Empirical correlations are given relating the mixture-ratio distributions produced by various configurations of impinging-stream injectors and the ratios of density, velocity, and orifice cross-sectional area of the two fluids being mixed. Injector-element designs studied are two-on-one, two-on-two, and four-on-one

Elverum, G. W., Jr.

Morey, T. F.

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CASE FILE 
COPY
1S2O'7 7& 
MEMORANDUM NO. 30-5 
CRITERIA FOR OPTIMUM MIXTURE-RATIO DISTRIBUTION 
USING SEVERAL TYPES OF IMPINGING-STREAM 
INJECTOR ELEMENTS 
G. W. ELVERUM, JR.
T. F. MOREY 
JET PROPULSION LABORATORY 
CALIFORNIA INSTITUTE OF TECHNOLOGY
PASADENA, CALIFORNIA 
FEBRUARY 25, 1959
https://ntrs.nasa.gov/search.jsp?R=20150018528 2019-08-31T06:02:18+00:00Z
National Aeronautics and Space Administration

Contract No. NASw-6 
Memorandum No. 30-5 
CRITERIA FOR OPTIMUM MIXTURE - RATIO DISTRIBUTION

USING SEVERAL TYPES OF IMPINGING-STREAM

INJECTOR ELEMENTS 
G. W. Elverum, Jr.

T. F. Moray 
D. R. Bartz, Chef 
Powerplant Research Section 
Copy NO.HC252 
pp. iii, 1-11
JET PROPULSION LABORATORY
California Institute of Technology

Pasadena, California 
February 25, 1959
Copyright ® 1959

Jet Propulsion Laboratory

California Institute of Technology
Jet Propulsion Laboratory	 Memorandum No. 30-5 
CONTENTS
Page 
I. Introduction ................................ . ................................................................................................... 	 1 
II. The Use of Impinging Streams .................................................................................................... 2 
Ill.	 Results .......................................................................................................................................... 3 
A. The One-on-One Element ..................................................................................................... 3 
B. The Two-on-Two Element .................................................................................................... 4 
C. The Two-on-One Element....................................................................................................5 
D. The Four-on-One Element...... .............................................................................................. 	 6 
IV.	 Conclusions .................................................................................................................................. 7 
References .............................................................................................................................................. 9 
Figures.................................................................................................................................................... 
FIGURES 
1. Typical Quantity Distribution for Two-on-Two Injector .............................................................	 10 
2. Typical Mixture-Ratio Distribution for Two-on-Two Injector ................................................... 10 
3. Volume Mixture-Ratio Distributions for 60-deg Triplet Injector .............................................. 	 fl 
Page iii
Jet Propulsion Laboratory 	 Memorandum No. 30-5 
ABSTRACT 
I Empirical correlations are given relating the 
miture-ratio distributions produced by various configura-
tions of impinging-stream injectors and the ratios of 
density, velocity, and orifice cross-sectional area of the 
two fluids being mixed. Injector-element designs studied 
are two-on-one, two-on-two, and four-on-one. I
I. INTRODUCTION 
The primary function of the injector in a liquid rocket engine is to deliver the propellants 
to the combustion chamber in such a manner that complete and stable combustion in a minimum I volume will be achieved. While a number of factors can influence the stability of combustion, the 
efficiency attained is primarily dependent on the uniformity of the mixture-ratio distribution pro-
duced by the injector. 
Most engines are operated near to over-all mixture ratios corresponding to the maximum I	 of the theoretical-performance curve. Since any deviation from this mixture ratio therefore results in lower performance, it is apparent that not only over-all but local mixture ratio must be accurately 
controlled if highest performance is to be attained. Combustion may be kinetically complete in 
relatively short distances over a wide range- of mixture ratios for any particular propellant 
combination. However, at any over-all mixture ratio near maximum performance, the sum of energy I	 released by complete combustion- of propellants operating at various local mixture ratios will always be less than that produced by having all local mixture ratios equal to the over-all ratio. 
Any deviations in local mixture ratio produced by an injector element can be corrected only by I turbulent mixing and diffusion in a relatively low-density accelerating fluid. In normal chamber 
configurations, such a process requires fairly long chamber lengths proportional to the size of the 
I
Page 1 1
Memorandum No. 30.5	 -	 Jet Propulsion Laboratory. 
non-uniform local mixture-ratio regions. Therefore, unless a very large number of injector elements 
is used, the optimum mixture-ratio distribution produced by each element is one which is as uniform 
as possible throughout its entire spray. In order to achieve good uniformity, it is apparent that 
certain hydraulic and relative velocity conditions must be met. 
II. THE USE OF IMPINGING STREAMS 
One conventional method of mixing liquid propellants is through the use of impinging 
streams. However, in many injector designs, little attention is given to stream stability or 
relative stream momentum between fuel and oxidizer. It is frequently assumed that general 
spatial alignment of stream centerlines is all that is required to produce a uniform spray, and 
that fuel and oxidizer orifice pressure drops may therefore be arbitrarily assigned any convenient 
values.
It has been shown by Rupe (Ref. 1) that consistent distributions of mixture ratio can be 
obtained from impinging streams only if the free streams have stable velocity profiles. In 
addition, for uniform distribution, the velocity profiles should be symmetrical and have similar 
centerline to mean-stream pressure ratios. As described in Ref. 1, this can be most easily 
achieved through the use of a fully developed turbulent stream. One orifice configuration which 
will produce an adequate stable velocity profile consists of a contoured entry, a turbulence-
inducing section, and an over-all length of about twenty hole-diameters. in addition, care must be 
taken to assure as uniform a flow as possible in the manifold feeding the orifices. 
The tests summarized in this Memorandum wrre made using orifices of the type described 
above. Water and kerosene were used as the two fluids, and mixture-ratio distributions were 
determined from the volume ratio of collected samples. The sprays were sampled by a row of 
1/4-in, diameter tubes discharging into graduated glass cylinders. The total mixture ratio was 
varied for each type of injector element until the ratio could be determined which produced the 
most uniform distribution throughout the entire spray. The effect of density ratio was checked by 
interchanging the water and kerosene, and sometimes by using carbon-tetrachloride in place of 
kerosene The results obtained, therefore, apply specifically over a density ratio p 2/p1 from 
0.54 to 1.85. 
Page 2
Jet Propulsion Laboratory 	 Memorandum No. 30-5 
It should be noted that the mixing criteria given here apply in particular to propellant 
systems which, because of their nature, permit appreciable liquid-phase mixing. These same 
criteria may also be valid for hypergolic combinations which have a slight delay between mixing 
and subsequent heat release. However, for extremely reactive propellants such as N204—N2114, 
the mixture-ratio distributions are believed to be greatly affected by gas evolution at the 
impingement points (Ref. 2), so that uniform distributions cannot be easily obtained. 
Ill.	 RESULTS 
A.	 The One-on-One Element 
The results of studies of a pair of impinging streams were reported by Rupe in Ref. 3. It 
was shown that the most uniform mixture-ratio distribution is obtained when the product of 
velocity-head ratio and diameter ratio of the two streams is unity; that is, 
	
