DESIGN OF A ROCKET INJECTOR
FOR A LIQUID BI-PROPELLANT
SYSTEM
Presented by:
Andrew Schwarz
Woon-Ho Cho
Simtha Sankaran
AE 267
Instructor: Dr Periklis E. Papadopoulos
December 7, 2004
Objective
Obtain the optimum propellant mixture ratio
based on different injector parameters. The
resultant mixture should impinge in an axial
direction along the combustion chamber
axis.
Assumptions
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




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Hypergolic ignition (no need for igniter)
Incompressible fluid
Resultant momentum at the point of impingement
between the fuel and oxidizer flow is axially directed
Optimum mixture ratio based on optimum Isp
Adiabatic combustion and isentropic expansion of an
ideal gas
Optimum expansion at nozzle exit (1 atm)
Combustion chamber pressure of 1000 psia (6895
kN/m2)
Parameters

Input variables
•
•
•
•
•
•

Propellant combination (densities of fuel and ox)
Pressure Drop (across injector plate)
Discharge Coefficient (depends on quality of orifice)
Injector hole pattern (spacing and number of holes)
Diameter of oxidizer orifice
Diameter of fuel orifice
Output Values
•
•
•
•
•
Volume flow rate
Mixture ratio
Injection velocity
Combustion chamber cross-sectional area
Angle of impingement
Cd - Coefficient of discharge
A –Total injector area
p- Pressure Drop across injector
Equations
 –Density of propellant
Injection velocity
vi  Cd
2 p

vi ( o )  Cd
2p
o
vi ( f )  Cd
2p
f
Volume flow rate
Q  Cd A
2p
Mass flow rate
m  Q

Qo  Cd Ao
m o   oQo
m f   f Q f
2p
o
Q f  Cd A f
2p
f
m o
r
m f
Suffix o and f denotes
oxidizer and fuel
Injector Hole Pattern
Equations (cont.)
 Area
• Ao(total) = No Ao
• Af(total) = Nf Af
 Hole pattern
Cn = π(nD)
Nn = Cn/d
N = ΣNn
Nf=N/2 No=N/2
Suffix o and f denotes oxidizer
and fuel
D – Spacing between each concentric circle
d - Spacing between each hole
C – Circumference
n - nth circle
N – Total number of holes
A – Area of hole
Equations (cont.)
m o vo sin  o  m f v f sin  f
tan  
m o vo cos  o  m f v f cos  f
m o vo sin  o  m f vf sin  f
Axial flow (tan  = 0)
Propellant combinations
Oxidizers
Fuels
Nitrogen Tetroxide ( N2O4)
Ammonia (NH3 )
Hydrogen Peroxide (H2O2)
Analine (C6H5NH2)
Nitric Acid (H2NO3 )
Ethanol (C2H5OH)
Liquid Oxygen (O2)
Hydrazine (N2H4)
Liquid Hydrogen (H2)
Monomethyl-hydrazine (CH3)2NNH2 (MMH)
Propellant Reactions
N2O4 + N2H4
N2O4 + MMH
H2O2 + N2H4
H2O2 + MMH
H2O2 + NH3
H2O2 + C2H5OH
H2O2 + H2
O2 + C6H5NH2
H2NO3 + N2H4
H2NO3 + MMH
Baseline
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




