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Numerical Gas Dynamics of Internal and External Flows in Gun Barrels. Oktay Baysal Louisiana State University and Agricultural & Mechanical College

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Numerical Gas Dynamics of Internal and External Flows in Gun Barrels. Oktay Baysal Louisiana State University and Agricultural & Mechanical College Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1982 Numerical Gas Dynamics of Internal and External Flows in Gun Barrels. Oktay Baysal Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Baysal, Oktay, "Numerical Gas Dynamics of Internal and External Flows in Gun Barrels." (1982). LSU Historical Dissertations and Theses. 3747. https://digitalcommons.lsu.edu/gradschool_disstheses/3747 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. INFORMATION TO USERS This reproduction was made from a copy of a document sent to us for microfilming. While the most advanced technology has been used to photograph and reproduce this document, the quality of the reproduction is heavily dependent upon the quality of the material submitted. The following explanation of techniques is provided to help clarify markings or notations which may appear on this reproduction. 1. The sign or “target” for pages apparently lacking from the document photographed is “Missing Page(s)”. If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting through an image and duplicating adjacent pages to assure complete continuity. 2. When an image on the film is obliterated with a round black mark, it is an indication of either blurred copy because of movement during exposure, duplicate copy, or copyrighted materials that should not have been filmed. For blurred pages, a good image of the page can be found in the adjacent frame. If copyrighted materials were deleted, a target note will appear listing the pages in the adjacent frame. 3. When a map, drawing or chart, etc., is part of the material being photographed, a definite method of “sectioning” the material has been followed. It is customary to begin filming at the upper left hand comer of a large sheet and to continue from left to right in equal sections with small overlaps. If necessary, sectioning is continued again—beginning below the first row and continuing on until complete. 4. For illustrations that cannot be satisfactorily reproduced by xerographic means, photographic prints can be purchased at additional cost and inserted into your xerographic copy. These prints are available upon request from the Dissertations Customer Services Department. 5. Some pages in any document may have indistinct print. In all cases the best available copy has been filmed. Universfc/ Microfilms International 300 N. Zeeb Road Ann Arbor, Ml 48106 8229490 Baysal, Oktay NUMERICAL GAS DYNAMICS OF INTERNAL AND EXTERNAL FLOWS IN GUN BARRELS The Louisiana State University and Agricultural and Mechanical Col PH.D. 1982 University Microfilms International 300 N. Zeeb Road, Ann Arbor, MI 48106 PLEASE NOTE: In all cases this material has been filmed in the best possible way from the available copy. Problems encountered with this document have been identified here with a check mark V . 1. Glossy photographs or pages _____ 2. Colored illustrations, paper or print _____ 3. Photographs with dark background _____ 4. Illustrations are poor copy ______ 5. Pages with black marks, not original copy ______ 6. 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Other_______________________________________________________________ University Microfilms International NUMERICAL GAS DYNAMICS OF INTERNAL AND EXTERNAL FLOWS IN GUN BARRELS A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College In partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering Oktay Baysal B.5., The Technical University of Istanbul, Turkey, 1976 M.Sw, The University of Birmingham, U.K., 1978 August 1982 ACKNOWLEDGEMENTS I am deeply indebted to my research advisor, Dr. Robert W. Courter, for his helpful advice, supervision and encouragement with upmost sincerity and unseifishness. Beyond any doubt, the completion of this work is owed to Professor Andrew 3. McPhate*s hours of revealing conversation and discussion. I would also like to express my deepest gratitude to my committee members, Dr. Ozer A. Arnas, Dr. Magd E. Zohdi, Dr. John A. Hiidebrant and Dr. Daniel W. Yannitell for their guidance and assistance. Sincere appreciation and thanks are due the department chairman, Dr. William N. Sharpe, for allowing me to use the computer and departmental facilities freely. I also gratefully acknowledge the patience and punctuality of my manuscript typist, Ms. Dawn A. Tipton. Last, but certainly not the least, I would like to reiterate my gratitude, respect and deep love to my mother and father who have always been most supportive, encouraging and caring without which all would have been absolutely impossible. TABLE OF CONTENTS Page Acknowledgment ii List of Tables v List of Figures vi List of Symbols ix Abstract xii Introduction 1 Gun Barrel Flows 2 Muzzle Blast Flows 4 Theory 7 Internal Flow 7 External Flow 11 Numerical Methods of Analysis 18 Internal Flow 18 External Flow 22 Results 30 Discussion and Conclusions 39 Figures 46 References 94 i i i Appendices A. Analysis of One-dimensional Steep-Fronted Wave B. Analysis of One-dimensional Non-Steep Wave C. Program Listing LIST OF TABLES Page TABLE 1. Summary of Results for Test Cases 32 TABLE 2. Results for One Dimensional Shock Propagation 36 TABLE 3. Results for Spherical Non-self-similar Shock Propagation 38 v UST OF FIGURES A Typical Two Stage Gun 47 Aeroballistic Research Facility 48 Muzzle Performance 49 Experimental Results from Seigel 50 Characteristics Around the Projectile and the Initiation of Shock on Time-Distance Plot 51 A Schematic of a Barrel and Projectile Assembly 52 Characteristics of an Unsteady, One Dimensional Flow 53 Finite Difference Grid Based on Inverse Marching Method of Hartree 54 Shock Wave Calculation with the Aid of Characteristics 55 Moving Shock-Stationary Shock Transformation 56 Projectile Motion Calculation with the Aid of Characteristics 57 Finite Difference Grid Based on MacCormack Scheme 58 Sample Mesh for External Flow Computation 59 Projectile Time Versus Projectile Travel 60 Projectile Base Pressure Versus Projectile Travel 61 Projectile Base Density Versus Projectile Travel 62 Projectile Acceleration Versus Projectile Travel 63 Projectile Velocity Versus Projectile Travel 64 vi Page 19. Nose Pressure of the Projectile Versus Projectile Travel 65 20. Pressure Contours. Cycle 211 66 21. Pressure Contours. Cycle 214 67 22. Flow Field of Cycle 214 68 23. Pressure Contours. Cycle 216 69 24. Flow Field of Cycle 216 70 25. Pressure Contours. Cycle 217 71 26. Flow Field of Cycle 217 72 27. Pressure Contours. Cycle 218 73 28. Flow Field of Cycle 218 74 29. Axial Distribution of Pressure. Cycle 218, Row 7 75 30. Axial Distribution of Pressure. Cycle 218, Row 10 76 31. Pressure Contours. Cycle 219 77 32. Projectile Time Versus Projectile Travel and Shock Time Versus Shock Travel 78 33. Shock Pressure Versus Shock Travel 79 34. Shock Velocity Versus Shock Travel 80 35. Projectile Base Pressure Versus Projectile Travel 81 36. Projectile Base Density Versus Projectile Travel 82 37. Projectile Acceleration Versus Projectile Travel 83 38. Projectile Velocity Versus Projectile Travel 84 39. Nose Pressure of the Projectile Versus Projectile Travel 85 40. Pressure Contours. Cycle 60 86 41. Flow Field of Cycle 60 87 v ii Page 42. Axial Distribution of Pressure. Cycle 60, Row 10 88 43. Pressure Contours. Cycle 64 89 44. Pressure Contours. Cycle 71 90 45. Flow Field of Cycle 71 91 46. Pressure Contours. Cycle 72 92 47. Flow of Cycle 72. 93 v i i i LIST OF SYMBOLS A area (m2) a speed of sound (m/s) C a constant c speed of wave propagation (m/s) D inner diameter (m) h enthalpy (J/kg) K a constant k coefficient of heat conductivity (W/m- M Mach number m mass (kg) P pressure (Pa) Q total of viscous terms (m/s2) R gas constant (N-m/i r radial axis S slope T temperature <°K) t time (s) u axial component of particle velocity (m/s) V partical velocity (m/s) V radial component of particle velocity (m/s) X axial displacement (m) y radial displacement (m) z axial displacement (m) ix f ratio of specific heats 0 angle (deg) 2 \ second coefficient of viscosity (N-s/m ) F first coefficient of viscosity (N-s/m ) Superscripts, subscripts b back f front in inner 1 any integer number L axiaJ subscript M radial subscript N time subscript 0 pathline ou outer r reference s shock Other D_ DT substantial derivative (1/s) DT change in time (s) DX change in axial direction (m) DY change in radial direction (m) P predictor value of property p 1 t absolute value ^ change V gradient diver gence UPR03 ; velocity of projectile (m/s) UMUZ : velocity of flow at the muzzle plane (m/s) Pshock : pressure at shock front (Pa) Pprecursor : pressure at precursor shock front (Pa) XBRRL : length of barrel (m) AO : initial acceleration (m/s2) PBAS : initial base pressure of projectile (Pa) RBAS : initial base density of projectile (kg/m3) PAMB : ambient pressure (Pa) WMUZ : velocity of shock at the muzzle plane (m/s) xi ABSTRACT A computational combined solution to the internal and external flows in gun barrels is devised.
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