RESEARCH MEMORANDUM

PERFORMANCE CHARACTERISTICS OF AIRCRAFT COOLING

EJECTORS HAVING SHORT CYLINDRICAL SHROUDS

By Fred D. Kochendorfer and Morris D. Rousso

Lewis Flight Propulsion Laboratory

b

Cleveland, Ohio-I mitm’h e,ac1.0( I!,IP%+’.ll$,.LJ.ML%S..%H%A< y

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NATIONAL ADVISORY COMMITTEEFOR AERONAUTICS

WASHINGTONMay 22, 1951

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https://ntrs.nasa.gov/search.jsp?R=19930086635 2020-06-22T16:50:55+00:00Z

TECH LIBRARYKAFB, NM

NACA RM E51EOl-~

NATIONAL ADVISORY COMMITTEE FOR

RESWCH mowm

1:1111111111111111101143202

AJ3RONAUTICS

F PERFORMANCE CHARACTERISTICS OF AIRCRAFT COOLING EJXCTORS~

HIWING SHORT CYLINDRICAL SHRCUDS

By Fred D. Kochendorfer and

SUl@MRY

The factors affecting the performance

Morris D. Rousso

of ejectors suitable for air-craft cooling cureinvestigated theoretically and experimentally. Theinvestigation covers a range of shroud-to-nozzle diameter ratios from1.1 to 1.6, of shroud lengths from 0.2 to 2.28 nozzle diameters, ofsecondary-to-primaryweight-flaw ratios from O to 0.12, and of ambient-to-nozzle pressure ratios from 0.7 to 0.06.

It is shown that for low values of the ratio of the jet ambientpressure to the nozzle-inlet total pressure the primary jet expands toa supersonic velocity as it leaves the nozzle. For the case with nosecondary flow, the expansion continues until the jet strikes the shroudwall and a stable supersonic flow in which the primary stream completelyfills the shroud is established. With secondary flow, both streams

\ accelerate until the secondary Mach number equsls unity, that is, untilthe shroud “chokes.” In both cases the flow up to the shroud section

b for which the e~ansion ceases is relatively independent of mixingeffects.

The results of a simplified theoretical analysis based on eachtype of flow are in good agreement with those experimentally obtained.

INTRODUCTION

Ejectors are currently being considered to provide combustion-chamber and tail-pipe cooling for high-speed jet aircraft because theymay meet the cooling ~equirements with little loss or possibly withsome gain in thrust characteristics. The usual advantages of ejectorsover other pumping ’devices- lightness and simplicity of constructionand maintenance - =e also important factors.

V?xriousdesign considerations distinguish the ejector suitable for*aircraft cooling from tbe type commonly employed heretofore. A COOli~

ejector must pump a small amount of cooling air (probably about 5 per-* cent of the combustion air) through a small pressure rise. In fact,

depending on the type of cooling-air intake employed and on the ducting

I’ERI’HAH[NTd;i.. .,r.- ,-. * ~

2 NACA RM 3Z53X01n

losses, a pressure drop may be available for an appreciable range offlight speeds. One of the most impo%ant geometrical requirements

.b

for an aircraft installation is that the shroud or nixing section be...

as short es possillle. In addition, current aircraft design practice.

usually includes a convergent primary nozzle rather than the convorgent-divergent t~e commonly used with indrdmial eJectors. As a result of ithese differences, few existing performance data are applicable to the .+

design of aircmiit ejectors.-

An investi~tion of cooling ejectors is therefore beimg conductedat the NACA Lewis laboratory. The performance of short, conical-

—

shroud ejectors reported in references 1 and 2 represents the firstphase of these studies. The internal flow is studied herein in detailto gain an understanding of the o@?ating yinciples. In order tosimplify the interml flow as much as pssiblel cylindrical shroudswere employed. .—

The investigation covered a range of shroud-to-nozzle diameterratios from 1.10 to 1.60, shroud lengths up tosecondary-to-@mary weight-flow ratios from Oambient-to-primary pressure ratios from 0.7 to

sYME?oLs

The

A

a

cD

iz

L

(L~p)c

M

P

P

(p#3)m..

follow~ s~bols

area

area ratio, AS/AP

constant

diameter

acceleration of

shroud length

critical shroud

Mach number

total pressure

static pressure

ni~~ eJector

2.28 nozzle diameters,to 12 percent, and

—

0.06.

are used in this report: 4

d

gravity

length

pressure ratior —

r ‘W%!s!a

NACA RVE5UZ01.

4

NPCMN

(po/pp)bbre*-of’f Primary press~e ratio

R gas constant

T total temperature

v velocity

w weight flow

x distance downstream of nozzle exit, primry diameters

a area ratio, A1/~

1- ratio of specific heats

P mass density

T temperature ratio, Ts/Tp

m weight-flow ratio, ws/wp

Subscripts:

P primary stream at nozzle exit

s secondary stream at nozzle exit

w shroud wall

o Jet ambient conditions

1 primary stream after acceleration

2 secondary stream after acceleration

APPARATUS AND XmmmIRE

The ej~ctor apparatus schematically shown in figure 1 consisted offour interchangeable primary nozzles, a p~te containing the outer wallof tinesecondary passage, a secondary chamber, and a number d cylindri-cal titerlockjng shroud rings.

