JPRS ID: 8540 TRANSLATIONS ON USSR SCIENCES AND TECHNOLOGY PHYSICAL SCIENCES AND TECHNOLOGY PHYSICS OF COMBUSTION AND EXPLOSION

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WCOMBUSTION PHYSICS AND EXPLOSION
25 JUNE 1979 (FOUQ 35!79) i OF i
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JPRS L/8540
25 June 1979
TRANSLATIONS ON USSR SCIENCE AND TECHNOLOGY
PHYSICAL SCIENCES AND TECHNOLOGY
(FOUO 35/79)
PHYSICS OF COMBUSTION AND EXPLOSION
U. S. JOINT PUBLICATIONS RESEARCH SERVICE
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JPRS L/8540
25 7une 1979
- TRANSLATIONS ON USSR SCIENCE AND TECWNOLOGY
PHYSiCAL SCiENCES ANn TECHNOLOGY
(FOUO 35/79)
PHYStCS OF COMBJSTinN AND EXPLOSION
Moscow FZZIKA GORENIYA Z VZRYVA in Russian Vol 15, No. 1.,
Jan-Feb 7' pp 84-102, 119-125
[5eleated articl.es �rom journal edi.ted by L.S. Kravchenko,
Izdatel.'stvo "Nauka", 1625 copies, 128 pages]
.di
CONTENTS
PHYSICS
PAGE
The Flvw FYeld and Gaina in the Resonator Cavity of a Gas
Dynami.c Laser Using I{erosene Combustion Products.
A Two-Dimensional Cfzlculation and Experimental �
Compariaon
(M. G. Y:talkherrnan, et al.) 1
A Numerical. Ana.tysis of the Vibrational. Mode of a CW
Chemical HF Lctiser
(A. V. Lavrov, et al.) 9
An Experimental Study of the T~afluence of the Mixing
Conditions in a Le.val Nozzle on the Gain in a
Supersoni.c Flow
(B. G. Yefimov, L. A. Zaklyaz'minskiy) 20
An Experimental Study of the Diesociation of Iodine and
Bromine Molecuips in Mi.-turea of I2-He a.nd Br2-He at
High Temperatures
(N. A. Generalov, et al.) 28
The Vibrational Band Temperature of Carbon Dioxide Gas
in a CC2 + N2 + H2 Gas Dynamic Is,ser
(N. N. Kudryavtsev, et al.) 33
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PHYSTCS
'CHE FLOW FIELU ANU GAINS IN THE RESONATOR CAVITY OF A GAS DYNr1MIC 1LASER
USING KE-ROSENE COMBUSTION COMBU5TION PRODUCTS. A TWO-D2MENSIONAL CALCULATION
ANb EXPEI2IMENTAL COMF'ARTSON
Novosibirsk FIZIKA GOItENIYA I V2ItYVA in Russian Vol 15 No 1, Jan-Feb 79
' pp 84-89
(ArCicle by M.G. KCAlkherman, V.A. Levin, V.M. Malkov and Yu.V. Tunik,
Moscow, Novosibirsk, manuscript received 28 Mar 78)
[Text] A purely experimental aenrch for the optimum opernCionnl condirions
of a GDL [gas dynamic laser] and the shape oF iCs nozzle is roo labor intensive,
and for this reason, numerical modeling of the phyeical proceases in high
power laser systems acquires considerable significance in Cheir deaign.
~ The solution of problems of the outflow of ttie relaxing mixture of gases from
a GDL nozzle is usually managed uaing one-dimeneional approximations [1J,
which most often are in qualitative agreement with experimental findinga..
The actual picture of the flow in a resonator cavity is characterized by the
presence of viscous trails and shock waves, which exert a conaiderable influ-
ence on the amplifying properties of the medium [2]. Under these conditiona,
the use af one-dimens'Lonal calculations yields a roo approxitnaCe picture of
the flow, since the parameters transverse to the flow can vary significantly.
Both experimenCs and calculations indicate this.
A two-dimensional calculation procedure was employed in [3] for the flow of
a relaxing mixture, which permits distinguishing the shock waves in Che nozzle.
For a correct comparison of this procedure with experimenCa, datu are needed
on the flow structure, since in nozzles with a point of inflection and large
initial aperture angles, which are usually employed in GDL's, the flow can be
far from one-dimensional and the appearance of shocks is possible. Such
information is usually lacking in papers dealing with the meaeurements of
ga:tr. We will also note that the divergence of the numerical results from
experimental ones can be due to the indeCerminancy in the constants for re-
laxation processes [4].
A comparison of two-dimensional cnlculations of the flow fields and the gains
in a constant cross-section channel adjacent to a nozzle is presented in this
1
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paper. The sCructuxe oE the flow in the chunnel wns charnctexized by riie
presettce of ehock waves. The agreement beeween the matihemnticQ1 model und
the aceual processes under ehese cnndirions is sub1eceed ro nserious check.
At the present tima, Cbl.'s usin}; thci combuHClot1 producly nf 11.nuid hydrn-
cArhonfuels nre exrxemely promising [5 - 11, becuuqe oE r.he accessibil.iey of
the tuel nncl the relttrive simpliciey in obCainittg ].Arge mass rntes of flow
oE the acCive lasing medin wiG{i nccepCable nmpliPicntion properties. The
amplification properCie3 oC kersene combusrion products, flowing our Erom n
radius nozzle, nnd the main aerodynamic chnrncrerisCics of the f1ow in the
channel nd;jncent Co it were compuCed nnd measured in Chig work.
Radius nozzleg - nozzles with nn inflection poine - where the supersonic poreion
of the nor.zles is profiled ns the arc of a circle, are oE interest because oE
Cheir technologicnl qualiCies.
The busic geomeCric parnmeCers of
the nozzle are: the criCicul cross-
secCion heighC h* = 0.7 mm, the
output cross-secCion, 11 = 20 mm.
There is a small band 0.2 mm wtde
in the criticnl region, which Uy
means of rounding off to a radius
Higurc 1. A shadow photograph of the
oF 0.5 mm was mated to the wedge-
shaped subsonic section (Che hfi1C-
flow in the channel.
angle of the wedge is 60 The
ra-_'ius of the supersonic section
profile was equal to 37.5 mm. The initial
half-angle of the nozzle aperture
wis dH = 42�. The nozzle was smoothly mated to the constanC cross-section
channel with a heighC of 20 mtn. The width
of the channel in the souriding
direction wns 180 mm.
A derniled descriprion of the setup and procedure for the measuremenCs were
given in [6]. A slight clifference in the measuremenC circuiC, related to
the specific f.eatures of the given experiments, consisted in the fact ChaC
the beam of the sounding laser was collimated, and a diuphragm stop 1.5--2 mm
in diameter was placed ahead of the input window. Any poinC in the chaunel
could be probed. The trials were conducted aC a braking temperarure of To _
_?,000--1,600� K and a pressure in the precombustion chnmber of po Itf] _
= 20 atm.
A special working section, consisring of a similar nozzle wirh a 110 mm long
channel was fabricated for the aerodynamic measurements (in cold air). The
widCh of the working section was 80 mm, and the side wal'!.s were made of opti-
cul glass. The visualization of the flow was realized using a direct shadow
method. During the measurement of the staric pressures, the glass in the
siue walls was replaced by drain inserts. There were also drain holes in the
shaped portion of the nozzle and in the center of the upper wall of the
channel.
2
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A pI1oL�obrnph of the Elow picturc obtnined in trials wiCh cold air is shown
in rigure 1. The strucCure of the flow can be cleurly seen. Tlie shocks
inCergecL ae a disCance of u 56 mm frnm the criCicn1 cross-secCion (tlte
numbers along the boCtom of the channel give an idea of the scale). The
canFiguraeion oP the shock waves found by cnlcu7.aCion is ahown in Figure 2.
As can be seen, the agreemenr ia practically eoCn1.
'Phe distrLburion of the static presaure p/pg at the side wa11 (y = 0) and
the shaped wa11 nf the working section is stiown in rigure 3, where x is
Che di.sCance from CEie criCical section. The observed pressure peak ar the
shaped wa11 corresponds Co the poinC of shock departure. Thereafter, the
pressure Pn11s ofP, and at a distance of 75--80 nun approaches a vnlue oC
p/pf - 1.5 � 10'3, which was fovnd from one-dimensional calculations. The
pressure nC the side wall reaches a minimum in the output cross-secCion of
the noxzle (pmin/pg = 1.5 - 10'3). The pressure increase at the side wall
on Che downsCream side is due to shock waves, where pmax/Pmin � 3� A
doubling of the pressure in the precombusCion chamber (from 21 to 41 atm)
does not change the disrribuCion of p/pf, something which indicaCes the
insignificanC influence of viscous effects under the conditions of the ex-
perimenC (rhe Reynolds number, computed From the rarameters of the tlow in
the critical cross-section and its height was Reh* 2 3.8 � 105 nt pg a 30 atm).
Figure 2. The configuraCion of the shock waves in the channel
(calculated).