Theoretical values for optimum mixture ratio
p is 15% - 25% of Pc
Pc is 1000 psia
Cylindrical injector and hole pattern
Like-unlike stream pattern
Experimental values of Cd
Stream Pattern
Discharge Coefficient
Procedure
 Program layout to find number of injector
orifices
# of concentric
circles
Circumference of nth circle
Spacing
between circles
# of orifices on nth circle
Spacing
between holes
Total number of orifices
Number of
oxidizer and
fuel orifices
Program outline to find optimum mixture ratio
•Pressure Drop
•Density
•Coefficient of
discharge
•Area
•Total propellant flow
• Volume flow rate
•Injection velocity
Condition for axial
flow
Mixture
ratio
Injection Velocity Performnace for Different Orifice Types
90
80
Injection velocity, v
i (in/s)
70
Cd = 0.1
60
Cd = 0.2
Cd = 0.3
50
Cd = 0.4
Cd = 0.5
40
Cd = 0.6
Cd = 0.7
30
Cd = 0.8
20
10
0
150
160
170
180
190
200
210
p (lbf/in )
2
220
230
240
250
Injector Flow Rates for Different Orifice Types
(N2O4 + N2H4)
0.025
Cd = 0.9
Cd = 0.8
0.02
Cd = 0.7
mdot (in/s)
Cd = 0.6
0.015
Cd = 0.5
Cd = 0.4
0.01
Cd = 0.3
Cd = 0.2
0.005
Cd = 0.1
0
150
160
170
180
190
200
210
p (lbf/in )
2
220
230
240
250
0.10
0.08
0.07
0.06
0.05
0.04
0.03
0.09
Dox =
Dox =
Dox =
Dox =
Dox =
Dox =
Dox =
Dox =
5
Fuel and Oxidizer Orifice Sizing
(N2O4 + N2H4)
Dox = 0.02
4.5
4
Mixture Ratio, r
3.5
3
2.5
2
1.5
Optimum mixture, r = 1.34
Dox = 0.01
1
0.5
0
0.01
0.02
0.03
0.04
0.05
0.06
Fuel Orifice Diameter, Dfuel (in)
0.07
0.08
0.09
0.1
Dox =
Dox =
Dox =
Dox =
Dox =
Dox =
Dox =
Dox =
Dox =
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
5
Fuel and Oxidizer Orifice Sizing
(N2O4 + MMH)
4.5
4
Mixture ratio, r
3.5
3
2.5
Optimum mixture, 2.17
2
1.5
Dox = 0.01
1
0.5
0
0.01
0.02
0.03
0.04
0.05
0.06
Fuel Orifice Diameter, Dfuel (in)
0.07
0.08
0.09
0.1
Sample Data for Hole Pattern Calculation
in
mm
in
mm
D
0.25
6.3500
d
0.25
6.3500
n
Cn
N
Nactual
SNtotal
dactual
d
1
0.78540
3.14159
4
4
0.19635
0.05365
2
1.57080
6.28319
6
10
0.26180
0.01180
3
2.35619
9.42478
10
20
0.23562
0.01438
4
3.14159
12.56637
12
32
0.26180
0.01180
5
3.92699
15.70796
16
48
0.24544
0.00456
6
4.71239
18.84956
18
66
0.26180
0.01180
7
5.49779
21.99115
22
88
0.24990
0.00010
8
6.28319
25.13274
26
114
0.24166
0.00834
9
7.06858
28.27433
28
142
0.25245
0.00245
10
7.85398
31.41593
32
174
0.24544
0.00456
11
8.63938
34.55752
34
208
0.25410
0.00410
12
9.42478
37.69911
38
246
0.24802
0.00198
Results
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The size of the fuel and oxidizer orifices directly affect the mixture
ratio.
Changing the hole pattern only adds more mass flow to the
combustion chamber. Mixture ratio stays the same.
The quality of the orifices (Cd) affects both the propellant flow
characteristics and mixing properties.
Conclusion
Remarks
Further applications can be applied:
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


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Study heat transfer in combustion chamber wall near
injector surface
Real gas chemical equilibrium combustion
Study combustion stability (pressure propagation and
vibration)
Flow characteristics of the injector’s internal piping
(more pressure losses)
Transient effects (starting and stopping conditions)
References
Rocket Propulsion Elements, George P. Sutton, Oscar Biblarz. 7th Edition.
Wiley-Interscience, 2001
Mechanics and Thermodynamics of Propulsion, Philip Hill and Carl Peterson.
2nd Edition. Addison-Wesley, 1992
Aerothermodynamics of Gas Turbine and Rocket Propulsion, Gordon C.
Oates. 3rd Edition. AIAA Series, 1997
Modern Compressible Flow, John D. Anderson. 3rd edition. Mc Graw Hill, 2003
Building GUIs with MATLAB, Version 5. The Mathworks Inc., June 1997
Encyclopaedia Britannica, 2004. Encyclopaedia Britannica Premium Service,
Dec. 7, 2004