4 NACA RM E51EOl.

All shroud rings had an inside diameter of 1.40 inches. Byselecting the proper rings, tinetotal shroud length could be variedfrom O to 4.0 inches in 0.25-inch increments. Shroud-wall pressureorifices were 0.020-inch dismeter holes spaced 0.25 inch betweencenters.

The throat diameters of the primary nozzles were such that theavailable secondary-to-primary@iameter ratios were 1.10, 1.20, 1.40~and 1.60. The constant-area throat sections were 1.5 inches long. Aprelimi.nsrytest showed that the total-pressure loss through the nozzlewas less than 0.4 percent of the inlet totsl pressure for all nozzles.Consequently, the primary total pressure was assumed to be atmospheric.

The secondary passage was designed so that the secondary stresm-entered the shroud almost axially. At the shroud entrance, the anglesbetween the center line and a tangent to the outside and insidesurfaces of the passage were 0° and 5°} respectively. A check on thesecondary flow near the shroud entrance showed that the curvature ofthe passage resulted in a static-pressuredifference between the insideand outside passage walls of about 0.4 percent of the average staticpressure. The passage friction loss was found to be less than 0.5 ler-cent of the secondary-chambertotal pressure for all required secondaryflows. The chsmber pressure was therefore used as a measure of thesecondary total.pressure.

The ejector assembly was mounted on a low-pressure receiver havingan 8- by 9-inch cross section. The receiver was connected to thelaboratory exhauster systemj any pressure between 2 inches of mercuryabsolute and atmospheric could be obtained by throttling. The jetambient pressure was measured by four static orifices in the receiverwall ●

Atmospheric air was used as both the primary and secondary fluid.The primary air entered the nozzle directly from the room, whereas thesecondary air passed through a calibrated rotameter and a throttlingvalve and was then divided into two streams that entered the secondarychamber at diametrically opposite points.

During the course of the preliminary investigation, humidity wasfound b effect ejector performance; this effect, slthough small, wasnot negligible if reproducible results were to be obtained. It wasfound that if the air used had a temperature of 70 + 5° F and a dewpoint of 20 + 10° F the spread in data in no case e=ceedeci2 percent.Consequently; these limitations were used for,all runs reportedherein.

k

—

—.

NACA RM E51E01 5

?

●

For each ejector conf@uration, the secondary weight flow was heldconstant and the jet ambient pressure was varied in steps from a lowvalue to a value such that the primary nozzle was just choked, that is,to a value such that the ratio of the shroud-wall static pressure forthe orifice nearest the primary nozzle exit to the primary total pres-sure equalled 0.528. This limitation frequently resulted in smbient-to-pr=y total-pressure ratios as lsrge as 0.7. For each value of theambient pressure, readings of the shroud-wall pressures and of thesecondary total pressure were taken.

EXPERIMENTAL RESULTS

The experimental ejector-performance curves sre presented in fig-ures 2 to 5 for shroud-to-nozzle diameter ratios of 1.60J 1.40~ 1.20Yand 1.10, respectively. For each curve the ejector pressure ratio

%/pp is shownas a function of the primary pressure ratio p~Pp for

a constant value of tineweight-flow parameter afi, which is definedas the ratio of secondary-to-primaryweight flows multiplied by thesquare root of the ratio of secondsry-to-primsrytotsl temperatures.Although the primsry and secondsry temperatures were equal (T = 1) forall runs reported herein, ~~ will subsequentlybe shown to be theproper =iable for short ejectors.

An inspection of figures 2 to 5 shows that for the lower values ofthe Fritnsxypressure ratio the ejector pressure ratio for each curve isindependent of the primary pressure ratio and represents the minimumvalue obtainable for the particular value of the weight-flow parameter.As the primary pressure ratio is increased a value, which will be here-inafter called the break-off pressure ratio, is reached for which theejector pressure ratio increases. It can be seen that at break-off theabruptness of the change in ejector pressure ratio decreases tithincreasing values of the weight-flow paraneter. For vslues above break-off, the ejector pressure ratio increases almost linearly with theprimary pressure ratio.

Because of the irregularity of the performance curves, the selec-tion of an ejector to fulfill specific coding requirements will involvea careful evaluation of the effects of ejector geometry on performance.For example, at a constant ejector pressure ratio an increase in thedisrneterratio or a decrease in the shroud length results in an increasein the weight-flow parameter for primary pressure ratios less thanbreak-off, but usually results in a decrease in the weight-flow parsm-eter for pressure ratios ‘greaterthan break-off.

In order to illustrate these effects, the flight performance of a. few typical ejectors was determined. In all.cases it was assumed that

6 NACA R.ME51.EO1.

the efficiencypressure ratio

of primary diffusion was 0.95 and that the totalacross the engine was 2.0. Secondary-diffuserefficien- b

ci.es were taken as O and 0.6. Curves of weight-flow parameter as afunction of primary pressure ratio or flight Mach number are presentedin figure 6. The effects of changes in diameter ratio can be foundbycomparing curves A and B or C and D. For the assumed conditions, ‘--increasing the diameter ratio increases the weight-flow parameter overthe entire range of flight Mach numbers. On the other hand, theeffects of increasing the shroud length (curves A and C or B and D) aresuch that the weight-flow parameter is increased for low Mach numbersand decreased for high Mach numbers. If the efficiency of secondarydiffusion is increased to 0.6 (curves E and F), the curves intersectat a lower Mach number and the shorter eJector has a greater pumpingability over a large part of the Mach number range. Obviously, thereis no “best” ejector. Even when cooling requirements are specified,tinechoice may not be clear cut, particularly when the effect ofejector geometry on the net thrust minus drag is considered.

