SCIENTIFIC ABSTRACT LYUBIMOV, G.A. - LYUBIMOV, G.P.

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• Collection: Scientific Abstracts
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• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 31, 2001
• Sequence Number: 8
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

LYTJ13D-!OV, Georgiy Aleksandrovich; L' ' , borl@-, ',@()r,,-i--evich;
U .1 : I-
GEYMAN. M.A., nauchn. red.; SHVETSOVA, E.i.;. . vec. red. ;
,E2.'YAhIR.Y,L,, tekhri. red.
[Theory and design of a-xial multistage turbodrill turbines]
0
Teoriia i raschet osevykh mnogostupanchatykh turbin turbo-
burov. Leningrad, Gostoptekhizdat, 1963. 1718. @.
( NII.' A 17 : -11 )

6
10(7)
AUTHORs Lyubimov, G.A. SOV/55-5,9-5-6/34
TITLEs On the Influence of Viscosity and Thermal Conductivity on the
Gas Flow Behind a Strongly Curved Shock Wave (0 viiyanii vyaz-
kosti i teploprovodnosti na techeniye gaza za sillno iskriv-
lennoy udarnoy volnoy)
PERIODICAL: Vestnik Moskovskogo universiteta,Seriyi@ matemtiki., mekhow1ki,
astronomii,, fiziki, khlmli, '958,,Nr 5, PP 53 - 5b @UssR)
ABSTRACT: In [Ref 1,7 L.I. Sedov and othern gave formulas for the re-
lations of the braking temperatures and pressures in front of
and behind a curved shock wave tinder consideration of vis-
cosity and heat conduction of the gas, whereby plane and axial-
symmetric waves were considered. The author generalizes these
results to shock waves of arbitrary form.
There are 2 figuresgand 1 Soviet reference.
ASSOCIATIONs Kafedra gidromekhaniki (Chair of' Hydromechanics)
SUBMITTED: May 28, 1958
Card 1/1

Aa-
Pp
jw:
cl

24 (1)
AUTHOR: Lyubimov, G. A. SOV/ 55-5a-6-3/31
-------------
TITLE: -On the Compression of a Gas Cylinder by Means of Current (0
szhatii gazovogo tailindra tolcom)
PERIODICAL: Vestnik Moskovskogo universiteta. Seriya matematiki, mekhaniki,
astronomii, fiziki, khimii, 1998, Nr 6, PP 13 - 17 (USSR)
ABSTRACT: In the present paper the solu,;ion of the problem mentioned in
the title is carried out. In -this investigation - in contrast
to other papers (Refs 1,2) - '.he shock wave which forms due to
a magnetic field is taken into account. This magnetic field
forms due to the feeding of V-,e --3 ny:inder with ele-,tric
rent. The solu+ion is obtaint::` 31@ a series, leval.-
oped according to low powers ,fc" 1:. 3 c -, _n oc t I D@-, 6 d e -
notes the ratio of the gas dersity @,._-Ld behind the shqc@-,
wave. For the solution first --.he eq!_atinns ('1
ar 2 a ar
r Y- (L-1- "= -, ".@ set
2 m 9 97m - Y-r
9t
tance of the particles from the a_@-is ,f V,.e c,',inder, J-'@
ity, p - pressure) for the ! - -.- 1, aal ur.,@Asttlrbel. mo_'i -,.,I
Card 1/3 of an ideal gas with a const2-t th-.-na@ -a@;acity r after Vte

On the Compression of a Gas Cylinder by Mear5 @J 15-7/51r-58"3i'31
Current
introduction of the Lagrange variabie m (dzi-y'(a)RdR R. di3-
1
tance of the particles from the cylinder axis at the tlmi tmD
and O(R) - the initial distribution of density@. The shock
wave is taken into account by tie following condition8:?
0 2 0-1 (1 _62 @1*2 0 0 0 1
P=Pl +(l-F-)?Or-* , i-i 1 2 1 (2) where 9 1 P P1 I 1 1 d@-nG c
the density, pressure and heat volume of tl,e gas before the
shock wave and 9, p, i the same behind the shock wave. 1* da-
notes the velocity of propagation of the shock wave. For the
solution of the system of equations (1) the following series
are set up in powers of F- and inserted into (1)? -S 0/E+g,4 - ..'
P=PO+Epl ...... r-r 0+6rI ........ Moreover, these expansions i.,-
to series (3) and r r*+Er ....... are introduced in the con-
0 1
ditions for the shock wave (2). The series r,nr oc +Er IC +.- (c
cylinder) is set up for the motion of the external boundary of
the cylinder and the pressure conditions are obtained (8). By
Card 2/3 means of the energy integral equation for the mentioned prob-

On the Compression of a Gas Cylinder by Means SOV//55-58-6-3/31
of Current
lam with the mentioned conditions, equal;ionB for the determination
ro(t) and roc(t) (9) and (1-1) and for r-*(t) (10) may be
obtained by an expansion into a series according to powers of
Further, a comparison is made of the reSUItS with those from refer-
ence 2. An agreement was found between the results of the compres-
sion periods of the cylinder and also with the experimental results.
The method described here permits also the computation of a.11 para-
meters of motion behind the shock wave. The numerical computations
were carried out by means of an eler-troala d-igita.1 r!ompatez-. `Ttare
are 1 figure and 4 Soviet references.
ASSOCIATION: Kafedra gidromekhani1ki (Chair of Hydroolecha-nics)
SUBMITTED: June 25, 1958
Card 3/3

