Influence of Heavy Gas Blowing into the Wall Layer of the Supersonic Boundary-layer on its Transition

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1 Influnc of Havy Gas Blowing into th Wall Layr of th Suprsonic Boundary-layr on its Transition S.A.GAPONOV, V.I.LYSENKO, B.V.SMORODSKY, YU.G.ERMOLAEV, A.D.KOSINOV, N.V.SEMIONOV, A.A.YATSKIKH Khristianovich Institut of Thortical and Applid Mchanics Novosibirsk, RUSSIA Abstract: - Th xprimntal invstigation of th influnc of th distributd blowing of havy gas (sulfur hxafluorid, SF ) into th wall layr of a suprsonic boundary layr on a flat plat (at fr stram Mach numbr M=) on th laminar-turbulnt transition hav bn prformd. It is shown xprimntally for th first tim that in cas of such blowing thr is th boundary layr stabilization, and th laminar-turbulnt transition is rmovd downstram from th modl lading dg. Ky-Words: - Comprssibl boundary layr, xprimntal, blowing, havy gas, stability, transition Introduction In a numbr of tasks, th qustion ariss about th boundary layr control. On of mthods of such control is th gas suction from a boundary layr through a prmabl surfac which slowdown th turbulization procss. Th stabilizing rol of suction is xplaind by th thicknss rduction of a boundary layr and th formation of a mor stabl vlocity profil. Mthods of th flow stabilization (both at subsonic, and at suprsonic spds) ar discussd in books [, ]. At th sam tim in rsarchs on th boundary layr stability at th suction it is ncssary to considr proprtis of prmabl surfacs which can influnc on th stability significantly. For th first tim an influnc of prmabl covring proprtis on th subsonic boundary layr stability was invstigatd thortically by Gaponov [3]. In th subsqunt papr [3] h offrd th impdanc ratio btwn vlocity and prssur prturbations on th prmabl surfac, taking into account th gas comprssibility. It has bn usd for rsarchs both for subsonic [3] and for low suprsonic flows [4]. For a long tim ths thortical works wr singl in th world, and xprimntal studis of this problm wr not availabl at all that was causd first of all by lack of qualitativ prmabl matrials. But now th situation has changd. In rcnt yars xprimnts on stability both hyprsonic [5-8], and a suprsonic boundary layr wr conductd [9-3]. Rsults of ths xprimnts indicat on thir satisfactory agrmnt with data of th linar thory [3-4] both for suprsonic [9-3] and for hyprsonic [4-5] spds. At rsarchs of th laminar-turbulnt transition and stability of a boundary layr, both in natural conditions, and at introduction of artificial disturbancs [9-3], it was obtaind that th porous coating acclrats a prturbations incras of a low frquncy (th first mod) and dstabilizs a boundary layr. Howvr, calculations [-7] showd that it is possibl to stabiliz a suprsonic boundary layr by mans of an injction of th havy gas into th wall ara. This work is dvotd to th xprimntal vrification of ths thortical conclusions. Th aim of this work is th xprimntal study of th influnc of th havy gas injction (sulfur hxafluorid, SF ) in a suprsonic boundary layr on its stability and th laminar-turbulnt transition at Mach numbr М =. Exprimntal tchniqu Th xprimnts wr prformd in th suprsonic wind tunnl T-35 of th Institut of Thortical and Applid Mchanics of th Russian Acadmy of Scincs with th tst sction dimnsions mm at Mach numbr M=, stagnation tmpratur T 0 90º К and unit Rynolds numbrs R U / ( and.) 0 / m; U, th vlocity and kinmatic viscosity at th boundary layr dg. E-ISSN: Volum, 07

