Rocket Engine Coolant Manifold Flow Study
Frederick H. Reardon
Department of Mechanical Engineering
California State University, Sacramento
6001 J Street, Sacramento, CA 95819-6031
ABSTRACT
To provide data for the design of regeneratively-cooled rocket engines,Tte flow of
liquid water through orifices with cross flow at the inlet has been studied experimentally
to determine the effect of the cross flow velocity on the flow through the orifice,
measured by the discharge coefficient. The test apparatus consisted of a manifold of
square cross section with five active orifices along its length having their centerlines
normal to the centerline of the manifold. The manifold design allowed for two values of
orifice diameter, two values of orifice length, and two values of orifice inlet configuration,
chamfered and non-chamfered. The flow control system allowed for independent
control of manifold pressure and flow velocity. The test results showed a relatively
small decrease in discharge coefficient with increasing cross flow velocity. This
decrease was most clearly evident for non-chamfered orifices with larger length-todiameter ratio.
INTRODUCTION
Regeneratively-cooled combustion chambers and nozzles for liquid propellant
rocket engines are commonly made by joining parallel cooling tubes that are bent to
form the chamber/nozzle shape (see Figure 1). One of the problems in designing such
an engine is ensuring that the coolant flow rate is the same for each cooling passage.
As shown in Figure 1, the coolant (one of the propellants) is supplied to the cooling
passages by means of a manifold. However, in such a manifold, the flow properties,
such as pressure and velocity, vary along the length of the manifold, leading to nonuniform flow rates in the manifold passages. It has been found that a more uniform flow
can be obtained if the coolant passes through a small orifice at the entrance of each
coolant passage.
In designing the manifold, it is desired that the flow rate through each orifice be
the same. There is evidence that the flow rate through each orifice is dependent on the
flow rate past the orifice entrance. This behavior is usually expressed in terms of the
dependence of the orifice discharge coefficient (Cd) on the cross velocity, where the
discharge coefficient is defined by the equation
Q  C d Ao 2P

where
Q = volumetric flow through the orifice
(1)
Cd = discharge coefficient
Ao = orifice cross-sectional area
P = pressure drop across the orifice
 = density of fluid
Orifice flow has primarily been studied in regard to the measurement of flow. In
such applications, the flow approaching the orifice is parallel to the centerline of the
orifice; there is no cross flow. Much information exists concerning the effects of the
orifice shape on the discharge coefficient. Rupe [Ref. 1], in his review of liquid
propellant rocket injection processes, illustrated the effect of the orfiice shape on the
injection stream as shown in Figure 2. He noted that (a) and (c), even though they have
significantly different orifice lengths, typically have Cd values between 0.6 and 0.7,
whereas (d) , where the flow reattaches to the wall, has values between 0.8 and 0.85.
Configurations (b) and (e) are characterized by Cd values near 1.0. It should also be
noted that the orifice geometry for (c) and (d) is identical, but the flow patterns are quite
different. Depending on the pressure drop, length-to-diameter-ratio (L/D), and cross
velocity, an orifice can switch from one flow pattern to the other, giving rise to the name
of "hydraulic flip" for this phenomenon. Some data of Northrup [Ref. 2], included in the
article by Rupe, is shown in Figure 3. These data show that hydraulic flip, as well as the
effect of cross velocity on Cd , also depends on the L/D of the orifice and the pressure
drop across the orifice.
The test program described in this paper was undertaken, under the sponsorship
of GenCorp Aerojet, Sacramento, to gather new experimental data on the discharge
coefficient of an orifice with cross flow. The manifold and orifice dimensions were
selected to match approximately those on a typical rocket engine developed by Aerojet.
APPARATUS AND TESTING PROCEDURE
The experimental apparatus (Figure 4) was designed to permit the evaluation of
the effects of orifice diameter, length-to-diameter ratio, spacing, and inlet shape, with
the manifold pressure and cross velocity controlled independently. The manifold has a
one inch square cross section. It is made in two pieces, a base and a cap, with the
orifices and outlet tubes in the cap. Eight caps were made, allowing for two values each
of orifice diameter (0.080 and 0.090 in.), length (0.25 and 0.50 in.), and inlet
configuration (square and 45 chamfer). There are ten orifices in each cap, allowing for
the variation of orifice spacing. However, only one spacing (0.74 in) has been
investigated to date.
It can be seen that the orifices are not located in the center of the manifold
length. This was done to allow the velocity profile to stabilize after the transition from a
circular inlet pipe to the square manifold. A computational fluid dynamic (CFD)
simulation of the flow (Figure 5) indicated that the velocity profile would stabilize nearly
half way along the length. Thus, the series of orifices was located starting at 40% of the
manifold length from the inlet.
The testing was conducted in the Mechanical Engineering Department's Energy
Systems Laboratory, using the test apparatus shown in Figure 6. The results presented
are for two values of manifold pressure (5.5 and 11.0 psi), and three values of cross
flow velocity (0, 4, 8 ft/sec). The inlet, outlet, and bypass valves were used to control
the flow rate and pressure in the manifold. A pressure gage was installed in the
manifold to measure the static pressure in the vicinity of the flow orifices (Figure 7).
Each test section configuration has 10 identical orifices. However, in the testing, only
orifices numbered 1,3,5,7, and 9 were used. The other orifices were closed off using
plastic caps. The water from each orifice was collected in a graduated cylinder by
means of a collector hose. Although they are not all shown in Figure 7, a three-footlong collector hose was attached to each of the active orifices for all tests. In addition to
making the testing easier, these hoses provided some simulation of the rocket chamber
coolant passages. The time required to flow a fixed volume was measured using a
stopwatch. The average of five time measurements was used to determine the
discharge coefficient for each orifice.
