ADP000536
ADP000536
ADP000536
AND EXPERIMENTS
* r
W
tA
u
"
^_
"T^*^*
A. L. Addyf f
J- Craig Dutton.*
C. C. Mikkelsenm
OH
August 1981
Supported by
U.S. Army Research Offica
Grant Number DAHC 04-74-G-0112
and
Department of Mechanical and Industrial Engineering
University of Illinois at Urbana-Champaign
Urbana, Illinois 61801
,rt
963
*f&m -
Mtt
TABLE OF CONTENTS
A*
Page
v
ix
-
x1
INTRODUCTION
3
3
4
6
10
16
18
13
27
31
31
33
35
39
39
3.0
71
71
71
79
EXPERIMENTAL INVESTIGATION
3.1 COLD-FLOW, AIR-TO-AIR, EJECTOR EXPERIMENTS
3.1.1 Experimental apparatus and procedure
3.1.2 Experimental results
47
53
56
58
65
65
4.0 CONCLUSIONS
101
5.0 REFERENCES
103
FII*ED
965
. B^T^^PBB^P'^-'
-
t^zmmmmmmmmfmmmm
HP-1*!* VP-W-'s.;1'.-
L|
' JBWOT
ffij^pWjg
T
Page
6.0 APPENDICES
6.1 CONSTANT-PRESSURE EJECTOR COMPUTER PROGRAM (CPE)
5.1.1 Computer program
6.1.2 Sample timeshare input/output
6.2 CONSTANT-AREA EJECTOR COMPUTER PROGRAM (CAE)
6.2.1 Computer program
6.2.2 Sample timeshare input/output
105
105
105
109
112
112
124
i
7
li
966
**dm-(W*M
-
&flf.;**-;. :",
LIST OF FIGURES
Page
Figure 2.1-1
Figure 2.1-2
' SO
PO
ATW
P0 '
Figure 2.1-3
Figure 2.1-4
Intersection of the w /w
constant Pso/Ppo
Intersection of the w /w
Figure 2.1-5
Figure 2.1-6
11
12
13
WV ' so/ PO
Figure 2.1-7
Intersection of the M
stant
Figure 2.1-3
ATM/ PO
Intersection of the M
^ant Psl/Pp0
Figure 2.2-1
17
Figure 2.2-2
19
Figure 2.2-3
28
Figure 2.2-4
30
Figure 2.2-5
34
Figure 2.3-1
36
Figure 2.3-2
40
Figure 2.3-3
49
Figure 2.3-4
60
60
61
--
62
967
<-<;
_
-*
mmmmmmmmmmm
Page
(d)
(e)
64
Figure 2.4-1
66
Figure 3.1-1
72
Axisymmetric ejector with (left to right) variablearea mixing tube with diffuser; 1.245 in I.D.
constant-area mixing tube installed; and 0.995 in.
I.D. constant-area mixing tube
73
Figure 3.1-3
74
Figure 3.1-4
75
75
75
75
Figure 3.1-2
Figure 3.1-5
!
63
l*\
ij
\
j
--
Figure 3.1-6
Figure 3.1-7
Figure 3.1-8
/A
PI
MS
/A
PI
"PI
= 2-0)
80
and
*Vi
2,0)
81
WJ
-330, '516,
and M
PI
s 2,5)
83
84
85
Pl
Figure 3.1-11
and
77
Figure 3.1-10
-330, -516,
---
Figure 3.1-9
76
76
76
76
76
MS
PI
968
-i-.
Page
Figure 3.1-12
Figure 3.1-13
Figure 3.1-14
86
88
89
P1
Figure 3.1-15
I"
Figure 3.1-16
Figure 3.1-17
Figure 3.1-19
Figure 3.1-20
Figure 3.1-21
-516'
P1
= 2 0
and P
P0/PAT,
- '
= 5 6)
'
90
91
'516' \l
2 5
and
' '
P0/PATM
5 6
' > -
92
93
95
96
p /p
P0
Figure 3.1-22
<\l'\.
Figure 3.1-18
P1
ATM
= 5.6) V..JP.
I.
97
969
i -^i iTf'i-
ii --* ,-,
,-
UMM^AMMJ
"""*?
LIST OF TABLES
Page
Table 2.2-1
32
Table 2.2-2
32
Table 2.2-3
33
Table 2.3-1
57
Table 2.3-2
58
Table 2.3-3
59
Table 2.4-1
Ejector specifications
68
Table 2.4-2
69
971
-*--
--
-...
- -
-a
P!!Pil!^i^'^a^^^&.SKrtV,.t,tl,-:; i^j^^ppi*?*-^
NOMENCLATURE
Symbols
Area
A
C
Diameter
f( )
Function
V< ).V )
g.g( )
Specific enthalpy
Length
Mach number
Mw
Molecular weight
Pressure
Gas constant
1'C2'C3
Time
Magnitude of velocity
Mass flowrate
v 7
Coordinates
Density
973
-S^^a
i ii ii ijiiwM"ga
Subscripts
1,2,3,4
System locations
ATM
Atmosphere
Back
30
Break-off conditions
cs
Control surface
Mixed
MAX
Maximum
Primary
Secondary
Total
X,Y
LV
974
mmmm
....
T.e^Ci' ;: .'";'> w
ff
1.0
INTRODUCTION
These applications
In chemical laser systems, the flow and lasing zones within the laser
cavity are established by the interaction, mixing, and reaction of multiple, two-dimensional, supersonic streams at relatively low absolute
static pressure levels.
must then be pumped to ambient conditions so that the lasing process can
be started and sustained.
tions for which the primary stream enters th mixing tube supersonically
975
*.: *s*^Si3iH*"V
The theoretical
In the experimental
976
-^____
iaj-ttumaij
il i MMaMMMWMHMWi agw
(2)
(3)
(4)
ing the calculations are described; detailed program listings and sample
input/output data are included; and representative cases are presented
and discussed.
models.
The computer programs have been written with both straightforward
subsystems calculations and overall systems studies in mind.
It is
2.1
977
1
-'- -
m-iliM
iftiiiEMiMiMBilfr
"*./
describing the performance of these systems and how their form is dependent on the internal flow phenomena.
A representative ejector configuration and the associated notation
are shown in Fig. 2.1-1.
from the stagnation state (PpoTpo) through a supersonic nozzle and the
secondary stream is supplied from the stagnation state (PS0JS0).
The
This interaction, as
well as the mixing between the streams, continues to the shroud exit
where they are discharged to the ambient pressure level P.ATM .
2.1.1
Performance characteristics
The objective of any ejector analysis is to establish, tor a
functionally by:
V*P
=f P
< S0/VPATM/PP0>
<2-M>
'
i.e., they are dependent on the stagnation pressure and back pressure
ratios.