Pressure profiles were obtained in several channel cross-sections using
probes. The distribution of p'0/pf over the height of the channel is shown
in Figure 3(p6 is the pressure behind a forward shock). The point of shock
passage and the perturbation it induces, by the amount p6/pf, can be clearly
seen. The statLc pressure profiles were measured at Chese same cross-sections
and several of them are given below. Local Mach numbers were determined from
the quantity p/p6� In the central portion of the flow at the outlet from the
nozzle, M= 4.6, and at the section x= 100 mm, M= 4.1. The static pressure
at these secrions differs by almost a facCOr of two. We will note that the
on=-dimensional calculation yields M= 5.1 (for an adiabatic exponent of
K = 1.4).
The previously developed orocedure of [3), the use of which makes it possible
to single out the shock waves arising in the flow, and which brings the
3
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~
maehematical model close to acCunl flows, was employed in the ewo-dimenaional
cal.culations of the flnw of a relaxing gas in a nozzle. The relaxation equa-
Cions were solved simultaneously wi.Ch the equations of motion, conCinuity
and energy. The solueion was based on a difgerence scheme using the rhrough
count procedure for supersonic flows. The details of the numerical culcula-
eions can be Eound in [3, 81.
Pf
15 ~
10
5
0
(a)
(J,MM
10
Po/Pq)'103
1o 70 6 (b)
20
30
y
: $C
� 70 90
�
;.'x-MM
�
0

I ~ 0
4., �
~
. ~
\
~
\
0 20
n,� I
o,� ?
0
~


`~~-----Q-
~
QO BO 8.0 ac~NM
Figure 3. The pressure distribution at the walls (a) and the
quantities p0/pf over the height of the channel (b)
(the dark doCs are for pf = 21 atm, and the light
ones are for pf � 41 atm).
Key: 1. Profiled wall;
2. Side wall.
The resulCs of recent work on the determination of relaxarion transition
constants, a review of which was pulbished in [9], were employed to describe
the oscillaCory exchange processes. The constants employed in the work are
given in Table 1. The composiCion of the kerosene combusCion products in air
are presented in Table 2.
4
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Table 1
Process n'voaecc
M
M Kjf, .rwIc
atmo ec
C02(v1-}-v2)+M; C02-}-M
COa
lgt - 17,42Xx-7,85
,
Ne
16,65 X x-8,06
(YT)
0,
16,55Xx-8,06
H,0
t=3 - l0'0
N02+M=Nl-}-A1
C0s
Ig t= 104x x-11,2
N,
99,6X x-10,76
(VT)
H'
96,SXx-10,76
O
36,8X z-9,812
CO%(v3)-}-Dt4--CO:(v1-(-v2)-}-bt
C02
tno=-9,456-}-218,23Xx-
Q=8 -106
-1687,7X xi-}-3909,3X x3
(V7)
Na
i -15,457-}-424,03Xz-3852,7X
X zl-~1n672,2X x3
Oa
-15,457-{-424,03X z-
--3852,7 X xt-}-10672, 2 X x3
H,0
iqQ-4,62+I1,2kx
C02(v$.1--M;=C02-{-MV
( N'
I 1gQ=7,42-(,65-(0"'�T-}-5,T.10"7 -r
Note: xa.T-1/3
The following oscillatory energy exchange processes were taken inCo account:
COz (vi+vz) -{-M:;-tCOz-;-Ai,
NZ-{-M:;t IVs -f- M,
COs (v3) -{-N1:;7--C02 (vi-I-vs) -f-M,
COz (v3) -{-MwCOz-}-M�.
In accordance with the procedure proposed in [1C], nonequilibrium oscillatory
Cemperatures were introduced to describe the kinetic processes: T1 a T2 are
the gymmetric and deformational modes of C02, T3 is the antisymmetric mode
of C02, and T4 is for nitrogen. The enuations for the ei =[exp (Ai/Ti) -11'1
have the form: d = Xs (es - ez) T
~t = - ~Dsa ~ ~2~ai~
5
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di (e,,-- e�) P ,
ej= ei (2e,-{- 1), a., = (1 2e2)'I (1 6e, 6e".) .
Hexe, p is the pressure, T is the remperature, ep is the value of ei at
Ti = T, ~l is the molar concenrrntion of C02, ~2 ia �or N2, ~g is for 02
and &4 is for H20;
~ (Du=pQuWu;
(et 1)3 - exp [(34! - 6l117'1 (el 1) ei (t, 2,3)
~ej
ej (ei l) exp [(0j - 61)IT1-- ei (et 1) ~~,1 = l~~)
6ij are the probab3liCies of the exchange (V - V)-processes; the relaxation
4
times Ti are computed from the relationghips Til =jE1EjT~~; Ai are the charac-
�
terisCic remperatures of Che corzesponding oscillaCion modes.
The Eollowing chlracteristic sections were selected for detailed calculations
and measurements: 37, 56 and 104 mm. Tn the first, the parameters of Che flow
in the central portion are close to the parameCers ar the outlet from the noz-
zle, the.second is located in the intersection region of Che shocks, while the
third is iocated in the region where the shocks are reflected from the channel
walls (see Figure 1).
Table 2
The comparison results are shown in Figure 4,
where the distribuC3on of the gain k over
ll
i
ven, as we
the height of the channel is g
r.. r,
c:o, I
li,o i
v, ( o,
as the staeic pressure p/p f, Che flow temp-
erature T and the quanCities T 2, T 3 and
1000
cta
O
0,015
0,765
0,I5
T4 at Tp = 1,400� K and pf = 20 atm. The
1200
,
0,05
0,055
0,76.5
0,13
good qualiCative and altogether satisfacCory
I-400
0,0625
o,Ut;;S
0,76
0,11
quantitaCive agreement of the calculated
1~~00
0,075
0,08
0,755
0,09
and measured values can be cited. When
passing Chrough a shock, the quantities k,
p, T and T2 change sharply. The observed
decreas
e in the gain is due to
the increzse in the static pressure and the
flow temperaCure, which lead to
an intensification of the relaxation processes,
and in
the final analysis, Co a
n increase in the population of the lower lasing
level.
A reduction in k in C
his case is extremely important. Thus, on the
channel
axis (y = 0), according
to the measurements, the gain at the 104 mm
section
is 2.5 times less Chan
at the 37 mm section.
The influence of shock waves on the amplifying properties of the medium dif-
fers throughout the entire range of change in the parameters. Figure 5
6
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o (.a~
Fox orFzcinr, usE ortt,Y
.iop
To,K
1000
800
600
400
200
k. M- � .
0,4
0,2
0
1000 400 1800 T, K
Figure 5. A comparison of the experi-
menCal and calculated gains
as a function of tempera-
ture (1-4 are calculated,
5-8 are experimental).
Key: 1,5. x= 37 mm, y= 0;
2,6. x= 56 mm, y= 4 mm;
3,7. x= 56 mm, y= 7 mm;
4,8. x= 104 mm, y= 0.
.
6 (b)
7,5 r�, K
k'M_iI q,�io=
1000
Td
0
4
9,4
,
T3 .
QDO
3
0
D,3
Ap
,
0,2 600
L
0,2
k ~
D,l 400
T2---
0;!

.
200
0
0 015 1,0 yIN 0 0, 5 1,0 y/N
Figure 4. Profiles of the temperatures, pressure and gains.
a) x= 56 mm, Tp = 1,400� K;
b) x= 104 mm, Tp a 1,400� K;
1. k;
2. p/p f.
~
� t
~
1
2
�5
�
3
6
7
q
e8
T, K
400
300
200
100
t
2
k
~r----

T
?
~

i
T
T2
T
k
k,M"~ i
r
0,4
O"r
02
,
0,/
p 0,5 ,o y/H
Figure 6. Temperature profiles
and gains at the sec-
tion x = 37 mm.
Key: 1. Tp = 1,400� k;
2, To = 1,000� K.
7
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illustrates eh3.s, where the Eunction lc(TO) is p1otCed at several poinCs in
the selecred crnes-secrion. Tr can be seen rhar with an increase in TO, the
influence oE shock waves increases, but it is insignificant (for the given
nozzle) up to To = 1,150� K. This is related ro the fucC that an increaseo
in the Forward temperature and 'r2 followinb a shock up to a value of x 300 K
does not lead Co a marked rise in the populaCion of the lower lasitrg 1eve1.
The graph in Figure 6 3s chttracrerisCic in this sense. Tn boCh cases, the
change in the Cemperarure in A SIIQCIC iS idenC3.ca1, but for To = 1,000� K,
the forward Cemperature following a shock is low and the change in the gain
is insignif3.cant. For nozzles with alarge ratio of (H/h*), the value of Tp,
up to which shock waves have a slight influence on the size of k, wi11
apparanCly increase (for the close pressures in the resonator).
In conclusion, the authors would like Co thank N.A. Ruban and Ya.I.
Kharitonova for assisCing in the conducC of the experimene and the process-
ing of the resulCs.
