Hybrid Riemann/Self-Similar Flow Structure by Steady- and Unsteady-Wave Interaction

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Hybrid Riemann/Self-Similar Flow Structure by Steady- and Unsteady-Wave Interaction

Bai, Chen-Yuan

The Heaslet–Lomax [“Two-Dimensional Unsteady Lift Problems in Supersonic FIight,” Technical Report Archive and Image Library 945 (FormerIy NACA-TN-1621), 1949] problem of a supersonic airfoil experiencing a sudden angle-of-attack change or encountering a crossflow is of primary importance in aeroelasticity or jet-obstacle interaction. This flow involves the interaction of steady and unsteady waves, which leads to a secondary wave with a self-similar flow structure in linear case. In this paper, the difference of flow parameters of steady and unsteady waves is viewed as an initial discontinuity of the classical Riemann problem, the solution of which suggests additional left- and right-going shock, or rarefaction waves bounding the secondary wave. A numerical computation indeed identifies a left-going shock wave on the leeward side even for a very small angle of attack. This means that the interaction leads to a hybrid Riemann/self-similar flow structure. The revealing of this new flow structure is meaningful for the Heaslet–Lomax problem at a high angle of attack. Moreover, the present study of steady/unsteady-wave interaction also enriches the knowledge of shock-interaction problems, because past studies only treat interactions between steady waves or interactions between unsteady waves.