ANALYSIS AND DISCUSSION

Examination of the experimental curves shows that ejector perforni-ance for the lower values of primary pressure ratio will be completelydetermined if the factors that affect the values of the minimum ejectorpressure ratio and the break-off pressure ratio can be evaluated. Somecharacteristicsof the internal shroud flow can be immediately seen.The fact that the ejector pressure ratio canbe independent of the pri-mary pressure ratio indicates that a sonic or supersonic flow is estab~””lished in which the primary and secondary streams completely fill the

.. shroud. The abmpt change in ejector pressure ratiO that OCCurS fOr 10W

values of the weight-flow parameter is further evidence of supersonicflow because this is exactly the characteristicthat would result fromthe passage of a shock upstre~ to the section at which the expandingprimary stream meets the shroud. In addition, the fact that decreasi~the shroud length resulted in an increase in the weight-flow parametersuggests that mixing is not the principal factor affecting ejector per-formance for low primary pressure ratios.

An idealized flow will be assumed in which the primary streamexpands to some lower pressure as it leaves the nozzle and establishesa condition of supersonic flow. Mixing effects till be neglected.The cases with and without secondary flow will be discussed separately.In each case, the first step in the atiysis will be to compare thecharacteristicsof an idealized frictionless flow with tiaoseexperi-mentally observed. If the agreement is good, the next step will be tocompare the ‘experimental results quantitativelywith those obtained byapplying the equations of conservation-ofmgssidealized flow.

and momentum to the

?“

6

.

. P.–-

.

NAC!ARM E5U301

No Secondary Flow

7

r.?1--1

If the expanding primary Set strikes the shroud wall and estab-lishes a s’tble supersonic flow in which the stream completely fillsThe shroud, the general effects of variations in the primary pressureratio upon the shroud-wall-pressuredistribution should be similar tothose observed with convergent-divergentnozzles.

l%rperimentalshroud-wall-pressuredistributions for several veluesof the primary pressure ratio ~e shown in figure 7 for a typicalejector. The curves illustrate the effect of primary pressure ratioupon the well-pressure distribution.

For low values of the primary pressure ratio, the internal flow iscompletely supersonic, the ejector pressure ratio is eq@l to (Ps/Pp)m,

and the wall-pressure distribution (curve A) is independent of theprimary pressure ratio. The peak in the wall-pressure curve (x% 0.4)marks the position of the oblique shock that results when the primarystream strikes the wall. As the primsry pressure ratio increases, thewall pressures in the downstream section of the shroud are affected byshocks that move upstream. Because the flow in the upstream section isstill supersonic, however, the ejector pressure ratio remains equal to(@’p)m. When the primary pressure ratio reaches break-off, the shock

has moved upstream to the section at which the stream strikes the walland the wall-pressure distribution (curve B) therefore represents themaximum pressure ratio that can exist at each station for a flow inwhich the stresm fills the shroud. As the value of the primry pressureretio increases above break-off, the stream can no longer fill theshroud, an annulus of semidead air surrounds the jet, and the ejectorpressure ratio increases abruptly (curve C).

If the prim=y pressure ratio is decreased from a value greaterthan break-off, the orde”rof events may not be completely reversed.Above break-off the,pressure ratio that governs the amount of primaryexpansion (that is, the ejector pressure ratio) is less than theprimary pressure ratio by a factor that depends on the mount of mixing.A decrease in the primary pressure ratio causes a greater decrease inthe ejector pressure ratio because the increased expansion results inlarger shear forces. A primary pressure ratio is finally reached forwhich the flaw is unstable to small disturbances and changes abruptlyto the type in which the stream fills the shroud. Because the criter-ions that determine this pressure ratio are quite different fron thosethat determine the break-off pressure ratio, the two ratios may not beequal and hysteresis may result. As would be expected, the effect ismost pronounced for cases having the least shear, that is, for largedismeter ratios and small shroud-length ratios. Examples of hmrkeresis

u can be seen in figures 2(a) and 2(b)~

8 NACA RM E51EOl.

Because the wall-pressure distributions confirm the assumed flow,it is reasonable to compare quantitativelythe results of an analysisbased on the assumed flow with those experimentally observed. The one-dimensional equations for conservation of mass and momentum can bewritten for the section of the shroud between the primary-nozzle exitand a hypothetical station at which the stream fills the tube and theMach number M, and pressure p, =e uniform (section between sta-tions I and II; fig. 8). If a v’~ue is assumed for

and (pS/pp)m then become functions of the diameter

The difference between ~ and Ps depends onwhich in turn depends on tineflow that circulates in

rati~ Ds/Dp..-

the wall friction,the re@on between

the shroud wall ‘&d the expanding Jet. Because the jet strikes thewall within a relatively short distance (x s0.4 for the case of fig. 7),however, mixing effects and the resulting wall friction shouldbe smalland it can be assumed that

Although the value of the minimum ejector pressure ratio isindependent of shroud length for the preceding analysis, an internslflow of the type assumed cannot exist umless the shroud is long enoughto intercept the expanding jet. The tin- ejector pressure ratioshould therefore be independent of shroud length only for shroud lengthslonger thana critical value (L/Dp)c that depends upon the diameter

ratio. For shroud lengths shorter than the-critical value, it isreasonable to assume that the minimum ejector pressure ratio is thevalue corresponding to a l&andtl-Meyer expansion through an angle suchthat the jet just strikes the shroud exit.

