Reference Enthalpy Method Developed from Solutions of the Boundary-Layer Equations

Abstract

A simple average of local enthalpy over the velocity profile is proposed as the proper definition of reference enthalpy for the purpose of quasi-one-dimensional treatment of compressible boundary layers. Use of Van Driest's nearly exact solutions of the laminar boundary-layer equations shows that this definition produces Eckert's reference enthalpy formulation for the special case of an adiabatic wall. For surfaces other than adiabatic, either Eckert's form should be replaced by that of Young and Janssen, or the coefficient in Eckert's viscous heating term should be slightly modified. A similar analysis was conducted for turbulent flows using Whitfield and High's simplified solutions of the turbulent boundary-layer equations. Dorrance's derivation of reference quantities is also addressed. This work provides a theoretical basis for the empirical reference enthalpy formulas of Eckert and others and supplies practical expressions for the reference enthalpy of both laminar and turbulent compressible boundary layers.