Recasting the Fay-Riddell formulae for computing the stagnation point heat flux

Abstract

The Fay-Riddell formulae, used to compute the heat flux at the stagnation point of spherical bodies in very high speed, laminar flow and dissociating air, have been revived and recast. As these formulae were obtained by fitting a number of results of the original Fay-Riddell computing procedure, which suffered from inaccuracies concerning operative parameters, it is to be expected that these inaccuracies also influence the correctness of the formulae. A sensitivity analysis has been made in order to identify the most critical parameter. Recast formulae have been calibrated using the results of the improved version of the Fay-Riddell computing procedure and then validated both by numerical results of a Navier-Stokes code and by experimental data. For this purpose two sets of heat flux measurements have been made in HEBDAF (high enthalpy blown-down arc facility) at the University of Naples, matching the operating conditions of the formula for a frozen boundary layer and non-catalytic wall. Recast formulae are valid in the range of free-stream total enthalpy between 3 and 37 MJ/kg.