SOV/179-59-1-32/36
A,UTHULL: Lyubimov, G, A. (Moscow)
TITLE,: Flow of Non-ideaf Gas with a Great Supersonic Speed Around
a Body (Obtekaniye tel potokom neideal'nogo gaza s bol'shimi
sverkhzvukovymi skorostyami)
PERIODICAL: Izvestiya Akademii nauk SSSR, Otdeleniye tekhnicheskikh
nauk, Nlekhanika i mashinostroyeniye, 1959, Nr 1, PP 173-176
(USSR
ABSTRACT: A method is described in Ref.1 which is applied in this
work to the case of supersonic flow round either a rotating
body or a flat contour with an arbitrary relationship of
pressure and temperature. The fundamental equations and
their solutions are based on a system olf' coordinates as shown
in Fig.l. When the function of the current q)Isdenoted as:
--;@ - 1 1) -1
dd@ = PuIr dy - pvr (l dx
then the equation of motion of gas in the system of coordinates
Card 1/5

SOV/179 -59-1-32/36
Flow of Non-ideal Gas with a Great Supersonic Speed Around a Body
X, 0 will take the form of Eqs.(l) where u and v
components of velocity along x and y p S -
C)
pressure, density, entropy of gas, R - radius of the eon-
tour of flow* I
I )) - 1 2 for a flat or rotating body res-
pectively, r - distance from the axis of symmetry, a -
an 'gle between the tangent to the contour of the body and
the direction of incoming flow. The solutions of the above
equations in respest to ths main shock wave are based on
Eqs.(2), where p, I YJ I U - parameters of gas in
the incomin- flow, i - heat content, Y*(x) - surface
equation of the shock wave, angle between tangent to
the surface of the shock wave @-nd the direction of incom-
ing flow, e - ratio of densities in flow and behind the
shock wave which in the case of' a curved wave becomes a
function x Generally, the solution of Eq.(l) can be
obtained when the series:
p @ p + Ep, +..., U =-Uo + Ell, 92- +
0 E
Card 2/5 V = E;v0+... 1. y @ Ey 1)

SOV/179-59-1-32/36
Flow of Non-ideal Gas with a Great Supersonic Speed Around a Body
with a step E are introduced. Thus the Eqs.(3) are der-
ived. The limiting conditions will be defined when
0 = O(x) which is an equation of shock wave in the co-
ordinates x , 0 . In this case:
0 *V
?l Ur OU O'D iK Cos a
+ Eq) r VEY 0
0 V o r
where (xq))r) and the conditions to satisfy the
0 YO 0
equation - @ are shown in Eqs.(4). These conditions are
derived from the first three equations of Eqs.(2). The
fourth equation of Eqs.(2) can be found in an identical way
and the last equation of Eq.(2) can be expressed as:
i Po - i(plo, 910) 1 2 2
( Pol T-) 7 U s in OL (l +.VE;
From this expression the value of E(x) can be determined.
Card 3/5

SOV/179-59-1-32/36
Flow of Non-ideal Gas with a areat Supersonic Speed Around a Body
As bn example, the problem of airflow around a cone is con-
sidered. In this case the flow of the shock wave is taken
as linear and F_ - const (0= 2) . The solutions of Eqs.(3)
and the limiting conditions of Eqs.(4) will take the form
of the expressions to the left of Fig.4, P 1?5. The Figs.2
to 4 illustrate the results of the calculation when oL = 25,
T 10 =220, pl 0 = 0.1 atm. The va-lues of E and T 0 are
determined from:
Pi0 0 o 1 2 2
p(T i(T i(q,
E; 0PO 01 Po 1 1 pi sin oL(i +
(f(T, p) and i(T, p) are taken from tables in Refs.4 and 6
T e points in the figures ma ked with crosses denote the
values when the characteristics of air at higher temperatures
were considered, Fig.2 shows the relation of the density of
the shock wave to the number M of the incoming flow. When
M - 20 the temperature behind the shock wave rises to 30000c,
causing the dissociation of the air; the density of the shock
wave increases more rapidly in comparison with that at lower
Card 4/5 temperatures. Fig.3 gives thE? relation of the angle of the

SOV/r9-59-1-32/36
Flow of Non-ideal Gas with a Great - Sipersonic Speed Around a Bod7
shock wave 0 to the number 11 . Fig.4 gives the value of
the coefficient of resistance as calculated from the formula
at the bottom of P l?5 (black dots represent the values taken
from Ref.5). All the results were calculated from the theo-
retical formula and show a 1 to 1.5% accurac,y in comparison
with the same results obtained in the Laboratory of Physics
of Fire in the Institute of Power, Academy of Sciences USSR,
imeni G. M. Krzhizhanovskiy. ' "Phere are 4 figures and 6
references of which 2 are Soviet and 4 are English.
I C)
SUBMITTED: April 7, 1958,
Card 5/5

'24 (3)
AUTHORS: Knlikovskiy, A. G ' Lyubimov G. A. SOV/179-59-4-16/40
(Moscow) ...a
TITLE: On the Possible Kinds of Crack, With a Conductivity Jump
PERIODICAL: Izvestiya Akf4demii nauk S33R. Otdeloniye teklinichoskikh nauk.
Mekhanika i mushinostroyeniye, 1959, Nr 4, pp 130-131 (USSR)
ABSTRACT: If in a flo,-v of gas there is e. surface with a jump-like change
of its p,.rameters, the Ma33-9 momentum- and energy-conservation
laws must be observed in the passing through this surface.
Under certain assumptions made here,these laws are indicated
in the form of formulas (1) (Ref 1). At given parameters of
the approaching f low as well as of the elec tromagne tic f ield
in front of the discontinuity surface, the formulas N
determine the flow- and field parameters behind the discontinu-
ity. It is shown that the presenc6 of a single steady surface
at given parameters of the approaching flow does not yet make
it possible to solve only an Unsteady problem with cracks of
similar kind (e. g. the problem of the motion of a flat piston).
The structure of the discontinuity surface with a conductivity
jump is investigated. The procedure is similar to that doscribed
Card 1/2 in the papers (Refs 2,3). The curve ABC shown in the figure is

