CURRENT RF._ULTS AND PROPOSED ACnvn.t.e;S

IN MICROGRAVITY FLUID DYNAMICS

V.I. Polezhaev

Russian Acaclc_ of Sci.Inst/t_ for Problems in Mcchmcs,

Prospect Vm'nadskogo 101, Moscow, 117526, Russia

ABSTRACT

Ov_Xew of the resutts in microgravity fluid dynamics during last two years with a goal to discuss the

problems, which may be ofi_rest for the Intmmtional cooperation is done.

INTRODUCTION

The Inst/tute for Problems in Mechanics _ is the _ _ in Mechanics in Russ/an Academy of SCI.

It includes depm'tments of class/cal mechanics (analytical mechanics, gyroscopes, navigation, optimal control mud

robots) as well as solid state mechanics (elasticity and deformation, shell's oscillations, lubrication etc.) and fluid

mechanics, including combustion, plasma and laser gasdynamics.

Laboratory of the mathematical and physical modelling in fluid mechanics of this In.Cdmte develops models,methods and software for analysis of fluid flow, istalality analysis, direct munetical modelling and semi empirical

models of turbulence as well as experimental research and verification of the models and applications in

technological fluid dynamics, microgravity fluid mechanics, geophysics and a ntmaber of enlOneeting problems.

This paper .prcscutsov_ew of the results in rrdcrogravity fluid d_cs duringlast two years since 2ridMicrogravity Fluid Physics Conference (J'tme,1994, Cleveland) and Zst Intematonsl Aerospace Congress

(August, 1994, Moscow), which enhanced lmematonal cooperation in Mierogravity in Russia. Nonlinear

problems ofwceldy compressible and compressible fluid flows arc discussed. Scientific ba._s of this research is

contained in the books [1,2].

THERMAI_DINAMICAL ACTIONS FOR CONTROL OF CONVECTION DURING CRYSTAL

GROWTH

Cr_erai idea of this work is investigation altcmati_ microgravity possibifities to reduce iahomogcncttics in

semiconductors that are induced by gravitational or nongravit_onal types of convection interrestrial

environments [3,4]. Low energetic thermal/dynmnical actiom for the growth of scmiisolating GaAs monoaystals

with low dmuity dislocations (thmnal waves, steady state and unsteady rotation and/or varaten) are used in

modified ground-based Czoctnlsk'y techniques with diagnostic of the GaAs monocrystals. Developing of the

methods for experimental and theoretical reccarch and comparison the results are prescmcd below.For measurements oftemperatun distribution during single crystal growth modification of the sysmn for the

temperature field dyagnostic was carried out in the Branch of the Institute of Ct3m_ography, Kaluga [5]

(Fig.Z). The #ot crystal's models mmmfacU_d of special ceramics having thcrmophysical propmics similar tothose of CmAs were used to make pr¢_ measurements of temperature distribution ina system

investigated. Thermocouples were installed into these _ot models which provided a stfe contact between the

thermocouples and the object measured.The amplitude-frequency characteristicsofthmnocouples weredetermined before-hand which then made it possible to estimate the frequency spcctnun of temperaturefluctuations in the melt and across the crystal GaAs single crystals with the diameter of about 80 mm were

grown under the same thmnal conditions. The growth direction was (001) and the chan_ of the dismcter didnot exceed 2 nan at puIiing rate 2-3 mm/h. Single crystals were grown at constant temperstme of the heater.

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The experimental investigation was also made concerning the temperature change in subcrysta_e region andacross the crystal at iso- and countcrrotation 6fthc cwstal and the crudbl¢ with the melt and rotation of the

crucible with the melt under acceleration These actions caused considerable change in the spectx_a of

temperature fluctuations and were much more sensitive in comparison with the heating controL The descn'bed

actions and some other onessimilar in influencing the process of singlec_ystal growth are classifiedby as "lowenergetic" actions because of in that case change in power suppficd to the heater was small (no t more than 1%)as compared to fixed power.

