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Proceedings ArticleDOI

DNS of High-Enthalpy Effects on Turbulent Flows

About: The article was published on 2019-01-07. It has received None citations till now.
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Book
01 Jan 1990
TL;DR: In this paper, the authors describe the derivation of conservation laws and apply them to linear systems, including the linear advection equation, the Euler equation, and the Riemann problem.
Abstract: I Mathematical Theory- 1 Introduction- 11 Conservation laws- 12 Applications- 13 Mathematical difficulties- 14 Numerical difficulties- 15 Some references- 2 The Derivation of Conservation Laws- 21 Integral and differential forms- 22 Scalar equations- 23 Diffusion- 3 Scalar Conservation Laws- 31 The linear advection equation- 311 Domain of dependence- 312 Nonsmooth data- 32 Burgers' equation- 33 Shock formation- 34 Weak solutions- 35 The Riemann Problem- 36 Shock speed- 37 Manipulating conservation laws- 38 Entropy conditions- 381 Entropy functions- 4 Some Scalar Examples- 41 Traffic flow- 411 Characteristics and "sound speed"- 42 Two phase flow- 5 Some Nonlinear Systems- 51 The Euler equations- 511 Ideal gas- 512 Entropy- 52 Isentropic flow- 53 Isothermal flow- 54 The shallow water equations- 6 Linear Hyperbolic Systems 58- 61 Characteristic variables- 62 Simple waves- 63 The wave equation- 64 Linearization of nonlinear systems- 641 Sound waves- 65 The Riemann Problem- 651 The phase plane- 7 Shocks and the Hugoniot Locus- 71 The Hugoniot locus- 72 Solution of the Riemann problem- 721 Riemann problems with no solution- 73 Genuine nonlinearity- 74 The Lax entropy condition- 75 Linear degeneracy- 76 The Riemann problem- 8 Rarefaction Waves and Integral Curves- 81 Integral curves- 82 Rarefaction waves- 83 General solution of the Riemann problem- 84 Shock collisions- 9 The Riemann problem for the Euler equations- 91 Contact discontinuities- 92 Solution to the Riemann problem- II Numerical Methods- 10 Numerical Methods for Linear Equations- 101 The global error and convergence- 102 Norms- 103 Local truncation error- 104 Stability- 105 The Lax Equivalence Theorem- 106 The CFL condition- 107 Upwind methods- 11 Computing Discontinuous Solutions- 111 Modified equations- 1111 First order methods and diffusion- 1112 Second order methods and dispersion- 112 Accuracy- 12 Conservative Methods for Nonlinear Problems- 121 Conservative methods- 122 Consistency- 123 Discrete conservation- 124 The Lax-Wendroff Theorem- 125 The entropy condition- 13 Godunov's Method- 131 The Courant-Isaacson-Rees method- 132 Godunov's method- 133 Linear systems- 134 The entropy condition- 135 Scalar conservation laws- 14 Approximate Riemann Solvers- 141 General theory- 1411 The entropy condition- 1412 Modified conservation laws- 142 Roe's approximate Riemann solver- 1421 The numerical flux function for Roe's solver- 1422 A sonic entropy fix- 1423 The scalar case- 1424 A Roe matrix for isothermal flow- 15 Nonlinear Stability- 151 Convergence notions- 152 Compactness- 153 Total variation stability- 154 Total variation diminishing methods- 155 Monotonicity preserving methods- 156 l1-contracting numerical methods- 157 Monotone methods- 16 High Resolution Methods- 161 Artificial Viscosity- 162 Flux-limiter methods- 1621 Linear systems- 163 Slope-limiter methods- 1631 Linear Systems- 1632 Nonlinear scalar equations- 1633 Nonlinear Systems- 17 Semi-discrete Methods- 171 Evolution equations for the cell averages- 172 Spatial accuracy- 173 Reconstruction by primitive functions- 174 ENO schemes- 18 Multidimensional Problems- 181 Semi-discrete methods- 182 Splitting methods- 183 TVD Methods- 184 Multidimensional approaches

3,827 citations

Journal ArticleDOI
TL;DR: In this paper, the previous equation of Buddenberg and the author has been modified to give a general equation for viscosity as a function of molecular weights and viscosities of the pure components of the mixture.
Abstract: By application of the kinetic theory, with several simplifying assumptions, the previous equation of Buddenberg and the author has been modified to give a general equation for viscosity as a function of molecular weights and viscosities of the pure components of the mixture. Agreement of the equation with experimental data is demonstrated for a number of highly irregular binary gas systems and mixtures of three to seven components.

2,183 citations

Journal ArticleDOI
TL;DR: In this article, a large number of data points for the vibrational relaxation time (pτv in atm sec) of simple systems have been logarithmically plotted vs (T°K)-⅓.
Abstract: A large number of data points for the vibrational relaxation time (pτv in atm sec) of simple systems have been logarithmically plotted vs (T°K)—⅓. It appears that each system is well represented by a straight line, and that most of these straight lines when extended to higher temperatures intersect near the point [pτv=10—8 atm sec, (T°K)—⅓=0.03]. Systems with a small reduced mass μ are exceptions to such a simple convergence, and in an improved scheme, the location of the convergence point is dependent on the reduced mass. Such a presentation has lead to an empirical equation correlating available measurements of vibrational relaxation times: log10(pτv)=(5.0×10−4)μ12θ43[T−13−0.015μ14]−8.00, where θ is the characteristic temperature of the oscillator in K deg. This equation reproduces the measured times within 50% for systems as diverse as N2, I2, and O2–H2. In the worst case thus far, O2–Ar near 1000°K, it is off by a factor of 5.

1,678 citations

Book
Chul Park1
01 Jan 1989
TL;DR: In this paper, nonequilibrium phenomena in hypersonic flows are examined on the basis of theoretical models and selected experimental data, in an introduction intended for second-year graduate students of aerospace engineering.
Abstract: Nonequilibrium phenomena in hypersonic flows are examined on the basis of theoretical models and selected experimental data, in an introduction intended for second-year graduate students of aerospace engineering. Chapters are devoted to the physical nature of gas atoms and molecules, transitions of internal states, the formulation of the master equation of aerothermodynamics, the conservation equations, chemical reactions in CFD, the behavior of air flows in nonequilibrium, experimental aspects of nonequilibrium flow, a review of experimental results, and gas-solid interaction. Diagrams, graphs, and tables of numerical data are provided.

1,331 citations

ReportDOI
01 Jan 1971
TL;DR: A general computer program was developed for solving the laminar boundary layer equations with a finite-difference method as discussed by the authors, in which the governing equations are solved in an uncoupled manner in order that a gas mixture with a large number of chemical species can be readily handled.
Abstract: A general computer program was developed for solving the laminar boundary layer equations with a finite-difference method. The governing equations are solved in an uncoupled manner in order that a gas mixture with a large number of chemical species can be readily handled. The program has been written with various options to provide a flexibility that allows a variety of problems to be solved with only a change in the input data.

485 citations