On the Possible Kinds of Crack With a Conductivity SOV/179-59-4-16/40
Jump
obtained. It expresses the connection between the volume v
and the magnetic field strength H. It is shown that - if the
structure of the discontinuity surface is investigated at
6'= 6(T), the conductivity 6@being Equaltozero,, for T-values
smaller than a certain T - there is only one point on the
ABC-curve which depends on T*and the initial values of the
parameters, and from which the motion can be continued until
o-6 . This points to a certain connection between H1and H21
which is not a consequence of the conservation laws, formula (1).
This additional relationship, together with the conservation
laws in unsteady problems, determines the intensity of the
electromagnetic wave emitted, and makes the solution of such
problems a unique one. There are 1 figure and 3 Soviet
references.
SUBMITTED: February 19, 1959
Card 212

67585
2- 72 0 SUV/179-59-5-3/41
AUTHOR* Lyubimov, G.A- (Moscow)
---------------
TITLE: Investigation of' Stationary Surfaces of Discontinuity with
a Conductivity Step of a Gas in an Electromagnetic Field
PERIODICAL41zvestiya Akademii nauk SSSR, Otdelenlye tekhn.Lcheskikh
nauk, Mekhanika i mashinostroyenlye, 1959. Nr 5.
PP 9-15 (USSR) 1,
ABSTRACT- Surfaces of discontinuity in ordinary gas dynamics are
well known, including their structure and stability.
In magnetic gas dynamics surfaces of discontinuity have
been studied in an infinitely conductLng medium
(eg Syrovatskiy, S.I. "On the Stability of Shock Waves in
Magneto-HydrodynamicsVIN Zh ETF, 1958, Nr 6)@ The present
work considers stationary surfaces of discontinuity wherein,
apart from the thermodynamic quantities of flow and
velocity, the conductivity of the gas also suffers a
discontinuity. First, the @@!-Ffect of an electromagnetic
field on discontinuities is considered generally and it is
found that surfaces of discont:Lnuity may appear in
addition to those arising from ordinary gas dynamic laws.
For example ` a discontinuity combining a pressure rise and
a drop in density is possible. The specific effect of
Card 1/3 changes in conductivity is then analysed. It 15 concluded

67585
SOV/179-59-3-3/41
Investigation of Stationary Surfaces of Discontinuity with a
Conductivity Si;ji of' a Gas in an Electromagnetic Field
that not all surfaces of discontinuity which satisfy
the laws of conservation can be considered as the
limits of continuous flows with varying conductivity.
Surfaces of discontinuity with a conductivity step which
can be considered as limits of continuous flows are either
density increases with a rise in the magnetic field or
density reductions with a diminishing magnetic field,
Taking into account the viscosity and heat conductivity
of the gas, shows that stationary flows are only possibie
at certain initial values of the parameters. Thus, in
the flow of an ideal Zas containing a surface of
discontinuity with a conductivity step, an electromagnetic
wave will propagate ahead of the step which changes the
initial parameters of the field. Finally, discontinuity
surfaces with a conductivity step are considered on
whose fronts energy is released. In the ordinary I gas
dynamics-it is riot possible to achieve detonation
conditions wherein the velocity of the gas behind the
detonation wave is larger than the velocity of sound unless
Card 2/3 energy is absorbed at the detonation front. If, however, 41-,

67585
It SOV/i79-59-5-3/41
Investigation of Stationary Surfaces of D:LSCOntinuity with a
Conductivity Step of a Gas in an Electromagnetic Field
the detonation proceeds in an electromagnetic field and
the conductivity of the medium has a step at the
detonation wave front, such conditions are possible at
certain values of the initial parameters. Examples of
such detonation waves were given by the author's
earlier work ("Effect of Electromagnetic Fields on the
Conditions of Detonation", DAN SSSR, 1959, Vol 126, Nr 3),
There are 8 figures and 8 Soviet references.
SUBMITTED, March 13, 1959 Lr
Card 3/3

KULIKOVSKIV. L.G.; L-UB11,UV, G.A.
In connection with V.A.Belokonla article "Permanent qt!-,i@7ture
of abock waves with Joule dissipation." Zbur.e1:sp.i
37 no.4:1173-1174 0 159. (MIRh 13:5)
(Shock wavos) (Belokon, V.A.)

