1. Lunar Lander Propulsion System: 100% Design Review
AE 445 Spacecraft Detail Design
Department of Aerospace Engineering
Embry-Riddle Aeronautical University, Daytona Beach
Instructor: Eric Perrell, Ph.D.
23 April 2008
2. Lunar Lander Vehicle Propulsion System: 100% Design Review
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Team Members
Executive Staff
Nicholas H. Perry, Project Manager
John C. Swatkowski, Research Director
Mitchell Graves, Budget Manager
Shailesh Kumar, System Safety Officer
Mission Assurance Division
Johann Schrell, Lead
Eric McLaughlin
Brendan McMahon
Configuration Management Division
Robert J. Scheid, Lead
Jessica Chen
Todd A. Snyder
Thermal Management Division
Jade Pomerleau, Lead
Ben Klamm
Chi Zhang
Manufacturing, Division
Chukwuma Akosionu, Lead
Kristopher Greer
Joe Tabor
Systems Integration & Testing Division
Eric J. Thompson, Lead
Maggie Cordova
Autumn Gee
Gary Kelley
Andrew Kreshek
Nicholas Rehak
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Special Thanks
Team Cynthion would like to thank the following people who helped make this project a
reality:
to Bogdan Udrea, Ph.D., for collaborating with Team Cynthion to make the lunar lander
propulsion system a reality,
to Brian Ruby, for helping machine the rocket engine,
to Geoffrey Kain, Ph.D., for funding the Lunar Lander project,
to Richard Hedge, for all of his hard work machining the majority of the rocket engine,
and finally, a very special thanks to Eric Perrell, Ph. D., for all of his hard work with the
project as a mentor and instructor.
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Table of Contents
1. Introduction ................................................................................................................. 1
2. Main Rocket Thrusters Design Parameters................................................................. 2
2.1. Performance Metrics ............................................................................................ 2
2.2. Engine Dimensions ............................................................................................ 12
2.3. Injector Design ................................................................................................... 13
2.4. Engine Throttling ............................................................................................... 14
2.5. Ignition System .................................................................................................. 15
2.6. Backup Ignition System ..................................................................................... 15
2.7. ERPL Liquid Rocket Engine Creator ................................................................. 16
2.8. NASA Chemical Equilibrium Analysis ............................................................. 19
3. Propulsion System Configuration ............................................................................. 20
3.1. CATIA................................................................................................................ 20
3.2. Connections and Assembly ................................................................................ 27
3.3. NASTRAN Pressure Analysis ........................................................................... 29
3.4. Mass Budget ....................................................................................................... 39
5. Manufacturing Plan ................................................................................................... 68
5.1. Raw Materials and Hardware ............................................................................. 68
5.2. Fabrication Process ............................................................................................ 70
5.3. Assembly Process ............................................................................................... 82
5.4. Part Assembly .................................................................................................... 82
6. Systems Integration & Testing.................................................................................. 84
6.1. Feedline System ................................................................................................. 84
6.2. Electrical System for Solenoid Valves ............................................................... 85
6.3. Test Stand ........................................................................................................... 86
6.4. Data Acquisition (DAQ) .................................................................................... 87
6.5. Test Preparation Procedures ............................................................................... 93
6.6. Fuel Tank Air Evacuation .................................................................................. 95
6.7. Fuel Tank Fill (Propane) .................................................................................... 97
6.8. Fuel Tank Fill (Water)........................................................................................ 99
6.9. Assembly Procedure ......................................................................................... 100
6.10. Test Area Overview ...................................................................................... 103
6.11. Feed Line System Testing Overview............................................................ 114
6.12. Instrumentation ............................................................................................. 120
6.13. Igniter Testing Procedure ............................................................................. 122
6.14. Ignition Test Results ..................................................................................... 123
6.15. Engine Firing Test ........................................................................................ 125
7. Project Economics .................................................................................................. 128
8. System Safety Program Plan ................................................................................... 131
9. Appendix ................................................................................................................. 158
9.1. NASA CEA Output .......................................................................................... 158
10. References ............................................................................................................ 198
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Table of Figures, Tables, and Equations
Figure 1: Determination of Nozzle Expansion Ratio .......................................................... 2
Figure 2: Nozzle Performance for Major Thrust Levels ..................................................... 3
Figure 3: Specific Impulse for Varied O/F Ratio................................................................ 4
Figure 4: Characteristic Velocity for Varied O/F Ratio...................................................... 4
Figure 5: Chamber Temperature for Varied O/F Ratio ...................................................... 5
Figure 6: Exit Mach Number for Varied O/F Ratio ............................................................ 5
Figure 7: Nozzle Exit Pressure for Varied O/F Ratio ......................................................... 6
Figure 8: Coefficient of Thrust for Varied O/F Ratio ......................................................... 6
Figure 9: Chamber Mass Flow Rate for Varied O/F Ratio ................................................. 7
Figure 10: Exit Pressure Over Thrust Range ...................................................................... 8
Figure 11: Mass Flow Rate Over Thrust Range ................................................................. 9
Figure 12: Specific Impulse Over Thrust Range ................................................................ 9
Figure 13: Chamber Temperature Over Thrust Range ..................................................... 10
Figure 14: Assembled Engine ........................................................................................... 21
Figure 15: Supersonic Nozzle ........................................................................................... 22
Figure 16: Combustion Chamber ...................................................................................... 22
Figure 17: Cooling Jacket ................................................................................................. 23
Figure 18: Fuel Inlet Manifold .......................................................................................... 23
Figure 19: Nitrous Injection Plate ..................................................................................... 24
Figure 20: Nitrous Injection Dome ................................................................................... 25
Figure 21: Steel Connection Ring ..................................................................................... 25
Figure 22: Copper Connection Ring ................................................................................. 25
Figure 23: Exploded Assembly drawing........................................................................... 27
Figure 24: Section Cut: Deformation of Dome and Plates ............................................... 30
Figure 25: Section Cut: Mean Pressure Distribution of Dome and Plates ........................ 31
Figure 26: Section Cut: Von Mises Stress of Dome and Plates ........................................ 32
Figure 27: Isometric Cut: Von Mises Stress of Plates ..................................................... 33
Figure 28: Section Cut: Deformation of Jacket, Nozzle, Chamber and Manifold ............ 34
Figure 29: Section Cut: Mean Pressure Distribution of Jacket, Nozzle, Chamber and
Manifold ............................................................................................................................ 35
Figure 30: Section Cut: Von Mises Stress of Jacket Nozzle Chamber and Manifold ...... 36
Figure 31: Section Cut of Jacket and Chamber: Von Mises Stress of Assembly ............. 37
Figure 32: Section Cut of Jacket and Chamber: Von Mises Stress of Jacket and Chamber
........................................................................................................................................... 38
Figure 33: Coordinate Axis System .................................................................................. 41
Figure 34: Engine Wall Temperature from MATLAB ..................................................... 46
Figure 35: Coolant Temperature from MATLAB ............................................................ 47
Figure 36: Coolant Pressure from MATLAB ................................................................... 48
Figure 37: Gas Wall Temperature from Excel .................................................................. 49
Figure 38: Coolant Temperature from Excel .................................................................... 50
Figure 39: Coolant Pressure from Excel ........................................................................... 50
Figure 40: Transient Analysis Diagram ............................................................................ 51
Figure 41: Time Step and Stability Data for Each Disk ................................................... 54
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Figure 42: Transient Gas/Wall Interface Temperatures for Disk 1 .................................. 55
Figure 43: CFD Simulation Configuration ....................................................................... 56
Figure 44: Gas Streamlines through Engine, Axial View................................................. 57
Figure 45: Gas Streamlines Through Section 2 Region, Top View ................................. 58
Figure 46: Conic vs. Cylindrical Surface Area ................................................................. 59
