JPRS ID: 9335 USSR REPORT ENGINEERING AND EQUIPMENT

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(FOUO 6/a~ )
8 OCTOBER 1980
I ~,i
~ ~F IL
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JPRS L/9335
8 October 1980
USSR Report
ENGINEERING AND EQUIPMENT
(FOUO si8o)
,
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USS R REPORT
ENGINEERING AND EQUIPMENT
(FOUO 6/80)
CONTENTS
JPRS L/9335
8 October 1980
NON-NUCLEAR EIv'ERGY
The Development of Solar Batteries for the Interplanetary Auto-
matic Stations 'Venera-9,' 'Venera-10' and for the 'Lunokhod'
Program 1
- HIGH-ENERGY DEVICES, OPTICS AND PHOTOGRAPHY
Angular Coefficients for a Partly Shielded Cylindrical Surface. 11
FLUID MECHANICS
Experimental Study of the Influence That Pliable Surfaces Have
on the Integral Characteristics of a Boundary Layer.......... 13
Concerning the Effect of White Noise on the Process of
Inertial Separation 14
Radiative Heat Exchange in a System of 'Itao Coaxial Cylinders
With an Intermediate Perforated Cylinder 16
Heat Exchar.ge of a Two-Layer Plate With a Moving Radiating
and Scattering Medium 18
- Dynamic Temperature Fields in Hollow Homogeneous Spherical
_ Bodies 20
Calculation of Surface Friction of the Initial Sections of
Pipes in a Turbulent Boundary Layer With Swirling of the
' Flow at the Inlet 23
Concerning the Problem of the Role of Cavitation in the Ultra-
sonic Capillary Effect 25
MECHANICS OF SOLIDS
General Solution of the Thermoelastic Problem for an
Asymmetrically Heated Solid Cylinder 27
-a- [III - USSR - 21F S&T FOUO]
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l
NON-NUCLEAR ENERGY
UDC 621.472,621.383.5(063)
THE DEVEIAPMENT OF SOIrAR BATTERIES FOR THE INTERPLANETARY AUTO-
MATIC STATIONS 'VENERA-9,' 'VENERA-10' AND FQR THE 'ZUNOKHOD'
PROGRAM
Tashkent GEI;IOTEKHNIKA in Russian No 4, Apr 80 pp 3-9
[Article by G. S. Daletskiy, M. B. Kagan, M. M. Koltun and
V. M. Kuznetsov]
[Text] The utilization of solar batteries as the basic primaxy
electric power-supply sources on space vehicles directed to-
ward Venus or operating on the lunar surface possesses a num-
ber of specific features that preclude the application of sili-
con solar batteries of the usual design.
Chief among the operational peculiarities of solar batteries
is the increase in the level of solar radiation reaching the
battery along with the simultaneous rise in the operating tem-
perature of the solax batteries (iii the case of vehicles trav-
eling to Venus) and the significant increase in the level of
equilibrium operating temperatures of solar batteries exposed
to constant solax radiation. This is in comparison with ve-
hicles that operate in near-Earth space (as in the case of
automatic self-propelled vehicles of the "Lunokhod" type, de-
signed for extended operation on the lunar surface).
Calculations have shown that the equilibrium operating temper-
ature is established at a level of 125-145�C for the solar bat-
teries on the "Lunokhod" which are illuminated by,the Sun and
heated by the Moon's own considerable thermal radiation. For
solar batteries composed of silicon solar cells of the usual
design, a gradual increase in temperature from 65 to 150�C
takes place along the flight path from Earth to Venus.
The application of passive temperature regulating methods for
reducing the equilibrium operating temperature (for example,
not tilting the panels directly at the Sun) or a basic`decrease
1
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in the panel s' space factor in the aforementioned cases
is not possible in view of the stringent demands an the dimEn-
sions arld over-all design of the vehicles.
We have adopted the following as basic directions for the de-
- velopment of solar batteries in the given program: 1) the de-
velopment of a model of a silicon solar cell which, fo-- any
level o-f solar radiation that reaches the cell, posses ses a
loweredi equilibrium tempefiature in comparison with the usual
design; 2) the creation of solar batteries with the he 1p of a
semiconducting material that has a broader forbidden band than
silicon and ahich possesses an optimum combination of photo-
electric and operational properties--gallium axsenide.
