Steady Shock Transitions which are Shaped by Viscosity, Heat Conduction, Chemical Reaction and a Simple External Source.

It is the objective of this thesis is to acquire a better understanding of steady, one-dimensional shock transition layers by considering solutions to a differential system, {cal D}, which is comprised of conservation laws and phenomenological relations and which prescribes the transition of material elements through a shock layer. The structure of a shock layer is determined uniquely by the transport properties and equation of state of the material through which it propagates and by an external source, if present. An equation of state prescribing the recombination of hydrogen is assumed as a paradigm. Shock layers which are shaped by (a) viscosity and heat conduction, (b) viscosity and chemical reaction, (c) heat conduction and chemical reaction, and (d) viscosity, heat conduction and chemical reaction are considered. For cases a and b the effect of an idealized external source is illustrated. The results for case d are the main contribution of this thesis. Thermodynamic restrictions on the solutions to {cal D} are presented and cases a, b, c and d are then undertaken. It is demonstrated that externally added energy can cause a shock transition to bifurcate and can control the speed of a leading, bifurcated shock transition. Case d requires understanding a three dimensional critical point character which is present along the equilibrium Hugoniot. It is found that heat conduction introduces a saddle-like character which greatly restricts the range of ignition states for which steady shock transitions are possible. The limiting cases of small heat conduction, small viscosity and slow reaction rate are understood and the structure of phase space is presented. It is demonstrated that the ZND model is not recovered in the limit of infinitesimal reaction rate.