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FTD—ID(RS)T—1876—78

&FOREIGN TECHNOLOGY DIVISION

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LAYER ON A CIRCULAR CONE WITH THE EXTERNAL~~~~ VORTICAL INTERACTION OF A SPATIAL LAMINAR BOUNDARY

(NONVISCOUS) FLOW AT SUPERSONIC SPEEDS

by

B. M. Bulakh

D D C

Approved for public release;distribution unlimited.

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FTD —ID(RS)T—1876—78

EDITED TR ANSLATION

FTD—ID(RS)T—1876—78 ~ December 1978

MICROFICHE NR: -

~ -~Q /4c2~ZVORTICAL INTERACTION OF A SPATIAL LAMINAR BOUND ARYLAYER ON A CIRCULAR CONE WITH THE EXTERNAL ( NONVISCO US )FLOW AT SUPERSONIC SPEEDS

By: B. M. Bulakh

English pages: 3

Source: Materialy Nauchno—Tekhnicheskoy Konferentsii,Issue ~~, Leningrad , 1971, pp. l~46~ i~ 7.

Country of Origin : USSRTranslated by: Sgt Martin J. FoJ.anRequester: TQTAApproved for public release; distribution un1imi~~~~~_ _ _ _______

~tc~~~~~~cr ~~~Nf IS GRA&IDL~C T[~

ElJu s ti f ien t i

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By________ _____

D 1str~ b u i ~~i:L _____

_________________________________________ Avc~11 ~b~ U t y Co~~~k~~ii1 and/ or

THIS TRANS LAti ON IS A RENDITION OF THE ORIGI. This apoclalHAL FOR EIGN T EXT WI THOUT ANY ANAL YT ICAL OREDITORIAL COMMENT. STATEMENTS OR THEORIES PREPARED BY:ADVOCATED OR IMPLIED ARE THOSE OP THE SOURCEAND DO NOT NECESSARILY REFLECT t ~OS!TION TRANSLATION DIVISIONOR OPINtON OF THE FOREIGN TECHI ‘~- ‘ Y DI. FOREj G~l !ECHNOLOGY DIVISIONVISION. WP .AFB , OHIO.

• FTD —ID (RS ) T— 1 876— 78 Date L~ Dec 19 78

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U. S. BOARD ON GEOGRAPHIC NAMES TRANSLITERATION SYSTEM

Block Italic Transliteration Block Italic Transliteration

A a A a A , a P p p p R , r

5 6 £ 5 B , b C c C c S , sS B B • V , v T T T mr r r a G , g Y y y y U , u

l i D D, d 0 ~

F, fE e E a Ye , ye; E, e* X x X x Kh , kh

Zh , zh Lt q LI q Ts , ts3~~ 3 , Z , z

~i v Ch , chI’I H H ” I, i W w L U w Sh, shP1 ~ R S Y , y U4 w, J1J ~q Shch , shch

X x K, k

~L J 1 f l A L, l Y , yM sv M , m b b b ~

H H . H s ~ N , n 3 3 j , E , eD o O o O , o Yu , y uf l n fi st P , p R H N a Ya , y a

*~~~ init ial ly, after vowels , and after ~~~, ~

; e elsewhere .When written as ë In Russian , transliterate as y~ or e.

RUSSIAN AND ENGLISH TRIGONOMETRIC FUNCTIONS

Russian English Russian English Russian English

sin sin sh sinh arc sh sinh~~cos cos - ch cosh arc ch cosh 1tg tan th tanh arc th tanh_1ctg cot cth coth arc cth coth_1sec see sch sech arc sch sech_1cosec csc csch csch arc csch csch

Russian English

rot curllg log

I

.. — w~ -~~-_ — - - - — - -.--

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1’

VORTICAL IN TERACTIO N OF A SPATIAL LAMINAR BOUNDARY LAYER ON A CIR—

CULAR CONE WITH THE EXTERNAL (N ONV IsCOU S) PLOW AT SUPERSONIC SPEEDS

B. 1. Bulakh

lIe have detected the nhen omenon of a vortical interaction of

a boundar ” layer and external flo~’ with moderate supersonic speeds.

It was shown that for a circular cone the nhenomenon of vortical

inter action is described h” a self -mode lin q solution.

