U. S. DEPARTMENT DIF COMMERCE

Transcription

1 II A AD THE.NON-STATIONARY FL:OW OF AN ANOMALOUS VISCOUS LIQUID * 0. K. Fedorov Foreign Technology' Division Wright-Patterson Air Force Base, Ohio 17 November 1972 A I, * 3 DISTRIBUTED BY, U. S. DEPARTMENT DIF COMMERCE 428 Port.Royal Road, Springfield Va

2 FTD-HT FOREIGN TECHNOLOGY DIVISION THE NOUl-STATIONARY FLOW 'F AN., ANOMALOUS VISCOUS LIQUTD by 0. K. Fedorov *.. Reproduced by NATIONAL TECHNICAL INFORMATION SERVICE S U S Deportment Spr/ngfiedVA of Commerce Api roved for public ri'f(a:,; c.1' tip uti en uriliviltod. ga

3 -~~~~~~~~- -. ~ ~ r , ~- - I e~mt~'.i*i&i..*~ DOCUMUMT CONTROL DATA. R & D hevfimet.el.i.e U VNIIOINATIN4 ACTIVITY (USIeesw 4umej W. RNPORT ORCURITY CLO SSIPSCATI@N FrinTcn3oyDivision Ai~r F'orce SZystems Comm~and go. GROUP U. S. AIr Force THE!ION-STATIONA!RY PLOW; 0r All ANV'ALOU'S V1."rOoU.Q'; :edorov, O.K. T.TTLN.O AE bn.~ I. Napo"? OAW;7.TTL O FPS$ 6 o I p tur I". FOOTRACT Go-GRANT NO. REPORT NumPeaisi A 046jacT me F~rD-HVT ; to I. OISTRIOUTIS" STATEMENT Annroveý;."or public release; distribution unlimiited. 1WII. SUPPI691041TARY "eyes T2. SPONSORING MILITART ACTIVITY 1 L Foreirn Technolory D)ivisio'n j Wright-Patterson A-7-3, Ohio YSspeed. '-he author solves the rrobleir of' a non 3tationar lw nh, snael(e of' linu."d (thie nroblem. of Rswleirh), havinr the f'ollowilnr 7 rnrorert -f'-ý disnlacement speed F-amfma-l-ess- th-arrpamraj than- ~aq --Fkt-viscositY.-af_,, 4 ul but at g.amma,treater than ramr-a 0, it4 has a viscosit:y of '-1u -It is assured thot the liiu~i was initiallv at rest. At R;e initial moment of time the surf'ace, on top of which t.e libi sfud etyins to move with con.tat Thus a boundary arinea3 senaratinr* liquids with..vis coiiz.k 1 ndu, On this boundary forward zree'i and. drift sneed are t6 be continuous, The soluition is exnresse..i Phuh a Lanlace function. in the stat~enent of the nrohlemn c'on~dered nv the author surface forc.es should act on the separntior...urfaces, because each :;tress "M the nassare from on- ref-!.on t.-, an-ither, und'err--es an inerar~n Secunsty clasqiuieation

4 lie **Mori es e.it a I mrc p c!ethod Fl uldýisco ] I ViwiycOase3ityle

5 FTD -HT EDITED TRANSLATION FTD-HT THE NON-STATIONARY FLOW OF A:: ANOMALOUS VISCOUS LIQUID By: 0. K. Fedorov English pages: 4 Source: Trudy. Leningradsk ogo Tekhnologicheskogo nzt ''-,#uti Tse 1 lyulozno-bumazhnov Promyshlennosti, Izd-.'c Lesnayi Promyshlenrir,,', :.'oscow, NIo on 2,-22, Requester: ASD Translated: Charles T. Ostertur Jr. A Appr'oved fo:' i'ublic release; d!'3tr~ibu.,on L11111m~ted. THIS TRANJSLATION IS A RENDITION OF THE ORI0I. NAL FOREIGN TEXT WITHOUT ANY ANALYTICAL OR EDITORIAL COMMENT. STATEMENTS OR THEORIES PREPARED SY: ADVOCATED OR IMPLIED ARE THOSE OF THE SOURCE AND DO NOT NECESSARILY REFLECT THE POSITION TRANSLATION DIVISION OR OPINION OF THE FOREIGN TECHNOLOGY DI. FOREIGN TECHNOLOGY DIVISION VISION. WP.AFS, OHIO. FTD-HT Date 1" :Nov 19 ('2

