AD Asbi 475 FOREZIN TECI*dOt.Ol *~~~ USHNESS,(U) ~ SEP 77 S Y ICR ~~ F 4SNTEYN ~ UNCLASSIFIED FTD t C ~~ ~~ 1569 T7 P4. 1 ~~~ !

Transcription

1 !-! ~~~~~~~~~~ AD Asbi 475 FOREZIN TECI*dOtOl *~~~ 3HfrPATTERSON AFO OHIO F/S 20/ft FLOW STABILITY W ~~~~~~~~ 1 ~~~ USHNESS,(U) ~ SEP 77 S Y ICR ~~ F 4SNTEYN ~ UNCLASSIFIED FTD t C ~~ ~~ ~ 1569 T7 P4 U - * H

2 FTD ID (RS)T FOREIGN TECHNOLOGY DIVISION FLOW STABILITY BEYOND UNIT ROUGHNESS by S Ya Gertsenshteyn App roved for public release; distribution unlimited I

3 r ~ ~~~~~~ - ~~~ ~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~ FTD~ ID(Rs)T_lc6g_77 EDITED TRANSLATI ON FTD ID (RS ) T September 1977 MICROFICHE NR: FLOW STABILITY BEYOND UNIT ROUGHNESS By: S Ya Gertsenshteyn English pages:1o Source : Nauchnyye Trudy Institut Mekhaniki, Mo scow, Number 9, 1971, page s 29 3 ~ 4 Country of origin : USSR Translated by: LINGUISTICS SYSTEMS, INC F D 0389 Robert T Creutz Requester: FTD/PDRS Approved for public release; ~~~~~ a_ distribution unlimited V ~~~~~~~~~~~~~~~ o ~~~~~~~~ irr urt ~ R HIj THIS TRANSLATION IS A RENDITION OF THE ORIGI HAL FOR EIGN TEXT WITHOUT ANY ANALYTICAL OR EDITORIAL COMMENT STATEMENTS OR THEORIES PREPARED BY: ADVOCA TEDOR IMPLIEDARE THOSE OF THE SOURCE AND DO NOT NECESSARILY REFLECT THE POSITION TRANSLATION DIVISION OR OP INION OF THE FOREIGN TECHNOLOGY DI FOREIGN TECHNOLOGY DIVISION VISION WPAFB OHIO FTD ID(Rs)T l Date 27 Seo

4 - ~~~~~~~ ~~~~~~~~~~~~~~~~~ ~~ U S BOARD ON GEOGRAPH IC NAMES TRANSLITERATION SYSTEM Block Italic Transliteration Block Italic Transliteration A a A a A, a Pp p p R, r So 6 B, b Cc C c S B B S V, v IT T m T, t rr r a G,g Y y Y y U, u D, d ~ ~ ~ 0 0 F, I E e B a Ye, ye; E, e* X x X x Kh, kh ~ 4 ~ Zh, zh 4 ~ LI q Ts, ts 3 ~ 3 S Z, z ~ I v Ch, oh M U I, i Ili w LU iw Sh, sh XX Y, y 14 u ~ ill iq Shch, shc h K, k 5 ~ n 17 A L, 1 b Ib U ~ i Y, y ~ 1M M M M, m bb b B HH H H N, n 33 9 ~ E, e o , 0 FO ia Yu, yu fl n /7 i i F, p R H Ya, ya *~~~~ initially, after vowels, and after b, ~~ ; e elsewhere When written as ~ in Russ ian, transliterate as ye or ë The use of diacritical marks is preferred, but such mar ks may be omitted when expediency dictates GREEK ALPHABET Alph a A c ~ Nu N v Beta B ~ Xi (amm a F Omicron 0 o Delta L ~ 6 pj Epsilon E c ~ Rho P p e Zeta Z ~ Sigm a a c Eta H n Tau 2 t Theta 0 0 $ Upsilon T u Iota I i Phi Kappa K )t ~ Chi X x Lambda A X Psi Mu M ~ i Omega I

5 RU SSIAN AND ENGLIS H TRIGONOMETRIC Russ ian En glish FUNCTIONS sin cos tg ctg sec cosec sh ch th cth sc h cs ch sin cos tan cot sec csc sinh cosh tanh coth sec h csch ar c sin sin ~~ arc cos c os ~~ arc tg tan ~~ arc ctg cot ~~ arc sec sec ~~ arc cosec arc s h sinh ~~ arc ch cos h ~~ arc th tanh ~~ l arc cth coth arc sc h sec h ~~ arc csc h csc h ~~ ro t lg curl log GRAPHICS DISCLAIMER All fi gures, graphics, tables, eq uations, e tc merged into this translation were extracted from the best quality copy available

