Selfsimilar solution of the spherical detonation problem
Abstract
Under polytropic equation of state and strong shock assumptions, grouptheoretic methods are used to obtain a class of selfsimilar solutions to a onedimensional problem in reactive shock hydrodynamics with spherical symmetry and to characterize the class of all statedependent chemical reaction rates under which such solutions exist. In the special case that the reaction rate is proportional to the internal energy, the system of ordinary differential equations describing the selfsimilar solution can be reduced to a single, firstorder differential equation for which a phaseplane analysis yields the nature of the solution near the equation's critical points. Further, a modeling parameter which characterizes the flow is identified.
 Publication:

Combustion and Flame
 Pub Date:
 June 1982
 Bibcode:
 1982CoFl...46..253L
 Keywords:

 Combustible Flow;
 Detonation Waves;
 Hydrodynamic Equations;
 Reaction Kinetics;
 Shock Wave Propagation;
 Similarity Theorem;
 Spherical Waves;
 Differential Equations;
 Equations Of State;
 Flow Characteristics;
 Group Theory;
 Internal Energy;
 Polytropic Processes;
 Waveforms;
 Fluid Mechanics and Heat Transfer