The integration of ejectors into forebodies is considered for transonic and supersonic flight. Topics discussed include mixing flow in ducts, prediction of flow fields and external aerodynamics

Duvvuri, T.

English

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INTEGRATION OF EJECTORS INTO HIGH-SPEED AIRCRAFT
T [rumalesa l)uvvur.i
Duwuri Research Associates
Chula Vista, California
The subject I will talk about is of interest in the sense that most of
the studies and analyses that are done on the ejectors are for static case
and do not attend to the forebody effects. Because most of the ejectors
are mounted on something, we might call the analysis that we have essen-
tially isolated ejector analysis.
Now everything that we normally see in these analyses is what we might
caJl rect[llnear mixing; in other words, we assume that the two flows, the
primary and the secondary, are more or less parallel. But even a very small
pressure differential could create a curvature in the flow, and then the
rectiJlnear ;nixing has to be modified to account for the curvature. For
example, tllis would modify the eddy viscosity, and in cases where you |lave
coanda jet, the flow will be completely as_nmetric. There is no asymmetric
in the flow at all inside the ejector. In addition to this, when the fore-
body is put in there, the flow that enters the ejector is not a very simple
f]ow. So we have the question, what happens? We spend money developing a
beautifu] ejector producing 2.5 to 3 augmentation. Then we put it on a
machine that we would like to fly and find it doesn't work. The problem
that I am talking about is essentially the integration of ejectors into
aircraft (fig. I).
In general terms, what 1 am saying is valid whether you're considering
subsonic, transonic, supersonic, or whatever sonic you're considering
because you always have the same problems except that there may be differ-
ences in the actual flow field. For the purpose of illustration, I have
just shown here two cases: one for the transonic and one for the super-
sonic case. As far as the forebody is concerned, it could be either a
fuselage, a wing, a nacelle, or anything. It doesn't matter. I have just
shown a type ol airfoil situation there.
Before we look into the flow field that is shown there, let us first
ca_ic_l the transonic case. In the transonic situation the flow that enters
it|to the ejector is that flow which is downstream of the shock boundary-
layer iilteraction region. If there is no shock wave, in other words, we
have a smootll supersonic flow, then we still |lave a boundary layer that
eqt_,rs into the ejector. Depending on the width and the thickness of the
bou_dary layer the' flow that enters into the ejector will have a very
_lonunilorm flow. _:ven if you consider a situation where you don't have a
boundary layer, you still have the pressure field due to the forebody
whi_:h is not uniform necessarily in front of the ejector. Also, if you
,-onsider the upper and lower sides, the pressure distribution is not neces-
sarily the same all the time, so you have asymmetry. All these factors are
225
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very important in finding out whether the ejector will do what we want it to
do, as far as tile inlet portion of the ejector is concerned.
With tile exit portion we have to consider the question of matching
between the flow inside and outside --tile external flow coming over the
ejector flap and that which is coming from inside where they are mixing. So
this is the other aspect that is very important in analyzing the integration
of the ejector into the aircraft. Below I showa situation where we have
a supersonic flow. Of course, under these conditions you have a bow shock,
then subsonic region, then a sonic and a supersonic flow. This can shock
down into the ejector. All these things are going to makea lot of differ-
ence. If the flow inside is supersonic, it will have to match that external
flow through Prandtl-Meyer expansion. All these things are very important
in terms of the actual usages of an ejector, whether it be in flight or
hover, in transition, or a few minutes after takeoff while it's going up -
wherever there's a flow over the forebody.
What we are really saying is that the whole problem should be looked
into as a single problem. Of course, one can divide up the analysis of each
of these items separately. For example, one can develop a mixing analysis
for tile flow inside, just as I have seen several very nice analyses today.
Or you might just develop an external aerodynamics analys_s to present what
Lhe flow would look llke outside. But then these have to be matched
together in order to get the actual flow field and see whether the ejector
w_ll do the job we want it to do. Naturally we'll also be interested in
finding out whether we could design an ejector for a given type of pressure
distribution in the exit plane, which meansthat we should be able to modify
the shape of the ejector flaps or the forebody, whatever it be.
