FLUID DYNAMICS 23

CONTRIBUT ION TO THE THEORY OF THE H IGH COMPRESSION RAT IO GAS E JECTOR WITH CYL INDRICAL MIX ING CHAMBER

G. L. Grodzovsk i i

Izv. AN SSSR. Mekhan ika Zh idkost i i Gaza, Vol. 3, No. 3, pp. 35 -44 , 1968

Ways of improving the operation of a gas ejector with a high com- pression ratio are investigated. The conditions for obtaining the maximal compression ratio at the critical operating regime of the gas ejector are studied theoretically and experimentally with account for mixing of the supersonic injecting and subsonic ejected streams ahead of the choking section. The principles for the rational utilization of the effect of stream mixing in the ejector ahead of the choking section are indicated; the use of these principles permits a several-fold in- crease of the compression ratio of the supersonic ejector. A theory is given for the critical regime of the gas ejector with uniformly perfor- ated nozzle, and the hydraulic parameters of the required wall per- forations are determined. It is shown that perforation as a hydraulic factor can improve significantly the parameters of the sonic ejector in the critical regime.

The foundations of modern gas ejector theory were developed by Kbxistianovich [1, 2]. In these studies he established the relationship between the parameters of the flow at the end of the mixing chamber (section 3, p~' is the total pressure, k" is the reduced velocity) and the parameters of the: ejecting (section 1, p~,k') and the ejected (p01,kr) flows with account for compressibility for the ejector with a cylindrical mixing chamber (Fig. la). The ejector theory [1, 2] (see also [3, 4]) is given in the hydraulic approximation: the flow at the end of the mix- ing chamber is assumed uniform, flow friction on the mixing chamber walls is neglected. The use of the gasdynamic functions [5-9] made it possible to obtain computational equations for the ejector in a con- venient form and to extend them to the case of mixing of gases with different thermophysieal properties. We note that for subsonic veloci- ties of the ejecting and ejected flows the system of ejector equations [1, 2] is supplemented by the condition of equality of the static pres- sures p' = p~ at the stream contact section 1.

The results of extensive experimental studies of subsonic ejectors are in good agreement with the results of this theory.

For sonic or supersonic velocity of the ejecting gas (X' _> 1) the condition p' = p~ is not satisfied in the general case. Fundamental for the development of ejector theory was the establishment by Million- shchikov and Ryabinkov in 1948 of the existence of a critical operating regime of the supersonic ejector [7,10]. They showed that the limiting operating regimes of the gas ejector for high pressure differentials o = = P~/P01 are determined by the conditions for the choking of the ejected jet by the expanding supersonic ejecting flow. With the occurrence of the critical regime the velocity of the ejected jet at the choking sec- tion (section 2, Fig, la) reaches the speed of sound (X = 1); this limits the further increase of the pressure ratio o and the ejector compression ratio e = Pg/Pd for a given ejection coefficient k (k is the ratio of the ejected and ejecting gas flow rates). The relationships between these flow parameters at sections 2 and 1 supplement the system of ejector equations and permit determining its critical characteristics.

Millionshchikov and Ryabinkov showed that for moderate values of the pressure ratio o good a~eement of the theoretical and experimen- tal ejector characteristics are given by the assumption of constant stat- ic press~e P2 = const at section 2 (Fig. la).

The limit of the appiicability of the theory based on the condition P2 = = const, o ~ 4 was studied experimentally by Lyzhin [1O].

The theory of the critical regime of the gas ejector was developed in 1988 in studies of Nikol'skii, Shustov, Vasfl'ev, Taganov, and Mezhirov [1O, 11]. Nikol'skii showed that the condition of constant static pressure at the choking section is not in agreement with the mo- mentum equation.

For a more rigorous theoretical determination of the critical ejec- tor regime he proposed joining between sections 1 and 2 (Fig. la) the caleu_tation of the ejecting jet using the method of characteristics and the hydraulic calculation of the ejected jet; example calculations were made by Nikol'skii and Shustov. Taganov and Mezhirov sug- gested a method for calculating the ejector critical regime using a linear distribution of the pressure in the supersonic ejecting jet (at the choking section 2).

A simple and successful method for calculating the ejector criti- cal regime was given by Vasil'ev, who used the hydraulic representa- tion of the ejecting and ejected flows in the choking section; both flows are assumed uniform at section 2, the static pressures in these flows in the general case are different and are determined by the mo- mentum equation. A simLlar theory for the ejector critical regime was developed independently in [t2, 18], and the theory with account for the supersonic ejecting flow (ahead of the choking section) was developed using the method of characteristics in [14].