The Optical and Radiation Chaxacteristics of Silicon P!-iotoelec-
tric Cells and of Solar Battery Models That Possess Re duced
Equilibrium Temperatures. When operating under conditions of
radiation heat exchange, the lower the equilibrium temperature
of p-n junction semiconductor photoelectric transducers and
the higher the electric output they produce, the lower the ra-
tio of the integral coefficient of solax radiation abs orption
as to the integral coefficient of thermal radiation E a t the
surface. When utilizing optical coatings--radiation-
resistant glass [1] or transparent s:ilicone lacquer [2]--the
normal coefficient e at the surface of the photoelectric trans-
ducer becomes equal to 0.9-0.92, instead of 0.2-0.25 in the
absence of the coating, approaching its own limit of
f'A950l.BlACK BODY-1�0. The coefficient of radiation e into the hemi-
sphere is 0 e 84-0 .86. The coefficient �S for a photoelectric
cell of the usual design is 0.92-0.93, which is considerably
higher than its minimum value of 0.67, which can be achieved
without reduci.ng its efficiency.
~ Photoelectric cells of the usual design C31, as our me asure-
ments have shown, axe opaque in the entire solar spec trum in-
terval from 0.2 to 0.3 �m. This occurs because of radiation
absorption by the free charge carriers in the comparatively
thick, 2-3 �m, heavily doped surface layer of a photoe lectric
cell with a p-n junction, in the solid metallic backsid.e ele-
ment and at the semiconductor-metal interface.
The photoelectric transducer becomes transparent in the infra-
red region of the solar spectrum from 1.1 to 3.0 �m when a num-
_ ber of conditions are met [4] : the depth of, the semiconduc-
tor's heavily doped upper layer is not to be more than 0.5�-1.0
,um thick, the contact grid on the back side of the device is
not to occupy more than 5-10 percent of the surface, the back side is to
be highly polished and there is to be an effective reflection redu cing
coating on both surfaces of the device. With a transparent or wid e-meshed
supporting surface made from materials propoaed, for example, in work [5],
a sular battery made from
2
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such photoelectra_c transducers possesses 80-90 percent less
absorption in the region of the 1.1-3.0 �m spectrum than an
ordinary battery. In this case, the coefficient as is equal to
0.7-0.72, while c remains at a level of 0.9.
In place of white enamels that darken when expoaed to the Sun's
ultraviolet radiation, a stable selective coating has been de-
veloped. This coating possesses a low ratio of as/e (less than
0.2) and is based upon glass films made from radiation-
resistant glass with a vaporized aluminum or silver coating
on thn back surface [6]. This coating was utilized success-
fully to protect the cooling radiator on "Lunokhod" I and II
from overheating.
In order to obtain such a low ratio of as/E for photoelectric
transducers that are occupied by the contacts, it was decided
(in the design of parallel modules in which one piece of glass
protects several large photaelectric transducers simultaneous-
ly) that the back sLirface of the glass be coated in a high
vacuum with a grid made from a highly reflective metal--silver
or aluminum--before it is bound to the medules.
Such a mirror mosaic is created by vacuum plating alumir_um or
silver through masks, thanks to which the configuratiorl of the
grid strips reiterates the arrangement of power distri'oution
contacts and the intercontact gaps in the parallel modules.
Because of the reflective grid on the back side of the glass,
those spots occupied by the contacts reflect 84 percent of the
solar radiation (in the case of aZuminum) or 92-94 percent (in
the case of silver). The absorptivity of those spots occupied
by the contacts decreases because of this reflective grid from
0.75 to 0.16 or even 0.06-0.08, while the hemispheric emittance
E remains high, equal to 0.86, for both the silicon photoelec-
tric transducers and the surface of the contacts. This Is 'lie
also to the outer glass coating. The equilibrium temperature
at those places occupied by the contacts drops, and the heat
overflow from the heated semiconductor surface to the cooled
contact spots leads to a reduction in the average equilibrium
temperature of solax batteries.