An alternate formulation of the pumping characteristics in terms of
the initial secondary stream Mach number, M$l, the static pressure ratio
P
/P
ATM
/P
, is given in functional
form by:
M
Sl
=f P
( Sl/PPO.fWPP0)
(?-'-2>
978
HBSBSi.^?r,-W^'^.-,-^r
^*?a*'vv*~rtfsr*KH^nw?,i:
c
o
o
c
a
<0
c
o
3
fc.
u
so
u
CM
s.
979
&MMM
MHHMMf
ipwpt,mipi
y'^'*""":...:.':~:.:'''".:,\ '-'"-r'r"^^^^^
This selection of variables, although less obvious, is convenient for performing the numerical calculations involved in many theoretical ejector
analyses.
In addition to establishing the functional form of the pumping characteristics, another quantity of interest is the shroud wall pressure
distribution given functionally by:
distribution.
fl
2.1.1.1
ATM/ PO>
and
/P
< SI SI
PO' W PO>'
respectively.
delineates the flow regimes wherein the mas* flow characteristics are
independent or dependent on the ambient pressure level.
These flow
980
- -
'Mr "***-
IM
wr^r^'^''-*^r^'~^-iM'!mmmgi^^
i,uWW..I.1-....,.i,, "wqBWBMMiW
o
CO
u
J10
4.
0)
-t->
O
3
i-
10
to
fc.
o
4->
CN4
I
981
. ,. .-
HM&aiMMi
,M
.-,..,
.......,7^.,;. .,,-,-;,.,,.
!T
TOWP^^MBtw^ffW^^
be represented by:
W
s/WP
when P
/P
ATM
PO
(2.1-4)
f P
( 30/PP0)
- ^ATM^PO^BO-
'
"break-ff curve"
= 0 (base
=f P
ATM/PP0
( S0/PP0.PATM/PP0)
(PATM/PPO>BO-
In principle, ,..
However, the
Points on
the "break-off curve" are determined by the condition that transition from
dependence to independence of the mass flow characteristics on the
ambient pressure level will occur when the secondary stream just attains
sonic conditions either inside the mixing tube or at its entrance.
This
C
9b2
i mm
MmM
Break-off
Curve
i.A.
/P
ATM
PO* Dependent
^Tn/Ppo
Figure 2.1-3
983
^^J^.^....... - .
..
--
-:
.,*
^^^Jt.
M^aaiAliM
*m
wmmmmmm
wmmmt^mm.wwmmm>Mm!Bm
/P
ATff
P0
-inde[7end'
Figures 2.1-2 and 2.1-3 generally have their principal value in presenting
an overview of the performance characteristics of typical ejector systems.
In theoretical analyses or experimental programs, it is often more convenient to consider two-dimensional parametric representations of these
operating surfaces.
i.A.
of constant
Fig. 2.1-5.
p
ATM/ pot
S</ PO
surface by planes
ATI/ PO
Fig
2 1-6
latter
situation corresponds to
984
i ii
HI in ma
i * nliiiia^-r..i
tJSmm^mmm
M^MaMMaHMkBBMd
v,,,-.-,
ii^iamill
'WiiWWU.||
o
0.
5
O O O 0) E
-t->
o
SO g d>
o
o
0?
<0
li
s10
c
o
u
m
fc.
C\4
a
u
985
Ai
nrMiiDMIMli miMH
- "
^PW^SB^TT^^JT^
4P
o
a.
o
CO
(0
c
o
o
l/>
r'
Q.
XI
u
<-
s-
3
in
2
<u
c
o
0)
i.
IT)
I
CM
t3
986
-*i MWHife*
-
^pww^r.
,:<r^^>vrr^~<r7*r*'>*^^
'^-wr^
o
a.
o
to
Q.
II
o
a.
5
0)
ItJ
o
i.
5
0>
0)
I
CM
987
^^~>rw^~,~~^,mmvw,,.isiiu.)m,,j
i(W
5
c
<0
+>
1
c
o
u
en
0)
<0
I
Q.
0)
i.
l/l
0)
x:
*.
c
o
0)
t.
01
988
-^
..^w^~r^~-*~~^r-,^
o
a.
c
to
c
o
o
in
0)
u
i.
3
'i
fi
ft)
u
o>
01
00
989
^BU^MB
^^^kMiMiHiM
O
2,2
CONSTANT-PRESSURE EJECTOR
A schematic of a constant-pressure ejector is shown in Fig. 2.2-1.
the mixing section, the mixing section area distribution must be different
for each operating point of the ejector.
no problems from a theoretical standpoint, it does present several problems from a practical hardware standpoint.
analysis does not provide any information on the mixing section area distribution between the entrance and uniform flow sections, Sections 1 and
2, respectively, in Fig. 2.2-1.
Assuming
for which the static pressure is constant for a given ejector geometry and
990
m0tKm^tmmmmammti
Constant-pressure
mixing section
Subsonic
secondary flow
*'
'/////////tftf/tf(///////////////////////S///////////////.
Uniform
>-supersonic
mixed f'ow
1)
Uniform
subsonic
mixed flow
Figura 2.LA
991
1
kMKU
operating point, the operation of this ejector at any point other than the
design point would, most probably, result in a significant mismatch of the
system and operating conditions, thus causing poor ejector performance.
Downstream of the mixing section, the uniform mixed flow is diffused
and discharged to ambient conditions.
A simple
lQ =
(1)
Steady flow,
(2,
at "
Section 2.
(3)
(4)
(5)
(6)
992
,,^.nfmm-m-
Tm.^,^-
,_J^MMto.A,
if^fc^
u =
PI
i<W>
PO
Mw.
(2.2-5)
VvMpT)
SO
, was used.
(2.2-6)
= (l+u)
PI
^P
"T
where P,
= P.
was assumed.
PI
RC
For steady flow, the momentum equation for the flow direction is
VF.
cs
Vx(PV.dA)
(2.2-7)
Neglecting wall shear stresses, the summation of forces acting on the control volume in the flow direction is
*+ 5'F = P A
+ P A
-PA
* x
PIPI
sisi
ta M2
i
PdA
(2.2-8)
w
or simplifying
A
t
^ I x '
+ P
s,
PA>
S1
M\a
PdA
'
(2.2-9)
U2
where A
= A
+ A
* 0 in
to
995
---
'^-^-^
ite
^MM
T~
pM
P1 P1^>1
+ pk
Sl S1S1
= pM
M2 M2 M2
(2
2-10)
V
'
**
With assumption (9), Ppi = P$1 = P^, Eq. (2.2-10) can be expressed in the
more convenient form
SI
<Ai
_ *va
yj
s si
M:
(2.2-11)
gw
0g
ss _
0t ' nt
cs
h + Y + gz pV dA
(2.2-12)
(hQ)pV dA = 0
where hQ = h + -*- .
(2.2-13)
wh + wh =h
p po
s so
(2.2-14)
K MO
po
nu'
TWi
*x
(Cj
V y5
1 U JJJ-j-
,
'p
T.50
r~
(2.2-15)
PO
The relationships between the stagnation and static pressures for the
primary and secondary flows are determined in the following way.