We are examining the problem of a boundary layer on a circular

cone, streamlined by a uniform supersonic flow of gas under the

anp].e 01 at tac k •~~~. The aut hor established earlier (In a work pub-

lished at the “-IZhG) tha t in a system of spherical coordinates r,

ø.c. where axis e=o - colncides with the axis of symmetry of the

cone, the behavior of density ~~, component of speed u, w, in the

direction of an increase, respectively, of r and c in the vicinity

of’ the surface of’ the cone is determined by the formula

f f ~( ?) f ~( #) e ~~s)a _

~ ... , ( 1)

where I~ ?, as. z~; fo f ~ — some func t ions of ~r:& — angle of the par—

tial opening of the cone; 13 — the constant which in the majority of

1

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cases Is less than a unit; a dotted line designates the members of

a higher order of snallness wi th respect to ~~~~~~~~~~~~ th :~~ those

given. For cases of B<<l the nonviscous flow near the surface of

the cone whirls powerfully , which renders a significant influence

on the boundary layer. If T~e is the Reynolds number of the problen,

(Rj~~~ then in the system of coordinates where s is read off

fror. the top of the cone along its generatrix, n — along the normal

to the surface of t he cone, the solution to the problem on the

boundary layer has the form :U — u,(~,~) +z’ s 1” ts~ (~,~~)~~~O(,t),w .— w,(~,~) -f — :8 s— ’ ’w2 (~ ,~ )+o(s’),

V — ~~ [ i i ii;.,~ + z~ s~~~’ V,(c,~)+

(2)

~ ~~~~. — Z ~~3~~~~~~(;; : — - ~~~

—c t~ -

here u, v, w — components of the speed of particles of gas in the

direct ion of an Increa se, respectively, of s. n. ç: ~~. p — density

and pressure, T — absolute temperature : ;=—~~,.V=~~~ .

The members with subscript “1” in formulas (2) give the known

(self—mo delinr) solution to the problem of boundary layer; members

with subscript “2” occur as a result of the vortical Interaction

of the external flow and the boundary layer. Equations for ‘~~

~~:. t:, V~ are analogous to the ecuat ions for U :. ‘~.• ~~~ .

. t~. U: boundary con-

ditions are different ; therefore they are given thusly :

:=O. u,—V . — _.,_Q• t — T ,.;—~c. U i 4U

~ (~~) . ~~~~~~~~~~~ t , —.t,(~ );

; = 0. u~ — t ~ —0 , t~ — 0,.— X ~ Zt1~...1 (

~ );~ ~~ (:~~;1,

2

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I

Here funct ions :.. are determined from the solu—

tion to the problem for the external, nonviscous flow; T~ — tem per-

ature of the surface of the cone. An indirect evaluation of the

value of a check for the results of’ the normal theory of the boun-

dary layer due to the vortical interaction can be done by means of

evaluating the multiplier z’ in formulas (2).

~or example, for the ‘lach number of an Undisturbed flow M 5

~_2o:: a—IO°, B 0.33: for values M~7 ø~ —30°. a”5. B~ 0.o;~ If we take

Re” 106, then ~=1O~~. and for the modes given above the flows of the

cone are, respectively:

,B -.,.~)l and ~~~~~

Con seouentlv , we can anticipate that the corresponding checks

are achieved In a number of cases to tens of percents.

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DISTRIBUTION LIST

DISTRIBUTION DIRE CT TO RECIPIENT

ORGANIZATION MICROFICHE ORGANIZATION MICROFICHE

A205 DMATC 1 E053 AF/INAKA 1A210 DMAAC 2 E017 AF/P .DXTR-W 1P344 DI?/RDS-3C 9 E403 AFSC/INA 1.C043 t’SA~4IIA 1 E404 AEDC 1C509 BALLISTIC RES LABS 1 E408 AFWL 1C510 AIR MOBILITY R&D 1 E410 ADTC 1.

LAB/Fl 0C513 PI CATINNY ARSENAL 1 FTDC535 AVIATION SYS COMD 1 CCN 1C591 FSTC 5 ASD/FTD/NIIS 3C619 MIA REDSTONE 1 NIA/PHS 1D008 NISC 1 HItS 2fl300 L’SAICE (USAREUP.) 1P005 DOE 1P050 CIA/CRB/AZ~D/SD 1NAVORDSTA (50L) 1NASA/KSI 1AFIT/LD 1T,LL/(’ode T—38 ~i 1

FTD—ID(RS)T—1876—78

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