.The details of the calculation based upon the assumptions are pre-

sented in appendix A and a comparison of theory and experiment (experi-mental values from figs. 2 to 5) is given in figure 9. The theoreticalvalues for shroud lengths both longer and shorter than the criticallength are seeb to be in good agreement with the corresponding experi-mental.values.

If the maximum value of the primary pressure ratio for which theassumed flow can exist can now be determined, the ejector characteris-tics for low primary pressure ratios will be completely explained. Thedifference between the vslue of the break-off pressure ratio and thevalue of the minimum ejector pressure ratio is due to the considerablepressure rise resulting from the shock configurationwithin the shroud.Because the value of the shroud Mach number Ml is known from the pre-

ceding analysis, the pressurethis lbch number can be found

increase resulting from a normal shock atas a function of the diameter ratio. The

.-

—

—

—

w

1

11

NACA RM E51EOl 9

‘detailsof the calculation are presented in appendix A and a comparisonof the theoretical and e~erimentsl values of the break-off pressureratio is given in figure 10. Also included are experimental wa3d.-pressure distributions at break-off conditions (similar to curve B offig. 7) for relatively long shrouds (L/DpZ 4). & wouldbe expected,

the wall-pressure curves for the long shrouds can be used to estimatebreak-off pressure ratios for shorter shrouds. For shroud-length ratiosor downstream distances greater than 1.0, the experimental curvesapproach vslues that ~e in good agreement with normal-shock theory.The fact that lengths of at least 1 shroud diameter are required toobtain the pressure increase corresponding to a normal shock is inagreement with the observations of other experimenters. (See, forexample, reference 3.)

Although for primary pressure ratios less than break-off, ejectorcharacteristics can be explained by a flow in which friction and mixingeffects are neglected, the difference between the primary pressureratio and the ejector pressure ratio for curve C of figure 7 is evidencethat mixing between the primary core and the semidead air region has animportant effect on the performance characteristics for primary pressureratios greater than break-off. As a result, ejector performance isrelatively dependent on shroud length for the higher primsry pressureratios. At a diameter ratio of 1.20, for example, increasing theshroud-length ratio from 0.43 to 1.29 (figs. 4(b} and 4(e)) causes adecrease of more than 20 percent in the ejector pressure ratio for aprimcry pressure ratio greater than break-off, whereas the same increasein shroud length changes the ejector pressure ratio by 0nly5 percentfor low primsry pressure ratios. For primsry pressure ratios such that(PO/pD)b‘ PO/Pm ‘ 0.7} mixing effects sre almost independent of pres-sure ~atio fid ;he ejector pressure ratio is given

where C depends only on ejector configurations.

Secondary Flow

Because the static pressure of the secondarylower than that of the primady for the station atexit, the primary stream expands as it leaves the

by

(1)

stream is ordinarilythe primary-nozzlenozzle. Because this

expansion reduces the secondary-flow s&ea, the secondary stresm acceler-ates and, if it is assumed that little energy exchange occurs, the pres-

. sure drops causing a further expansion of the primary.

It has been shown that along a curve of constant weight flow theu ejector pressure ratio becomes independent of the primary-pressure

10

ratio. Consequently, the streams must accelerateMach number equals Unity and the shroud “chokes.”

NACA RM E5JE01.

until the secondarySo far, the process w

does not depe&3 on mixi&. It should be noted, however, that secondaryacceleration beyond sonic velocity is impossible in a constant-areashroud unless accompanied by energy exchange.

Wall-pressure distributions can again be used as a check on theassumed flow. The curves of figure 11 are typical of the experimentaldistributions for ejectors with secondary flow. For low primary pres-sure ratios, the wall-pressure distribution (curve A) is independent ofyrimary pressure ratio and the ejector pressure equals its minimumvalue. The sharp increase in wall-pressure ratio observed for the casewith no secondary flow (fig. 7) is absent and the wall-pressure ratiodrops with downstream distance in accordance tith the assumed flow. Asthe-primary pressure ratio increases above that corresponding tocurve A, a shock moves upstream into the primary core. Because mixingeffects are probably small, the secondary Mach number cannot be muchgreater than unity and the pressure rise required of the secondarystream must be obtained principally by diffusion. Ihring this processthe flow area of the secondary stresm increases and that of the primarydecreases the requirement of constant total erea can therefore be Sat-

isfied. At break-off (curve B), the pressure rise of the secondarystream equals the maximum value available from the combined effects ofmixing and diffusion. Consequently, any further increase in the pri-mery pressure ratio requires an increase in the ejector pressure ratio.For the ejector and weight-flow condition of figure 10, the ejectorpressure ratio does not change abruptly but Increases &ost linearlywith primary pressure ratio. In addition, the combined effects ofmixing and diffusion are,such that the break off pressure ratio approx-imately equals the minimum ejector pressure ratio; that is, the over-alleffect is the same as that which would result if the secondary streamwere diffused isentiopically to zero velocity.