- For the solar batteries on the automatic interplanetary station
"Venera-9," parallel modules made from silicon photoelectric
cells are utilized which are transparent in the solar spec-
trum's infrared range. Heat-reflective coatings of vacuum-
plated aluminum are also used on 10-12 percent of the internal
surface o.f the protective glass on the parallel module. Pro-
- tective radiation-resistant glass of 170 and 300 �m thicknes-
- ses was used in the modules. Also, the advantage of using one
over-all coverglass for several photoelectric cells (a module
consists of 4 to 6 photoelectric cells, each about 5 cm' in
suxface) is the improvemen-t in radiaticn protection reliability.
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Calculations have shown that the equilibrium temperature oi
such solar batteries should be 30-35�C lower along the entire
Eaxth-Venus flight path in comparison with solar batteries of
the usual d.esign.
Tsmperature and Electrophysical Characteristics of High-
Efficiency Photoelectric Cells Exposed to Elevated Tempera-
tures. In accordance with the theory of photoelectric trans-
ducers with a p-n junction, developed in works [7-9], there
exists a broad class of semiconductor compounds that have an
advantage over silicon in the maximum feasible efficiency as
well as in a iiumber of operational characteristics. To this
grouR of emiconductors belong the intermetallic compounds
of the A,BS system--gallium arsenide, ir.dium phosphide, gallium
phosphide as wel' as various combinations of these compounds.
The most promisii.g material from this group from the point of
view of the production level and the results achieved is gal-
lium arsenide (GaAs).
The temperature characteristics of these types of pho�oe3ec-
tric transducers make it possible to obtain high specific
characteristics. The difference ir_ the dependence of the ab-
sorptivity upon the wavelength in comparison with silicon leads
�o yet anottier important feature of gallium arsenide photo-
electric transducers--the contribution of the base toward the
over-all collector efficiency is considerably less than the
contribution of the diffusion region for the most probable
parameters of the source material and the p-n junction. This
means that the losses due to radiation transmission without
absorption in gallium arsenide are considerably less. Thus,
the same collector efficiencies and, consequently, the same
over-all efficiencies can be obtained for gallium arsenide
photelectric transducers with considerably thinner base layers.
Because of this, one can obtain at least the same specif ic
chaxacteristics for photoelectric transducers made from sili-
con and gallium arsenide at room temperature,, despite the doub-
led specific weight of gallium arsenide.
The temperature characteristics of the power parameters of the
photocurrent, the photoelectromotive force and the efficiency
of gallium arsenide photoelectric transducers have been studi-
ed in the +20 to +200�C temperature range. The results ob-
tained for the efficiency are cited in fig. i(curves 1a, b).
For comparison, the temperature dependeizce of the efficiency
of silicon photoelectric tra:nsducers is also shown (curve 2,
according to the data in work [101). The indices a and b ap-
ply to samples that have a different magnitude of series resis-
tance. From fig. 2 it is apparent that gallium arsenide-based
photoelectric transducers have approximately one half the tem-
perature gradient of efficiency in compaxison with silicon
4
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(-0.025J10C for galliui.l arsenide). This difference is ex-
plained by the lesser dependence of the load current on the
temperature in the interval studied and the greater initial
values of the photoelec+romotive force of the photoelectric
transducers based on gallium arsenide.
~ An analysis has shown [l1] that the attainment of minimum val-
ues for the inverse dark current of the p-n junction is deci-
sive in obtaining temperature-stable solar cells. For gallium
arsenide photoelectric transducers a value of 10-� to 10-10 A/cm'
~ far the inverse dark current is characteristic, while at the
same time the vaJ_ues for this parameter for silicon photoelec-
_ tric transducE:rs lie in the 10-� to 10-' A/cm' interval.
r
ia
,b ~
~i
~
l00 ,ao T oC feo
Flg. 1
Temperature dependence of gallium
arsenide (curves ia, b) and silicon
(curve 2) photoelectric transducers.
The increase in the photocurrent when the light flux increases
leads to a noticeable reduction in the optimum output tempera-
ture gradients of semiconductor photoelectric transducers.
This condition must be taken into account wtien designing solar
batteries for interplanetary solar stations directed toward
the Sun.
It is apparent from fig. I that for the same initial efficien-
cies (at conditions of room temperature), gallium arsenide
photoelectric transducers begin to surpass silicon photoelec-
tric transducers by more than a factor of two at temperatures
of 130 to 140�C, temperatures which were expected according to
calculated data for the solax batteries on "Lunokhod."