It should be noted that the results of the calculations of the criti- cal characteristics of the ejectors using all three of these methods were practically indentical and in good agreement with experiment for large and moderate values of the ejection coefficients. We emphasize that in the theories of the ejector critical regime the flow mixing be- tween sections 1 and 2 is neglected.

The critical regime theory hnposes significant ]imitations on the possible characteristics of the gas ejector, first of all. on the achiev- able compression ratio s = p~/p~. Thus, from the data of [10], even for a pressure ratio o = 1000 the maximal theoretical vahe of the compression ratio for the supersonic ejector does not exceed e ~ 40 (see in Fig. 2 the limiting ejector characteristics based on the critical regime theory); for the sonic air ejector (k' = 1) the theoretical value of s -< 3.5 (see Fig. 9b on p. 26). Therefore it is important to analyze the methods for influencing the esitical regime parameters in order to determine ways to improve the operation of the gas ejector with a high compression ratio.

w Opt imizat ion of gas ejector parameters with account fo r mix ing of the supersonic e jec t ing and sub- son ic ejected flows ahead of the choking section. In 1953 we showed that fo r h igh compress ion ra t ios e and cor respond ing ly fo r smal l e jec t ion coef f i c ients k, mix ing of the f lows in the e jec tor ahead of the chok ing

sect ion has a s ign i f i cant e f fec t on e jec tor parameters . M ix ing of the f lows ahead of the chok ing sect ion in - c reases the tota l p ressure in the e jec ted gas je t (in

sect ion 2, F ig . 1) and improves the e jec tor charac - te r i s t i cs cor respond ing ly . To ampl i fy th is e f fec t we

must s t r ive for a g reater re la t ive f low mix ing sur - face in the e jec tor ahead of the chok ing sect ion . In par t i cu la r , fo r ax i symmetr i c e jec tor s the cent ra l l o - ca t ion of the e jec t ing nozz le is more favorab le in com-

par i son w i th the per iphera l (annular ) locat ion.

Th is p red ic t ion was conf i rmed by tes ts made with a ser ies of son ic e jec tors (F ig . 3 and F ig. 9a be low) .

F igure 3 shows the character i s t i cs of an ax isymmet -

r i c son ic e jec tor ~ = 1, a -- F1/F ' = 7~. The dashed

curves are f rom the c r i t i ca l reg ime theory : 1 is f rom

exper iment wi th a per iphera l e jec t ing jet (Taganov,

24 IV IEKHANIKA ZHIDKOSTI I GAZA

Mezhirov, Kharitonov), 2 is for exper iment with a centra l e ject ing jet (Grodzovski i , Ravdin), 3 is ema x f rom cr i t i ca l reg ime theory, 4 is emax f rom the

9 f 2

t ~'g :' l;'~, k ;

Fig. 1. Flow pattern in the e jector .

Kors t theory. We see that for the case of an area ra - t io a = F1/F T = 7.0 of the low-veloc i ty and h igh-ve loc - ity flows at the entrance to the e jector (Fig. 3) the ex - per imenta l character i s t i cs of the ax isymmetr ic e jec - tor with annular per iphera l e ject ing nozzle pract i ca l ly coincided with the calculat ion based on the c r i t i ca l reg ime theory. Change to the scheme with the cent ra l e ject ing nozzle s igni f icant ly improved the e jector character i s t i cs in the region of high compress ion ra - t ios for d ischarge coeff ic ients less than K _< 0.20. Thus, for ~ = 19.2 ( l imit ing for the per iphera l scheme, where k = 0) the e ject ion coeff ic ient inc reased by A k

0.09; the e jector max imal compress ion rat io (for k = 0) inc reased by 1.7 t imes and reached ema x

5.45.

t

3g

zs /,~

0 r

290

o I / o n~:ouz

-----'-T ~ '.o0~O

FLUID DYNAMICS 25

(F ig. 1) w i th account fo r (1. i ) may be wr i t ten in the fo rm

pO(U,a,k ) p2~( F,) --~ - - a = (1 .2 ) ~p(~:) -k v ,

aq(~) (~= P~ (1.3) = ~q (V-----~ p0~-'

z(U') = .kz(Li) q- z(M). (1.4) t+k '

P~ ) o'q(~') O. + z~) (~ = -7 ' (1.5) 8= (t + a)q(~"-7 \

Here p( / ) , q ( l ) , and z(/) a re known gasdynamic func-

t ions of the pressure , f low ra te , and momentum [5-7]~

9 ~ ~

0.~ T

0 O.Ot O.OZ (r Fig, 5. Effect of relative flow ra te of secondary f low on the

magn i tude of the base pres -

sure p* = P l /P ' fo r super - son ic f low past a two-d imen-

s iona l s tep .