In order to obtain quantitativeresults for the assumed flow, theconditions for conservation of mass and momentum are employed for thesection of the shroud between stations I and II (fig. 12), As in the

case of no secondary flow, if an assumption is made as to the Tressureat the downstream station, the value of (Ps/Pp)m canbe obtained as afunction of Or and %@ “ The fact that the wall-pressure curve

of figure 11 is smooth and continuous for the region near the nozzleexit suggests that the primary expansion may be nearly isentropic. Ananalysis based on the proposed flow and on the assumption that the pri-mary flow is isentroplc up to the section at which the secondary Machnumber equals unity is Tresented in appendix B and the results aregiven in figure 13. The curves represent the theoretical variation of-the minimum ejector pressure ratio with dismeter ratio for severalvalues of the weight-flow parameter. For completeness the values for(lJfT=o are also included.

—

—.

?=

—

4

.—

—

—

m

w

‘?

?fACARM E51EOl 11 -

Tne theoretical and experimental values are compared in figure 14.u As in the case of no flow, a value of the shroud-length ratio exists

beyond which the experimental velues of the minimum ejector pressureM are independent of shroud-length ratio. The experimental values forPPA shroud lengths greater than critical are in good agreement with the cor-n> responding theoretical values. For the range of the variables covered

in the investigation, the assumption of isentropic primary expansiontherefore appears to be Justified.

Because the ~ pressu,e increase that can be supported by thesecondary fluid depends on the amount of mixing between the primary andsecondary streams and on the amount of secondary diffusion that can beaccommodated, no simple analytical method for the determination of thevalue of the break-off pressure ratio could be found for the case ofsecondary flow.

In a similar manner, the relation between the ejector pressureratio and the primary pressure ratio for values Of primary pressureratio greater than break-off depends on the effects of mixing and dif-fusion. In general, equation (1) is still valid but the value of theconstant C depends on the weight-flow perameter as well as on theejector confi~ation.

SUMMARY OF RESULTS1

The following results were obtained in an investigation of air-craft cooling eJectors having short cylindrical shrouds:

#

1. For low values of the ratio of the jet ambient pressure to theprimary total pressure, the performance of aircraft cooling ejectorscould be adequately explained by the methods of nonviscous fluidmechanics. Mixing effects could be neglected.

2. When no secondary flow existed, the expanding primary jetstmck the shroud wall and established a stable supersonic flow inwhich the stream completely filled the shroud. The Mach number of theexpanded flow and the ejector pressure ratio depended only on the ratioof the shroud to nozzle diameters except for tinevery short shroudlengths. The ejector pressure ratio was independent of the primarypressure ratio until the primary pressure ratio reached a value corres-ponding to a normal.shock at the expanded Mach nuniber. The supersonicflow then broke down and the stream no longer filled the shroud.

3. For the case of secondary flow, both streams accelerated untila condition was reached such that the secondary Mach number was unity.The ejector pressure ratio depended upon the ratio of secondary-to-.primary weight flow, the ratio of secondary to primsry temperature, andthe di’ameterratio.

12~

NACA RM E51EOl

4. The theoretical values obtained by employing the equations forconservation of mass and momentum were in good agreement with thecorresponding experimental values.

Lewis Flight Propulsion Laboratory,National Advisory Committee for

Cleveland, Ohio.Aeronautics,

NACA RM E51EOl

*

APPENDDY

A- EJECTOR THEORY - NO SECONDARY FLOW

Shroud-Len@n Ratios Greater Than (L/Dp)cNG The one-dimensional equations for the conserntion of mass andh..-

momentum is written for the section of the shroud between stations Iand II (fig. 8). First, in accordance with the proposed flow, thefollowing

(1)

(2)

(3)

assumptions can be made:

Adiabatic flow,‘P

= T1

P~/Pp= (p&)m

%=1

Let a=As/~- (D~/Dp)2. The equation for the conservation of massis then

‘p =W1

or

and the equation for the conservation of momentum isw

2pp+pvPP

ap, +aplVl2+ (a-l)pl = _

or

Pp(l+r) + (a-l)pl = ap1(l+tiJ12)

Equations (2) and (5) can be combined ta give

a= 1

(2(7-+1) 1 i-IQ2 !12)

- yM12

13

(2)

(3)

(4)

14 NACA RM E53E01

The

(1]

(2)

Thebe found

(1)

(2)

The

4

method of solution is as follows:“

Assume Ml

Calculate a and pl/Pp = (P~/Pp)m from equation (41 $.

corresponding value of the break-off pressure ratio can thenas follows:

Find static-pressureratio across_normalshock at Ml> Py/Px

C!d.c~ate (p~/pp]b = (~/pp)(pY/px)

ratios (Po/pn)b and (p~/pD)m are nowtion as ~nctionsof a and therefore

Assume that the

a; functions of ;he dismeter ratio Ds/Dp.

Shroud Lengths Less Than

primary fluid undergoes a

(L/Dp)~

l?randtl-Meyerexpansionfor the

——such that it ~ust strikes the shroud exit. Assume also that

diameter ratios under consideration two-dimensional flow is sufficientlyaccurate.

