Numerical Simulation on Supersonic Turbulent Flow past Backward Facing Rounded Step Utilizing Hybrid RANS-LES

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1 Numercal Smulaon on Supersonc Turbulen Flow pas Backward Facng Rounded Sep Ulzng Hybrd RANS-LES Absrac Dr. Nrmal Kumar Kund Assocae Professor, Deparmen of Producon Engneerng Veer Surendra Sa Unversy of Technology, Burla, Odsha, Inda A D compuaonal model s developed o sudy he supersonc flow pas backward facng rounded sep usng he hybrd RANS-LES urbulence model, whch makes use of a vscosy-lke workng varable (ṽ. Furhermore, he model also encompasses more sgnfcan coness lke producon, dffuson and desrucon erms apar from he very usual ssues relang o he curren sudes. The numercal smulaons are execued wh he saed urbulence model wh he nflow free sream Mach number of.5 correspondng o he free sream pressure and velocy of N/m and m/s, respecvely. The smulaon resuls dsclose ha he gradual expanson goes on over he rounded sep causng he delay n vscous layer separaon. Indeed, resuls n he formaon of relavely shorer shear layer ogeher wh he farly shorer recrculaon regon, approachng owards he dead ar regon of he boom wall. Furhermore, s very clear from he curren sudy ha here s dmnshng of shock owng o he use of rounded sep. Keywords: Supersonc, Turbulen Flow, Backward Facng, Rounded Sep, Hybrd RANS-LES. 1. Inroducon Flow over backward-facng sep s one of he suably vvacous perspecves and has ncreased clear-cu aenon because of no us mnmalsm bu for exensve ndusral and scenfc pracces. The expermenal nvesgaons on flow feld along wh he hea ransfer, downsream of a rearward facng sep n supersonc flow s carred ou by Smh [1]. The energy dsspaon model of urbulence s nroduced by Launder and Sharma [], o examne he flow feld whn he vcny of a spnnng dsc. Boh expermenal and heorecal nvesgaons on backward facng sep flow are also repored by Armaly e al. [3]. A oneequaon urbulence model s used by Spalar and Allmaras [4], o analyse aerodynamc flow behavours. The fundamenal and ye comprehensve along wh he llusrous dscussons abou he CFD s also repored by Anderson and Wend [5]. Boh DNS and LES are ulzed by Neumann and Wengle [6], o nvesgae he passvely conrolled urbulen flow of backwardfacng sep. The numercal smulaons of fludc conrol for ransonc cavy flows s also conduced by Hamed e al. [7]. The expermenal nvesgaons on fne srucures of supersonc lamnar along wh urbulen flow over a backward-facng sep by usng Nano-based Planar Laser Scaerng (NPLS are also done by Chen e al. [8]. The numercal sudes on he effecs of nflow Mach number and sep hegh on supersonc flows over a backward-facng sep are carred ou by Lu e al. [9]. The expermenal sudes on he separaed flow behavor behnd a backward-facng sep ogeher wh he passve dsurbance are also execued by Terekhov e al. [10]. From he aforemenoned sudes, o he bes of auhor undersandng, s observed ha here s no a sngle full numercal nvesgaon on supersonc urbulen flow over a backward facng rounded sep by means of hybrd RANS-LES mehod. Wh hs oulook, he curren sudy exhbs he numercal sudes on flow characerscs over a backward facng rounded sep by consderng he hybrd RANS-LES mehod. Furhermore, he numercal model also ncludes addonal sgnfcan facors lke producon, dffuson and desrucon erms above and beyond he normal ssues concernng he curren physcal research problem. In addon, he Page No:547

2 specfed model also nroduces boh compressbly as well as eddy vscous effecs. The model s superbly demonsraed for he horough numercal nvesgaons on flud flow behavors relang o flow over a backward facng rounded sep by presenng he nflow free sream velocy ogeher wh he correspondng Mach number as he mporan model parameers. Fnally, he model predcons wh reference o he saed mporan model parameers are along he lnes of expecaons as well. Ulmaely, he curren case of fully supersonc urbulen flud flow over he backward facng rounded sep smulaed hrough he hybrd RANS-LES also accompanyng he vscosy-lke varable wnessed ha he dmnshng of shocks s only due o he geomerc changes n he seps. A. Geomerc model. Descrpon of Physcal Problem Fgure 1 llumnaes he sysem srucure for analysng he backward facng rounded sep flow over rounded sep geomery nvolvng sep hegh H = m, upsream dsance from nle o sep L u = m, downsream dsance from rounded sep o oule L d = m and he rounded sep radus H = m. The dsance from downsream o upper boundary layer Z = m, spanwse dsance L= m along wh he wdh B = m. Besdes, boh separaon (S and reaachmen (R pons are lkely o be wnessed from he numercal smulaon. Fg 1. Backward facng rounded sep. Fg. Mesh of backward rounded sep. B. Inal and boundary condons The nflow Mach number Ma =.5 Ma, assocaed wh he specfed nflow sac pressure of abou p n = N/m along wh he free sream velocy of U n = m/s. The emperaure o he lef of he rounded sep s mananed a T n = 169. K. For fully feelng he effecs of urbulence, he hybrd RANS-LES model s nroduced. 3. Mahemacal Formulaon and Numercal Procedures A. Generalzed governng ranspor equaons Very generalzed governng ranspor equaons of mass, momenum and energy saed n he conservave form of Naver-Sokes equaon for compressble flow n assocaon wh he nfluences of urbulence are as follows. ( u Connuy: 0 (1 x Momenum: Energy: u E x ( u u x p x x x ( S T u E p k k S u Sh x ( (3 Page No:548

3 u u u Where, p p p (4 T T T p v Toal energy, E e k h (5 The Reynolds sress erm s modeled n erms of he eddy vscosy and s represened by: ( S S / 3 k / 3 (6 nn The eddy vscosy s defned as a funcon of he urbulen knec energy k, and he urbulen dsspaon rae ε, and s represened by: c f k / (7 B. Hybrd RANS-LES Turbulence Modellng The Hybrd RANS-LES/Spalar Allmaras urbulence model also oherwse called as Deached Eddy Smulaon (DES model s a one-equaon model for he eddy vscosy. The dfferenal equaon s derved from emprcsm and argumens of dmensonal analyss, Gallean nvarance and seleced dependence on he molecular vscosy. Grd resoluon s no necessarly fner for hs model, bu, one can essenally capure he flow feld wh he relaed algebrac models. The ranspor equaon for he workng varable (oherwse known as Spalar Allmaras varable.e. vscosy-lke varable (ṽ s represened by: ~ ~ 1 ~ ~ ~ ~ ~ ~ ~ ~ u cb 1S cb c 1 f (8 w w x x x x x d ~ f 1 The eddy vscosy s represened by: v (9 In addon, all he model erms/symbols/coeffcens/funcons have her usual meanngs and values. C. Numercal echnques The ransformed governng ranspor equaons are solved by expendng pressure based coupled framework relang o fne volume mehod (FVM usng he SIMPLER algorhm. Fgure demonsraes ha he grd of he compuaonal doman s aken o be non-unform and also grd s refned near he vcny where he hgh graden s expeced. A comprehensve grd-ndependence es s carred ou o develop an approprae spaal dscrezaon, and he levels of eraon convergence crera o be used. As a resul of hs es, number of non-unform grds are used for he fnal smulaon. Correspondng me sep chosen n he curren smulaon s seconds. A. Pressure dsrbuon 4. Resuls and Dscussons Fgure 3 shows he coloured pressure feld ogeher wh he vercal scale bar, demonsrang he gradual decrease n pressure near he vcny of he expanson fan regon, whle, he reaachmen shock regon has also noced gradual ncrease n pressure. Furhermore, he recrculaon vcny.e. dead ar regon has realzed he leas pressure because of nvscd roaon. Addonally, he supersonc urbulen flow over he backward facng rounded sep has also wnessed gradual pressure flucuaons beween expanson fan as well as reaachmen shock wave regons. In addon, s raher apparen ha due o he gradual expanson (because of very less pressure graden over he rounded sep here s smooh and flawless flud flow. In oher words, he pressure graden beween he expanson fan and reaachmen shock s very consderably low. Hence, he relavely less pressure graden helps he flow feld o be effcen, effecve and uneven. Besdes, fgure 3 also llusraes he physcs behnd he pressure graden owng o wo parallel weak shocks. Page No:549

