Flow and Force for Plate Undergoing Stopping Motion in Supersonic Flow

Abstract

Linear and nonlinear models have been studied in the past for supersonic starting flow due to forward step motion of an airfoil where the airfoil gains an angle of attack. This Paper considers the inverse problem, supersonic stopping flow due to backward step motion of a flat plate, where the plate initially having an angle of attack reduces its angle of attack to a smaller one. The wave structures and their time evolution are clarified numerically, and a theory is built to predict the pressure along the airfoil, various wave speeds and indicial force. It is found that shock and rarefaction waves are produced to replace or complement the initial flow structure and the interaction between two adjacent new waves produces secondary waves with dimple-shape pressure profile. The indicial force first drops from the initial value to a smaller one and then evolves following a three-stage behavior. The force increases or decreases during the first stage where the secondary waves are upstream of the trailing edge, drops monotonically during the second stage where the secondary waves are leaving the trailing edge, and reaches its final steady state value after the secondary waves have left the trailing edge.