Figure 47: Jacket Thickness from MATLAB ................................................................... 60
Figure 48: Jacket Thickness from Excel ........................................................................... 60
Figure 49: Nitrous Oxide Thermal Conductivity .............................................................. 62
Figure 50: Nitrous Oxide Cp............................................................................................. 63
Figure 51: Nitrous Oxide Density ..................................................................................... 63
Figure 52: Time to Reach Critical Wall Temperature for Each Disk ............................... 65
Figure 53: Steady State and Transient Wall Temperature Comparison ........................... 66
Figure 54: C14500 Tellurium Copper Round Solid Bar ................................................... 68
Figure 55: Stainless Steel Round Solid Bar ...................................................................... 69
Figure 56: Brass Round Solid Bar .................................................................................... 69
Figure 57: Steel Round Solid Bar ..................................................................................... 69
Figure 58: End Mills ......................................................................................................... 71
Figure 59: Boring Bars...................................................................................................... 71
Figure 60: Rough and Finish Bar ...................................................................................... 71
Figure 61: Mandrel Piece (Lower) .................................................................................... 72
Figure 62: Mandrel Piece (Upper) .................................................................................... 72
Figure 63: Mandrel Assembly .......................................................................................... 73
Figure 64: Supersonic Nozzle (front elevation) ................................................................ 74
Figure 65: Supersonic Nozzle (looking down at top) ....................................................... 74
Figure 66: Nozzle and Chamber ....................................................................................... 75
Figure 67: Cooling Jacket (nozzle portion) ...................................................................... 77
Figure 68: Injection Dome (while being machined) ......................................................... 79
Figure 69: Manifold Ring ................................................................................................. 80
Figure 70: Propane Manifold Assembly ........................................................................... 80
Figure 71: Test Stand ........................................................................................................ 81
Figure 72: Connector Blocks ............................................................................................ 81
Figure 73: Electrical System for Solenoid Valve and Indicator Light.............................. 85
Figure 74: Steel Mounting Block ...................................................................................... 87
Figure 75: Oxidizer Stand with Two Tanks ...................................................................... 89
Figure 76: Half of the Symmetrical Load Cell Electrical Circuit ..................................... 89
Figure 77: Testing Software Front Panel GUI .................................................................. 91
Figure 78: LabVIEW Code. .............................................................................................. 92
Figure 79: Top View of Housing Compartments ........................................................... 103
Figure 80: Housing Illustration, Top View ..................................................................... 104
Figure 81: Testing container as viewed in Catia ............................................................. 106
Figure 82: Testing Container Illustration, Front View ................................................... 107
Figure 83: Primary test site easily accessible from IC Auditorium parking lot.............. 109
Figure 84: Primary test site easily accessible from Clyde Morris Blvd. ........................ 110
Figure 85: Alternate test site easily accessible from ROTC parking lot......................... 112
Figure 86: Alternate test site easily accessible from Richard Petty Blvd. ...................... 114
Figure 87: Feed System .................................................................................................. 116
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Figure 88: Oxidizer System ............................................................................................ 117
Figure 89: Pressurant System.......................................................................................... 118
Figure 90: Fuel System ................................................................................................... 120
Figure 91: Fault Tree Analysis ....................................................................................... 145
Table 1: Summary of Changes in Performance for Varied O/F ......................................... 7
Table 2: Performance Metrics for Thrust Chamber at Nominal at O/F=7 ........................ 11
Table 3: Performance Metrics for Thrust Chamber at 60% Nominal at O/F=7 ............... 11
Table 4: Performance Metrics for Thrust Chamber at Nominal at O/F=3 ........................ 11
Table 5: Performance Metrics for Thrust Chamber at 60% Nominal at O/F=3 ............... 12
Table 6: Dimensions of the Thrust Chamber .................................................................... 12
Table 7: Requirements for Injector Design at 60% Nominal 0/F=7 ................................. 13
Table 8: Requirements for Injector Design at 60% Nominal 0/F=3 ................................. 13
Table 9: Properties of Propellant Injectors O/F=7 ............................................................ 13
Table 10: Determination of Minimum Stable Thrust at O/F=7 ........................................ 14
Table 11: Determination of Minimum Stable Thrust at O/F=3 ........................................ 14
Table 12: Single Engine Mass Budget (without feedline) ................................................ 39
Table 13: Variable Gas Properties .................................................................................... 43
Table 14: Analysis Inputs ................................................................................................. 46
Table 15: Propane Thermodynamic Properties................................................................. 64
Table 16: Nitrous Oxide Thermodynamic Properties ....................................................... 64
Table 17: Fabricated Parts List ......................................................................................... 82
Table 18: Hardware and COTS List ................................................................................. 82
Table 19: Feedline System Parts and Components ........................................................... 84
Table 20: Total Cost Estimate......................................................................................... 129
Table 21: Current Budget................................................................................................ 130
Table 22: Propulsion System Total Cost ........................................................................ 130
Equation 1: Gas/Wall Heat Transfer Coefficient .............................................................. 40
Equation 2: Coolant/Wall Heat Transfer Coefficient ....................................................... 40
Equation 3: Mach-Area Relationship................................................................................ 41
Equation 4: Section 1 y-position Equations ...................................................................... 42
Equation 5: Section 2 y-position Equation ....................................................................... 42
Equation 6: Section 3 y-position Equations ...................................................................... 42
Equation 7: Section 4 y-position Equations ...................................................................... 42
Equation 8: Section 5 y-position Equation ....................................................................... 42
Equation 9: Gas Static Temperature ................................................................................. 42
Equation 10: Gas Static Pressure ...................................................................................... 43
Equation 11: Heat Transfer Between the Gas and Wall ................................................... 43
Equation 12: Heat Transfer Through the Wall ................................................................. 43
Equation 13: Heat Transfer Between the Wall and Coolant ............................................. 43
Equation 14: Coolant Temperature Rise ........................................................................... 44
Equation 15: Gas Wall Temperature................................................................................. 44
Equation 16: Coolant Wall Temperature .......................................................................... 44
Equation 17: Coolant Temperature at End of Disc ........................................................... 44
Equation 18: Surface Area of a Body of Revolution ........................................................ 44
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Equation 19: Section 5 Surface Area ................................................................................ 45
Equation 20: Coolant Pressure .......................................................................................... 45
Equation 21: Differential Transient Heat Transfer Equation ............................................ 51
Equation 22: Simplified Transient Heat Transfer Equation ............................................. 51
Equation 23: Difference Quotient for Time Partial Derivative ........................................ 52
Equation 24: Difference Quotient for Position 2nd Order Partial Derivative .................... 52
Equation 25: Finite Difference Numerical Solution Through the Wall ............................ 52
Equation 26: Modulus of the Finite Difference Formula.................................................. 52
Equation 27: Differential Heat Transfer Boundary Equation ........................................... 52
Equation 28: Difference Quotient for Heat Transfer Boundary Condition ...................... 52
Equation 29: Coolant Boundary Finite Difference Numerical Solution ........................... 53
Equation 30: Gas Boundary Finite Difference Numerical Solution ................................. 53
Equation 31: Biot Number for Finite Difference Method ................................................ 53
Equation 32: Wall Stability Criteria ................................................................................. 53
Equation 33: Coolant Boundary Stability Criteria ............................................................ 53
Equation 34: Gas Boundary Stability Criteria .................................................................. 53
Equation 35: Roy and Thodos Estimation Technique ...................................................... 61
Equation 36: Generalized Excess Conductivity Correlation ............................................ 61
Equation 37: Specific Heat Equation ................................................................................ 62
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1. Introduction
Teams from AE 445 Sections 01 and 02 have collaborated together in order to
design a viable entry in the Northrop Grumman X-Prize Lunar Lander Challenge.
