Effect of Combustion Heat Release on the Stability of Confined Boundary/mixing-layer Confluent flow

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1 Availabl onlin at ScincDirct Procdia Enginring (4) APISA4, 4 Asia-Pacific Intrnational Symposium on Arospac chnology, APISA4 Effct of Combustion Hat Rlas on th Stability of Confind Boundary/mixing-layr Conflunt flow Liu Zhiyong a, *, Shang Qing a, Liu Xiaoyong b, Fi Lisn b, Liu Fngjun b a China Acadmy of Arospac and Arodynamics, Bijing, 74, China b Bijing Powr Machinry Institut, Bijing, 74, China Abstract h issu of mixing nhancmnt of th ful and oxidizr in th combustor of a ramjt has rcivd mor and mor attntion. Various injction ways wr dsignd and justifid to improv th mixing procss by producing mor multiplscal vortx structurs. ndr th rstriction of compact configuration of th combustor in an intgral rockt dual combustion ramjt, a bttr way to nhanc mixing is turning th laminar flow to turbulnt flow. h prsnt study focuss on th stability analysis of th boundary/mixing-layr conflunt flow affctd by th combustion hat rlas in th combustion chambr. wo typs of basic flows ar formd for linar stability analysis both from a thortical modl and numrical computation. Eignvalu spctra and ignfunctions ar obtaind and compard. h rsults show that th hatrlas ffct stabilizs th conflunt mixing flow. 4 h Authors. Publishd by Elsvir Ltd. Pr-rviw undr rsponsibility of Chins Socity of Aronautics and Astronautics (CSAA). Kywords: Conflunt flow; mixing layr; linar stability; hat rlas. Introduction Mixing flows hav a numbr of industrial applications. h mixing of ful and oxidizr is of grat significanc to combustion and rsarchrs pay a lot attntion to mixing nhancmnt in powr dvics, such as ngins, ful clls tc. In th combustor of an intgral rockt dual combustion ramjt, th mixing ara lis adjacnt to th wall thus th * Corrsponding author. l.: ;. addrss: liuzhiyongtv@6.com h Authors. Publishd by Elsvir Ltd. Pr-rviw undr rsponsibility of Chins Socity of Aronautics and Astronautics (CSAA).

2 Liu Zhiyong/ Procdia Enginring (4) mixing procss is badly affctd by th confinmnt of walls. h prsnt study was incitd by this spcifid application and instability analysis was invstigatd to xplor th mchanism of mixing augmntation. Many progrsss about sking th mchanism of mixing nhancmnt in mixing layrs hav bn mad in rcnt dcads. Kumar t al. [] rportd an oscillating shock can incras th mixing-layr turbulnc lvls and thus nhanc mixing. Computational invstigations [] hav shown that stramwis vorticity inducd by baroclinic torqus in th mixing layrs nabls mixing nhancmnt. Whil rlativly lss attntion has bn paid to th confind mixing layr which is a bttr modl of actual dvics, spcially combustors. Linar stability thory (LS) and dirct numrical simulation (DNS) wr adoptd by Grnough t al. [] to study th wall ffct on th instability of comprssibl mixing layrs. hy found two typs unstabl mods, i.. K-H mod and suprsonic wall mod. Hu [4] studid th dvlopmnt procss of disturbanc in confind mixing layrs and found that vn if th disturbancs of two mods propagat linarly and sparatly, th disturbanc nrgy grow oscillatorily, and priodic structurs wr discovrd. Hudson t al. [5] compard th computational and xprimntal rsults of confind comprssibl mixing layrs and rportd that th growth rat corrsponds wll with th xprimnt in th inlt ara, whil discrpancy appars downstram. hy considrd th diffrnc rsultd from th wall ffct and fluid viscosity. Liu t al. [6] usd a boundary layr to modl th wall ffct and studid th instability faturs of half unboundd wak/boundary layr conflunt flow. Diffrnt distancs btwn th wak and th boundary layr wr invstigatd and th bst spacing for mixing nhancmnt was found. Basd on th primary rsarch on th instability of comprssibl boundary/mixing layrs conflunt flow in a twodimnsional planar channl [7], th prsnt study focuss on th ffct of hat rlas on th linar stability of th conflunt flow. wo man flows gnratd both by a thortical modl and numrical computation ar considrd. h hydrodynamic computation softwar Flunt is adoptd to conduct numrical simulations and th mixing of thyln and air is simulatd. Dtaild stability charactristics ar compard and analyzd.. chnical approachs Comprssibl linar stability quations ar adoptd undr th assumption that th basic flow is locally paralll, and th drivation can b radily found in th litratur [7]. h spatial scals in Cartsian coordinat systm ar * * * * nondimnsionalizd by x / u, prssur by u and othr quantitis by corrsponding fr stram valus of outr flow. W assum that th viscosity and thrmal conductivity satisfy Suthrland's law. h idal gas assumption is also adoptd. Instantanous flow variabls ar dcomposd into a bas and a fluctuation quantity and th disturbancs can b writtn as,,,, ˆ, ˆ, ˆ, ˆ, ˆ i x z t u v w p u y v y w y p y y () () in which α and β ar stramwis and spanwis wavnumbrs, ω is circular frquncy. h boundary conditions can b writtn as y H, uˆ vˆ wˆ ˆ y H, uˆ vˆ wˆ ˆ () whr H is half-width of th channl. Spatial instability is invstigatd in th prsnt study and thus ω is ral whil α and β ar complx. A fourth-ordraccurat diffrnc mthod [8] is applid to discrtiz th stability quations and thn a systm of homognous quations can b got, i.. F Müllr mthod and QZ algorithm ar mployd to calculat th ignvalu α, and furthr th corrsponding ()

