اسم المؤلف
Mark C. Schnabel
التاريخ
25 يوليو 2022
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591
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رسالة ماجستير بعنوان
Pressure Distribution and Performance Impacts of Aerospike Nozzles on Rotating Detonation Engines
by
Mark C. Schnabel
Ensign, United States Navy
B.S., United States Naval Academy, 2016
Submitted in partial fulfillment of the
requirements for the degree of
MASTER OF SCIENCE IN MECHANICAL ENGINEERING
from the
NAVAL POSTGRADUATE SCHOOL
June 2017
Approved by: Christopher M. Brophy
Thesis Advisor
David F. Dausen
Second Reader
Garth V. Hobson
Chair, Department of Mechanical and Aerospace Engineering
TABLE OF CONTENTS
I. INTRODUCTION 1
A. OVERVIEW .1
B. MOTIVATION 4
C. OBJECTIVES AND APPROACH .4
II. BACKGROUND 7
A. THRUST .7
B. NOZZLES .10
- Basic Design 10
- Shortcomings of Conventional Nozzles 10
- Altitude Compensation: An Alternative to Conventional
Nozzles .13
C. INTRODUCTION TO AEROSPIKE NOZZLES 14
D. CLASSIFICATION OF AEROSPIKE NOZZLES 16 - Annular Aerospike Nozzles .16
- Linear Aerospike Nozzles 18
- Truncation of Aerospike Nozzles 19
E. FLOW PHYSICS OF PLUG NOZZLES 20 - Flow Features in Quiescent Air 21
- Flow Features in a Supersonic Free Stream 25
F. FLOW PHYSICS OF THE NOZZLE BASE 27 - The Open Wake Regime 27
- The Closed Wake Regime .28
- Open/Closed Transition .28
- Base Pressure Prediction .32
III. NOZZLE DESIGN METHOD .35
A. INTRODUCTION 35
B. DESIGN APPROACH: THE SIMPLE APPROXIMATE
METHOD .36
C. DERIVATION 37
IV. NOZZLE DESIGN FOR THE RDE 43
A. NOZZLE DESIGN ASSUMPTIONS .43 - Assumption of Purely Axial Flow .43
- Nonuniform Throat Conditions 44
- Expected Pressure Ratio 46viii
- Ideal Design Pressure Ratio 47
B. APPLICATION TO THE CURRENT RDE .48 - Determination of Input Parameters .48
- Computed Results 49
C. SOLIDWORKS DESIGN .53
V. CFD ANALYSIS 57
A. OVERVIEW .57
B. FLUID DOMAIN .57
C. COMPUTATIONAL MESH PARAMETERS .58 - Common Mesh Settings .59
- Face Sizing and Meshing .60
D. CFD ASSUMPTIONS .61 - Non-Reacting Flow Modeled as Combustion Products 61
- Uniform Inlet Flow in the Radial and Circumferential
Directions 63
E. SOLVER DEFINITION AND BOUNDARY CONDITIONS .64
F. TEST MATRIX 68
VI. CFD RESULTS 69
A. QUIESCENT AIR 69 - Nondimensional Wall Distance and Turbulence Modeling .69
- Validation of the Experimental Nozzle Design 70
- Steady-State Pressure Distribution along the Aerospike .72
- Steady-State Base Pressure Distribution .74
- Steady-State Thrust Computation 75
- Steady-State Thrust Coefficient 79
B. SUPERSONIC FREE-STREAM 81
C. MESH SENSITIVITY AND TURBULENCE MODELING .83
VII. SUMMARY 85
A. DESIGN GUIDELINES 85
B. FUTURE WORK .85
APPENDIX A. MATLAB CODE 87
APPENDIX B. CEA DETONATION ANALYSIS .91
APPENDIX C. TRANSITION PRESSURE RATIO ANALYSIS .95ix
APPENDIX D. CEA DEFLAGRATION ANALYSIS 97
LIST OF REFERENCES 101
INITIAL DISTRIBUTION LIST
LIST OF FIGURES
Figure 1. Numerical Simulation of a Generic RDE. Source: [1]. .2
Figure 2. Unrolled Numerical Simulation of a Hydrogen-Air RDE. Source:
[2] .3
Figure 3. Engine Diagram—Exploded View. Source: [1]. .5
Figure 4. Pressure Distribution on a Simplified Rocket Casing. Adapted from
[11] .7
Figure 5. Internal Total Pressure and Thrust Distribution in a Turbojet Engine.
Adapted from [11] 8
Figure 6. Well-Prescribed Control Volume for a Simplified Rocket Geometry.
