Compressibility corrections for multifoil sections

Abstract

HE calculation of compressible flow about multifoil sections has not developed at the same rate as that for single foils. Flap configurations are generally used at low Mach numbers where the inclusion of viscous effects is somewhat more important than the inclusion of compressibili ty effects, with the result that the latter is often neglected. The evolution at de Havilland of the transonic multifoil (Fig. 1) from the proven STOL capable augmentor wing1 has necessitated the parallel development of multifoil compressible methods. To date this has centered around the use of a standard surface singularity potential flow technique that incorporates compressibility by using the Goethert transformation and corrections similar to those developed by Wilby 2 and Labrujere.3 However, the application of these compressibility corrections to the geometry of Fig. 1 is fraught with difficulty. First, the foils are very thick, typically in the range 18-30%, while the compressibility corrections have been developed for thinner sections. Second, the combination of internal and external flow regions has not been addressed by these methods. For a number of years, the accepted method for obtaining the compressible flow within a duct has been that due to Lieblein and Stockman (LS).4 This has been shown to be reliable.5 However, until recently, it suffered from the absence of a counterpart for external flow and, therefore, could not be applied to general configurations. This deficiency has been remedied by Dietrich, Oehler, and Stockman (DOS),6 who have modified the internal flow method to produce a compressible flow correction for external flow. Apart from the attraction of now having consistent corrections for all regions of the flow about a general flap configuration, there is also the advantage of them being based on incompressible calculations and, therefore, allowing the combination of solutions. It is the application of the LS and DOS methods in concert to the geometry of Fig. 1 that is the subject of this paper. Basic Formulation