According to assumption (1U), the flows between the primary and secondary
stagnation states and Section (1) are assumed to be isentropic.
with P
Thus,
given by
996
*mt^
g^MJBaaBTOB^1 g* "".gsfays^
(2.2-16)
where the isentropic pressure ratio function f
(Y.M)
is defined by
n-YMY"1)
^-M
f2(Y,M)
(2.2-17)
sc
M2 -
SO
SI _ , ,
(2.2-18)
so
The preceding equations are the basis for determining the operating
characteristics of the constant-pressure mixing section.
However, before
997
.I
(Cp)p
Hod.
(2.2-19)
1+
In Eq. (2.2-19), the ratio of specific heats at constant pressure for the
secondary and primary gases can be expressed alternatively in terms of
other gas properties by
(Cp)s
(Yp-1)
YS
=
Tc^
Mwp
(2.2-20)
YP
Mw.M
!
(1+uJ
Mw.
(2.2-21)
Mwp
1 +
Mw"
r
*M
Yp-1
1 - {-L-}
{1 + U
{1
+ u
!p *
vT
-l
Mw
4}
Uj
/
TY^TF
(2.2-22)
}
"
* ^r
S
Equations (2.2-19) to (2.2-22) define the mixed gas properties completely in terms of the properties of the primary and secondary gases and
the mass flowrate ratio, u.
998
--
IMU'I
''
IIHIMIM
are, of course, unique, the preference of one approach or set of variables over another is one of convenience.
herein is to specify parametrically the secondary-to-primary mass flowrate ratio, u, and then to determine the corresponding values of the
ejector driving stagnation pressure ratio, PDn
/P-SO
n, and the overall
r 0
ejector compression ratio,. PM/PS0-
tt
,f0
'S0J
s'
^L
' Mw
J
* T
JL k
PO
'A
PI
V,
> 1
MwM
JTC'
p'
1
YM
M)
/T
PO
. can then be
999
i mimi
-j -J
i iv
..
, iirftif-^ '*-"
MM
MMM
MvHJs
LlJ
1/2
^^'
(2.2-23)
V PH. \?
A;;
Mwp
MO
-\
^M(V" :>
\z'
1/ 2
1/2
W^
(2.2-24)
The next steps in the solution procedure are to determine Agl/Api and
M
< 1.
< 1 is
uf^Yp.M,,)
\l
'l/k^l
The result-
-rl/ 2
PO
so
(2.2-25)
1/ 2
si
(2.2-26)
i + (2c;-ihs
After determining M
si
PI
1
- Y M2 -Y M2
Ap yuua YpnPi
(2.2-27)
's st
1000
^.
-r
laiiiiin i m
].
A-./A-,
<V')
M2
><I
"2YM
(2.2-28)
'P PI
where
b = OnOVv^)/
mwM
Mw
-rl/2
PO
(2.2-29)
hi
Experimental
on these data are shown in Fig. 2.2-3; these results are taken from [2].
1001
i-jij*Kwfc-^
Mti
MM
MB
'
---
16
14 -
MJ
T \
12-
Ls
10
8 -
6 -
4 -
0.1
0.2
03
0.4
0.6
05
0.7
0.
0.9
M-
Figure 2.2-3
1002
III!
- -*
-- -
1 0
usually expressed in terms of the pressure rise that would exist across
a corresponding normal shock wave of negligible thickness occurring at
the duct entrance supersonic Mach number.
fuser of Fig. 2.2-4, the static pressure rise across the duct is
expressed by
M3
(2.2-30)
M2
where rd is an empirical
pressure rise coefficient and f5 (v'M ,MISC )' is the
r
normal shock static pressure ratio function.
^.I'T^rr2 -fel}
(2-2-31)
left as an input value to the computer program for estimating constantpressure ejector performance.
1003
--
, .-~.
M.HMMI
MMflM
ffiSJ-:..-.LJ.'IFV^-r.*5 ;_-,
iui"T/'ii-.'.i * />-
T'-
-r-r--T'-n'i<
'--^HT^.
^*^^^.'CTM|jTgyyTTirillT'iTI "
^^/^^ssss
VVM3' P M3'
V
M2'
M2'
MM2>1
L/D> Minimum requ ired value from F ig. 2.2-3
Figure 2.2-4
Constant-area s
1004
mi
ii
- - . .
^g^^
_^__^>
"J,-^^^"1
'
^y^w-iS-vraa^^-^^-"^^.->'h^^
2.2.1.3
For
given values of
&. YP .*,/*, Tso/Tpo .AM2/Api ,M^l]
and a parametric value of u, the values of
can be determined.
ratios
PP0/Pso'VPso3
can then be found.
For a given value of the diffuser pressure-rise coefficient, the
diffuser static-pressure rise ratio, P./P,, can then be determined.
Ms
Ifi
The
J.
IS
- p
SO
1.2
MS
- jF
SO
(2-2-32)
M2
where Pm/Psc and P^/P^ are from Eqs. (2.2-18) and (2.2-30),
respectively.
The operation of the constant-pressure ejector is then established
in terms of the variables [u.pF0/pS0.Pw/pso]2.2.2
Appendix 6.1.
1005
-"""*
--
Bt^'^i^r-'
"''
?>r-^.
JHWIWPWwi^
The input variables, their symbols, and their default values are summarized in Table 2.2-1.
in Table 2.2-2.
Table 2.2M
Input variables for program CPE
Variable
Symbol
GS
1.405
GP
1.405
Mws/Mwp
MWSP
1.0
TS0P0
1.0
Ys
*p
SO/ PO
*wv
MP1
(>1.0)
1.0
RD
u=ws/wp
WSPI
CASE
"NEW"
AM2P1
\l
\i
Default value
Table 2.2-2
Output variables for program CPE
Variable
Symbol
GM
^M
Mw^MWp
MWMP
NCASE
MM2
MSI
SI
AS1P1
Asi/Si
P
>o/Pso
PP0S0
VPso
PM3S0
1006
tit^^mmm
MMM
ms^&g*??*'^^
rw i, i -ww.^i^Jiiigipjjiijti^si'
71
2.2.3
Representative results
To demonstrate typical operating characteristics of a
Table 2.2-3
Representative constant-pressure ejector configuration
Variable
Value
1.4
1.4
^P
Mw5 /MwP
1.0
1.0
SO/ PO
3.0,4.0
Wi
4.0
\l
1.0
Varied
ejector solution exists for each area ratio over only a relatively snail
range of mass flowrate ratios.
M
< 1.
The compression
SI
, it is seen that A
5.
/A
F1
In the neighborhood of
varies significantly.
1007
i .r ,!-. i
-^u -- IHM/
1.2
1.0
0.8
0.6
0.4
/A
"M2'"P1
o.2^
3.0
4.0
0L_
19
7s-7Pa 1.405
Mws/MWp = 1.0
io
<
<
=1
SO/ PO
-0
Mpi = 4.0
5
0L-
y
i
o.
\\J
L
100
200
Ppc/Pso
Figure 2.J-5
...
.- ... .