5
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Operatiilg Conditions and Operational Characteristics of tr,a
Solar Batteries on "Lunokhod-I" and "Lunokhod-II." Semicori-
ductor solar batteries for "Lunokhod-I" and "Lunokhod-II,"
_ made from gallium arsenide-based photoelectric transducers,
are located on the inside of the lunar vehicle's roof, which,
in its closed position, rests on the upper part of the body.
In the operating position, the solar battery panel can be in-
clined at various angles, which makes possible the optimum
utilization of the Sun's energy when its elevation over the
lunar horizon varies.
In f ig. 2 is represented the variation in the parameters of
the "Lunokhod-II's" solar batteries over the course of the se-
cond and fourth lunar days. The,operational temperature con-
ditions are given as well. The slight increase in the ik_
current from the solar batteries at the beginning and end of
the lunar day is explained by the effect of the cooling ra3ia-
tor in "Lunokhod's" thermoregulating system when the Sun is at
low angles over the lunar horizon.
In fig. 3 the variation in the current from "Lunokhod-I's" so-
lar batteries is shown. When the Sun's elevation over the lu-
nar horizon is greater than 34�, the solar battery in the
transport position (angle~p=0) makes it possible to obtain a
current from the solar battery of not less than 4A, which in-
sures the "Lunokhod's" operational routine when it is in mo-
tion.
The solar batt2ry on "Lunokhod-I," the vehicle which was de-
livered to the Moon's surface on 17 November, 1970, functioned
successfully over the course of IO lunar days up through 4
October, 1971. In 10.5 months the degradation of the solar
battery's working current amounted to about 6 percent. The so-
lar batteries on "Lunokhod-II," delivered to the Moon's sur-
face on 16 Janizary, 1973, are based on gallium arsenide photo-
electric transducers. They operated successfuZly for the en-
tire period of the planned program of five lunax days without
degradation of their electrophysical characteristics.
Experimental Investigations Into Certain Characteristics of the
Solar Batteries on the Automatic Interplanetary Stations (AMS's)
"Venera-9" and "Venera-S0." The solar batteries on AMS's
"Venera-9" and "Venera-10" consist of two rectangular panels
of approximately 4 m' in surface area at each station. The
panels are oricnted toward the Sun along with the automatic
interplanetary station itself.
The plane modules of the silicon photoelectric transducers,
transparent in the IR-region of the solar spectrum when used
in combination with the mirror mosaic over the current pick-
, off contacts, are fixed to the supporting surface of the panels.
6
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~
(D -0- 3
~ A~~%
I ~
~ I 1
O
.rj Ju-
~ L
~ ~ '~0~ -I140
N 110
~ ' J 5 7 9 /f 1J . f5
- U)
Eartn days
Fig. 2
- Variations in the parameters of the
solar batteries on the "Lunokhod-II"
1,2 - Solar battery current variation on "Lunokhod-II" during
the course of the second and fourth lunar days;
3- Solar battery temperature variation on "Lunokhod-II" during
the second lunar day;
I- Variation in the Sun,s elevation during the second lunar
day, 8-22 February, 1973� '
The panels have low thermal conductivity but, like the photo-
electric transducers, they are transparent i.n the rR-region o#'
the solar spectrum. The Space factor of the panels with
solar battery modules is 0.0.
- In fig. 4 is shown the vasiation in the ~rreddaa.ce on
the panel of solax batteries on the "Venera-9" and "Venera-10"
automatic interplanetary stations. The abrupt variation in the
currents from the solar batteries is explained by the switching
- on and off of portions of the solar battery as provided for in
the station' s program.
7
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v.. ~vinu vau viri.a
J, A e
B ~
a!�J4�
4?� O ?
4 p
6 r-,P4*
2n 417 BO f20 f60 200
Earth days
Fig. 3
Solar battery current variation on "Lunokhod-I" when the
panel was used to scan the Sun's elevation at various po-
sitions. When the normal to the solar battery was orien-
ted toward the Sun along an azimuth having an error no
greater than � 4�, � is the Sun's elevation over the lunar ~
horizon; v is the inclination of the solar battery rela-
tive to the horizon. i- Solar batteries; 2- Cooling
radiator of the thermoregulating system.
Nd
,5
3
/
i? T
2~_0 N
~
!S:,
240
Fig. 4
Va,Y'iation in the ixradiance of the solar battery
panel on the "Venera-9" (i) and "Venera-IO" (2) automatic
interplanetary stations along the stations' flight path.
