Analysis of Bridging Formulae in Transitional Regime

Abstract

The most suitable method to compute aerodynamic forces of a spacecraft, at first stage of a design, relies on bridging formulae. There are two kinds of bridging formulae: global and local. The global formulae rely on knowledge of spacecraft aerodynamic force coefficients in continuum and in free molecular flow. The local formulae calculate the skin friction and pressure coefficients on the body surface; the global aerodynamic coefficients are then computed by integration. The aim of this work is to analyze the widely accepted local formulae by Potter and by Kotov. To this purpose, a simple body, like a sphere, has been preliminary considered and the results have been compared with those from the DSMC code DS2V. This comparison led to the corrections of the computation of the skin friction and pressure coefficients. These corrections have been applied to the Potter formula. On the other hand the original Kotov formula showed good results for the pressure coefficient at high altitudes. Therefore a merge of the corrected Potter formula and of the Kotov formula has been made. This methodology, called “new” bridging formula, has been successfully applied to sphere. The “new” formula has been also applied to EXPERT and ORION capsules, but it has to be pointed out that, in this application at low altitudes, a failure of the panel method starts to appear. Both local and global coefficients have been compared with the results by the DS2/3V codes. Finally, for these capsules, the global formula by Wilmoth has been also used by tuning the adjustable parameters.