BIBLiOGRAPHY
1. S.A. Losev, "Gazodinamicheskiye lazery" ["Gas Dynamic Lasers"], Moscow,
Nauka, 1977.
2. R.I. Soloukhin, N.A. Fomin, DOKL. AN SSSR [REPORTS OF THE USSR ACADEMY
OF SCTENCES], 1976, 228, 3, 596.
3. V.A. Levin, Yu.V. Tunik, TZV. AN SSSR. MZhG [PROCEEDINGS OF TIIE USSR
ACADErtY OP SCIENCE5, MZhG (expansion unknown)], 1976, l, 118.
4. J.D. Anderson, AIAA Paper, No 74-176.
5. J.D. Anderson, ACTA ASTRONAUTICA, 1975, 2, 911.
6. M.G. K-1-alkherman, V.N. Maltkov, et al., KVANTOVAYA ELEKTRONIKA [QUANTUM
ELECTRONICS], 1977, 4, 173.
7. M.G. KCalkherman, V.M. Maltkuv, et al., FGV [COMBUSTION AND EXPLOSION
PHYSTCS], 1977, 13, 6, 939.
8. V.A. Levin, Yu.V. Tunik, OTCHET INS^tITUTA MEKHATIIKI MGU [REPORT THE
MECHANICS TPTSTITUTE OF MOSCOW STATE UNTVERSITY], No 1928, 1977.
9. S.A. Losev, FGV, 1976, 12, 3.
Ia. A.S. Biryukov, B.F. Gordiyets, L.A. Shelepin, ZhETF [JOURNAL OF EXPERIMENTAL
AND THEORETTCAL PHYSICS], 19o7s 53, 1822.
COPYRIGHT: Izdatel'stvo "Nauka", ":~'izika Goreniya i Vzryva", 1979
8225
CS0:8144/1260
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PHY5IC3
AMEttICAL ANALYSIS OF TllE VIBItA'fInNAi. MOUE Op A CW GHEMICAL NF LA3ER
Novneibirsk FIZIKA GORENIYA Y VZRYVA in Rueeian Vol. 15 No 1, Jan-Feb 79
rp 89-97
[Article by A.V. Lavrov, V.A. Pospelov, A.V. PedoCov and M.L. 5hur,
Leningrad, mgnuscript received 23 Jan 781
(Textj The developmenC of Polanyils concept (1] of thp creation of un in-
verted medium in the procesa of exothermal chemical reactioris leade to the
deeign o� superaonic chemicai diffusion type lasera 12, 31. At the present
time, it can be considered as an established fact that one of the most pro-
mising systpme of this eype is the laser uaing the hydrogen flouride 1F
moleculp. An HF lager is treated in this paper, in which separate feeds of
the Euel (molecular hydrogen) and the oxidant with a dilucing agent (parCially
or completely diegociaCed fluorine and helium) in a syatem of plane parnllel
gtreamg (Figure 1) are used Co produce g medium with an inverted population.
The vibrutional excitpd molecules of hydrogzn fluoride aYe formed in the
regnnator when the streame of the fuel and the oxidaat mix as a reeult of
pumping:
F-{-Hz--- HF(v) -f-H-f-Qj, v < 3, (1)
Fz-}-H h1F (v) -}-F-}-Qs v o, *=o, af/01h =o;
x>0, vn.u 01l0*=O;
const
u p
.
a
J d*
p
u
The following symbols are introduced in (13) -(16)s
au1 a au
~~/o a ~ (�Pu ~p-x/0a ~l~[J~-~CPC-~'u
\x'!e " J$/ + pu .
(16)
cl>>
(is)
(19)
The following method was employed to determine the presaure gradient and
the radiation intensity. We differentiate the condition for the preservation
ofthe mase rate of flow (18) with respect to s. By varying the order of
differentiation with respect to x and integraCing with respect to and
substituring the values of the derivatives fram (13) -(16), taking (9) into
account we obtain: N'-j
' q&.}. Bjl{ D = 0,
(20)
VE
where Az i I 1 I ~
o pu C P Pu' P~nT ) d ~
ts a! 1 MHP n f1 �
E, _
CpT Pu, r 1+,~,Y�y, ch~ _ h~+i)~ dV~;
I ~
a~ y t a~~
D a~ Pu u td)o-M MiCd,o-
I
T
- cpT ~az~a"-~h'ldx):,-u~ax~o ~lax~oJ~nidT d~.
13
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In a eimilar faeh3.on, taking (3) fxom (19) into account, ona can derives
N~--1
E~ ~ Rijfl �1- Q ~ 0.
(21) .
here . r
ts .
Ei'~, ~ prt Cr,
u! J ~~~'i
ac~+~ ~il1 o r~ac,1 _
Qt �s S ;i ~F2.1 C dXo Fl,+ (ax lol ~ c
p C~/. h`l dx /u
0
T
.N
a~ S ~ acntdT - Pu ~ a ~o dV~,
~
o
. Yc ~ .
,
R~ f~- j pPu, (1 ~vi(h~ - h1~'1)] d~p -4-
o 1
~s
. - f p~ (Fs, --F,.t) d*. 1= t.
0
it?
+ hNA x u,Lj Fz,td* )='i 1+ i
~ T.
~s � -
- f p F,,~d+~~ j a!-1; _
0
dF2.t dFt,t :
X1 ~ C1+1 dT CI dT '
,f
In this way, Che problem of determining the pressure gradient and the radia- '
Cion inCensity has been reduced to the solution of a system of lineat- alge- 4
braic equations (20) and (21), where the number of equations depends on the
number of radiative transitions. An explicit four-point finite difference
scheme with a variable step with respect Co * with iterations was employed for
the numerical integration of system (13) -(16). ~
The basic resuZts. A series of calculations for a CW chemical laser were
performed using the procedure set forth here, where the laser was chaYacterized
by Che following parameters (see [81): an optical path length of L s 175 tmn, ~
,
reflection factors of the reflectors of ro = 0.98 and rL s 0.85, reflector ;
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absorpCion �ncC,oxs of ap = aL m 0.02, a halF-he ght of the outiput croeg-secCion
nF the "fluorine" nozzle of 2 mm, nn expunsion fnctor of the fluorine nozzle
oE 10, and the ha].f-heighC of the ouCput crose-eectiion of the "hydrogen"
nozzle wag 0.5 nua.
It was aaeumed ehat for a specified eempernrure Tk pregsure pk and degree of
dilueidn with gn inere gnx of S= YHe/yF2 (yget YF2 nre the molar concenera-
zinns of 1{e and F2)in the precombusrion chamber, Chere ie equilibrium dig-
gnciarion nf the fluorine. Further, the mixeure of molecular and nromin fluo-
rine and helium expands in the system of supersonic nozzles, the flow in which
ig assumed to be unigorm, nonviecous, adiabaeic and the chemical reuctians are
conaidered eo be quenched. The degree of diseociation of the Fluorine a g n
cdge are shown
incFF'icF 2 F2 asandfuthe ncrionWOfgCheetemperaku e"inuthenchamber~e The vQlocity
gure
gt the outpue of Che "hydrogen" nozzle was see equal Co 2,500 m/sec, the
temper.gture aC 200� K, while the pressure was nsswned equal to the preasure
at the ouCpue at the "flunrine" n o~z1e.
M/C . As a resulr of the calculations
m/s RF 0,5~ 7,
V~
which were per�ormed, curves were
3400,o e,01 940 obtnined for the main character-
v a isCics of the laser (the genera-
~ r ~ Cion power P, the energy yield
0. t s,5 afeo per unit of oxidanC mass E, the
2900 o,s
chemicul efficiency r1) As a func-
2400 0 L2o tion of the parameters in the pre-
io 14 ie 22 id?r�K combusCion chamber. The curves
Cigure 2. The flow parameters at the for P, E and r1 are shown as a
edge of the "fluorine" function of Tk in Figure 3(P and
�nozzle. E IIpply to values when Tk �
= 2,000� K). IC is easy Co see
that alChough t'ne maximum efficiency corresponds to operaCion with complete
Eluorine dissociation (Tk = 2,000� K), the specific energy yield reaches the
greatesr level ,3t Tu 1,100� K. The power generaCed in this case is 1.5
times greater than the radiation power at Tk o 2,000� K, something which is
also related to the increase in the mass rate of �low of the components.
Thus, for a specified geometry of the nozzle unit, one can anticipate an in-
crease in the radiation power when making a transition to low levels of
fluorine dissociation.
It can be seen from Figure 3a that the funcCion n(Tk) is in qualitative
agreeraent with the resulCs of [8]. A.long with ehis, there are rather signif-
icant quantitative differences. Thus, at a precombusion chamber temperature
of 2,000� K, the efficieccies differ by 1.5 times; a low dissociation levels,
the "flame front" model prEdicts a value of the efficiently approximaCely the
same as at a dissociation level of ag = 1, while in Chis work, the efficiency
at Tk = 1,100� K falls off by 1.7 tiir.es as compared to Tk = 2,000 K.
