Interaction of a Shock wave with a Homogeneous Field of Acoustic Waves: Theory and Simulation

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A shock wave occurs when a wave moves faster than the speed of sound in a fluid. The interaction of a shock wave with compressible turbulence is relevant to a wide range of engineering applications including aeronautics (supersonic flight and propulsion), energy (fusion), medicine (shock wave lithotripsy), and space physics (star formation and supernovae explosions). Understanding the physics of the interaction between a shock wave and a homogeneous field of acoustic waves (shock/acoustics interaction) are of major theoretical and practical importance. Given that the coexistence of shock waves with background acoustic noise is an almost unavoidable feature for any experiments conducted in supersonic wind tunnels, the study of shock/acoustics interaction is particularly important to the characterization of background acoustic disturbances in supersonic wind tunnels and to the extrapolation of measurement data obtained in noisy supersonic wind tunnels to free flight. The experiences and results gained from the research effort are being incorporated into education activities including classroom teaching, research training, and outreach activities via involvement in Missouri S&T Student Diversity, Outreach and Women?s Programs in order to engage students to consider careers in STEM fields. In this research project, significant flow characteristics associated with a homogeneous field of acoustic waves passing through a nominally normal shock wave are quantified using direct numerical simulations and linear interaction analysis. The full-fledged nonlinear simulations and the linear analysis are enabled by a pre-cursor numerical database of boundary-layer acoustic radiation that provides incident acoustic fields with a high degree of physical realism and applicability. This study advances the state of the art knowledge of shock/acoustics interaction, including (1) the generic statistical and spectral features of the post-shock fluctuations and their dependence on flow parameters; (2) the distinctions between linear and nonlinear mechanisms; and (3) the transfer function associated with the total pressure and the contribution of individual Kovasznay modes to the post-shock total pressure. This research contributes to the fundamental understanding of the interaction of a shock wave with a field of turbulence by characterizing its behaviors in the pure dilatational limit and complements existing studies of shock/turbulence interaction with a vorticity-dominated incident turbulent field. The project also provides the basis for measuring tunnel freestream noise with intrusive probes in noisy supersonic wind tunnels and for elucidating the impact of facility noise on the experimental data obtained in such wind tunnels.