Vaxiation in the solar battery operating currents on the
= 8
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"Venera-9" (3) and "Venera-10" (4) automatic inter-
planetary stations along the Earth-Venus flight paths
(segment "a" ) and along the orbits of artificial sat-
ellites of Venus ( segtnent "b" ) .
V, �c
130 ~
~
%/0 =
i
i
I
SD -
~
JJ ~
30 I. _
20
� I
. I
I
i
a b
~
~
~ 1 I I ~ 1 I ~
so ;oc >ao icla
Days
- Fig. 5
- Variation in operating temperatures of the photo-
electric transducers in the solar batteries of
"Venera-9" and "Venera-IO" (i) and of silicon photo-
electric transducers of the usual design that are
not transparent in the IR-.region of" the solar spec-
trum, with a mirror mosaic over the contacts (2)
and without it (3) along the Earth-Venus flight paths
_ (segment "a" ) and along orbits of artificial satel-
lites of Venus (segment "b").
In fig. 5 are represented the variations in the operating tem-
peratures of the photoelectric transducers of the solar bat-
teries on "Venera-9" and "Venera-I0," which had practically
the same tempera.ture variation along the entire f,light path
(a). Photoelectric transducers of the usual design were mourit-
ed a,l.ongside the panels of solar batteries on "Venera-9" and
"Venera'10" in the form of sensors on frame-extension brackets.
The utilization of the mirror mosaic leads to a 15�C decrease
in the operational equilibrium temperature of photoelectric
transducers of the usual design, while the simultaneous appli-
cation of the wirror mosaic and photoelectric transducers that
are transparent in the 'Ilkregion of the solar spectrum leads
9
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to a 33-35"C reduction in the operational equilibrium tnm-
_ perature along the entire flight path of the "Venera-9" ana
"Venera-10" automatic interplanetary stations.
As a result of the research that has been carried out, h:igh ef-
_ ficiency silicon- and gallium arsenide-based solar batteries
- have been developed which successfully insure the operation of
the Soviet "Venera-9" and "Venera-10" automatic stations and
the "I,unokhod" vehicles. The results of development and re-
search have been confirmed by successful testing of the solar batteries under operating conditions.
BI BLIO GRAPHY
1. Koltun, M. M. and Landsman, A. P. "Preobrazovateli
solnechnoy energii na poluprovodnikakh" [Semiconductor
Solar Energy Transducers], Moscow, 1968.
2. Koltun, M. M. and Zandsman, A. P. KOSMICHESKIYE
ISSLEDOVANIYA, No 2, 1964.
3. Koltun, M. M. and Landsman, A. P. OPTIKA I SI'EKTROSKOPIYA,
No 26, 1969.
4. Thelen, A. Conf . paper 1296-60, ARS Conf Santa Monica,
California, 27 Sep 60. ~
5. SPACEFLIGHT, No 9, 1967.
6. Koltun, M. M. GELIOTEKHNIKA, No 6, 1970.
7. Loferski, I. I. J. APPL, PHYS., Vol 27, No 7, 1956.
8. Laferski, I. I. ACTA ELECTRONICA, Vol 5, No 3, 1961.
9. Toss, T. S. SOLID STATE ELECTRONICS, Vol 12, No 4, 1961.
10. Zaytseva, A. K. and Gliberman, A. Ya. "Kremnlyevyye
solnechnyye batarei" [Silicon Solar Batteries], Moscow,
1961.
11. Kagan, M. B., Landsman, A. P. and Lyubashevskaya, T. L. -
KOSMICHESKIYE ISSLEDOVANIYA, Vol 9, No 4, 1971.