The goal of this challenge is to design and build a Lunar Lander Vehicle
(henceforth referred to as LLV) which could potentially explore the Moon. The
requirements of this vehicle are that it must carry a payload of at least 25 kg, rise to
an altitude of at least 50 m, translate a distance of 120 m, land and perform a similar
path but in the reverse direction. It is the responsibility of Team Cynthion to design
the main rocket thrusters, the fuel system, and the attitude control thrusters that
meet the LLV structure and control system team's requirements.
It is the intention of this report to provide a complete record of Team Cynthion's
design project since the fusion of Team ALLSTAR and Team Medea. A full
overview of the has been included.
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2. Main Rocket Thrusters Design Parameters
2.1. Performance Metrics
The first priority was to quickly explore ideal average operating conditions for the
given flight requirements where the minimum thrust is 1,633 N and nominal thrust
is 4,000 N. The NASA Chemical Equilibrium with Applications (CEA) program
was run, using an Oxidizer to Fuel (O/F) ratio of 7 and a chamber contraction ratio
Ac/At of 8, to compare exit pressures and expansion ratios at given chamber
pressures. These chamber pressures represent the range of engine thrust. It was
decided from the data shown in Figure 1 to consider 60 percent nominal thrust to be
the operating thrust level. This corresponds to a thrust of 3,053.2 N and a chamber
pressure of 29 bar. This decision was based on the thrust level that would provide
an even range of exit pressures over the flight profile.
3
2.5
2 Pc =10
Pc = 15
Pc = 20
1.5 Pc = 25
Pc = 30
Pc = 35
1 Pc = 38
0.5
0
0 1 2 3 4 5 6
Ae/At
Figure 1: Determination of Nozzle Expansion Ratio
NASA CEA was run again at this chamber pressure and the extreme thrust level
chamber pressures with different expansion ratios. The resulting plotted data is
shown in Figure 2. The regression equation for the average thrust was found and
used to obtain the expansion ratio at which the exit pressure reached atmospheric
conditions of 1 bar. The resulting expansion ratio was determined to be 4.7.
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3
y = 0.0066x4 - 0.1435x3 + 1.228x2 - 5.0356x + 9.153
2.5
2
Tave
1.5 Tmin
Tmax
1
0.5
0
0 1 2 3 4 5 6
Ae/At
Figure 2: Nozzle Performance for Major Thrust Levels
The next priority was to explore the expected performance values for the given
flight requirements where the minimum thrust is 1,635 N and nominal thrust is
4,000 N. NASA CEA was run, using O/F ratios of 3,4,5,6, and 7 and a chamber
contraction ratio Ac/At of 8. This was done to obtain values needed for input into
the Liquid Rocket Engine Creator (LREC) whose output was plotted versus the
varying O/F ratio. The results of this are shown in Figure 3, Figure 4, Figure 5,
Figure 6, Figure 7, Figure 8 andFigure 9.
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1.55
1.5
1.45
1.4
1.35
1.3
1.25
0 1 2 3 4 5 6 7 8
O/F
Figure 9: Chamber Mass Flow Rate for Varied O/F Ratio
It can be seen from Figure 3Figure 4, Figure 8 that the performance efficiency of
the engine drops quite substantially as the O/F ratio drops from seven to three. The
exit pressure, seen in Figure 7, at an O/F ratio of 3 is the same as that at the ratio of
7, so there is no drop in nozzle efficiency.
Though the performance drops more than desired at the testing oxidizer to fuel
ratio, the thermal effects of lowering the ratio are very desirable. Seen in Figure 5,
the temperature of the combustion products drops very much at the testing O/F ratio
of 3. Another desirable effect on the cooling is that the required total mass flow rate
increases (Figure 9), thus allowing the propane coolant to remove heat conducted
through the thrust chamber wall at a faster rate.
Though the exit pressure increased slightly more towards 1 bar, this may not be a
good thing. This may have the effect of creating undesirably low exit pressures
when the engine is throttled down. A summary of the changes as the oxidizer to fuel
ratio drops to three is shown in Table 1.
Table 1: Summary of Changes in Performance for Varied O/F
O/F Isp (sec) Cstar (m/sec) Tc (K) Me Pe (Pa) Cf M_dot (kg/s)
3 204.2288 1365.9 1772 2.718563 98587 1.466286 1.524465748
4 225.3369 1503.3 2389.76 2.903947 82626 1.469966 1.381663499
5 236.3192 1576.6 2819.35 2.871345 86783 1.469935 1.317454153
6 242.1622 1615.3 3093.78 2.834992 90922 1.470191 1.285666161
7 244.7421 1629.9 3237.06 2.79647 95900 1.472544 1.272113662
% Diff -18.0472 -17.62467454 -58.4964 -2.82526 2.763167 -0.42591 18.04719617
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With the average thrust at 3,053 N and the expansion ratio at 4.7, some engine
parameters were analyzed again using NASA CEA and the LREC tool. The exit
pressure, mass flow rate, specific impulse, and chamber temperature were computed
over the range of thrust and are shown in Figure 10, Figure 11,Figure 12, Figure 13,
respectively. It can be seen here that the exit pressure and mass flow rate change
proportionally to the thrust, while the chamber temperature increases proportionally
to the specific impulse. Also, it can be seen how these values differ when the O/F
ratio is dropped from the design value 7 to the expected testing value 3.
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Thrust (N)
Figure 10: Exit Pressure Over Thrust Range
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1.80000
1.60000
1.40000
1.20000
1.00000
0.80000
0.60000
0.40000
0.20000
0.00000
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Thrust (N)
Figure 11: Mass Flow Rate Over Thrust Range
245.2
245
244.8
244.6
244.4
244.2
244
243.8
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Thrust (N)
Figure 12: Specific Impulse Over Thrust Range
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Table 2 and Table 3 represent the performance metrics for full nominal thrust and
for the operating thrust at sixty percent of nominal thrust for O/F ratios of seven and
three.
Table 2: Performance Metrics for Thrust Chamber at Nominal at O/F=7
Nominal Performance Metrics
Thrust 4000 N
Chamber Pressure 38 bar
Specific Impulse 245.03 sec
Characteristic Velocity 1632.3 m/s
Characteristic Length 0.89 m
Mass Flow Rate 1.664 kg/s
Exit Pressure 1.25 bar
Exit Mach 2.799
Ae/At 4.7
Ac/At 8
Table 3: Performance Metrics for Thrust Chamber at 60% Nominal at O/F=7
Operating Performance Metrics
Thrust 3053
Chamber Pressure 29 bar
Specific Impulse 244.74 sec
Characteristic Velocity 1629.9 m/s
Characteristic Length 0.89 m
Mass Flow Rate 1.272 kg/s
Exit Pressure 0.959 bar
Exit Mach 2.796
Ae/At 4.7
Ac/At 8
Table 4: Performance Metrics for Thrust Chamber at Nominal at O/F=3
Nominal Performance Metrics
Thrust 4000 N
Chamber Pressure 38 bar
Specific Impulse 204.57 sec
Characteristic Velocity 1367.7 m/s
Characteristic Length 0.89 m
Mass Flow Rate 1.994 kg/s
Exit Pressure 1.30 bar
Exit Mach 2.799
Ae/At 4.7
Ac/At 8
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Table 5: Performance Metrics for Thrust Chamber at 60% Nominal at O/F=3
Operating Performance Metrics
Thrust 3053
Chamber Pressure 29 bar
Specific Impulse 204.23 sec
Characteristic Velocity 1365.9 m/s
Characteristic Length 0.89 m
Mass Flow Rate 1.524 kg/s
Exit Pressure 0.986 bar
Exit Mach 2.719
Ae/At 4.7
Ac/At 8
2.2. Engine Dimensions
C tool and remain
unchanged. These dimensions are shown in Table 6.