Mathematical modelling was made,using model of Czochralsky crystal growth which includes

bydrodyn_fics and heat U'ansfer in the crucible on the basis of unsteady Na'_er-Stokes equations (Boussinesque

approach) and a model of a crystal as rota1_xg disc on the melt surface ffigl). Special version oft'C - based

system which is extension of the system "COMGA" was used for this approach. It includes now as a part of

Computer laboratory on the basis oftl_ system [6]. Cylindrical crudble radius Re= 7 em which filled by Ga_

melt to height H---4 cm and crystal radius Rs=3.8 cm was considered. The crudble wall temp_ was

uniform and in general case can be dependent on time. Temperat_e on the solid/liquid interface was supply as1511 K and interface between melt and encapsulant is adiabatic. No-slip conditions for radial velocity and free

condition for angu_ velodty arc assumed on the LEC inted'ac¢. The cruc1"oleand crystal rotate with constant

angular vcloc_es wc = 16 rpm and ws= -6 rpm. l_'andfl mu_ber was assumedas _ 0.0"7. Using the scale oflen_h for this problem is the cmcz%leradius Re,one can obtainnondimensional parameters are Grashof number

Gr= 7.8 107 , crudble Reynolds number Rec= 1.6 10'* and crystal Reynolds number Re_ 6 103. The

calculations were made on nonuniform grid 75"51 nodes, stretching to crudble wails and solid/liquid interface(minimum space step was equal to 0.2 ram). The computer code was tested for the problem on thermal

convection with low Prandtl number fluid (0.015) for Grashofnumber. 1.6 10 _. Maxinnnn value of s_eam

function was in a good agreement with the results [7] as weft as our previous results [I]. The calculation of

unsteady problem for constant crucible temperatme Tc=1541K including thermal convection and rotations of

the cn_%le and the crystal was made. As it was obtained for such values of parameters in previous works ( see

[I, 5] the nonrcgular undamped oscillations of tcmpcratme field and motion stmctm'c induced by convective

instability are observed. Fig 2 iau.Cwatesthe complex interaction between thermal and force convections (the

instantaneous patems oft_peratme, rotation moment and stream function are shown). The dependence of the

measured (a) and calculated (b) melt tez_erature in the point near the axis (2 mm below the liquid/solid

interface) is given in Fig.3. The oscillations with maximum temperature amplitude fill to one degree are good

visible. Using descn%ed technique the influence of harmonic crucible tempcratme changing on the amplitude of

these oscillations near solid/liquid interface was investigated [5] and analysis of the dym'nrfical actions is in

progress.

ANALYSIS OF NEAR CRITICAL PROCESSES ON THE BASIS OF COMPRESSIBLE FLUID

MODEL

The goal of this work is study compress£ole fluid flow and host ¢ansfer near critical point for quanlitative

analysis of the microgravity experiments and analysis of gravitation semiti_y for certification of the orbital

complexes for near critical expcx_uentsin rnicrogI_n/ity. Spedal numerical schemes and computer codes for 1Dand 213 approaches are developed on the basis of Navier-Stokes equations for compressible fluid with Van der

Waals thermodynamics state equation [8]. The results one-dimensional analysis for the problem with rigid wall

heating in zero gravity is in well agreemen_ with previous results of B.Zappofi and co-work,s, where "piston

effect" was calculated on the basis of direct numerical simulation (see [9,10 ] and cited references).

Fig.4 shows new results for two-dimensional thermoacousfic - dominated regime processes in the earlier

stage of'switch on" the heat pulse in zero gravity. Two-dimensional density isolines which wm be of interest to

registrate in the earlier stage of"switch on" the heat pulse in microgravity in a model of near crytical point

instrument (see [10] mad cited references) with the goal of benchmark mathematical models and analysis ofgravitational sensifi'_y near-critical fluid processes.

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The _ for Problems in Mechanics have presented a proposal and scientific plan for the use of the

French insmnncnt "Alice-l" for coopera_e investigation in a framework of the plan for analysis of gravitational

sensilivity in liquid/gas systems and convective sensor with the Penn University. Insmnnent "Alice-l" is exist

now in the working state aboard _ station and it is property of R.KK "Energiya', but "know-how" ofthis

insmunent is a property of CN_. Program rcalizsfion of the orbital experiment for near critical C02 and _F6

was presented by CNES using ordinary procedure [10]. Experiment was realized 30.09-4.10, 1995 by Russiankosmonavt S.V.Avdecv. Preparation and analysis of the results arc in progress. For the use of'Alice-l"

insmanent as a tool for measm'ement gravitational sensiti""_y of compressible liquid/gas systems evolution of the

optical pictures to density fields in quantitative form should be done.

