod, re presented nd disussed elow. The results t M2is=0.83 re presented in the three frmes of Figure 3, where frme () evidenes n exellent greement etween the experimentl nd the numeril isentropi Mh numer distriution ll long the lde surfe. As evidened y frme (), the finl numeril CFD set up, sed on n upwind sheme, orretly predits the presene of the isentropi plteu outside of the wke, ut slightly underestimtes the kineti energy loss peks ssoited with the mximum veloity defet in the wke. This differene n e sried to n exessive diffusion operted y the CFD ode. 6

7 d e Figure 4: S11 t M2,is=1.19: pithwise distriution of ζ () nd flow ngle () t x/= 0.33; Isentropi Mh numer on lde surfes (); shlieren piture (d) nd mgnitude of the stremwise density grdient from CFD dt (e). Moreover, the profile kineti energy loss otined y CFD, evluted oth y pithwise mss verged or y mixed out proedure, only slightly differs from tht evluted y the experiments s it will e shown in the following. Figure 3 frme () shows tht CFD underestimtes the verged flow defletion y pproximtely one degree, while the experimentl distriution evidenes higher flow ngle vrition long the pith, onfirming the lredy mentioned exessive numeril diffusion. The omprison of results for the low supersoni se M2is=1.19 is presented in Figure 4, where the shlieren piture nd the stremwise projeted density grdient ontours derived y the CFD dt re reported in frme (d) nd (e). From the omprison etween the experimentl nd numeril shlieren pitures (frme (d) nd (e)) it is possile to infer tht the min shok struture is well predited y the omputtion s witnessed y the very well ptured diretion nd position of the two shoks strting from the triling edge. Conversely, the numeril flow model does not orretly predit the omplex phenomenon ssoited to the impingement of the shok on the SS oundry lyer, remrkle in the shlieren piture. A loser look t the intertion region for the sme se of Figure 4 frme (d) is reported in Figure 5. The inoming shok nd the two generted shoks nd d n e esily identified. The very smll white region lose to the wll (lel ), where the negtive sptil density grdient inreses, n e identified with n expnsion fn. Unfortuntely, the outer region of the fn nnot e identified due to the very low vlue of the density grdient. The mehnism evidened y the shlieren piture n e onsistent with the intertion of the shok with lminr oundry lyer, s desried y Shpiro (1953) nd reported in Figure 5 (left frme). As the shok enters the oundry lyer, it wekens due to the progressive Mh numer redution pprohing the wll. Finlly, the shok vnishes in the inner susoni oundry lyer. d Figure 5: Intertion of shok wve with lminr oundry lyer. Left: sketh tken from Shpiro (1953); right: lol zoom from Figure 4 (frme (d)). 7

8 The pressure inrese generted downstrem of the shok propgtes upstrem through the susoni oundry lyer ner the wll, generting seprtion zone used y the steep dverse pressure grdient. This seprtion ule fores the supersoni inoming flow to deflet ounterlokwise through series of ompression wves tht merge to form new shok wve. Afterwrd, the flow follows the profile of the seprted region turning lokwise through n expnsion fn. Before returning to follow the wll, the flow must experiene nother ounterlokwise rottion, otined through series of ompression wves d tht finlly merge into nother shok wve further downstrem. One the flow hs pssed the seprtion ule, it returns to follow the lde profile regulrly. In onlusion, the intertion of shok produes two shoks nd d nd n expnsion fn. The presene of lminr oundry lyer on the rer prt of supersoni turine nozzle n e onsidered s surprising ut it is not novelty. Váhová et l. (2015) evidened similr differene etween flow visuliztions nd numeril omputtions, while testing the pplition of Trnsition Model on supersoni turine t n outlet Re of out nd for n outlet isentropi Mh similr to the se reported in Figure 5. They showed tht the presene of single refleted shok wve in the CFD results (s lso reported in Figure 4 frme (e)) n e relted to the setting of fully turulent omputtion (s in the present se). Conversely, when lminr omputtion or proper trnsition model is onsidered, seond refleted shok ppers downstrem, in ordne with the shlieren visuliztion reported in the present pper s well s in Váhová et l. (2015) nd with the sheme presented in the left frme of Figure 5. Moreover, in the sme region, the isentropi Mh numer distriution (Figure 4, frme ()) presents slightly different vlues etween experimentl nd numeril results where the shok impts on the profile SS. The numeril kineti energy loss trverse evidenes in the wke region pek vlues slightly underestimted ompred to the experimentl ones. Furthermore, the experimentl loss distriution shows flututions long the pith, lerly ssoited with the shok refletions oming from the tilord nd from the neighouring sution side. The sme feture n lso e found in the experimentl pithwise distriution of α2, showing high disontinuities long the lde pith. It is evident tht the downstrem tilord introdues, for the prtiulr se, disturnes nd modifition in the flow field, with respet to the tul pplition. This limit in liner sde testing t supersoni Mh numer is well known nd n hrdly e voided, s lso reported y Wolf et l. (2010). Moreover, sine the lotion of the shok refleted y the tilord is funtion of oth the Mh numer nd the position of the tilord, the test ondition mostly ffeted y this spurious effet nnot e esily foreseen. The representtive quntities otined for the high supersoni se t M2is =1.67 re presented in Figure 6. d e Figure 6: S11 t M2,is=1.67: pithwise distriution of ζ () nd flow ngle () t x/= 33%; Isentropi Mh numer distriution on lde surfes (); shlieren piture (d) nd mgnitude of the stremwise density grdient from CFD dt (e). 8