Table 6: Dimensions of the Thrust Chamber
Thrust Chamber Dimensions (m)
Chamber ID 0.08460
Chamber OD 0.08740
Chamber Length 0.11905
Nozzle Entrance Length 0.01590
Total Chamber Length 0.13495
Nozzle Exit Length 0.06450
Nozzle Total Length 0.0804
Total Length 0.19945
Entrance Diameter 0.08460
Exit Diameter 0.06485
Throat Diameter 0.02991
Note that the nozzle dimensions are based on a 60/15 conical nozzle and thus they
are different than the dimensions of the parabolic nozzle using these dimensions
discussed later.
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2.3. Injector Design
The propellant injector requirements have changed with the decision to test the
engine at an O/F ratio of 3. The new requirements are shown in Table 7 and Table
8. Though the requirements did change, the design has been frozen. This does not
pose a problem because fewer injectors would be required at the average thrust
level. This means the required mass flow rate will still be able to be accommodated.
Table 7: Requirements for Injector Design at 60% Nominal 0/F=7
Injector Requirements
Propane Nitrous Oxide
Chamber Mass Flow 1.272 kg/s Chamber Mass Flow 1.272 kg/s
Pressure Drop 0.87 MPa (0.3 Pc) Pressure Drop 0.87 MPa (0.3 Pc)
Liquid Density 582 kg/m3 Liquid Density 1222.8 kg/m3
Cd 0.8 Cd 0.8
K 1.7 K 1.7
Table 8: Requirements for Injector Design at 60% Nominal 0/F=3
Injector Requirements
Propane Nitrous Oxide
Chamber Mass Flow 1.524 kg/s Chamber Mass Flow 1.524 kg/s
Pressure Drop 0.87 MPa (0.3 Pc) Pressure Drop 0.87 MPa (0.3 Pc)
Liquid Density 582 kg/m3 Liquid Density 1222.8 kg/m3
Cd 0.8 Cd 0.8
K 1.7 K 1.7
The number of injectors at designed operating thrust is 132 for propane and 91 for
nitrous oxide. A summary of the production injector information is shown in Table
9.
Table 9: Properties of Propellant Injectors O/F=7
Injector Properties
Propane Nitrous Oxide
Material Copper Material Stainless Steel
Diameter Diameter 90o
Type Alternating Linear - Plain Type Shower Head - Countersunk
Number 147 3 Rows Number 102 5 Rows
Speed 38.4 m/s Speed 26.5 m/s
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2.4. Engine Throttling
The throttled engine data was recomputed to confirm that the minimum stable thrust
had not increased above the required value of 1,635 N with the variation of the O/F
ratio. With the new CEA data, thrust data was computed using the LREC tool. The
thrust did change, however it decrease which is good. This means that the engine
may have the ability to throttle well below the requirement. The minimum stable
thrusts were determined to be 1,633 N and 1,357 N, less than the desired 1,635 N.
Also, the performance metrics changed with the drop in oxidizer similar to the
changes at the operating thrust level. The resulting data is shown in Table 10 and
Table 11.
Table 10: Determination of Minimum Stable Thrust at O/F=7
Throttle Capability
Thrust 1626.04 N
Exit Pressure 40759 Pa
Mass Flow 0.68 kg/s
Oxidizer Injector Velocity 10.82 m/s
Fuel Injector Velocity 15.68 m/s
Exit Velocity 2392.99 m/s
Exit Mach 2.734
Oxidizer Pressure Drop w/ % Pc 190000.56 5.00
Fuel Pressure Drop w/ % Pc 190000.56 5.00
% Required Minimum Thrust 100.6
Table 11: Determination of Minimum Stable Thrust at O/F=3
Throttle Capability
Thrust 1356.54 N
Exit Pressure 46313 Pa
Mass Flow 0.68 kg/s
Oxidizer Injector Velocity 10.82 m/s
Fuel Injector Velocity 15.68 m/s
Exit Velocity 1995.82 m/s
Exit Mach 2.837
Oxidizer Pressure Drop w/ % Pc 189995.31 5.00
Fuel Pressure Drop w/ % Pc 189995.31 5.00
% Required Minimum Thrust 120.5
At the lower oxidizer to fuel ratio, a lower minimum thrust can be attained,
assuming the five percent pressure drop as the minimum stable thrust point.
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2.5. Ignition System
An igniter is needed to start the combustion of the mixture of fuel and oxidizer
entering the combustion chamber. Research conducted showed that the best igniter
for the engine was a glow plug. A glow plug is a device that has a heating element
or filament coiled up. The filament acts as a resistor, similar to a light bulb filament,
and heats up when an electric current is passed through it, igniting the reactants.
The glow plug resembles a short spark plug with a heating filament fitted into its tip
but does not extrude out into the chamber like the spark plug would. It requires less
hardware and power to operate than a spark plug, while being widely available.
The glow plug that will be used is the R8 extra cold glow plug made by Axe Motor
Rossi. A spark plug would produce a higher temperature which would result in an
easier start of the combustion, but the voltage required to produce the spark is too
high and would require cumbersome equipment. The R8 extra cold glow plug will
still be able to reach a temperature for the mixture to combust while using a voltage
that can be obtained through a variable power source.
Assuming the glow plug must be white hot to ignite the reactants, a single glow
plug requires around 2 volts and 5 amps. There will be a headlock connector on the
glow plug serving as the electrical connection to the power source. Three igniters
will be used to ensure consistent combustion and injection pattern, while also acting
as a safeguard in the case that one or more igniters fail. The three glow plugs will
be assembled in a parallel arrangement. Though this requires a larger current than a
series connection, if one fails the other two will still be operable.
The variable voltage source must be as close as possible to the igniters to maintain a
low wire resistance while being protected by a steel barrier. The power source also
has a port that will be connected to a computer to monitor the current and voltage
and more importantly allow the user to control the igniters from a safe distance.
Tests are to be conducted to determine a more accurate voltage and current needed
to ignite an oxidizer rich propane mixture.
2.6. Backup Ignition System
The proposed backup ignition system that will be utilized will be a hybrid/solid
rocket ignition system. This ignition system is composed of two wires covered with
Pyrogen. There will be a current applied to the wires that will ignite the Pyrogen.
The Pyrogen then ignites a piece of ammonium perchlorate from a hobby rocket
motor to start the ignition. This is a crude method of igniting our engine but has
proven to be effective as seen in hybrid and solid rockets. This would be taped
lightly inside the engine. If the glow plugs begin the combustion, the backup system
will be ejected out the nozzle. If the glow plugs do not do their job, the backup
system may be used to continue the testing. This will provide ignition but will not
be a restarting or reusable ignition system. This system shall only be used for the
continuing of a test fire to enable the collection of performance data.
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2.7. ERPL Liquid Rocket Engine Creator
Description:
The Liquid Rocket Engine Creator (LREC) is a proprietary design spreadsheet. It
was developed in Microsoft Excel by Embry-
Propulsion Labs (ERPL). This spreadsheet is composed of eight sheets which take
in some required user inputs and outputs nominal design data useful in the design of
a liquid propellant rocket engine. The eight sheets are titled Inputs, Nozzle,
Chamber, Throttle, Ox Injectors, Fuel Injectors, Heat Transfer, and Dimensions.