2 Th insulatd flat plat was usd as modl (Fig. ) which was mad from stainlss stl X8H9T. Its sizs wr: long mm, thick - 0 mm and wid - 00 mm. Th plat front was skwd at an angl4 0. Th blunting radius of th front dg was about 0.05 mm. M Fig.. Th xprimntal modl in th plan. All porous insrt is markd with blu shading (x=50 70mm), prmabl its part is markd with rd shading (x=5 55mm). Th bginning of th longitudinal coordinat x (along th dirction of an xtrnal flow) is on a lading dg of a modl. On th sction of a working surfac x=50 70mm (on th whol width of th plat) th groov was mad in th modl whr th flat porous insrt was insrtd (a flush with th main modl surfac). Th porous insrt was mad from stainlss stl ПНС-8. Its proprtis wr th following: th porosity - 39%, th filtration purity (an analogu of a por siz) -0µm, th thicknss -.5mm, th surfac roughnss R z - µm. Th surfac roughnss was masurd by th optical profilomtr (Zygo Nw Viw 7300). Structur of th porous insrts is shown in Fig.. According to th modl construction, th prmabl part of a porous insrt sttld down on th sction x=5 55mm and -85mm<z<. Th plat was attachd to sid walls of th wind tunnl working rigidly and it was installd undr a zro attack angl. (а) (б) Fig.. Schmatic rprsntation of porous insrts: plan viw (a) cross-sction (b). If th working modl was circulatd in xprimnts by air, thn as a gas which was injctd in a boundary layr through a prmabl surfac was chosn th sulfur hxafluorid, SF. Molcular wight of this gas m 4.07 and its dnsity at rfrnc conditions is qual to.5 kg/m³, i.. it is about 5 tims havir than air. Exprimnts wr z x 00 mad for a diffrnt xpns of th sulfur hxafluorid at its injction in a wall sction of th boundary layr. Masurmnt of a boundary layr transition location and its stability to natural prturbations wr prformd using th constant tmpratur anmomtr (CTA) with th snsor from tungstn hot-wir which had th diamtr qual to 0 µm and th long qual to.5mm. Th snsor ovrhating valu was qual to 0.8. Thrfor it is possibl to claim that pulsations of mass flow wr fixd mainly. Amplitud masurmnts of natural disturbancs in th boundary layr wr conductd in a location whr thr wr th highst pulsations at constant E (E is an avrag voltag in a bridg diagonal of an anmomtr) that corrspond to th lins of a constant mass flow. Th pulsation and avrag charactristics of a flow wr masurd by mans of th automatd systm of th data collction [8] which th wind tunnl of T-35 is quippd. Th pulsation signal from a hot-wir anmomtr is rgistrd by -bit 750 khz analog-to-digital convrtr. Lngth of ralization was 553 points. For monitoring of th rsults rpatability four masurmnts wr carrid out at ach point. Man voltag valus from th hotwir anmomtr wr masurd by th digital voltmtr Agilnt 3440А and ntrd into th computr. As a rul indications of avrag and pulsation charactristics of a flow wr rgistrd through ach mm on longitudinal coordinat x. Amplitud-frquncy spctrum A( f, x ) was calculatd as a rsult of th powr spctra avraging, which was carrid out on 0 points that thr corrspondd to a strip. khz. 3 Flow Stability calculations Dynamics of a binary mixtur of viscous hatconducting comprssibl gass is dscribd by a common systm of diffrntial quations in partial drivativs which can find in [9, 0]. From ths common quations authors of this papr obtaind th systm of quations in an approximation of a local slf-similarity of a flow for a flow dscription in a two-dimnsional (D) stationary suprsonic boundary layr of binary gass mixturs in an absnc of chmical ractions []. Ths quations tak into account diffusion, thrmal diffusion and a longitudinal prssur gradint. Th most important paramtrs that influnc on a dynamics of th mixtur ar: m, m -molcular wights and C p, C p - spcific hat capacitis of a main gas and an E-ISSN: Volum, 07

