Numerical Studies on Lip Shock Flow Behaviors over Backward Facing Sharp Edge Step with Hybrid RANS-LES

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1 Numercal Sudes on Lp Shock Flow Behavors over Backward Facng Sharp Edge Sep wh Hybrd RANS-LES Dr. Nrmal Kumar Kund 1 1 Deparmen of Producon Engneerng 1 Veer Surendra Sa Unversy of Technology, Burla, Odsha, Inda Absrac- In he presen research, a 2D numercal model s developed o nvesgae supersonc urbulen flud flow over a backward facng sharp edge sep by usng hybrd RANS-LES model. I perans o he Spalar-Allmaras model nvolvng a vscosy-lke varable (ṽ). The model also akes no accoun he addonal mporan facors lke producon, dffuson and desrucon erms above and beyond he very common aspecs relaed o he presen research problem. The numercal smulaons are performed usng he saed urbulence model wh he nflow free sream Mach number of 2.5 correspondng o free sream pressure and velocy of N/m2 and m/s2, respecvely. The smulaon predcons are compared wh he correspondng expermenal resuls exsng n he leraure. The hybrd RANS-LES model gves farly beer and conssen resuls hroughou he enre flow regon and hence, s used for all furher sudes. I s also observed ha he sudden vscous layer separaon s he man cause of he shock generaons. Furhermore, he uneven pressure recovery s because of he sudden expanson flow over he sharp edge sep. And also, he sudden expanson flow ncreases he shock nensy whch resuls n uneven flow characerscs. Ceranly, he presen sudy s very much advanageous o realze he flow behavors over any knd of backward facng sharp edge seps. Keywords- Supersonc, Turbulen Flow, Backward Facng, Sharp Edge Sep, Hybrd RANS-LES, Lp Shock. Page 36 I. INTRODUCTION Flud flow over backward-facng sep s one of he cenral frameworks and has ganed specfc focus on accoun of no us smplcy bu for volumnous ndusralal applcaons. In appled aerodynamcs, s also used o sudy many complcaed srucures, ncludng separaon and reaachmen. In he feld of research of hgh Mach number flow, he backward facng sep s always consdered as a complex confguraon for gnon n a scrame, where he recrculaon vcny has a sgnfcan role n sablzng he frng of he engne. Seps on he surfaces of hypersonc or supersonc arcrafs make he flow regme more complcaed and hence sgnfcan nvesgaons are very much essenal for mprovng he lvely desgn of arcrafs. II. LITERATURE REVIEW Smh [1] performed expermenal examnaons on he flow feld and hea ransfer downsream of a rearward facng sep n supersonc flow. Launder and Sharma [2] used he energy dsspaon model of urbulence o analyse he flow feld around a spnnng dsc. Armaly e al. [3] conduced boh expermenal and heorecal sudes on backward facng sep flow. Spalar and Allmaras [4] nroduced a one-equaon urbulence model for assessng aerodynamc flows. Anderson and Wend [5] repored llusrous and comprehensve descrpons of compuaonal flud dynamcs. Neumann and Wengle [6] used boh DNS and LES for examnng passvely conrolled urbulen flow of backward-facng sep. Hamed e al. [7] performed he numercal smulaons of fludc conrol for ransonc cavy flows. Chen e al. [8] suded expermenally on fne srucures of supersonc lamnar as well as urbulen flow over a backward-facng sep by usng Nanobased Planar Laser Scaerng (NPLS). Lu e al. [9] nvesgaed numercally on he nfluences of nflow Mach number and sep hegh on supersonc flows over a backwardfacng sep. Terekhov e al. [10] done he expermenal sudes on he separaed flow srucure behnd a backward-facng sep over and above he passve dsurbance. III. OBJECTIVES OF PRESENT RESEARCH WORK From he repored researches, o he bes of auhor undersandng, s noced ha here s no a sngle complee numercal sudy on flow over a backward facng sharp edge sep (nvolvng shock generaons) by usng hybrd RANS- LES echnque. Wh hs perspecve, he presen research demonsraes he numercal sudes on flow behavors over a backward facng sharp edge sep usng hybrd RANS-LES mehod. Furhermore, he numercal model also nvolves addonal mporan feaures namely producon, dffuson and