6 ~~ - --_ --* _- - ::J ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~ ~, Flow Stability Beyond Unit Roughness SYa Gertsenshteyn Roughness of a body s surface is one of the main factors influencing the position of the point of transition between a laminar boundary layer and a turbulent one This paper explains the influence of two dimensional unit roughness on the origin of turbulence More accurately, a study is made here of flow stability beyond two dimensional unit roughness Many experimental studies have been devoted to studying the influence of two dimensional unit roughness on the origin of turbulence [1] This is explained by the value this problem has for practical application As a very simple example can be given the problem of selecting the depth and shape of a welding seam, questions relating to aircraft, etc If, as Is usually the case, the flow far from the surface is considered close to plane parallel, then the problem of flow stability as far as infinitely small disturbances are concerned boils down to the problem of finding eigenvalues of the Orr Sommerfeld equation with homogeneous boundary conditions : (ç/v ~ ~~~~~c ) U_c) ~~ ~~ WU ~~~ 0, (1) ~ o(o) ~ o, ~ o( oo) = o, ~~ (c) ~~ O,q ( ao) =O (2) Here, U(y) is the velocity beyond unit roughness, R = u 0 9/ v is the local Reynolds number (d is the depth of roughness; u 0 is the velocity at a roughness level remote from the surface, and 1 L _

7 v is the coefficient of viscosity) All remaining symbols here are defined by the fact that flow function for a disturbance of 11 5s written in the form: Entering the discussion below will be one more Reynolds number : and a frequency of - dq ~ = f ~ ~~ ( ~ = ~~~~ Z) A solution to the problem was sought for eigenvalues according to [2] Calculations were made for different positions of the unit surface with respect to the front edge of a plate with a fixed external streamline flow velocity (ie, wl ~ h different Reynolds numbers for the main stream, R = U 6/v ) The velocity profile, 1 U*(y), beyond the unit surface was taken in the following form: ~ j when ~ y ~ 11(,) when <00 Here U(y) is the Blasius profile, u(y) is the velocity profile beyond the unit surface computed in [3] with a corresponding Reynolds number value of Neutral curves and steady growth curves were plotted, giving the relationship between the local Reynolds number, = u d/v 0, the wavelength of the perturbation, A = 2 ir/ c ~ r, the frequency of per I turbation, y=cçc, and the gain, ct ~ Typically, the first manifest ations of instability (with small values of the local Reynolds number, are observed in experiments sufficiently far beyond the unit surface, ie, exactly where the flow is close to plane parallel Here the velocity profile, U(y), in specific computations corresponds to a2

8 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ velocity distribution in the stream at a distance of five gauge numbers downstream from the unit surface (the depth of the unit surface, d, is understood to be typical) As a result of calculations of flow instability beyond the unit surface it w ~ s found that the unit surface can show a stabilizing effcct with a sufficiently low local Reynolds number Apparently, the appearance of a point of inflection in the velocity profile near the wall has an insubstantial influence on stability owing to the stabilizing effect of the wall, and the increase in fullness of the velocity profile proves to be more important Furthermore, the fullness of the velocity profile increases at a very dangerous point in the vicinity of the critical layer Critical Reynolds numbers for the main stream with similar comparatively moderate distortions of the initial profile increase markedly For example, when = u 0f/v = 3 and d = (l/2s)5, the maxiu ~ al relative deviation from the initial profile, max [U*(y) U(y)]/U(l), is less than one percent in absolute value, and the critical Reynolds number for this slightly altered profile increases by almost a factor of 15 (Fig 2 and 3) I Fig 1 3

9 ~ I; ~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 15D0 A, - ~~ Fig 2 /0 / ~~~~~~~~~~~~~~~ I4 ~ OO, ~~ ~ SOO Fig ~~~~~~~~ ---- ~~~~~~

10 r ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - ~~~~~ -- -ww ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - - U qz ça, 5 _ Fig 4 (S x 4a# ~~ Fig 5 5 1

