adp000536
TRANSCRIPT
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* r
S U P E R S O N I C E J E C T O R - D I F F U S E R
T H E O R Y
A N D E X P E R I M E N T S
W
_
_
.
L . A d d y
f
f
tA
T^*^*
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C r a i g
D u t t o n . *
u
.
C .
M i k k e l s e n
m
OH
A u g u s t
1 9 8 1
S u p p o r t e d
b y
U . S . A r m y R e s e a r c h O f f i c a
G r a n t N u m b e r
D A H C 0 4 - 7 4 - G - 0 1 1 2
a n d
Department
ofMechanical
nd
ndustrialngineering
Universityofllinois
at
rbana-Champaign
Urbana,
Illinois1801
T
Professor
nd
Associate
ead,
epartment
of
Mechanical
nd
ndustrial
Engineering,
niversity
of
llinois
t
rbana-Champaign,
rbana,
Illinois.
Assistant
Professor,
epartmentofMechanicalngineering,exas *M
University,
ollegetation,exas.
,rt
Aerospace
Engineer,
.S .
rmyMICOM,
edstoneArsenal, labama.
96 3
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A*
T A B L E O F C O N T E N T S
P a g e
L I S T O F F I G U R E S -
L I S T O F
T A B L E S
x
N O M E N C L A T U R E
1
1 . 0
N T R O D U C T I O N
2 . 0 H E O R E T I C A LI N V E S T I G A T I O N
2 . 1
U P E R S O N I C
E J E C T O R S Y S T E M
C H A R A C T E R I S T I C S
2 . 1 . 1
e r f o r m a n c e
c h a r a c t e r i s t i c s
2 . 1 . 1 . 1
h r e e - d i m e n s i o n a lp e r f o r m a n c e s u r f a c e s
- -
2 . 1 . 1 . 2
w o - d i m e n s i o n a l
p a r a m e t r i c c u r v e s
0
2 . 2
O N S T A N T - P R E S S U R E E J E C T O R
6
2 . 2 . 1
o n s t a n t - p r e s s u r e
ejector
a n a l y s i s
8
2 . 2 . 1 . 1
o n s t a n t - p r e s s u r e
m i x i n g
s e c t i o n
3
2 . 2 . 1 . 2o n s t a n t - a r e a s u p e r s o n i c
diffuser
7
2 . 2 . 1 . 3v e r a l l
e j e c t o r
a n a l y s i s
1
2 . 2 . 2o n s t a n t - p r e s s u r e ejector c o m p u t e r p r o g r a m( C P E )-1
2 . 2 . 3
e p r e s e n t a t i v e
r e s u l t s - 3
2 . 3
O N S T A N T - A R E A
E J E C T O R
5
2 . 3 . 1
o n s t a n t - a r e a
e j e c t o r
a n a l y s i s 9
2 . 3 . 1 . 1n e - d i m e n s i o n a l
o v e r a l l
m i x i n g - s e c t i o n
9
a n a l y s i s
- -
2 . 3 . 1 . 2
j e c t o r f l o w r e g i m e s a n d
t h e i r
c r i t e r i a
-
7
2 . 3 . 1 . 3o m p u t a t i o n a l
p r o c e d u r
e
- -
3
2 . 3 . 2o n s t a n t - a r e a e j e c t o r c o m p u t e r p r o g r a m( C A E ) 6
2 . 3 . 3
e p r e s e n t a t i v e
r e s u l t s
8
2 . 4T A G E D
C O N S T A N T - A R E A
E J E C T O R S Y S T E M 5
2 . 4 . 1
y s t e m
c o n f i g u r a t i o n
5
3 . 0
X P E R I M E N T A L
I N V E S T I G A T I O N 1
3 . 1
O L D - F L O W ,A I R - T O - A I R ,E J E C T O R
E X P E R I M E N T S
1
3 . 1 . 1
x p e r i m e n t a la p p a r a t u s a n d p r o c e d u r e 1
3 . 1 . 2x p e r i m e n t a l
r e s u l t s
9
4 . 0
O N C L U S I O N S
0 1
5 . 0
E F E R E N C E S
0 3
tfacMmaa
FiOi
BUNc-Nor
FII*ED
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B^T^^PBB^P
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zmmmmmmmmmmmm
H P-
* *
VP-W-'s.;
'.-
JBWOT
ffij^pWjg
Page
6 . 0 P P E N D I C E S
0 5
6 . 1
O N S T A N T - P R E S S U R E
E J E C T O R
COMPUTER
P R O G R A M
( C P E ) 0 5
5 . 1 . 1
o m p u t e r
p r o g r a m0 5
6 . 1 . 2
a m p l e t i m e s h a r e i n p u t / o u t p u t0 9
6 . 2
O N S T A N T - A R E A E J E C T O R
C O M P U T E R P R O G R A M
( C A E )
1 2
6 . 2 . 1
o m p u t e r
p r o g r a m
1 2
6 . 2 . 2
a m p l e
t i m e s h a r ei n p u t / o u t p u t
2 4
966
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flf.;
-;.
:
F ig ure
2 . 1 - 1
F ig ure
2.1-2
F ig ure
2.1-3
F ig ure
2.1-4
F ig ure
2.1-5
F ig ure
2.1-6
F ig ure
2.1-7
F ig ure
2.1-3
F ig ure
2.2-1
F ig ure
2.2-2
F ig ure
2.2-3
F ig ure2.2-4
F ig ure
2.2-5
F ig ure
2 . 3 - 1
F ig ure
2.3-2
F ig ure
2.3-3
F ig ure 2.3-4
LIST
O F
FIGURES
Page
Ejector onfiguration ndnotation 5
Ejector
mass
low
haracteristic
urface,
S P
SO
PO
AT W
P0
E j e c t o r
characteristic
surface,
I n t e r s e c t i o n
o f
the
w/w
urface
withplanes
o f
constant
P
aTM
/P
B
.
1
ATM
P 0
I n t e r s e c t i o n
o f
the
w
/wurface
with
planes
o f
constant P
so
/P
po
2
I n t e r s e c t i o n
o f
t h e
w /w
urface
with
a
plane
WV
'
P
s o /
P
P O
13
Intersectionof
he
surfacewith
lanes
of
on-
stan
ATM/
P
PO
14
Intersection
of
he
surface
with lanes
f on -
^ant
s
/
p0
15
Constant-pressure
ejector onfiguration 17
Constant-pressure
mixing
ection
ontrol volume
19
Empiricalorrelation
or
ength-to-diameter atio
of onstant-areaupersonic
diffusers
from
R e f e r e n c e[ 2 ] ) 28
Constant-areaupersonic
diffuser
notation
-
30
Representative
haracteristics
or
onstant-
pressure
ejector 34
Cor.stant-area
jector onfiguration36
Constant-areamixingectionontrol
olume
40
Contrololumeor
Fabrichoking"nalysis 49
Constant-areaejector
haracteristics
0
(a )
ass
lowrate haracteristics 0
(b )ompressionharacteristics 1
(c)
ompressionharacteristicsorparametric
ari-
ations
n
w
Mw
2
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Page
(d)ompression haracteristics
or
variation
in
p
A j
63
(e)asslow
nd
ompression
haracteristicsor
a
ariation
n
64
Figure
.4-1 Stagedejector onfigurationnd
otation 66
Figure.1-1 Cont inuous
lowacilitywithaxisymmetricejector
and
econdary,
ass
low
measurementection
installed 72
Figure .1-2
Axisymmetric
ejectorwithlefto
ight)ariable-
areamixing
ube
with
diffuser;. 2 45
n
.D.
constant-areamixing
ube
nstalled;
nd
.995n.
