Shock wave in transonic small-disturbance flow Original Research Article

The Rankine-Hugoniot relation of shock wave in transonic small-disturbance flow is studied by inner and outer expansions. The inner expansion to the second-order approximation shows that the inner shock wave is perpendicular to the free-stream velocity. The outer expansion shows that the outer shock wave obeys the transonic equivalence rule with lift of Cheng and Hafez [Cheng and Hafez, J. Fluid Mech. 72 (Part 1) (1975) 161–187]. Numerical solutions by the full potential code of Jameson and Caughey [Jameson and Caughey, Proc. Third Computational Fluid Dynamics Conference, AIAA, Albuquerque, New Mexico (June 27–28, 1977) 35–54] for three-dimensional wings at free-stream Mach number 0.94 confirm the perpendicularity property of inner shock wave. The admittance of shock wave in inner flow by the asymptotic matching theory is discussed.