Interaction of a shock wave with two counter-rotating vortices: Shock dynamics and sound production

Abstract

In the present paper the interaction of a planar shock wave with a pair of counter-rotating vortices is studied by means of extensive numerical simulations. The main objective of the study is to characterize the shock pattern and the nature of the acoustic field. For the purpose of shedding some light into the mechanism of sound generation, the acoustic analogy developed by the present authors for the interaction of a shock wave with an isolated vortex has been extended to the case of a vortex pair, so as to obtain a closed form solution for the acoustic far field pressure in the limit of weak vortices. The effect of various parameters, such as the shock and vortex strengths and the initial vortex separation distance has been investigated, and their influence on the dynamics has been assessed. In addition, we have also considered both the case of passing and colliding pairs. In the case of a colliding pair five types of interactions are found to occur, depending upon the value of the interaction parameter, defined as the ratio of the vortex pair intensity over the shock strength. With regard to the acoustic field, the simulations have shown that the latter is the result of two mechanisms: the one directly associated to the interaction itself, and the one related to the coupling process of the vortex pair. The former mechanism is controlling if the interaction is weak, while for strong interactions the acoustic field is also controlled by the sound generated through the coupling process. For all cases the acoustic pressure field exhibits a multipolar directivity pattern with at least four sound peaks along the radial direction; however, if the vortex pair intensity is large the sound waves trailing the precursor are not clearly distinguishable. Shock wave–passing vortex pair interactions exhibit only three types of shock patterns, as in the case of shock wave–isolated vortex interaction; however, the acoustic field exhibits the same features as in the colliding case.