3 impurity, rspctivly and a impurity flow rat through a modl surfac: fw wvw R, whr w mixtur dnsity on a wall th normalizd at a dnsity on xtrnal boundary layr dg, V w normal componnt of a vlocity on th wall normalizd at a vlocity on xtrnal boundary layr dg, R Rynolds numbr constructd on Blasius's scal of a laminar boundary layr x/ U. It is possibl to s that th injction paramtr actually is th normalizd mass flow of th mixtur through th prmabl surfac. Calculations of viscosity and hat conductivity cofficints of componnts of binary mixturs and diffusion cofficints of an impurity wr carrid out within th kintic thory [9] with us Lonard- Jons potntial. To calculat th viscosity and thrmal conductivity of a binary mixtur th rlations [3] hav bn usd. For calculations of a thrmal conductivity of polyatomic gass Euckn's corrction [4] was takn into account also. Th boundary layr quations of th binary gas mixturs was intgratd numrically by mans of th Rung - Кутта mthod of th fourth ordr. Th quations, boundary conditions and numrical mthods which wr usd in this papr ar prsntd in mor dtail in []. Th linar stability thory of boundary layrs of binary mixturs was dvlopd by authors of this papr and prsntd in [4, 5]. Th linarization of th dimnsionlss quations of th viscous hatconducting binary gas mixturs motion for quasiharmonic on spac and tim disturbanc of a viw qx, y, z, t q yxpi x z Ct rducs to th following systm of ordinary diffrntial quations: d dv i ( U C) v i( u w) 0, dy dy du ip d u i( U C) u v, dy M R dy dp i U Cv, M dy ip dw i ( U C) w, () M R dy d c dc i U Cc v, dy RSm dy dh i U Ch v i U C p dy, d h d c h h R Pr dy R Sm Pr dy whr u, v, w, h, c disturbancs of thr vlocity componnts, an nthalpy and an impurity concntration rspctivly;, longitudinal and transvrsal wav numbrs; f U a nondimnsional frquncy; f frquncy in Hz; C / ; F / R f U frquncy paramtr. Th systm () is solvd with th following homognous boundary conditions on th surfac and on th outr dg of th boundary layr: dc u, w, h, fwc wd 0 при y 0 dy, () u, w, h, c 0 при y Intgration of th ignvalu problm (-) was carrid out numrically with using of a orthogonalizations mthod. Th numrical solution mthod of th stability quations is dscribd in [] in mor dtail. Stability calculations of th boundary layr of th binary gas mixtur had bn carrid out invstigatd in [5]. 4 Rsults In this xprimnt th laminar- turbulnt transition location on a flat plat was invstigatd in a dpndnc on th mass flow injctd of th sulfur hxafluorid in a wall layr of a boundary layr. R t Q, г/см мин Fig. 3. Dpndnc of th transition Rynolds numbr on th mass flow of th injctd sulfur hxafluorid Th transition Rynolds numbr was dtrmind * * as Rt xr, whr R a unit Rynolds numbr at which th maximal valu of a snsor signal of a anmomtr was rachd at x =40 mm. Exprimnts wr mad at thr mass flow valus of th blown sulfur hxafluorid: Q=(0, 0.085, 0.8) g/(cm min.). Th rcivd rsults on th influnc E-ISSN: Volum, 07

4 of such injction on th transition location at R 0 / m ar shown in Fig. 3. From Fig. 3 it follows that transition Rynolds numbr incrass with an incras of th sulfur hxafluorid xpns. At R. 0 / m th natural disturbancs dvlopmnt on a porous plat at Q=(0, 0.085) g/(cm min.) and th solid plat was invstigatd xprimntally. All ths data wr compard with calculations rsults in accordanc with th linar stability thory. insrt without an injction (Q=0), th porous insrt with th sulfur hxafluorid injction (Q=0.085 g / (cm min.)). Incras amplituds ar normalizd on thir valu at x = 70 mm, Ax70mm.5 A x, мм 0 Fig. 4 Nondimnsional spatial amplification rats α i for 3D prturbations vrsus angl χ It is known [] that an amplification rat of