COPYRIGHT: Izdatel'stvo "Fan" Uzbekskoy SSR, 1979
[8144/1143-9512] �
9512
CSO: 8144/1143
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HIGH-ENERGY DEVICES, OPTICS AND PHOTOGRAPHY
UDC 536.3
ANGULAR COEFFICIENTS FOR A PARTLY SHIELDED CYLINDRICAL SURFACE
- Minsk INZHENERNO-FIZICHESKIY ZHURN_AI. in Russian Vol 37, No 3, Sep 79
pp 522-523
[Annotation of deposited article by V. A. Arkhipov, registration number
1377-79 Dep.] I
[Text] A method of numerical integration is used to determine the
angular coefficients of radiation between the surfaces of a disk and an
infinite cylinder separated by a screen that is oriented parallel to the
disk and has a diaphragm coaxial with the disk. The normal to the center
of the disk passes through the axia of the cylinder and is perpendicular to
this axis. A configuration of this type is of interest in particular in
the design of opto-electronic equipment for laser diagnoais of axisym-
metric plasma jets. The average angular coefficient was calculated from
the general formula for ~1,2 written for application to the given
geometry:
4R k _ ik r~ -
{ar1~ dz S (L - R cos E).dE ~ rdr x
0
sa
x (rs1ll1ilA* -}-L ms6 -R)d+p
(RI -I- L' -f- zi -I-rs -2RLcosE -2srcos~-2rRsint sJnV)s .
For the variables of the limits of integra.tion zk(r, ,Ek(r, that
determine the field of view, we get the analytical expressiona
L-Roo'st `~I (L Q RcosatnM) 2-rc05
~ e are sin ~L ~ ale + r~ - r s1n
R YZ+"+ (r- o --r-Isn` arctg t-r-~' -
On the basis of an algorithm derived in this paper, numerical calculations
are done and curves are plotted for the average angular coefficients, and
- for local angular coefficients (with contraction of the disk Co an
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element of area) for different values of the geometric parameters of the
given radiating system.
Notation
Z--distance between disk and screen; L--distance between disk and axis
, of cylinder; r, ~--cylindrical coordinates of a point on the surface of
the disk; rl--radius of the ciisk; r2--radius of the diaphragm; R--radius
of the cylinder; z, C--cylindrical coordinates of a point on the surface
of the cylinder..
COPYRIGHT: "Inzhenerno-fizicheskiy zhurr:i", 1979
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FLUID MECHANICS
UDC 532.526-597.31
EXPERIMENTAL STUDY OF THE INFLUENCE THAT PLIABLE SURFACES HAVE ON THE
INTRGRAL CHARACTERISTICS OF A BOUNDARY LAYER
Minsk INZHENERNO-FIZICHESKIY ZIIURNAL in Russian Vol 37, No 3, Sep 79
p 518
[Annotation of deposited article by V. I. Korobov, registration number
1368-79 Dep.]
[Text] Previous research has been done on the interaction between plia-
ble boundaries and an oncoming flow. Most of these studies have been
done in air and on surfaces of diaphragm type. Based on hydrobionic
studles, there is an opinion that elastic surfaces such as animal hides
play an activP functional part in the hydrodynamics of aquatic animals.
The paper gives the results of an experimental stud}� of the hydrodynamic
friction of pliable surfaces of monolithic type, with coneideration of
the morphofunctional structure of the outer hides of aquatic animals.
The experiments were done in a hydrochute, using an insert placed on a
strain-gage bracket in the lower wall of the working section.
The principal results of the work can be formulated as follows.
Pliable surfaces may have an appreciable effect on the integral charac-
teristics of a boundary layer; a pliable surface with conatant meehanical
characteristics has its own comparatively narrow range with respect to
Reynolds numbers with an extremum of effective action on a boundary layer
with position and extent that depend on a number of surface parameters.
COPYRIGHT: "Inzhenerno-fizicheskiy zhumal", 1979
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UDC 531.38
CONCERNING THE EFFECT OF WHITE NOISE ON THE PROCESS OF INERTIAL SEPARATION
Minsk INZIiENERNO-FIZICHESKIY ZHURNAL in Russian Vol 37, No 3, Sep 79
pp 519-520
~ [Annotation of deposited article by Ye. A. Yeseyev, registration number
1375-79 Dep.]
[Text] The stochastic differential equation
_ az
-F
W a s ^ Pi 1 t (t) (1)
is valid for steady-state turbulent motion of a swirling dispersed system
in which it is assumed that the trajectories of all particlea of the
carrier fluid are ares of concentric circles on the average, and the
motion of the suspended matter (Stokes fractions) relative to,the dis-
persion medium is quasi-steady. Ref. 2 tells us that the equation

aQ' d'i (lo) s~l _ Pl df (ro) (2)
s a, lh ~ ~e dre s -
corresponds to (1).