Then (Ps/PP)m is the pressure ratio corresponding to an expan-sion through an angle u (see for example, reference 4), where

v. tan-l Ds/~ - 1

~

The ratio (Ps/PP)m is thus a known function of D@p and L/Dp.

u.

—

NAC!ARM E5UZOI

*

APPENDIX B - EZECTOR THEORYu

15

- SECONDARY FLOW

The equations for the conservation of mass and momentum will be*.

~written for the section of the shroud between stations I and II(fig. 12). The following assumptions will be made:

(1) P~=P~

(2) N$=W=l

(3) No energy interchange, Tp = T1 and T~ =T2

(4) Primary eQansion is isentropic

n

Let a = A=/Ap and

primary stream is then

a = A=/~; conservation of mass

and for the secondary stream

for the

(5)

& Conservation of momentum for the combined flow is

or

~(~+-r) + (.-UPS(1 + %2) = qpl(l +TM12) + (a-a)pl(l+r) (7)

Equations (5), (6), and (7) can be combined to give

“F= %/pp * = (=-0) P1/Pp ==+s s-

(8)

where.

.

16 NACA RM E51EOl

and

F/F* .

A/A*.

The

(1)

(2)

method of solution is as follows:

Assume Ml ad Ms Y

(F/F*)s, =d(A/A~s

(3) Compute CDF= (F/F~l -2/( F/F~s -1

( r %(4) Compute a = ~ ‘-1 ~ ~ + u

CJF (A/A7s

(5) Compute (Ps/Pp)m= ~-1

8

4

Because the values of (Ps/Pp)m, a, and u~ can be obtained ~or

any assumed set of values for Ml and Ms, (Ps/Pp)m canbe obtained

as a function of a and w~.

REFE13ENCI13 ~~~ -—

1. lh.dd.ledionjS. C. wil~ted, H. D., and Elli~} C. W.: Performanceof Several Air fiJectorswith Conical Mixing Sections and Smllsecondary Flow ~tes. NACA ml E8D23~ 1948=

2. Wilsted, H. D., IIuddleston,S. C., and Ellis, C. W.: Effect ofTemperature on Performance of Several Ejector Configuratims.NACARME9E16, 1949.

3, Bailey, i’?.P.: Abrupt ~rgy Transformation in Flowing Gases.A.S.M.E. Trans., vo1. 69} no. 7) Ott* ~947~ PPo 749-757;discussion, pp. 758-763.

4. The Staff of the Ames 1- b~ 3-Foot Su rsonic Wind-Tunnel Section:rNotes and Tables for use In the Ana ysis of Supersonic Flow.

NACA TN 1428, 1947.

—

.

3 NACARM E51EOl*

Primsr flow

I

Secondary

m Z%

HillY

Shroud lengthvaried by vary-ing nuniberofrings

\ ‘“eT’=’I

Po

Figure 1. -.Diagramof ejector apparatus.

U3 NACA RM E51XOl..

.6

/

.5

.4

Weight-flow

.3rmrameter

/

// ‘ // /

.1

.4

.3

.2

.1

0

1 I 1 1 1

(a)Wrmud-lengthra~i.,L/Dp,0.57.

I

d ‘

/ //

/

dA

A? ?

?f

t‘+- .

~.1 .2 .3 .4 .5 .6 .7

Primarypresswe ratio,p~Pp

(b) Shroud-lengthratio,L/~, 1.14.

—

——

“.-.-y.

a

‘

.

Figure 2. - Ejeotor perfo~ce curves. Diameterratio D@p, 1.60.

~=

/

NACA RM E51XOl

n.

.

.

h5 (c)Shroud-lengthratio,~, 1.71.:.

>

1 1 1 1 1 1 t 1 , , t I

p!?+iqI

o .1 .2 .3 .4 .5 .6 .7

Prhary preamre ratio, P~pp

(d)Shroud-lengthratio,L/Dp, 2.28.

F@mre 2. - Conaluded. EJectorperformancecumvea. DiameterratioD@p, 1.60.

19

NACA RM E51EOl

.6,

.5

A

.4 A

.3 A

Weight-f’lowparameter

J Uw

T

i

- /

8

0.2 .041

.0s3

.123/

CT’.1>

.2udLlo

g .6 .

(a) Shroud-length ratio, L\l+, 0.25.

mal&9+

8/

:.5

%A

M

.4

,

.3

m ~ -

.2-v

/

n ov

.10 .1 .2 .3 .4 .5 .6 .7

Primary pressure ratio, p~Pp

(b) Shroud-length ratio,L/Dp,0.5,Figure 3. - Ejector performance curves. Diameter ratio DJDP, 1.40.

u

-—_

-.

,.

.:

..-

..-

—

.

NACA RM E51EOl 21

.6

.5 A %

)

4 A

/

Weight-flow

.3parameter

WC

~ !+00

‘8.041.063

.2 > A .123

.1

(c) Shroud-lengt hratio,L/Dp, 0.75.

.7-

.6

.5

.4

.3—- — k — A

.2

.10 .1 .2 .3 .4 .5 .6 .7

Frlmary pressure ratio, p~Pp

(d) Shroud-length ratio: L/Dp, 1.0.

