Dependence of the Shape of a Detonation Wave Front on the Detonation Wave Velocity upon Detonation of a Cylindrical Charge

The transition of a system of partial differential equations which describe the sta-tionary flow behind the shock-wave front of a detonation complex upon detonation of a cylindrical charge to a system of ordinary differential equations is performed by means of the series expansion in terms of the radial variable. The necessary equations for determination of the derivatives of solutions with respect to the parameters and the initial conditions for them are formulated. Imposing the condition of continuous extendibility of the solutions leads to equations that allow one to determine the shape of a shock-wave front as a function of wave velocity. The attempt is made to construct a consistent method of determining the shape of the shock-wave front of a detonation complex upon detonation of a cylindrical charge of finite diameter in the case where the detonation velocity deviates insignificantly from the Chapman–Jouguet velocity. This problem can be solved, disregarding the problems connected with the description of the flow near the charge edge. This problem was considered earlier (see, e.g., [1, 2]), but in the solution of it, the authors restricted them-selves only to the determination of the curvature of the front, i.e., the first expansion coefficient of the function describing the front shape in terms of the powers of its argument. The distinguishing feature of the proposed approach is the fundamental possi-bility of determining the shape of the front with no matter how high accuracy. We write a system of equations that determines the axisymmetric stationary flow in the presence of a chemical reaction characterized by the unique vari-able λ (fraction of the reacted substance) in the cylin-drical coordinate system: v ∂