Numerical Studies on Flow Features past a Backward Facing Sharp Edge Step Introducing Hybrid RANS-LES

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1 ISSN NO : Numercal Studes on Flow Features past a Backward Facng Sharp Edge Step Introducng Hybrd RANS-LES Abstract Dr. Nrmal Kumar Kund Assocate Professor, Department of Producton Engneerng Veer Surendra Sa Unversty of Technology, Burla, Odsha, Inda nrmalkund@gmal.com The current nvestgaton nvolves the development of a D numercal model for examnng the flud flow behavors over a backward facng sharp edge step deployng the hybrd RANS-LES turbulent model whch also ncludes a vscosty-lke varable. The model encompasses key ssues lke producton, dffuson and destructon terms. The smulatons are done wth nflow free stream Mach number of.5 correspondng to free stream pressure and velocty of N/m and m/s, respectvely. The smulaton predctons of densty, vortcty and Mach number are observed to be farly consstent and also along the expected lnes all over the whole flow regme. It s observed that both vortcty ntensty and Mach number are qute hgh at the expanson fan near the lp of the separaton as well as near the reattachment shock, whereas, the flud densty s qute low at the same. Furthermore, t s also notced that the recrculaton vcnty whch s also otherwse called as dead ar regon has experenced the least flud densty, vortcty along wth the Mach number owng to non-vscous rotaton. In addton, both densty feld and Mach number beneft us n understandng whether the flud flow s compressble or ncompressble nature. In addton, the sudden change wthn the flow feld causes the vortcty generaton resultng n uneven flow performances. Keywords: Densty, Vortcty, Mach number, Backward Facng, Sharp Edge Step, Hybrd RANS-LES. 1. Introducton Steps on the surfaces of hypersonc or supersonc arcrafts make the flow regon more challengng and hence sgnfcant researches are really essental for refnng the dynamc desgn of arcrafts. Smth [1] executed expermental studes on the flow feld and heat transfer downstream of a rearward facng step n supersonc flow. Launder and Sharma [] appled the energy dsspaton model of turbulence to nvestgate the flow feld around a spnnng dsc. Armaly et al. [3] conducted both expermental and theoretcal studes on backward facng step flow. Spalart and Allmaras [4] presented a one-equaton turbulence model for evaluatng aerodynamc flows. Anderson and Wendt [5] testfed llustrous and complete descrptons of computatonal flud dynamcs. Neumann and Wengle [6] used both DNS and LES for nvestgatng passvely controlled turbulent flow of backward-facng step. Hamed et al. [7] done the numercal smulatons of fludc control for transonc cavty flows. Chen et al. [8] expermentally nvestgated on fne structures of supersonc lamnar and turbulent flow over a backward-facng step through the Nano-based Planar Laser Scatterng (NPLS). Lu et al. [9] numercally studed on the nfluences of nflow Mach number and step heght on supersonc flows over a backward-facng step. Terekhov et al. [10] accomplshed the expermental nvestgatons on the separated flow structure behnd a backward-facng step over and above the passve dsturbance. Volume 8, Issue VI, JUNE/018 Page No:438

2 ISSN NO : From the reported studes, to the best of author nformaton, t s observed that there s not a sngle extensve numercal study on flow over a backward facng sharp edge step by means of hybrd RANS-LES technque. Wth ths standpont, the current nvestgaton establshes the numercal studes on flow characterstcs over a backward facng sharp edge step by means of hybrd RANS-LES method. Furthermore, the numercal model also ncludes key features namely producton, dffuson and destructon terms apart from the usual ssues pertanng to the present physcal problem. Addtonally, the specfed model also ncludes both compressblty and eddy vscous effects. The model s thoroughly demonstrated for the careful numercal studes on flud flow behavours relatng to flow over a backward facng sharp edge step by usng the nflow free stream velocty and the correspondng Mach number as the mportant model parameters. Eventually, a D numercal model s developed to nvestgate the flow characterstcs, pertanng to densty, vortcty and Mach number dstrbutons, over a backward facng sharp edge step usng the hybrd RANS-LES/Spalart-Allmaras turbulent model whch also ncludes a vscosty-lke varable. Fnally, the smulaton predctons of densty, vortcty and Mach number are found to be qute consstent and also along the expected lnes throughout the entre flow regme. A. Geometrc model. Descrpton of Physcal Problem Fgure 1 embodes the setup confguraton for testng the backward facng sharp edge step flow over sharp edge geometry separatng at a step heght H = m, upstream dstance from nlet to step L u = m and downstream dstance from sharp edge step to outlet L d = 0.03 m. The dstance from downstream to upper boundary layer Z = m, spanwse dstance L= m and wdth B = m. The separaton and reattachment ponts are denoted by S and R respectvely and are lkely to be obtaned after carryng out numercal smulaton. Fg 1. Backward sharp edge step. B. Intal and boundary condtons Fg. Mesh of backward sharp edge step. The nflow free stream velocty U n = m/s, for whch the dentfed statc free stream pressure p n = N/m corresponds to the Mach number Ma =.5. At the left sde ahead of the step, the ntal temperature s mantaned at 169. K. The ntal condtons whch are set on the upstream are really useful durng the smulaton along the spanwse drecton, for obtanng the flow features beyond the step. Volume 8, Issue VI, JUNE/018 Page No:439

