Computational Physics of Electric Discharges in Gas Flows (eBook)

Sergey T. Surzhikov (Autor)

eBook Download: PDF

2013
439 Seiten
De Gruyter (Verlag)
978-3-11-027041-9 (ISBN)

Infos

Gas discharges are of interest for many processes in mechanics, manufacturing, materials science and aerophysics. To understand the physics behind the phenomena is of key importance for the effective use and development of gas discharge devices.

This worktreats methods of computational modeling of electrodischarge processes and dynamics of partially ionized gases. These methods are necessary to tackleproblems of physical mechanics, physics of gas discharges and aerophysics.Particular attention is given to a solution of two-dimensional problems of physical mechanics of glow discharges.The use ofglow discharges in aerospace technology is discussed as well.

Sergey T. Surzhikov, Institute for Problems in Mechanics,Russian Academy of Sciences, Moscow, Russia.

Autor

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Sergey T. Surzhikov, Institute for Problems in Mechanics,Russian Academy of Sciences, Moscow, Russia.

Inhalt

Preface 5
I Elements of the theory of numerical modeling of gas-discharge phenomena 13
1 Models of gas-discharge physical mechanics 15
1.1 Models of homogeneous chemically equilibrium plasma 17
1.1.1 Mathematical model of radio-frequency (RF) plasma generator 26
1.1.2 Mathematical model of electric-arc (EA) plasma generator 31
1.1.3 Models of micro-wave (MW) plasma generators 34
1.1.4 Models of laser supported plasma generators (LSPG) 37
1.1.5 Numerical simulation models of steady-state radiative gas dynamics of RF-, EA-, MW-, and LSW-plasma generators 45
1.1.6 Method of numerical simulation of non-stationary radiative gas-dynamic processes in subsonic plasma flows. The method of unsteady dynamic variables 59
1.2 Models of nonuniform chemically equilibrium and nonequilibrium plasma 61
1.2.1 Model of the five-component RF plasma generator 66
1.2.2 Model of the three-component RF plasma generator 69
1.2.3 Two-temperature model of RF plasma under ionization equilibrium 71
1.2.4 One-liquid two-temperature model of laser supported plasma 73
2 Application of numerical simulation models for the investigation of laser supported waves 76
2.1 Air laser supported plasma generator 76
2.2 Hydrogen laser supported plasma generator 86
2.3 Bifurcation of subsonic gas flows in the vicinity of localized heat release regions 93
2.3.1 Statement of the problem 95
2.3.2 Qualitative analysis of the phenomenon 96
2.3.3 Quantitative results of numerical simulation 97
2.4 Laser supported waves in the field of gravity 103
3 Computational models of magnetohydrodynamic processes 116
3.1 General relations 117
3.2 Vector form of Navier-Stokes equations 118
3.3 System of equations of magnetic induction 119
3.4 Force acting on ionized gas from electric and magnetic fields 123
3.5 A heat emission caused by action of electromagnetic forces 124
3.6 Complete set of the MHD equations in a flux form 126
3.6.1 The MHD equations in projections 127
3.6.2 Completely conservative form of the MHD equations 129
3.7 The flux form of MHD equations in a dimensionless form 132
3.7.1 Definition of the normalizing parameters 132
3.7.2 Nondimension system of the MHD equations in flux form 134
3.8 The MHD equations in the flux form. The use of pressure instead of specific internal energy 138
3.9 Eigenvectors and eigenvalues of Jacobian matrixes for transformation of the MHD equations from conservative to the quasilinear form. Statement of nonstationary boundary conditions 141
3.9.1 Jacobian matrixes of passage from conservative to the quasilinear form of the equations 141
3.10 A singularity of Jacobian matrixes for transformation of the equations formulated in the conservative form 145
3.11 System of the MHD equations without singular transfer matrixes 152
3.12 Eigenvalues and eigenvectors of nonsingular matrixes of quasilinear system of the MHD equations 156
3.12.1 Matrix Ãx 156
3.12.2 Matrix Ãy 160
3.12.3 Matrix Ãz 163
3.13 A method of splitting for three-dimensional (3D) MHD equations 165
3.14 Application of a splitting method for nonstationary 3D MHD flow field, generated by plasma plume in the ionosphere 173
II Numerical simulation models of glow discharge 181
4 The physical mechanics of direct current glow discharge 183
4.1 Fundamentals of the physics of direct current glow discharge. The Engel-Steenbeck theory of a cathode layer 184
4.2 Drift-diffusion model of glow discharge 190
4.2.1 Governing equations 190
4.2.2 Reduction of governing equations to a form convenient for numerical solution 193
4.2.3 Initial conditions of the boundary value problem for the glow discharge 196
4.2.4 Glow discharge with heat of gas 198
4.2.5 Estimation of typical time scales of the solved problem 199
4.3 Finite-difference methods for the drift-diffusion model 206
4.3.1 Finite-difference scheme for the Poisson equation 206
4.3.2 Finite-difference scheme for the equation of charge motion 209