9 The omprison etween the Mh numer distriutions in frme () shows tht the impt of the shok on ft prt of the lde SS is slightly dvned y the numeril results. This differene is lso reported in the two imges presented in frme (d) nd (e), where some differenes in the shok strutures n e identified: the position of the shok impt on the SS is dvned nd, s onsequene, the refleted shok lso shows different inlintion. It is interesting to notie tht the shlieren piture lso evidenes tht the shok struture is not perfetly periodi euse of the presene of the refleted shok oming from the tilord, influening the development of the SS oundry lyer. The lde positioned on the right side of frme (d) shows etter greement of the shok struture with the numeril solution: this ondition my e relted to the sene of the spurious effet produed y refletion on the tilord, hrdly reognizle in this pssge. Nevertheless, oth ζ nd α2 distriution evidene quite perfet periodiity ondition. The kineti energy loss distriution (frme ()) onfirms good greement of the loss level ssoited with the wkes nd slightly higher experimentl vlue in the entrl prt of the hnnel outside of the wke. Moreover, the overshooting shown in the experimentl dt extly orresponds to the strong shok dething from the SS of the triling edge. As previously disussed, the pssge of the proe hed through the strong shok leds lso to n overestimtion of the flow ngle, displyed in frme () y similr overshoot positioned extly t the sme tngentil lotion. Figure 7 presents nd ompres the experimentl nd numeril profile losses vs. the mixed out isentropi Mh numer, in terms of kineti energy loss oeffiient omputed strting from the flow mixed out quntities. Strting from the susoni rnge up to low supersoni regime good greement etween experimentl nd numeril profile losses n e oserved. In the high supersoni regime the experimentl vlues re lwys higher thn the numeril ones. Even if the effets produed y the shoks refleted from the tilord my generlly led to n overestimtion of losses - s lso reported y Wolf et l. (2010) -, it should e remrked tht the lol loss vlues ssoited with the Figure 7: Experimentl nd numeril mixed out kineti energy loss for the S11 profile. triling edge shok system in CFD results re, in generl, very low, ontriuting to the remrkle differene oserved t the higher expnsion rtios. CD2: onvergent-divergent supersoni sttor profile Three ses rnging from trnsoni to supersoni regime re presented for the onvergent-divergent profile. Figure 8 shows the results otined for M2is=1.03. d e Figure 8: CD2 t M2,is=1.03: pithwise distriution of ζ () nd flow ngle () t x/= 33%; Isentropi Mh numer distriution on lde surfes (); shlieren piture (d) nd mgnitude of the stremwise density grdient from CFD dt (e). 9

10 d e Figure 9: CD2 t M2,is=1.26: pithwise distriution of ζ () nd flow ngle () t x/= 33%; Isentropi Mh numer distriution on lde surfes (); shlieren piture (d) nd mgnitude of the stremwise density grdient from CFD dt (e). Although this trnsoni ondition ws quite unstle during the tests, the experimentl isentropi Mh numer distriution long the lde profile (frme ()) is in good greement with the numeril solution: the extent nd the lotion of the norml shok ourring t the exit of the lde hnnel is well predited s lso onfirmed y the shlieren pitures. With referene to Figure 8 frme (), the zone loted etween two djent wkes evidenes non-zero loss plteu relted to the norml shok tht develops in the rer prt of the lded hnnels. The pek losses only revel smll differene etween CFD nd experiments. The ngle distriution in frme () shows firly good greement in the verged vlue, ut, s in the previous ses, the CFD distriution is drmtilly smoother thn the experimentl referene, with pek differenes up to 4. The low supersoni se orresponding to M2is=1.26 is summrized y the 5 frmes in Figure 9, presenting flow fetures very similr to those disussed ove. The intensity nd the position of the olique shok strting from the triling edge re well predited s n e oserved from the two shlieren imges in frmes (d) nd (e). The low loss peks ppering etween the wkes re ssoited to the shok strting from the triling edge nd impting on the SS of the djent lde. Although in the imge tht represents the density grdient mgnitude the tre of the refletion ppers, the numeril predition of the ssoited loss on the mesuring trverse is negligile, s lredy evidened in other similr ses. d e Figure 10: CD2 t M2,is=1.614: pithwise distriution of ζ () nd flow ngle () t x/= 0.33; Isentropi Mh numer on lde surfes (); shlieren piture (d) nd mgnitude of the stremwise density grdient from CFD dt (e). 10

