Nonlinear Stability of Weak Detonation Waves¶for a Combustion Model

1999 ◽  
Vol 204 (3) ◽  
pp. 551-586 ◽  
Author(s):  
Tai-Ping Liu ◽  
Shih-Hsien Yu
Keyword(s):  
Nonlinear Stability ◽  
Combustion Model ◽  
Detonation Waves ◽  
Weak Detonation

scholarly journals Stability of Viscous Weak Detonation Waves for Majda’s Model

2015 ◽  
Vol 27 (2) ◽  
pp. 237-260 ◽  
Author(s):  
Jeffrey Hendricks ◽  
Jeffrey Humpherys ◽  
Gregory Lyng ◽  
Kevin Zumbrun
Keyword(s):  
Detonation Waves ◽  
Weak Detonation

scholarly journals Structure of shock wave for a viscous combustion model

Filomat ◽  
2012 ◽  
Vol 26 (2) ◽  
pp. 389-395 ◽  
Author(s):  
Abdolrahman Razania
Keyword(s):  
Shock Wave ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Heteroclinic Orbits ◽  
Combustion Model ◽  
Detonation Waves ◽  
Dimensional System ◽  
3 Dimensional

In this article, the existence of weak and strong detonation waves for a viscous combustion model is proved. In order to prove the existence of this kind of waves, it is necessary to consider a 3-dimensional system of ordinary differential equations and prove the existence of heteroclinic orbits of it. In order to prove this, topological arguments are mainly tools.

The dynamics of spinning detonation waves

1976 ◽  
Vol 348 (1654) ◽  
pp. 299-316 ◽  
Keyword(s):  
Detonation Wave ◽  
Acoustic Waves ◽  
Fluid Motion ◽  
Dynamical Theory ◽  
Detonation Waves ◽  
Spinning Detonation ◽  
Rate Of Reaction ◽  
Rotating Wave ◽  
Chemically Reacting ◽  
Weak Detonation

The fluid motion of chemically reacting gases in a weak detonation wave is examined with a view to finding a dynamical theory of the spin phenomenon. It is shown that a reacting gas in which the rate of reaction increases with temperature is unstable with respect to wave motion. The amplitude of any wave tends to increase exponentially with time until the growth rate is checked by some dissipative process. Two such processes are examined: first, the drag on a rotating wave at the boundary of the tube, and secondly, the development of weak transverse shocks from the large amplitude acoustic waves in the reaction zone. The formulae obtained are compared with observations and are shown to be not inconsistent with the proposed mechanism of the spinning detonation wave.

scholarly journals Nonlinear Stability of Strong Detonation Waves for a Dissipative Model

1999 ◽  
Vol 151 (1) ◽  
pp. 134-160 ◽  
Author(s):  
Lung-an Ying ◽  
Tong Yang ◽  
Changjiang Zhu
Keyword(s):  
Nonlinear Stability ◽  
Detonation Waves ◽  
Dissipative Model

Parametric Studies of an Aluminum Combustion Model for Simulations of Detonation Waves

AIAA Journal ◽  
2006 ◽  
Vol 44 (3) ◽  
pp. 608-619 ◽  
Author(s):  
Krzysztof Benkiewicz ◽  
A. Koichi Hayashi
Keyword(s):  
Combustion Model ◽  
Detonation Waves ◽  
Aluminum Combustion ◽  
Parametric Studies

THE WEAK DETONATION SOLUTIONS TO THE SIMPLEST COMBUSTION MODEL

1993 ◽  
Vol 13 (3) ◽  
pp. 282-292 ◽  
Author(s):  
Dechun Tan ◽  
Tong Zhang
Keyword(s):  
Combustion Model ◽  
Weak Detonation

Nonlinear stability of strong detonation waves in gas dynamical combustion

Nonlinearity ◽  
1997 ◽  
Vol 10 (2) ◽  
pp. 355-376 ◽  
Author(s):  
Dechun Tan ◽  
Alberto Tesei
Keyword(s):  
Nonlinear Stability ◽  
Detonation Waves
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