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1 »»ƒœ» Õ À Õ»»ŒÕ»«Œ ÕÕ «Œ / * M = : [ 3] [] [; 3]. [3] [4] -. - * ( )..... // : ISSN ÂÒÚÌËÍ Õ. ÂË: ËÁËÍ. 06. ÓÏ.. ÔÓÌÓ.. ÏÓÓ ÒÍËÈ 06

2 6 ËÁËÍ ÊË ÍÓÒÚË ÌÂÈÚ Î Ì Ë ËÓÌËÁÓ ÌÌ ÁÓ [5 7]. [8; 9] () -. - [0]. [; ] [3]. - - [4 7] :. [8] :. - m - m. - [8; 0]. [8]. - (s y) s y ( U) ( V) 0 () s y U U P U U V () s y s y y h h P q U U V U (3) s y s y y c c j U V (4) s y y m mm RT P RT (5) m ( m m ) c m T q h h j y (6) RTT j m m m m m c c c T c T D j. (7) y T y

3 ÔÓÌÓ.. ÏÓÓ ÒÍËÈ.. À ÏËÌ ÌÈ ÔÓ ÌË ÌÈ ÒÎÓÈ ËÌ ÌÓÈ ÒÏÂÒË ÁÓ 7 U V s- y-- ; ; h - ; P ; T ; q j y-; ; R ; D ; T : V U Gsin U U G cos dt at a 0 dy c T c c T V c D. (8) y T y j v c (. [8]). : U=U T=T c. P = P () (5) UP VP 0 s RT y RT U V dp U srt yrt P ds RT (9) [] - y U V dp dy (0) 0 RT s RT P ds (0) P y 0 (9) V dp 0. () y s RT P ds ( s y) N() s f( y) U( s y) U () s U( y) ( s y) () s ( y) () y y () s. dp du = U ds ds dh dp du U. ds ds ds (0) RT RTN y df P y df U N. U y U y dy U y dy [] s / / (3) 0 N() sp U ds s s 0 s U ds. / = s / U df df U dy dy F f. (4) (0) (4) [] a a () s a( y) a a U V s y (5) da f a da UUa. ds s dy () d du du s du F U. (6) dy dy dy U ds - - / ( s ) q( y) q U h. - (3) (5) dq sdu dh MU h F dy Uds dy (7) du M. dy c h =c p T h h c T p cp Tc cpt c cp c T c T p

4 8 ËÁËÍ ÊË ÍÓÒÚË ÌÂÈÚ Î Ì Ë ËÓÌËÁÓ ÌÌ ÁÓ cp cp cp cp = =. (8) cp cp (4) (6) (7) : / dj dc ( s ) F j j (9) dy dy u dt q h h j dy (0) R T T c m m m m m c j p dc c T c dt j D () dy T dy D D. c p (4) (7) (9) () (8) - (5) T m= m m m. () z F z ( du / dy) z3 U z4 s du q z5 T z6 j z7 c u U ds (4) (7) (9) () dz z3 dz zz z3 u dy dy dz3 z dy dz4 dh Mz3h u z dy y M z3 dz5 R T z4 cp z5 z5 dy cp m z6 m m m mc dz 6 c T c dz 5 z z6 D dy D z5 dy dz 7 z T 7 z 7 dz 5 z6 D. dy D z5 dy (8) () dh dy = h c z z p 7 5 m m m m m m z z 7 5 dz p p dh dz c 7 5 z5 c z7 dy dy dy T z7 z7 dz 5 cp z5 z6 D D z5 dy R p p z6. m m m mz7 T c z7 z4 c z5 z5 c p m (8) F=z V/U. () V dp RT s P ds. N f y N dp f N f s y s P ds y 0 y s 0 RT U dln Np fn u u ds RT RT f F / RT s RT R / R s /. ( ) R Ux /. F R vv / ( R T). - () - R z Gsin z RT 3 G cos dz5 az 5a 0 dy dz z 7 T 7 z 7 dz 5 D dy z 5 y RT z z 0. 7 z 7 z 3 =z 5 =. (3)

5 ÔÓÌÓ.. ÏÓÓ ÒÍËÈ.. À ÏËÌ ÌÈ ÔÓ ÌË ÌÈ ÒÎÓÈ ËÌ ÌÓÈ ÒÏÂÒË ÁÓ 9 [] (0) - ( ) ( u 0 ) dz z3 dz zz dy dy dz3 z dy dz4 dh z M z3 (4) dy y dz5 z4 cp cp z5z6 dy dz6 z6 dz7 z6 z dy D dy D dh z dy c c z 6 cp cp z5 D p p 7 z4 cp cp z5z6. : D dz dy R T z z 0. (5) 7 7 [] - X G X X X G X X G X cm / m X cm/ m m m 4 8 m m G [ m m ] 8 m m 4 -. X X X.065G X X.065G X Eu i i Eu Cpi Ri cp i 5R i mi m m 4 G 8 m m m m 4 G. 8 m m - * * 6 mt i * 5 R * i * () i i. di 4 mi 7 D D T m m mm * * P T D - = ( + )/ - P T -. ()* (4) -. - (3) (5). ()* - - M = : - (CCl 4 ) (X) (H). - -