p1vD 
= 1	 (1) 
p2vD2 I
where p is specific gravity, v is velocity, D is orifice diameter, and subscripts 1 and 2 denote the 1	 two fluids being mixed. 
Since the stream momentum M is equal to the product of the velocity head and the orifice I	 area A, and the area is proportional to the diameter squared, it can be shown that if the criterion of Eq. 1 is satisfied, the momenta of the two shown are related by 
	
I
p1vD =	
(2) 
2p2 
I	 4 
i	
Page 3 I
Memorandum No. 30-5	 Jet Propulsion Laboratory 
Thus, for a pair of streams having diameter ratios between one and about three, the best mixture-
ratio distribution is obtained when the stream-momentum ratio is equal to the stream-diameter ratio 
Because the mixture ratio b0/viii, and not the velocity ratio, is the parameter of interest in 
rocket-motor studies, the following more useful relationship can be derived from Eq. (2):
&I p2D 2 M 1	 D 1 - 
(3) 
M 2	 D2	
zvp1D 
Or, if we let i	 = oxidizer flow rate and 
€0 2 = fuel flow rate, then 
3 
2 Pf 
( Df 
r	 =1 
PDX	
0. )
The doublet element is not always useful for some propellant combinations, particularly 
when only single or a very limited number of elements are desired. Distributions were studied, 
therefore, using several other element configurations having axially symmetrical resultant 
momentum lines. Only three such elements appeared to he of interest. They are planar triplets, 
two oxidizer streams and two fuel streams impinging at a common point, and four streams 
symmetrically impinging on one center stream. 
B.	 The Two-on-Two Element 
The two-on-two configuration has two opposed fuel streams at right angles to two opposed 
oxidizer streams, with both pairs impinging at the same angle. It is important that the centerlines 
of the jet meet at the same spatial point. For this element, the resultant spray is symmetrical 
across either pair of orifices regardless of mixture ratio. The smoothed mass distribution and 
volume-mixture-ratio distribution for a representative test close to optimum mixing of a two-on-two 
element are shown in Figs. 1 and 2. The cross penetration by the spray fan from each pair of jets 
is a characteristic of this orifice configuration. However, a relatively small amount of mass is 
involved at the outside of the spray, where fairly large deviations in mixture ratio occur. An 
additional feature of this type of element is the presence of a backspray. Approximately 10% of 
the mass is directed into a narrow cone to the rear of the impingement point. The combustion of 
this backspray has served to stabilize the main spray flame in certain cases (Ref. 4).
(4) 
Page 4
I
Jet-Propulsion Laboratory	 Memorandum No. 30-5 
I 
I Since this injector element is symmetrical with respect to the two propellants, it would be expected that the constant on the right-hand side of Eq. (4) would be equal to unity, as in the 
case of a doublet. The experimental results confirmed this expectation, and the most uniform or 
I
optimum distribution occurred at the mixture ratio determined from the expression 
I r2 
__	
= Ic	 (5) 
PIX 
where k = 1 for all impingement angles. The two-on-two elements studied during this program 
I had area ratios from 1 to 3.5. 
As in the case of the doublet, the optimum mixing criterion may require that two-on-two I elements employ widely different orifice diameters for certain mixture ratios and propellant 
densities. The two-on-one and four-on-one elements were therefore investigated, since they per-
mit the use of more nearly equal orifice diameters with mixture ratios greatly different from one. 
Because these two element types are not symmetrical with respect to propellants, the constant in 
any expression similar to Eq. (5) would not be expected to equal one, and furthermore, may be a I function of the included impingement angle. 
1	 C.	 The Two-on-One Element 
I
On the basis of limited tests with several two-on-one injector elements having various 
outer to center orifice-area ratios, the following equation was found to fit the data best for a 
60-deg included impingement angle. 
I '2 (A2\ 1.75 (-I
	