CONVECTIVE INSTABKII'Y AND SPATIAL STRUCTURE OF CONVECTION IN

PARAI J._.KPIPED

A probl_a of convecl_ instab_y and convection s-lmct_ in boat-type configuration reJated to macro-and

microinhomogeneities of crystals grown from the melts has a long-term history [1-4, 11]. A focus of this part ofthe work is concentrated on the analysis of spatial structure of thermal gravitational conveclion in a long

parallelepiped with differently heated side boundaries, using both stabt_ty analysis tccl_que and directnumerical calculation on the basis of three-dimensional Navier-Stokes equations.

Three dimensional unsteady Navier-Stokes equations (Boussinesquc approach) arc solved in the form of

velocity-pressure variables with governing parameters Grashof, Prandtl nmnbers md two aspect ratios W/H and

L/H. An equation for two dimensional basic flow was found, using definition ofbasic flow in the case ofinfinitc

length for a closed flow in rectangle and boundary conditions [12]. It's solution contains Bir_h.type basic flow

[13] in the limiting case of W>>K Spatial slrucU_e of convection in a parallelepiped including basic flow arc

shown in Fig 5. Dependency of the critical Grashof nmnber on the W/H using linear stability analysis ofthebasic flow is corr$1atcd with results of direct mnnerical solution of3D Navier.Stokes equations for the case of

Pr-_, L/H --20, Gr=200000 (Ftg.SB). Velocity field structure in supcrcritical domain near critical line is shown

on the Fig.SC. Strong dependency of the crytical Grashofmnnber with reduce of the W/H shows "geometric"

possl"b_-ly for control of gravitational cenvcclion.

COMPUTER LABORATORY FOR CONVECTION AND HEAT/MASS TRANSFER IN

MICROGRAVITY

Computer laboratory is intellectual shell of the system "COMGA', including help in the statement of the

problem, benchmmtt of computer results stud multiparamctrical analysis of fundmnental and applied problems.

was recently.developed and described in [6]. Pc-based system as a core of computer laboratory contains all

tools which need for modefling hydrodynamics, heat/mass transfer processes and collected in personal

computer. Each of separate version of the this rystcm occupies memory on one disk and presents a flc-_Ic and

convenient software tool for modelling of forced, gravity-driven and surface tension-driven

thcrmoconccntrational convection on the basis of Navicr-Stokes equations in Boussinesquc and Boussincsquc.

Darcy approach (see detailed references in [6D. This version of the system is based on the two-dimensional(plane or axisymmctrical - with three velocity components) unsteady Navier-Stokes equations. Temporalbehavior (rotation, vibration) of body force is taken in account.

Contents of computer laboratory includes forced flows of isothermal liqmd,.natural gravitational convection,surfac tension-driven convection, interaction between different types of convection and applications.Each task

can supports of text books on viscous flows and heat Iransfer or monographs on buoyancy-induced flows and

transport or convective stabtlity and applied problems in microgravity and supplied by additional references on

experimental and theoretical researches (see references in [6]). Special sign (*) in the cox_-nts of computer

laboratory marks problem, solved in previous works, using different kind of methods and sol_qrc. Other sign

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(*_ marks problem solved in previous works or renewed _ "CObiC_" system stud sign(*'*) - newproblems solved with ahdp of this systms.

F'_6A-C showssome results of steady-st_ and umt_dy problems ofthermal gravitational mdthermocst_try convection (vertical layers with side heating for ordinary md porous media md omet oflhezmMgravitational convection _ suddcolybottom heating and thermocapi]]arconvection and inst_ in floatingzone). Fig.6C showsnew result of this computer laboratory-benchmark of the flow/',zmperature _ngtm'c andoscglafiom due to convective instability in depeMmcy on biarangoni manbcr _md aspectratio usingHP 735

workstation [14]. It is shown that azisynmxelricalmode c_ts for high Pr number and n:sults corrdatc withexperimental data [15] (seereferences and discussionin [14]).

Special pm of the systemuses real microaccelcrations data mcasurcd by means ofan accderomctcr orcalculated in space flight [16].

Computer laboratory should be used also as a tool for education _om _ comes ofpbysics (hydrostatics,

hydrodynmmcs and dcmentmy transport processes) for definition and demonstration buoyancy phenomena(st_ of hy&'ostafic =_), laminar flows, boundmy layer ca:. (see, rrfini-phmof Computer Laboratory[17] ). For spccial courses in fluid mechanics and heat ta'msfcr computer support of ekmeuts boundary L_/cr

theory, _ and turbuknce can be done. For engineering courses on fundammtals of heat transfer theory ofheat conductivity can be cLemom-tr_d as well as convective heat transfer across layers with demonstration of

s-m_an_ and heaffmass transfer charactcri_'cs. A number of mentioned problems of Compmer laboratory may

be recommended to use for gntduatcd education in micro_-avity fluid mechanics [6,17].