6 0 ËÁËÍ ÊË ÍÓÒÚË ÌÂÈÚ Î Ì Ë ËÓÌËÁÓ ÌÌ ÁÓ 0.3 c m d A /K K C p H H N Air Kr X SF CCl f y/ c f y/ c c y f ; () CCl 4 () - M -. - : c c y/ - f () () M. f. c - y (. ) (. ): - - CCl U Uy - - f. (. ) (. ) M y - H (. 3 ) CCl 4 (. 3 ) - M. ( -. ) f (. ) f

7 ÔÓÌÓ.. ÏÓÓ ÒÍËÈ.. À ÏËÌ ÌÈ ÔÓ ÌË ÌÈ ÒÎÓÈ ËÌ ÌÓÈ ÒÏÂÒË ÁÓ U.0 U.0 -f f () () y y U Uy 0 ; () CCl 4 () = f f () -f () y y y 0 ; () CCl 4 () = f.8 T f ().8 T f () 0 4 y y T T y 0 ; () CCl 4 () = f. 4 T T y. (. 4 )

8 ËÁËÍ ÊË ÍÓÒÚË ÌÂÈÚ Î Ì Ë ËÓÌËÁÓ ÌÌ ÁÓ C f R H Air f C f R f ; = C f R X Air H T /T C R - f T T ; 0 = St/St(f ) f T /T. 7. T T St - - = 07 X Air H X. (. 4 ) f T 65 T (.. ) C R C f.. 6 C f R. T -. (.. 5) f 0 - f 0. T T T T (0) - f

9 ÔÓÌÓ.. ÏÓÓ ÒÍËÈ.. À ÏËÌ ÌÈ ÔÓ ÌË ÌÈ ÒÎÓÈ ËÌ ÌÓÈ ÒÏÂÒË ÁÓ (0) - T T ( - ) du dy - (. 8 ) (. 8 ) (. 8 ). - ddy dudy 0 ( ) - - [8] f du dy (. 8 ) (.3) Cp Cp d d T (du/dy) f y (du/dy) f y (du/dy) f y du dy - () () CCl 4 () 0 0; = f ( f 0 ) - f 0 - : 05 m m () () ()

10 4 ËÁËÍ ÊË ÍÓÒÚË ÌÂÈÚ Î Ì Ë ËÓÌËÁÓ ÌÌ ÁÓ m /m =8 -f () y m /m =8 4 -f 0 4 y y 05 m m 8 ; f 0 = ; - () T T 05 (). 9 - T T m m m m () Smith J. W. Eckrt E. R. G. Schnidr P. J. Fauldrs C. R. Effct of diffusion filds on th laminar boundary layr // J. Aro. Sci Vol.. P Eckrt E. R. G. Schnidr P. J. Effct of diffusion in an isothrmal boundary layr // J. Aro. Sci Vol. 3. P Fauldrs C. R. A not on laminar boundary layr skin friction undr th influnc of forign gas injction // J. Aro. Spac Sci. 96. Vol. 8. P Korobkin I. Th ffcts of th molcular proprtis of an injctd gas on comprssibl laminar boundary layr skin friction and hat transfr // U.S. Naval Ordnanc Laboratory Rport Cravn A. H. Th comprssibl laminar boundary layr ith forign gas injction // Collg of Aronautics Cranfild Rport No Albact L. M. Gloacki W. J. Skin friction and hat transfr charactristics of th comprssibl laminar boundary layr ith injction of a light mdium and havy gas // NOLTR Adams E. W. Warmbrod J. D. Fox C. L. Huffakr R. M. Hat and mass transfr in binary inrt gas flo for distributions of tmpratur and concntration rndring th proprtis narly constant // MTP-AERO // // :

11 ÔÓÌÓ.. ÏÓÓ ÒÍËÈ.. À ÏËÌ ÌÈ ÔÓ ÌË ÌÈ ÒÎÓÈ ËÌ ÌÓÈ ÒÏÂÒË ÁÓ 5. Volchkov E. P. Concrning th hat and mass transfr faturs on prmabl surfacs // Int. J. Hat Mass Transfr Vol. 49. P // : // // // // : : : : // S. A. Gaponov B. V. Smorodsky S. A. Khristianovich Institut of Thortical and Applid Mchanics SB RAS 4/ Institutskaya Str. Novosibirsk Russian Fdration gaponov@itam.nsc.ru smorodsk@itam.nsc.ru LAMINAR SUPERSONIC BOUNDARY LAYER OF THE BINARY GAS MIXTURE Thortical invstigation of th proprtis of a comprssibl binary-mixtur boundary-layr in th framork of local slf-similar boundary-layr quations. W hav considrd th problm hn th forign gas of various molcular ights lightr and havir than air has bn injctd into th flat-plat boundary-layr through th prmabl modl surfac. Computations of th binarymixtur vlocity dnsity and tmpratur profils as ll as forign gas concntration in such boundary layrs at diffrnt Mach numbrs hav bn prformd. It has bn found that incras of a forign gas injction lads to a monotonous dcras of th skin friction and hat transfr cofficints. It has bn stablishd that at fr stram Mach numbr M action of a havy gas injction from th modl surfac into th boundary layr is similar to th action of th modl cooling. This injction incrass th dnsity of th mixtur nar th all. As a rsult th profils of th suprsonic boundary layr ar modifid in such a ay that th boundary-layr linar stability should b incrasd ith injction of a forign gas ith high molcular ight. This in turn should lad to a shift in position of th laminar-turbulnt transition donstram. Kyords: suprsonic boundary layr hydrodynamic stability laminar-turbulnt transition binary gas mixturs.

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

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