10(6), 21M
AUTHOR: Lyubimov, G. A. SOV/20-126- 2- le/6-1
TITLE: A Shock Wave With a Discortin,_t.ty of the Conductivity of @'@_,F tc,
an Electromagnetic Field (Tjdaniaya volna so ska,21al-oir,
gaza v elektromagnitrxn pole)
PERIODICAL: Doklady Akademii nauk 33SP, 19"9, Vol 1216, 11.'r 2, --)p 29- - 2c4
ABSTRACT: A gas current passing throtzgh a strcng shock -Rave '-s
such temperatures at which the L:,.3 iE li--jociated a@.d ion_-@@-
Under these conditions wid in -@hp_ D:7c3e..(:;e of bi-, e):; e_"
electromagnetic field, tl!e ggas current lue"ind t'ac
on no account be assurned to be non-conductive. Me,.@efcra, i-@-' .'ts
also of interest to ir.-vestigate a. s'iocl( wave
of gas conductivity on the fl-01.1t Df t@_iS 1.7,aVe. ThJ 'ielle
investigates a steady shock wa-,-e FL6-ain& which t r ._" @i
nonconductive gas (conductiltit:T 61 zl) flo-i,,.. S`Iuc'@ @%t_ve
the conductivity of the gas is assumed to be infinitely great
On the basis of these assumptions the relations or,- the shock .v-,v--
(law of conservation for mas3, monentum, ersergy, and for ti-e
tangential component of the electric field have the fo---m
Card 114

A Shock Wave With a Discontinuity of the Conductivity of SOV/20-126-2-18/64
Gas in an Electromagnetic Field
2 1 H2 2
H2.
P1 vj 'J@v2; PI +-'RV1 +- 8ir2 2 + P2v2 + 81W ' 21
2 V
I j- c 2 4-1 c
?-I V1 I -4f A " 92v2 (e 2)- -4Y2H2; YY - .-'cv2l'2
Here i denotes the heat content of the unit of mass of the gas,
c - the velocity of light, and the remaining denotations are
generally known. The given shock wave may also be determined as
the limiting case of a certain constant steady solution of the
equations of magnetic hydrodynamics with variable conductiv--'T,- ('.f
magnetic field strength iracreas-@s during passage through the s-,o-k
wave). If there is no electric field in. front of tte shock wav, ,
the magnetic field also does not penetrate into the doVr. beh'-,'A
the shock wave. In this case a current of the densit-i i c
4
flows on the surface of the ShOck wave. Ir ti-.(, case 'L,:I=
(where k:r fl/Y2 holds in the ordixary r,-P-s dyraziz s-hocs, Ti-,h
the same parameters of the onc-minv flowl, it follows that I !.' H29
Card 2/4 i. e. there is no discontinuity of the ma,-xietic fiela in such ;-

A Shock Wave With a Discontinuity of the Conductivity of SOV20-126-2-18/54
Gas in an Electromagnetic Field
wave, and the other quantities vary in the same mzwnar as in an
ordinary shook wave. The Hugoniot adiabatic of the slhock. wave
under investigation has the equation
P2 +PA , 1 2 2
----,-(V -V H 2-V 0
2-@-I 2 2 1 2-H I)(V -4@F"V2(111-'@-2)
where 6 denotes the internal energy of the ur-.it of mass of t'-Ie Oas
and V - the specific volume. With HI=H 2 this adiabatic gy-es over
into the ordinary Hugonio adiabatic, and with E,,=O it has the f,rm
P -P 111
V I)+ 14 V 1 4J2)'=O. Small disturbances with an
2 2-V
infinite disoanthdV of conductivity are impossible. Not only
expansion disoaiLinuitles,but al,3o compressior. discontiruizies
a slight increase of press-are are forbidden. In the case of the
permitted compression discontinuities higher degrees of compression
are possible than in ordinary shock waves. With increasing press-are
density behind these discontinuities decreases. As an example, the
author investigates the steady flow of a gas current round plane
Card 3/4 contours, which takes place wi-@h supersonic velocity in ar, external

A Shock Wave With a Discontinuity of the Conductivity of SOV20-126-2-18/64
Gas in an Electromagnetic Field
electromngnetic field. In this ca.se the conductivity of the gas
behind the frontal shock wave becomes high Pvt a very high velocity
of the oncoming current, and within this range the equations of
magnetic hydrodynamics must be applied. The problem of steadiness
is not investigated. There are 2 figures.
ASSOCIATION: Moskovskiy gosudarstvennyy universitet im. M. V. Lomonosova
(Moscow State University imeni Yj. V. Lomonosov)
PRESENTED: February 11, 1959 by L. 1. Sedoir, AcadeLdcian
SUEMITTED: February 5, 1959
Card 414

1-0 (7)
AUTHOR:
TITLE:
PERIODICA1:
Lyubimov, G. A. SOV/20-126-3-20/69
The Influence of an Electromagnetic Field on the Development
of a Detonation (Vliyaniye elektromagnitnogo polya na rezhim
detonatsii)
Doklady Akademii nauk SSSR, 19@9, Vol 126, Nr
Pp 532-533 (USSR)
ABSTRACT: When solving the problem of thE propagation of detonation
waves of gases in electromagnetic fields, the fact must be
taken into account that after the passage of the detonation
wave the gas becomes electrical,ly conductive. In the introduction
to the present paper a steady detonation wave is investigated,
and it is assumed that before the detonation wave the
conductivity of the gas is equal to zero, and behind it, it is
infinitely great. By basing on these assumptions, the conditions
prevailing in the detonation wave are described by the syntem
of equations (1), and for the adiabatic the equation (2) is
given. In the first part of the paper a steady detonation
wave without a field is first dealt with, and it is shorir
that in this case the aforementioned formula for the adiabatic
Card 1/2 goes over into that of the ordinary adiabatic. Next, the