Source: [11] 9
Figure 7. Nozzle Configurations. Source: [14]. 11
Figure 8. Bell Nozzle Exhaust Plume Comparison. Adapted from [14] .13
Figure 9. Annular Aerospike Nozzle. Source: [18] .14
Figure 10. Aerospike Exhaust Plume Comparison. Adapted from [14]. 15
Figure 11. Completely External Aerospike. Adapted from [20] .16
Figure 12. Internal-External Aerospike. Adapted from [20] .17
Figure 13. Completely Internal Aerospike. Adapted from [20] 17
Figure 14. Alternate Combustion Chamber Arrangement. Source: [24]. .18
Figure 15. Linear Aerospike Nozzle. Source: [26]. 19
Figure 16. Aerospike Terminology. Adapted from: [27]. .21
Figure 17. Flow Features of a Plug Nozzle. Adapted from [29] .22
Figure 18. Mach Isolines and Jet Boundary in a Linear Full-Length Plug.
Source: [27] 24
Figure 19. Plug Nozzle Flow Field at Various Jet Pressures. Adapted from [15]. .25xii
Figure 20. Schematic View of the Interaction Between Exhaust and External
Supersonic Jets Behind the Primary Nozzle External Shroud. Source:
[27] .26
Figure 21. Schematic View of Closed Wake Operation. Source: [37] 29
Figure 22. Closed-Open Wake Transition. Source: [37] .29
Figure 23. Schematic of Characteristic Lines at Closed-Open Wake Transition.
Source: [37] 30
Figure 24. Expansion Characteristic Lines 36
Figure 25. Throat Angle Orientation with Respect to Contour Geometry 37
Figure 26. Local Characteristic Line Geometry 38
Figure 27. Approximate Method Contour Geometry 39
Figure 28. Inlet (Solid) and Outlet (Dashed) Velocities as a Function of
Azimuthal Location for a Generic RDE Simulation. Source: [49] 44
Figure 29. Inlet (Solid) and Outlet (Dashed) Pressures and Temperatures as a
Function of Azimuthal Location for a Generic RDE Simulation.
Source: [49] 45
Figure 30. Expected Nonuniform Throat Conditions 46
Figure 31. Aerospike Contour for PRdesign = 10:1 .50
Figure 32. Cowl Contour for PRdesign = 10:1 .50
Figure 33. Spike and Cowl Configuration for PRdesign = 10:1 .51
Figure 34. Spike and Cowl Configuration for PRdesign = 25:1 .52
Figure 35. Spike and Cowl Configuration for PRdesign = 40:1 .52
Figure 36. Aerospike SolidWorks Model 53
Figure 37. Cowl SolidWorks Model .54
Figure 38. Center Body SolidWorks Model 54
Figure 39. Integration with Current RDE Hardware .55
Figure 40. Experimental Fluid Domain Geometry for PRdesign = 10:1 58xiii
Figure 41. ANSYS Domain Mesh for PRdesign = 10:1 .60
Figure 42. Variability of Properties with Ratio of Specific Heats. Source: [10]. .62
Figure 43. Boundary Conditions for the PRdesign = 10:1 Case .64
Figure 44. Mach Number Distribution along the Nozzle Exit Plane at Various
Pressure Ratios for the Quiescent Air Hydrogen Fuel Case, PRdesign =
10:1 71
Figure 45. Steady-State Nozzle Pressure Distribution at Various Pressure
Ratios for the Quiescent Air Hydrogen Fuel Case, PRdesign = 10:1 .72
Figure 46. Steady-State Nozzle Pressure Distribution at Various Pressure Ratios
for the Quiescent Air Hydrogen Fuel Case, PRdesign = 25:1 .73
Figure 47. Steady-State Nozzle Pressure Distribution at Various Pressure Ratios
for the Quiescent Air Hydrogen Fuel Case, PRdesign = 40:1 .74
Figure 48. Steady-State Base Pressure Distribution at Various Pressure Ratios
for the Quiescent Air Hydrogen Fuel Case, PRdesign = 10:1 .75
Figure 49. Designation of the RDE Control Volume 76
Figure 50. Control Surfaces Over Which ANSYS Force Function Was Applied
in the X-Direction, PRdesign = 10:1 .77
Figure 51. Thrust Contribution for Control Surfaces 1, 2, and 6 for the
Quiescent Air Hydrogen and Ethylene Fuel Cases, PRdesign = 10:1 .78
Figure 52. Gross Thrust vs Pressure Ratio for H2 Fuel Case 79
Figure 53. Thrust Coefficient vs Pressure Ratio for H2 Fuel Case 80
Figure 54. Plot of Mach Numbers for Supersonic Free-Stream Case, No Base
Bleed 81
Figure 55. Mach Number Distribution along the Nozzle Exit Plane at Various
Pressure Ratios for the Supersonic Free-Stream Hydrogen-Air Case .82
Figure 56. Steady-State Nozzle Pressure Distribution at Various Pressure Ratios
for the Supersonic Free-Stream Hydrogen-Air Case, PRdesign = 10:1 82
Figure 57. Effect of Base Bleed on Base Pressure Distribution, PRdesign = 10:1,
H2 Fuel Case 83
Figure 58. Mesh Sensitivity and Turbulence Model Analysis 84
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