Computer Simulation Of Shaped Charge Problems

by Wen Ho Lee

Overview

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.

Product Details

ISBN-13:	9789812566232
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	05/18/2006
Edition description:	New Edition
Pages:	396
Product dimensions:	9.20(w) x 6.20(h) x 1.00(d)

Table of Contents

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