!,he Influence of an Electromagnetic Field on the SOV/20-126-5-20/69
Development of a Detonation
process in the case of the existence of a field is investigated,
and a formula is given for the propagation rate of minor
disturbances behind the wave, from which it follows that their
propagation rate behind the wave is higher, so that a decrease
of density and pressure takes place. In the second part a
cylindrical detonation wave propagating in a medium of constant
density is investigated, and E 1 P g1l is assumed to
c
hold. The system of equati3ns (3) then describes the motion;
as is shown by an analysis of t',.is system, a decrease of
pressure and density oc-urs, rnd it is impossible in ordinary
cases to bring about this sort )f detonation without loss of
energy. There are 2 Soviet refe-ences.
LSSOCIATION: Moskovskiy gonudarstvennyy universitet im. 'Y. V. Lomonosova
(moscow state University imeni IM. V. Lomon03O-.r)
PRESENTED: February 11, 1959, by L. I. Sedov, Academician
SUBMITTED; February 5, 1059
Card 2/2

101(4) SCV/2 o- 12 05-Z - 12/ I'D 2
AUTHOR: Lyubimov, G. A.
TITLE: The Steady- FIdW_ R6iind a Comer of the Current of an !:@f ini' Ij
Conductive Gas (Stat9ionarnoye obtekaniye ugla potokom b-sko-
nechno provodyashche-o gaza)
PEiiIODICAL: Doklady Akademiii nauk 535R, 1q59, Vol 126, Nr 4,
pp 733 - 77)5 (USSR)
ABSTRACT: By means of the system of e iuations (1 the systpr. ef e -,!-at iins
of magnetic hydrodynamics in tfte caac of an irffinit,--ly Great
conductivity of the aiedium is represertud J.r; ;)olar cocrdinate_s,
and in the first part, the solutions of (1) are giver, rcr a
progressive stream and a rotational wave according to Prandti-
Mayer. For the flovi round an infinitely conductive angle there
are solutions which depend only on the coordinate p; the ex-
teinal magnetic field must be parallel to the surface of the
angle. These solutions are developed and written aown with the
system of equations (6). For determination of the fanction
@(p) the ordinary differei)tial equation (7) is inte=ated and
o
z round of a
hen 9(y) is substituted into (6@. Finally, the floy
non-conductive angle is dealt rith. For the solution of this
problem, the general system of equ-tions (1) must be calculated
Card 1/2 and with equation (8) the integral of this systern is -,tritten

The Steady Flow Round a Corner of the Current of an
Infinitely Conductive G-s
down. The results obtained 3ilow that, if an ccn-
ductive gas flows round an angle, the velocity v. i-2 e ual
0 i
to the velocity of sound, 3iriilar to what is the @ase in or@-J-
nary gas dynamicq There are 1 f igure and :' Sov i,et
ASSOCIAT ION: Moskovskiy gosudarst7enniy universitet im. M. V. Lc,.1onr's'--'va
(Moscow State iniversity ia:eni M. V. Lomonosov)
PRESENTE'D: February 21, 1959, by L. 1. @iednv, Academician
SUBYITTED: December 3, 1958
Card 2/2

6 64 6 7
(A)
2 7 )
-k',TT!I0-,iS - K-alikovskiy, k L,':i'c -.mo v A
T :T L Z' '.1a @-nc- nm.,, ic ,as - ion @ zi.,,.g Shc ok 'Kav(-S

P ER -1 0: 1 CA L . Doklad.' A@ademif !@ajk S.SSR. Vc 1 12@,
-2 5@ (-Ssia)
A E, Sr RA C' An elec.romagnetic wavp -.,ay move in frorit a
-, n unsteady @rob le@i.s , In which shocle. waves
@)resen'. ,r. an electromagnetic field For knorr. ve--oci%-, C,'

shcok wave, *@-e b=d--.ry cordit-cns
,a s p r: i
Tiav,, expr es s ng t nt n.; @ ty of the
e r C i a s w e 1 a s t- e X e 3 0 f T. a
a n rl energy are not su f f ic ient to dft emino s - a!@
Intens i @ ies of the shock wave and of the em-, , ed Ple
im a ve A n a d d i t 4. o -, a 1. r e 1 a t i -- n b e t w e e r. qu a nt Pg e f i-I r a
',ii nd ".lie
9, -ck .-iave 4s furnished y
str-ct-;re --f' '!-,e waves of the ab.,)vp @y.
and, ir. cons e-i.;ence , alteration of a] 1 '-.'Ian@
sh--ck wava ess@-nti-Rl:y on t'-.e au-.@-,;nt -,f
retween the --'is3--pat,.cn coefficient!, @viscosi-y,
Card 4 d@;ctivlty, and ma,gnetic viscosity@, in the trsr@-
I

C, V
A-(@dy nam-.(- 'as -.n @ z -E a ves
r. cond--- v e .@a s s @, 3 i
e n ep-ps @nt @a@:er:
incticn t!m -1 e -a t -, r
'Ir h @-: s t r
@* a@-:d !> 0 fjr T > V*
@@-.at c=0 if T@.
,
slr.@--:@..@ wa-ie. n'r J -@i mc,ips r. a a a' a
p a r s
a-9 -,s ar- r e -i p h 2
a a :_3 s s a:@d @cjlar vis.
-Dnd v- r
are ass,;m@-Jl
e - - r a., 4 e
-a r. -.a ra 1 to. p a n@,
r vl@ r, -zat F t.-le r Jy

n a s e s a n s- @ r @ I e x -, la
ly
x e f -a -m 1 n r a I
r: a
v
s a 1: 0 ar,
m
T, 5- -,@@k -Nav- ::@ay be represented by t n s
n t o a z r T.,
:)ass @@v,@r Iozrpssl ve f" -
'-ese sc@ it :@@ns a!" derivations conver@e tcwarus as x a-
4 1-:,i t ;i W'I I @l MOVOS 1*0111 X=
T(

