Computational Electromagnetic-Aerodynamics E-Book

Joseph J. S. Shang

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: IEEE Press Series on RF and Microwave Technology
• Sprache: Englisch

Seitenzahl: 709

Veröffentlichungsjahr: 2016

Beschreibung

Presents numerical algorithms, procedures, and techniques required to solve engineering problems relating to the interactions between electromagnetic fields and fluid flow and interdisciplinary technology for aerodynamics, electromagnetics, chemical-physic kinetics, and plasmadynamics * Integrates interlinking computational model and simulation techniques of aerodynamics and electromagnetics * Combines classic plasma drift-diffusion theory and electron impact ionization modeling for electromagnetic-aerodynamic interactions * Describes models of internal degrees of freedom for vibration relaxation and electron excitations

Leseprobe

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Ziaoou Li

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Pui-In Mak

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MengChu Zhou

Kenneth Moore, Director of IEEE Book and Information Services (BIS)

Technical Reviewer

Frank Lu, University of Texas at Arlington

COMPUTATIONAL ELECTROMAGNETIC AERODYNAMICS

JOSEPH J.S. SHANG

Emeritus Research Professor of Wright State University Emeritus Scientist of US Air Force Research Laboratory

Copyright © 2016 by The Institute of Electrical and Electronics Engineers, Inc.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. All rights reserved Published simultaneously in Canada