15
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Apparently, the quantitgeive difference in the resultig i.g primarily relaeed
Co the presenca of a considerable amount of inhomogeneity in the proitles
of the gas dynamic ParanatierA (see, for example, F3$ure 4), which is noti
tiaken ineo account "in titi`he q egaiCh3sicann e lead[to.n Because
strong non~.ineariCy of quatiions
ence in the results,
a (a) 6 (b)
079
Figure 3. The ef�iciency (a), power and energy yield (b) as a funcCion
o� the temperature in the precombustiun chamber.
Key: 1. This paper;
2. Paper [8].
At high temperatures in the precombusCion chamber (a g= 1), the pumping ia
determined only by the first term of (1), which has a high velocity. Because
of this, the reaction takes place in a narrow region and the flame approxi-
maeion is observed rather well (Figure 4b). At low temperatures, a consid-
The velocity
erable quantity of molecular fluorine is present in the flow.
constant of the second term is considerably less Chan the first, and for this
reason, the intense development of a chain mechaniem begins only at the this
of the reaction region following sufficienr heating of the mixCure.
point in Cime, the molecular fluorine is already rather well intermixed with
the hydrogen, and the reacti~e takes region considnd
therefore, the use of the fl
erably less precise.
The laser parameters are shown in Figure 5 as a function of the reflecCion
factor of the semitransparentreflector and the degree of inert gas dilutiou,
S. If the efficiency increases monotonically with an increase in B, some-
thing which is related to a reduction in the part played by oscillatoY; de-
acCivation, then the radiation power has a maximum at $ C 15. When 6 150
p falls off, since an increase in the efficiency cannot compensate for a
reducCion in the fluorineflow a;theesignificanteincreasesinrthertemperthe
specific characteristics related to
ature in the reaction region.
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1,0 !o9
TK.IvO, K
1,0 f,q foB

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G (a) r
7.ro?
~N2
Olu ~ 0P8
F7 .77
0,4
0
I
�
. a Ca1
CH:
0,8
0,4 0,8 ylyE
CF2
0,4
0,4 0t2
0
p a, a 08 y/yf
Figure 4. The profiles of the gas dynamic parametera aC various
values of the longitudinal coordinate; Tk a 1,1.00� K.
a) x is equal to 7.8 cm (1), 6 cm (2), 4 cm (3) and
0 (4);
b,c) x is equal to zero (1), 6 cm (2) and 7.8 cm (3).
A comparison was also made within the framework of Che model considered here
with the results of paper [11], in which the small signal gain mode is studied
on the basis of complete Navier-SCokes equations. In the case where a sma11
amount of dilutant is present in the flow, the divergence with respect to
all parameters did not exceed 50%, and with a large amount of dilutant, the
divergence was smaller (up to 20%). Considering the fact Chat the reaction
rate constants and the matrix elements of the dipole momenC used fn [11]
wexe not given, such a divergence must be considered satisfactor,y. We will
noCe thaC the basic reason for the difference in the results apparently con-
sisCs in Che nresence of a transverse pressure gradient, Which is related Co
the considerable heat liberation in the regions Where the exothermal reactions
occur (it is not taken into account in our work). In this regard, one can
anticipate that in the vibrational mode, where part of the energy is split
out in the form of radiaCion, the divergence from the preciae solution wi11
decrease.
17
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0t4
, 6 (b)
c
1
I
~IX.
2
I
3 Q
D,6
o,a
~
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o (a~ ,
q,%
20
!0
0
o to 20 p
6 ~b)
~ 1,00 P/pmos
0,95
0,90
o,s o,7 o,e, rL
,
Figure S. The laser paramerers ae a function of the degree of
dilution (a) and the reflecCion �actor of the semi-
transparent reflecCor (b).
In conclusion, we sha11 formulate the main reaults of this paper.
1. Express3ons were derived �or the integral characteristics of a CW chem-
ical HF governing parameuers,
make it possible Co give
operational modes.
2. Expressions Eor the efficiency as a funcCion of the temperature in the
precombusrion chamber were compared with dara derived on the basis of a
quasi-one-dimensional model [8]. Despite the qualitative agreement of the
nature of thein fuacCransition two-dimensional dissocie
gain when mak g
ation.
3. A comparison with the precise solutions of the complete system of NavieY-
Stokes equaCions [11] demonstrated thaC at least aC large dilution levels,
the model employed yields sufficiently good results.
The authors consider it their pleasant duty to express their gratitude Co
professor Yu.V. Lapin and M.Kh. Strelets for their numerous useful discussions
' of the results o� the work.
BIBLTOGRAPHY
1. J.C. Polanyi, J. CHEM. PHYS., 1961, 40 1, 347.
2. T.A. Cool, R.R. Stepttens, T.J. Falk, INT. J. CHFM. KINETICS, 1969, 11
9, 495.
3. N.G. Basov, V.V. Gromov, et al., PIS'MA V 19 1F 13ET9ER496~ THE JOURNAL
OF EXPERIMENTAL AND THEORETTCAL PHYSTCSI, , 18
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_0
4. W.S. King, H. Mirels, AIAA J., 1912, 109 120 1647.
S. R. Tripodi, I.J. Coulteti, a.o., AIAA J., 19759 130 60 776.
6. V.I. Golovichev, N.G. Preobrazhenekiy, FCV [COMBUSTION AND EXPLOSION
PHY5ICS], 19779 130 3$ 66.
1. G. Cmanuel, J. TSRT, 1973, 13, 12, 1365.
8. V.G. KruCavg, A.N. Orayevakiy, et al., KVANTOVAYA ELEKTRONIlU1, 19760
3, 9, 1919. .
9. W.L. Shackleford, A.B. Witte, J.E. Brogdwell, AIAA J., 1974, 12, 8,
].009.
10. L.G. Loytsyanskiy, "Mekhanika zhidkosti i gaza" ["Flu~~' and Gas Mechanics"),
Moscow, Nauka Publishers, 1973.
11. A.P. Kothari, J.D. Anderaon, E. Jones, AIAA J., 1977, 15, 1, 92.
COF'YRIGHT: IzdaCel'stvo "Nauka", "Fizika Goreniya i Vzryva", 1979.
8225
cso:si4Wi26o
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PHYSICS
AN EXPERIMENTAL STUDY OF THE INFLUENCE OF THE MIXING CONDITIONS IN A LAVAL
NOZZLE ON THE GATN TN A SUPERSONIC FLOW
Novosibirsk FIZIKA GORENTYA I V21tYVA in Russian Vol 15 No 1, Jan-Feb 79
PP 97-102
[ArCicle by B.G. Yefimov and L.A. Zaklyaztminskiy, Moscow, manuscript
received 21 Mar 781
[Text] A large amounr of experimental research studying the influence of
gas dynamic mixing condit3ons 3n flows of working and auxiliary gases on the
inverCed population of the working gas molecules has been recently carried
out. This research has confirmed the theoretical conclusion of [1] that it
is possible to obtain greater inversion when admixing carbon dioxide into
the flow of the thermally excited auxiliary gas (nierogen) expanding in a
nozzle as compared to the expansion of a mixture prepared beforehand. In
fact, in papers [2, 3] when carbon diozide and helium were injected into
nitrogen heaCed up to a temperature of Tp Y 3,000� K, a small signal gain of
kv = 3 m-1 was achieved.
The higher efficiency in obtaining an inverted population when gas flows in
a supersonic nozzle with Che admixCure of a cold working gas Co Che auxiliary
gas is due Co Che fact that: a) the optimum value of the gain is obtained at
greaCer auxiliary gas temperatures (To = 2,000--4,000� K), i.e., with a
greater reserve of oscillatory energy in it; b) the energy expenditures for
preliminary heating of the C02 are reduced.
Maximally optimal from the viewpoinC of obtaining the max3.mum inver sion is
the injection o� the working gas inCo the supersonic flow of Che auxiliary
gas in a uniform manner over its cross-secCion. It is impossible to do Chis
in practice though, sirLca the arrangement oi a large number of fnjection
points into the supersonci flow leads to the appearance of shock waves, and
possibly, to blocking of the flow. Tt is not possible at the present time
to theoretically analyze the flow in a nozzle with the admixture of a cold
gas because of the great complexity of the system of gas dynamic equations,
which Cake into account turbulenC mixing and Che kinetics of oscillaCory
energy exchange, as well as because of the absence of rel3able data on the
turbulent mixing process under these conditions.