Because of the flow in the manifold, the discharge coefficient values reported are
based on the total pressure in the manifold. That is, P in Eq.(1) was taken to be
P  PT manifold  Patmosphere
(2)
where
PT manifold  P manifold   V manifold 2
2
(3)
and Vmanifold is the mean value of the velocity of the water in the manifold, accounting for
the outflows though the orifices. It can be seen that even when there was no flow out of
the downstream end of the manifold, the value of Vmanifold was never zero.
RESULTS
The test results are shown in Figures 8 - 11. Each figure shows the discharge
coefficient for one value of orifice diameter and L/D as a function of the mean velocity in
the manifold. Error bars are shown to indicate the uncertainty in the discharge
coefficient value. The discharge coefficient values shown represent the average for all
five orifices, because the differences in individual orifice Cd values did not show any
systematic trends with regard to location.
As would be expected, the greatest effect on the discharge coefficient was that of
the orifice inlet configuration. All of the Cd values were in the range 0.95 - 1.01 for the
chamfered inlet orifices and in the range 0.78 - 0.86 for the non-chamfered inlets. This
result is in general agreement with the data discussed by Rupe. Based on the latter, it
appears that the flow reattached to the wall in the case of the non-chamfered orifices.
Figures 8 - 11 also show a decrease in Cd values for increasing cross flow
velocity, although this effect is not consistent among the configurations tested. Small
effects of orifice diameter, L/D and manifold pressure can be seen, but not consistently.
To look more closely at these trends, the data were replotted in terms of a
normalized discharge coefficient, Cd/Cdo, where Cdo is the discharge coefficient for
(nearly) zero cross velocity. Figures 12 and 13 show the normalized discharge
coefficient values separated into two groups on the basis of orifice diameter, plotted
against cross velocity. Similarly, Figures 14 and 15 compare the data on the basis of
orifice L/D, and Figures 16 and 17 show the effects of manifold pressure. In each chart,
trendlines have been added to show mean effects in view of the considerable scatter.
Figures 12 and 13 show that there is very little effect of orifice diameter for the
non-chamfered orifices, but there appears to be a small effect for the chamfered ones,
although the data scatter for the latter is greater. Except for the smaller chamfered
orifices, the data show a decrease of the discharge coefficient for increasing cross
velocity.
The effect of orifice L/D is shown in Figures 14 and 15. In this case, the
chamfered orifice results show little effect of L/D or cross velocity, but there appears to
be a greater effect of cross velocity on Cd with larger L/D for non-chamfered orifices.
Figures 16 and 17 present the variation of the normalized discharge coefficient
with manifold pressure and cross velocity. There appears to be no effect of manifold
pressure on the results. Also, the cross velocity seems to have no effect on the
discharge coefficient for chamfered orifices, whereas the non-chamfered orifice tests
show that the Cd decreased with increasing cross velocity. These results do not agree
with the data of Northrup [Ref. 2], shown in Figure 18. The latter indicate that the
discharge coefficient decreases with increasing cross velocity and for decreasing
manifold pressure. Unfortunately, the orifice configuration used by Northrup is not
known.
CONCLUSIONS
There appears to be an effect of cross velocity on discharge coefficient, at least
for non-chamfered-inlet orifices, such that increasing the cross velocity results in a
decreased discharge coefficient. The effects of orifice diameter, L/D, and manifold
pressure are smaller and less consistent, and fall within the range of uncertainty. The
major source of uncertainty in the data was the fluctuation of the manifold pressure.
This fluctuation was reduced, but not eliminated, by the use of a settling tank between
the water pump and the test apparatus. Additional testing is needed, to determine the
source of the pressure fluctuations and to reduce the inconsistencies that can be seen
in the results.
ACKNOWLEDGMENTS
It is a pleasure to acknowlege the efforts of Khosrow Zardkoohi and Vinh
Nguyen, seniors in the Mechanical Engineering Technology program, who designed the
test apparatus, conducted the test program, and did much of the data analysis. Also,
thanks are due to technicians Bruce Scott and Jim Penaluna for their help in fabricating
the apparatus and setting up the test facility.
REFERENCES
1. Rupe, J. H., "Jet Properties," in Liquid Propellant Rocket Combustion Instability,
NASA SP-194, National Aeronautics and Space Administration, Washington D.C.,
1972
2. Northrup, R. P., "Flow Stability in Small Orifices," paper presented at the 1951 ARS
Annual Meeting, Atlantic City, N.J., November, 1951
Figure 1. Typical Liquid Propellant Rocket Chamber and Nozzle
Figure 2. Effect of Orifice Shape on Injection Spray [from Ref. 1]
Figure 3. Typical Variation of Flow Coefficient with Pressure and Cross Velocity
Figure 4. Manifold for Orifice Flow Studies
Figure 5. Velocity Profiles in Manifold
Figure 6. Schematic of Flow Test Setup
Figure 7. Flow Test Apparatus
Figure 8. Discharge Coefficient Values for D = 0.080 in, L/D = 3
Figure 9. Discharge Coefficient Values for D = 0.080 in, L/D = 6
Figure 10. Discharge Coefficient Values for D = 0.090 in, L/D = 3
Figure 11. Discharge Coefficient Values for D = 0.090 in, L/D = 6
Figure 12. Effect of Orifice Diameter for Chamfered Orifice
Figure 13. Effect of Orifice Diameter for Non-chamfered Orifice
Figure 14. Effect of L/D for Chamfered Orifice
Figure 15. Effect of L/D for Non-chamfered Orifice
Figure 16. Effect of Pressure for Chamfered Orifice
Figure 17. Effect of Pressure for Non-chamfered Orifice
Figure 18. Effect of Pressure and Cross Velocity, Northrup's Data [Ref. 2]