3 ISSN NO : Mathematcal Formulaton and Numercal Procedures A. Generalzed governng transport equatons Very generalzed governng transport equatons of mass, momentum and energy stated n the conservatve form of Naver-Stokes equaton for compressble flow n assocaton wth the nfluences of turbulence are as follows. ( u ) Contnuty: 0 (1) t x Momentum: Energy: Where, u t E t x u ( u u x ) p x x x ( S T u E p k kt S tu Sh u p p T T u p T p x t ) () (3) v Total energy, E e k h (5) The Reynolds stress term s modeled n terms of the eddy vscosty and s represented by: ( S S / 3 ) k / 3 (6) t t nn The eddy vscosty s defned as a functon of the turbulent knetc energy k, and the turbulent dsspaton rate ε, and s represented by: c f k / t (7) Besdes, all the model terms/symbols/coeffcents/functons have ther usual meanngs and values. B. Hybrd RANS-LES Turbulence Modellng The Hybrd RANS-LES/Spalart Allmaras turbulence model also otherwse called as Detached Eddy Smulaton (DES) model s a one-equaton model for the eddy vscosty. The dfferental equaton s derved from emprcsm and arguments of dmensonal analyss, Gallean nvarance and selected dependence on the molecular vscosty. Grd resoluton s not necessarly fner for ths model, but, one can essentally capture the flow feld wth the related algebrac models. The transport equaton for the workng varable (otherwse known as Spalart Allmaras varable).e. vscosty-lke varable (ṽ) s represented by: ~ ~ 1 ~ ~ ~ ~ ~ ~ ~ ~ u cb 1S cb c 1 f (8) w w t x x x x x d t ~ f 1 The eddy vscosty s represented by: v t (9) In addton, all the model terms/symbols/coeffcents/functons have ther usual meanngs and values. C. Numercal technques The transformed governng transport equatons are solved by expendng pressure based coupled framework relatng to fnte volume method (FVM) usng the SIMPLER algorthm. Fgure demonstrates that the grd of the computatonal doman s taken to be (4) Volume 8, Issue VI, JUNE/018 Page No:440

4 ISSN NO : non-unform and also grd s refned near the vcnty where the hgh gradent s expected. A comprehensve grd-ndependence test s carred out to develop an approprate spatal dscretzaton, and the levels of teraton convergence crtera to be used. As a consequence of ths test, we have used non-unform grds for the fnal smulaton. Correspondng tme step taken n the smulaton s seconds. A. Densty dstrbuton 4. Results and Dscussons It s qute obvous that the hgh Mach nflow s the cause of more densty gradent wthn the flow feld. Moreover, t s rather apparent that because of the shock generaton, densty recovery behnd the sharp edge step s also not flawless enough for smooth and sound flud flow. Addtonally, the physcs behnd the densty gradent due to two parallel shocks can smply be understood from the coloured densty feld together wth the correspondng vertcal scale bar, as llustrated n fgure 3. If the flow feld experences densty varaton more than fve present then the flow s consdered to be compressble flow whch may be observed from the densty feld. In other words, the densty feld helps us n understandng whether the flow s compressble or ncompressble nature. Fg 3. Densty feld for flow past backward facng sharp edge step. B. Vortcty dstrbuton Fgure 4 demonstrates the coloured vortcty dstrbuton together wth the correspondng vertcal scale bar, wthn the flow feld. It may be observed that the vortcty ntensty s qute hgh at the expanson fan near the lp of the separaton as well as near the reattachment shock. Owng to vscous layer separaton at the separaton edge, the generaton of lp shock has taken place, n addton, the nteracton of shock and expanson fan has led to the generaton of vortcty. The vortcty generaton s due to sudden change wthn the flow feld. Furthermore, the vortcty generaton becomes predomnant because of the turbulent boundary layer separaton. Fg 4. Vortcty dstrbuton for flow past backward facng sharp edge step. Volume 8, Issue VI, JUNE/018 Page No:441