3 Liu Zhiyong/ Procdia Enginring (4) ignfunction φ. h basic flow consists of two flows with diffrnt vlocitis. Boundary layrs li adjacnt to th walls btwn th outr flows and th walls and th mixing layrs li nar th cntrlin btwn th outr flows and innr flow. For th boundary layr flow th vlocity and tmpratur profils ar obtaind from similarity quations with adiabatic wall. For mixing layrs th vlocity is of hyprbolic tangnt form, i.. in which R=(- )/(+ ) is dimnsionlss spd ratio and σ is a positiv paramtr dtrmining th gradint of vlocity. h tmpratur profil is obtaind from a thortical modl basd on larg activation nrgy asymtotics[9], i.. for th outr flow: u u hr M u u u (5) and for th innr flow: R y u y (6) R whr γ is th ratio of hat spcific, β and β u ar th ratios of tmpratur and vlocity in th outr main flow to thos in th innr main flow. β hr is th cofficint of hat rlas. Largr valu implis strongr ffct of hat rlas. h prssur is assumd uniform in th wall-normal dirction as p / M. In th prsnt study w st σ=.4, and γ=.4.. Rsults and discussion u M u u hr u u tanh Spatial linar stability of th conflunt flow is studid and th gomtry of th channl is two-dimnsional with half width H=6. h width of innr flow is 5.5 thus th mixing layrs li at ym=± In th fr stram of outr flow th vlocity *=m/s and tmpratur *=7K. Whil in th innr flow *=5m/s and *=K. h convctiv Mach numbr Mc=.4 in this cas. During th numrical computation, actual siz of th plat dividing th two flows is considrd and th width D=7.5 and lngth L=6. h vlocity and tmpratur of basic flow ar shown in Fig. (Not that th lngth is scald by δ in th computation domain). u (4).. Stability faturs without hat-rlas ffct Fig.. Numrical rsults of basic flow. vlocity; tmpratur h mixing flow without hat rlas is invstigatd in this sction. For th thortical modl, th cofficint of hat rlas is st to b. Corrspondingly, combustion is not takn into considration in th numrical

4 4 Liu Zhiyong/ Procdia Enginring (4) computation. h profils of vlocity and tmpratur ar displayd in Fig.. A major diffrnc btwn th two vlocity profils lis in th wak rgion causd by th dividing plat. his rsults in th apparanc of additional inflctional points, which indicats mor complicatd stability charactristics Fig.. Basic flow without hat rlas. thortical modl ; numrical computation h ignvalu spctra (Fig. ) confirm th prvious prsumption. For th basic flow from thortical modl, only on unstabl mod xists on th spctra map. Whras, th computational flow xhibits mor instabilitis; thr unstabl mods appar on this map. h most unstabl mod, or th main unstabl mod, is of most intrst. Comparably, th growth rat of th main unstabl mod is almost tripl as larg as that of th thortical modl. Evn th scond most unstabl mod has largr growth rat than th lattr. hus th computational basic flow is mor unstabl..5 computational thortical. - i r Fig.. Eignvalu spctra in absnc of hat rlas, ω=., β=, R=.5E4 h corrsponding ignfunctions of two basic flows also diffr from ach othr obviously, as shown in Fig. 4. hr is a major diffrnc btwn th two flows on th symmtry charactristics. Both th ral and imaginary parts of th stramwis disturbing vlocity of th computational flow ar symmtric, whil th othr is antisymmtric. Dtaild comparison rvals that th disturbanc fluctuats mor rmarkably nar th mixing layrs for th main unstabl mod of computational basic flow.

5 Liu Zhiyong/ Procdia Enginring (4) u_ral u_imag. u_ral u_imag Stability faturs with hat-rlas ffct Fig. 4. Eignfuctions of u, R=.5E4, ω=., α= i, β= thortical modl; main unstabl mod of computational basic flow h mixing combustion flow of thyln and air is numrically simulatd. h vlocity and tmpratur profils at x=.7 ar adoptd as basic flow to conduct linar stability analysis (Fig. 5). h thortical modl givs th basic flow with hat-rlas cofficint βhr=. (Fig. 5). ndr th assumption of larg activation nrgy, th mixing layr is thinnr than that of basic flow without hat rlas. Whil th basic flow from computation has comparably thick mixing layr. For th numrical rsults, th hat rlas rsulting from combustion mak th tmpratur mildly highr, and two paks appar at th innr sid of conflunt flow bsid th mixing layrs. h influnc of wak rgion is also lssnd by hat rlas according to th vlocity profil. h ffct of hat rlas slightly affcts th basic flow as th slctd profils locat at a somwhat upstram position whr combustion is not strong nough Fig. 5 Basic flow with hat rlas. thortical modl, β hr=.; numrical computation h stability ignvalu spctra ar computd for th two basic flows (Fig. 6). Paramtrs ar th sam with Fig.. hr unstabl mods still xist for th computational basic flow. h main unstabl mod has growth rat twic