I.D.
onstant-area
mixingube
73
Figure .1-3
Schematic
ofaxisymmetricejector
onfiguration
----
74
Figure
.1-4
Schematics nd
specifications
ofejectorprimary
nozzles
5
( a ) a s i c
c o n i c a l
n o z z l e
5
( b ) l o t t e d e x t e n s i o n f o r n o z z l e
5
( c )
o z z l e
s p e c i f i c a t i o n s
-5
F i g u r e 3 . 1 - 5
S c h e m a t i c s a n d
s p e c i f i c a t i o n s
o f
e j e c t o r
m i x i n g
s e c t i o n s
6
( a ) a r i a b l e - a r e a m i x i n g s e c t i o n 6
b )
o n s t a n t - a r e a m i x i n g
s e c t i o n
6
c )
i x i n g
s e c t i o n
s p e c i f i c a t i o n s 6
d )
u b s o n i c d i f f u s e r
s e c t i o n
- - - 6
F i g u r e
3 . 1 - 6
E x p e r i m e n t a l
e j e c t o r
s e t - u p
a n d
n o t a t i o n
- - 7 7
F i g u r e 3 . 1 - 7
C o n s t a n t - a r e a
e j e c t o r m a s s
f l o w c h a r a c t e r i s t i c s
(\i
/
o -
3
30,
-
516,
nd
PI
-0)
80
Figure
.1-8
Constant-area
ejector
ompressionharacteristics
(A
PI
/
M S -
33
0,
-
5
6
,
nd
Vi
s
,0)
81
Figure.1-9
Constant-area
ejector
mass
low
haracteristics
(A
PI
/
W J
-
3
30,
5
1
6
,
nd
PI
2,5)
83
Figure.1-10 Constant-areaejector ompressionharacteristics
(A
/A
=
.330,
.516,
nd
=
.5)
84
P
l M S I
Figure. 1 -11 Constant-area,
lotted-no2zle
ejector
mass
low
characteristics
A/A
.330,
.516,nd
M^
=
.5)
L-K. 85
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Figure.1-12
Figure
.1-13
Figure.1-14
Figure .1-15
Figure
.1-16
Figure
.1-17
Figure
.1-18
Figure
.1-19
Figure
.1-20
Figure
.1-21
F i g u r e
3 . 1 - 2 2
P a g e
C o n s t a n t - a r e a ,
s l o t t e d - n o z z l e
e j e c t o r c o m p r e s s i o n
c h a r a c t e r i s t i c s(A/A,
r t
= 0 . 3 3 0 ,0 . 5 1 6 ,a n d
M
pl
=
.5)
1
- -
86
Variable-areaejector
mass
low
haracteristics
(A
pl
/
f3
. 516 nd
pi
=
.0,
.5) 88
Variable-areaejector
ompression
haracteristics
(A
/A
0.516
nd =
.0,
.5) 89
P
Variable-areaejectorwall
ressure
distributions
(VM 5
=
-
5
16
M
P 1
=
2
-
0
'
and
P
P
0
/A T ,
=
5
'
6)
90
Variable-areaejector
wall
ressure
distributions
(\i/A*
-
516
Vi
-Z.0.a
fl
dP,
0
/P
AT11
-4
1)
-
9 1
Variable-area
jector
wallressure
distributions
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LIST
F
ABLES
Page
Table
.2-1
Input
ariables
or
rogram
P E
2
Table
.2-2 Outpu t
ariables
or
rogram P E
2
Table
.2-3
Representativeonstant-pressure
ejector
onfiguration
3
Table
.3-1 Inputor
rogram
A E
7
Table
.3-2
Ou tpu tor rogram A E 8
Table
.3-3
Representative
onstant-area
ejector
onfiguration
9
Table
.4-1
Ejector
pecifications
8
Table
.4-2
Single
nd
taged
ejector
erformance
omparison
9
PWBCJLUli^AO ILAMMJO T1L*XD
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P Pil i ' a ^
&SK
t
V
, .
t tl
,- ;
i^j^^ppi *?* -^
NOMENCLATURE
Symbols
A
Area
C
1'
C
2
3
Constants
efined
next
C
P
Specific
eatat
onstant
ressure
D
Diameter
f(
Function
V
i . e . ,t h e y
a r e
d e p e n d e n t
o n t h e s t a g n a t i o n p r e s s u r e a n d b a c k p r e s s u r e
r a t i o s .
A n
a l t e r n a t e
f o r m u l a t i o n
o f
t h e
p u m p i n g c h a r a c t e r i s t i c s
i n t e r m s
o f
t h ei n i t i a ls e c o n d a r y s t r e a m M a c h n u m b e r ,M
$l
,t h e s t a t i c p r e s s u r er a t i o
PP
o f t h e s e c o n d a r y s t r e a m
a t
t h e
p o i n t
of c o n f l u e n c e o f t h e t w o
s t r e a m s ,
a n d
t h e a m b i e n t p r e s s u r e
r a t i o ,
P / P i s g i v e n
i n
f u n c t i o n a l
ATM
0
form
y:
M
S
l
=
(
P
S
l
/PO .
f
W
P
0
)
?
-
-
2
>
"*
978
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^*?a*'vv*~rtfsr*KH^nw?,i:
HBSBSr
- .-
,- r
c
o
o
c
a
c
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y'^'* :...:.
'
:
~ : . :
''
.
,
\'-
-
r
r
^ ^ ^
,
Thiselection
f
ariables,lthough
ess
bvious,sonvenient
orper-
forming
he
umer ical
alculations
nvolved
n
many
heoretical
jector
analyses.
In
ddition
oestablishingheunctional
orm
of
he
umping
har-
acteristics,nother
quantity
of
nterest
s
hehroudwallressure
distribution iven
unctionally
y :
where sheaxialoordinate.
Afterestablishinghe
bove
unctional
relationships,
hehrust
characteristicsf ystem an
henedetermined
n
hehrust
ugmenta-
tionapplication.
In
ractice,
hiss
ccomplished
y
onsidering
he
contributionsn
hexial
irection
of
he nteringmomentumluxes
f
the
primary nd
econdary
t reams
ndhe
ntegrated
hroud
wall pressure
distribution.
2.1.1.1
Three-dimensional
erformance
urfaces
Theunctional
relations,
2.1-1)
nd
2.1-2),har-
acterizehepumping"
haracte-'stics
f
nejector ystem
nd
epresent
surfaces
nhepacesescribed yheoordinates
W
S
/
W
P
P
S(
/
*
P
ATM/
P
PO >
nd
M
SI
P
SI
/
PO'
F
WPO>'
espectively.
Theumping
haracteristics
of
ypical
jector ystem
n
erms
f
the
irst
et
of
ariables
are
hown
n
ig.
.1-2.
This
urface
learly
delineates
he
low egimeswhereinhemas*
low
haracteristicsre
independent
or
ependent
n
he
mbientpressure
evel. These
low
regimes
merge
ogether
long
he
break-off
urve"
nd ,
n
rinciple,
thisondition
erves
o
niquely
efine
his
urve.
980
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wr
r
- r ~
-
mmmg
,
u
.. . -..
.
.,. ,,
wq
o
o
o
C O
u
J-
10
4.
0)
-t->
O
3
i-
10
to
f c .
o
4- >
u
CN 4
I
3
981
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,
M
.-,..,
.......,
7
,
,,-,-;,.,,.
T
TOWP^ MBtw
ffW
^y
w
y py
.w r
1
"
.
"TTP**
WtilHHWIJ
... v*.-,,,::. , .,; ^/
. "'
-.v-v^^i;
W
s/
W
P =
f
(
P
30/
P
P0
)
VP
=
(
P
S0/
P
P0.