This constant-pressure ejector configuration was chosen for comparison with a constant-area ejector with a similar configuration,
Section 2.3.3.
A comparison of the compression pressure ratio characteristics of the
constant-pressure ejector (Fig. 2.2-5) and constant-area ejectors
(Figs. 2.3-4b,d) with the same values of \s/\1 and M
, shows that
used to make these studies only after a baseline configuration has been
established.
I
2.3
CONSTANT-AREA EJECTOR
A schematic of a constant-area ejector is shown in Fig. 2.3-1.
The
regimes which are identified according to whether the mass flowrate characteristics of the ejector are dependent or independent of the backpressure level imposed at the ejector exit.
1009
**W
-
V/////////////////////////////////////////////^^^^
Secondary I
M <1!
Uniform
mixed
flow
M
M3<1
Figure 2.3-1
1010
tmmat
"saturated-supersonic" regimes.
confluence of the flows must be such that the supersonic primary flow
expands and interacts with the subsonic secondary flow causing it to
reach sonic flow conditions at the aerodynamically formed minimum
secondary flow area.
reaches sonic flow conditions at the geometric minimum area at the confluence of the primary and secondary flows (Section 1).
flowrate characteristics of the ejector are independent of the backpressure conditions while the recompression flow process is not.
1011
--
The "mixed" regime includes all ejector operating conditions for which
the secondary mass flowrate is dependent on the back-press>,re level.
This
dependency is the result of the secondary flow not attaining sonic flow
conditions at either the confluence of the streams or within the downstream
interaction region.
A.
with this model are in good agreement with experiment, the computational
time requirements and complexities eliminate this technique as an effective method for making broad-band parametric studies of ejector operation.
As a consequence, the study herein is restricted to the constant-area
ejector which exhibits all of the operational characteristics of more complex geometries but yet can still be analyzed by simplified onedimensional methods.
si
< P
PI
1012
i - - iariiiiri i -
_
r--
I,-
._._ - - ,
^_,..a^,. ...
._..
a\jr****IM
-__
"~
~ '!_
Ill |
result of the expanding supersonic primary flow interacting with the mixing-section wall.
model should not cause significant problems as long as there is an awareness of the existence and causes of the problem.
The components of the constant-area ejector model, their analyses,
and the computational approach will now be discussed.
2.3.1
inviscid interaction region just downstream of the confluence of the primary and secondary flows.
analysis from which the "break-off" conditions, the mass flowrate characteristics, and the compression characteristics can be determined.
This analysis is based on the work of Fabri, et al., [3,4].
2.3.1.1
As a con-
sequence of the existence of the "mixed" and "supersonic" or "saturatedsupersonic" regimes, the application of the conservation relations to
this control volume does not, in general, result in a unique solution for
the flow in the mixing section.
MmMmmmmmmmmmmm
--
*i
V S1
rv,M3
-Vpi*
Control volume
Figure 2.3-2
1014
*w*t&ntt. .
^ __^_^^ ^
"saturated-supersonic" regimes since the secondary mass flowrate characteristics are independent of the back-pressure level at Section 3 for
these regimes.
are provided by the secondary flow choking phenomenon which is the result
of the interaction of the primary and secondary flows downstream of their
confluence.
other than satisfying the boundary condition at the ejector exit plane
that the exit-plane pressure is equal to the ambient pressure level.
The transition between these regimes defines the "break-off" conditions,
i.e., the conditions for which a unique solution can be found that
simultaneously satisfies the "supersonic" or "saturated-supersonic"
regimes and the "mixed" regime.
s
ft
The analysis of the overall mixing section is based on the application of the conservation equations and the following assumptions to the
control volume of Fig. 2.3-2.
(1)
Steady flow, ^- = 0.
(2)
(3)
(4)
(5)
(6)
(7)
1015
>HJ*
(8)
(9)
The primary and secondary flows are assumed to be isentropic from their respective stagnation states to the
states at Section 1.
pV dA = 0
cs
and with assumption (2) becomes
^PAI
<2-3-2)
ws + wP = w,r
_W_
PA
-,1/2
r-
,\
. -.1/2
i-.
To
Mw
(2.3-4)
rowp
MS
T "l
MwM
PI
1/ 2
MO
TPO
The result is
T*PI1
(Hu)
(2.3-5)
L_]
si
si I*-.
POT
V>VMs>>
(2.3-6)
The static pressure ratio, Psl/ppl. can be expressed from Eq. (2.3-6) as
1016
"*--'-^
--
SI
PI
P1
si
-.1/2
so
PO
(2.3-7)
v (pv-dA)
(2.3-8)
Jcs
Fl\l
+ P
S1
S1 -
*A
= P
+ P
S1ASIVS,)
'
(2.3-9)
Equation (2.3-9) can be expressed in a more convenient form by
P..
A..
. \
. .
P.-
Pi
>t
<
'
-1
pi
A
pi
the result is
-11/2
f
5(v
Pi> +VvMsl>
Mv'W-
[Tlw
_MO
' T
SO
PO
(2.3-11)
-.1/2
P_
Mw
(1+u)
PO
(HyM2)
(2.3-12)
-,1/ 2
M Yd Y-M2}
The relationship, f3(y,M)
M, as
*>17
1/ 2
a/ 2
(2.3-13)
1017
(2.3-14)
h + ^-+ gz (pV-dA)
cs
_
h0(PV-dA) - 0
^'J . h V*/2.
(2.3-15)
+ w h
s so
"A*
'
and y
Wg/Wp
temperature ratio.
'IB
ILV
(2.3-16)
The result is
no
P
'
( P>S
(2.3-17)
sol
W
oy
(2.3-18)
determ
ined
function is defined by
y (Y-1)
; f2(Y,M)
(2.3-19)
1018
.....*....,..... -
'
-1
so
J yvMpl}
(2.3-20)
PO
gas by applying Dal ton's law of partial pressures to a hypothetical mixing process at constant volume for the respective mass fractions of the
primary and secondary perfect gases.
(1+u)
< P>P
^PX
Mw,
M
Mw~
1 + li
w:
w>,
(2.3-21)
(1+u)
(2.3-22)
Mw
1 + u Mw~
f
and
Mw.
-l
" - si-
v1
(2.3-23)
'M
(1 + u
7TTirr}
Yp TVTTMW
S
The ratio of specific heats at constant pressure can be expressed in terms
of other properties by
C
( P>S
(Yr-D
Mw.
(2.3-24)
1019
___B_^_^
iMaaaa
P'
SO
_UB_
Mwp * T7T
' A_. ' ">!
F
po ' \l
'
If the primary nozzle base area is assumed to be negligible, the constantarea mixing section requirement is
si
fAMJ
P!
PI
(2.3-25)
Using these data and a parametric value of u, the mixed gas properties at
Section 3 can be determined from Eqs. (2.3-21) to (2.3-23); the results
are
v\
Mw..
'M
P ~
si ' p
PI
W P~
PI
I
1020
,.- aiSAk,.-
variables M
relationship, as will be discussed in the following sections, is determined by the operating regime.