The characteristic curves for the relative base pressure p~ are shown in Figs. 5-7 [16, 23], Figure 5 shows the effect of the relative flow rate of the secondary stream on the magnitude of the base pressure

t7o . . . . .

X\ 2/I/I/ ,, e;'," /

". i o,,'~ - \ i

r 3 ~r

F ig, 6. The dashed curve is base pressure on the end of a cy l inder in an in f in i te su -

person ic s t ream, the so l id curve is the same beh ind a two-d imens iona l s tep in a

superson ic s t ream, and the dash-dot curve

is the base pressure beh ind an annu lar s tep in a channe l with expans ion ra t io a =

= 1.56.

p~ = pffp' for supersonic flow about a two-dimensional step. We see that the relative pressure p* decreases monotonically with reduction of the ejection coefficient k (proportional to cq). Therefore, in accord-

ante with [1.2)-(1.5) the maximal compression ratio of the ejector is naturally reached for k = 0. The effect of the flow geometry on the base pressure p~ is illustrated by the data of Fig. 6, where the dashed

a

F ig. 7. E f fec t of annu lar

s tep expans ion ra t io a = = F JF ' on the value of

the re la t ive base pres - sure for X' = 1.

curve is the base pressure on the end of a cylinder in an infinite super- sonic stream, the solid curve is the same behind a two-dimen- sional step in a supersonic stream, and the dash-dot curve is the base pressure behind an annular step in a channel with expansion ratio a = = 1.56. We see that transition from the flat-end cylindrical step to a two-dimensional step, and further to the peripheral armular step, re- duces the base pressure sequentially and increases the compression ra- tio in the ejector correspondingly. Therefore, other conditions being equal, the axisymmetric ejector with a cen~al ejecting jet gives a larger compression ratio s than the ejector with an atmular peripheral jet (Fig. 3). The base pressure behind the annular step decreases monotonically with increase of the channel expansion ratio a = F1/F' (Fig. 7).

"i fl/(-- 0

z , g

fl/

Fig . 8 . The so l id curve is f rom Kors t

theory , the dashed curve is f rom cr i t - ica l reg ime theory ; the po in ts a re an

exper imenta l s tudy of a ser ies of son ic e jec tors wi th cent ra l e jec t ing je t

(Grodzovsk i i , Ravdin , 1953).

The relations for p* presented from Korst theory together with the system of equations (1.2)-(1.6) permit determining the limiting char- acteristics of ga~ ejectors. As an example, Fig. 8 present~ for sonic ejectors (k' = 1) the theoretical and experimental curves for the limit- ing pressure ral2o across the ejector Omax as a function of the area ratio a ~ F1/F' of the ejected and ejecting gases, where the solid curve is from Korst theory, the dashed curve is from the critical re- gime theory, and the points are an experimental study of a series of sonic ejectors with central ejecting jet (Grodzovskii, Ravdin, 1953). We see that the Korst theory is in good agreement with the experi- mentally studied series of sonic ejectors; the critical regime theory (without account for flow mixing ahead of the ejector choking section) yields restfits which are lower by more than a factor of two with re- gard to Omax. Figure 9a presents the experimental grid of values of

26 MEKI-IANIKA ZHIDKOSTI I GAZA

the compression ratio ~ for this same series of sonic ejectors; the cal- culated curve for emax using the theory presented above is in good agreement with experiment. Figure 9b shows the calculated grid of

So

~0

~0

a b

/o 20 30 ~0 o /o zO

Fig. 9. a) Exper imenta l gr id : compress ion ra t io for a ser ies of sonic e jec tors ; b) com- press ion ra t io fo r sonic e jec tors f rom the

c r i t i ca l reg ime theory .

values of ~ from the critical regime theory. In comparing the theoret- ical and experimental values of the ejector compression ratio ~ here and in the following, we must bear in mind that in the experiments the total compression ratio was determined with account for the degree of recovery of the total pressure )'9 = Pop"/P;' in the subsonic diffusor (Fig. 1). (The quantity Y9 naturally includes also the flow friction losses on the walls of the ejector mixing chamber, which are not taken into account in the hydraulic theory.) The values 1'9 depend on the dif- fusor performance and Y9 ~ 0.90-0.85.

