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 _.
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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)
8O3
io &
1 I r
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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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