Scaling for Hypersonic Entropy Layers on Blunt-Nosed Wedges

A simple method is presented for calculating the structure of entropy layers generated by bow shocks over blunt-nosed wedges in hypersonic flow. The model employs a streamfunction-based framework to track entropy jumps introduced at the bow shock. It is shown that entropy conservation along streamlines, combined with the condition of uniform total enthalpy, determines the transverse profiles of velocity and thermodynamic properties in the downstream parallel-flow region at distances much larger than the wedge radius. A key finding is that the variation of entropy with streamfunction, computed numerically for ideal gas at freestream Mach numbers ranging from 3 to 10 and wedge half-angles ranging from 0 to 10 degrees, identifies a specific nondimensional streamfunction scaled by freestream parameters that collapses the entropy data onto a single quasi-universal curve. The proposed model provides a robust and efficient means of reconstructing the density and velocity fields within the entropy layer for prescribed freestream Mach number and wedge angle, eliminating the need for direct CFD simulation and enabling rapid generation of base states for stability analysis and preliminary design.