11 Figure 12: Experimentl mixed out kineti energy loss for the three sttors s funtion of the outlet isentropi Mh numer in the onsidered rnge of inidene ngles. Figure 11: Experimentl nd numeril mixed out kineti energy loss for the CD2 profile. Figure 13: Experimentl nd numeril mixed out kineti energy loss for 0747 rotor profile. Figure 10 reports the results otined t the highest supersoni test, orresponding to M2is = The numeril isentropi Mh numer distriution long the lde is gin in good ordne with the experimentl one, exept for the impt zone of the shok on the sution side; it is lso possile to suppose tht only the Mis pek vlue is lost in the experiment, due to the very steep grdient nd to the pressure tp disretiztion. It is remrkle tht the pressure trend upstrem of the shok mthes perfetly. The experimentl kineti energy loss trverse presents three regions of loss long the lde pith: the higher pek n e relted to the tre of the strong SS shok strting from the lde triling edge, remrkle in the shlieren piture, while seond one is ssoited with the wke. The third nd lower pek is ssoited with the shok refleted y the lde SS. The sme shok system is not so evident in the CFD results of frme (), oth due to the lower loss level lwys ssoited to the shoks nd to smll differene in the shok ngle. As result, the min shok leving the lde triling edge nd the one refleted y the lde SS, merge with the wke lmost in the sme xil position of the trverse reported in frme (). Therefore, only for this se, the pek vlues of losses ssoited to the wke re higher in CFD results thn in the mesurements. Figure 11 shows the omprison etween experimentl nd numeril mixed out vlues of kineti energy loss s funtion of the mixed out isentropi Mh numer. As lredy oserved for the S11 profile, very good greement n e found etween experimentl nd numeril vlues from the susoni to the low supersoni regime whilst signifint divergene emerges in the supersoni regime, only prtly justified y the presene of the tilord refleted shoks tht, for the prtiulr ses, did not ply relevnt role. Figure 12 summrizes the experimentl results relted to the three nozzles, in terms of ζ mmmmmm for ll onsidered inidene ngles nd Mh numers. The plot displys tht oth the onvergent divergent nozzles re quite insensitive to the onsidered inidene vrition. At the sme time signifint loss redution in the rnge 2 5% is hieved for Mh numer higher thn : rotor profile In order to verify the sensitivity to inidene onditions of the newly designed impulse profile in the high susoni/trnsoni regime, experimentl tests nd CFD lultions t inlet flow ngles lower thn nominl hve een lso performed. The mixed out kineti energy loss for the most severe inlet flow ngle (pproximtely 18, orresponding to 2 of positive inidene) in the onsidered Mh numer rnge is shown in Figure 13. A generl good greement in the design operting rnge (M2is>0.9) n e oserved in the plot, while the dt present n inresing differene reduing the Mh numer elow the design rnge. Experimentl nd numeril flow field detils for the nominl outlet Mh numer (M2is=1.03) re shown in Figure 14. The numeril nlysis well ptures the presene of the shok t the lde leding edge, s remrked in the projeted density grdient representtion. Moreover, the experimentl isentropi Mh numer profile lso identifies the sme pek 11