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ISBN: 978-1-110-15592-8

CONTENTS

Preface

Chapter 1 Plasma Fundamentals

Introduction

1.1 Electromagnetic Field

1.2 Debye Length

1.3 Plasma Frequency

1.4 Poisson Equation of Plasmadynamics

1.5 Electric Conductivity

1.6 Generalized Ohm'S Law

1.7 Maxwell's Equations

1.8 Waves in Plasma

1.9 Electromagnetic Waves Propagation

1.10 Joule Heating

1.11 Transport Properties

1.12 Ambipolar Diffusion

References

Chapter 2 Ionization Processes

Introduction

2.1 Microscopic Description of Gas

2.2 Macroscopic Description of Gas

2.3 Chemical Reactions and Equilibrium

2.4 Saha Equation of Ionization

2.5 Ionization Mechanisms

2.6 Photoionization

2.7 Thermal Ionization

2.8 Electron Impact Ionization

References

Chapter 3 Magnetohydrodynamics Formulation

Introduction

3.1 Basic Assumptions of MHD

3.2 Ideal MHD Equations

3.3 Eigenvalues of Ideal MHD Equation

3.4 Full MHD Equations

3.5 Shock Jump Condition in Plasma

3.6 Solutions of MHD Equations

References

Chapter 4 Computational Electromagnetics

Introduction

4.1 Time-Dependent Maxwell Equations

4.2 Characteristic-Based Formulation

4.3 Governing Equations on Curvilinear Coordinates

4.4 Far Field Boundary Conditions

4.5 Finite-Difference Approximation

4.6 Finite-Volume Approximation

4.7 High-Resolution Algorithms

References

Chapter 5 Electromagnetic Wave Propagation and Scattering

Introduction

5.1 Plane Electromagnetic Waves

5.2 Motion in Waveguide

5.3 Wave Passes through Plasma Sheet

5.4 Pyramidal Horn Antenna

5.5 Wave Reflection and Scattering

5.6 Radar Signature Reduction

5.7 A Prospective of CEM in the Time Domain

References

Chapter 6 Computational Fluid Dynamics

Introduction

6.1 Governing Equations

6.2 Viscous–Inviscid Interactions

6.3 Self-Sustained Oscillations

6.4 Vortical Dynamics

6.5 Laminar–Turbulent Transition

References

Chapter 7 Computational Electromagnetic-Aerodynamics

Introduction

7.1 Multifluid Plasma Model

7.2 Governing Equations of CEA

7.3 Chemical Kinetics for Thermal Ionization

7.4 Chemical Kinetics for Electron Impact Ionization

7.5 Transport Properties

7.6 Numerical Algorithms

References

Chapter 8 Modeling Electron Impact Ionization

Introduction

8.1 Transport Property via Drift-Diffusion Theory

8.2 Drift-Diffusion Theory in Transverse Magnetic Field

8.3 Boundary Conditions on Electrodes

8.4 Quantum Chemical Kinetics

8.5 Numerical Algorithms

8.6 Innovative Numerical Procedures

References

Chapter 9 Joule-Heating Actuators

Introduction

9.1 Features of Direct Current Discharge

9.2 Virtual Leading Edge Strake

9.3 Magnetic Field Amplification

9.4 Virtual Variable Geometry Cowl

9.5 Trailing Edge of Airfoil

9.6 Hydrodynamic Stability and Self-Oscillation

References

Chapter 10 Lorentz-Force Actuator

Introduction

10.1 Remote Energy Deposition

10.2 Stagnation Point Heat Transfer Mitigation

10.3 Features of Dielectric Barrier Discharge

10.4 Periodic Electrostatic Force

10.5 DBD Flow Control Actuator

10.6 Laminar–Turbulent Transition

10.7 Ion Thrusters for Space Exploration

10.8 Plasma Micro Jet

References

Index

RF and Microwave Technology

EULA

List of Tables

Chapter 2

Table 2.1

Table 2.2

Table 2.3

Chapter 3

Table 3.1

Chapter 7

Table 7.1

Table 7.2

Table 7.3

Guide

Cover

Table of Contents

Preface

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PREFACE

Tremendous amounts of research results have been accumulated to the information pool for plasmadynamics and plasma, which is the most common state of matter in the universe by either mass or volume. The underlying physics occurs mostly at the molecular and atomic scales and often under an extremely high enthalpy condition or in a strong electromagnetic field; these phenomena must be analyzed by physics-based modeling. The research progress faces formidable challenges because the compositions of non–equilibrium-ionized gas are always in transient quantum states where the fundamental chemical-physics processes are the least understood. Furthermore, the validating experimental data are also very sparse.

In spite of these limitations, thousands of conference papers and articles on this subject are still persistently releasing to the open literature annually. Meanwhile, the electromagnetics is increasingly recognized to broadening physical dimensions for interdisciplinary science and technology to meet engineering requirements. For the rapidly advancing scientific field, outstanding and fundamental technical references are published mostly in the period from the middle 1960s to later 1980s. Although all these illuminating accomplishments have withheld the test of time but have not been updated by converting information into knowledge for practical engineering applications. It is appropriate and timely that summarization of these impressive scientific accomplishments and a systematic review on the progress of this scientific discipline are needed for future development.

The inherent nature of interdisciplinary computational electromagnetic-aerodynamics links five major scientific disciplines from aerodynamics, electromagnetics, chemical-physics kinetics, plasmadynamics, to computational modeling and simulations. The knowledge of each individual discipline has been developed over centuries and numerous treatises on these subject areas have been published and firmly established for understanding. There are also some path-finding articles in classic magnetohydrodynamics that detail the magnetic field–dominated astrophysics around 50 years ago, but none have been documented for computational electromagnetic-aerodynamics to reach a comprehensive status in providing a practical working knowledge. For this reason, an attempt is made here to integrate these pertaining disciplines to supply a working knowledge for engineering and to suggest the best practice in applications. Hopefully this effort can be a viable reference for professional development and graduate studies.

The text is organized in 10 chapters, with the first three chapters consisting of introductions to fundamental knowledge of plasmadynamics, chemical-physics of ionization, formulations of classical magnetohydrodynamics, and their extension to low magnetic Reynolds number electromagnetic-aerodynamics conditions. In fact, most plasma-based flow control actuators, high-speed flows of interplanetary reentry, and ion thrusters in space exploration are operating under this environment.

For fundamental knowledge, a brief review of unique features of the plasma medium is presented in terms of the Debye shielding length, Coulomb and Lorentz forces, Joule heating, plasma frequency, and plasma waves. All these unique characteristics of ionized gas in an electromagnetic field are intermediately related to outstanding engineering applications of computational electromagnetic aerodynamics. Then the statistical thermodynamics that bridges the microscopic to macroscopic thermodynamics is introduced for the ionization processes. The mechanisms of photoionization, thermal excitation, and electron impact ionization are discussed on the basis of the most recent research findings.

The hierarchal relationship among fundamental formulations for plasmadynamics and their valid domains of approximation is outlined and reviewed next. The basic assumptions for the classic magnetohydrodynamics formulation are articulated, and detailed derivations from ideal to full magnetohydrodynamics equation, as well as the low magnetic Reynolds number equations system, are delineated. These governing equations, in fact, define the limitations and physical fidelity of all computational simulations. From the eigenvalues and eigenvectors analyses of the magnetohydrodynamics equations, correlations are revealed between propagating speeds of Alfven, entropy, contact surface, slow and fast plasma waves.

A peculiar property of plasma in an electromagnetic field is that it does not exist as an unrealistic one-dimensional phenomenon. Therefore, the shock jump condition must be formulated, at least by tangential and normal components across a discrete wave. The simplest shock in the electromagnetic field is essentially a two-dimensional oblique wave. When the macroscopic conservative equation is integrated across the shock, and it requires that the normal components of the magnetic flux density and the tangential component of the electric field intensity are continuously across any interface. As a consequence, the Rankine–Hugoniot relationship of gas dynamics across a shock is significantly modified in an ionized gas to become a unique feature of the plasma medium.

The next three chapters of the book provide in-depth and specific descriptions of numerical algorithms and procedures for solving Maxwell's equation in the time domain for computational electromagnetics, plasma wave propagation, and fluid dynamics. All these detailed numerical algorithms and computational procedures are the shared knowledge for the interdisciplinary computational modeling and simulation science and technology. The highlights are especially placed on overlapping areas of technical issues and realizable application opportunities.