Taking v= const rw, and approximat3ng some tangential velocity profile of
the carrter fluid by Y= 0.5, we write (1) in d.imensionless form
a A~s ) (3)
0 0
_ where a, S are the dimensionless coefficients of diffusion and drift
respectively.
If equation (2) is considered in conjunction with the boundary conditions
_ _
df o� f (R.) + ~ d ~ o, (4)
. .
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it has the solutiori
1 (ro) = R' a ~0-- lexP a Cro - Rl)~
`eXP L- a (Rs - Rl)J~ + exp (R~ _ Rl~l~� (5)
J
Here R1, R2 are the inner and outer boundaries of the separation zone,
a is a parameter that characterizes the intensity of burbling of the
particles of some fraction from boundary R2. It is apparent from (5)
that the first term is always positive, the second is always negative,
and the third is determined by the parameter A.
Verification of the feasibility of result (5) with some other empirical
values of vp specifically when y= 1, -1, based on numerical integration
of the direct Fokker-Planck-Kolmogorov equation for probability density
w(r, E) of process r(f)with conditions on R1, R2 analogous to (4) showed
complete agreement between the data of the calculation and (5). As the
coefficient a increases, there is an increase in the calculated fraction
efficiencies for the corresponding values of t of the interval of process
duration, and this trend is not at all disrupted by the form of vo.
No ta tion
r, �--polar coordinates; t--time; v~--tangential component of the veloci-
ty field of the dispersion medium; T--relaxation time of a separated
particle; p, pl--physical densi+ties of inedium and particle respectively;
g--parameter that characterizes the specific dispersed system; e--
white nmise and its inL-ensity respec:tively; f--average time for a particle
to reach the boundary; rp--initial distribution of polar radius;
2rp
rp = R1 + R2, f, etc.--dimensionless characteristica of the corresponding
quantities.
REFERENCES
- 1. N. A. Fuks "Mekhanika aerozoley" [Mechanics of Aerosols], Moscow,
Academy of Sciences USSR, 1955.
2. Yu. V. Prokhorov, Yu. A. Rozanov, "Spravochnaya matematicheskaya
biblioteka. Teoriya veroyatnostey. Osnovnyye ponyatiya. Predel'nyye
teoremy. Sluchaynyye protsessy" [Mathematics Reference Library.
Probability T'ileory. Basic Concepts. Limit Theorems. Random Processes],
Moscow, Nauka, 1967.
3. E. Rammler, R. Beuerfeind, STAUB, 134, No 5, 1959.
COPYRIGHT: "Inzhenerno-fizicheskiy zhurnal", 1979
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- UDC 536.24
RADIATIVE HEAT EXCHANGB IN A SYSTEM OF TWO COAXIAL CYLINDERS WITH AN
INTERMEDIATE PERFORATED CYLINDER
Minsk INZHENERNO-FIZICHESKIY ZHURNAL in"Russian Vol 37, No 3, Sep 79
p 522
[Annotation of deposited article by A. V. Rumyantsev, 0. N. Bryukhanov
and V. R. Bazilevich, registration number 1374-79 Dep.]
[Text] The resultant radiation energy fluxes between the componenta of
a system of three infinitely long coaxial cylinders with perforations in
the middle cylinder Are found in the diffuse approximation from pre-
determined temperatures and geometric-optics properties. The problem is
- solved by a generalized zonal method. For this purpose, expressions were
found for the average angular coefficients of radiation:
-
Here ~ik = Di/Dk is the ratio o# di.ameters o# th.e c}rlindrtcal surfaces,
S is the degree of perforation of surface F2. Quantities relating to
convex surfaces have subecripts l and 3, while those referring to concave
surfaces have subscripts 2 and 4.
Numerical analysis of the resultant computational relations shows non-
linear dependence of the resultant energy fluxes rfi.3iated by surfaces
F2 and Fy as a function of S. The tnergy flux from surface F1 increases
monotonically with increasing R, which is attributed ta the reduction in
screening action of the perforated cylinder. The energy flux radiated
by surface F3 falls linearly with increasing $ due to the reduction in
its area. The energy flwces radiated by surfaces F2 and F4 are nonl3near
functions of the variable S.
The function that describes the resultant flux from surface F2 to surface
F4 has a maximum that shifts toward smaller R as the valuea of e decrease.
