## Reacting Flows: Combustion and Chemical Reactors, Part 1: Combustion and Chemical ReactorsThese two volumes represent the culmination of the Special Year `84-'85 in Reacting Flows held at Cornell University. As the proceedings of the 1985 AMS/SIAM Summer Seminar in Applied Mathematics, the volumes focus on both mathematical and computational questions in combustion and chemical reactors. They are addressed to researchers and graduate students in the theory of reacting flows. Together they provide a sound basis and many incentives for future research, especially in computational aspects of reacting flows. Although the theory of reacting flows has developed rapidly, researchers in the two subareas of combustion and chemical reactors have not communicated. The main goal of this seminar was to synthesize the mathematical theory and bring it to the interface with large-scale computing. All of the papers have high research value, but the first five introductory lectures should be especially noted. |

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### Contents

Preface | 8 |

Low Mach Number Combustion | 8 |

The Mathematical Background of Chemical Reactor | 75 |

Dynamic Behavior of Continuous StirredTank Reactors with | 104 |

High Mach Number Combustion | 109 |

Global Bifurcations in Simple Models of a Chemical Reactor | 163 |

Methods of Singularity Theory in the Analysis of Dynamics | 175 |

Numerical Calculation of the Interaction of Pressure Waves | 185 |

Mathematical Analysis of Tubular Reactors | 317 |

The WellStirred | 331 |

A Systematic Derivation of the Constitutive Properties | 357 |

Nonlinear Stability of Solid Propellant Combustion | 375 |

Two Asymptotic Models for Solid Propellant Combustion | 395 |

Plane Shock Initiation of Homogeneous and Heterogeneous | 403 |

Adaptive Numerical Methods for Unsteady Flame Propogation | 415 |

The Structure and Stability of Plane Detonation Waves | 419 |

Computational Methods in Turbulent Reacting Flow | 199 |

Mathematical Questions | 215 |

Premixed Laminar Flames as Travelling Waves | 229 |

Mathematical Study of a Model with No Ignition | 239 |

WellPosedness of the Nonlinear Equations for Zero Mach | 264 |

Flame Resonance and Acoustics in the Presence of Heat Loss | 269 |

Flame Structure for Reaction Networks with Chain | 273 |

The Asymptotic Analysis of Ignition Events with Detailed | 303 |

Mach Stems | 431 |

Using Computers to Answer Fundamental Questions | 437 |

Fractional Step Methods for Reacting Shock Waves | 459 |

Roles of Perturbation Methods for Turbulent Diffusion Flame | 467 |

Modeling and Computation of DeflagrationtoDetonation | 479 |

Singular Perturbation for Stiff Equations Using Numerical | 485 |

The Lifting of Turbulent Diffusion Flames and the Noise | 489 |

### Other editions - View all

Reacting flows: combustion and chemical reactors ; [proceedings of ..., Volume 2 G. S. S. Ludford No preview available - 1986 |

Reacting Flows: Combustion and Chemical Reactors : [proceedings of ..., Part 1 No preview available - 1986 |

### Common terms and phrases

acoustic activation energy adiabatic analysis approximation asymptotic boundary conditions burning Chapman-Jouget chemical coefficients combustion compressible computational constant coordinate curve deflagration density derived detonation wave diffusion flames dynamics effect equations Euler equations explosion limit Figure finite flame front flame propagation flame sheet flow fluid function Ghoniem heat loss heat release hydrodynamic ignition induction zone initial instability interaction interface inviscid jump conditions kinetics Lewis number linear stability Mach number Mach stem Majda mathematical methods mixture Navier-Stokes equations neutral stability non-dimensional nondimensional nonlinear obtained parameter perturbation Phys planar plane premixed premixed flames pressure problem qualitative reactants reacting shock reaction rate regime region Reynolds number second explosion limit Sethian shock front shock wave Sivashinsky solution species speed steady structure temperature theory thermal expansion tion transverse transverse wave turbulent unburned variables velocity viscosity vortex vorticity weak detonation