Hey, Detonation Numerical Simulation Research

In the engineering systems which are large enough compared to their reaction zones, when explosives can be initiated by the detonator, we ignore the initiation and study the well-developed divergent detonation front only. For the simulation of diverg-ing detonation, this paper study the numerical method of computing the relationship between velocity of detonation and curvature and the numerical method of simulating the propagation of the detonation front on the unstructured mesh.Simplified methods of getting the relationship between velocity of detonation and curvature are studied based on reactive Euler equations. For plane detonation, study the numerical method computing the detonation reaction zone. By the use of JWL equations of state and mixing rules of temperature and pressure equilibrium, ZND re-action zone is gotten for plane detonation. Basing on the results of plane detonation, equations of the divergent detonation are derived introducing the quasi-steady assump-tion. General CJ condition is derived from the equations of the divergent detonation. One well-posed problem is composed of equations of divergent detonation, general CJ condition, equations of state of reactant and product, reaction rate and mixing rules. This well-posed problem derives the relationship between velocity of detonation, phys-ical variables in the sonic point and curvature, the length of detonation driving zone and physical variables in the detonation driving zone. The relationship between veloc-ity of detonation and curvature are gotten separately using the Ignition-Growth and wide-ranging reaction rate. They show that reaction rates have evident influence on the relationship between velocity of detonation and curvature.When the relationships between detonation velocity and curvature are known, nu-merical method is studied to simulate the moving of detonation front. Level set method is used here because of its advantage of dealing with the topological changes of fronts. In order to meet the need of simulating the detonation front of Lagrangian method, level set equations are discretised on unstructured meshes. Assuming the linear relationship between velocity of detonation and curvature, level set equation in the cylindrical-symmetry coordinate is derived by the use of coordinate transformation. The term independent on curvature is discretized by positive scheme, and the term on curvature is discretized by Galerkin isoparametric finite element method and semi-implicit time stepping. We apply the reinitiation method satisfying the Huygens principle to re-initiate the level sets. The numerical methods of level set method in this paper are first order on the triangles and quadrilaterals. Multiple examples show that this numerical schemes of level set equations are feasible and valid.