This is a problem that we think is very important, and in my review
for all the available literature, I haven't comeacross anything that has
been done to this end. Consequently, we have developed a methodology on
how to do the various aspects. I'm going to talk about those, and of course
wc arc interested in finding someonewho might be interesting in supporting
it. The way we say it can be done is, for example, I was talking about
boundary-layer mixing; this is the type of thing that has primary and
secondary flows, so when i say parallel, I don't meanexactly parallel -
there could be slight differences in angle. But whenever there are pressure
diflerentials between the lower and upper, or anywhere, there is going to
be a correction AP which is simply related to the curvature of the flow.
So tl_c curvature is very important. What I'm going to show is the work we
have done in this connection as a starting point. The work is connected w_th
taking into account the effect of curvature on the mixing inside a given duct,
and that's what I'm going to show in the next few figures. After I will
show how we have developed a methodology to match the external and internal
flows for a simple case of a kind of average velocity assumedon these two
_][dcs two different velocities, naturally. Thenwe'll examine the
methodology for predicting the flow field over a system like this (fig. 2).
Nowhere we are considering a situation where we have a differential
bctw_.cn the secondary and the primary, and this leads naturally to correcting
226
the flow. Tile mixing region will be curved, and the flow within the duct will
be entirely nonsymmetric. It is quite possible that the jet boundary will
reach the wall either on the lower or upper side first, and this makesa
difference as to what kind of pressure profile you're going to have within
tile duct. Also, depending on the length of the duct, the pressure profile
at tile exit then is going to be different. Here this is just nomenclature
to show: rlui simply meansthe inner jet boundary, etc. Nowour analysis
modifies the eddy viscosity to account for the curvature, and with that we
have someresults which I will show.
Figure 3 showsessentially the various types of nonuniformity that you
can find within an ejector, depending on what type of curvature you have in
tile initial flow region. For example, the upper jet boundary may reach tile
wall earlier or later. The main jet itself may extend beyond the point
where the lower and upper boundaries reach the walls. Eachof these makes
a different type of nonuniformity. Even if you have a pipe-type of flow
where everything is turbulent, you still have a nonuniform profile.
In figure 4(a) we have taken a duct inclined to a primary at 45°,
and we have considered a centerline jet of I00 ft/sec, about 40 ft/sec on
tl_e top, and 20 ft/sec on the bottom. This produces a certain curvature.
You can see that the lower jet already reaches the wall muchbefore tile
upper jet boundary reaches the wall. The center line is also curved, but
[t naturally uncurves itself as soon as it reaches the lower boundary.
You can see that there is already a nonuniformity. For example, the
._econdaryflow that is coming from outside and this is all the mixed
turbulent flow.
Figure 4(b) shows the velocity distribution at the three places. We
have a hundred ft per second centerline velocity decaying naturally as you
go along tile duct. You can see that the centerline velocity and the velocity
in the lower boundary becomealmost equal. But tl_e upper velocity does
not it still takes a lot of time. For example, in this case, at 8 ft
we still haven't reached equilibrium or a completely mixed flow yet.
Figure 4(c) shows the pressure distribution. This is a pressure which
is i,litially constant in the jet-core region, and the pressure increases
as we go ¢Io_I along the duct and this line. Both tile pressures on either
side are like that; you see the difference is very sma]l. You can see also
that even that small difference (less than a pound or half a pound) could
still produce a curvature that has very large effect on the flow field within
the duct. Figure 4(d) showswhat happens to the velocity profile within the
duct. To start with, you have the natural top hat, but an asymmetric top l_at,
because the velocities are not the sameon both sides. They gradually mix
xo t lmt the invlscid core is gradually annihilated. Finally, it reaches the
area where the mixing is taking place. Hereafter there is a situation where
one side has reached the wall and the other side has not reached the wa]].
';'his shows the velocity profile in the duct.
Esscnt/a[]y what these figures show is that even a small amount of
pressure differential across the primary could lead to very important effects
227
within the duct with manynonuniformities. Any analysis of ejectors should
take this fact into account, and the question of matching becomesmore urgent
because it cannot match and simply say the pressure is ambient outside. Then
you'll have a very long ejector -- i00 ft longer or 200 ft longer before
you reach complete matching of pressures from either side.