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Because of thi.s, experimental studies have been made of the efficiency of
various configurations for the inserCion df the cold working gas in the flow
oC the auxil3ary gas in a superaonic nozzle: 'L) the mixing oE supersonic
flows of caxbon d3oxide and nitrogen traveling Cagether in A channel with a
constanC cross-section following the nozzle [4, 51; 2) the in3ection of
carbon diexide inCo Che formed supersonic flow of nitrogen perpettdiculAr to
the directinn of flow [6]; 3) the injecCion of carbon dioxide through s1nCs
in the wa11s of a f1.ar nozzle in its aubcrit:Lcal secCion wiCh subsequenC ex-
punsion of the flow [3, 71; 4) the injection of carbon dioxide in the vici-
niCy o� the cr3tical cross-secCion of the nozzle Chrough sloCs axranged in
the plane o� symmetr}r of the nozzle [2, 81,
Experiments in which the carbon dioxide wae introduced Chrough tubes w3.th r
holes, where the tubes were inserCed aC the cr3Cica1 cross-secCion of the
nozzle, were performed Co obCain uniform mixture of the working gas and the
aux3'1.iary gas aC the nozzle outler [9]. However, the question of the choice
oP the poinC of injection of the work3ng gas, and iCs nature to ebtain a
homogeneously intermixed flow at the ouCpuC from the nozzle, and the opimum
value of the gain, was nonetheless not sufficiently resolved in these ex-
perimenCs. The system of tubes, positioned in the critical cross-section of
the nozzle [9], apparently provides for rather good 3ntermixing of the gas
componenCs, but is diff 3cu1t Co realize in practice aC small values of the
height of h* of the criCical nozzle cross-section (h* u 0.5 mm) and for the
case of a large mass raCe of flow of the gas, when instead of one nozzle,
an entire assembly is used: an array of nozzles.
Moreuver, in all of the experimental works indicated here, nitrogen or air
was used as the auxiliary gas, which was heated by an electric arc or in a
shock wave, while the carbon dioxide gas was introduced in a mixture with
helium. Since the most accessible method of heating a large quaneity of
auxiliary gas is the combustion of some kind of fuel (for example, CO + H2,
kerosene, benzene) 3n air, then it is expedient to study the admixture of
the working gas (pure carbon dioxide) to the auxiliary gas, which is close
in terms of its composiCion to the combustion producCs of the fuel, i.e.,
which conrains a cerCain amount of carbon dioxide and water.
The purpose of the experiments set forth below is Co study the influence of
the locaCion and nature of the introduction of the carbon dioxide gas and the
composition of the auxiliary gas on the gain. The experiments were performed
using an array, consisting of 14 flat nozzlPS with h* = 1.2 mm and an overall
cross-sectional area of the gas flow at the output of 30 x 300 mm2. The
supersonic portion of the minimum length nozzles (with an inflection point)
was designed to obtain a Mach number of M= 4.5 at braking parameters of
p0 = 2. 106 Pa and TD = 1,400� K[10], Air served as the auxiliary gap,
in which water was added at a consider.able distance from the array, while
carbon dioxide was employed as the working gas.
The carbon dioxide was injected in only the subsonic portion of the nozzle.
It was assumed that the admixture of C02 in the supersonic section cannot
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be effectii.ve, since rurbulent m3.xing of two par.ny.le:1 supersonic Elows, be-
cause o� the sma7.l size ot the rario oE the intensiry of the CurUulence to
the average velocity u zd0,01-0,02) occura at a relatively great length
`
L 41(a')~~^-~ 10'h (npFt l= O,lh),
where h is the nozzle height aC the outlee, while Z is the length of the
mixing paeh. The 3ntroduction of streams wiCh a large amount of moCion at
an angle to the supersonic flow of Che auxiliary bas ehough leads to the
appearance of intense shock waves.
Aix . Aix
eoaayx++2o �2 ao3ayx+co2+H2o
----4W- /
C02
Figure 1. The configuration for the combined injecCion of C02
into the auxiliary gas f1ow.
In the general case, turbulent intermi.xing of the stream of the working gas
with the auxiliary gas is realized so that the interpenetration of the large
Curbulent moles occurs at the outset with their subsequent "breaking up"
into smaller ones. Since the transfer of the vibrational energy from Che
auxiliary gas to the working gas occtirs only during collisions at the molecu-
lar 1eve1, this transfer will bas3cally occur when there is Curbulent mixing
down to moles of a minimum size, which will already be intermixed by means of
molecular diffusion.
The least path length which the particles of the working gas will travel
from the po3nt of their injection before mixing at the level of minimum
sized moles can be roughly estimated from formula (1), if it is assumed Chat
h/2 = h, and breakaway zones are formed in the region of working gas intro-
duction, and then Z= h*, and (u'7)1/2 = u[11]. In Chis case~ Lmin = h*,
and then the greatest length will be on the order of I,m~ = 10 h*.
It follows from these qualitative considerations and rough estimates Chat if
the system for injecting the working gas is insCalled in the subsonic sec-
tion of Che nozzle at a distance of (0--10) h* from the critical cross-sec-
tion, upstream of it, then the mixirg from the minimum sized moles to the
molecular level with the transfer of vibrational energy from the auxiliary
gas to the molecules of the working gas will practically occur early in the
supersonic flow. This circumstance governed the selection of the system for
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admixing the Cd2, the configurnei.dn df whiclt in depi.cCed in Figur@ 1. 'Che
working goa Was fed through ho1Ps in the waiia of the nazzien, piaeed ae a
diAtance o4 m 3 mm from the criricai eroon-seceion, an aei1 as through elota
drranged aiong the cenerai iines of the aozzles over rheir QnCire height.
The device with the elota couid be moved along the fiow at a diACance of from
1 rd d 50 mm from the ariticai necCion.
The digtribution of the carbon dioxide
rco4~''~i~ conceneraeion in the supereonic flow
o to0 0 at the outiet from the array of nozziee
~ 0 9 : o .o Q wag man;tored indireetly: baeed on the
fiow braking temperature drop, produced ;
~ e by the injection of cold C02 inro the
heated fiow of air. The braking tmnper-
~ ature Was meaeurnd using shieided
Chromei-Alumel thermocoupiQS. The COZ
o concencraeion was eatimaeed on the basie
N of the meaeured temperatures from the
heat balance equetion, aith the aesump- -
tion that the digtxibueion of the con-
Figure 2. The distributi.on of the centratione and the temperatures ere
relaCive concentretion similar. The disCribution of the C02
r~~2/rC2 over the concentrarions ati the outlet from the
h~ight H~f the f~ow nozzle over its height Which aere ob-
at the outlet from the tained in thie fashion and referenced
nozzle. to their maximum valuea, is ehovn in
Pigure 2, Where one ie for the injec-
tion of coid cerbon dioxide through
holeg in the Walle of the nozzle; in Figure 2, ahere 2 is for the injection
through slots positioned in the piane of symmetry of the nozzle at a epacing
ot 2.5 mm from the criticai section; and also in Pigure 2, ahere 3 ie
for the cnse of combined C02 injection, i.e., through the holes in the walls
of the nozzle (602 carbon dioxide) and through the elots gimultAneouely. it
can be seen that the injection of carbon dioxide solely through the holes ir
the ndzzle walls or solely through centrnl elots does not allow for a unifocm
distribuCion of itg concentration over the croee-aection of the floa at the
outlet from the nozzle.
The small signal gain wae measured from the increase in the beam inteneity
of a diagnostic C02 laeer ahen its passed through the eupersonic gas floa
at a disCance of a 10 mm from the output edges of the nozzie array. A
"5vnd" type photn resieCor served as the receiver af the radiation.
The resulte of ineasuring the gain for various configuretiona of carbon
dioxide injecrion are shown in Figure 3. All of the data irere obtained at
the sa:ne values of the pressure, temperature and mixture compostion. It
is apparent thae the greatest value of ky is acfiieved for the case of combi-
natioa injection of the C02 (Pigure 3, 3), in accordance with the most uni-
23
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uniform dieexibueion of ehd GOZ concentiraei.on ae the nozzle ouC1et (eee
F3gure 2). The opeimal paint for admi.xing the C02 ig locnted at a dintanea
of 2--5 mm groar the crietcal eeeCion i.n the subsdnie section of the nozzLe.
When the admixing peint 3e removed more ehan 5--6 rom from the criticain~c-
tian, the gain inieial7.y graree to fa11 off sharply, and then alowiy: `
when removed by :o 40 mm, it appronches the vglus �or a working gas mixrure
prepared beforphand (in the case of C02 injectidtt aaly through the slots
ioeated in the piane of symmerry of the nozzle). When admixing carbon di.ox-
ide at poines failing at a distance of Z< 2 mm from the eritical section
and upsereamm of it, the gain 1ikewige fails off, since the C02 apparenrly
doas noe have time to int@rmix sufftcientL,v well wtth the ai.r by the tine of
exit from the nozzie, something ahich fs attested to by the eitghe increase
in the gain in the working gecrion downgtream of the ouepuC edges of the
array of nozzlas.
Figure 3. The influence of the posftion of the point of C02
injection relative to the critical ctioss-section of
the noxzle on the size of the gain kv
Key: 1. Holes in the aalls af the nozzles;
2. Slots in the planes of symmetry of the nozales;
3. The combined injection of C02.
Values of the gain are shown in Pigure 4 as a function of the air braking :
temperature in the precombustion chamber of the setup. It cen be seen that
the injecrion of coid carbon dioxide leads to a substantial inerease in the
efficiency of freezing the vibrational energy in the nozzle array, and is
gxeateY the higher the temperature of the auxiliary gas.