disturbancs dpnds on th transvrsal wav numbr β. For vry on β thr is a sliding angl χ=arctg(β/α r ). In Fig. 4 dpndncs of amplification rats on th sliding angl ar shows at diffrnt valus of th sulfur hxafluorid injction. It is possibl to s, that maximal amplification of disturbancs corrsponds to th sliding angl χ 0. Howvr in wind tunnls T-35 and othrs ons acoustic wavs with th sliding angl χ 40 prvail []. Exactly thrfor disturbancs with χ 40 ar gnratd in a boundary layr of a plat, that it was supportd by calculations of th stability of th boundary layr on a smooth solid plat for th studid frquncy rang at a simpl Rynolds numbr R. 0 / m. Th bst agrmnt of thortical incras curvs of disturbancs with xprimntal data was rachd at a slipping angl of disturbancs rlativ to main flow χ=40. This valu χ was usd in calculations of incras curvs of disturbancs in a boundary layr on a porous insrt. In Fig. 5 incras curvs of amplituds disturbancs, A=A (x), on longitudinal coordinat x (both th xprimntal, and calculatd (χ=40 )) at R. 0 m - and f=0khz for thr cass ar givn: 0 th solid smooth insrt, th porous Fig. 5 Incras curvs of disturbancs amplituds at th frquncy f=0 кгц по продольной координате. R =. 0 /m, calculation at χ=40 (dottd lins) and xprimnt (symbol), 0 th smooth solid insrt, th porous insrt without an injction (Q=0), th porous insrt with th sulfur hxafluorid injction, SF (Q=0.085 g/(sm min.)). From Fig. 5 it is visibl th rathr good agrmnt of calculations with xprimntal data. Th dviation of th xprimntal curvs from of th linar thory data indicats about a non-linar stag of a disturbancs dvlopmnt and th bginning of a laminar - turbulnt transition. This happns at x 40 mm on smooth solid plat (0), at x 0 mm on th modl with th porous insrt without blowing () and at х>0 mm on modls with th sulfur hxafluorid blowing, Q = g/(cm min) (). Fig. 5 shows clar that without an injction th surfac porosity dstabilizs a suprsonic boundary layr (M =) bcaus of a roughnss xistnc, but th havy gas injction stabilizs it significantly, it bcoms mor stabl vn in comparison with th boundary layr stability on a smooth solid surfac. 5 Conclusion Th xprimntal study of th influnc of th distributd havy gas (th sulfur hxafluorid, SF ) blowing in a wall rgion of a boundary layr on a laminar-turbulnt transition of a suprsonic boundary layr at Mach numbr M = was carrid out for th first tim. Exprimnts show that th havy gas blowing stabilizs a suprsonic boundary E-ISSN: Volum, 07

5 layr and incrass th transition Rynolds numbr. Th xprimntal data of disturbancs amplituds incras curvs agr with thortical rsults. This papr has bn supportd by Russian Foundation for Basic Rsarch (projct No a) and Russian Acadmy of Scincs (projct ). Rfrncs: [] S.A. Gaponov and A.A. Maslov, Disturbanc Dvlopmnt in Comprssibl Flows (in Russian), Novosibirsk, Nauka (980). [] S.A. Gaponov, Effct of gas comprssibility on th stability of a boundary layr abov a prmabl surfac at subsonic vlocitis, Journal of Applid Mchanics and Tchnical Physics, 975, Vol., No, pp [3] S.A. Gaponov, Stability of a suprsonic boundary layr on a prmabl surfac with hat transfr, Fluid Dynamics, Vol., No, 977, pp [4] Fomin V.M., Fdorov A.V., Shiplyuk A.N., Maslov A.A., Burov E.V., Malmuth N.D. Stabilization of a hyprsonic boundary layr by ultrasound-absorbing coatings, Doklady Physics, Vol.47, No5, 00, pp [5] V.M. Fomin, A.A. Maslov, B.Yu.Zanin, A.A. Sidornko, V.P.Fomichv, B.V.Postnikov, N. Malmuth, Elctric-discharg control ovr a vortx flow around bodis of rvolution, Doklady Physics, Vol.49, No., 004, pp [] N. Chokani, D.A. Bountin, A.N. Shiplyuk, A.A. Maslov, Nonlinar aspcts of hyprsonic