2 desrucon erms besdes he common ssues relang o he presen physcal problem. Furhermore, he specfed model also ncludes boh compressbly and eddy vscous effecs. The model s very well demonsraed for he meculous numercal sudes on flud flow characerscs peranng o flow over a backward facng sharp edge sep by nroducng he nflow free sream velocy along wh he correspondng Mach number as he key model parameers. Evenually, he numercal predcons from he presen case of flow over backward facng sharp edge sep usng he hybrd RANS- LES/Spalar-Allmaras urbulence model also nvolvng vscosy-lke varable, are compared wh he expermenal resuls of leraure. The model predcons peranng o he saed key model parameers are also along he expeced lnes and are n very good agreemen wh he correspondng expermenal resuls. Fnally, he presence of prey srong lp shock (caused by vscous layer separaon) exacly near he lp of separaon s realzed. IV. DESCRIPTION OF PHYSICAL PROBLEM Backward facng sharp edge sep havng wde range of applcaons n appled aerodynamcs s nvesgaed n he presen research. The geomerc confguraon along wh nal and boundary condons are referred from he expermenal research repor of Smh [1]. B. Inal and boundary condons The nflow free sream velocy U n = m/s, for whch he known sac free sream pressure pn = N/m2 corresponds o he Mach number M a = 2.5. A he lef sde ahead of he sep, he nal emperaure s mananed a K. The nal condons whch are se on he upsream are very much useful hroughou he smulaon along he spanwse drecon, for geng he flow characerscs beyond he sep. For he urbulence, he hybrd RANS-LES (oherwse ermed as Deached Eddy Smulaon, DES) model s aken no accoun. The boundary condons for he geomery represened by fgure 2 are as follows: Pressure p = kpa, everywhere else for pressure for he hybrd RANS-LES model. Temperaure T n = K, everywhere else for emperaure for he hybrd RANS-LES model. Velocy U n = m/s a he nle, no-slp wall a he lower boundary, slp wall a he upper boundary and zero velocy graden a he oule are se for boh he models. A. Geomerc model Fgure 1 represens he seup confguraon for esng he backward facng sharp edge sep flow over sharp edge geomery separang a a sep hegh H = m, upsream dsance from nle o sep L u = m and downsream dsance from sharp edge sep o oule L d = m. The dsance from downsream o upper boundary layer Z = m, spanwse dsance L= m and wdh B = m. The separaon and reaachmen pons are represened by S and R respecvely and are expeced o be observed afer performng numercal smulaon. Fgure 2. Backward facng sharp edge sep boundary represenaon V. MATHEMATICAL FORMULATION A. Generalzed governng ranspor equaons The mos generalzed governng ranspor equaons of mass, momenum and energy expressed n he conservave form of Naver-Sokes equaon for compressble flow accompanyng he nfluences of urbulence are as menoned underneah. Connuy: Fgure 1. Flow specfcaon of he backward facng sharp edge sep Page 37

3 ( u x Momenum: u Energy: Page 38 E x Where, ) 0 ( u u x ) p x x x (2 S (1) (2) T u E p k k 2S u Sh u u p p T T u p T Toal energy, E e k h x 2 p v 2 (3) The Reynolds sress erm s modeled n erms of he eddy vscosy and s expressed as: 2 ( S S nn / 3) 2 k / 3 The eddy vscosy s defned as a funcon of he urbulen knec energy k, and he urbulen dsspaon rae ε, and s expressed as: 2 c f k / In addon, all he model erms/symbols/coeffcens/funcons have her usual meanngs and values. B. Hybrd RANS-LES urbulence modellng The Spalar Allmaras urbulence model s a oneequaon model for he eddy vscosy. The use of hs model s oherwse known as Hybrd RANS-LES modellng or Deached Eddy Smulaon (DES) modellng. The dfferenal (4) (5) (6) (7) ) equaon s derved by usng emprcsm and argumens of dmensonal analyss, Gallean nvarance and seleced dependence on he molecular vscosy. Grd resoluon does no need o be fner for hs model, however, one can essenally apprehend he velocy feld graden wh he assocaed algebrac models. The ranspor equaon for he