Spaid, Frank W.

Zukoski, Edward E.

English

Caltech Authors - Main

Further Experiments Concerning 
Secondary Injection of Gases into a 
Supersonic Flow 
FRANK W. SPAID* AND EDWARD E. ZUKOSKlt 
California Institute of Technology, Pasadena, Calif. 
NOlnenclature 
c discharge coefficient 
Cp * pressure coefficient corresponding to stagnation condi-
tions behind a normal shock in the undisturbed flow 
d hole diameter 
h scale parameter 
M Mach number 
P static pressure 
Po stagnation pressure 
ReL Reynolds number based on distance between leading 
edge of the plate and injector centerline 
x, y, z·= coordinate axes 
')' specific heat ratio 
il boundary-layer thickness 
Subscripts 
j = injectant stream 
OD = primary stream 
AN earlier paper presented by the authors l described a study of the flowfield associated with the sonic injection 
of a gas through a wall and normal to a supersonic primary 
flow that is uniform and rectilinear outside a wall boundary 
layer. The results of a series of wind-tunnel experiments 
were presented, and a scale parameter was proposed, based 
upon a simple, inviscid model of the flowfield. New informa-
Received September 22, 1965; revision received August 17, 
1966. 
* Graduate Student; now Engineer/Scientist Specialist, Mis-
sile and Space Systems Division, Douglas Aircraft Co. Inc., 
Santa Monica, Calif. Member AIAA. 
t Professor of Jet Propulsion. A5sociate Fellow AIAA. 
Reprinted from AIAA JOURNAL· 
Copyright, 1966, by the American Institute of Aeronautics and Astronautics, and reprinted by permission of the copyright owner 
DECEMBER 1966 TECHNICAL NOTES 2217 
tion, resulting from an additional set of wind-tunnel experi-
ments, is presented in this note, which extends the range of 
the data published previously and which enables a more 
precise determination of the limits of applicability of the 
scale parameter. These experiments were conducted in 
the 20-in. supersonic wind tunnel at the Jet Propulsion 
Laboratory (JPL). The analysis of Ref. 1 and all of the 
experimental data pertaining to injection through circular 
holes are given in Ref. 2. 
The right-handed Cartesian coordinate system, which is 
used for describing the flowfield, is as follows: the x axis 
lies in the plane of the wall, passes through the center of the 
circular injection port, and is parallel to the primary flow. 
The origin is the point of intersection of an extrapolation 
of the bow shock wave caused by injection with the x axis 
and the direction of the primary flow is taken as positive: 
The wall is the x-y plane, and the z axis is normal to it. 
The proposed scale parameter, a characteristic length scale 
for the flowfield, was calculated from a momentum balance 
in the x direction. The equation for this scale parameter 
h is as follows: 
d(~1/2 = [(~J(~: ~: C:*Y'2 X 
{
_2_ (_2_)('Yi+1)!(1'i-ll[1 _ (Pm)(1'i- 1l/-Yi]}114] 
"Ii - 1 "Ii + 1 POj 
(1) 
Figure 1 is a plot of normalized static pressure P /P ro vs 
the dimensionless distance along the x axis, x/h. Data are 
presented for a variation of h of a factor of about 4, for 
gaseous nitrogen, and for helium injectants. The primary-
stream Mach number was 3.50, and the boundary layer in the 
vicinity of the injection port was turbulent. In Ref. 1, 
only laminar boundary-layer data were presented at this 
Mach number. It can be seen that the scaling is reasonably 
good, but that some discrepancies exist. 
The region where the nitrogen injection data of Fig. 1 show 
the poorest agreement is 3 ::; x/h ::; 5. This region has been 
called the reattachment region, because it is believed to be 
the region in which the injectant jet attaches to the wall. 
In Ref. 1, the authors suggested that the pressure variation 
in this region was a function of the injectant-to-freestream 
pressure ratio POi/Pro. This assertion was tested by com-
paring pressure distributions of flows for which the total 
pressure of the injectant was held fixed and for which h was 
changed by changing the diameter of the injector. The re-
sults (see Fig. 2) clearly show that the pressure overshoot 
changes rapidly with hole size, and therefore that this sug-
gestion is incorrect. 
2.5 
2.0 
1.5 
0.5 -
o 
-6 -4 
L \ 
-2 o 2 4 
X!h 
SYMBOL h.cm INJECTANT 
, 0.503 HELIUM 
0 1.012 NITROGEN 
-- 2.03 NITROGEN 
--- 0.515 NITROGEN 
Po= = 2.38 atm. 
R'L = 2.24 x 10
6 
M== 3.50 
d ...;c = 0.250 em 
6 8 10 12 
Fig. 1 Influence of scale height on flat-plate static-pres-
sure distributions in plane of injector: turbulent boun-
dary layer. 
2.5 
SYMBOL h. Cm dYc:~m PO;/Fl 
0 0.620 0.075 16.85 
2.0 ~ '" 2.06 0.250 16.70 
<l> 4.06 0.500 16.38 
p,,= = 1.32 atm. 
~ ReL = 1.99 X 10· 
M= = 2.61 1.5 
<l> 
1.5 
~~6-----4~---~2~--~0~Y-h~2----~4----6~---8L---~10--~'2 
Fig.2 Flat-plate static-pressure distrihutions in plane of 
injector with constant injection pressure ratio: turbulent 
boundary layer. 
A second hypothesis was proposed in which the ratio of h to 
the boundary-layer thickness {j was the important parameter. 