CONCLUDING REMARKS

Above mentioned problems as study temp_ oscx_ttious in the melts and thermal/dytmmical control of

crystal growth, analysis of near critical fluid processes, _ and spatial strucUu¢ of convection in the melts

may be potential directions for future projects. T'zn'cetopics in cooperation of IPMech with other o_ons

may be add :

1. lviicroaccelcr_on and gravitational s_ analysis on the orbital complexes (with_ddysh Ins',. of AppliedMath., _ "Eucr_ ", lost. for Problems in Mech.) [6, lg]

2. Theoretical and cy)crm_cntal study and flight experiment on Microcravi_ Sensor, proposed on MIR (LSS).

"Faer_ia', lust for _ololcms in MeclL and Perm State U_) [6, 19]3.EAucation on Mlcro_'avity Fluid Mechamics _ compum" laboratory (Inst. for l_'oblcms in Mech. and Pcrm

State Universe)[6, 17].

ACKNOWLEDGMENTS

These works were supported partly by NASA (NAS-15-10110), Russim Fond of Fundmnental Research

(94-01-01551), TntcmationalScience Foundation (N3_I00), RKK "Energia" and _.

REFERENCES

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mass umnsferon thebasisofNavier-Stokesequations,M., Nauka,1987,(inRussian).

2.PolczhaevV.I.Bcno M.S.,VercsubN.A. et al Convectiveprocessesinmicrogravity, M., Nauka,

1991,240p.(inRussian).

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3. Matthiesen D.H.,Wargo M.J.,W'_ A.F. Opportunities for Academic Research in a Low-

Environmmt : Crystal Growth In. : Opportunities for Academic Rcscw_ in a Low- C,rav_

Environment : Crystal Growth (Eds. G.A. Hazdfigg, J.M. Reynolds), Progress in Am'onanfics

and Aeronautics, V.108, pp.125-141, AIAA, N.¥.,1986

4. Midler G. Convection md inhomogencitics in crystal growth from the mall In: Crystals: Growth,

Properties and Applications. Berlin, Springer 1988, V.12, 1-133.

5. Kosushkin V.G., Polezhacv V.l, Zakharov B.G. G_round-based experiments and alternatives in

CmAs crystal growth. In. : Procccdin_ of the iV_crogravity Science and Applic_ons S_sion.

Int_'mational Aerospace Congress, Moscow, (Eds.) R.K.Crouch, V.L Polezhacv, 1995, p.141-146.

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7. Bot_ro A. and Zcbib A./l:'l_ysics of fluids A, 1988, V31, p.495.

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gas, Seminar on numerical methods in heat and mass Q'ansf_ probl_as led by V.LPolezha_,LA. Chudov and G.G. Gtushko, Fluid Dynamics VoL29 No5, 1994, 7"34.

9. Beysens D. New Critical Phenomena ()bserved Under Wcighticsmess In: _ and Fluids

under low gravity, L.Ratke, H.Walter, B. Fetrbacher, (F.,ds.), Proceedings of the IXth European

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May, 1995, Lecture Notes in Physics, V.464, Spfingcr-Vedag, 1996, P. :3.25.

10. Zappoli B., Durand-Daub in A. Heat and mass transport in a near super critical fluid//Physicsof Fluids. 1994, May.V.6. N 5. P.1929-1936.(Amcrican Institute of Physics)

11. Rotvc B, (Ed.) Numerical simulation of oscillatory convection in low - Pr fluids. Notes on

Num_cal Fluid Mcchaxdcs, 27. Viewcg, 1990, 365 p.