P
A T M /
P
P0)
Toheeftofhebreak-off urve""supersonic"ndsaturated
supersonic"
egimes),
he
ass
low
haracteristics
re
ndependent
of
P
ATM
/P
p0
nd
he
urfaces
ylindricalith
ts
eneratorparallel
to
the
ATM
/P
po
xis. Forheseegimes,he
mass
low haracteristicsan
be
epresented
y :
(2.1-4)
when
A TM
/P
P O
ATM^PO^BO-
To
he
1
9
ht
of
he
bre
a
k
-
ff
urve"
("mixed"
egime),
he
urface
s
hree-dimensional
in
ature
nd
xtends
fromhe
spatial "break-off
urve"
o
helane
here
w
=
base
pressureplane);ence,
WhenP
A TM
/P
P0
P
ATM/
P
PO>BO-
In
principle,.. "break-off
urve"
epresents imultaneousolu-
tion
of
heunctional
relationships
2.1-4)
nd2.1-5).
However,
he
"break-off
urve"
lso
as henomenological interpretationased
n
he
flowfield
nteractions
occurring
within
he
ejector
hroud.
Points
n
thebreak-off
urve"
re
determined
y
he
onditionhatransition
rom
dependenceondependence
ofhe
mass
low
haracteristics
nhe
ambient
pressure
evelwill
ccur
henheecondarytreamust
attains
sonic
onditions
either
nside
hemixingube
or
at
ts
ntrance.
This
point
will
e
urther
amplified
n
he
discussion
of
he
onstant-area
ejector.
An
alternative
epresentation
of
he
umpingharacteristics
n
terms
of
he
ariables
M
S1
,P
S1
/P
po
.P
ATM
/P
p0
)siven
nig..1-3.
9b2
C
-
~
MmM
-
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P
AT M
/PpQ- Independent
Psi
/Ppo
Break-off
Curve
P
A T M
/P
PO*
Dependent
^Tn/Ppo
Figure2.1-3
Ejector
characteristic
urface
$1
=
(P
sl
/
po
P
ATI|
/P p
0
)
983
-
7/26/2019 ADP000536
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wmmmt mm.wwmmm> m m
,
, .
.. m
.
n u
. mmwm mmm mm
wmmmmmm
m
For
hisurface,
here
re
direct
ounterpartsohe
/P
- inde[7end-
ATff
P
0
e n t
a n d
P
A
,/P-dependentr e g i m e so ft h e w / w
u r f a c e .
AT M
P OP
2 . 1 . 1 . 2
w o - d i m e n s i o n a l
p a r a m e t r i c
c u r v e s
The
hree-dimensional
erformance
urfaces
f
Figures.1-2
nd
.1-3 enerallyave
heirprincipal
alue
n
resenting
an
overview
of
heerformanceharacteristics
f
ypical
jector
ystems.
Inheoretical
nalyses
r
xperimentalrograms,
ts
often
more
on-
veniento
onsider
wo-dimensional
arametric
epresentations
f
hese
operating
urfaces.
These
parametric
urves
sually
epresent
nothing
morehanntersectionsof
he
erformance
urfaces
witharious
lanes
corresponding
o
onstant
alues
of
he
espectiveariables.
T w o
of
he
moreuseful parametricepresentationsfhemasslow
characteristics re
obtained yntersectinghe
w/w surfacey lanes
of
onstant
ATM
/
p
po
t
ig..1-4,
ndlanesof onstant
so
/
P
po
i
Fig.
.1-5.
Another
nteresting
nd
seful
arametric
urve
an
e
obtained
yntersecting
he
w surface
y
lane
or
hich
P
S
-
7/26/2019 ADP000536
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wr w vw
w ~ - a .
v
- : .
,
. -
,,.- , .-,-
,-_-,
.
,,-.-
,
'WiiWW
o
0.
0?
O O O 0)
E
SO g>
5
3
o
- t - >
c
o
o
c
-
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mmss
PW SB TT JT
4P
o
a.
o
C O
c
(0
c
o
o
l/>
V
c
r'
Q.
XI
u
The
specification
fA^/A^
instead
of
/A^
is
onvenience
or
later
omparisons
etween onstant-pressure nd
onstant-areaejectors.
Utilizing
he
oregoing
ata
nd
parametric
alue
of
u,
he
mixed
as
properties
1C
M w
*
P
'?
JTC'
%
p'
YM
J
can
e
eterminedrom qs . (2.2-19),
(2.2-21),
nd
2.2-22),
espectively.
Tnemixed-to-primary tagnation
emperature
atio,
/T .an
hene
M) PO
*
N u m b e r si n
b r a c k e t s
refer
t o
e n t r i e si nR E F E R E N C E S .
^Unfortunately,
t h e
c o n s t a n t - p r e s s u r e e j e c t o r
m o d e l
i s
i n c a p a b l e
o f
d e a l -
i n g w i t h
t h i sr e a l i t y of
j e c t o r
o p e r a t i o n .
h i s
p o i n t w i l lb e c o n -
s i d e r e di nd e t a i li n S e c t i o n
2 . 3
w h e r e i nt h ec o n s t a n t - a r e a
e j e c t o r
i s
a n a l y z e d .o t e
t h a t
t h i s
s e l e c t i o n of v a r i a b l e si s
s o m e w h a t
d i f f e r e n t
t h a n
t h o s e u s e d i nS e c t i o n
2 . 1 .
999
MM
MMM
-
7/26/2019 ADP000536
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d e t e r m i n e d
f r o m
E q .
( 2 . 2 - 1 5 ) .
s i n g
t h e s e
d a t a ,t h e s o l u t i o n v a l u e
o f
M
i s
d e t e r m i n e d
f r o m E q .( 2 . 2 - 6 )
b y
s o l v i n g
Mv
H
J
s
lJ
^'
V
P H .
\?
1/2
A;;
M w
p
M O
( 2 . 2 - 2 3 )
T h e
s o l u t i o n v a l u e
f o r M
s u p e r s o n i c r o o t )i s
M2
\z
2,
1/ 2
(
MV"
C
:>\
W
1 /
2
( 2 . 2 - 2 4 )
The
nexttepsnhe
solution
rocedure
re
oetermine
gl
/
pi
and
M
1
V P
M
3' M 3'
L/D>
Minimum
requ
ired
valuefromF i g .
2.2-3
F i g u r e
2 . 2 - 4o n s t a n t - a r e a s
u p e r s o n i c d i f f u s e r n o t a t i o n
1004
-
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^y^w-iS-vraa^^-^^- ^ .->h^
2.2.1.3
Overalljectoranalysis
The
operatingharacteristics
ofhe
onstant-pressure
mixing
ection
an
e
etermined
s
utlined
n
ection
.2.1.1.
For
givenalues
of
&.
Y
P
/*, T
so
/T
po
.A
M2
/A
pi
,M l]
and arametric alue
of
u,he aluesf
can
e
determined.
Utilizinghesealues,
he
mixing ectionressure
ratios
P
P
0
/
P
soV
so3
can
heneound.
For
iven
alue
of
heiffuserpressure-riseoefficient,he
diffuserstatic-pressureise
atio,
./P,,
anhen
e
etermined.
The
M s
Ifi
overall
jector
omptossion
atio
setermined
rom
S
.2
S
P -
F 2-2-32)
S O
O
2
where
m
/P
sc
ndP /P^
re
rom qs. (2.2-18)nd2.2-30),
respectively.
The
operation
f
he
onstant-pressure
ejector
shen
stablished
inerms
f
he
ariablesu.
p
F0
/
p
S0
.
w
p
so
]
2.2.2
Constant-pressure
ejector
omputer
rogram
CPE)
A
omputer rogram
as
written,
ased
n
heanalysis
of
Section
.2.1,o
etermine
he
perating
haracteristics
f
onstant-
pressure jectors. Aomplete
istingof
his
rograms
iven
n
Appendix
.1.