Thus, with the aforementioned input data, a parametric value of u,
and a presumed relationship between (MSI , P_,/P,),
all values at
SI
?1
Section 3 can be determined by the foregoing analysis.
The subroutine, CAEOCV(...) has been written, based on the foregoing analysis for the overall control volume, to carry out the computations as just describe'.
CAEOCV (GP, MP1, GS, MSI, MWSP, TS0PP, PS1P1, AP1M3, NERROR,
MM3, PP0S0, PM3S0, PM0S0).
For input values of (GP, MP1, GS, MSI, MWSP, TS0P0, PS1P1, AP1M3), the
subroutine either returns a set of solution values for (MM3, PM3S0,
PM3S1, PP0S0, PM0S0) or a no-solution error indicator NERROR.
A listing of this subroutine is included in Appendix 6.2.
2.3.1.2
and
supersonic" or the "mixed" regime because (1) the minimum secondary flow
area is equal to the geometric secondary flow area at Section 1, and (2)
the secondary flow is subsonic upstream of Section 1 thus limiting MS 1
to the range, 0 < M
<^ 1.
1021
< P
acts with the secondary flow to form a minimum secondary flew area, i.e.,
an "aerodynamic" throat, in the primary-secondary interaction region,
Section 2, Figs. 2.3-2, 2.3-3.
< 1, the
< 1.
S2
flowrate is
area location.
The determination of the break-off conditions for transition from
one operating regime to another is an important consideration in the
analysis of an ejector system.
(1)
(2)
(3)
The criteria for determining each transition are based on the relationship
between the pressures, P
and P
1022
-ML-.-
- .- ... -m
MX!
>r
'S2
hv S
V
*-H
'P2
%~
Control volume
Figure 2.3-3
1023
^.^(afcv*-^-^^*>~
HHMaAiMlMltfWaMilB
at the minimum flow area is unity, the ejector operates in either the
"saturated-supersonic" or the "supersonic" regime; while if this Mach
number is less than unity, the ejector operates in the "mixed" regime.
The break-off conditions for transition between the various regimes
must satisfy the following conditions.
(1)
(2)
They are:
< 1,
|1
if\
(M )
For case (3), the transition requirements are special since the value of
!
i'l
Jl
(Msi'BO
) < 1 must be determined based on the requirements that
(P
/P .) < 1 and (MS2 ) BO =1.
* $1 PI BO
Kabri, et al. [3,4], for analyzing the "supersonic" regime will now be
discussed.
The control volume for this analysis extends between Sections 1 and
2, Fig. 2.3-3. In addition to the assumptions listed in Section 2.3.1.1,
the following additional assumptions are made:
(1) The streams remain distinct and do not mix between
Sections 1 and 2.
(2) The flow is isentrcpic for each stream between
Sections 1 and 2.
(3) The average pressures of the streams can be different at
each cross-section.
C.
1024
: *****
,.
. -
..
.._ _
|._
-^^^tom^*Mn_*i^^mm-^mmi
WRNPBP^*
(4)
(5)
>p
Pi
S1-
For an assumed value of Mg), and since Mg2 = 1, the secondary flow
area at Section 2 can be expressed in terms of the secondary flow area at
Section 1 by the isentropic area-ratio function
(2.3-26)
S2
where
,( Y*1)/2(Y-1)
^(Y.M) = M-1[^|1T.{1+^M2}]
The primary flow Mach number M
(2.3-27)
fl
<vvaw4(Y,.va>-J
whee f4(y ,M
T*J& A
8
^g^^(v^)^
)
function is used.
The momentum equation for this flow and the control volume shown in
Fig. 2.3-3 is
P
\.t1+V$i>
MVMJ
= P
sA2<1+V
+ P
1+
M\a<
V4.>
(2.3-2S)
1025
/P
P P,
si
P
P1
PO>
< PA>
[1-<W
TW ('%<.] ('%<.]]
I \,"L J [_
IP,,/!1,,,)
('V
(P /P
S1 so)
^s^
(2.3-30)
the variables to determine the "supersonic" ejector operating characteristics and the transition between the "supersonic" and "mixed" regimes.
A computer subroutine, CAEFC(...), has been written based on the
etc
-^
can
1026
't^HS/Htj'
*" .,_mMaMa,
B-^^M
required.
M5
= P
The
ATM
Computational procedure
As is the case in many compressible flow problems,
Vso^
F r
9iVen
V3lueS
f <V V W W
Sv
SO/TPO
Hpi > 1), the mass flowrate ratio, u = constant, is specified parametrically and the range and solution values of (PPn0/Pen
, P./P
) are to be
en
50
M5
50
determined.
The first step in this procedure is to determine, for the parametric
value of u, whether the ejector would operate in the "saturatedsupersonic" or "supersonic" regime for a very low back pressure.
determination is made in the following way.
This
Note that this choice of variables is somewhat different than those used
in Section 2.1.
1027
'
'""
"
wan
(P.,/P
,)Dn
DPI
51
BO
1-
and
( P</ SO^BO
are
The remainder
of the ejector operating characteristics in the "mixed" regime are determined by arbitrarily varying M
51
in the range (M
SIM in
< M
S1
Si
For
for %\e parametric value of u from Eq. (2.3-7); the lower limit for Mej
in this analysis is set by arbitrarily limiting P.,/P_.
to the range
51
PI
(PSl'/PPI'BO
)
< P SI'/P PI < (P
/P )
V
SI' PI'MAX
v
where (P
' Sl
/P
PI
MAX
r(vH,)sVv^)
PI
P.
(2.3-3D
MAX
1028
For the "supersonic" regime and the parametric value of 0 < u < u ,
J
<
must be detenT,ined b
an
(MS1). in the range 0 < (l^j)- < 1; from Section 2.3.1.2, a value of
(P../P.,)Si
r1 %
can be
determined.
, (psl/pP1)B0}
for tne
"supersonic" regime.
tlie
>
F r
in the range
(psl/pP1)B0
is
in this analysis is
For each set of values (u, Msi , Psi /PPI ), the values of the variables
(P
MS
/P
SO
, P
FO
/P
so
1029
eafttfM
n
The program is
(1) CAE:
i
i
'
j\
Main program.
(4) CAEFC(...):
(5)
MSAR(...):
(6)
ITER(...):
The input variables and their computer symbols, default values, and
input format are given in Table 2.3-1.
The output from CAE can be selected in either of two forms depending
on the value of PRINT.
1030
w^ftSlfcJ
Table 2.3-1
Input for program CAE
Variable
Ys
Y
Mw/Mw
S
\i>**
Symbol
Default value
GS
1.405
GP
1.405
MWSP
1.0
___t
AP1M3
__f
MP1
\x
so' PO
1.0
TS0P0
___t
V * ws/wp
WSPI
CASE
"NEW"
"ALL"
These data values must be input for at least the first case in a series
of cases.