Each sheet has color-coding. Yellow indicates a user input while light blue indicates
a computed output.
Please note that this valuable computational tool should only be used by a person
skilled and knowledgeable in rocket engine fundamentals and design. Some of the
data that is output may require some interpretation and many of the inputs require
values from a chemical equilibrium analysis similar to NASA CEA. While any
value may be entered, this does not mean it is a smart input and only personnel
trained in rocketry should make these decisions. Also, this tool is still considered
experimental and is being tested for the use of simple hybrid rockets as well as
liquid rockets.
The first sheet is the Inputs page of LREC and has six sections. General Inputs
includes desired engine performance data, such as thrust and chamber pressure, and
data obtained from NASA CEA Analyses. Other sections are Nozzle Inputs,
Chamber Inputs, Fuel Injector Inputs, Ox Injector Inputs and Material Properties.
The Nozzle sheet in LREC is where all the rocket calculations are performed to
obtain dimensions, temperatures, pressures, velocities, and so on. This is divided
into Throat and Exit sections.
The Chamber sheet consists of outputs to rocket equations. The outputs of this sheet
are similar data types as in the Nozzle sheet. Also included is a calculation of
working hoop stress and wall thickness with from user inputs, including desired
safety factor.
The Throttle sheet is calculator for the throttling capability of the engine. This
allows the user to find the thrust they can throttle down to based on CEA data input
and desired pressure drop. It also outputs important design information such as flow
rates, velocities, pressures, and temperature.
The Ox Injectors and Fuel Injectors sheets are identical. These sheets take values
from Input sheet and calculate injector data such as number of injectors, pressures,
flow rates, and velocities. This sheet is useful in the dynamic design of injector
configurations.
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The Heat Transfer sheet is still in construction. This sheet requires a large amount
of data input by the user, much of which can come from NASA CEA, and outputs
the wall temperature and its difference from critical temperature at four main points
through the engine.
The final sheet of LREC is the Dimensions page. This sheet has two sections. In
one, many useful required dimensions of the engine are calculated. In the other
section, the volume and mass of propellant needed is shown as well as an estimate
of the engine mass. Shown below is a list of the inputs and outputs within the LREC
spreadsheet.
Inputs:
General:
CEA Data:
Chamber Temperature
Chamber Pressure
Specific Heat Ratios
Molar Masses
Specific Impulse
Desired Thrust
Burn Time
Fuel and Oxidizer Densities
Oxidizer to Fuel Ratio
Nozzle:
Nozzle Half Angles (i.e. 15/60)
CEA Characteristic Velocity
CEA Exit Pressure
CEA Exit Temperature
Chamber:
Characteristic Length
Injectors:
Coefficient of Discharge
Head Loss Coefficient
Orifice Diameter
Pressure Drop
Material Properties:
Throttling:
CEA Data:
Temperatures
Specific Heat Ratios
Molar Masses
Specific Impulse
Exit Mach Number
Desired Thrust
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Outputs:
General:
Specific Heat (constant pressure)
Nozzle:
Specific Gas Constant
Throat and Exit Area
Exit to Throat Area Ratio
Pressure at Throat
Temperature at Throat
Throat and Exit Diameters
Velocity at Throat and Exit
Ideal Exit Velocity
Mach at Exit
Throat and Exit Sonic Velocity
Chamber, Throat, and Combined Specific Volumes
Coefficient of Thrust
Chamber:
Area
Volume
Length
Mass Flow Rate
Stagnation Temperature
Stagnation Pressure
Fuel, Oxidizer, and Combined Mass in Chamber
Mach in Chamber
Chamber to Throat Area Ratio
Injectors:
Orifice Area
Individual and Total Mass Flow Rate
Individual and Total Volume Flow Rate
Change in Pressure
Pressure into Injectors
Injection Velocity
Combined Injector Area
Number of Injectors
Throttling:
Exit Pressure
Mass Flow Rate
Injector Velocities
Injector Pressure Drops
Exit Velocity
Throat Velocity
Stagnation Temperature
Percent of Minimum Required Thrust
Dimensions:
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Chamber Inner Diameter
Chamber Outer Diameter
Chamber Length
Nozzle Entrance Length
Total Chamber Length
Nozzle Exit Length
Total Length
Nozzle Entrance, Throat, and Exit Diameter
Wall Thickness
Quantities:
Total Propellant Needed
Fuel and Oxidizer Needed
Estimated Mass of Engine
Oxidizer to Fuel Ratio Check
2.8. NASA Chemical Equilibrium Analysis
the design of rocket engines. Though it can be used for many other applications, the
Rocket problem is what has been used for this project. A new window appears
when Rocket is selected. This allows the user to input chamber pressure(s), assign
or estimate a combustion temperature, nozzle expansion ratio(s), and calculation
type. The two types are infinite and finite area combustor.
For preliminary engine design it may be best to use infinite area combustor and
compare results for frozen and equilibrium calculations. When looking at the frozen
calculations, the freezing point may be critical as it determines where CEA assumes
the combustion process stops.
The finite area combustor option is more appropriate for detail design as the user
should have a good enough idea of the thrust chamber dimensions to use a
contraction ratio. Once the user inputs their requirements of this page and saves it,
the user enters desired oxidizer to fuel ratio(s) on the first page titled Problem.
On the next page, titled Reactant, the user must input the desired propellants and
their injection temperatures. The next three pages titled Only, Omit, and Insert
allows the user to specify or ignore certain gas species to be included in
calculations. These inputs are not required. The last page is Output and here the
user chooses the data needed to be displayed after calculation.
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3. Propulsion System Configuration
3.1. CATIA
A total of 15 parts have been modeled in CATIA, including eight original parts, three
stock standard parts based off dimensions from the McMaster-Carr website, an
igniter, two O-rings and one additional part for the test stand which is not included in
the models below. The current assembly of the entire rocket, shown in Figure
14Error! Reference source not found., without the feed line system attachments
and piping, is 296.0mm tall, 217.7mm wide at the widest part (the connection plates)
and is predicted to mass about 9.3kg.
In Figure 14, the combustion chamber, supersonic nozzle, four washers and the four
nuts are not visible. The washers and nuts are below the bottom of the three plates
near the top, and the nozzle and combustion chamber are hidden by the cooling
jacket.
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Nozzle
The supersonic nozzle, depicted in Figure 15, is 106.6mm
tall; 90.2mm wide; has a thickness of 3.175mm at all
points except the top flange; and a predicted mass of
0.625kg, assuming general material properties of
tellurium copper. The bell is a fully expanded (100%)
parabolic nozzle; the convergent region has a 60° half-
angle linear convergent section. The throat has a
diameter of 29.83mm, and the exit has a diameter of
68.69mm, giving an expansion ratio of 5.301. This
expansion ratio was used to get the initial parabola angle
of 20.178°.
The top of the nozzle has a lip 1.588mm thick to allow
for joining with the bottom of the combustion chamber. Figure 15: Supersonic
The lip is designed to provide a 6.35mm flat area that can Nozzle
be welded or brazed to the combustion chamber, reducing the probability of leaks
without the need for threading (which would be difficult considering the thickness of
the part, the material and the expected operating temperatures.
Combustion Chamber
As shown in Figure 16, the combustion chamber remains a
hollow cylinder made of tellurium copper. The chamber has an
inner diameter of 84.15mm for the whole of its 131.7mm
length, but the thickness again changes for the bottom 6.35mm
of the length from 3.175mm to 1.588mm. It masses
approximately 0.994kg.