200 z,~Og

F ig . 10. The so l id curve is f rom Kors t theory , the dashed curve is f rom cr i t - ica l reg ime theory [10], dash-dot curve represents the opt ima l va lues X'opt; exper imenta l data a re f rom

1 [19], 2 [14], 3 [24].

The system of equations (!.2)-(i.~) permits solving the important extremal problem of the maximal achievable ejector compression ra- tio amax for a given pressuxe ratio across the ejector o = P6/P0p Anal- ysis shows that in this formulation area x is reached for zero ejection coefficient k = 0 and an infinitesimal ejected flow a --~ 0. Figure 10 gives the variation of Smax as a function of o and indicates the opti- mal values of the ejecting flow reduced velocity Mopt. The solid curve is from Korst theory, the dashed curve is from the critical regime theory [10], the dash-dot curves are the optimal values k'opt, the experimental data on Smax are from 1129], 2114], 3[24]. Com- parison of the measured values of emax with the data of the critical regime theory (see Fig. 2) shows the possibility of obtaining compres- sion ratios in the ejectors which exceed by several fold the theoretical values, which do not take into account the flow mixing ahead of the ejector choking section.

For illustration Fig. 10 also shows experimental values of emax for several of the tested ejectors. Of particular interest are the results of an experimental study of Arkadov [24] of his proposed ejectors with a slotted (perforated) nozzle mounted in the mixing chamber at the exit from the supersonic ejecting nozzle (several other modifications

of the ejectors proposed by Arkadov with improved (in comparison with the theory of [10]) characteristics are comidered in [26] ). The slotted perforation (about 8 longitudinal slots with permeability coefficient S-= 10-15%) provides a combination of the favorable properties of the self-regulated supersonic nozzle [25] and the system with extended mixing surface of the ejecting and ejected jets ahead of the choking section. As a resuh, the ejector a = 0.5, X' = 1.925, studied in detail in [24], with a slotted extention L/D = 1.89, S = 10%, with a quite broad regulation characteristic in the region of low ejection coeffi- cients k (Fig. 11) provided a high compression ratio, close to &max given by the theory of the present section. In Fig. 11 the dashed curve is from the critical regime theory without perforation, 1) is the test of the ejector without perforation, 2) is the test of the ejector with per- foration, 3) is ~max from the critical regime theory.

For ejectors exhausting into the atmosphere, the variation of the maximal compression ratio ~max with the high-velocity gas relative pressure o/e = p~/p~' is of importance. The data of Fig. 12 show that the ejector designed with account for flow mixing ahead of the chok- ing section provides a considerable (several fold) increase of the com- pression ratio Sma x in comparison with the "limiting" values from the critical regime theory [10] ; in Fig. 12 the solid curve is from the theory with account for flow mixing ahead of the ejector choking sec- tion, while the dashed curve is from the critical regime theory [10].

/i to, 1"-- - -~ 0z

0 t0o 20o 300 ~oo

Fig . 11. The dashed curve is f rom er i t i ca l re - g ime theory w i thout per fo ra t ion . 1) tes ts of

e jec tor wi thout per fo ra t ion ; 2) tes ts of e jec tor

wi th per fo ra t ions ; 3) area x f rom the c r i t i ca l reg ime theory .

w Theory of the c r i t i ca l reg ime of a gas e jec tor

w i th un i fo rmly per fo ra ted nozz le extens ion . Rat iona l u t i l i za t ion of s t ream mix ing in the e jec tor ahead of the chok ing sect ion improves the e jec tor character - i s t i cs fo r low e jec t ion coef f i c ients of the order of k <

< 0.1. We sha l l show that in many cases the charac - te r i s t i cs of the e jec tor c r i t i ca l reg ime may be im-

proved s ign i f i cant ly by us ing a un i fo rmly per fo ra ted nozz le extens ion (see d iagram of F ig. 13).