Notes:
(1)
(2)
/P
1031
I II ! I I
I-
'
Table 2.3-2
Output for program CAE
Variable
Symbol
MSI
S!
PS1P1
Wl
MM3
NCASE
PPO'/P SO
PP0PS0
PM3S0
/p
M5'
SO
PMO'SO
/P
Notes:
(1)
PM0S0
"saturated-supersonic"
regime = MR.
(2)
2.3.3
Representative results
To demonstrate typical operating characteristics of a
= 4.0 and
1032
--
HiHialllMita
aMMMiiawirtMai
Yl/AM3
-25, '333
and Fi9
- 2'3_4(e)
f0r
'Vi
= 5 and
^i/^o
'25-
Table 2.3-3
Representative constant-area ejector
configuration
Variable
Value
1.405
YP
1.405
0.5,1.0,2.0
Mws/Mwp
T
1.0
SO/ PO
0.25,0.333
*'*
4.0,5.0
%i
2.0-20.0
?' s
the figure.
1033
111
-IT
- - "*"*"**-*~--""
LMtiftiiin
nrirf
"
~*
20
MR1-4
Mws/MWp = 1
16
Ap,/AM3 - 0.333 /
yo.250
"
4 -
200
100
PP0/r
/PS0
r
(a)
1034
--
'
'
--*-
300
12
MP1 = 4
10-
= 0.25
P1'^M3 '
7p = 7S "
8-
1.4
Mws/MWp
= 1.0
1.0
Ps1/Ppi=1.2.48<wp/ws<20
^J;}
4 -
! >.V
2-
wp/ws = 2
I
2.48
(b)
8
J
100
L
PP0/r
/PS0
10
200
15
J
'
20
'
'
300
Compression characteristics
Figure 2.3-<
Continued
1035
--1
..--...
aMakMM,
M^MB
12
ir
M,pi--'
10
AP1/AM30.25
Tp"V 1.4
1.0
~so'' PO
.'I
Mws/Mwp = 0.5
Mws/Mwp 2.0
>, 6
2pWp/ws 2
15
J
100
20
300
PrPO/r
I?SO
(c)
1036
-"--"-""-'^-j~-
I II ! II !
11 mi
- '
* in
12
MP1 = 4
AP1/AM3 = 0.333
10 -
7P=7S = 1.4
Mws/MWp = 1
' so' P0 ~
6 -
4-
wp/ws = 2
15
j
100
20
I
200
W:so
(d)
Figure 2.3-4
1037
"I
-*""*' --'-~-vrr -
Continued
14,
12
10t
.8 L
n
2
p/Ws=2
10
15
20
20
Mp,=5
Mws/Mwf, = 1
"Tso/Tpo = 1
ys=yP = 1.4
A
P1/AM3 = 0.250
16
I LV
4^-
800
P
P(/
(e)
1000
so
V,
Figure 2.3-4
Concluded
1038
..,...-... ,., ., - ..
I II
.>-..
._.._*.~^a
m.
= P
limited and thus does not present a complete picture of the overall
ejector operating characteristics.
2.4
compression-pressure ratio greater than 7-10, considerations of optimization, operating pressure levels, mass flowrate ratio, etc., indicate that
a multi-staged ejector system should be used.
each stage must pump a_H of the mass flow through the preceding stages
unless interstage condensation is used.
If interstage condensation is
not practical, the size and total primary mass flowrate requirements
effectively limit, except in very special cases, the number of ejector
stages to two.
System configuration
A block diagram of a staged ejector system is shown in
Fig. 2.4-1.
1039
.i..n,r,
. I
M*Ml
2
0.
o
c
o
c
c
o
S3
en
c
o
(J
s.
o
o
4-
"-)
<u
o
eu
CT)
<0
s-
CT)
II
ii
IN
CM
2
O
a.
1040
'
''"*>
'-.
-^mmk^
-.-^-f"- --
- -
--
"
(ws/wp)1
(w )
=
(2.4-1)
{i + D + K'/WplJ/K^pV
T^T;
<Pso>*
MS
(2.4-2)
MS
so
SO
first-stage exit and the second-stage stagnation chamber; for the purposes
of this example, a value of 90% of the isentropic pressure rise,
r
That is,
n
11
Vr
P
;
2
( S0
so)
2
(2.4-3)
_M?_
^7" lV
The individual stage operating pressure ratios are (Ppo/P.0),
(P
(P
/P
/P
an
));; the
the second-stage
second-stage press
pressure ratio can be expressed in terms of
P0S02
PO
^oX
so
P M5 I
MO
r
MS
SO
(2.4-4)
1
i^iirfSfc."
*-~-
v~-..~
IIIIIII
liiMiMi'niiWIliaiittliiiWiilii^ilil
ri^M^
*#
r 1/ 2
MS
SO 1.2
np^)2/(pso);
r (p /p r
(2.4-5)
For this example, the specifications for each stage are identical in
non-dimensional form.
also, note that an overall compression ratio of 7.6 was assumed for this
system.
Table 2 .4-1
Ejector spec ifications
Variable
Value
1.405
fr8)l|2
(
1.405
(Mws/Mwp)i)2
1.0
YP)l,2
li!
\ SO'
i.
1.0
PO 'l ,2
(V/\J1>2
0.25
(^)2/(Pso),
7.6
K\,2
4.0
2.68 ;
so
1,2
the remainder of the operating characteristics for the staged ejector are
given in Table 2.4-2.
Thus, a comparison of the values in Table 2.4-2 shows that some
gains can be made by staging.
requires approximately 39% less primary mass flow and about 16% less
1042
IbU
^...r
n-
T n.
.-,.,.
_*
Table 2.4-2
Si ngle and staged ejector performance comparison
Value
Variable
(1)
Two-staged ejector
<VWA,2
0.47
(p
2.67
/p
0.497
"**
68
(PPO'/pSO'l,2
)
v
194
(2)
^V^I
7.6
(ws)1/(wp)T
0.114
Single-stage ejector
0.082
(ws/wp)
-7.6
<VPso>
0.43
231
(PPo/Pso)
The result of this simple example indicates the need for further and
broader parametric studies of the two-stage versus one-stage ejector
system.
1043
"*&*-
<M-..^.--^--:,
- ...*..>.
----nifi^riiiigfai
.-.,. , --n
atm ---^ai
3.0
EXPERIMENTAL INVESTIGATION
include:
(1)
constant-area ejectors,
(2)
(3)
slotted-nozzle ejectors.
The experiments provide a data base for comparison with the theory
developed in the preceding section and they also provide information on
the details of the ejector fiowfields which cannot be predicted with the
simplified models.
ij J
Descriptions of the experimental apparatus and procedure and discussions of the results are contained in the following sections.
3.1
ous flow facility with the axisymmetric ejector and secondary, mass flow
measurement section installed.
trol panel, and manometer bank.
Also visible are the test stands, conA second photograph of the axisymmetric
ejector is presented in Fig. 3.1-2 with the three mixing tubes used in
the experimental investigation.