The top of the combustion chamber contains three rows of 49
holes apiece. The holes are 0.397mm in diameter, equivalent
to a 1/32 inch drill bit, and are evenly distributed around the
circumference in staggered rows. These rows begin 15.875mm
from the top edge of the combustion chamber and are separated
by 1.588mm vertically. The volume from just above the top
Figure 16: Combustion Chamber
row of injectors to the top of the combustion chamber will be
used for mounting other components.
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Cooling Jacket
Overall, the jacket is 226.2mm tall and 101.6mm wide. It
incorporates a linear section to provide cooling past the
combustion chamber and a tapered outline of the nozzle to
regulate coolant flow speed past different parts of the nozzle.
The cooling channel is just under 1.5mm wide at the base of the
inlet, narrowing to 1mm near the throat and then gradually
expanding to 2.27mm at the bottom of the combustion chamber.
It remains 2.27mm up to the injection holes.
Because this jacket will be carrying the full pressure of the fuel
as it flows to the combustion chamber, 3.175mm thick steel was
chosen for the material. This material should not pose problems
because it will not be exposed to full combustion temperatures,
but it will need to handle moderate temperatures and high
pressures during operation and in the event of a catastrophic
failure of the engine. Using steel of this thickness will add a Figure 17: Cooling Jacket
measure of safety to the r
mass will be about 1.57kg, making it the second most massive component on the
rocket.
After fabrication, the jacket will be cut axially into halves, which will be fitted around
the combustion chamber and nozzle and then welded shut. 1mm tolerances represent
approximately 10 times the maximum manufacturing machine tolerance in the
Lehman manufacturing lab, but this narrow a channel may experience problems if the
welding process produces debris in the channel.
Fuel Inlet Manifold
The fuel inlet manifold will be constructed out of red brass, which has a similar
coefficient of thermal expansion as the copper
nozzle (pure copper has an expansion coefficient
of 16 to 17 parts per million per degree C, while
red brasses are in the range of 18 to 20 and
stainless steels can vary from nine to 17,
depending on the alloy and amount of austenite.
Considering the necessity of buying materials
from scrapyards, the brass is a more consistent
material without the need for identifying the steel
Figure 18: Fuel Inlet Manifold
alloy).
The manifold is 21.6mm tall and has an overall width of 109.9mm. The top and
bottom are 3.175mm thick, while the side wall is 6.35mm thick. Mass is predicted to
be about 0.50kg.
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National Pipe Taper (NPT) is a standard that dictates how fluid-carrying pipes and
holes must be constructed to create tight seals. Instead of holes using Unified
which slopes to close the hole the deeper it is drilled. When a pipe using NPT
threading is screwed into the hole, the straight sides of the pipe are held more and
more tightly by the closing hole, creating a seal which is more resistant to leaks than
straight threading.
Four 1/8 inch NPT holes will be drilled into the sides to accept connections to the
feed line system. These holes have 27 threads per inch, are just under 10.3mm wide
and require a depth of 6.35mm to form a good seal. These minimums dictate the
outer dimensions and sidewall thickness of the part.
Nitrous Injection Plate
The nitrous injection plate, shown in Figure 19, will be constructed of stainless steel
to prevent oxidation during exposure to the nitrous oxide. It has a diameter of
217.7mm, a thickness of 6.35mm at most points, and will mass about 1.81kg. The
bottom of the plate has a 1.588mm deep, 3.175mm wide semicircular groove for an
O-ring seal between it and the copper connection plate beneath.
Nitrous oxide will flow through the
102 0.397mm diameter holes
arrayed within the projected area
above the combustion chamber.
They have been spaced so as to
maximize cooling through the plate
while still being easily machinable.
Four half-inch holes with 13
threads per inch are spaced around
the disk at 83.5mm from the
center, for connection with the
other connection rings and the test Figure 19: Nitrous Injection Plate
stand. Three smaller holes for the igniters, with a diameter of ¼ inch and 32 threads
per inch (Unified National Extra Fine threading), are spaced at 120 degree angles
with their axes 38.5mm from the center of the disk.
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Nitrous Injection Dome
The nitrous injection dome will be
welded to the top of the nitrous
injection plate, creating a hard seal to
contain the nitrous oxide flowing in
through the 3/4 inch NPT (21.3mm
wide, 14.2mm deep) hole at the top
and out through the small holes in the
plate. The added tube-like section at
this inlet, shown in Figure 20, is
necessary to ensure proper thickness
for threading and to provide a
minimum depth for the NPT to make a
good seal. Figure 20: Nitrous Injection Dome
Overall, the height will be 51.2mm and the outer diameter will be 100.1mm. The
mass will be 0.321kg, using stainless steel as the material. However, the
manufacturing lab may elect to increase the bottom ridge downward to make
fabrication easier; this extra material at the bottom may be left on for testing
purposes, since it does not impact engine operation, or it may be cut off after the rest
of the part has been finished.
Copper and Steel Connection Rings
The connection rings are designed to
provide the combustion chamber/nozzle
assembly and the cooling jacket structural
support, a point of connection between
different metals at a location removed from
heat (to avoid problems with thermal
expansion), a point of connection and load
bearing to the test stand, and help with
assembly. The steel ring will connect to the
Figure 22: Copper Connection Ring
outside of the top 6.35mm of the cooling
jacket after it has been assembled around the
combustion chamber and nozzle. The
copper ring will be brazed to the top
6.35mm of the combustion chamber. Both
have an outer diameter of 217.7mm, with ½
inch threaded holes to match with the holes
in the nitrous injection plate. However, their
inner diameters vary because of the different
Figure 21: Steel Connection Ring parts they must encompass; the copper ring
has an inner diameter of 45.3mm, and the
steel ring has an inner diameter of 50.8mm. The copper ring is expected to mass
1.685kg, and the steel ring will mass 1.417kg.
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The steel ring has a 1.588mm deep, 3.175mm wide semicircular groove at a radius of
55.9mm for an O-ring seal between it and the copper ring; the copper ring has a
similar groove on its underside, and a groove with the same depth and width at
63.4mm from the center to house the O-ring between it and the nitrous injection plate.
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3.2. Connections and Assembly
All 29 engine parts and a general assembly sequence are shown in Figure 23.
Figure 23: Exploded Assembly drawing
To fit the cooling jacket around the combustion chamber it will be necessary to cut
the cooling jacket into two parts and then weld the two pieces back together around
the combustion chamber. Centerlines can be seen showing the assembly order of the
flanges (and accompanying nuts, washers and bolts) as well as the injector assembly.
Part of the main engine contains several flanges that provide a mounting surface for
attachment to the superstructure and also bridges between the combustion
chamber/cooling jacket and the injector assembly. As these flanges will be fastened
by nuts, washers and bolts, it is necessary for an O-ring or gasket to be between them,
in order to prevent hot-gas leakage.
For this purpose, Permatex High-Temperature Anaerobic Flange Sealant may be
used. The use of this material will allow a custom gasket to be made for the current
design, while no reliance on the design fitting the O-ring will be necessary. This
gasket- -
applied. It protects up to 400° F (205° C) in continuous exposure, and has no
restrictions on use in highly oxidizing environments. Cure time from initial exposure
to assembly is one hour, with full cure occurring after a period of 24 hours.
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The nuts, bolts and washers to be used for fastening of the flanges may be purchased
from McMaster-Carr or most hardware stores and will be of standard size and
threading. The bolts (McMaster- -
inch. They will be hex-headed cap screw
type of grade-5 zinc-plated steel with an ultimate strength of 120 ksi (827.37 MPa).
This is preferred as a corrosion (in this case oxidation) inhibitor in case of direct
contact with the hot-gases in use.