1005
-
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r-
-
-
-
mm w
''
-
,.,'--~w..-'.*-. --''
.;,.*
..,
i-.^^.wf)^i.,iJ
..
....u.-
>r-
JHWIWPW
w
Thenputariables,
heir
ymbols,
ndheirdefault
alues
re
um-
marized
n
able
.2-1.
Theutputariablesnd
ymbols
re
ummarized
in
able
.2-2.
Table
.2
M
Input
variables
or
rogram
P E
Variable
Symbol
Default
alue
Y
s
G S
1.405
*p
G P
1.405
M w
s
/w
p
M W S P
1.0
T
SO/
T
PO
TS0P0
1.0
*w v
A M 2 P 1
l
M P 1
(>1.0)
r
d
R D
1.0
u= w
s
/
p
WSPI
C A S E
"NEW"
Table.2-2
Outputariables
orrogram
P E
Variable Symbol
^
M
G M
M w ^ M W p
M W M P
N C A S E
m
M M 2
SI
M S I
Asi/Si
AS1P1
P
>o/
P
s o
PP0S0
Vs o
PM3 S0
I
1006
-
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ms g
w
,
w
w.
g
p
i
i si
7
2.2.3
Representative
esults
T o
emonstrate
ypicalperating haracteristics
f
constant-pressureejector,
heejector
onfiguration
ummarized
n
Table .2-3 aselected.
Table
.2-3
Representative
onstant-pressure
ejector
onfiguration
Variable
Value
Y
s
1.4
^P
1.4
M w
Mw
5 P
1.0
T
SO/
T
PO
1.0
W
3.0,4.0
l
4.0
r
d
1.0
u
Varied
The
operating
haracteristics
of
his
ejector
ystem
are
ummarized
inig.
.2-5. From
hisigure, itslearhatheonstant-pressure
ejector
solutionexistsor
ach re a
atiooveronly
elativelysnail
range
ofmass
lowrateatios.
Corresponding
o
his
ange,
he aluef
M varies
hroughoutts
possible
ange,
-
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1. 2
1. 0
0.8
0.6
0.4
o.2^
0L_
A /A
"M2'"P1
3. 0
4.0
19
7
s
-
P
a
.405
M w
s
/
Wp
.0
T
S O/
T
PO
=1
-0
o
-
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This
onstant-pressure
ejector
onfiguration ashosenor
ompar-
isonwith onstant-areaejector
with
imilar
onfiguration,
Section
.3.3.
A
omparison
f
he
ompression
ressure
atio
haracteristics
f
he
constant-pressure
ejector
Fig..2-5)nd
onstant-area
ejectors
(Figs..3-4b,d)
ith
he
ame
alues
of\
/
\nd
,
hows
hat
both jectors
aveapproximatelyhe ame
maximum
ompressionressure
ratios.
However,
heonstant-area
ejector
s
een
o
ave
uch
roader
range
of
possible
olutions.
D u e
o
he
arge
umber
or
ariables
nvolved,
o
ttempt
as
ade
topresenterein
omprehensive
arametrictudy
of
he
onstant-
pressure
ejector
or
xpectedrends
s
onsequence
ofariationsn
theseariables. Rather,t
s
econmendedhathe omputer rogram
e
used
o
make
hese
tudies
nlyafter
aseline
onfigurationaseen
established.
.3
C O N S T A N T - A R E A
J E C T O R
A
chematic
of
onstant-area
jector
s
hownn
ig.
2.3-1. The
ejector onsistsf
onstant-areamixing
ectionwherein
he
i
nary
and
econdary
lowsnteract ndmixo
orm
niform
mixedlow
at
he
ejector
exit.
The
onstant-areaejector
as
w odistinctoperating
regimes hich
re
dentified
accordingo
hether
hemass
lowratehar-
acteristics
of
he
ejector
are ependent
or
ndependent
of
he ack-
pressureevel
imposedathe
ejector
exit. In
he
iterature
3,4],
he
back-pressure ependent
egime
s
eferred
o
s
he
mixed"
regime
nd
the ack-pressurendependen t
egime s
hesupersonic"
nd
1009
** W
m
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-Constant-area
mixing
section-
V/////////////////////////////////////////////^^^^
Secondary
M
-
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saturated- supersonic
regimes.
hile
these
designations
are
somewhat
misnomers,
theyd o ,
how ever,d e s c r i b e
the
operating
reg imes
o f
a n
e j e c t o r
i n
analogy
to
a
conventional
c onve r g in g - d ive r g in g
nozzle
[ 1 ] .
The
performance
o f
a n
e j e c t o r system
c a n
only
be
analyzed
by
estab-
lishingbotht he
conditions
f o r thesef l o wreg imest o
e x i s t
and
t he
c o n d i t i o n sfo r t r a n s i t i o n
betw een
these
reg imes.
he
transitionc o n d i -
tions
betw een
the
mixed and
supersonic or
saturated- supersonic
reg imes
a r ereferredt o
a s
the
break-off c o n d i t i o n s .
The supersonic reg ime
of
a n
e j e c t o r
i st heresult
of
the nearly
inviscidi n t e r a c t i o n
betw een
the
primary
a n dsecondary
streams
downstream
o f
their confluence,S e c t i o n
1 ,
F i g .
2.3-1.
hestatic
pressuresa tthe
confluence
of
the
flows
must
b esuchthatt h e
supersonic
primary
flow
expandsandinteracts
with
t hesubsonic
secondary
flowcausing
i t
t o
reachsonic
flow
conditionsa tt he aerodynamicallyf o r m e d
m in im um
secondary
flow
area.
sa
consequence
o f thissecondary
f l o w chok ing
phenomenon,
the
secondary
mass
flow rate
i sd e t e r m i n e d
independent
o f
back-
pressureconditions.hile
t h e
e j e c t o r
massflowrate
characteristics
are
independent
o f
t h e
back-pressure
level,
the
complex
shock,
mixing,and
i n t e r a c t i o nflow s t r u c t u r ethat g overnst h e
pressurer e c o v e r yi sdepend-
ent
o n
t h e
back-pressurel e v e l .
The
saturated- supersonic
regime
i s
a
limiting
case
o f
t h e
super-
sonic
regime.
he
e j e c t o r
conditionsar e
such
that
the
secondary
flow
reaches
sonic
flow
conditions
at
t h e
g e o m e t r i c
m in im um
area
at
t h e
conflu-
ence o f
t h e
primaryand
secondaryflows(Section1 ) .
gain,
the
mass
flow rate
characteristics
of
the
e j e c t o r
areindependent
o f
the
back-
pressurec o n d i t i o n s
while
t h er e c o mp r e s s i o nflowprocessi sn o t .
1 0 1 1
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The
mixed"
egimencludes
all
jectoroperatingonditions
or
hich
the
econdarymasslowrate
s
ependent
n
he ack-press>,reevel.
This
dependency
s
he
esult
of
heecondarylownotattainingonic
low
conditionsteitherhe
onfluence
of
he
treams
r
withinhe ownstream
interaction
egion. Consequently,oth
he
econdary
mass
lowrate ndhe
ejector ecompressionrocessreependent nhe ack-pressureevel.
The
criteria
ordetermining
he
break-off"
onditions
areerived
fromhe
equirementhat
ontinuous
ransition
etween
he
supersonic"
or
saturated-supersonic"
egimes
nd
hemixed"
egime
mustxist.
These
riteria
nd
he
etermination
of
he
break-off"
onditions
re
importantactorsn
nalyzing
nd
nderstanding
ejectoroperation.
The
onstant-area jector aseennalyzed y
detailed
nteraction
model
p,5]
hichas
een eneralized
onclude
ariable-area
mixing
sectionejectors6]. While
he
operationalharacteristicspredicted
withhisodelrenood greementwith xperiment,
he
omputational
time
equirementsnd
omplexities
liminate
his
echnique
s
n
effec-
tive
methodor
makingroad-band
parametric
tudies
f
ejector
operation.