24
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ExpprimmenCs were aigo per.formed ta Beudq the infiuence of the water vgpor
coneene in the auxSli.ary gag (th~ air) on the gain. ValUes of kv $r@ ehown
in Fi.gure Sag a functidn of the molar cont@nt af waeer vapors in the gna
for the various merhods of inCroducing the coid cgrban dioxide. Curvea 1
and 2 3n Figute y were obrained when carbon dioxide wag ineroduced ehrough
ho1QS in the wa119 in the wniis of the noz�leg, and i.n this caee, curve i
correspondg to the i.neermixing of carbon dioxid@ at the seart of the eriti-
cai secti.on 1 m wide, whiie cUrve 2 corresponda to intermicin$ ae a diseance
of 3 mm from the crieieal eection. Curve 3 w8a obtained for the caee of
the combinaefon injeceian of COZ, ahere in conjUnceion with injecCion ttirough
the holes in the noz�ie walls, earbnn dioxide was aiso fed in through aloea
arranged in the pianee of symmetry af the noxxiea at n disCance af 2 mm from
the CrieiCal seceion. The someahae different nature of the behavior of the
curves aith the sma11 waeer vapor eontent in the mixture, which is relaeed
to the diaplacement of the point of C02 injecCion in en upetream direction
cati be cieariy geen.
Pigure 4. The gain as a function
of the air braking temp-
eraCurc.
Key: t. Experimeneal data for the
combined injection of C02;
2. Experimental data for the
injection Of C02 through
holes in the aalls of the
nozzle;
3. Calculation for the flow
of a mixCure of air + C02
+ H20 prEpared beforehand,
pp ft 106 Pa, rH20 = 0.01.
if the carbon dioxidp is intro-
duced close to the Critical section,
then the (100) C02 level prnctically
does not have Cime to pdpulate, and
the maximum valup of the gein ig ob-
tained ahere aater ie absent in the
mixture. When eerbon dtoxide fg
introducpd at a dietance of 1 )0 3 mm
from the critical secCion, the muxi-
mum of the gain is obtained When the
waCer content is rN p2 0.01: With
large gmounCs of Wa ~er vapor, the
dependence of icv on the vepor con-
tent in the Working gag is similar
tn that for a mixture prepared be-
forehand. Since during the inter-
action of the Working gas with the
clectromagnptic field in the reso-
nntor, to depnpulate the loaer (100)
C02 level, the ggs ehould contain a
aeregin amount of Water, so thnt in
the case Where carbon dioxide is Ad-
mixed in the noxzle nrray, its opti-
mel content will algo be equal to
0.01--0.03.
An example of the gain es a function
of the amounc of carbon dioxide
intrvduced in the nozzle array is
ehown in Figure 6. It can be seen
that the optimal velue oF the
25
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re1gei.vg mags rate of �low of carbon dioacide ie samaahae hi.gher than for
the case og a preliminarily pr@pared mixture of gAgeR, nnd iR equal to
0.2--0.25.
k,j
M.1
of
.
0~
A3
ae
0
0,4
0 4
4
R
R.._,.�tG~
i-
Pigure 5. The infiuence of the Waeer vapor content in the mixture on
the gain; po a 105 Pa, Tp = 1,500� K and rC02 u 0.10--0.12.
Figure 6. The gain as a function of the carbon
dioxide content in the mixture; pp a 106 Pa,
Tp 2 10500' K and rg20 a 0.01.
The authors aould like to tinank G.V. Gembarzhevakiy and V.N. Skirda for
assisting in the experiment.
j
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BIBLIOGRAPNY '
i. N.G. Basov, A.N. Orsyevakiy, V.A. 9hchog].ov, ZhTF [JOU1tNAL 0F ENGINEERZNG
PNYSZC3], 1970, 400 1.
2. R. Borghi, A.F. Carrega, at al., APPL. PNY3. LETTERS, 19739 220 12.
3. V.N. Kroshko, R.I. 9oloukhin, N.A. Fomin, FGV [CQM8U3TION AND EXPL03YON
PNYSIC515 1974, 109 4.
4. I. Milewski, M. Brunne, BULL. ACM. POLON. 3Ci., 1972, 200 73.
5. R. Borghi, M. Charpenel, ASTItONAUTICA ACTA, 1972, 179 49 S.
6. B.R. gronfin, L.R. Boedeker, J.P. Cheyer, APPL. PKY5. LETT., 19700 169 5.
7. V.N. Kroghko, R.N. Saloukhin, DOKt.. AN S3SR, 1973, 211, 4.
8. J.-P. E. Taran, M. Charpenel, R. Borghi, AIAA PAPEtt, 1973, N 73-622.
9. L.V. Krauklis, V.N. Kroehko, R.I. Soloukhin, FGV, 1976, 120 S.
10. V.P. Verkhovakiy, TR. TsAGi (PROCBLDINGS OF TNE CENTRAL AEttO-HYDRODYNAMIC
INSTITUTE IMENI N.YE. 2NUKOVSKIYI, No 1680, 1975.
11. B.E. Launder, D.B. Spalding, "Lecturea in Mathematical Models of Turbulence",
Londnn and New York, Acad. Prees, 1972.
COPYRIGNT: Izdatellstvo "Nauka"o "Fizika Goreniya i Vzryva", 1979.
$225
CSp:8144/1260
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PHY3ICS TATION (N EXPERIMENTAL BTUDY OF THE He gATCK GK TI~ERATURE3~ gR~INE MOLECULES :
ZN MIXTURE3 OF T2�Nb AND Br2
Novoeibirek FIZIKA GORENIYA i VZRYVA in Russian Vol 15 No 1, Jan-Feb 79
pp 119-121
[Article by N.A. Generalov, V.D. Kosynkin, V.A. Makaimenko and V.Ya. .
Ovechkin, Moecow, manuacript received 7 Sep 771
(Text] The existing experimental data on tion8 dwhereitheodissociationgand _
gases were primarily obCained under conditi temperatures
oscillatory relnxation processes o~hQrchseparately aracteriatic, At oscillatory tempera-
which are many times greater than _
ture, the proceeses of oscillatory relaxation and dissociation begin to _
overlap. The apecific featurea of this phegome~he theoretically etudies
dicCed in [2 - 8], however, only recently h
appeared 19 - 111. This has become possible due ro the simultaneous measure-
ment of a number of parameters of a reacting system 191�
The results of studying the disaociation prooeas of~edoverlapping ofethele-
cules in a tempeYature range of 1,000--4,000 K, whe
dissociation and oscillatory relaxation processesis8entalrsetuped :
in this communication. The studies aere made using the exPerisn ~
of [12], which consista of a shock tube, and ayatems for recording the ab- ~
sorptivity of the gases in the vii8~ionregion of the spectrum at Cwo wave-
lengths as well as soft X-ray radThe dissociation kinetica were atudied in mixtu~ssoffthe gas (Tk, vT~o[T ~ith
inert gases. The profiles of the main paramete a 8re the preseure, `
are the oscillatory and progreasive temperatures; p. for P, denaiey and degree of dissociation). The procedure obtainwhening indi-
cated parametera is aet forth in [9]. Tt has been shown
> 2,000' K, T and Tk differ markedly from each other for a considerable '
time (a 10 --p20 usec).
The results of an exper3mental measurement of Tk/Tp BSgshock wavesDofTp
(D is the dissociation energy) are shown in Figure 1 for _
28 `Y
N& 0171OtAL gIf ONLY
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varioue inCeneiCies. The calcu-
,
o,A
o,s
0.4
T~T~
�
0 0.
r�
Q
03
o
.
'
�4
1aCed values obtained from rheory
15 - 8] are p].otted in Figure 1
(1, 2) ia a parameter def ining
the separaCion boundary of the
regione of relaeively fast and slow
quanea exchange, where tihie boundary
ie due eo the anharmonic nature oE
the molecular oacillationa). It
can be seen that the experimental
and theoreCical values are in agree-
ment wieh each other. The absence
of equilibrium wieh respect eo the
3
to 15 a/KTn
oscillatory degrezs of freedom has
a subatanCial influence on the dis-
sociation proceas. The diseociation
Figure 1.
Values of the ratio Tk/Tp
rate coneCant KD becomes dependent
as a function of D/kT .
p
not on].y on T but also on T1~. An
p
resaion for KD/iCD as
analytical ex
= Key: l.
S= 1;
a funcrion o� Tp and Tk ia given
2.
S~ 0.8;
in [2 - 81:
3.
12;
H T.
4.
Br2.