6 U. S. BOARD ON GEOGRAPHIC NAMES TRANSLITERATION VA'ST"FN Block Italic Transliteration Block Italic Transliteration Aa Aa A, a Pp P R, r B.b CvC Cv Ss Ba abe V" v T7 Tm T,9t r r r o G,,g Y Y Y y U'Vu AX ga Do d i F0 f 3* 5'0 Ye. ye;e.e ~ X X X X Khp kh AN *w Zh, zh U Llq To,,to 8a 3 Z.,z 4 VCh. ch MuX Ha U 10 Wil W 11W Sh, sh RK RD Y, Wna 11 L q Shch, shch Kx Xi K0k lb% P to An q jia. Lo 1 bi W k/ Y, y M X M M M0m bb b h H K Npn a8 a 9E, 1~e , o0 10 Ynyu1 n 17 p 1 p I X R to, ya * e initially, after vowels, and after 1,; e eltsewh,-re. Wen written as V in Russian, trans iteratu a ym..r. The use of diacritical marks is preferred, but e'uch..,l. may be omitted when expediency dlctates. FTD-HT iv

7 THE NON-STATIONARY FLOW OF AN ANOMALOUS VISCOUS LIQUID 0. K. Pedorov I During the flow of a dispersed system the effect of a sharp, drop in viscosity is observed at a certain rate of deformation of displacement [1]. Such an anomaly in viscosity can lead to a unique situation when two areas of liquid flow are formed: an' area of low velocities of displacement, characterized by a high value of viscosity, and a low-viscosity area, corresponding to high velocities of displacement. Below an anlaysis is made of the problem of the plane-parallel flow of such a liquid caused by the movement of flat wall. 4 During the flow of an anomalous viscous liquid the stress of the displacement T is connected with the velocity of displacement I by the dependence I (1) where u(i) -viscosity, depending on the velocity of displacement. At 1 10 there is a drop in viscosity, since the flow of a liquid at _0 can be characterized by the viscosity 1j 1 (the greatest Newtonian viscosity), and at j > 10 -by P2 (the least Newtonian viscosity). the viscosity FTD-IIT

8 The liquid occupies the half space y > 0 and is in contact with the wall y = 0, The wall moves uniformly at a constant rate u directed along the axis X. The velocity v of plane-parallel flow of a liquid will be a function of time t and coordinate y. The field of velocities of displacement deformation of the liquid corresponds to two values of viscosity pi the two areas of flow. areas is and U2' characterizing The surface of separation between the determined by coordinate Y(t), whereas on this surface the conditions of continuity of the field of velocities Vl,2 and the field of velocities of displacement I,2 should be satisfied (subscripts 1, 2 are taken for areas with the corresponding values of viscosity ui and U2). On the moving wall' = 0, therefore the area with viscosity u 1 adjoins it. It follows from the Navier-Stokes equations that without a calculation for the pres.ure gradient. -- a (I-- 1," 2), (2) where vi it o - density of the liquid. Let us present the boundary conditions in the form vl-=n when y-0, %,-O when y-oq, (3) VS-. L_ when Y--YO). (4) Serving for the determination of th,'ž surface of separation is the condition that the velocity of dis!,lacer.wt on it is equal to 10 Sat y,--y(,). (5) In such a formulation the examined problem Ii close to the known,t;r.fan problem concerning the freezinp, of J,;,, [2].,"TD-HT

9 The solution of equation (2), satisfying the boundary conditions (3), we present in the form and I Here -- * 0 is the Laplace function; A and B arbitrary constants. Using conditions (I) and (5) we obtain Yj 0 *(2ý.)(6 I and where j ).2t~ O=j.i 2 whereas Y(t) is determined from the equation I - *(2)() 140(8 4" (00) 2 4(2I 1-.0) rj 0 Expressions (6) and (7) are the solutions of the problem which satisfyv the following conditions: f =0, Y = 0, v 2 =0, I.e., at the initial moment all the liqluid Is stationary. FTD-WiT L

10 We will make use of the fact that usually I, >>» 2; then a << 1. Using for the Lapalce function the concept in the form of a series and retaining in it only the first member, we obtain the following expression for the velocity of flow of a liquid in a highly viscous area S~(9) We arrive at such an expression if we examine the flow of a liquid at f. From here it follows that in a highly viscous wall zone the flow is established very rapidly and it depends on the rate of movement of the wall u and the velocity of displacement 'O" BIBLIOGRAPHY 1. P e 6 ita. e p 11. A. Aono.,emit K nepenoo.y peo.moran. Pew.oor.uf. MA Kap oy r.. Erep A Ten.onpoSo.1ocm, TeepATux H.e, 1.80so!I ~'T-HT-23PL2 I -7!I, I.