Because the boundary-layer thickness was not changed, this 
suggestion was tested by varying the injector diameter and 
injection pressure ratio in such a manner that h was held 
fixed. Three comparisons were made with Mro = 2.61, 
h/{j = 5.8; Mro = 2.61, h/{j = 1.5; and Mro = 3.5, h/{j = 
5.8; and in each, the injector diameter was changed by a 
factor of 2. The results, an example of which is presented 
in Fig. 3, are in excellent agreement, despite the two-to-one 
change in injector diameter. This suggests that the ratio 
h/{j is important in fixing the phenomena responsible for the 
pressure overshoot at the reattachment point. Data are 
also presented in Ref. 2 which indicate that the scaling pro-
cedure begins to fail when the ratio of h to the injector diam-
eter hid approaches unity. 
The data of Fig. 1 also exhibit a discrepancy between data 
for nitrogen and helium injection in the region downstream 
of the injection port. Additional data for a direct COill-
2.0 
IS 
p 
p= 
1.0 
0.5 
0 
-6 
2.0 
~/h .:; 1.1 
y/h o 0 
~ .. J 
-2 0 
'in 
A/h .:; 2.1 
Poco = 1.32 otms 
Rl"L':; I gg II 10 
Mao= 2.61 
8 1.0 1.2 
0',';-0 ---7-, ---:!-2 --~3 O.\---L., ---'2!-"'-'3 0:c----7----,..---,3c-~,----: 
Yin yin 2 Yin 4 
Fig. 3 Flat-plate static-pressure distrihutions in several 
planes with constant scale height hut with different injec-
tion port diameters: turhulent boundary layer. 
2218 AIAA JOURNAL VOL. 4, NO. '12 
y/h = 0 
2.0 
1.5 
P 
p~ 
1.0 
0.5 
0 
-6 -4 -2 
~~5b~h = -0.64 
.0 
10 I 
I 2 3 
Y/h 
b) 
0 2 
Xfh 
4 8 10 12 
a) 
1.5 
x/h = 3. 
0.5 
°0~--~--~2--~3~~4~--~ 
Y/h 
c) 
Fig. 4 Influence of injectant properties on flat-plate sta-
tic-pressure distributions in several planes: lalllinar 
boundary layer. 
parison between nitrogen and helium injection at a Mach 
number of 3.50 and with a laminar boundary layer near the 
injection port are presented in Fig. 4. The value of h is ap-
proximately the same for the two cases that are shown here. 
Figure 4a gives the pressure distributions along the x axis, 
and Fig. 4b shows the pressure distributions along lines 
parallel to the y axis at values of x/h of -0.64, -1.75, and 
3.4. The distributions upstream of the injector, at -0.64 
and -1.75, are identical. However, there is a systematic 
difference in the downstream distributions; this difference 
is illustrated by the example shown here, at x/h = 3.4. 
This difference is most important at the x axis, and it decreases 
with increasing y/h. Note that, for this off-axis cut, the 
difference between the two pressure distributions at the x 
axis was approximately maximum. In this experiment, 
h/o is constant and h/d(c)1/2 is much greater than 1; conse-
quently, the differences shown by the curves of Fig. 4 are 
most probably due to changes in injectant composition. 
Data presented in Ref. 2 comparing nitrogen and helium 
injection at a Mach number of 2.61 exhibit characteristics 
similar to those shown in Fig. 4, except that the lower Mach 
number data show a much less pronounced difference between 
the nitrogen and helium injection. These data indicate 
that the shock system and boundary-layer separation caused 
by injection of helium and nitrogen are the same when equal 
values of h are used and that the effective obstacles created 
by injection are the same. However, the markedly higher 
pressures observed in the reattachment region for injection 
with helium indicate that this zone is strongly affected by 
the composition of the injectant. 
The data presented here support the validity of the scaling 
procedure proposed in Ref. 1. These results indicate that 
h/o should be matched for accurate scaling of the attachment 
region of the jet, and that the precise value of the pressure 
ratio POj/P", is relatively unimportant if h/o is matched. 
This result applies if POj/ P '" is sufficiently large such that 
hid is not near unity. Experiments with nitrogen and helium 
injection indicate that the effective obstacles created by 
nitrogen and helium injection are the same if h is matched, 
but that differences in the pressure distributions occur in the 
region near the x axis and immediately downstream of the 
injector. 
References 
1 Zukoski, E. E. and Spaid, F. W., "Secondary injection of 
gases into a supersonic flow," AIAA J. 2, 1689-1696 (1964). 
2 Spaid, F. W., Zukoski, E. E., and Rosen, R., "A study of 
secondary injection of gases into a supersonic flow," Jet Pro-
pulsion Lab. TR 32-834 (March 1, 1966). 


Further experiments concerning secondary injection of gases into a supersonic flow

A study of secondary injection of gases into a supersonic flow,&quot; Jet Pro pulsion Lab.

A study of secondary injection of gases into a supersonic flow,&quot; Jet Propulsion Lab.

Secondary injection of gases into a supersonic flow,&quot;

https://authors.library.caltech.edu/21557/1/178_Spaid_FW_1966.pdf

Further experiments concerning secondary injection of gases into a supersonic flow

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