r2A)	
= 0.66	 (6) 
\w21  
I
	
	
where the subscript 1 denotes the two outside streams and 2 the center stream, A 2 = area of the
center orifice, A 1 = area-of one of the outerorifices, and t1 = total flow through both outer 
orifices. Equation (6) reduces to the following form: 
I Page 5 1
Memorandum No. 30.5	 Jet Propulsion Laboratory 
0.25 
ivi (±	
= k'	 (7) 
p2v	 A2) 
(The total area ratios (A 2 /2A 1 ) covered experimentally had values from 0.3 to 1.0.) This can be 
compared to Eq. (1) for a doublet, which may be written 
0 50 
Piv 
(A2 (8) 
p2v) 
In a limited investigation (see Ref. 5 for report), it was found that if a correlation 
equation of the form of Eq. 8 was used for triplet elements, the value of k was 0.625, as 
determined from elements having values of D 21D 1 of 1.0 and 0.776. At a value of D 21D 1 of 
0.79, both correlation equations (7 and 8) give the same result but diverge for D 2/D 1 different 
from 0.79. For example, at D 21D 1 of 1.41 (the maximum value of the ratio in the present study), 
the optimum mixture ratio predicted by Eq. 7 would be 15% different from that predicted by Eq. 8, 
with k of 0.625. At present, there are insufficient data to resolve this difference in the effect of 
the ratio of D 2/D 1 ; hence, probably neither equation should be used for values of D 2/D 1 very 
far from 0.79. 
The triplet-element distribution is quite sensitive to deviations from optimum mixture 
ratio. The results for one element at three different volume-flow ratios are shown in Fig. 3. It 
can be seen that, even for volume ratios not too different from the optimum, the spray becomes 
very non-uniform with respect to mixture ratio. The effect of such distribution changes on the 
resulting combustion is shown and discussed in Ref. 2. For a 90-deg included impingement angle, 
the value of k' in Eq. (7) was found to be 0.42. 
D.	 The Four-on-On. Element 
A series of tests with several four-on-one injector elements at 90-deg total impingement 
angle indicated that the most uniform distribution occurred when 
Page 6
I
Jet Propulsion Laboratory	 Memorandum No. 30-5 
I
i. '	 IA	 1.25 
,W1 2 	 2 '2 1n1\ 
•	 I -	 -	 = 2.75	 (9) \w2	 1 J 	 \4A1J 
where A 2 = area of the center stream, A 1 = area of one of the outer streams, the subscript 1 I	 denotes the outer-stream parameters and 2 the center-stream parameters, and	 = the total flowthrough all four outer orifices. 
I
At 60-deg included impingement angle, the constant on the right-hand side of Eq. (9) that 
best correlates the data is equal to 2.90. Sufficient tests were not made, however, to determine 
the functional relation between this constant and the impingement angle. The total area ratios I (A 2/4A 2) studied were between 0.25 and 0.75. 
IV. CONCLUSIONS 
As shown in Ref. 3, an empirical correlation can be obtained by relating the mixture-ratio 
distribution produced by a pair of impinging streams and the ratios of density, velocity, and orifice 
I
cross-sectional area of the two fluids. The results given in this Memorandum indicate similar 
relationships for other types of impinging stream elements. The equations given for optimum 
I
mixture-ratio distribution show the following characteristics. 
At a given mixture ratio, the element composed of two oxidizer streams on two fuel streams I
	