KD Tn fprI 111

r
~-~p
KD TK
T~lJ'
L'~lTo
where Itp is
the equilibrium value of the dissociation rate conatant; k ia
Boltzmann's
constant. The value of the
nonequilibrium dissociation rate
conatant was determined in mixturea of
20% (I2, Br2) and 80% (HeNe). In
the initial
stage of the diasociaCion p
rocesa, one can assume the following
decomposition scheme:
M2+A-* M + M + A
(M2 and M are the halogen molecules and atoms; A are the inert gas atoms),
which is described by the phenomenological equation for the dissociation
kinetics: L�
Knsc,-anx.nn, (2)
where nM2 and nA are the concentrations.
Values of KD I2-He in a temperature range of 2,000-4,000� K and KD Br2-Ne
in a range of 1,000-2,300� K were determined by means of equation (2).
These resulta are shoWn in Figure 2. The cu*:ves are the result of the
29
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'I

u
.o
~
~
u
YA
Figure 2. Values of the disaociation rate constanC for iodine
and bromine molecules as a function of the gas temper-
ture.
Key: 1. I2-Ke;
2. Br2-Ne;
KD, (moles � sec)'1 � cm3.
0'J
10 ft
h
~
u

u
e� 109
0
1
~CQ
t0 ,
I
105
0,25 0,50 0,75 1~T � l0; K'
Figure 3. 1nKD as a function of 1/Tp.
Key: 192. Approximations based on Arrhenius' formula;
3. TZ-He;
4. Br2-Ne.
KD (moles � sec)-1 � cm3.
30
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theoreCical cnlculaCion [7] bnsed on the gnlurion uf Fokker-rl.anck's
equation, enking into ttccoune the muCual influences of the osaillaCory
relaxaCion and d3ssoci~tion processes for the hard ephere model. The
good agreemenC of the experimenCal and CheoreCica1 valuee of KD ehrough-
out the entire temperature range considered here ehonld be cired.
The equilibrium values of were compuCed from �ormula (1). If the reaults
obtained are preseneed in t e form of 1nICD ae afunctiion oE 1/Tp , ehen the
AcCivaCion energies of the TZ and Br2 molecules can be estimaCed from the
elope. In facC, iC can be seen from Figure 3 Chae this funcCion ig linear,
sometAing which attests to the correctness o� Arrhenius' formula:
s
K�a - Aer "r,
where A is a congrant; E ia the activation energy. The value of E
esCimaCed in this �aehion for iodine molenules is equnl to 35.5 Kcal/mo1e,
and C 44 Kcal/mole for the bromine molecule (rhe di.ssociation energy is
45,5 Kcal/mole).
BZBLIOGRAPHY
1. Ye.V. Stupochenko, S.A. Losev, Aj. Osipoy, "Relaksatsionnyye protsessy
v udarnykh volnakh" ["Relaxation Processes in Shock Waves"], Moscow,
Nauka Publishers, 1965.
2. R. Nammerling, J. Teare, V. Kivel, PHYS. FLUIDS, 1959, 2, 41 422.
39 S.A. Losev, N.A. Generalov, DOKL. AN 5S5R [REPORTS OF THE USSR ACADEMY
OF SCIENCES], 1961, 141, 1072.
4. P.V. Marrone, C.E. Treanore, PHYS. FLUIDS, 19630 60 91 1215.
5. N.M. Kuznetsov, DOKL. AN SSSR, 1965, 164, 5, 1097.
6. A.I. Osipov, TEOR. I EKSP, KHIMIYA [THEORETICAL AND EkPERIMF.NTAL
CHEh1ISTRY], 1966, 2, 649.
7. M.N. Safaryan, Ye.V. Stupochenko, KhVE [expansion unknown], 1971, 5, 195. ~
89 N.M. Kuznetsov, TEOR. I EKSP. KHIMIYA, 1971, 7, 1, 24.
9. N.A. Generalov, V.Ya. Ovechkin, TEOR. I EK5P. KHIMIYA, 1968, 4, 6, 829.
10. M.S. Yalovik, S.A. Losev, TR. INSTITUTA MEKHANIKI MCU [PROCEEDINGS OF
THE MECHANICS INSTITUTE OF MOSCOW STATE UNIVERSITY], No 18, Moscow,
Moscow State University Publishers, 1972.
31
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11. S.A. Lnsev, FGV, 1973, 9, 6, 767.
12. V.Yg. Ovechkin, N.A. Generglov, VESTNIK MGU. FIZIKA, ASTRONOMIYA
[BULLETIN OF MOSCOW STATE UNIVERSITY. PHYSICS9 ASTRONOMY], 1969,
6, 3.
COPYRIGHT: Izdatellstvo "Nauka", "Fizika Goreniya i Vzryva", 1979
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PKYSICS
THE VIB1tATTONAL BAND TEMPERATURE OF CARBON DTOXIDE GAS ZN A C02 + NZ + HZ
GAS llYNAMTC LASER .
Novoeibirek FIZTKA GORENIYA I VZRYVA in Rueaian Vol 15 No 1, Jan-Feb 79
pP 122-125
[Article by N.N. KudryavCsev, S.S. Novikov and Y.B. SveClichnyy, Moscow,
manuscript received 1 Dec 771
[TexC] The possibility of using molecular hydrogen in a C02 GDL [gas
dynamic laser] was danonstrated in [1, 2]. The results of ineasuring the
gain aC a wavelength of X = 10.6 um and the intensity of the spontaneous
IR rudiaeion in the 4.3 um band of the C02 molecule for the case of super-
sonic expansion of a mixture of C02 + N2 + HZ and at pp = 5--25 aCm and
PD = 800--3,000� K ahead of the nozzle are given in [3]. The vibrational
Cemperature of the Tg asymmetrical mode of carbon dioxide gas was determined
in [4] on the basis of ineasurements of the radiaCion inteneity in the 4.3Um
band wieh the assumpCion that the combined�C02 mode (symmetrical and deform-
ational modes) were in equilibrium with the progressive degrees of freedom
(T2 = T).
As was shown in [5], the simultaneous measurement of the spontaneous radi-
ation intensity of C02 in the 4.3 um band, I, and the gain in the radiation
of a probing C02 laser, Kp, allows for an experimeneal determination of the
population, and conaequently, the vibrational temperatures of both working
lasing transition levels (001-100) of the C02 molecule. Aeterminations of
the vibrational temperatures of the asymmetrical (T3) and combined (T2) modes ~
of carbon dioxide gas based on the vglues of the quantities Kp and T,
measured in [3] for the case of GDL's operating on a mixture of COZ + N2 + H20
are given in this paper.
The following reacCion occurs in the mixture of carbon dioxide with molecular
hydrogen aC high temperatures:
COz-}-HzZ;:kCO-}-H,O. (1)
The CO molecules and especially the H20 molecules, formed in reaction (1)
can have a substantial influence on the vibraCional energy exchange in
33
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the mixCures beiitg eGudied~ ~t is also necessary tio tgke i.ntio account the
redUCtion in the COZ concentxation as a result of the reaction.
The calculation of the chemical composiCion og the mixture in the volume
ahead of the nozzle was based on the experimental daCa of [6] for the
kineCica of the overall reacCion (J.). According to [6], the waeer vapor
contenC in the mixture is deCermined by the relationahip:
tx,o = G,o I 1 - exP ki (tH,)�,a IM] 0)), (2)
1 ' o~o,: A p 81,4 2,3
where k~ 10' ~x RT )(cm3/mole � sec); CK20 ~ H20/[M] is the
~
relative concentrati8n of the water molecules; 9~0 is the corresponding
equ~.librium value; &HZ is the inieial relatiive h rogen concentration; [M]
is the total particle density; and t is time.
Ao 4 B.
~ ~ Co~toa ewecu
= Y
3
0,ICOj;�0,89N
4
O,ICOa.11.0.85N=-11.
-I-0,05Hz
5
0,ICO,�{-0.8N,
-!�O.IFi:
G
To Mr
7
S
�
0,1(:02�;�0.7`j-{-
O,:FI.
~
0
tH,0.101 npn To. K
pn. oTi 11750 1 1975 1 2000 12125 12250 12373 12500 14750 1 1000
6.0 1.5
0,002
0,009
6,0~ 1,5
0,01
0,07
6,04.1,5
0.03
0,13
7,5,~ 13
0,05
0.26
13+25
0.1
0,51
G,O~-I,J
0,05
0,4
0,03
0,1
0,25
0,53
0,81
0,98
0,99
0,1
0,72
1,8
3,2
�1,2
4;4
4,5
047
I,,1
3.1
.1,li
7,0
i,:
7,3
0,9
2,5
4.7
6,8
7,1
7,2
i,;i
I, i
4,1
G,0
6,8
7.1
i,:
77,3
7
0
1
2
4,7
7,6
8,8
8,9
9,0
,
.
4
4
Key: A. Number of the mixCure;
B. MixCure composition.
Note: The percentage water vapor content in the studied mixtures was
deeermined for the case of t= 0.15--0.25 msec.