Figure 5 shows the other aspect of which I was talking. Namely, how
do you know what flow or what velocity should be there in the inlet portion,
in order to arrive at a matched pressure at the exit plane? Of course, we
developed the methodology, and it depends on what we call parametric differ-
entlation. It sLarted with the usual differential equations of all the flow.
Each of the variables is a function for the geometries of the pressures of
the in|tial velocities, and so on. You can differentiate each of the flow
equations and comeup with a set of equations which are functions of the
parametric planes. IIere I am showing, for example, a simple situation
where you assume that the flow velocity on one side is U]g and on the
_ther side is U2g ("g" for guess). You get a pressure from that, then you
integrate the basic and parametric differential equations. You can use
several analyses or parametric methods, and you come down to the exit plane
and ask whether the pressure difference on the lower side is less than a
given value. If it is less, see what happens on the upper side. But also,
if it's the correct thing, no problem. Otherwise, you have to correct the
initial guess that Ulg is corrected by the factor &Ulg which comes out
of this solution. As we proceed along the gU that we calculated at the
end and that can be substituted, you get a new value of the U1g and U2g.
You go ahead and iterate until you get a convergent solution. This is the
second aspect of how to match these two things. Of course, I have done it
for a single velocity on either side, but this could be done for a velocity
distribution. You can assume that UI$ is like an average velocity and
you have a certain distribution over t_at place. You can still do the
same thing.
The third aspect that I will talk about is shown in figure 6 - the
externa] aerodynamics. Here we are considering a simple forebody. You
c:an ]lave any type of forebody- you can have a nacelle if you want. You
can still do the same type of work. What we're simply showing, for example,
is the stagnation streamline of the forebody. There are two stagnation
streamlines off the ejector flaps in the two-dimension_l case. It simply
shows the amount of in-flow that is ingested into the ejector from the top
and the bottom. Then you have a certain jet that is coming out of the exit
plalle. This jet naturally is also going to produce some lift, as you have
seen in the paper by Bevelaqua, considering this particular aspect. I won't
go Lnto any great detail except to say that in the analysis for _ the
velocity potential, _ is the stream function and, as you know, the circu-
lation is related to the &_ jump. If you take two points on a particular
line on this jet, they don't have the same potential. There will be a
potential jump between those two points.
Th_s methodology is valid for high subsonic and also small supersonic
flows that have no shocks. But if you have shocks, then the analysis that
1 have to talk about here must be modified. The center will have to come
228
up with someother method, like transonic analysis, that is available right
now, manynumerical analyses using relaxation methods. But this is valid
for subsonic incompressible flow up to high subsonic speeds, and you don't
have to makeany changes in the methodology -- it remains the same. It
becomesvery simple for incompressible flow, and the methodology is very
similar to Spence's work. _lat you essentially do from this physical
plane is go into a complex potential plane where the airfoil and the
augmenter flaps and the jet becomea cut on the _ axis. You see this,
of course, is the jump because of the amount of flow ingested into the
ejector. This distribution is essentially the amount that has been ingested
at different points around the boundary. From there we can transform this
to another situation where it becomesjust a simple cut on the _ axis, real
axls. Wecan makeanother transformation so that the whole flow field,
essentially the upper portion of the semi-infinite plane, with the airfoil
and the _et being reduced to a small piece D' to D' on the axis.
There are different methods. For example, this morning you heard of
a method of how to account for the flap which was a one-sided flap in the
paper by Mr. Woolard. Thosemethods all assumethat the ejector is very
thin almost like one singular line. This method that we have developed here,
however, is valid even if you get a very thick jet. The boundary condition
matching happens right at each of the upper trailing edges and lower trailing
edges of the ejector flaps. Pressure matching has t_ be done there. Also,
for example, if one wants to design something; say that I give you this
kind of pressure distribution, why don't you give mewhat the ejector should
look like, what the forebody should look like. That can be done. You can
impose the pressure distribution that is required in one of these planes.
The pressure distribution is translated into the velocity which you impose
and that way you can do this work. Of course this leads to integral differ-
ential equations that have to be solved and this is where we are right now.