Figure 3. - Continued. Ejector performance curves. Dl&meter ratio,

-

22 NACA RM E5N301

.6

.5

.4

.3

.4

.3

.2

Weight-flowparameter

I II + I l-lP I I dl I I I I I(e) Shroud-length ratio, L/Dp, 1.50,

r I I I I I 1 I I I I I I I I

L1

.10 .1 .2 .3. .4 _ .5. .6 .7

Primary pressure ratio, p~Pp

(f) Shroud-length ratio, L/~, 2.0.

Figure 3. - Concluded. Ejector performance curves. Diameter ratio,D~Dp, 1.40. ‘L-

—

. —@—

I?ACARM E51XOl 23.

5

A

“-tlllll M/7Htl

wlow

.+’/ t I

Weight-f:parameter

.~fi

8

0.041.083

A .123.

n A J

.1(a) Shroud-lengthratio, L\4, 0.21.

1 /1

.7.

d.6-

/ / /

.5 / ‘L

A {

.4 f

/ ‘

.3 A Jv {

.2. 0

-y9y.10 .1 .2 .3 .4 .5 .6 .7

Prlmery pressure ratio, ~Pp

(b) .Wroud-lengthratio, L/Dp, 0.43.

Figure 4. - Ejectorperformance curvee. Diameter ratio D~Dp, 1.20.

NACARM E51XOl

Weight-flowparameter

W*

‘ s

o.041.08s

A .123

il (a) Shroud-lengthratio, L/Dp, 0.64.

Figure 4. -

.1 .2 .3 .4 .5 .6Primary pressure ratio, pp/Pp

(d) Shroud-lengthratio, L/~, 0.86.

Continued, Ejector Performancecurves. Diameter ratio

.-l .8

D~~, 1.20.

..

$.

A

.

‘-mulB ‘“---—

4*

.

h

NACARM E51EOl 25

.7

.6J {

.5

A

/- /

.4 J1 AWeight-flowparameter

0 IWV<F

8 0.3- .041

z.083.123

[<.2 - i I e\al

o w

.:Qah .1

(e) Shroud-lengthratio, L&, 1.29.

Primary prenmre ratio, p~Pp

iP

(f) Shroud-lengthratio, . .

Figure 4. - Concluded. Ejector performance curves.

~L%::::rat10 ‘J%’ ‘m

26 NACA RM ESIEOl

.8

/.7. f-r‘

6.

.5

&

.4/ Ifelght-flow

v/ parameter

Mm00

Q .~

z

.029~ .041&* .093.:

-

*efi .2 Y-J

(a) Shroud-lengthratio, L/~, 0.20.$ .8❑

Eo!

k.lJj .7

-c ~

w

.6- >

/

.5 /

c //“

f.4

1

.3 x

r\- ~

.2,_

o .1 .2 .3 .4 .5 .6 .7primary pressure ratio, p~Pp

(b) Shroud-lengthratio, L/~, 0.39.

Figure 5. - Ejector performanceourves. Diameter ratio DJDn, 1.10.

ESIEO1

.

.

a)h

.8.

/

.7 -n T/

/

.6 . / q

$ ~/ /{

.5.4

“ /

t

v T~

.4Weight-flowparameter

~fl1

00.3

(v

? a ~ 8

.029

.041

.083

.2

(c) Shroud-lengthratio, L\~, 0.59.

0 .1 .2 .3 .4 .5Primary preesure ra’clo,pJPp

(d) Shroud-lengthratio, L&,

Figure 5. - CMt~nue~.EJeotorperrommncecurves.

0.79.

Diameter ratio D&, 1.10.

1

NACARM E51EOl

.8

.7

.6

.5

.4Weight-flowparameter

.3

2.(e) Shroud-lengthratio, L\~, 1 16

.8

4 x — ‘.7

61

/I

/

v

s / / ‘

4

3 H

F2.-0 -.1

Figure 5. - Concluded.

.2 .3 .4 .5 .6

Primary presOure ratio, p~Pp

(f) %roud-lengthratio, I@, 1.57.

Ejeotor performance curves. Diameter ratio

.7 .6

D8/Dp, 1.10.

.

*

..*.,

E.,~....:.+..-

4

.

-.

. .a .a

=

d.L

.<

.-.

G

.

-—-.

●

.

.-

NACA RM E51EOl.

,

29

.

●

Curve Diameter Shroud-length Secondary.ratio ratio diffuser%/% L/4 efficiency

A 1.20B

0.211.40

0

c.25

1.200

D.64

1.400

E.75

1.20 .640

F 1.20.6

.21 .6

.12

Lt-

3 %

h’al .0s / /*

/ ~

[ D

&/

g

q .04

~~*

o .1 .2 .3 .4 .5primary pressure ratio, PO@p -

I1.5

J1.0 .5 0

Flight Mach number, ~

. Figure 6. - Variation of weight-flow parameter with primary pressureratio or flight Mach number for several ejectors. Primary diffuf3erefficiency, 0.95; engine pressure ratio, 2.0.

>

.6T

.5

.1

0

/

//

c

*-u

E

~ ‘--.. -- >

r/

I/

-6A —

1. / ----- -. -

I II / f I

ejector

pressure ratio1 J y

%

//

\ A-

I

IL “EJector (A) Maximum pressure retio for which shroud flow

I presswe ia coqletely independent of pressure ratio

t

ratio, P~/Pp _ (B) i?rimuy pressure ~tio SII@E tie br~-OffPrimarypressure

ratio

(c) F-r- presue ratio +x=ter t~ ~~-firatio, p#*

ratio I

I-- .-

0 .2 .4 .6 .U J..u L.G

Distance kmnetream of nozzle, x, diam

?@re 7. - !Fypieal variation of ahmmd wall pressure distribution with primry preseure ratio. Diamterratio D#$, 1.20; ehroud-lewth ratio L/1$, 1.29. lioseccaderp flar.