~max / 108 /

/

so

#

F ig . 12. The so l id curve is f rom theory with account

fo r f low mix ing ahead of the e jec tor chok ing sect ion , dashed curve is f rom the c r i t i ca l reg ime theory [10].

The genera l p roper t ies of superson ic gas f lows in

per fo ra ted boundar ies were s tud ied in [25], where

FLUID DYNAMICS 27

cases were also investigated of the use of an ejector (autosuction) to provide in the chamber of an Eifel wind tlmnei the requ i red flow through the perforated walls of the working section.

Following [25] we shall consider in the hydraul ic formulat ion the effect of a un i lormly perforated noz- zle extension on the cr i t ica l operating regime of a gas ejector. Accordingly, there will be three gas s t reams in the choking section 2 (Fig. 13).

1) supersonic flow of the ejecting gas of area F ' with the reduced velocity X~ and total p ressure p~;

2) the port ion of the ejecting gas flow which has passed through the perforat ion with losses of total p ressure ; the area of this port ion of the flow is F~, the reduced velocity is X n , and the total p ressure is vnP o' _< p0 ~ (1 - vn is the perforat ion loss coefficient);

3) the ejected gas flowing with sonic velocity, with flow section area F , , reduced velocity k = 1, total p ressure P01 (without account for flow mixing ahead of

ie iiiKl/,'llIlzl///I/,'Iz/ ,i/lit/

Fig. 13. Arrangement of ejector with uniformly perforated nozzle

extension AB.

the choking section). (The hydraul ic effect of the per - foration which is studied in this section and the effect of flow mixing ahead of the choking section which was analyzed previous ly must be summed in the real e jec- tor). For a uni formly permeable perforat ion of suff i - c ient length the Mi l l ionshchikov-Ryabinkov condition P2 = const will be satisf ied at the choking section 2.

/0 gg "38 a

Fig, 14. Calculated character i s t i cs of the sonic ejector with a = 10.

In this case the equations of mechanics for the gas flows between sect ions 1 and 2 (Fig~ 13) may bewr i t - ten in the form

q(k,)F~ -~ q(f)F.,

q(U)F' --~ q(kz')F'-}- v~q (,'k2"' ~,',

q(k~)z(k,) F, + aq(U) z()J) F" : , q( l )z(t )F , q-

+ .v,oq (k~ '~) z (k~'~)F,~ ' + ~q (~,Z) z(k , ' )F ,

F,, '- I - F . = FI, F~ l F ' = a,

p(k=') ~p( t ) / (~ , p(~=~') ~- - -p ( i ) /vn(~. (2.1)

Analogous equations of mechanics in discharge form were wr i t ten independently by Yu. K. Arkadov in the

/ g

- - - f - ~ ~_[Z

/ "

Y,f / /.,l.r _ .

N 20 "30

Fig. 15. Calculated character - ist ic gr id of a ser ies of sonic e jectors with uni formly per -

forated nozzle extension.

analys is of an ejector [24]. The absence in these equa- t ions in expl icit form of the total p ressure losses for the port ion of the flow which passes through the per - forat ion did not permit screening out the unreal izable (within the f ramework of the theory) flow reg imes,

~n

0. 75

0.5#

i ___ ,_

M a=15

o I /0 20 30

Fig. 16. Required hydraul ic character i s t i cs of the per - forat ion for a ser ies of sonic

e jectors .

to determine the requi red perforat ion character is t ics and establ ish the region of prof itable use of the uni - formly permeable perforat ion. It should be noted that such theory is not applicable at all for the e jector con- s idered by Arkadov [24] s ince for X' = 1.925 and a = = 0.5 this theory yields v n > 1.

The system of equations (2.1) can be t rans formed to the following form, which is convenient for calcu- lat ing the character i s t i cs of an ejector with uni formly perforated nozzle extension.