12 Figure 14: Rotor profile 0747 t M2,is=1.03: pithwise distriution of ζ t x/= 0.33 (); Isentropi Mh numer on lde surfes (); mgnitude of the tngentil density grdient from CFD dt (). Figure 15: Rotor profile 0747 t M2,is=0.75: pithwise distriution of ζ t x/= 0.33 () nd Isentropi Mh numer on lde surfes (). veloity in the initil prt of the sution side, ut shows higher vlues long the sution side of the hnnel nd highlights the presene of seond shok impting the rer prt of the sution side whih is not deteted y the numeril results. The loss trverse indites good greement in terms of wke width predition, ut the pek loss vlues ssoited with the wke pper to e underestimted y the omputtion, most likely due to the mislignment etween the grid nd the wke diretion. Fousing now on the susoni se orresponding to M2is= 0.75 (Figure 15), the kineti energy loss trverse presents differenes of the sme order of the nominl se in the enter of the wke. On the ontrry, the width of the wke is drmtilly underestimted y CFD evidening n isentropi flow region extending for ¼ of the pith, while only one mesuring point shows zero vlue long the pith. Consistently, the surfe isentropi Mh numer distriution mesured on the profile SS, displys signifint higher deelertion on the front prt, proly not urtely predited y the omputtion, sed on more stle fully turulent modeling. A similr trend, hrterized y smller differene, n e notied on the enter prt of PS distriution. Both mentioned diffusions suggest more intense thikening of the oundry lyer in the lde hnnel, leding to the remrkle differene experiened in the profile loss vlue evidened in Figure 15 frme (). CONCLUSIONS Experimentl tests were rried out on two supersoni nozzle profiles nd on moving lde profile developed for pplition in highly loded impulse stges. Tests were lso performed on referene trnsoni nozzle of onventionl design. Test dt were ompred over wide rnge of operting onditions ginst the results of omputtions performed with ommeril CFD ode. Only seleted relevnt ses re shown in the pper. For susoni nd trnsoni onditions good greement ws generlly hieved etween CFD nd tests. The detiled flow field omprison llowed lso to improve the physil onsisteny of the omputtionl results y mens of onvenient seletion of the min numeril setup prmeters. Only for some ses t the highest supersoni regime, some differenes etween experimentl nd numeril results were found, highlighting some diffiulties in resolving the flow fetures with oth pprohes. Nevertheless, detiled nlysis of most relevnt ses, lso supported y shlieren imges, llowed to ttriute the mentioned disrepnies minly to ode diffusivity nd to the effets produed y high grdients on the mesurement proe. In some prtiulr ses, shok refletions from the solid tilord produed spurious effets on the downstrem flow field. Moreover, the test results onfirmed tht the gols of the profile design proedure were stisftorily hieved: the performne of the two nozzles in the expeted operting rnge (M2is>1.2) turned out to e onsiderly higher thn the referene trnsoni nozzle. At the sme 12

13 time, the loss inrese in the susoni rnge is limited, llowing the profile to e sfely used lso in off-design fr from the onditions onsidered in the design proess, whih mostly ddressed supersoni expnsion rtios. For the moving lde the minimum loss opertion is indeed found to our in the expeted Mh numer rnge for ll the onsidered inidene ngles. Despite the numeril nd experimentl mixed out losses show omprle vlues in the design high Mh numer regime, the detiled flow field omprison highlights res where signifint differenes our, most likely due to oth numeril nd physil effets, nd further reserh tivity would e needed to improve the flow field understnding nd identify the soures of the ove mentioned differenes. ACKNOWLEDGEMENTS The work presented in this pper ws rried out within the frmework of the Itlin reserh projet FluMrTur DM62588 funded y MIUR (Ministry of University nd Reserh) nd DLTM (Distretto Ligure delle Tenologie Mrine), whose support is grtefully knowledged. REFERENCES Shpiro A.H (1953) The Dynmis nd Thermodynmis of Compressile Fluid Flow, John Wiley & Sons In. Dossen V., Osnghi C. et l., On Testing The Aerodynmis Of Film-Cooled Bldes, (1996). Proeedings of the XIII th Symposium on mesuring tehniques on trnsoni nd supersoni flows in sdes nd turomhines, Zurih Dossen, V., Perdihizzi, A., nd Svini, M., (1999), The Influene of Endwll Contouring on the Performne of Turine Nozzle Guide Vne ASME J. Turomh., 121(2), pp D Ippolito, G., Dossen, V., nd Mor, A., (2011), The Influene of Blde Len on Stright nd Annulr Turine Csde Flow Field, ASME J. Turomh., 133(1), p Sonod, T., Arim, T., Olhofer, M., Sendhoff, B., Kost, F., Giess, P.-A., (2006). A Study of Advned High-Loded Trnsoni Turine Airfoils. Trns. of the ASME, Vol. 128, Otoer 2006 Rshid, S., Tremmel, M., Wggot, J., Moll, R., (2007). Curtis Stge Nozzle/Rotor Aerodynmi Intertion nd the Effet on Stge Performne. Journl of Turomhinery, Vol. 129, July 2007 Wolf, T., Kost, F., Jnke, E., Hselh, F., Willer, L., (2010). Experimentl nd Numeril Studies on Highly Loded Supersoni Axil Turine Csdes. Proeedings of ASME Turo Expo 2010: Power for Lnd, Se nd Air, GT , June 14-18, 2010, Glsgow, UK Váhová, J., Lux, M., Príhod, J., Šimurd, D., (2015). Trnsition Model Applition on Mid- Setion Turine Blde Csde. Proeedings of the 12 th Interntionl Symposium on Experimentl Computtionl Aerothermodynmis of Internl Flows, July 2015, Lerii, Itly 13