As onsequence,he
tudy
herein
sestricted
ohe onstant-area
ejector
hich
exhibits
ll
f
heoperational
haracteristicsf
more
om-
plex eometriesut et an
till
benalyzed yimplified
ne-
dimensional
ethods.
The
one-dimensional
nalysis
rovides
esults
hat
are enerallynood greementwith
xperiment
xceptat
mal l
secondary
flowrates
hen
HJ*
-
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( 8 )
n e g l i g i b l e c h a n g e i n p o t e n t i a l
e n e r g y
d u e t ov a r i a t i o n s
i n
e l e v a t i o n
i n
t h e
m i x i n g
s e c t i o n .
( 9 )
h e
p r i m a r y
a n d
s e c o n d a r y
f l o w s
a r e
a s s u m e d
t o
b e
i s e n -
t r o p i c f r o m t h e i r r e s p e c t i v e s t a g n a t i o ns t a t e s
t o
t h e
s t a t e s
a t
S e c t i o n
1 .
T h e c o n t i n u i t y e q u a t i o ni s
p V
d A
=
0
( 2 . 3 - 1 )
c s
and
with
ssumption
2)
ecomes
PAI
+
hx\Ax
"
>**
2
-
3
-
2
)
In
erms
fhemasslowrates,
AV,
he ontinuity quation
s
w
+ = ,
s P
r
(2.3-3)
The
masslowrate, ,
sxpressed
n
erms
of
he
mass
low
unction
y
-,1/2-,\
.
-.1/2
_ W _
P A
i-.
M w o
(2.3-4)
Introducing
he
econdary-to-prirnarymasslowrateatio,
s
/w
p
,
nd
E q. (2.3-4)nto q. (2.3-3)
esults
n
n
xpression
orhe
stitic
pressureatioP../P.,
Theesults
0
PI
M S
P I
r o w
Tl
1/
T *
1
M O
PI
M w
T
M
P O
L_]
(Hu)
(2.3-5)
I n t e r m s o f t h e
m a s s
f l o w
f u n c t i o n ,t h e m a s sf l o w r a t e r a t i o ,u ,i s
(2.3-6)
P
si
A
si
I*-.
T
POT
2
V>V
M
s > >
T h e s t a t i c p r e s s u r e r a t i o ,P
s l
/
p
pl
.c a n b e
e x p r e s s e d
f r o m
E q .
( 2 . 3 - 6 )a s
1016
*-- -
-
-
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SI
P I
P
so
P
P1 s i
- . 1 / 2
S
P O
( 2 . 3 - 7 )
T h e m o m e n t u m e q u a t i o n i n
t h e
f l o w
d i r e c t i o n i s
+ +
IF
v
pv-dA)
Jcs
(2.3-8)
With
he
oregoingssumptions,hemomentum quation ecomes
P
Fl\l
+
P
S1
A
S 1
-
P
*
=
P
MsVL
"
tP,-Vt
1
i
i
Equations2.3-5).2.3-7),nd2.3-10)aneombined nd
rearrangednto
ormhats
articularly
onvenient
or
omputation;
theesults
Mv'W-
f
5
(
vPi>
Vv
sl
>
P
O
S
O
-11/2
[ T l w
_MO
M w
W
O
-.1/2
(2.3-11)
(1+u)
where
he
unction
y.M)
is
efined s
f
3
( ,M )
(HyM
2
)
M
Yd
Y-M}
-,1/
(2.3-12)
The
elationship,
3
(y
,M)
onstant,an
e
olvedor
he
a c h
umber,
M ,
s
a/
2
Lff-jiJv.
2
|\
2 ( 1 = 1 1 [ ,
1 7
1/
(2.3-13)
1017
IIIMil 1 III
-
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T h e e n e r g y e q u a t i o n
i s
P Q .
s
P t t
c s
h
+ ^-+ g z
( p V - d A )
( 2 . 3 - 1 4 )
W i t h
s i m p l i f y i n g
a s s u m p t i o n s
( 6 , 7 , 8 ) ,
t h e
e n e r g y
e q u a t i o n
b e c o m e s
_ 2 . 3 - 1 5 )
{ h
0
(
P
V - d A )
-0
^ J
. h
V * / 2 .
o r t h e
o v e r a l l
*ixin
9
s e c t i o n
c o n t r o l
1.
t h e
(2.3-16)
energy
quationecomes
wAo
s
h
soA* '
Tne
ontinuity nd nergy quationsane
ombined
longwith
Q
p
T
,
and
Wg/Wp
o
evelop
n xpression
or
he
mixed-to-primary
tagnation
temperature
atio.
The
esult
s
T n o
'I B
P
'
C
P>S
T
s
ol
(2.3-17)
THe
secono -to-P rv
tagnation
pressure
atio an
e
xpressed
oy
(2.3-18)
nerehe
ressure
atios/>
fl
nd
s
,/
s0
-*-*" >
ined
or
sentropicl o w .
For
sentropic
low,
ne
ressure
at,o
d e t e r m
f u n c t i o n
i s
d e f i n e d b y
0
Thus ,q.
(2-3-18)
ecomes
y
(Y-
1
)
;
2
(
Y
,M)
(2.3-19)
1018
-
7/26/2019 ADP000536
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so
P O
9
v
pl
}
(2.3-20)
In
he
preceding
quations,
he
as
roperties
f
he
mixed
low
at
Section must e nown. Thesepropertiesreeterminedorhemixed
gas
y
applying al
ton's
awofpartial
ressureso
hypothetical
ix-
ing rocess
t
onstantolume
orhe espective
mass
ractions
f
he
primary nd
econdary
perfect
ases.
The
mixed as
roperties
re
expressed
nermsfhesecondary-to-primarymasslowrateatio
nd
theprimaryndecondaryas
ropertiesy
P
^PX
(1+u)
M w ,
M w ~
M
1
+
li
(1+u)
w:
w > ,
(2.3-21)
1
M w
p
M w ~
(2.3-22)
and
v
Mw .
"
+
-
s i -
'M
(1
7TTirr}
-l
(2.3-23)
Y
p
VTTMW
S
The
atio
of
specific
eatst onstantressure an
e
xpressedn
erms
of
other
properties
y
M w .
(
C
P>S
(Y
r
-
D
(2.3-24)
1019
-
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E q u a t i o n s
( 2 . 3 - 2 1 )
t o
( 2 . 3 - 2 4 )
d e f i n e
t h e m i x e d g d s
p r o p e r t i e s
c o m p l e t e l y
i nt e r m s of
t h e
p r o p e r t i e s
o f
t h e
p r i m a r y a n d
s e c o n d a r y g a s e s
a n d
t h e
m a s s
f l o w r a t er a t i o ,u .
T h e
c o m p u t a t i o n a l
p r o c e d u r e a d o p t e d
h e r e i n
w i l l
n o w
b e
d i s c u s s e d .
A t t h e
o u t s e t ,
t h e f o l l o w i n g
d a t a
a r e
a s s u m e d
t o
b e
k n o w n
S
O
_ UB_
M
V
P w
p
7T
_ .
>
po
\l
Ifhe
primary
nozzle
ase
re a
s
ssumed
o
e
negligible,he
onstant-
area
mixing
ection
equirement
s
si
A
P
f A
M J
P I
1
( 2 . 3 - 2 5 )
U s i n g
t h e s e
d a t a
a n d a
p a r a m e t r i c
v a l u e
o f
u ,
t h e m i x e d
g a s p r o p e r t i e s
a t
S e c t i o n 3
c a n b e d e t e r m i n e d
f r o m
E q s .
( 2 . 3 - 2 1 )
t o
( 2 . 3 - 2 3 ) ;t h e
r e s u l t s
a r e
M w . .