Wehave reached the stage where all the equations will double up then, and
it is a question of implementing the equations, writing the difference
equations, and so on.
Onepoint I want to makevery clear is what happens to B' to C'.
Let meget that number, what is it? Which is the boundary? What are the
flow velocities there, etc. Nowthis is essentially where this matching
analysis comes: the matching procedure. You start at a certain distribu-
tion of Ulg or Up on either side, then carry out the matching procedureto find out what th_s meansin terms of the pressure differential at the
end. if it's wrong, then you proceed. The important point essentially is
that once you assumea certain thing, go ahead and compute the whole flow
[ield, and match it to the ejector exit plane. Then whatever is happening
here becomespart of the solution.
Jn summary,we feel that it is very important to do this analysis and
take the integration of ejectors into whatever forebody you are having, from
the beginning. At the sametime you should have isolated ejector analysis,
experiments, and things like that to get them up to beautiful augmentations.
Thank you very much.
229
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TRANSON IC
'1=,
y
SHOCK BOUNDARY-LAYER
INTERACTION
f A / JBOUNDARY LAYER
TERNAL FLOW MATCHING
INDUCEu _ / -- INTERNAL FLOW
SECONDARY J I_, /
FLOW / i _ /
PRIMARY i _'_
NONUNIFORM
INLET FLOW
Uoo >1
SUPERSONIC
BOW
s.oc \ soN,c
_ LINE SUPERSONIC
'SUBSO_NIC EXTERNAL SHOCK
FLOW J_=._.---..._FLOW -._d WAVE
_*'/__ ---'-.__ EXTERNAL FLOW
SEPAR._.TED) _\____ ,_,T=,',_,^, ,-, _,
IDEALIZED MIXING
PRIMARY
\,.ouoEo  EXTE.NA.CONTOU.J°PT'M'sE°
FLOW
Figure I.- Schematic of ejector integration problem.
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(a) Jet mixing zone boundaries, jet centerline and mixing duct walls.
Figure 4.- Flow-field characteristics inside the duct. Inclined ducted jet
mixing; table V, case ii.
233
CJ
W
O]
D_
>-
[_)
_D
__J
W
700
600
.500
400
300
200
tO0
0
X (FT)
(b) Velocity distribution along the jet centerline and along the upper
and lower duct walls.
Figure 4.- Continued.
234
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[b
tO
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2600
2500
2qO0
2300
2200
2100
2000 ......'.....I ' I ' I ' -4- '
0 2 4 6 B tO
X (FT]
(c) Pressure distribution along the jet centerline and along the upper and
lower duct walls.
Figure 4.- Continued.
235
qU_
I,I
3
0
-I
-2
-3
0 2 4 8 8 tO
XI (FT)
(d) Velocity profile across the mixing duct for increasing distance along
the jet centerline _.
Figure 4.- Concluded.
236
4 I' -- _
I
f
1
I
F
!
r_
i
_o_
P
compute PI,P2 via
Bernoulli Equation
Integrate the Basic and the ]
Parametric Differential Equations,
Eqs C.3,C.6,C.7, by Runge-Kutta
or other Suitable Method
Yes
/
No
No
r+l r ^ _ [
Ulq =Ulg-aU_% I
r_l r
Ifrom Eqs C.39_
I C.40
Figure 5.- Flow chart for the iterative solution to determine correct entrain-
ment velocities of secondary flow at the mixing duct entrance.
237
_p=K
__oo__,_ / \_;. "../
(a) PHYSICAL PLANE; Z= X+iY "..-._/p/O/_............ - ....
E"
F_OO
(b) COMPLEX POTENTIAL PLANE; w = _0+ i_
\ ,
I
I
t-
I
D E_
F oo A' B C
- I l
I
D'
(c) COMPLEX POTENTIAL PLANE; ws = _;s+ iCs
EL
E&o
E--
'5F o= D' C' B' A
-- 1 1
(d) AUXILIARY PLANE;x = _ + i6
BC
I I
D
EC_
Figure 6.- The problem in Z_ w_
238
w and ×
s
planes; nomenclature.


Integration of ejectors into high-speed aircraft

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