f a v - S 7 v
n r al' rve a nd e -,n- T: T'k T
@c t icn ie- enois -_,@l h@, 2harac ter -.,s t L-s
w I a o - r, e r
.I- *-ans it- -n ZD!,- e r el a t @@,n H H E
' 4 'L t 0
ar, ad- -. ,ra' ',o@ndary cr@ndi- o n R s Ll Ds t
snock viav-@, a 3teady I'lcw . If ont@ f t@ie @is@3
c en t s , s c o, d e r a b r :?a 'er tnan o e 1* s :3 a
ncla ry @-n @nay e a 4 r e n
t v e S - a jle!',@r4ed
n e S 1 '1 1 r, n 3 T' ar P r F7-
n a vil r', v F. t
AS@ S 1 A :,,a t P:-,,i c @i y A va A K
Ma h e:-a i - a s 7 n V . A E 1 :-. v

r J as -
T 1@ T., A t: a d
C a r d

/0. @2ooo(A) 66448
M-r-A (T-tri+ A 122 0 )
AUTHORS: Kulikovskiy, A. G., hyubimov SOV120-1 29-3-14/70
TITUs The Simplest Problems Concerning a Gas-ionizing Shock Wave in
an Electromagnetic Field
PERIODICAL: Doklady Akademii nauk SSSR, 1959, Vol 129, Nr 3, PP 525-528 (UM)
ABSTRACT: If the conductivity of the gas before the shock wave vanishes
and is finite behind the shock wave, the theorems of
conservation read: @jvj P1 + V2 + (1/81r)H2
@2vV
2
2 2
v + (1/8TE)H , ?1vi(v1- + i + (c/41T)E1E1
= P2 + 92 2 2 2 1
2
- 92v2 (v2 +12) + (c/4w)E 2H 2, E, - E LH . The electric
2 2 C 2
and the magnetic field strength are, for the purpose of
simplifying matters, assumed to be parallel to the wave
front and perpendicular to each other. The shock waves
ionizing a gas may be considered to be the limit of a
certain continuous motion of a viscous heat-conducting gas,
Card 1/3 the conductivity 6 of which is considered to be a known

66448
The Simplest Problems Concerning a Cas-ionizing SOV/20-129-3-14/70
Shook Wave in an Electromagnetic Field
function of the temperature T (T ---- 'r*, U > 0 at T > T*). This
as well as other facts mentioned here indicate the following:
The solution of problems concernLng ionizing shock waves will
differ from the solutions of the corresponding problems in
gasdyna.mics and magnetognsdynamics. This difference exists not
only in the electromagnetic wave, but also in the variation
of the gas-dynamical parameters of the motion. In gas-
ionizing s@.ock waves compression is not higher than in gas-
dynamic o"h.,>ck waves and not less than in magnetogasdynamic
shock waves which have the same parameters of the incoming
flow and the same magnetic fiele. strength before the
discontinuity. Also the other quantities behind the gas-
ionizing shock wave attain val'.@()s which are between the
oc=eepculing values behind the gas-dynamic shock wave and a
magnetogaadynamic shcck wave. !,.i the first part of the
present paper the prcblem of tha motion of a plane piston is
dealt with. In this case the presence of an electromagnetic
field increases the velocity of the shock wave and reduces the
compression in it compared to the gasdynamic solution at the
Card 2/3 same piston velocity, The second part deals with the flow

66448
The Simplest Problems Concerning a Gas-ionizing SOV/20-129-3-14/70
Shock Wave in an Electromagnetic Field
PRESENTED:
SUBMITTED.
round a wedge. The velocity component which is tangential with
respect to the shock wave remains oonseTvad dia-ing passege through tJie
shock wave, and the variations of normal velocity and of the
other quantities mav be dealt NAth in the same manner as in the
first part. A surface charge must exist on the shock wave.
There are 2 figures and 3 Soviet references.
July 14, 1959, by L. 1. Sedov, Academician
July 7, 1959
Card 3/3

KTILIKOVSKIY, ancl. IVUBD4C)V,
)n. Gas-lonizirir -r
I .- . - - --@Cl: .
report pre5ented a' the Tnt.1 '--inposiur. on 7- '- "- , -
- )
Comont@ - P :)4 Feb

LYUBIMOV, G.A.; LTU CHOI-SIMf [Liu Chlazt-- sh6n]
Testing the elastic mterials of a turbodrill shoe under static
and dynamic load conditions. Izv. v7t. uchea. zav.; neft' i
gaz 3 no.11:25-32 160. (MIRA 14: 1)
1. Moakovski7 instJtut neftkhimicheekoy i gazovoy procWslalennoati
imeai akademika I.M. Gubkina i Vaesoyuznyy nauchno-isaledovateliskiy
institut burovo7 tekhniki.
(Turbodrills-Testing,'l

89394
ZbOO S/040/61/025/001/013/022
2,1,_2'@ 11 B125/B204
AUTHORSi Kulikovskiy, A. G.,'Lyubimov, G. A. (moscow)
TITLEt The structure of an inclined riagnetohydrodynamic shock wave
PERIODICALi Prikladnaya matematika i mekhanika, v. 25, no. 1, 1961,
125-131
TEXT: The present paper investigates the flow within the zone of the shock
wave when the dissipation of energy in the wave is caused by magnetic
viscosity and by the second kinematic vis(,osity. In the problem of the
structure of a magnetohydrodynamic shock wave, the solutions of the
equations of the magnetohydrodynamics of a non-perfect gas are to be
determined, whose values with x - + co) satisfy the known laws of conserva-
tion. If only the magnetic viscosfty and. the second viscosity are non-
vanishing, the equationsof the steady onodimensional flows of-A--Perfect
gas read dH I
HJ - J,
Vn uH - vll,, cE, Lu =, p + PO
il d,
PUV H,,H J,, PU =M' H@ = const MI
Card 1/7 PU 7 P + + V1)] CL'H = U
I I -f - i _P2 - 4,;x