' M
Themixed-to-primarylow tagnation
emperature
atio,
/T
an
hen
be
ound
rom q. (2.3-17)
A n xamination
of
qs .
(2.3-5),
(2.3-7),
nd
2.3-11)
hows
hat
he
followingariables
re
till to edetermined;
hey
re
P
M
si
W
~
PII
T h u s ,
t h i s
s e t
of e q u a t i o n s
m u s t
b e
s u p p l e m e n t e d ,
a s
d i s c u s s e d
i n
t h e
f o r e g o i n g
s e c t i o n s ,
w i t h
a n
a d d i t i o n a lr e l a t i o n s h i p b e f o r e u n i q u e e j e c t o r
s o l u t i o n s
c a n
b e d e t e r m i n e d .
h e
n e e d e d
r e l a t i o n s h i p
i s
b e t w e e n
t h e
1020
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, . -
aiSAk,.-
-
-
7/26/2019 ADP000536
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v a r i a b l e s
M
a n d P . , / P _ , o r
a
p a r a m e t r i c
v a l u e
o f
p .
h e
f o r m
o f
t h i s
r e l a t i o n s h i p ,
a s
w i l l
b e d i s c u s s e d
i n t h e
f o l l o w i n g
s e c t i o n s ,
i s
d e t e r -
m i n e d
b y
t h e o p e r a t i n g r e g i m e .
T h u s ,
w i t h
t h e
a f o r e m e n t i o n e d
i n p u t
d a t a ,
a
p a r a m e t r i c
v a l u e
o f
u ,
a n d
a
p r e s u m e d r e l a t i o n s h i p b e t w e e n
( M
P _ , / P , ) ,
a l lv a l u e s
a t
SI
SI
?
1
S e c t i o n3
c a n
b e d e t e r m i n e d
b y
t h e f o r e g o i n g
a n a l y s i s .
T h e
s u b r o u t i n e ,
C A E O C V ( . . . )
h a s
b e e n
w r i t t e n ,
b a s e d
o n
t h e
f o r e -
g o i n g a n a l y s i sf o r
t h e
o v e r a l l
c o n t r o l
v o l u m e ,
t o
c a r r y
o u t
t h e c o m p u t a -
t i o n s a s j u s t
d e s c r i b e ' .
h e s u b r o u t i n e h a s
t h e
f o r m
C A E O C V
( G P ,M P 1 ,G S ,
M S I ,
M W S P ,
T S 0 P P ,
P S 1 P 1 , A P 1 M 3 ,
N E R R O R ,
M M 3 ,
P P 0 S 0 ,
P M 3 S 0 ,P M 0 S 0 ) .
F o r
i n p u t
v a l u e s
o f( G P ,M P 1 ,G S ,
M S I ,
M W S P ,
T S 0 P 0 ,P S 1 P 1 ,
A P 1 M 3 ) ,
t h e
s u b r o u t i n e
e i t h e r r e t u r n s a
s e t
o f
s o l u t i o n
v a l u e s
f o r
( M M 3 ,
P M 3 S 0 ,
P M 3 S 1 ,
P P 0 S 0 ,
P M 0 S 0 )
o r
a
n o - s o l u t i o n e r r o r i n d i c a t o r
N E R R O R .
A
l i s t i n g o f t h i s
s u b r o u t i n e
i si n c l u d e d
i n
A p p e n d i x
6 . 2 .
2 . 3 . 1 . 2j e c t o r f l o w
r e g i m e s
a n d
t h e i r
c r i t e r i a
T h e
r e l : i o n s h i p
b e t w e e n
t h e
s t a t i c
p r e s s u r e s ,
P
a n d
P
d e t e r m i n e s
t h e
o p e r a t i n g
r e g r e
of
a n
e j e c t o r .
I f
P
P . t h e e j e c t o r o p e r a t e s
i n
e i t h e r
t h e
s a t u r a t e d -
s i
i
s u p e r s o n i c
o r t h e
m i x e d
r e g i m e
b e c a u s e
( 1 )
t h e
minimum
s e c o n d a r y
f l o w
a r e a
i s e q u a lt o
t h e g e o m e t r i c
s e c o n d a r y f l o w
a r e a a t
S e c t i o n
1 ,
a n d
( 2 )
t h e s e c o n d a r y
f l o w
i s
s u b s o n i c
u p s t r e a m
of
S e c t i o n
1
t h u s
l i m i t i n g
M
S 1
to
he
ange ,
< ^
. For
hesaturated-supersonic"egime,
he
secondary
lo ws
onict
ection
,
=1,
ndheecondary
a s s
flowrate
s
eterminedolely
y
he
pstream
onditions.
Forhe
mixed"
1021
-
7/26/2019 ADP000536
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regime,
he
econdary
low
at
Section
subsonic,
-
7/26/2019 ADP000536
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0
>r
h v
V
V
-H
ontrol
volume
'S 2
'P 2
S
F i g u r e 2 . 3 - 3
o n t r o lv o l u m e
f o r
F a b r i
c h o k i n g
a n a l y s i s
1023
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-
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at
he
minimum low
rea
s
nity,
heejector
perates
n itherhe
"saturated-supersonic"
r
he
supersonic"egime;
while
if
his a c h
number
s
ess
han
unity,
he
ejector
perates
n
he
mixed"
egime.
Thebreak-off onditions
or
ransition
etween
he
arious
egimes
must
satisfy
he
ollowing onditions. They re :
(1 )or
he
uncture
of
he
saturated-supersonic"
nd
"supersonic"
egimes:
( M
S1
)
B
0
ndP
sl
/
pi
)
B
0
;
(2 )or
hesaturated-supersonic"
nd
mixed"
egimes:
( M
e
,)
on
ndP
c
,/
ol
L>; nd
S I
O
S I
P I
O-
( 3 ) o r t h e
s u p e r s o n i c a n d m i x e d r e g i m e s :M
2
0.25
( )/
(
P
so),
7.6
K\,2
4.0
U s i n g
p r o g r a m
C A E ,
t h e i n d i v i d u a l
s t a g e
c o m p r e s s i o n
r a t i oi sf o u n d
f r o m
E q .
2 . 4 - 5 )t o b e
a p p r o x i m a t e l y
f , 0
s o
2 . 6 8
;
1, 2
t h e r e m a i n d e r o f t h e o p e r a t i n g c h a r a c t e r i s t i c s f o r t h e s t a g e d e j e c t o r a r e
g i v e n
i n
T a b l e 2 . 4 - 2 .
T h u s ,a c o m p a r i s o n
o f
t h e
v a l u e s
i n
T a b l e 2 . 4 - 2
s h o w s
t h a t
s o m e
g a i n s
c a n
b e
m a d e
b y
s t a g i n g .
h e
t w o - s t a g e
ejector
i n
t h e
a b o v e
e x a m p l e
r e q u i r e s
a p p r o x i m a t e l y 3 9 %
l e s s
p r i m a r y
m a s s
f l o w
a n d
a b o u t1 6 % l e s s
L
1042
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n.
- , . , .
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-
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m a x i m u m
rimary
ressure.
However,
n
roader iewhese ains
might
not
esignificantw h e n onsiderations
iven
o
he
additional
ardware
required. Also,
more early
ptimum
single-stage jector
ould,n
all
probability,
e
oundorhispplication.