boundary-layr stability on a porous surfac, AIAA Journal. Vol.43. No., 005, pp [7] A. Rashd, H.G. Hornung, A.V. Fdorov, N.D. Malmuth, Exprimnts on passiv hyprvlocity boundary-layr control using a ultrasonically absorptiv surfac, AIAA Journal, V.40, No.3, 00, pp [8] S.A. Gaponov, Y.G.Yrmolav, A.D.Kosinov, V.I. Lysnko, N.V. Smionov, B.V.Smorodsky, Th influnc of surfac porosity on th stability and transition of suprsonic boundary layr on a flat plat, Thrmophysics and Aromchanics, Vol.7, No., 00, pp [9] S.A. Gaponov, Y.G.Ermolav, A.D. Kosinov, V.I. Lysnko, N.V. Smnov, B.V.Smorodsky, Influnc of porous-coating thicknss on th stability and transition of flat-plat suprsonic boundary layr, Thrmophysics and Aromchanics, Vol.9, No.4, 0, pp [0] Yu.G. Ermolav, A.D. Kosinov, V.I. Lysnko, N.V. Smnov, B.V. Smorodskii, Joint prmability and roughnss ffct on th suprsonic flat-plat boundary layr stability and transition, Fluid Dynamics, Vol. 49, No 5, 04, pp [] S.A. Gaponov, Yu.G. Ermolav, A.D. Kosinov, V.I. Lysnko, N.V. Smionov, B.V. Smorodsky Stability of Suprsonic Boundary Layr on Prmabl Surfac, Archivs of Mchanics, Vol., No., 04, pp [] S.A.Gaponov, Yu.G. Ermolav, A.D. Kosinov, V.I. Lysnko, N.V. Smionov, B.V. Smorodsky, Thortical and Exprimntal Invstigation of th Stability of Suprsonic Boundary Layr on Porous Coating, Intrnational Journal of Thortical and Applid Mchanics, Vol., 0, pp [3] V.I.Lysnko, S.A.Gaponov, B.V. Smorodsky, Yu.G. Yrmolav, A.D. Kosinov, N.V. Smionov, Combind Influnc of Coating Prmability and Roughnss on Suprsonic Boundary Layr Stability and Transition, J. Fluid Mch., Vol.798, 0, pp [4] A.V. Fdorov, N.D. Malmuth, A. Rashd, H.G. Hornung, Stabilization of hyprsonic boundary layrs by porous coatings, AIAA Journal, Vol.39, No.4, 00, pp [5] A.V. Fdorov, A.N. Shiplyuk, A.A. Maslov, E.V. Burov, N.D. Malmuth, Stabilization of a hyprsonic boundary layr using an ultrasonically absorptiv coating, J. Fluid Mch., Vol.479, 003, pp [] S.A. Gaponov, B.V. Smorodsky, Suprsonic Boundary Layr of Binary Mixtur and its Stability, Intrnational Journal of Mchanics, Vol.0, 0, pp [7] S.A. Gaponov, B.V. Smorodsky, On stability of th suprsonic boundary layr with a forign gas injction, 8 th Intrnational Confrnc on Mthods of Arophysical Rsarch (ICMAR- 0), AIP Confrnc Procdings, Vol.770, Nol, 0, pp [8] A.D. Kosinov, Yu.G. Ermolav, N.N. Nikolav, N.N. Smionov, A.I. Smisynov, On th masurmnts of th pulsation in suprsonic boundary layr by constant tmpratur hot-wir anmomtr, Proc. 3d Int. Conf. on th Mthods of Arophysical Rsarch, Paralll, Pt 5, 007, pp [9] J.O. Hirschfldr, C.F. Curtiss, R.B. Bird, Molcular Thory of Gass and Liquids, John Wily and Sons, 954. E-ISSN: Volum, 07

6 [0] S.A. Gaponov, G.V. Ptrov, Stability of th boundary layr with nonquilibrium gas dissociation, Scinc, 03 (in Russian). [] S.A Gaponov, B.V Smorodskiy, Suprsonic laminar boundary layr of a binary gas mixturs, Hrald of NSU, Physics, Vol., No, 0, pp.5-5 (In Russian) [] W.H. Dorranc, Viscous Hyprsonic Flow, McGraw-Hill, 9. [3] A. Euckn, Übr di wärmlitfähigkit und untr Ribung dr gas, Physikalisch Zitschr., Vol.3, No4, 93, pp.34. [4] S.A Gaponov, B.V Smorodskiy, Control of suprsonic boundary layr paramtrs by blowing forign gas, Modrn Scinc: Rsarchs, Idas, Rsults, Tchnologis, SPIC "Triacon", N(), 05, pp [5] S.A. Gaponov, B.V. Smorodsky, Suprsonic boundary layr of binary mixtur and its stability, Intrnational Journal of Mchanics, Vol.0, 0, pp [] J. Laufr, Som Statistical Proprtis of th Prssur Fild Radiatd by a Turbulnt Boundary Layr, Th Physics of Fluids, Vol. 7, No 8, 94, pp E-ISSN: 4-34 Volum, 07

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