Two major foci of the present objective are to integrate the interlinking computational modeling and simulation techniques of aerodynamics and electromagnetics. To make the procedure tractable, the computational approach is further restricted to the continuum regime so the approach is built on the frameworks of the time-dependent Maxwell equations and the compressible Navier–Stokes equations. It should be recognized that the Maxwell equations constitute the hyperbolic partial differential system and belong to a class of bondless initial-boundary-value problems. This unique feature poses a fundamental dilemma for all numerical analyses that must be carried out in a finite-size computational domain. However, the characteristic-based formulation can alleviate this constraint by achieving an invariant dependent variables grouping in the domain of dependence. This formulation permits all propagating electromagnetic waves exit through numerical boundary unimpeded. The computational electromagnetics technique is applying to the microwave propagation in waveguide, plasma wave diffraction and refraction, as well as the plasma diagnostic technique by microwave attenuation beyond Langmuir probes.

The last four chapters are focused on the modeling and simulation techniques for computational electromagnetic-aerodynamics. The most current progress in computational electromagnetic-aerodynamics is summarized for multifluid models, including chemical kinetics by nonequilibrium thermal excitations, chemical physics by electron impact ionization, transport property by gas kinetics, and numerical algorithms. The emphases are on the physical fidelity of computational models that describe the behavior of the direct current charge, dielectric barrier charges, microdischarge, and their interactions with aerodynamics through the mechanisms of Joule heating and Lorentz forces. Transport property by drift motions and diffusions of the charged particle is also described by the classical drift-diffusion theory. The interface boundary conditions between the chemically reacting media and solid surface are derived together with the requirements on electrodes in an externally applied electric field. The latter are described in detail in conjunction with the discharging electric circuit equation. On this frame of analysis, the secondary emission of electrons from the cathode, together for the self-limiting feature of dielectric barrier discharge by preventing transit to arc, is unambiguously illustrated. For the thermal ionizing model, the models of internal degrees of freedom for vibration relaxation and electron excitations are also described at practicing level. Some of the innovative numerical procedures are also included as bench marks for future progression.

It is important to acknowledge that the electromagnetic effect in most flow control applications appears only as a small perturbation. In general, the relative magnitude of aerodynamic inertia overwhelms the electromagnetic force by a thousand fold. In terms of magnetic Reynolds number for an electromagnetics–aerodynamics field that is measured by the ratio of inertia and the product of electric conductivity and magnetic permittivity , its magnitude is much smaller than unity. The plasma-based actuators are therefore observed to be the mostly effectiveness for flow control at a critical point of a bistable aerodynamic state or to the high-frequency, low-amplitude oscillations. Thus, aerodynamic phenomena are singling out for possibly enhancements by infusing electromagnetic effects. For this purpose, the aerodynamic bifurcations of viscous–inviscid interaction, including flow separation, self-sustained oscillation, vortical dynamics, and hydrodynamic instability leading to turbulent flow, are specifically included. In this approach, the rudimentary numerical algorithms of computational electromagnetics and computational fluid dynamics are introduced and the best practices for computational electromagnetic aerodynamics are also encompassed.

In the last two chapters, the presentations of plasma-based actuators for flow control are divided into two major categories according to the mechanisms, whether via Joule heating or by Lorentz force. For the former, the experimentally validated applications in virtual leading-edge strake and a virtual variable inlet cowl are described. Meanwhile, viable amplifications to electromagnetic–aerodynamic interaction by viscous–inviscid interaction and externally applied magnetic field are demonstrated. The actuator by Lorentz force for stagnation point heat transfer mitigation, remote energy deposition, and flow control via dielectric barrier discharge for lifting surface enhancement are elaborated. A quantification for the flow control effectiveness by dielectric barrier charge is given, and the potential application to hydrodynamic stability is revisited. The successful applications of ion engine or ion thruster by electrostatic force and plasma micro jet for enhancing combustion stability are also included to illustrate the possible future explorations.

Here, I would like to express my personal gratitude for lifelong association in the vast arena of science with Professors Robert W. MacCormack of Stanford University, David I. Gottlieb (deceased) of Brown University, and Joseph L. Steger (deceased) of University of California at Davis. I am equally indebted to the interactions and collaborations with Professor Sergey T. Surzhikov of Russian Academy of Sciences and my colleagues; Drs. Wilbur L. Hankey, Miguel R. Visbal, and Datta V. Gaitonde of the Center of Excellence for Computational Simulation, United States Air Force Research Laboratory, as well as Professor George P. Huang of Wright State University and Professor Hong Yan of North Western Polytechnic University of China.

I have gratefully received editorial supports from Professor Frank K. Lu of University of Texas at Arlington and James A. Menart of Wright State University. Their generous act of friendship and meticulous efforts are truly a humbling experience to me. At last, but by no mean the least, I earnestly acknowledge the unfailing devotion from my wife Karen. I dedicate this book to her.

JOSEPH J.S. SHANG

CHAPTER 1PLASMA FUNDAMENTALS