4 Fg 3. Pressure feld for flow pas backward facng rounded sep. B. Velocy dsrbuon Fg 4. Velocy vecor for flow pas backward facng rounded sep. Fgure 4 descrbes he velocy vecor peranng o he supersonc urbulen flud flow over he backward facng rounded sep. I s que obvous ha gradual expanson over he rounded sep leads o delay n vscous layer separaon resulng n he formaon of relavely shorer shear layer and reaachmen lengh over he boom wall assocaed wh he reaachmen shock and redevelopng boundary layer. Besdes, he flow around he shear layer approaches o he boom wall whch wll follow along he nal drecon. However, a par of he flow reverses o he dead ar regon whch causes as a recrculaon regon. However, he recrculaon regon ges reduced/mnmzed and he reaachmen lengh becomes shorer wh very less flow feld losses leadng o que smooh and flawless flow near he recrculaon vcny. Furhermore, he coloured velocy vecor ogeher wh he horzonal scale bar, whn he flud flow regon as superbly llusraed n fgure 4, also helps us for appropraely perfec undersandng of he reaachmen pon flow physcs proxmae o he boom wall regon. 5. Concluson In he curren nvesgaon, a D numercal model s developed o sudy he fully supersonc urbulen flow characerscs over a backward facng rounded sep. The model also ake accoun of exra mporan ssues lke producon, dffuson and desrucon facors, n addon o he very normal feaures on he subec of he curren sudy. The model s wonderfully esed for he horough numercal sudes on flud flow characerscs usng he compressble urbulen hybrd RANS-LES, whch nvolves a vscosy-lke workng varable (ṽ. The model ncludes he nflow free sream velocy and he correspondng Mach number as he mporan Page No:550

5 model parameers. Evenually, he model resuls relang o he saed val model parameers are also along he expeced lnes. In addon, he model s observed o gve farly beer and conssen resuls, and hence, s chosen for he presen research examnaons. Besdes, he smulaon resuls show ha he gradual expanson occurs over he rounded sep gvng rse o he delay n vscous layer separaon. Defnely, reasons he formaon of que shorer shear layer ogeher wh he equally shorer recrculaon regon, approachng owards he dead ar regon of he boom wall. Moreover, s que obvous abou he presence of very weak shock over he rounded sep. Therefore, s realzed ha here s dmnshng of shocks due o he modelng pracce wh rounded sep. Acknowledgmens The auhor would lke o hank he edor and he revewers for her noble houghs, valuable me ogeher wh conrbuons for exendng nsghful revews o he 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. [] 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 (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. 17, pp , (1983. [4] Spalar, Phllpe R., and Seven R. Allmaras. "A one-equaon urbulence model for aerodynamc flows." (199. [5] Anderson, John Davd, and J. F. Wend. Compuaonal flud dynamcs. Vol. 06. New York: McGraw-Hll, (1995. [6] Neumann, Jens, and Hans Wengle. "DNS and LES of passvely conrolled urbulen backwardfacng sep flow." Flow, urbulence and Combuson (003: [7] Hamed, A., K. Das, and D. Basu. "Numercal smulaons of fludc conrol for ransonc cavy flows." AIAA Paper 49, (004. [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, (01: [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 (013. [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, (016 pp Page No:551