89394
S/040/61/025/001/013/022
The structure of an inclined... B125/B204
They refer to a system of coordinates, in Which the flow is plane.
Hn , H, u, v are the components of the magnetic field and of the velocity
along the x- and y-axis, E - the z-component of the-electric field,
c - velocity of light; Jili 2 - the fluxes of the x- and y-components of
the momentum, U the energy flux, M tho mass flux. With the dimension-
2 (2) one obtains
less variables u u 1, V - U q, P U f4nQ Jh
0 0 0 0 0 0
Vm A = _'I@_ dv - h2
h (-c 10) e, 0+,r + ' - P
U. jz- Poll, TX 7
(3).
q - h@h 0, kOv + I T' + -!h,,'h* + eh = e
2 1
H, CE
k= h.= C=-: , P U
V'4-11pee V4.-cp,uo' P.U.' POU02).
2), 1 + e .1 2, 2 2)
Furthermore, e - h (1-h + T ho k9 + + h (1 h
0 n 0 0 2 0 2 n
holds. Besides, everywhere e> 0 is assumed. For reasons of simplicity,
here r< 2 is assumed. The real points cf the isoclinal line dT/dx - 0
Card 2/7

89394
S//040/61/025/001/013/022
The structure of an inclined ... B125/B204
are on both sides of the hyDerbola h a ePki - h 2 The maxima and minima
n
of the isoclinal line are on this hyperbola on such points i,-where the
discriminant of h 2 (kr-h2 2eh + (2k-l)T 2 _ 2kPT + 2& 0 (6) is equa! to
n 2
zero. The isoclinal line dT/dx - 0 has the asymptote -t hn/k. With in-
creasing a the roots of D(T) - 2a(P-1)[(1-kh')+k(h 2+k-2 )-c) -(k-c-h2) [(2k-1)-r2
n n n
-2kP,r + 2k(P-1)+11 change monotonically. In the plane of the variables
1 2 2
P - 1 - i ho + eo and hn, there is a curve which separates the domain of
existence of the three roots of the discrijoinant from that of a single
root with 190 . 0 (a - 1) (see Fig.1, curve ABCD). The curve ECF
illustrating the equation T - T* touches the curve ABCD at the point C.
To the left of ABCF, the discriminant has three roots with small a, and
with large a it has one root. For the remaining points of the variable
P-1,h 2, the discriminant, with small and large a, has three roots, but
n
with intermediary values of a, it has one single root. Case a): In the
Card 3/7

89394
S/040/61/025/001/013/022
The structure of an inclined... B12.5/B204
case of points lying simultaneously below the straight line -r h2/k and
2 2 2
hn /k - 1, two roots of the discriminant are greater than hn /k, and one is
smaller than h 2/k. Case b)t In all other cases with three roots, one rootp
n 2
is greater than h n/k, and the two others are smaller. These properties
permit the construction of the isoclinal line. For points above the
2
straight line -r - h n, the velocity is greater than Alfv6n velocity
a a 11 4nQo, and for points below this straight line it is smaller than
A n/ f
AlfvAn velocity. To the states before and behind the shook wave there
correspond the points of intersection of the isoclinal lines (6) and (8).
To the solution of the problem of the structure of the shock wave, there
corresponds the integral curve of the Eq. (9)
2 2 2
d-c h (k-r-hn 2eh + (2k-l)T 2kPT +
'@h 2k-r [h(,r - h2 ej which connects the singular
n
Card 4/7

89394
S/04 61/025/001/013/022
The structure of an inclined... B125%204
points lying in the region r> 0. With continually decreasing velocity, the
following singular points are possible3 1) Nodes, 2) saddle, 3) saddle,
4) nodes, into which the integral curves lead. If the curves (6)
h2 (k-r.-h2)-.2eh+(2k-l)T2_2kPr+2F - 0 have the shape indicated in Figs.2 and 4,
n,
then all singular points lie on the same branch of the curve (6). In -
Figs. 5 and 7/-/Q,VM is either small or large, respectively. In Fig.6, the
single value of/a/Q,%.)Mp at which the integral curve emerging from point 2
runs into point 3, corresponds to the value of (U/Qo')@M)e .The fast and
the slow waves thus have a structure with"an arbitrary ratio of dissipative
coefficients. In four singular points tae structure may also have inter-
mediary shock waves. The transition 2---jP3 is possible only in the case of
' J,- "' ), the transitions 1--+3 and 2--@,4 exist and are unique with
Q01 4L o' M/"'
I - -- '_>
90'M _V_) , and the transition 1-04 is possible with ')W I Q
o M Q, M 0 M/_
Card 5/7

89394
S/040/611/025/001/013/022
The structure of an inclined... B125/B204
and may also occur on an infinite number Df integral curves. The structure
of the "evolution" shook wrveB (in the sense of A. I. Akhiyezer et al.)
differs from the structure of the non-evolution shock waves by the fact
that only they have a structure at any ratio between the dissipative
coefficients. A. N. Voynov is mentioned. There are 7 figures and
4 references: 2 Soviet-bloc and 3 non-Soviet-bloo.
SUBMITTED: juiy 16, 196o
ly
Fig. 1
Card 6/7

