Transonic similarity laws

Abstract

This chapter starts the foundation with the small disturbance theory applied in the subsonic and supersonic flows. Both of these regimes are linear and thus fail at sonic speed, which is at the heart of transonic flow. Nonlinear small disturbance theory for the transonic regime is subsequently derived and discussed. With limited analytical options for the transonic nonlinear differential equation, special attention is directed to the development of similarity laws. These laws connect non-dimensional parameters such as pressure coefficient, lift and drag coefficients on families of affinely related bodies of different thickness or slenderness ratio and angle of attack. Brief discussion of hodograph transformation where switching between the dependent and independent variables causes the governing equation to be linear is presented. Finally, semi-empirical models on lift curve slope in the transonic regime and the approximate location of detached shocks in front of blunt bodies are developed and compared to experimental results. This chapter contains 12 examples and concludes with 39 practice problems.