Nuts used will be P/N 94805A224 or similar. Made from 316 steel, they are hex head
exterior and thus not subjected to any harsh oxidation environments. Washers to be
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3.3. NASTRAN Pressure Analysis
The assembly of the entire engine was overlaid with materials for each section; the
nozzle, combustion chamber and copper connection plate were overlaid with the
material properties of tellurium copper; the cooling jacket, nitrous dome, injection
plate and steel connection plate were overlaid with properties of steel; and the cooling
manifold used the material properties of red brass. The assembly was then overlaid
with pressures on both the inside, outside and in-between areas, simulating the flows
of gaseous combustion at different points, liquid cooling and injection of the liquid
propellants. The assembly was then separated into two sections: one section includes
the plates and injector dome, and the other includes the combustion chamber, nozzle,
cooling jacket and manifold.
Pressures overlaid on the assemblies are as follows:
Injector Plate/Injector Dome: 716.486 psi (4.94 MPa)
Inner Nozzle & Throat: 313.281 psi (2.16 MPa)
Inner Combustion Chamber: 551.143 psi (3.8 MPa)
Cooling: 744.044 psi (5.13 MPa)
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First Assembly: Injector Plate, Injector Dome and Connection Plates
Figure 24: Section Cut: Deformation of Dome and Plates
As seen above in Figure 24, the exaggerated warping deformation that is produced
from the injection pressure of the nitrous oxide will not cause any fluids to leak out,
due to the O-rings placed in between the plates, along with the tight clamp produced
by the bolts attached to the plates. This deformation has a maximum deflection of
0.005 in (0.127 mm) and will not affect the performance of the engine.
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Figure 25: Section Cut: Mean Pressure Distribution of Dome and Plates
A mean pressure distribution, as show in Figure 25, shows the areas in which pressure
from the fluid entering the assembly will be the greatest. Negative values are listed
because of the opposite force and direction that the pressure is being distributed (up
for positive and down for negative). This distribution map confirms the prediction
that the topside of the injector plate will be subjugated to the most pressure, due to the
direct, vertical injection of the nitrous oxide. The greatest amount of pressure, 79,000
process a fine enough mesh on the O-rings to produce a more accurate result.
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Figure 26: Section Cut: Von Mises Stress of Dome and Plates
The structural integrity of the plates and dome, as shown in Figure 26, is consistent
with predictions that the highest concentration of stress would be in the shower head
area of the injector plate. High concentrations of stress would also be on the areas in
which the bolts would clamp down onto the plates. These values range from 15,571
psi (107.38 MPa) to 31,148 psi (214.75 MPa). These values are well below the
maximum yield stress of steel, 78,300 psi (540 MPa) and therefore, will be able to
withstand the injection pressure.
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Figure 27: Isometric Cut: Von Mises Stress of Plates
Figure 27 shows the stress produced on the injector plate by the nitrous oxide. The
around the O-rings. The highest concentration on the steel injector plate is
significantly less than the maximum yield stress of steel and will not be structurally
compromised.
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Second Assembly: Cooling Jacket, Nozzle, Combustion Chamber and Manifold
Figure 28: Section Cut: Deformation of Jacket, Nozzle, Chamber and Manifold
Deformation of the second assembly, as shown in Figure 28, has a maximum of
0.00234 in (0.059 mm). It is shown in the angled section cut of the area joining the
combustion chamber with the nozzle and is due to the high pressure combustion of
the gases pushing towards the nozzle. The relative high pressure in the cooling jacket
will help to mitigate this deformation.
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Figure 29: Section Cut: Mean Pressure Distribution of Jacket, Nozzle, Chamber and Manifold
The mean pressure distribution of the assembly, as show in Figure 29, shows the
areas in which pressure from the fluid and gases entering will be the greatest.
Negative values are listed because of the opposite force and direction that the
pressure is being distributed (up for positive and down for negative). The greatest
pressure on the angled section cut of the assembly is at the throat of the cooling
jacket. This can be due to the cooling fluid flowing through the jacket in such a small
area, that pressing outwards will cause a great amount of force to be subjected to that
part of the assembly, with ambient pressure on the outside of the assembly. The
greatest pressure, 8,900 psi, can be attributed to NASTRAN being unable to process a
finer mesh on certain areas of the assembly.
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Figure 30: Section Cut: Von Mises Stress of Jacket Nozzle Chamber and Manifold
The structural stress that the assembly will be subjected to is shown in Figure 30.
The high stress concentrations are the top area of the assembly and the area just
before the throat of the nozzle. The stresses of these areas range from 10,051 psi
(69.30 MPa) to 15,237 psi (105.05 MPa). For the top area of the assembly, this high
concentration of stress is due to the fixed constraints. For the lower area just before
the throat, this is possibly due to the pressure build-up of the cooling fluid expanding
into a much larger lateral area. Please see Figure 31 and Figure 32 for details on this
particular section.
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Figure 31: Section Cut of Jacket and Chamber: Von Mises Stress of Assembly
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Figure 32: Section Cut of Jacket and Chamber: Von Mises Stress of Jacket and Chamber
Figure 31 and Figure 32 highlight the throat area stress that the cooling jacket will be
subjected to during engine firing. As listed earlier, the material that the cooling jacket
will be manufactured out of will be able to withstand the stress placed on it. The
stresses that the rest of the assembly will subjected to are also within acceptable
levels of material yield stress: 44 ksi (303.37 MPa) for tellurium copper, and 14 ksi
(96.53 MPa) for red brass. Therefore, the structural integrity of the assembly is not
compromised.
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3.4. Mass Budget
Table 12: Single Engine Mass Budget (without feedline)
Component Material Quantity Unit mass(kg) Mass (kg)
Combustion Chamber Tellurium Copper 1 0.994 0.994
Nozzle Tellurium Copper 1 0.625 0.625
Cooling Jacket Steel 1 1.565 1.565
Injector Plate Stainless Steel 1 1.813 1.813
Connection Ring (Copper) Tellurium Copper 1 1.685 1.685
Connection Ring (Steel) Steel 1 1.417 1.417
Fuel Inlet Manifold Red Brass 1 0.487 0.487
Injector Dome Stainless Steel 1 0.321 0.321
O-Rings Permatex Sealant 2 0.003 0.006
Bolts Steel 4 0.070 0.280
Igniter (several materials) 3 0.004 0.012
Washers Steel 8 0.008 0.064
Nuts Steel 4 0.015 0.060
Engine Total Mass 9.329
Table 12 describes the estimated masses of individual components and the total
predicted mass of a single engine without any attachments or feed line components.
Masses were estimated using CATIA and the application of material data to part files.
Where a specific material was not available, the closest available approximation was
used (e.g., tellurium copper was replaced with pure copper).
.
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4. Thermal Analysis
4.1. Introduction
The cooling system consists of propane as the coolant in a jacket around the engine.
There are no channels or spacing fins. There is an intake manifold at the bottom,
and the propane exits the cooling jacket through the combustion chamber injection
holes at the top.
Two methods were used to analyze the heat transfer through the wall: a steady state
analysis and a transient analysis. Maximum wall temperature (at steady state)
varied from one analysis to the other by 1.4%. This gives an average maximum
wall temperature of 2600K.
Transient analysis was applied to the wall only. Using the steady state analysis, the
maximum propane temperature is 782K. Nitrous oxide was also analyzed as a
coolant, using only steady state analysis, which predicts a maximum wall
temperature of 2898.68K, and a maximum coolant temperature of 311.58K.
