Study Of The Detonation Dynamic Based On The Analog System

Detonation is a kind of special explosion phenomenon accompanied by a large number of energy release,the communication and behavior of detonation has been a subject of current research.The original Euler system which simulates behavior of detonation contains too much physical details,these will cause mathematical difficulties because of the nonlinearity of the equations.To simplify the reactive Euler equation in the theory of detonation,the analog system of detonation which contains one or more partial differential equations is obtained.The analog system of detonation as a simple model to study detonation behavior,can capture a rich set of detonation phenomenon.In this dissertation,the source and forms of the analog system of detonation are introduced firstly.In order to study the influence of boundary conditions and the grain diameter condition caused by non-ideal detonation,the analog system of detonation with loss and the chemical reaction of two step reaction model is constructed in this dissertation,and the theoretical study on the non-ideal detonation related characteristics is made by using the system.And the analog system with Arrhenius reaction rate is used to study detonation instability with numerical simulation method,the main research content are as follows:1.The analog system of detonation with loss and the chemical reaction of two step reaction model is constructed,wherein an induction zone is followed by a energy and heat release zone.Steady state of detonation wave structures are obtained by analytic method.By changing the value of the sensitivity exponent of reaction rate n and the sensitivity coefficient of loss rate m,the diagrams of steady detonation velocity and the loss coefficient ? under the corresponding parameter and detonation failure of linear boundary can be obtained,and the parameters relation of critical characteristics of detonation failure is deduced,and the results are compared with those of numerical simulation.2.In view of the above established the analog system of detonation,through the linear stability of the normal mode analysis,it is clear to deduce the spreading condition by means of limiting the spread of the disturbance to the upstream,study the stability of the steady state solution under the condition of the ideal and non-ideal(with loss)analog system of detonation and the influence of related parameters on the stability.3.The analog system with Arrhenius reaction rate is established.It is bright to change the different control parameters of the analog system to study the one-dimensional detonation instability by direct numerical simulation,after the stability limit,the results show that the oscillation of the pressure of leading shock wave for single-mode condition to the period-doubling bifurcation and entering the chaos instability of the situation finally.At last,analysis of the instability mechanism is essential.