. . ,

NACA RM 1351ZOl.

.

31

.Figure 8. - Schematic diagram of internal flow. No secondary flow.

●

32 NACA W E51JZOl

0 .4 .8 1.2 1.6 2.0 2.46hroudlength,L/Dp

.

.

“

-.

Fiw.ue9. - Theoreticaland experimentalvariationof minimumeJectorpres-sureratiowith shroudlengthfor severaldiameterratios. No secondaryflow.

—

IWC?A“RME51zol 33

I 1Diameterratio,%/4 = 1.10

.64 \

o

-- . --- - -—-. .-—. ---- ---- ----

A.56— l— A .

A

.48

I A1

--—- — Normal-shocktheory”/‘ Fairedfromwall-pres-

suredatafor L/% m

.16 Fromfigures2 to 5symbol Diameterratioo 1.10

.08

0

/f

A 1.20

i 1.40: 1.60

I

v

.4 .8 1.2 1.6 2.0 2

8hroud-lengthratio, L/~ or

downstreamdistance,x,”diam

Figure 10. - Theoreticaland experimentalvariationof break-offpressureratio with shroud lengthratio for severaldiameterratios. No second-

.4

Sxy flow.

I &!

~ -

— -

— L - ~1 k — ~ “ ~ — ~ ~

* ejectorI

presfiure ratio1

. ---- -B

7 — -?-— - I

\I \* — ~ — ~ — ~ .— --I O- ~

— -- -- -

. / y P“ - I

/ {

I

1. / h- - —- A

–See Onaary Presmc e ratio, Pa/PpI

1/

I

1Ehrollaetit —— -

A Maximnmpremure ratio for which shroud flow I

is ccxupletelytidependent of primry pres6ure”ratio _ ,Primry premmre

IB Primary pressure ratio equals break-off ratio, pO/l?p— ‘ IC Primary prewmue ratio greater ~ bre&+fI-

11

I1,

I

.

0 .2 .4 .6 .8 1.0 1.2 1.4 1.6Mstance downatraam of nozzle, x, disau

-e ~. - NPi* ~ati~ of shroti wall pressme distribution with primmy pressoze ratio. Weight-‘lm P=t= W*, 0.@5; di=ter rEt10 11~~, 1.20j AIVUd-hIl@ ~tiO LA, 1.29.

., .

NACA RM E51XOl

*

.

Pp,

P2

M2 = 1.0

Figure 12. - Schematic diagram of internal ejector flow

for ease of seoondary flow.

35

36 NACA RM E51EOl

.8

.-?

\

.6

.029

.5

0\

.4

\

.3

,

.2

.1

01.0 1.1 1.2 1.3 1.4 1.5 “1.

Diameter ratio, D~/4

-H--k&d6

#

.

*

.

Figure13. - Theoreticalvariation of minimum ejector pressure ratio withdiameter ratio for several values of weight-flowparameter.

NACA RM E51E01

.*

●

.;al&

.

.

.

.

37

ExperimentD~/Dp

~ 1.1ov 1.20. 1.40

~ 1.60

----Theory

Diameterratio

.5 D@p ;1.10--- -—-. .-—- ---- ____ ___ . , ___

.4

— — — — —.A 1.20-.---- ___, .._____ ___ _____ __

.3 v

,/“ 1.40

.2

1.60

b A A

4.1

,

0 .4 .8 1.2 1.6 2.0Shroud-1engthratio, L/4

(a)Weight-flowparameter,um, 0.041.Figure 14. - Comparisonof theoreticalan~ experimentalvalues of minimum

ejectorpressureratio.

2.4

38 lWC?ARM E5XE01

.8

u o —.7 ~: \P c bt

Diamete~rat io

%/4

.61.10

Experiment%/Dp

, u 1.10A 1.20

.5 1.40A 1.60

---- Theory

‘A.4— — — ~o 2 1.20

-—-. ---- ——- -.—--- -— ---——- ----

4

.3

1

/’I’d.21 1 / I I I, 1 I I 1 .

.1

/

0 .4 .8 1.2 1.6 2.0

6hroud-lengthratio,L/%

(b) Weight-flowpsramet-: (Jfi, 0.083..

Figure 14. - ContLnued. Comparisonof theoreticaland experimental

2.4

values of

.

minimum ejectorpressureratio.

NACA RM E51XOl 39

.1

Experiment

w%

~ 1.20~ 1.40~ 1.60.---~ory

Diameterratio

JWp

QA

1.20—- -—— —-. .—-. -—- ——. —-.

0*/

——-----——— ——-,—--——--——

/1.60

A

—-- -——. -—— ——— ——- ——— —— -d

=3?$=

.

0 .4 .8 1.2 1.6 2.0 2.4Shroud-lengthratio, L/4

(c)Weight-flowparameter,uF, 0.123.

Figure14. - Concluded.Comparisonof theoreticaland experimentalvaluesofminimumejectorpressureratio.

NAcA.Langley.5.22-51 .495