workng varable (oherwse ermed as Spalar Allmaras varable).e. vscosy-lke varable (ṽ) s expressed as follows: u c b1 x 1 S x c x b 2 c w1 f x x (8) The eddy vscosy can be expressed as follows: f v 1 (9) w 2 d Furhermore, all he model erms/symbols/coeffcens/funcons have her usual meanngs and values. VI. NUMERICAL PROCEDURES A. Numercal scheme and soluon algorhm The aforesad governng ranspor equaons are ransformed no generalzed form as follows.. u. u S (10) The ransformed governng ranspor equaons are dscrezed by expendng a pressure based coupled framework relang o fne volume mehod (FVM) usng he SIMPLER algorhm, where ϕ represens any conserved varable and S s a source erm. The esablshed pressure based, fully coupled solver s used o predc flow behavors of he relaed flow varables n connecon wh supersonc urbulen flow over a backward facng sharp edge sep. B. Choce of grd sze, me sep and convergence crera Fgure 3 shows ha he grd of he compuaonal doman s consdered o be non-unform and also grd s refned near he vcny where he hgh graden s expeced.. In he presen work, he smulaon of boh he urbulence models wh dfferen wall dsance from grd s carred ou on

4 he compuaonal doman. A comprehensve grdndependence es s performed o esablsh a suable spaal dscrezaon, and he levels of eraon convergence crera o be used. As an oucome of hs es, we have used non-unform grds for he fnal smulaon. Correspondng me sep aken n he smulaon s seconds. Though, s checked wh smaller grds of n numbers, s observed ha a fner grd sysem does no aler he resuls sgnfcanly. Convergence n nner eraons s declared only when he condon s sasfed smulaneously for all varables, where φ sands for he feld varable a a grd pon a he curren eraon level, φold represens he correspondng value a he prevous eraon level, and φmax s he maxmum value of he varable a he curren eraon level n he enre doman. hybrd RANS-LES model, however, he non-unform srucured grd wh refnemen n he vcny of expeced hgh graden s very much suable and approprae for beer solver convergence and resoluon near he wall. Tha s why, n he presen nvesgaon he refnemen near he wall and he separaon lne s mananed wh y + of 1 and 11 and he correspondng resuls are as shown n fgure 7. The compuaonal me for y + = 1 s very consderably greaer han y + = 11. Neverheless, y + = 1 wh he hybrd RANS-LES has less compuaonal me comparable o Drec Numercal Soluon (DNS) and also boh converge wh he assocaed expermenal daa over and done wh he same accuracy. Fgure 4. Influence of y + over smulaon accuracy B. Pressure recovery dsrbuons Fgure 3. Mesh for backward facng sharp edge sep VII. RESULTS AND DISCUSSION Wh he already descrbed model condons, he numercal smulaons are performed for nvesgang he flud flow behavors of he assocaed flow varables peranng o supersonc urbulen flow over a backward facng sharp edge sep. A. Comparson wh expermens Fgure 5 depcs he spanwse pressure recovery dsrbuon whch s ploed agans he non-dmensonal dsance along he wall behnd he sep. The fgure shows a sudden pressure drop a he p of separaon whch s due o sudden expanson of flow. The pressure flucuaon s drecly responsble for he presence of shock. In hs fgure pressure flucuaes wo mes represenng wo shock waves whch are generaed across he flow feld. The sudden flucuaon ndcaes he nensy of shock wave. In oher words, hs plo represens he pressure recovery akng place under he shock waves whch also ncludes several losses o he flow feld. The smulaon accuracy s grealy relan on grds and non-dmensonal sublayer-scaled dsance y+.e. u y/ν. Fgure 7 exhbs he nfluences of varous y+ on smulaon accuracy of he RANS-LES urbulen model ploed agans he relaed expermenal daa. Even hough, for capurng velocy gradens fne grd resoluon s no necessary for Page 39