Table
.4-2
Si
ngle nd
taged
ejector
erformance omparison
Variable
Value
(1)
Two-staged
ejector
< V
W
A,2
0.47
(p
p
2 . 6 7
**
0.497
(P
/p )
PO
SO'l,2
68
o
a >
0 1
< _ >
si
00
o
(O
l*-
o
0J
$
^ ~
o
^ ~
f
IO
4-
+J
00
00
c
3
:
o
3
c :
C
o
r
r
4 ->
->
C U
o
< u
o
00
1046
n
a )
4-
CD
MMMM
a
ass
-
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Figure
.1-2
Axisymmetric
jector
with
nf*
i.
fixingube
with?ffu
(
15W
ar1
;
bl
e
"
mixing
ube
nstalled;
nd
95'n"
ons
J
an
-
mixing
ube
"
I
-
c
onstant-area
1047
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-
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DM
s
-
7/26/2019 ADP000536
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Static
pressure
w a l l
t aps
unzznm
S e c onda r yr
flow
s o
r
so
TzamzL
Mixingtube
( in te rchangeab le )
Primary
nozzle
( interchangeable )
Primary
flow
Figure3.1-3
chematic
ofaxisymmetric
ejectcr
configurati
o n
1048
^ V s t e * * - '
MMMB
-
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715"
diam
0.020"
0.715"
diam
(a)as icconical
nozzle.
12
Slots:
equay-
spaced,
0.020"
w i de
X
.190"long
* ozzle
exit
plane
(b)
Slotted
extension
for
nozzle.
Nozz le
M
p
,
0;n.
1
2
3*
2 .0
2 .5
2 .5
0 . 5 5 0
0 . 4 4 0
0 . 4 4 0
'Slotted
nozzle
(c)ozzlespecif icat ions.
Figure3.1-4
Schematics
a n d
speci
f
ication s
o f
e j e c t o r
primary
nozzles
1 0 4 9
i*-- '
m i n i
-
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Constant-area
section
6
C
converging
section
1.250"
(a)ar iab le-area
mixing
section.
re
\
L-l
i
Constant-area
section
mssssw
(b )
onstant-area
mixing
section.
Mixing
tube
Din.
Lin.
1
2
3*
0.995
1.245
0.995
12 .500
13.000
12.882
With
6converging
section
(c)
Mixingsectionspeci f icat ions.
1.939"
5.382"
0.995"
Id ) ubsonic
diffuser
section.
F i g u r e
. 1 - 5
c h e m a t i c s a n d s p e c i f i c a t i o n so f e j e c t o r
m i x i n g s e c t i o n s
1050
biMMiMiM
.
, . : . -
-
.
m
. . . .
. - .
-
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P
T
PSN' 'PSN
Primary
AP ,
PS N
V D I
standard
nozzle
Secondary*
>
From
atmosphere
V D I
standard
nozzle
AP
S S N
P
T
SSN'
S S N
W
W
^
S O
'so
P O
P O
P (X
.
44
+
X
Figure
.1-6
Experimental
jector
et-up
nd
otati
on
1051
feM.
-
7/26/2019 ADP000536
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conical
ozzle,
nd .5
lotted
nozzle
ofig..1-4)
n
ombination
with
ach
ofhenterchangeable
mixing
ubes
1.245nch.D.onstant-
area
ube,
.995
nch
.D.
onstant-area
ube,
nd
ariable-areaube
ofFig.
.1-5). The
exit
re a
of
he
primary
nozzles
as
onstant
pro-
vidingor
dentical
reaatiosL./A.ith
ach
mixingube.
Theariable-area
mixing
ube
as
onstructed
uchhat
he
ntrance
diameter
as qual
o
he
iameter
of
he
arger
. 2 4 5
nch
.D.onstant-
areaube
while
he
exitdiameter as
quivalent
o
he
diameter
of
he
smaller
.995
nch.D.onstant-area
ube.
Pressureaps
ere
dded
n
a
0.5
nch
pacing
hroughhe
apered
sectionof
he
ube
or
obtaining
th ewallressure
istribution.
Theubsoniciffuser
of
Fig.
.1-5
as
added
o
he
ariable-area
ubenall
ases
nd
o
he.995
nch
.D.
tuben
elected
ests.
Figure.1-6
s
chematic
of
he
est
et-up
withnotation
orhe
ejector
nd
he
rimary
nd
econdary
masslow
measurement
ections.
Air assed
or
oth
he
rimary
nd
econdary
ases
n
ach
xperiment
while
p0
as
eld
onstant
nd
B
ATM
;
hus,
he
atio
po
/
P
B
r
P .
i
5
.-
was
onstant.
In
ddition,
asonstant
or
ach
un
ince
PO A TM
t h e
p r i m a r y
f l o w
w a s
c h o k e d
i n
t h e s u p e r s o n i c
n o z z l e a n d
P
f0
w a s
c o n s t a n t .h e s e c o n d a r ys t r e a m w a s
d r a w n
f r o m
a t m o s p h e r e ;av a l v ei n t h e
s e c o n d a r y f l o w l i n e w a s u s e d t oc h a n g e w
$
a n d
P
SQ
.
e n c e ,
w
s
/ w
p
a n d
P
P
w e r e t h e v a r i a b l e s i n e a c h
e x p e r i m e n t .
i n c e
t h e
e x p e r i m e n t s
S O
PO
were
erformed
with onstant
aluesof
ATM
/P
p0
ihe
xperimental
results
m a y
e
hought
of sntersectionsf
he
hree-dimensional
perating
surfaces,igs.
.1-2
nd .1-3,
with
planes
of
ATU
/
p
p0
=
onstant.
Examples
ofheesultingwo-dimensional
arametric
urves
re
ketched
in
igs..1-4 nd
.1-7.
1052
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-
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3.1.2
Experimentalesults
The
xperimental
esults
orhe
onical
rimary
nozzle
nhe. 245nch.D.
(A
pi
/
R
.333)nd .995
nch
.D.
(Apj/ZLj
.516)
onstant-area
mixing
ubes
re
presented
n
igs.
.1-7
and
.1-8.
Figure.1-7
s
lotof
s
/
w
p
s
so
/
po
- The
xperimental
valuesieery loseohe
heoretical
reak-off urves
t
xcept
t
verymall
alues
f
e
/
D
here,
sreviously
discussed,
he
lowfield
becomes
wo-dimensional
in
nature.
The
ompression
atio
ATM
/P
S0
is
plottedagainst_
n
/
P
c
in
ig.
3.1-8. The xperimentalataoints
ie
below
heheoreticalreak-off
urves
hich
imply
ndicates
hathe
ejector
as
perating
nhe
p0
/
P
.
TM
ndependentegime.
H
D u eoheomewhatongested
nature
ofhe
heoretical
A
/P
TMo
v s
P
/ P
u r v e s ,
s i m i l a r
t o
t h o s e
s h o w ni n
F i g s .2 . 3 - 4 ( a - d ) ,
t h e
P O
so
theoreticalurves ereot
ompleted
n
he
po
/
p
ATfc
-
ndependent
egion
ofFig.
.1-8
xcept
or
c
/
D
=.316,
.108,.074,
nd
. 0 43at
5
P
A
/A , .330.
Comparisons
etween
he
heoretical
nd xperimental
results
erve
o
alidateheone-dimensional
flowmodel.
From
ig.
.1-8
t
ould ppearhat
heejector as
perating
closer
o
heheoretical
break-off
urveor /A
=
.330;
owever ,
PI
rO
a
ertical
line
rawnhroughhe xperimental
data
nd
he
heoretical
break-off urveodeterminehebreak-offpoints,ndicatesifferent
T
Recal l
that
he
heoretical
s
/
w
p
vs
so
/
P
pa
urve
s
nvariant
nd
identical
o
he
reak-off
urve
nheP
..ndependent
egime.
PO AT M
,T
Refer
ack
o
ection
.3 nd
ig.
2.3-4
or
more
omplete
presenta-
tionofhe
ypicalperating
haracteristicsf njector
ystem
s
determined
rom
heheoreticalonstant-areaejector
model.