4.2. Computational Tools Used
Two programs were used independently to analyze the heat flow: MATLAB and
Microsoft Excel. Both programs used numerical integration techniques with an
energy balance for the analysis. The engine was discretised and then analyzed.
StarCCM+ was used to perform CFD analysis on the flow of the combusted gas to
ensure that the geometry of the engine will not produce stagnant or extremely
turbulent flow.
The heat transfer coefficients for the gas/wall interface and the coolant/wall
interface were found using Equation 1 and Equation 2, respectively, for both steady
state and transient analysis.
g .8 .4
g g g
E
Equation 1: Gas/Wall Heat Transfer Coefficient
1/ 5 2/3
l l l l
Equation 2: Coolant/Wall Heat Transfer Coefficient
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Discretization Method
A coordinate system was set up as shown in Figure 33, where the r-axis is at the
throat and the y-axis is co-linear with the center line. The nozzle exit is at point 5.
Figure 33: Coordinate Axis System
The engine was discretised in the y-direction and an energy balance between the
combusted gas and the coolant was performed at each disc. The numerical
integration starts at the nozzle exit, and a disc is defined to be the space between the
inside engine wall and the inside jacket wall from yn to yn+1; yn is the beginning of
the disc and yn+1 is the end of the disc.
To discretise, the Mach number was set as the independent variable, varying by
.001, and Equation 3 was used to determine the associated area of the engine. The
throat area, A* , is known and is assumed to be constant for this part of the
analysis.
Equation 3: Mach-Area Relationship
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The radius, r, can be found directly from the area. The y-positions, which define
the discs, can then be found in each section using the following equations:
y rc1 sin
1 r rth
cos 1
rc1
Equation 4: Section 1 y-position Equations
Equation 5: Section 2 y-position Equation
y y3 rc 3 sin
r3 r
1 rc3
cos
rc 3
Equation 6: Section 3 y-position Equations
y rc 4 sin
1 r rth
cos 1
rc 4
Equation 7: Section 4 y-position Equations
Equation 8: Section 5 y-position Equation
Section 6 has a constant radius equal to the chamber radius, and the y-distance from
the bottom to the top is divided into 831 discs. Sections 1, 3, and 4 are portions of a
circle with radii of curvatures rc1, rc3, and rc4 respectively. rth is the throat radius,
and r1 and r3 correspond to the points in Figure 33. The angle of 60 in Equation 5
is the angle between the engine wall and the y-axis.
Steady State Analysis
The gas temperature at each disc was found using Equation 9. The total
temperature is the flame temperature. The gas pressure was found using Equation
10, with the total pressure being the chamber pressure. For these two equations,
was assumed to remain constant.
Equation 9: Gas Static Temperature
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1
0 0
Equation 10: Gas Static Pressure
CEA was used to find the gas properties at the injectors, the bottom of the
combustion chamber, the throat, and the nozzle exit as shown in Table 13.
Table 13: Variable Gas Properties
Therm
Temperature Density Viscosity Cp
Gamma Conduct
(K) (kg/m^3) (millipoise) (kJ/(kg*K))
(mW/(cm*K))
Injector 3317.83 4.45734 0.99321 1.1677 3.3285 7.0457
Combustor
End 3309.22 4.3193 0.9914 1.1677 3.3237 7.0228
Throat 3082.11 2.7089 0.94345 1.1757 2.88 5.5975
Exit 1707.12 0.17735 0.62716 1.2534 1.6351 1.5219
The NIST (National Institute of Standards and Technology) website was used to
find the properties for propane in 1K increments. The properties that were varied
are density, viscosity, specific heat capacity, and thermal conductivity. Each
property was found for the associated propane temperature, to the nearest 1K,
rounded down. For instance, if the propane temperature is 400.35K, the properties
would correspond to a temperature of 400K. The first set of properties is associated
with the initial coolant temperature.
The following equations describe the energy balance between the gas and the
coolant.
Equation 11: Heat Transfer Between the Gas and Wall
w
q Twg Twc
tw
Equation 12: Heat Transfer Through the Wall
Equation 13: Heat Transfer Between the Wall and Coolant
Equation 14 describes the temperature rise of the coolant across each disc for a
given amount of heat transferred to it, where hg and hc are the heat transfer
coefficients for the gas and coolant, respectively, is the thermal conductivity of
52. Lunar Lander Vehicle Propulsion System: 100% Design Review
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the wall, tw is the thickness of the wall, Cpc is the specific heat capacity of the wall,
and A is the coolant to wall surface area of the disc.
qA m Cp c Tc 2 Tc1
Equation 14: Coolant Temperature Rise
There are three unknown quantities between Equation 11, Equation 12, and
Equation 13; the gas wall temperature, the coolant wall temperature, and the heat
flow, Twg, Twc, and q respectively. By combining the three equations, the following
relationships are found to give the gas and coolant wall temperatures at the
beginning of the disc, where Tc is the coolant temperature at the beginning of the
disc:
w w
Tg 1 Tc
t w hc t w hg
Twg
w w w w
1 1
t w hc t w hg t w hc t w hg
Equation 15: Gas Wall Temperature
w
Twg Tc
t w hc
Twc
w
1
t w hc
Equation 16: Coolant Wall Temperature
By combining Equation 13 and Equation 14, the coolant temperature at the end of
the disc is found:
hc Twc 1 Tc1 A
Tc 2 Tc1
m Cp c
Equation 17: Coolant Temperature at End of Disc
The surface area, A, of the coolant/wall interface is found by using Equation 18.
2
1
Equation 18: Surface Area of a Body of Revolution
The y=f(r) functions, from Equation 4 through Equation 8, were solved for r in
order to get the derivative with respect to y. The right hand side of the r=f(y)
53. Lunar Lander Vehicle Propulsion System: 100% Design Review
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equation is substituted into Equation 18 for r, and the integral is carried out. The
only section this was not conducted for was Section 5. A closed form solution for
the integral could not be found. In that case, Equation 19 was used.
Equation 19: Section 5 Surface Area
Here, ds is the arc length of the disc and r is the average radius of the disc.
Numerical Integration
The integration process started at the nozzle exit, where the coolant enters the
cooling jacket, and the y-position is y1. Tc1 for this first iteration is the initial
coolant temperature, assumed to be 310K. The heat transfer coefficients for the gas
and coolant were calculated for y1. Gas and coolant wall temperatures were then
computed, and then the coolant temperature at the end of the disc, or at y2, was
calculated. The heat transfer coefficients were found for y2, and then the wall
temperatures, and then the coolant temperature at y3. This process continued
through all of the discs. Both MATLAB and Microsoft Excel were used to perform
this integration.
One main M-file was written in MATLAB, which called two separate M-file
functions. The main function first calculated the y-positions and associated gas
temperatures along the entire length of the engine. These were indexed in a master
matrix, which was then sent to the two separate functions. One function read the
gas properties of Table 13 from an Excel spreadsheet, performed linear
interpolations to find the properties corresponding to each of the indexed gas
temperatures, and then indexed these properties in the master matrix. The other
function read the propane properties from another Excel spreadsheet, found the
properties for each indexed temperature, and indexed them in the master matrix.
The main file then looped through the calculations of heat transfer coefficients, wall
temperatures, and coolant temperatures for one less iteration than the number of y-
positions. Coolant pressure was also calculated, using Equation 20, and indexed.
2
1.82 log 10 Re c 1.64 y 2 y1 c Vc2
P2 P1
2 HD g
Equation 20: Coolant Pressure
The required inputs for the MATLAB program are shown in Table 14. The outputs
are the wall temperature, coolant temperature, and coolant pressure profiles along
the engine, as shown in Figure 34, Figure 35, and Figure 36 respectively.