5 ISSN NO : C. Mach dstrbuton The physcs behnd the Mach number gradent due to two parallel shocks can smply be understood from the coloured Mach number feld together wth the correspondng vertcal scale bar, as llustrated n fgure 5. If the Mach number s more than 0.3 then the flud regon s consdered to be compressble whch may be observed from the Mach number feld. In other words, the Mach number feld helps us n understandng whether the flud regon s compressble or ncompressble nature. However, no such changes or extra specal effect s observed near the upper regon of flow feld. 5. Concluson Fg 5. Mach feld for flow past backward facng sharp edge step. A D numercal model s developed to predct the flud flow behavors over a backward facng sharp edge step wth the hybrd RANS-LES turbulent model whch comprses a vscosty-lke varable (ṽ). The model also ncorporates fundamental terms namely producton, dffuson and destructon n to account. The numercal smulatons are conducted wth nflow free stream Mach number of.5 correspondng to free stream pressure and velocty of N/m and m/s, respectvely. The smulaton results of densty, vortcty and Mach number are wtnessed to be qute consstent and also along the lnes of expectatons wthn the entre flow regme. It s notced that both vortcty ntensty and Mach number are rather hgh at the expanson fan near the lp of the separaton and near the reattachment shock, whle, the flud densty s rather low at the same. In addton, t s also observed that the recrculaton vcnty whch s also otherwse termed as dead ar regon has felt the lowest flud densty, vortcty together wth the Mach number because of non-vscous rotaton. Furthermore, both densty feld as well as Mach number helps us n realzng whether the flud flow s compressble or ncompressble nature. Also, the sudden change wthn the flow feld leads to the vortcty generaton causng the uneven flow behavors. Defntely, the present smulaton predctons wll be very much useful to get more flow performances. Acknowledgments The author would lke to thank the edtor and the revewers for ther noble thoughts, valuable tme together wth contrbutons for gvng nsghtful revews to the artcle. Volume 8, Issue VI, JUNE/018 Page No:44

6 ISSN NO : References [1] Smth, Howard E. The flow feld and heat transfer downstream of a rearward facng step n supersonc flow. No. ARL Aerospace Research Labs, Wrght Patterson AFB, Oho, (1967). [] Launder, B. E., and B. I. Sharma. "Applcaton of the energy-dsspaton model of turbulence to the calculaton of flow near a spnnng dsc." Letters n heat and mass transfer Vol. 1, Issue (1974): [3] Armaly B. F., Durst F., Perera J. C. F., and Schoenung B., Expermental and theoretcal nvestgaton of backward facng step flow, Journal of Flud Mechancs, Vol. 17, pp , (1983). [4] Spalart, Phllpe R., and Steven R. Allmaras. "A one-equaton turbulence model for aerodynamc flows." (199). [5] Anderson, John Davd, and J. F. Wendt. Computatonal flud dynamcs. Vol. 06. New York: McGraw- Hll, (1995). [6] Neumann, Jens, and Hans Wengle. "DNS and LES of passvely controlled turbulent backward-facng step flow." Flow, turbulence and Combuston (003): [7] Hamed, A., K. Das, and D. Basu. "Numercal smulatons of fludc control for transonc cavty flows." AIAA Paper 49, (004). [8] Chen, Zh, et al. "An expermental study on fne structures of supersonc lamnar/turbulent flow over a backward-facng step based on NPLS." Chnese Scence Bulletn, Vol. 57, Issue 6, (01): [9] Lu, Haxu, et al. "Effects of Inflow Mach Number and Step Heght on Supersonc Flows over a Backward-Facng Step." Advances n Mechancal Engneerng (013). [10] V. I. Terekhov, Ya. I. Smul sk, and K. A. Sharov, Expermental study of the separated flow structure behnd a backward-facng step and a passve dsturbance, Journal of Appled Mechancs and Techncal Physcs, Volume 57, Issue 1, (016) pp Volume 8, Issue VI, JUNE/018 Page No:443