1053
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aafk
-
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J
5
< o
u
iri
V /
n
2
OO
o
*
5
4)
a
X
CN
II
5 i
t
< />
d
n
5
8 .
o
a .
a.
in
" 5
e
^ r
*
6
in
r-
C M
10
r-
6
h
a
e
2
0
o
U II
6
5
-
O
Q.
o
o
a.
< /l
too
s
a.
fO
d
r
a.
t.r>
6
o
t- >
o
u
< y *
oO
m
m
0 )
o
j-
I
(0
t
o
5 5
a
d
M/
S
M
6
i
3
8
o
1054
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-
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A
P1
/A
M3
= 0 .516
2 4k
3\-
w
s
/
w
p
=0 . 043
Theoretical
break-off
curves
Experiments
M
p]
= 2
MWg/Mw,=
so''
P 0
=
7
P
=
7
S
=
1.4
5
-
5
-
7/26/2019 ADP000536
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valuesof
w
for
ach
re a
atio.
This
acts
orne
out
y
he ata
pointsor
s
/w
p
at
A^/A
=.330 nd
0.516;hesepoints
ndicate
thathe
jectors
ereperatedsignificantly
elow
he
applicable
reak-
off
urveatower
alues
f
g
/w
p
.
The
xperimental
esults
or
he
.5onicalrimary
nozzle
n
the. 2 45nch.D. (A /A^
=
.330)nd .995nch
.D.
(A /A^
=
.516)
constant-areamixing
ubes
s
iven
n
igs.
3.1-9 nd
.1-10
ollow
he
samerendssorhe
onicalozzle.
Again,
he xperimental
values
of
s
/
p
vs
so
/
po
re
n
ood
greement
with
heone-dimensional
flow
model
xceptatow
alues
f
s
/Wp. Since
he
xperimental
ata
points
or
ATH
/P
S0
s
po
/
so
lie
elow
he
heoretical
reak-off
curves,
jectoroperation
nhe
po
/
ATM
ndependentegime
sndicated.
Addition
of
heubsoniciffuserohe .995nch.D.onstant-area
ube
idnot
alter
hemasslow
haracteristics
f
Fig.
.1-9ince
he
diffuser
affects
nly
he
ecompression
hock
structure
within
he
ejector
in
he
p0
/
P
ATM
ndependent
egime. FromFig..1-10
ts
pparenthat
theejector asoperating
loser
ohe
heoreticalreak-off
urve
with
the
iffuser;
owever,he
xperiment
withhe
diffuser
nstalled as
conducted
at /P =
.5;
hereas,he
xperiment
without
hediffuser
PO ATM
wasp e r f o r m e d withPP
=
6 . 2 .
hed i f f e r e n c e
i n
P/P
A
, . . ,
a s w i l l
O
ATM
O
ATM
b e
d e m o n s t r a t e d
below,
should
have
been
responsible
for
t h e
d i f f e r e n c e s
i nP
?
values
withand w i t h o u t
t h e
subsonicdiffuse r.
ATM S O
The
xperimental
results
*orhe .5
lotted
primaryozzle
n
trie
. 245
nch
.D.
(A
/A
=
0.330)
nd
.995
nch
.D.
(A
/A
=
p
i
M S
i
.a
0.516)
onstant-area
ixing
ubes
reresented
n
igs. 3.1-11
and
3.1-12. FromFig. 3.1-11 the
xperimental
ata
or w vs
/P
PS0P0
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C O
u
CO
r-
_
< U
t- >
-
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12
A
P1
/A
M
3
=
0 . 516
Theoretical
break-off
curve
Experiments
M
p
,
=
2 .5
Mw
s
/
Mw
p
=
T
so/Tpo=1
5
-
5
-
7/26/2019 ADP000536
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I/)
i.
< D
+->
U
(O
S -
(O
-C
u
2
o
ifl
i.
n
0
4 ->
M
o
< U
I
-5
*?
N
O
N
O (0
c
1O
-a
c u
n
+J
+ Jo
o
r
t/ >
O
ro
ro
C Uo
s.
iq
n
= J
gt
* >v.
< />
*
t_)
.
ai
C 7 >
u.
1059
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18
16-
14
.
12
o
Z
10
U
i-
t- >
u
3
2
o
1
o
o
a ;
< u
^ ~
ID
0>
r
C V
rM
IS I
II
O
c
1
o
Z
0 )
JLJ
o
4J
c
o
-
I/I VO
I
in
a
0)
O
s -
(0
1
ii
i
a
1069
-
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1.5-
QL
J
'
I't-
xperiments
M
pl
-5
0.5-
A
P 1
/A
M
3
-
0.516
MWj/MWp
7
*r,
"
1.4
5. 6
I?
W'
ATM
o -
o . .
0 .5
1. 0
- . .
6
Curve
w
s
/w
p
1
2
3
0 .0
0.144
0.254
j_
.5
x,
n c h e s
2. 0
2 .5
3. 0
Figure
.1 -21
Variable-area,lotted-nozzlejector a ll
ressure
distributions
A^/A^
0.516,
2.5,
nd
P /P
to'
A TM
5.6)
1071
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-
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2.0,
1.5
?
..,....,0.
05-
o -
->
Q'o
p -
xperiments
M
p
,
2.5
A
P 1
/A
M3"-
5
6
M w
s
/ w
p
-
T
S (/
T
P 0
"
7p
-7
8
-
4
V
A TM 4- 2
0. 5
1.0
9
' " o
T4
Curve
w
s
/w
p
1
2
3
0.0
0.155
0.262
JL
1.5
x,nches
2. 0
2. 5
3.0
F i g u r e
3 . 1 - 2 2
a r i a b l e
a r e .
s l o t t e d - n o z z l e e j e c t o r
w a n
p r e s s u r e
d i s t r i b u t i o n s
U,//^
- 0 . 5 1 6 . ^
2 . 5 ,a n d
P O
ATM
1072
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nozzle s pposedo
he
onicalr imary ozzlesof igs.
.1 -15hrough
3.1-18
nd
m a y ccount
orhe
excellent
greement
ofhe
w
s
/ vs
P
so
/
po
ata
with
he
heoretical
reak-off
urve
of
ig .
.1-19,
althoughhe onstant-areamixing
ube
ata
f
ig .
.1-11
ould
preju-
dice
ny
onclusions ased
n
r imary
ozzle
esign
lone.
Again,
ote
that
nly
henitial
ortions
of
he allressure
distributions re
presentedn
igs.
.1-21
nd
. 1 - 22 .
1073
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-
. .-
4.0 C O N C L U S I O N S
Only
o m e
eneral
onclusions
will
e
rawn
n
his
ect ionince
specific
onclusions
erencluded
n
heoregoingections.
The
on -
clusions
re :
(1 )
he
onstant -area
jectorlo w
model
nd
omputer
rogram
should
edoptedshe
asis
oresignnd
ystem
tudies.
This
model
most
ealistically
predicts
he
operational
haracteristics
of
ejector
systems.
The
elationship
nd
orrespondence
etween
ariable-area
nd
constant -areamixing
ube
jectorshouldestablishedyot hxperi-
mentnd
analysis.
(2 )
he
analysisofvariable-areamix ing - tubejectors
hould
e
cont inued.
(3)heesign
fpotential
igh-performance
jector,
us t
mprove
mixing
ndo m e n t u mransfer;
e m eesigns
with
potentialre :
unsteady
flow,
eriodic
pulsating
low,
esonance
henomena,
nd /or
arious
nozz le
nd
mix ing - tube
eometr ies.
(4)
he
omputer
modelsevelooed
nhistudy
hould
eugmented
an d
ncorporated
ntonoverallystemrogram
nd
urthermprovement
of
ub-system
models
houldeont inued .
I
MBffiUAfiiai
BUMC-MOT
111*0
1075
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w w w s r v - - - - -
: