Computer Simulation of Shaped Charge Problems

By: LEE WEN HO

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Hardcover | 1 December 2005

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394 Pages

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22.86 x 15.24 x 2.24

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Devoted to the subject of shape charge design using numerical methods, this book offers the defense and commercial industries unique material not contained in any other single volume. The coverage of the Lagrangian and Eulerian methods as well as the equation of state provides first hand help to engineers working on shape charge problems.The book includes detailed descriptions of oil-well perforation not available from any other sources and, coupled with the material flow physics discussed in Chapters 2 and 3 and Appendix B, readers can design the fuel rod configurations for a nuclear reactor core. The equations of state and the constitutive models in Chapter 8 are among the best material models currently available.

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Preface	p. xv
Introduction	p. 1
Lagrangian Method	p. 5
Introduction	p. 6
Definition of Variable and Notation	p. 7
The Governing Equation	p. 13
Equation of State	p. 15
Calculation Procedures and Finite Differences	p. 15
Sliding Interface Treatments	p. 24
References	p. 30
Eulerian Method	p. 31
Introduction	p. 32
General Description of Physical Formulation	p. 33
The Conservation Equation for a Stress-Supporting Medium	p. 33
Equation of State	p. 34
Stress in Elastic Regime	p. 34
Stresses in Plastic Regime	p. 35
Hydrostatic Pressure	p. 36
Yield Criterion	p. 36
Stress Correction for Rigid Body Rotation	p. 37
Spall	p. 38
Melting	p. 38
Spall	p. 39
Fracture	p. 39
Computational Scheme	p. 39
General Discussion	p. 39
Summary of Calculation Procedure	p. 40
Phase I: Lagrangian Phase	p. 40
Phase II: Particle Transport and Remapping	p. 41
Lagrangian Phase	p. 41
Equations to be Solved in the Radial Direction	p. 41
Lagrangian Phase Calculation	p. 43
Summary of Equations in the Axial Direction	p. 49
Stress Calculation in the Plastic Regime of Flow	p. 51
Radial Direction	p. 51
Axial Direction	p. 54
Particle Transport and Remapping	p. 55
Average Velocity for the Particle	p. 55
Particle Treatment for Void or Multi-material Cell	p. 55
Computation for Spall	p. 58
When Spalled	p. 58
Recombination	p. 59
Propagation of Fracture Surface	p. 59
Time Step Control	p. 59
Truncation Error Analysis	p. 61
Mass	p. 61
Radial Momentum	p. 63
Axial Momentum	p. 66
Internal Energy	p. 68
Deviatoric Stresses	p. 69
Equivalent Plastic Strain	p. 70
FCT Applied to Second-Order PIC	p. 72
Introduction	p. 72
Modified Mass Transport	p. 72
The Modified FCT Analysis	p. 76
References	p. 78
Artificial Viscosity and Shock Calculations	p. 81
Introduction	p. 82
Basic Governing Equations	p. 83
Artificial Viscosity in One-Dimensional Code	p. 84
Artificial Viscosity in Two-Dimensional Code	p. 86
With and Without Artificial Viscosity Methods	p. 87
Sample Problem Calculations	p. 89
Conclusions and Discussions	p. 94
References	p. 97
Numerical Simulations of Oblique Shock-Wave Reflection	p. 99
Introduction	p. 100
Eulerian Method	p. 101
Lagrangian Method	p. 103
Numerical Calculations and Results	p. 105
Regular Reflection	p. 107
Mach Reflection	p. 112
Conclusions	p. 114
References	p. 115
Comparisons Between the Cell-Centered and Staggered Mesh Lagrangian Hydrodynamics	p. 117
Introduction	p. 118
A TVD Lagrangian Scheme	p. 120
The DIVU Limiter	p. 123
Vertex Velocity Definition	p. 123
Staggered Mesh	p. 125
The Mesa and Unicorn Method	p. 126
Sample Results	p. 128
Conclusions	p. 132
References	p. 135
Multiphase Flow Treatment	p. 137
Introduction	p. 138
Two-phase Flow Model Equations	p. 140
Basic Equation Set	p. 140
Soo's Momentum Equations	p. 142
Extended 'Rudinger-Chang' Momentum Equations	p. 143
Hancox et al. Momentum Equations	p. 144
Gidaspow's Momentum Equations	p. 145
Characterictics for the Five Two-phase Flow Equation Sets	p. 146
The Drag Function and Phase Change Rates	p. 148
Numerical Solution Procedure	p. 150
A More Stable Numerical Scheme	p. 152
Description of Test Problems	p. 153
Batch Settling of a Two-phase Mixture	p. 154
One-dimensional Fluidized Bed	p. 154
Simulation of Two-phase Jet Impinged on Vertical Plate	p. 155
Results of Computations and Discussion	p. 155
Conclusions	p. 161
References	p. 162
Equation of State, Constitutive Relationship and High Explosive	p. 165
Introduction to the Equation of State	p. 165
The Mie-Gruneisen EOS and the Simple u[subscript s], u[subscript p] Model	p. 165
The Osborne Model	p. 167
The Tillotson Equation of State	p. 167
Introduction to the Constitutive Relationship	p. 168
Quadratic Model	p. 168
Steinberg-Guinan Model	p. 169
Steinberg's New Model	p. 171
High Explosive	p. 174
Introduction	p. 174
JWL Equation of State	p. 175
Small Variation of JWL-EOS	p. 177
References	p. 177
Shaped Charge Problems	p. 179
Introduction	p. 179
Shaped Charge Calculations by Lagrangian Method without Slip	p. 179
Calculation of Shaped Charge Problem with Slip by Lagrangian Method	p. 180
Shaped Charge Calculations using Eulerian Method	p. 185
Viper Shaped Charge	p. 185
Tantalum Hemi-spherical Shaped Charge	p. 187
Bi-conical Copper Shaped Charge	p. 190
Oil Well Perforator P-C	p. 194
Copper Hemi-spherical Liner with PBX-W-113 (Energetic Explosive)	p. 194
Calculations of the Hemi-spherical Copper Shaped Charge	p. 194
Bi-conical Copper Shaped Charge with PBX-9404	p. 204
Calculations of the BRL Precision Copper Shaped Charge	p. 206
Shaped Charges of Tungsten-copper Alloy	p. 208
References	p. 215
Explosive Formed Projectile	p. 217
Introduction	p. 217
Calculation of Explosive Formed Projectile with Combination of Lagrangian and Eulerian Codes	p. 217
Copper EFP with Foam	p. 218
Copper EFP without Foam	p. 226
Non-axisymmetric Tantalum EFP Warhead	p. 226
The Penetration of Shaped Charge Jet	p. 233
Introduction	p. 233
Calculations of Tungsten Rod Penetrating Aluminum Target	p. 233
Calculations of Copper Rod Penetrating Steel Plate	p. 235
Tantalum Shaped Charge Penetrates into Steel Block	p. 238
Tantalum Shaped Charge Penetrates into Steel Plate, Water, and Another Steel Plate	p. 239
Copper-lead Shaped Charge Penetrates into Steel Block	p. 240
Bi-conical Copper-lead Powder Shaped Charge Penetrates into Steel Block	p. 246
Bi-conical Copper Shaped Charge Penetrates into Thin Steel Plate, Water, Thick Steel Plate and Rock	p. 246
Viper Shaped Charge Penetrates into Steel Block	p. 246
Computational Assessment of LEAP Performance with Different Lethality Enhancements	p. 252
Lethality Assessments for Ascent-phase Interceptor Impacts on a Generic Chemical Submunition Target	p. 256
References	p. 267
Oil Well Perforator Design Using 2D Eulerian Code	p. 269
Introduction	p. 270
Description of the 2D Eulerian Code	p. 274
Equation of State and Constitutive Relation	p. 277
Shaped Charge Jet Characteristics	p. 278
Jet Formation and Penetration as Compared with Experimental Data	p. 280
Perforators of 4.4 cm Charge Diameter	p. 283
Perforators of 3.6 cm Charge Diameter	p. 289
Discussions	p. 294
Conclusions	p. 298
References	p. 299
One Dimensional Radiation Hydrodynamics	p. 301
Introduction	p. 302
Mathematical Theory of Radiation Hydrodynamics	p. 303
Introduction	p. 303
Radiation Transport Equation	p. 305
Non-equilibrium Diffusion Equation with Compton Scattering	p. 307
Non-equilibrium Diffusion Equations in an Inertial Frame	p. 311
Conservation Laws	p. 314
Numerical Analysis	p. 316
Difference Equations	p. 316
Boundary Conditions	p. 324
Opacity Averaging Procedure	p. 326
Variable Eddington Factor	p. 330
Scattering Terms	p. 338
Difference Equation for the Conservation of Momentum and Energy	p. 345
Formulae for the First Moment of the Radiative Transfer Equation in ID Geometry	p. 347
Properties of an Implicit Difference Approximation to the Wave Equation	p. 353
References	p. 356
Thermonuclear Burn of Deuterium-Tritium Sphere	p. 357
Introduction	p. 358
The Governing Equations	p. 359
The Thermonuclear Reaction Rate	p. 362
Calculation Procedure	p. 364
Radiation Transport Calculation	p. 366
Some Important Fission Reactions	p. 369
References	p. 370
Hugoniot Data	p. 371
Author Index	p. 375
Subject Index	p. 377
Table of Contents provided by Ingram. All Rights Reserved.

Computer Simulation of Shaped Charge Problems

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