Initial-Value Problem for Small Perturbations in an Idealized Detonation in a Circular Pipe

Abstract

The thesis is devoted to the investigation of the initial-value problem for linearized Euler equations utilizing an idealized one-reaction detonation model in the case of three-dimensional perturbations in a circular pipe.The problem is solved using the Laplace transform in time, Fourier series in the azimuthal angle, and expansion into Bessel's functions of the radial variable.For each radial and azimuthal mode, the inverse Laplace transform can be presented as an expansion of the solution into the normal modes of discrete and continuous spectra. The dispersion relation for the discrete spectrum requires solving the homogeneous ordinary differential equations for the adjoint system and evaluation of an integral through the reaction zone.The solution of the initial-value problem gives a convenient tool for analysis of the flow receptivity to various types of perturbations in the reaction zone and in the quiescent gas.