4.3.3 Conservative properties of the finite-difference scheme for the motion equation 212
4.3.4 The order of accuracy of the finite-difference approximation used. The mesh diffusion 215
4.3.5 The finite-difference grids 219
4.3.6 Iterative methods for solving systems of linear algebraic equations in canonical form 222
4.3.7 An iterative algorithm for the solution of a self-consistent problem 233
4.3.8 Characteristic properties of a solution of a two-dimensional problem about glow discharge in a nonstationary statement 234
4.4 Numerical simulation of the one-dimensional glow discharge 237
4.4.1 Governing equations and boundary conditions 238
4.4.2 The elementary implicit finite-difference scheme 240
4.5 Diffusion of charges along a current line and effective method of grid diffusion elimination in calculations of glow discharges 241
4.5.1 Governing equations for the one-dimensional case 242
4.5.2 Boundary conditions 242
4.5.3 Numerical methods for the one-dimensional calculation case 243
4.5.4 Results of 1D numerical simulation 244
4.5.5 Method of fourth order accuracy for the solution of the drift-diffusion model equations 247
4.6 Two-dimensional structure of glow discharge regarding neutral gas heating 253
4.6.1 Statement of two-dimensional axially symmetric problem 254
4.6.2 Numerical simulation results 256
5 Drift-diffusion model of glow discharge in an external magnetic field 273
5.1 Derivation of the equations for calculation model 273
5.2 Numerical simulation results 278
5.3 Glow discharge in a cross magnetic field in view of heating of neutral gas 291
5.3.1 Problem formulation 292
5.3.2 Constitutive thermophysic and electrophysic parameters 293
5.3.3 The method of numerical integration 294
5.3.4 The finite-difference scheme 295
5.3.5 The method of numerical integration of the heat conductive equation 297
5.3.6 Numerical simulation results for glow discharge in a magnetic field in view of heating of gas 300
5.4 Glow discharge in the cross flow of neutral gas and in the magnetic field 308
5.4.1 Computational model of glow discharge with cross gas flow 308
5.4.2 Simplified hydrodynamic part of the problem under consideration. The Couette flow 317
5.4.3 Glow discharge in neutral gas flow. Numerical simulation results 317
5.5 Computing model of glow discharge in electronegative gas 326
5.5.1 Computational model 327
5.5.2 Numerical simulation results 335
5.6 Numerical modeling of glow discharge between electrodes arranged on the same surface 343
5.6.1 The equations of the drift-diffusion model for surface glow discharge 343
5.6.2 Boundary conditions for surface discharge 346
5.6.3 Initial conditions of numerical modeling 347
5.6.4 Numerical simulation results of surface glow discharge 347
III Ambipolar models of direct current discharges 355
6 Quasi-neutral model of gas discharge in an external magnetic field and in gas flow 357
6.1 The spatial scale of electric field shielding in plasma. The Debye radius 357
6.2 The ambipolar diffusion 359
6.3 Ambipolar diffusion in an external magnetic field 362
6.4 Two-dimensional model of ambipolar diffusion in an external magnetic field 364
6.5 Illustrative results of numerical simulation 366
7 Viscous interaction on a flat plate with surface discharge in a magnetic field 372
7.1 Statement of a problem about viscous interaction 374
7.2 Boundary conditions of the problem 377
7.3 Transfer and electro-physical properties of gas 378
7.4 The numerical method of solution 379
7.5 Numerical simulation results 379
7.5.1 The heat-insulated plate 381
7.5.2 Heating electrodes 382
7.5.3 The surface discharge 382
8 Hypersonic flow of rarefied gas in a channel with glow discharge in an external magnetic field 390
8.1 Model of gas dynamics 391
8.2 Model of electrodynamics of glow discharge in a magnetic field 392
8.3 Boundary conditions of the problem 393
8.4 Closing relations 394
8.5 Algorithm of solution of complete set of equations 396
8.6 Numerical simulation results 396
9 Hypersonic flow of rarefied gas in a curvilinear channel with glow discharge 410
9.1 Governing equations 411
9.2 Boundary conditions and closing relations 412
9.3 Numerical simulation results 413
A Appendix 423
A.1 Fundamental constants 423
A.2 Ratios between units of electricity and magnetism 424
Bibliography 427
Index 435

Rezensionen

lt;P>"This is a comprehensive book on mathematical modeling and numerical procedures of physical processes in gas discharge configurations that will prove useful for both professionals and graduate level students in the field." Zentralblatt für Mathematik

Produkt-Details

• Erscheint lt. Verlag: 19.12.2013
• Reihe/Serie: De Gruyter Studies in Mathematical Physics
• Reihe/Serie: De Gruyter Studies in Mathematical Physics
• Reihe/Serie: ISSN
• Reihe/Serie: ISSN
• Zusatzinfo: 161 b/w ill., 8 b/w tbl.
• Verlagsort: Berlin/Boston
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Gas Discharge • Gas Dynamics • heat transfer • Physical Mechanics
• ISBN-10: 3-11-027041-2 / 3110270412
• ISBN-13: 978-3-11-027041-9 / 9783110270419