12. N'ddlin S.A., Paviov'sky D.S., Polczhaev V.I. Stability and spatial convection structure in a long

horisontal layers with side heating, Izv. AN, MZG, 1996, N4, 28-37 ('mRussian)

13. Bir/kh P,_V., Termocat_lary convection in a horizontal liquid layer, PMM, 1966, 30, 356-361.

14. Griaznov V.L CTD Simulation of the Osdil_ory Heating-Zone convection for high Prandtlnumbers. Proceedings of the Microgravity Science and Applications session InternationalAerospace Congress, Moscow, August 16-17, 1994, NASA/IPMcch., Moscow, 1995, pp. 113-117

15. Vclten R., Schwab¢ D and Scharmmm A. The p_odic instatrt_y ofthermocapfllary conw_on

in cylindrical liquid bridges Phys. Fluids A, v.3, n2, 1991, 267-279

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16. Polezhaev V.L Toward the quanlRalive analysis and control of convective processes inmicrogravity. In: Microgravity _, 1994, voL 4, N 4, _ of the Intamafional

W'oAshop on Non-C_=vi_omd M.e_ of Convection and Heat/Mass Tnmsfcr', p.241-246.

17. M.K. Exmakov, S.A. _ V.L P0le.2flacv. New computer technology using PC-Based

system in education of fluid dynamics, heat- and mass wansfcr. International Conference on Eng.

Education, Moscow, May 21-23, 1995

18. 5azonov V.V., Komarov M.M., Belyacv M.Ya. ct. it Evaluation of quasi-state component inacceleration on board the cm'th m'tificill satellite. Inst. of AppL Math., prcptint N 45, 1993,

pp. 30. CmRussian).

19. G.P. Bogatyryov, G.F. Pufin, M.K. Ermakov, S.A. N'_fin ¢t al. A System for Analysis and

Measurement of Convection aboard Space Station: Objectives, Mathematical and Ground.Based

Modelgmg, AIAA 95-0890, 33rd Aerospace Sciences Meeting and F..zhibit,Jan. 9-12, 1995,Reno. NV.

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Schc'me of the tm_pm'amre mear, ncmcnts

sy_ in a melt and along the crystal1 - seed, 2 - float with thcrmocouplcs, 3 - heater,

4 - system for t_np_ratme measur_m_

and rc_rafion, 5 - crux'hie with a melt

Fig.2 Instantaneous fieldsoft_et_cramrt:, rotationmoment and stream function for thermal

convection (LXT=30 °K) and rotation of cm_le

(o¢ =, 16rpm) and crystal (co, =. -6rpm)

_5_+.o FJlI'' '' " ....... _-rFl:l?l -rlii,,i .

• I IIItJltlltlll ':f +, tllil *+1_"_151¢.0 IlltiIIIItlltll+i _lil _ _.i l_ ill I I.,t I I I I t i t,t t I1 I t I I_ I I I I ', : I I _ _ I I iiit litll I_,

_u_ 151 l.O _" I_.LLD.',Lm£;L_ ._J I ! I I llrl i( 1,14,.,Ll4,t_L..'Jl_l_i,i,.t *L-L__,_J,i{ll ! _ iI! _ r iI .... = ' _ Ii _]

1508.0 ............. , ...... ,0.0 300.0 600.0 900.0 1200.0 1500.0 ;800.0 2100.0 2,_00.0

time (see.)

b'1g.3 Measurements (a) and calculations (b) of the tcmpcratur, fluctuafiom in the melt nearaxis under constant cru_ie tcmpc-rature for a case ofthmnal convection and rotation of

cruta_ol¢ (16 rpm) and crystal (-6 rpm)

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A. B_ic flow for W/H---2 •

/sol/nesofveloc_ (a)and _-a_e (b)B. Dependency of the _ gruhofsmmbcr on tb¢ width

mb_ _b_is:finite _'Terence c-Xcul_/on" o. basic flow,

x- _oad_ smmare

,A

÷

s

$

o.)

!

C. Isolines of the vdocity component u in the

centr_cellof thei_cr:.

1 - r=10, 2 - r=10,7, 3 - z=11,35 (vertical crossection)

4- y=O,12._, 5 - y=0,5, 6 - y-,O,Sq5 (vcr_ic_ crosscc_on)"7. z=O,12_, 8- z=0,2_, 9 - z=O,_ (horizontal c_osscc_on)

Stability and spatial sU'ucuue of conveOion in

pm-allclcpipcd805

A. Thannd grsvity-ddvcn convcctiea in permeable ison'opic snd anisocopic porous vaficsl

layer with side besting _. (_ 10S (s), isou'opic Co) and misou'opic (c) porous media

I

E. Critical_u'mgoni nmnba,sforPt-='71 - plane A-Mn, 2 - pbmc A-Mn', cdml=ions3-pt=c A-Mn'. _ p_]

F_.6 _ of cakuiad.oaon.._:icbasis ot"Compu:¢_"laboratory:.

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