Let a, a, k' be given:

p(k2') = p(t) / a , (2.2)

~(k~-) = Aq(kt ) [z(~.,) - - 2] + B,

z~.[ t - q (~) ] = CT (Z~.). (2.3)

28 MEKHANIKA ZHIDKOSTI I GAZA

The fol lowing notations are introduced in (2.2) and (2.3):

a A- -

aIq (;~')-- q(~')] '

q(x~ )z(~ ) B = q(W)z( ) J ) - - ' " , q (;~') - - q (2~2")

C = {q(~;)-- q(Z2')] a 7" aT(1) , T(~.) = To ' (2.4)

p (~2") aq (~) ,Vr t - - ]s - - ~ p(Z2 n) ' crq(Z')

z(kn ) kz()~t) z()J) gq (k') ( i ---- , e - - 9 (2 .5 ) i k (t

The value of the reduced velocity X z' is determined f rom (2.2). The solution of the system (2.3) deter - mines the value of x2n and 2h(~ ). Then, f rom (2.4) and (2.5) we find the remain ing e jector parameters , in- cluding the perforat ion hydraul ic character i s t i c Pn.

q~

0s0

:0 Zr 30 6

Fig. 17. Var iat ion of reduced gas flow rate function q(Xi) versus the pressure rat io (r for per forated sonic e jectors .

Figures 14-17 show the results of the calculation of the charac- teristics of a series of sonic ejectors (k' = 1) with uniformly perforated nozzle extension. In Fig, 14 the characteristics of the sonic ejector with a = 10 with perforation (solid curves) are compared with the theoretical characteristics of an ejector without performation (dashed 9 curves, based on the critical regime theory) with the same nozzle geometry. We see that the use of perforation in the sonic ejector in- creases significantly the performance of an ejector for moderatevalues of the ejection coefficient of the order of k -< 1.0; for a given pressure differential o across the ejector, the ejection eoefficignt increases by about Lxk ~ 0.1. The calculated characteristic grid for a series of sonic ejectors with uniformly perforated nozzle extension is shown in Fig. 15. In the region of small values of the ejection coefficient of the order of k -< 0.1 we can expect that the experimental character- isties will lie above the theoretical values because of the effect of flow mixing ahead of the choking section, considered previously in section 1. Figure 16 shows the required hydraulic characteristics of the perforation for this series of sonic ejectors. Figure 17 shows the calculated values of the reduced low-velocity gas flow rate q(kl) as a function of the pressure differential o across the ejector. The data of Fig. 17 i11nstrate the broad regulation characteristics of the sonic ejectors with perforated nozzle extension.

As a whole the results of this study show the possibility of a sig- nificant improvement of the critical operating regime of the gas ejec- tor by rational utilization of flow mixing ahead of the choking section in the ejector chamber and the use of the hydraulically perforated nozzle extension.

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3. I. H. Keenan, E. P. Neuman, and F. Lustwerk, "An invest igat ion of e jector design by analysis and ex- per iment ," J. Appl. Mech. vol. 17, no. 3, 1950.

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14. W. L. Chow and A. L. Addy, " Interact ion be- tween pr imary and secondary s t reams of supersonic e jec tor systems and the i r per fo rmance character i s - t ics , " AIAA J . , vol. 2, no. 4, 1964.

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16. H. H. Korst, "Zur theoret ischen best immung des del lendruekes a lge lSster s t remmung," Oster r . Jng. Arch . , vol. 11, no. 3, 1957.

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18. D. R. Chapman, "An analys is of base pressure at supersonic ve loc i t ies an0 compar ison with exper i - ment," NACA Rep. , no. 1051, 1954.

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FLUID DYNAMICS 29

20. P. Cur r ie re and M. Siriex, "Facteures d' in- f luence du reco l lement d' un ~cou lement superson i - que," ONERA TM 20, 1961.

21. R. K. Tag i rov , "Effect of initial boundary layer on base pressure , " Izv. AN SSSR, MZhG [Fluid Dy- namics ] , no. 2, 1966.

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23. N. N. Slavyanov and R. K. Tagirov, "Exper i - mental study of the effect of specific heat rat io on base pressure behind an annular step," Izv. AN SSSR, MZhG [Fluid Dynamics], no. 4, 1967.

24. Yu. K. Arkadov , "Gas ejector with longitudinal nozz le per forated by longitudinal slots," Izv. AN SSSR, MZhG [Fluid Dynamics ] , no. 2, 1968.

25. G. L. Grodzovsk i i , A. A. Nikol'skii, G. P. Sv ishchev, and G. I. Taganov , Superson ic Gas F lows in Per fo ra ted Boundar ies [in Russian] , I zd-vo Ma- shinostroenie, 1967.

26. Yu. K. Arkadov , "On the possibility of improv- ing the character ist ics of the gas ejector by altering the chok ing condit ions," Repor t at Th i rd Conference on Mechan ics , Summar ies of Reports , AN SSSR, Mos- cow, 1968.

16 February 1968 Moscow