The peculiarities of radiation of this surface are due to the following
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factnrs that differ in their effect on the nature of radiation of this
surface: 1) the perforation effect (cavity effect); 2) change in the
radiation flux incident on the exposed surface with a change in the area
of the perforations; 3) change in the area of the radiating surface with
a change in s. These factora are responsible both for the nonlinearity
of the function and for the maximum in this function.
- 'Che intermediate perforated cylinder can be treated as a perforated
screen between the unperforated cylinders. A comparison of the ei:ergy
- fluxes incident on surface F4 with a perforated or an unperforated screen
in the system as plotted at identical temperatures shows that this ratio
� is greater than unity for any values of e and S. The difference between
fluxes increases with a reduction in e, which can be attributed to *he
perforation effect that has a considerable influence on the type of
radiation of surface F2.
The resultant computational formulas can also be used ,.o find the energy
radiated by a coaxial system made up of an inner unperforated cylinder
and an outer perforated cylinder.
COPYRIGHT: "Inzhenerno-fizicheakiy zhurnal", 1979.
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UDC 536.3
HEAT EXCHANGE OF A TWO-LAYER PLATE WITH A MOVING RADIATING AND SCATTERING
MEDIUM
Minsk INZHENERNO-FIZICHESKIY ZHURNAL in Russian Vol 37, No 3, Sep 79
pp 523-524
' [Annotation of deposited article by F. N. Lisin and I. F. Guletskaya,
registration number 1380-79 Dep.]
[Text] A gray radiating, absorbing and scattering medium moves in a slot
channel with gray walls. The lower wall is a two--layer plate with given
thickness and coefficient of thermal conductivity. The velocity profile
is parabolic. On the lower boundary of the two-layer plate the heat flux
is given as a function of the coordinate x. The temperature of the upper
wall TCT is constant. The problem is written in dimensionless form as
foll'ows:
equati.on of energy for the medium:
Pe u(~I) 89_ _ 829 _ pe
u dx - arf go
equation of heat transfer in the layers of the plate
=O, .i - 1, 2� are the numbers of the layers (2)
axi a~ .
with boundary conditions
0- t atx=0; 9~AcT *t x>0; q~
~ - ~ 4'- kl -,Oq at 'n = p; ,
0(x. 0)=ei(z. 0): ox sx- �0 $t '=0.x.L,
~i ~s k~ = a~ . ei (x. 9s (x. q) at n
olq
~t -
9s (x) at
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where rj =y/b; x=x/b: O=TITa; ki=Xi1X; k.=1i/1j; Sis Si/b: 9,sSal6; 9'= 9'(x)1Q0T10
�
' The divergence of radiant flux is found from solution of the transport
equation in the P1 approximation of the method of spherical harmonics,
and contains the average scattering cosine. The influence that optical
thickness has on the Nusselt numbers of radiant and convective heat
fluxes to the plate and to the upper wall is analyzed on the baeis of
the numerical solution. The amount of heat transferred by radiation to
the walls with changing Tp(1 - Y) passes through a maximum in the vic inity
of 1.1-1.2 (Tp is the optical thickn.ess, Y is the ratio of the scatt ering
- coefficient to the attenuation factor). Calculations are used to analyze
the influence that the ratio af the coefficients of thermal conductivity
of the plates k2 =X1/X2 has on heat exchange. As k2 increases, ther e
is a rise in temperature on the boundary r1= 0, which has an effect on
cooling of the medium in the channel. The higher the k2, the higher will
be the corresponding curves for the Nusselt numbers of the radiant heat
flux as dependent on channel length.
COPYRIGHT: "Inzhenerno-fizicheskiy zhurnal", 1979
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UDC 536.21
DYNAMIC TIIMPERATURE FIELDS IN HOLLOW HOMOGENEOUS SPHERICAL BODIES
Minsk INZHENERNO-FIZICHESKIY ZHURNAL in Russian Vol 37, No 3, Sep 79
Pp 527-529
[Annotation of deposited article by V. V. Semenyuk and M. P. Lenyuk,
registration number 1369-79 Dep.]
[Text] Dynamic problems of the claasical theory of linear thermo-
elasticity require knowledge of the true temperature field accompanying
high-intensity unsteady processes. In such processes the temperature
field in aa isotropic homogeneou.4 hollow spherical body D
- R1