5 Fgure 7. Lp shock represenaon near he separaon edge Fgure 5. Pressure recovery dsrbuons along flow drecon. C. Flow felds of pressure graden dsrbuons nvolvng presence of lp shock Fgure 6 represens he shock formaon n he flow feld capured from he pressure graden sandard devaon. Furhermore, fgure 7 shows he presence of lp shock exacly near he lp of separaon and he appearance of hs shock s due o vscous layer separaon. In addon, from fgure 7, s also easly noceable ha he nensy of lp shock s que srong. Alhough, he lp shock appears n he lower par of he expanson fan, however, he presen nvesgaon reveals ha he nensy of he lp shock s consdered o be really an mporan par of he flow feld. Ths shock s slghly curved n naure due o sudden expanson. The nensy s grealy srong for hgh Mach flow and causes losses o he flow feld as observed from he presen sudy. Fgure 6. Shock represenaon of he flow feld Also, he presence of lp shock can be seen n recovery curve of fgure 5, whch appears o be a hump lke srucure a he separaon edge. VIII. CONCLUSION A 2D numercal model s esablshed o sudy fully supersonc flud flow over a backward facng sharp edge sep by ncorporang hybrd RANS-LES urbulence model. I relaes o he Spalar-Allmaras model whch ncludes a vscosy-lke varable (ṽ). The model also consders he added essenal ssues namely producon, dffuson and desrucon facors n addon o he very normal aspecs assocaed wh he presen nvesgaon. The smulaons are done by he sad urbulen model wh he nflow free sream Mach number of 2.5 assocaed wh free sream pressure and velocy of N/m 2 and m/s 2, respecvely. The smulaon resuls are compared wh he correspondng expermenal resuls avalable n he leraure. The hybrd RANS-LES model gves reasonably beer and accurae resuls hroughou he enre flow doman and hence, s consdered for all furher nvesgaons. I s also wnessed ha he sudden vscous layer separaon s he cenral cause of he shock generaons. Addonally, he uneven pressure recovery s on accoun of he sudden expanson flow over he sharp edge sep. Furhermore, he sudden expanson flow ncreases he nensy of shock whch leads o he uneven flow behavors. Indeed, he presen nvesgaon s really valuable o undersand he flow characerscs over any ype of backward facng sharp edge seps. However, a numercal model peranng o use of backward facng rounded sep (.e. geomerc varaons n sep) s underway and s planned for he fuure o elmnae he lp shock compleely from flow feld for realzng he smooh and favourable flow. ACKNOWLEDGMENT The auhor would lke o hank he edor and he revewers for her noble houghs, valuable me and Page 40

6 conrbuons for exendng nsghful revews o he research arcle. REFERENCES [1] Smh, Howard E. The flow feld and hea ransfer downsream of a rearward facng sep n supersonc flow. No. ARL Aerospace Research Labs, Wrgh Paerson AFB, Oho, (1967). [2] Launder, B. E., and B. I. Sharma. "Applcaon of he energy-dsspaon model of urbulence o he calculaon of flow near a spnnng dsc." Leers n hea and mass ransfer Vol. 1, Issue 2 (1974): [3] Armaly B. F., Durs F., Perera J. C. F., and Schoenung B., Expermenal and heorecal nvesgaon of backward facng sep flow, Journal of Flud Mechancs, Vol. 127, pp , (1983). [4] Spalar, Phllpe R., and Seven R. Allmaras. "A oneequaon urbulence model for aerodynamc flows." (1992). [5] Anderson, John Davd, and J. F. Wend. Compuaonal flud dynamcs. Vol New York: McGraw-Hll, (1995). [6] Neumann, Jens, and Hans Wengle. "DNS and LES of passvely conrolled urbulen backward-facng sep flow." Flow, urbulence and Combuson (2003): [7] Hamed, A., K. Das, and D. Basu. "Numercal smulaons of fludc conrol for ransonc cavy flows." AIAA Paper 429, (2004). [8] Chen, Zh, e al. "An expermenal sudy on fne srucures of supersonc lamnar/urbulen flow over a backward-facng sep based on NPLS." Chnese Scence Bullen, Vol. 57, Issue 6, (2012): [9] Lu, Haxu, e al. "Effecs of Inflow Mach Number and Sep Hegh on Supersonc Flows over a Backward- Facng Sep." Advances n Mechancal Engneerng (2013). [10] V. I. Terekhov, Ya. I. Smul sk, and K. A. Sharov, Expermenal sudy of he separaed flow srucure behnd a backward-facng sep and a passve dsurbance, Journal of Appled Mechancs and Techncal Physcs, Volume 57, Issue 1, (2016) pp Page 41