6 6 Liu Zhiyong/ Procdia Enginring (4) as larg as that of th thortical modl. Discrpancis of th growth rat com forth for ach of th unstabl mods whn th hat-rlas ffct is takn into considration. ypically for th computational basic flow, th growth rat of main unstabl mod dcrass as much as 4%. For th thortical modl, th growth rat of th unstabl mod slightly dcrass about 8%...8 computational thortical.6 - i r Fig. 6. Eignvalu spctra with hat-rlas ffct, ω=., β=, R=.5E4 his rsult indicats that th hat-rlas ffct stabiliz th basic flows both from th thortical modl and th numrical computation. h supprssion on th instability is spcially ffctiv for th thyln/air combustion flow. h shap functions of vlocity disturbancs ar dpictd for th basic flows from thortical modl with/without hat rlas (Fig. 7). Evidntly, both disturbing vlocity componnts of th no-hat-rlas cas ar largr than thos of th hat-rlas cas. his also indicats that th hat-rlas ffct supprsss th disturbing activitis, spcially nar th mixing layrs u_with hat rlas v_with hat rlas u_without hat rlas v_without hat rlas Fig. 7 Eignfunctions of disturbing vlocity (thortical modl) h ffct of hat-rlas cofficint on th stability of basic flow from thortical modl is also invstigatd, as shown in Fig. 8. h maximum of growth-rat curv dcrass, and corrspondingly th unstabl frquncy rang narrows with th incras of hat-rlas cofficint. Both signs imply that th hat-rlas ffct stabiliz th

7 Liu Zhiyong/ Procdia Enginring (4) 7 conflunt flow Mc=.4 hat rlas cofficint hr =. hr =. hr =. hr =. hr =4. hr =5. - i Fig. 8. Variation of growth rat with hat-rlas cofficint (thortical modl) 4. Conclusions h linar stability of two-dimnsional comprssibl conflunt boundary/mixing layrs flow has bn studid. Hat rlas is takn into considration to prliminarily masur its ffct on th stability of basic flows both from a thortical modl and numrical simulation. h thyln and air ar adoptd to simulat th combustion mixing flow by numrical computation. Linar stability thory givs th ignvalu spctra which rval that thr unstabl mods xist for th computational basic flow whil only on for th thortical modl. h main unstabl mod of th computational flow has growth rat thr tims as larg as that of flow from thortical modl. hrfor, th computational flow is mor unstabl than th thortical on. h shap functions of disturbancs ar also compard for both flows. h hat-rlas ffct is thn takn into account. Linar stability analysis shows that th growth rat of main unstabl mod dcrass up to 4% than no-hat-rlas cas for th computational flow. Manwhil, for th basic flow from thortical modl, th disturbing growth rat dcrass with th incras of hat rlas cofficint. And th frquncy rang of linar instability bcoms narrow corrspondingly. Conclusivly, hat rlas ffct stabilizs th conflunt mixing flow. Linar stability analysis lays foundation for th mchanism rsarch of mixing nhancmnt for th spcifid confind conflunt flow. Furthr invstigations ar xpctd to simulat th volution of disturbancs with Parabolizd Stability Equation mthod in th nar futur. Rfrncs [] A. Kumar, D. M. Bushnll, M.. Hussaini, A mixing augmntation tchniqu for hyprvlocity scramjts, Journal of Propulsion and Powr, 5 (987) [] J. P. Drummond, M. H. Carpntr, D. W. Riggins, M. S. Adams, Mixing nhancmnt in a suprsonic combustor, AIAA Papr , 987. [] J. A. Grnough, J. J. Rily, M. Sotrisno, D. S. Ebrhardt, h ffcts of walls on a comprssibl mixing layr, AIAA Papr 89-7, 989. [4] F. Q. Hu, A numrical study of wav propagation in a confind mixing layr by ignfunction xpansions, ICASE Rport No. 9-8, 99. [5] D. A. Hudson, L. N. Long, P. J. Morris, Computation of a confind comprssibl mixing layr, AIAA-95-7, 995. [6] W. W. Liou, F. J. Liu, Comprssibl linar stability of conflunt wak/boundary layrs, AIAA Journal 4() [7] Z.. Liu, X. J. uan, X.. Liu, L. S. Fi, F. J. Liu, Stability analysis of suprsonic boundary/mixing layrs conflunt flow, Chins Journal of hortical and Applid Mchanics 46(4) 8-6. [8] M. R. Malik, S. Chuang, M.. Hussaini, Accurat numrical solution of comprssibl linar stability quations, ZAMP (98) 89-. [9]. L. Jackson, M.. Hussaini, An asymptotic analysis of suprsonic racting mixing layrs, ICASE Rport No. 87-7, 987.