Principle of Minimum Entropy Analysis Applied to Unsteady Flow in Three-Dimensional Hypersonic Inlets

Abstract

The stability of rectangular and three-dimensional hypersonic inlets to flow perturbations can be determined analytically from the princple of minimum entropy. According to the principle of minimum entropy, a stable thermodynamic state is one with the lowest entropy gain. A model based on piston theory was developed for applying the principle of minimum entropy to quasi-steady flow. Rectangular inlets that produce shocks that have normal Mach numbers less than 1.58, 2.19, and 1.25 should be stable to slight perturbations in Mach number, back pressure changes, and changes in the atmospheric conditions. Curved inlets and shocks are less stable than a stable rectangular inlet with the same mean normal Mach number, and in some cases, result in the unsteady shock having a lower entropy rise than the steady shock.