11 The range of dangerous wave numbers is somewhat reduced Fig 4 and 5 show the relationships between the local Reynolds number and the wave perturbation characteristics introduced above = a + ict ; y = cc) with main stream Reynolds numbers r, R = 1 1 = U(6 /v) equal respectively to 800, , 1200, and 1500 En Fig 5 the relationship between, a, and y is shown only for > 4 Calculations demonstrate that the most dangerous wave numbers in all cases considered lie approximately between 093 and 12 The frequencies corresponding to these wave numbers lie in the range of 03 to 04 The maximal values of wave numbers and frequencies on all neutral curves increase with an increase in the local Reynolds number, Within the range of variation of considered, the maximal value of the wave number is 17, and the maximal frequency value is y*= 072 The great relative wavelength of unstable perturbations draws attention In dimensional variables A ~ 2 ~ ~ 37 A similar feature mm is typical of the neutral curve computed by Tolmin [1] for the boundary layer, ~~~~ 66, where 6 = 52 I (vx/u ) is the distance to the forward edge, and u 0, is the velocity at infinity It is easy to see that the wavelengths of dangerous perturbations for the boundary layer are greater than in the case considered It can also be seen that the phase velocity, C r = 1/a r, on the neutral curve varies slightly For example, when the Reynolds number, Reynolds number of the main stream,, varies from 9 to 20 (the, equals 800), the phase velocity varies from 04 to 042 (for the upper branch of the neutral curve) or from 04 to 033 (for the lower branch of the neutral curve) Especially striking is the strong dependence of wave numbers, a r gain ci i, and frequency, y, on local Reynolds numbers When the Reynolds number, ~ = u 0 d/v, varies from six to ten (R 1 = 1000), the highest of the dangerous frequencies increases approximately twofold 6

12 - - ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (from 032 to 065), the frequency of the most dangerous perturbation increases approximately by 14 (from 031 to 043), and the wavelength of the most dangerous perturbation by 13 (from 091 to 118) The increase In the range of dangerous wave numbers and frequencies correspond s to the manifestation in the nroblem of one more characteristic dimension (the death of the unit roughness), which is considerably smaller than the thickness of the boundary layer The gain ( a ) even with moderate Reynolds numbers, = ui/v, varies considerably when the unit roughness is added to the stream In particular, when R = , for the Blasius profile max(_a ~ ) ~ 005, and when = 10 and R = 1000, max(- ~~ ) ~ 0064 We recall that for the Blasius profile max(_ci ) i ~ 003 9ven when R = 2500 The situation is somewhat more complex when R Reynolds numbers are close to 1 critical For example, when the Reynolds number is 1200 the flow in the boundary layer is unstable (max(_ci ) = 0002), and it can become stable i when the unit roughness is added So, when = 3 the flow is steady (max(_a ~ ) = ) The corresponding curves are shown in Fig 6 and Fig 7, I Fig 6 7 L - ~~~ t- -

13 1 1 / 4? Fig 7 From the data presented in Fig 4 and 5 it is possible to trace the nature of the change in different wave oscillations with an increase in the R = u 1 ~ 6, 1 /v Reynold ~~ number We notice first of 1 all that with an increase in R 1(~ ~~~ local critiëal Reynolds number is reduced : When R 1 = 800, 1000, 1200, and 1500, R* ~ 9,6,4, and 3 Obviously, with a sufficiently high R Reynolds number the local 1 critical I i ~ Reynolds number will equal zero The range of dangerous wave numbers and dangerous frequencies practically does not change with an increase in the R 1 Reynolds number within the limits con sidered With a fixed local ~ Reynolds number, with an increase in the R 1 Reynolds number the range of dangerous wave numbers and frequencies can both increase and be reduced all depends on the magnitudes of and R 1 If is sufficiently low, then obviously 8

14 the range of dangerous wave numbers and frequencies will first be expanded with an increase in the R number and then will be 1 narrowed, precisely the same as without roughness If the magnitude of is sufficiently great (on the order of 10), then the influence of the unit roughness is manifested as a shift in the direction of very small scaled pulsations (the range of dangerous frequencies increases and the possible wavelengths for dangerous perturbations are reduced) With an increase in the R Reynolds number a 1 reduction In the range of dangerous ~ ave numbers and frequencies predominates, owing to the suppressing influence of instability in the boundary layer itself Coumarison between the results obtained and experimantal data is satisfactory Analysis of the experimental data in [4] has demonstrated that an element of roughness becomes the cause of premature turbulence of the boundary layer when the R Reynolds 2 number, plotted for average velocity and average depth of the element, d, is greater than 30 to 40 Here, in our case, under conditions most close to experimental : ~~~ = ~ (5OO ), ~~~ 4o Bibliography 1 Illnsxmxr 1 Bo3nMK ~ iosew ~ e ryp ~ ynehtsocm VI3LI }fh na r, Moci ~ - as, repueriute ~ H C$10 vpex ~ epswx ao3mymeuas ~ x a Uorpaax ihom csioe, t ~~ r, NQ 4, repnehmt ~~ u Cu 0 BflffSiHBH en ~ na iso ~ wepoxoaarocrw H5 a03 - }u ~~ osenee Typ6yzzeHmocTn, M)K1, N ~ 2, SCHH AM, KopoTiwil A11 Yr paaizi ~ e UOI pabbmhb ~ M CJIOØM, H35 CynocTpoe ~ ae,

