Scholars' Mine Masters Theses Student Theses and Dissertations Spring 2012 Numerical investigation of second-law characteristics of ramjet throttling Jonathan Albert Sheldon Follow this and additional works at: https://scholarsmine.mst.edu/masters_theses Part of the Aerospace Engineering Commons Department: Recommended Citation Sheldon, Jonathan Albert, "Numerical investigation of second-law characteristics of ramjet throttling" (2012). Masters Theses. 5143. https://scholarsmine.mst.edu/masters_theses/5143 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. i NUMERICAL INVESTIGATION OF SECOND-LAW CHARACTERISTICS OF RAMJET THROTTLING by JONATHAN ALBERT SHELDON A THESIS Presented to the Faculty of the Graduate School of the MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE IN AEROSPACE ENGINEERING 2012 Approved by D. W. Riggins, Advisor K. M. Isaac S. Hosder ii 2012 Jonathan Albert Sheldon All Rights Reserved iii ABSTRACT A numerical study of a generic axisymmetric ramjet operating at conditions corresponding to flight Mach 3.0 and a standard altitude of 10 km is presented. The study includes both modeling of steady-state flowfields in the ramjet as well as transient throttling maneuvers in which the throttle is decreased or increased from maximum or minimum throttle positions. The results presented here focus on entropy generation and performance characteristics. Combustion-generated exothermic heat release is modeled using simple volumetric energy addition to the flow within a defined heat release zone. The study utilizes two levels of wall boundary modeling, corresponding respectively to inviscid and viscous walls in the ramjet. The second level of modeling (with viscous walls) presents many challenges due to the inherent tendency of the no-slip boundary condition to cause reverse flow to develop in the ramjet, particularly along the wetted surfaces of the inlet where the adverse pressure gradient associated with the deceleration and heat release in the ramjet has the largest initial impact. This separated flow results in eventual unstart of the ramjet due to large-scale propagation of the separation upstream; there is also inherent unsteadiness due to boundary layer effects. To address the challenges presented by the no-slip boundary condition, a bleed boundary condition specified at the inlet throat is incorporated. This bleed extracts approximately 10% of the mass flow. As an alternative to bleeding mass from the flow path of the ramjet, a generic (alternative) model of a ramjet dump combustor is also studied. This configuration has a geometry in which a constant area heat addition zone is located downstream of a large step at the exit of the ramjet inlet. This configuration is analyzed and compared to the original configuration without the dump combustor. It is found that both the bleed boundary condition and the dump combustor are extremely effective at preventing the normal shock from propagating upstream. iv ACKNOWLEDGMENTS This author would like to thank Dr. David Riggins for his invaluable guidance, patience, and assistance. Dr. Riggins’ continual advice and genuine friendship made this experience not only a learning endeavor but also an enjoyable one. Thanks also go to Dr. Serhat Hosder and Dr. Kakkattukuzhy Isaac for their contributions to the author’s educational experience and also for taking the time to review this material. Dr. Hosder supplied the author with invaluable computational resources, allowing this thesis to be done in a timely manner. Thank you also to the Missouri University of Science and Technology for their support through the Chancellor’s Fellowship and also to the Air Force Research Laboratory for their financial support during this work as well. Finally, I would like to thank my wife, Krista Sheldon, for her extraordinary love and support during my entire educational career. I would not be where I am today without her. v TABLE OF CONTENTS Page ABSTRACT ....................................................................................................................... iii ACKNOWLEDGMENTS ................................................................................................. iv LIST OF ILLUSTRATIONS ............................................................................................ vii LIST OF TABLES ............................................................................................................ xii NOMENCLATURE ........................................................................................................ xiii SECTION 1. INTRODUCTION ...................................................................................................... 1 2. RAMJET CFD TOOLS AND METHODOLOGY .................................................... 7 2.1. VULCAN CFD CODE ....................................................................................... 7 2.2. GEOMETRY AND GRID DEFINITION .......................................................... 8 2.3. PARALLELIZATION STRATEGY ................................................................ 11 2.4. POST PROCESSING RESULTS ..................................................................... 12 3. RAMJET THROTTLING ANALYTICAL MODELING ....................................... 13 3.1. THEORY .......................................................................................................... 13 3.2. ISSUES INVOLVING HEAT ADDITION MODELING FOR ENGINE THROTTLING MANEUVERS ....................................................................... 17 3.3. STEADY-STATE THROTTLING STUDY .................................................... 18 4. GRID CONVERGENCE STUDY ........................................................................... 20 5. TURBULENCE MODEL CASE STUDY ............................................................... 26 5.1. MENTER SST MODEL ................................................................................... 27 5.2. k-ω POPE MODEL ........................................................................................... 29 6. AXISYMMETRIC INVISCID WALL RESULTS .................................................. 33 6.1. STEADY-STATE THROTTLING ................................................................... 37 6.1.1. Conventional Design .............................................................................. 37 6.1.1.1 Fluid dynamics ............................................................................39 6.1.1.2 Performance and entropy results and analysis ............................39 vi 6.1.2. Dump Combustor ................................................................................... 49 6.1.2.1 Fluid dynamics ............................................................................51 6.1.2.2 Performance and entropy results and analysis ............................52 6.2. TRANSIENT THROTTLING .......................................................................... 61 6.2.1. Conventional Design .............................................................................. 61 6.2.1.1 Fluid dynamics ............................................................................61 6.2.1.2 Performance and entropy results and analysis ............................65 6.2.2. Dump Combustor ................................................................................... 68 6.2.2.1 Fluid dynamics ............................................................................68 6.2.2.2 Performance and entropy results and analysis ............................72 7. AXISYMMETRIC VISCOUS WALL RESULTS .................................................. 75 7.1. BLEED BOUNDARY CONDITION ............................................................... 76 7.2. STEADY-STATE THROTTLING ................................................................... 78 7.2.1. Fluid Dynamics ...................................................................................... 80 7.2.2. Performance and Entropy Results and Analysis .................................... 81 7.3. TRANSIENT THROTTLING .......................................................................... 90 7.3.1. Fluid Dynamics ...................................................................................... 90 7.3.2. Performance and Entropy Results and Analysis .................................... 95 8. SUMMARRY AND CONCLUSIONS .................................................................... 97 APPENDICES A. SAMPLE VULCAN INPUT DECK ..................................................................... 100 B. POST PROCESSING MATLAB CODE .............................................................. 107 C. ENTROPY CALCULATIONS ............................................................................. 131 D. QUASI-ONE-DIMENSIONAL ANALYTICAL THROTTLING MODEL ........ 134 BIBLIOGRAPHY ........................................................................................................... 137 VITA .............................................................................................................................. 139 vii LIST OF ILLUSTRATIONS Figure Page 2.1. Comparison Between Boundary Contours of Diverging Exit Nozzle Using Method of Characteristics and Cubic Spline Method