1045
^mv MB -**
Ma^amam a , m aiaJlMMiMM^^^^MiWMMJMMII
nu
c
a
E
a;
SS
s-
13
00
i
00
oo
ro
E
T3
e
o
u
<u
00
XJ
c
<o
so
o
a>
+->
01
<_>
si
00
(O
l*- o
0J
$
^~
^~
IO
4- +J
00
00 c
3
c:
o
3
C
r r
4->
->
o <u
o 00
n
a)
4-
CD
1046
MMMMI
ass
}\
Figure 3.1-2
1047
**=. ^" .
"- -
~1
DM
ssSJI
Mixing tube
(interchangeable)
Static
pressure
wall taps
unzznm
J!
Primary nozzle
(interchangeable)
so
r
so
Secondaryr
flow
TzamzL
Primary flow
Figure 3.1-3
1048
^Vste**-"'
MMMB
0.715" diam
0.715" diam
0.020"
12 Slots:
equayspaced,
0.020" wide
X 2.190" long
* Nozzle
exit
plane
(a) Basic conical nozzle.
f\
Nozzle
Mp,
0; in.
2.0
0.550
2.5
0.440
3*
2.5
0.440
'Slotted nozzle
1049
I
i*-- '
mini
- i
re
\
L-l
Constant-area
section
Constant-area 5
section
|
6C converging
section
mssssw
1.250"
(b) Constant-area mixing
section.
1.939"
Mixing
tube
D in.
Lin.
0.995
12.500
1.245
3*
0.995
13.000
12.882
5.382"
0.995"
(c) Mixing section specifications.
1050
biMMiMiM
. . . ,.:.- -
.... .-.
PPSN' T'PSN
AP,PSN
SO
P(X )
'so
Primary
Secondary * >
I S-'.
VDI
standard
nozzle
VDI
standard
nozzle
PO
44
PO
p.
From atmosphere
ft
I !
AP SSN
PSSN' T' SSN
Figure 3.1-6
1051
^fejM*.
with each of the interchangeable mixing tubes (1.245 inch I.D. constantarea tube, 0.995 inch I.D. constant-area tube, and variable-area tube
of Fig. 3.1-5).
viding for identical area ratios /L./A. with each mixing tube.
The variable-area mixing tube was constructed such that the entrance
diameter was equal to the diameter of the larger 1.245 inch I.D. constantarea tube while the exit diameter was equivalent to the diameter of the
smaller 0.995 inch I.D. constant-area tube.
a 0.5 inch spacing through the tapered section of the tube for obtaining
the wall pressure distribution.
added to the variable-area tube in all cases and to the 0.995 inch I.D.
tube in selected tests.
Figure 3.1-6 is a schematic of the test set-up with notation for the
ejector and the primary and secondary mass flow measurement sections.
Air was used for both the primary and secondary gases in each experiment
while Pp0 was held constant and PB = PATM; thus, the ratio Ppo/PB or
P. /i5.PO
ATM
was constant.
the primary flow was choked in the supersonic nozzle and Pf0 was
constant.
PO
p
ATU/ p0
constant.
3.1.2
Experimental results
The experimental results for the M = 2 conical primary
nozzle in the 1.245 inch I.D. (Api/AR = 0.333) and 0.995 inch I.D.
(Apj/ZLj - 0.516) constant-area mixing tubes are presented in Figs. 3.1-7
and 3.1-8.
The experimental
below the theoretical break-off curves which simply indicates that the
ejector was operating in the Pp0/P.TM independent regime.H
Due to the somewhat congested
nature of the theoretical PA
3
ATM
/P
so
,T
Refer back to Section 2.3 and Fig. 2.3-4 for a more complete presentation of the typical operating characteristics of an ejector system as
determined from the theoretical constant-area ejector model.
1053
'ft aafk
^r
*
6
in
r10
r-
haracter
2.0)
CM
o
6
U II
rJ
.)
o
a.
a.
a.
Q.
o
</l c
to ro
fO
r
t. tr>
o
t->
u
<y *
oO
\(
cu m
m
0) o
j-
II
iri
n
2 O (O
ro -
V/
o 9*
8C 23
-
^*
11
5-
0>
1
|
(0 tg
<o
4)
CN
II
X
UJ
*r
r-
ii
it
<
<t
a.
o
a.
</> d n
5
8 .
Zi v- f-
d d
i
a.
"5
in
e>
iri
(O IT)
< o
3
55
a
M/SM
1054
i- amMtittaaaifeatt
^sfcSjfc.
Theoretical break-off
curves
AP1/AM3 = 0.516
Experiments
Mp] = 2
MWg/Mw, = 1
so'' P0
7P=7S = 1.4
2
4k
5 5<P
P0/pA1M<5.6
ws/wp =0.043
Symbol
I
Ih
3\-
| hr^>ws/wp
074
Solid
AP1/AM3
0.516
0.330
s mbo|
y
s: w*S'"P
c/wD = 0
ws/wp --0.108
'^
ws/wp =0.316
10
20
30
40
50
60
/PS0
Figure 3.1-8
PAC
-330' -516
and
*Vi
= 2 0)
1055
._
. ....,: ,.^-w**---
*-.*&
>-~
Tr
- -
-^
- -
--
- :
.-
-- -I-
~ -
.- -
values of w /w
that the ejectors were operated significantly below the applicable breakoff curve at lower values of wg/wp.
The experimental results for the M = 2.5 conical primary nozzle in
the 1.245 inch I.D. (A^/A^ = 0.330) and 0.995 inch I.D. (A^/A^ = 0.516)
constant-area mixing tubes as given in Figs. 3.1-9 and 3.1-10 follow the
same trends as for the M = 2 conical nozzle.
tube did not alter the mass flow characteristics of Fig. 3.1-9 since the
diffuser affects only the recompression shock structure within the ejector
in the Pp0/PATM independent regime.
the ejector was operating closer to the theoretical break-off curve with
the diffuser; however, the experiment with the diffuser installed was
conducted at P
PO
/P
ATM
ATM
/?
SO
pi
/A
MS
pi
/A =
t.a
From Fig.
3.1-11 the experimental data for w /w
J
vs P
/P
3PS0P0
1056
CO
u
CO
r-
!_
<U
t->
<-)--
<0 CO
s_
(TJ CM
U II
O
T3
CO C
CO <o
e co
O
u o
o
Q.
CO
S_ CO
ty >
-JO
0) 00
3
CV O
s_
<e II
co
*
I
cx
1057
*J
12
AP1/AM3= 0.516
Theoretical break-off
curve
Experiments
Mp, = 2.5
Mws/Mwp = 1
T
so/Tpo=1
5 5<P
Symbol
A
0
V.
/P
PO
ATM<6-2
AP1/AM3
0.330
0.516
0.516 w/diff user
100
p P0/r
/pS0
Figure 3.1-10
1058
^**ai.
ii^ffarmnrimini'ii nftiirMiJ'iiUM 11 "in
I/)
i.
