Because the processes in the scramjet engines are governed by a mixture of fluids in motion undergoing chemical reactions, the fluid mechanics conservation equations along with transport properties and chemical kinetics must be solved simultaneously. This chapter treats the governing equations with distinction between field equations, also called conservation laws and constitutive equations; the one-dimensional (1D) flow simplification, which is often used when some fundamental processes in a scramjet engine are described, is also included. Equilibrium chemistry and the departure from equilibrium follow.
Field Equations and Constitutive Relations for Compressible Flows
The equations of motion, along with the constitutive equations, provide a system of mathematical expressions that model physical fluid properties under certain given boundary conditions.
Field Equations of Fluid Motion
The field equations of motion, also called conservation laws, are derived for gases or liquids, which, for dynamics studies, are similarly treated under the fluids category. Both exhibit the property of easy deformability dictated by the nature of the intermolecular forces. A detailed discussion of the distinction between gases and fluids is included, for example, in Batchelor (1994) and is not reproduced here. The fundamental assumption used in the derivation is that of continuum, granted by the sufficiently high density of the fluid, which eliminates the distinction between individual molecules and the intermolecular space within the entire volume of fluid under consideration.
The field equations include conservation of mass, momentum – also referred to as the Navier–Stokes equations – and energy.