The ampli�icaCion and radiation characteristics of the mixtures studied in
[31 were measured in a time range of 0.15--0.25 msec following reflecCion
from the end face of the tube of the incident shock wave. For this reason,
the results of calculating the water vapor concentration are given in the
table for this period of time in the studied mixt+ures as a function of the
temperature and pressure in the volume ahead of the nozzle. The numeration
of the mixtures in the table corresponds to the deaignations of the experi-
mental curvea in Pigures 1-4 and in [3]. The results obtained for the
0.1 C02 + 0.4 N+ 0.5 He mixture (the quantity po corresponds to the ehock
34
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adigbat wiCh nn initial value of the prssure df 0.2 atm) and for the 0.1
C02 + 0.9 N2 mi.xture (po d 6,0+ 1,5 atm) are designared in rigurea 1-4 and
i.n [3] wi.th the numbers 1 and 2 respeceively. According ro [7], the inf1u-
ence of the water molecules on the kinetics of the formaeion of invereed
popul~tiona in a C02 + N2 mixCure must conaidered when the H20 conCent in
the mixtiure exceeds 0.005. Tt can be aeen from the eable ar which values
of Tp the H20 content exceeds this value.
In accnrdance wirh the Cable dntia, a apecific composttion of the mixCure
aas employed in cglculaeing the vibrational tiemperatiures T3 and TZ from the
measuxed vgluea of Ko and T. The presence of carbon monoxide in the mix-
Cure, which is �ormed in react3on (1) when using a wideband dispersion fil-
Cer in the channel for recording the IR radiation, leade Co the necessity
of raking inro account the radiaCion of the CO moleculea in the 4.7 um
band [4).
The regulCs of ineaeuring the vibrational temperaCure of the asymmetrical
C02 mode as a funcCion of the Cemperature ahead of the nozzle for mixtures
1-5 and 8 are shown in Figure 1. Tg for the 0.1 C02 + 0.8 NZ + 0.1 H2
inixCUre is shown as a function of Cemperature in Figure 3 for various
pressures. The temperature in the criCical nozzle sect3on, T*, is shown
in Figures 1 and 2 wirh the dashed lines, and with the dashed and dotted
line for mixture 1.
A comparison of vibrational temperaCure values, obCained in this work,
with the values of T3 obrained for the same mixtures in [4], shows that
determining T3 using the approximaCe meChod of [4] leads to vnlues over-
stated by 40-120� K in a temperature range ahead of the nozzle of 800-
2,500� K. It was shown in [4] that because of the assumption of the thermal-
ization of the combined mode, the approximate method permits the obtaining
an upper estimate of T. It follows from a comparison of Figures 1 and 2
with the results of [4~ Chat the approximate method correctly reflects the
basic laws governing the change in T3 as a function of To, pp and the compo-
aieion of the mixtures. The following belong to Chese governing laws:
an increase in T3 and in the difference (T* - Tg) wiCh an increase in To,
a decrease in Tg with an increase in the initial hydrogen concentration
and an increase in the pressure from 5 to 25 atm. The greateaC values of
T3 are achieved with the expansion of the binary mixture 2(0.1 C02 + 0.9 N2);
the smallest values are obtained in mixture 1 *ith helium. It should be
noted that the value T* for mixCure 1 is substantially lower than the value
T* for mixCures 2-8.
The vibraCional temperature of the combined COZ mode as a function of the
Cemperature ahead of the nozzle for mixtures 1-5 and 8 at po = 6.0 + 1.5 atm
and for the mixture 0.1 C02 + 0.8 N2 + 0.1 H2 when the pressure varies from
5 to 25 atm are shown in Figures 3 and 4. The dashed lines in Figures 3
and 4 show the gas temperature in the working cross-secrion of the flow
35
FOR OFFICIAL USE ONLY
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APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000100060051-8
rOR OFFZCIAI, USC ONI,Y
1, 7
!14
0,8
r3 'O' K ~ i
i
x I
i/ 2 3
02 i
0 4
Ng / ~ ~ ~
0 ~i / � 5
i
0
i
0 o s
0 '
g ~,~xt~' t
~ ~ x x x
Ta- fO;' K
f,0
1,4
1,2
1,0
0,8
o,s
0,8
f'5 . 2,0 2,5
Figure 1.
73 10,3 K
~
S 1,440
s
~
00
x
7
/
r
1
qovo
'
j
x
X
~
x
c s
/
x7
/
x
/
x
�
x x
to�l0~ K
0,75
0,55
0,35
0,15'
1,0
1,5 ?,0 ?,S
Figuze 3,
for mixtures 2-89 whi1.e the dashed and
dotted line is for mixCure 1. For al1
oE the mixtures studied under the con-
diCions of this work (Tp = 800--3,000� K,
PO 0 5--25 aCm), n rising curve far T2
as a function of To Is observed. We
wi1l note the high degrEe of nonequi-
librium of the combined C02 mode: the
vibraCionay. eemperature exceeda the gas
temperAture by 1.5-2.0 times. For mix-
tures 4, 5 and 8 wiCh an additional
hydrogen conCent of 0.05, 0.1 and 0.2
% = 6.0 + 1.5 atm), the values of
T2 throughouti the entire range of Tp a
= 800--2,500� K are in agreement with-
in the limitis of the meas8 rement pre-
cision. For m3xture 3Q H2 - 0.01),
elevated values of T2 are observed at
Tp ~>.1,600� K. In this same ranee of
temperatures of Tp, binary mixture 2
possesses the greatesC vibrational
temperature T2. The value of T2 for
mixture 1, which conCains helium, is
suDstantially lower than for mixtures
2-5, and 8 wiCh added amounts of hydro-
gen.
The influence of the pressure on the
vibraCional temperature of the combi-
nation C02 mode for a mixture with
~H2 = 0.1 is illustrated by curves
5-7 in Figure 4. The measured values
of T2 or pp = 7--25 atm practically
coincide (see Figure 4, 6, 7) through-
ouC the entire investigated range of
TQ = 800--3,000� K. When pp = 6.0 +
+ 1.5 atm (see Figure 4, 5), the mag-
nitude of T2 is 60--100� K higher Chan
for pressures of 7.5--25 atm.
Thus, the increase determined in [3] for
the gain and in the relative inverted
population of the C02 lasing levels
when molecular hydrogen is added to a
Dinar}r mixture of C02 + N2 in the amount
of 1--5% is due to the more significant
36
FOR OFFICIAL USE OIdLY
f,4 2,0
Figure 2.
2,6 3,117
o_ . 0
T2�fO-,3 K
0 3 p
x ! O 4
.40
5
02 tk5
~
4,6,
8
03 06
0
~ooh
0
0
x
~J
~ 10
~
~I
X x
~

.
, /
~
,i
iP 00
i
T0~10?K
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FOR 0FFtCIAt. USE ONLY
0,7y
0,03
0,47
O,J
0.15
TQ,lO ',j K
~
o,?
0,6
s
o,s
x

00 ol
, ~5
�
00000
06
~

000 00,
~
'
01200.00
to,lo;'K
reduetinn in the pdpuiati,on of the
lower iasing ievei an comparefl eo
the upper one (nee curves 2-4 in
Figuren 1 end 7). The reductien in
the gein (see curves 5nnd 8 in Fig-
uree 3and 4(31) at high hydrogen
conrenrtiations (0.1--0.2) is determined
predominantly by the reduction in the
populaeion df the upper ].asing 1evei
T3 (see curveg 5and 8 in Figures 1
and 3). With an increaee in the gns
pregsure in the volume ahead of the
nozzle, the reduction in the gain
o,s . f,a 2,0 2t6 3,2 noted in thQ mixtura of 0.1 CA2 +
Figure 4. + 0.8 NZ + 0.1 HZ is related to the
. more rapid relaxarion of the gsym-
meCrical C02 mode us compared to the combination mode (see curves 5-7 in
Figures 2-4).
BI$LIOGRAPNY
1. A.B. Britan, S.A. Losev, O.P. 5hatelov, KVANTOVAYA Ei.EKTRONIKA [QUANTUM
ELECTRONICSJ, 19749 19 129 2620.
2. I. Rom, J. Stricker, ACTA ASTRONAUTICA, 1974, 19 1101.
3. N.N. Kudryavtsev, S.S. Novikov, I.B. SveClichnyy, FGV [COMBU5TION AND
EXPLO5ION PHYSIC5), 1976, 129 S.
4. N.N. Kudryavtsev, S.S. Novikov, I.B. SvetllcFnyy, FCV, 1977, 139 2.
5, N.N. Kudryavtsev, S.S. Novikov, I.B. Svetlichnyy, DOKL. AN SSSR [REPORTS
OF THE USSP. ACADEMY OP SCIElJCES], 1976, 231t 6.
6. J.M. Brupbacher, R.D. Kern, B.V. 0'Gady, J. PNYS. CHEM., 19769 80, 1031.
7. I.D. Anderson, "Gas Dynamic Lasers: An Intraduction", N.Y. Acad. Preae,
1976.
COPYRICHT: Izdatel'stvo "Nauka", "Pizika Corenfya i Vxryva", 1979
8225
CS0:8144/1250 END
37
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