A Stability Study Of ZND Detonation For Majda’s Model

Detonation is an explosion phenomenon that reacts quickly and releases a large amount of energy in a short period of time.Its various properties have been a hot topic of research.Previous detonation performance studies have been conducted using the Euler system.The Euler system contains a large amount of physical details,which causes the equations to be highly nonlinear.Therefore,mathematical calculations are very difficult.The analog system of detonation simplifies the Euler system and obtains the control equations that includes a partial differential equation and a reaction equation.The analog system not only evolves the mathematical calculation,but also captures a large number of detonation phenomena.This paper introduces the source and forms of the analog system of detonation.To study the stability of detonation,this paper constructs the Majda analog system in the form of ZND detonation,and uses the rate equation of the Arrhenius reaction type as the reaction equation to study the stability.Establishing condensate phase detonation analog system considering loss study critical characteristics.The main research content are as follows:1.The Majda analog system in the form of ZND detonation is constructed,in which the chemical reaction equation was a one-step Arrhenius reaction and ignition equation is more general.This model is used for detonation stability analysis.2.In the limit case,simulated activation energy parameter θ≠0,a relatively simple analog system was obtained and studied.Using the direct calculation method,the traveling wave solutions of the analog system and the steady-state detonation structure are obtained.The steady state detonation wave is added with perturbation to study the stability of detonation.Through the stability analysis of the normal mode,the determinant of the stability of the limiting perturbation propagation(Evans-Lopatinski determinant DZND(λ))and the determination principle of the stability are obtained.The detonation under the limit conditions is stable through the direct calculation method,and a stable detonation perturbation oscillation pattern is obtained.2.In the general form(θ≠0)of Majda analog system,the Arrhenius reaction equation is more complex and cannot be calculated directly.For such a model,a detonation steady-state solution is obtained by using a numerical calculation method,and stability determination is performed using a stability determinant.Since the solution is non-analytic,the stability determinant cannot be calculated directly.The winding number method was introduced to determine the stability.The one-dimensional detonation stability of the analog system under different parameters was obtained,and analyzed the physical rationality of the results are analyzed.