15 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - r ~~ ~~~~~ Key to bibliography: 1 Shlikhting, G, Origin of Turbulence, Foreign Literature Press, Moscow, 1962 H 2 Gertsenshteyn, SYa, Three Dimensional Perturbations in a Boundary Layer, NZhG [Gas and Fluid Mechanics ], No 4, Gertsenshteyn, SYa, The Influence of Unit Roughness on the Origin of Turbulence, MZhG, No 2, BasIn, A M, and Korotkin, A I, Controlling the Boundary Layer, Sudostroyeniye Press, L - ~~~~ - _-- ~~~~

16 r I ~ I UNCLASSIFIED SE C URITY CLASSIFICATION O F THIS PAGE (tthen Dei Enlered) DE DT r%isf I ~ J AAEkIT ATIAkI D Ar READ IN STRUCTIONS! I ~ ~~ JI ~ U I# J ~ IJ ITl I ~ II I I J I iij ~ ~~ ~ ~ E BEFORE COMPLETING FORM I REPORT NUMBER 2 GOVT ACCESSION NO 3 RECIPIENT S CATALOG NUMBER FTD ID( RS)T TITLE (and SubtItle) ~ FLOW STABILITY BEYOND UNIT ROUGHNESS TYPE OF REPORT 6 PERIOD COVERED TRANSLATION 6 PERFORMING ORG REPORT NUMBER 7 AUTHOR(s) 8 CONTRACT ORGRANTNUMBER(s) S Ya Gertsenshteyn 9 PERFO RMING ORGANIZATION NAME AND ADDRESS 10 PROGRAM ELEMENT PROJEC T, TASK AREA & WORK UNIT NUMBERS Foreign Technology Division Air Force Systems Comman d United States Air Force II CONTROLLING OFFIC E NAME AND ADDRESS 12 REPORT DATE NUMBEROFPAGES 14 MONITORING AG ENCY NAME & ADDRESS(if differen t from ConIrollin ~ Office) IS SECURITY CLA SS (of this report) 10 J ~~ CLASSIFIED IS DECLASS IFICATIDN /DOWNGRADING SCHEDULE 16 DISTRIBUTION STATEMENT (of th is Report) Approved for public release; distribution unlimited 17 DISTRIBUTION STATEMENT (of the abst ract entered in Block 20, If different from Report) l B SUPPLEMENTARY NOTES 19 KEY W ORDS (Continue on reverse side If necessary and Identify by block number) 20, ABSTRACT (Cont inue on reverse side if necessary and Identify by bloc k number) 20 DD jan EDITION OF I NOV 65 IS OBSOLETE SECURITY CLASSIFICATION OF THIS PAGE (I47,en Data EnIsrd)

17 DISTRIBUTION LIST DISTRIBUTION DmEC r TO RECIPIENT ORGABI ZATION!O CROFI cre ORGANIZATIO N MICROFICHE A205 DMP1TC 1 E053 AF/INAKA 1 ~ 2io DMAA 2 ~ EO1 7 AF/ RDXTR V 1 B3I ~ 4 DIA/RDS 3C 8 E404 AEDC 1 C0I ~ 3 USAMIIA I E408 AFWL 1 C509 BALLISTIC R ~ S LABS 1 E410 ADTC 1 C510 AIR MOBILITY R&D 1 E413 ESD 2 LAB/FIO FTD C513 PICATINWI AI ~ ENAL 1 cczr 1 C535 AVIATION SYS C( ~ 4D 1 ETID 3 C557 USAIIC 1 NIA/PRS 1 C59] FSTC 5 NICD 5 c619 ~~ A REI ~ TONE 1 D008 NISC 1 H300 USAI CE ( USAREUR ) 1 P005 ERDA J P055 CIA/CE/ADD/SD 1 NAVOR2 ~~ TA ( 50L) 1 NASA/KSI 1 AFIT/LD 1 FTD ID(RS ) T