Revisiting the Transonic Similarity Rule: Critical Mach Number Prediction Using Potential Flow Solutions

摘要

This paper revisits Von Karman's Transonic Similarity Rule as explained by Schlichting. This rule postulates that an equivalent incompressible geometry corresponds to any given subcritical, high speed aerodynamic shape. We utilize panel method as well as Navier-Stokes CFD tools to better understand the actual behavior of wings in wing sections in high speed flight. We provide evidence that the classical "stretching" explanations given by famous authors are mutually inconsistent with one another. We also show that for many, but not all cases, a better physical analogy has the engineer visualize the Transonic Similarity Rule as a non-linear transformation of the effective velocity or dynamic pressure. We also discovered notable discrepancies in the Critical Pressure Coefficient equation given by famous authors.