This work covers two distinct yet associated topics:​ modeling rapid evaporation waves and the development of a P(u,ρ) equation of state for use in reacting flow computations. Both subjects are concerned with flows that are changing phase. Because of this phase change, the thermodynamics of the fluids plays a central role in the computational analysis of the flows.

The effort in modeling rapid evaporation waves is centered around a model which treats an evaporation wave as a thermodynamic discontinuity, somewhat like a shockwave. The structure of the wave is captured inside a control volume and conservation relations are used to determine the downstream state. This model is applied to various situations, first considering rapid evaporation in water and refrigerants in an effort to confirm the model using available experimental data. Subsequently, the model is applied to multiphase mixtures of hot molten metal suspended in liquid water. These computations include the case where a constraint is added to the problem geometry which causes a precursor shockwave that runs out in front of the evaporation front. Both inert and reacting mixtures are considered, using hot molten tin and aluminum, respectively, as the metal component.

The work on reacting flow has a slightly different goal. An examination of the Euler equations reveals that the relevant thermodynamic properties for flow systems are pressure, internal energy and density. However, most equations of state available for flow calculations utilize pressure, density and temperature. This discrepancy in the properties necessary for solving reacting flow problems results in the need to iterate at every step which significantly increases computation time. A route is proposed to finding a new equation of state based on pressure, density and internal energy which is formulated specifically for solving reacting flow problems. Analytic derivations of P(u,ρ) type expressions for several cubic equations of state are shown. The difficulties in transforming a realistic equation of state for detonation products is discussed along with possible approaches to solving this problem.