<D
+->
U
(O
S(O
-C
u
2
o
ifl
i. in
0
4-> CM
o
<U II
"-5
*?
N "O
N C
O (0
c
1 VO
-a
cu in
+J
+J o
o
r
t/> O
i\
ro
ro .
CU o
s.
iq n
=J
eg t
*> -v.
</>
*
t_) .
ai
C7>
u.
1059
18
16-
Theoretical break-off
curves
14 .
AP1/AMS = 0.516
12
o
Z
10
<
Experiments
Mp, - 2.5
Mw./Mwp = 1
7\
T1 so'/T PO =1
Symbol
Ap,/AM3
0.330
0.516 w/diffuser
120
r
P
po'/P so
Figure 3.1-12
V, - 2-5)
1060
ii
However, deviations
than for
the M = 2.5 conical nozzle of Fig. 3.1-9, which is not unexpected considering the geometry of the slotted nozzle.
P0/PATM
independent regime.
ejector operating under the same conditions but with a constant-area mixing tube of Apj/A^j = 0.516.
The variation in P
PO
/P
ATM
P0
I?
values that are near the break-off curve in the independent regime.
Figure 3.1-14
Figure 3.1-5(a) shows this mixing section. The initial entrance diameter
is 1.250 inches converging at a wall angle of 6 to a minimum mixing tube
diameter of 0.995 inches.
1061
*r+>
CO
r-
s_
o
a
J--^
<o in
.c
U CM
o
o
oo
I- CM
10 II
to
2
8 5;
1!
3
QL
S-
o -o
u c
u <a
V
>->m
4) r
in
f
0) o
L.
<o n
s<*
j "x.
f-
5?
3
t- O
in
C
V
X
Ui
in
<3
in m o o
c\i CN r>i
<N
ii
E
>
a.
<3
>*-*
**
ro a:
rn
s.
0 O
V)
o
o
o
o
so
M/SAA
1062
18
XT
Theoretical break-off
curves
Experiments
MWg/Mw p"
so'' PO "= 1
7P = 7S 1.4
A
M
/A
P1'MM3
Symbol
A
Q
-
-,
= 0.516
P1
2.5
2.5
2.0
2.0
80
P0/PATM
5.5
4.1
5.6
4.1
100
120
P P0/r
/PS0
Figure 3.1-14
1063
*tt.
4.0
Experiments
MP1 = 2
^PV^M3
3.5j-
MWg/MWp, = 1
' SO'
P0 ~
7p - 7S
ws/wp
1
2
0.0
0.154
1
1.4
3.0H
Curve
= 0.516
25-
5!
a.
OA
2.01
n
15h
i
1.0
o...
'o-
05h
05
10
15
20
2.5
3.0
x, inches
Figure 3.1-15
1064
4.0
Experiments
MP1 = 2.0
AP1/AM3-0.516
3.6
Mwg/MwVp = 1
Tso/Tpo
7p = %. -1.4
3.0
P(/P ATM
4.1
a.
2.5
"6
en/
0
2.0
SL
1.5
Curve
ws/Wp
1
2
3
0.0
0.157
0.250
1.0
o**-::::X;i.,:
o J...to
0.5
0.5
10
1.5
A-
25
3.0
x, inches
Figure 3.1-16
1065
MMIISMIjiMgMBMBHMWWgggMWWaiBffaiWM
4.0
35L
3.0
2.5
1<
Experiments
MP1 - 2.5
Q.
2.0
AM/A-
0.516
Mws/Mwp = 1
VTpo "
1.5
1
2
3
7p 7S " 1.4
WATM
Curve
ws/wp
0.0
0.151
0.255
* 5.6
.<>
r*V
0.5
0.5
1.0
J_
1.5
2.0
2.5
S
3.0
x, inches
Figure 3.1-17
fSSj
4.0
3.5 i-
p.
3.0
o?-.
2.5
Experiments
MP1 = 2.5
A
P./AM3 '
5a.
20
0.516
Mws/Mwp = 1
Curve
so/TPO - 1
'P
P
P0/PATM
1.5
1.4
'S
4.1
ws/wp
1
2
3
0.0
0.152
0.52
2.0
25
'i
05 H
0.5
1.0
1.5
x. inches
^^^ss
JR
also shows that the ejector operated closer to the appropriate theoretical
break-off curve with the M = 2.5 conical primary nozzle; however, this is
due to the fact that for constant A^/A^ , an M = 2.5 nozzle requires a
higher value of Ppo/PATM than an M = 2 nozzle for Ppo/PB independent
operation.
P0/
ATM
dl
through 3.1-18 note that only the initial part of the wall pressure distributions near the primary/secondary confluence are shown and that the
final compression is to much higher levels of PATM/PS0
!jj
ejector operating under the same conditions but with a constant-area mixing tube of Apj/A,^ ~ 0.516, the area ratio corresponding to the constantarea section of the variable-area tube.
experimental values for ws/Wj, vs Pso/Ppo lie very close to the theoretical break-off curve even at low values of ws/v^,.
for P../P.
vs P.rn0/P.
as shown in Fig. 3.1-20 indicate that the ejector
ATM
aB
5"
was operated in the Pp0/PATM independent regime and re-emphasize the undesirability of operation at higher values of Ppo/PATM than required since
the mass flow characteristics of Fig. 3.1-19 were identical at each value
of P
PO
/P
ATM
tions at low w /w
3
1068
-- j-JiV ,
191&%
</>
U
it->
2
o
1
o
a;
<u ^~*
ID
0>
r
rM
CVJ
ISI II
o Z^
0)
JLJ
4J
!-
I/I
0
VO
I
in
a
0) O
s(0 ii
1
1069
o-
o..
1.5-
J'
QL
I 't-
-..
6'
Experiments
Mpl-2.5
AP1/AM3- 0.516
0.5-
MWj/MWp
Curve
1
2
3
5.6
j_
1.0
.5
2.0
ws/wp
0.0
0.144
0.254
2.5
3.0
x, inches
Figure 3.1-21
1071
"~-p&#*i
2.0,
o-
->
Q 'o
1.5
? '..,....,0.
pexperiments
05-
/A
51
P1 M3"- 6
Mws/Mwp - 1
Curve
S(/ P0 " 1
1
2
3
7p -78-1.4
P
V ATM
" 4-2
0.5
JL
1.5
1.0
2.0
'"o
Mp, 2.5
A
o .
T4
ws/vwp
0.0
0.155
0.262
2.5
3.0
x, inches
Figure 3.1-22
1072
Again, note
that only the initial portions of the wall pressure distributions are
presented in Figs. 3.1-21 and 3.1-22.
1073
^F-3P^.~>.-W^T TrV-r-^
4.0
CONCLUSIONS
The con-
clusions are:
(1)
This model
constant-area mixing tube ejectors should be established by both experiment and analysis.
(2)
continued.
(3)
unsteady
LA,
flow, periodic pulsating flow, resonance phenomena, and/or various
nozzle and mixing-tube geometries.
(4)
1075
5.0
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
1077