The structure of an inclined...
Onr, 5
S/04 61/025/001/013/022
B125%204
Fig- 5
Fig. 6
ftr. 6
Fig. 7
Card 7/7 ftr, 7

/0 (2,C)OO
.;Z6 /q/ 0 S/040/61/025/002/01)1/OP2
!@ @ q loq 0, D201/D302
ALI TIf OR -I,yubivmov, G.A. (Moscow)
TITLE: Thc structure of ma-neto fluid dyna;Ac rlioc!c --,,veri
0
in a gas with anisotropic conductivity
PERIODICAL: Prikladnaya matematika i mekhanika, v. 25, no. 2,
1961, 179 - 186
TEXT: For a gas with anisotropic conductivity flowinj- in a m-1-ne-
tic fiold vihich runt be wide enour-Ii to Rllow for @,. oili *[,.I. movel,lent
oi, @@I-ctro)'-,) the fol)owilir wil-1. 1IDDI.,;':
where w - 1,armor,a frequency; T - time betwcen collinions of cllic-
trons and ions. if Eq. (1) is to hold true for the ionization of
ga8l Ohm's law must be satisfied according to T. Kautling-(Ilcf- I.:
MaCnitnaya gidrodinamika, Izd. inostr. lit., 1959).
Card 1/9

'@^492
S/040/61/025/002/001/022
'Nio atructi4re of magneto ... D201/D302
cr(!"' + L V - 11 + -L grad 1) j + @2T i C?
c ne e H
,.,illcre cy' - conductivity in the absence of magnetic field; p
,rcuu of (-,lectrons; n - number of olectrons in unit volune; c
-c. Ience ono cv.n assume hydrodynumic cor(litloi C,
Obcctronn char
,.!it, ill t' iu, -ag. To 1,11c otrncturc of dh
0
L@xcul:xu t1l'A it occuPies a narrow vmnc in the curi-ent ficj.,'. Tn
thiG ZCIILC, the paraj,,eters of the current chan;u olo,-!ly. f".! tlv;
wave dics away the current becomes steady. It is aszjuned that in
tho core of the vave, only dissipation energy of electric current
is of any importance. The x-axia is taken at right angleskto the
normal of a wave I a eurf ace and the y and z lie in the wave I a -)1, ne
Then for the core of the wave (Maxwell'B equations being sat.1s-
fied@ the dimensionless condition I
U = U U'x V = U V* Vi u W* RT = eu 2 U*p = ?Ouo 2e (5)
r 0 0
0 0 qr
V8-x-?:@. 2h, (i = x, y, z)
Card 2/9

S/040/61/025/002/001/022
The structure of magneto De"Ol/D302
holds, where 8 - temperature, @,i - tlftc cimensionless, component of
the vector of magnetic field u*, v*, w* - dimensionless
comporients of velocity LAbstractor's r1().'.e: Other symbols not de-
fined]. Before the shock-wave
wo = 11 Z6 1j5- 1) (6)
holds. (Abstractor's note: J Jl; j,@T J 30 not defined]. Simplify-
ing and eliminating gives
(T + 1) U- (10)
2 1)
where asterisks denote dimension!@-sj
U and H are known to be parallei '1,jef_)rc
t10) determines the structure of the
gives the curve for the struc-ture of
Card 3/9
coordinates, and the vectors
and after the wave. Eq.
slock wave. If hz = 0, (10)
a magneto-hydrodynamic shock-
X

f3/040/61/025/002/uOl/022
The structure of maCneto ... :D201/D302
wave in an isotropic gas. If only t-re di!3Sipation coefficient a'
is given then
2 1) f,'h.h, - 0
The surface expressed by Eq. (10) _J3 found along the perpendicuiar
axis u* whose center lie on the hypertola
h 2 (12)
Y yu* 2(y 1) 1
In the case x oo,
(u* - 2h x2)(a*h X hY+ h Z) - allh x212 0 (13)
(u* - 2h 2 Cc Ni - h 12 0 (14)
Card 4/9 /1

ZO 28422
S 4016110251002ZOO11022
The structure of magneto D201/D302
From the above statements one may determine that in the v:Lcinity
of U*q h y, hz, corresponding to conditions before and after the
J'
wave, must lie intersections of the surface expressed in (10) and
hyperbolic cylinders Eq. 4,13) and Eq, (14). Also Eqs. (13) and (14)
lie on the hyperbola l(u* - 2hx2) hy -h X'j2* = 0 (15)
which lies in the plane h = 0. Therefore it is seen that a point
after and before the wave ziies in the plane ft. = 0 and occurs at
the points of intersection of the curves (111) and (15). The inter-
sections of curves (11) and (15) depend on parameters before and
after the shockwave. Investigating local properties of intersec-
tion points of the curves (11) and (15) one assumes that u* = 1,
hy = h yo , hz= 0. This may be obtained by scaling down coordinates
of the axis. Individual points of inter-section may be distinguished
by considering the discriminant D,
Card V9

2 .'% 9 2
13/040/61/025/002/001/022
The structu.re of magneto ... D201/D302
D + (i + [2!IaL - (I - 2hxs)x
rOo Too
(23)
VO + I'sh,'2
x (I + OC.2hx') 1, a (1 2/1,2) h" 2h,, I - 2h
T__r 6_._)1 It -too hyo
If D > 0, then the point is a node if
2h vo 1 - 2h x2
h (21)
0 yo
is satisfied, and a saddle-point if
2h vo 1 - 2h x2
T_ ye 0 hyo (20)
If D