The partial‐equilibrium approximation in reacting flows

Complex reaction systems that are subject to the partial‐equilibrium approximation are analyzed. In order to take proper account of equilibrium and finite rate reactions, a distinction is made between linearly independent and dependent species and reactions, respectively. The assumption of partial equilibrium removes short time scales from the problem and leads to a reduction in the number of independent thermodynamic variables. Making use of a fundamental property of equilibrium reactions, a general formulation for partial chemical equilibrium in complex reaction systems is obtained. Furthermore, a partially frozen sound speed is defined and an analytical expression for this sound speed is given. The concept of partial chemical equilibrium is applied to high‐speed reacting flows. A characteristic formulation of the conservation and rate equations is presented. Finally, a high‐enthalpy flow, namely the expansion of high‐temperature air through the axisymmetric nozzle of a shock tunnel, is calculated using the method of lines.