	
is optimized at the same velocity ratio of oxidizer to fuel as the doublet configuration. Like the 
doublet, this mixing criterion is independent of total included impingement angle, providing all 
four streams make the same angle with the axis of the spray. 
I The triplet element requires a lower oxidizer-to-fuel velocity ratio than the doublet for a 
given mixture ratio (where the center stream is assumed to be fuel). 
I
Page 7 
I
Memorandum Ho. 30.5	 Jet Propulsion Laboratory 
The four-on-one element shows an opposite effect in that it requires a higher ratio of the 
velocity of the outer streams to the velocity of the center stream. Thus, the center stream of the 
triplet requires more momentum to penetrate the two outer streams, while the center stream of the 
four-on-one is, in effect, pulled into the outer streams. 
It should be kept in mind that the results given are valid only for streams having 
symmetrical, turbulent velocity profiles. Because the mixture-ratio distribution of impinging-
stream-injector elements can be made uniform near only one set of conditions, it is advisable to 
determine experimentally the distribution for any proposed injector element before incorporating 
it into a developmental engine. 
Page 8
I 
I
Jet Propulsion Laboratory
	 Memorandum No. 30-5 
REFERENCES 
1.	 Rupe, J. H., The Liquid Phase Mixing of a Pair of impinging Streams, Progress Report I No. 20-195, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, 
California, August 6, 1953. 
I 2. Elverum, G. W., Jr., and Staudhammer, P., The Effect of Rapid Liquid-Phase Reactions on 
Injector Design and Combustion in Rocket Motors, Progress Report No. 30-4, Jet Propulsion 
I
Laboratory, California Institute of Technology, Pasadena, California
	 (to be published). 
3.	 Rupe, J. H., A Correlation Between the Dynamic Properties of a Pair of Impinging Streams 
I and the Uniformity of Mixture-Ratio Distribution in the Resulting Spray, Progress Report No. 20-209, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, 
California, March 28, 1956. 
4.	 Elverum, G. W., Jr., and Mason, David, M., The Effect of Chemical Composition of Fuming 
Nitric Acid and the Aniline-Fur furyl Alcohol System on Performance and ignition Delay in 1 Rocket Motors, Progress Report No. 20-261, Jet Propulsion Laboratory, California Institute 
of Technology, Pasadena, California, April 13, 1955. 
I 5. Combined Bimonthly Summary No. 59, Jet Propulsion Laboratory, California Institute of 
I
Technology, Pasadena, California, April 1, 1951 to June 1, 1957. Pp. 48-50.
I I I I I I
Page 9 
Memorandum No.. 30-5 	 Jet Propulsion Laboratory 
I!I 
[;i 
C2
Water through 0.070-in.-dia 
jets at 900 and 270° 
Kerosene through 0.082-in.-
\\
dia jets at 00 and 180° 
/
Samples taken 8 in. from  
impingement 
 Water AP
	
105 psi 
I, 
'! Kerosene	 P = 100 psi 
III
'\ (I / 
9O0
/1 2:25* 
	
-1.5	 -1.0	 -0.5	 0	 0.5	 1.0	 1.5	 2.0 
Distance from centerline, inches 
	
Fig. 1.	 Typical Quantity Distribution for Two-on-Two Injector 
CD
2C 
3.0 
a> 
0
ac 
0 
0> 
C 
0) 
U, 
2 
a) 
a, 
E 0.8 
0 
> 
.0 
0 
4-
0 
E 0.3 
4-
'C
02
900 
135° 
?'450
315° s  
2250 —22 °
180° 
Water through 0.070-in.-dia jets at 90 and 270 deg  
Kerosene through 0.082-in.-dia jets at 0 and 180 deg  
Overall mixture ratio 	 1.4 
Samples taken 8 in. from impingement 
Water EP = 105 psi	 Kerosene AP = 100 psi 
I	 I	 I	 I ________
-1.5	 -1.0	 -0.5	 0	 0.5	 1.0	 1.5	 2.0 
Distance from centerline, inches 
Fig. 2.	 Typical Mixture-Ratio Distribution for Two-on-Two Injector 
Page 10
Jet Propulsion Laboratory	 Memorandum No. 30-5 
3.0 
a) (4) 
2 2.0 
JX 
a, 
0 4-
a)
0.8 
02 
X -2.0	 -1.5	 -1.0	 -0.5	 0	 0.5	 1.0	 1.5	 2.0
Distance from centerline, inches 
Fig. 3.	 Volume Mixture-Ratio Distributions for 60-deg Triplet Injector
Page 11


Criteria for Optimum Mixture - Ratio Distribution Using Several Types of Impinging-Stream Injector Elements

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