Impacts of grid turbulence on the side projection of planar shock waves

Linear interaction analysis is a popular tool to analyze shock–turbulence interactions. With assumptions that simplify the complicated two-way interactions, linear analysis presents explicit solutions for post-shock turbulence. The present work extends the analytical expressions to pressure-dilatation. Both the streamwise and transverse components are presented as a function of mean Mach number and streamwise location. The proposed solutions for pressure-dilatation agree well with data from direct numerical simulations when the adopted assumptions in linear analysis are met. The spatial evolutions under different flow conditions are presented, and the asymptotic states observed with increasing Mach number are discussed.

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Local geometry of a weak normal shock wave interacting with turbulence

Kusuhata,

Tanaka,

Watanabe

et al. 2023

Physics of Fluids

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The shock surface geometry is investigated with direct numerical simulations of a weak normal shock wave propagating in turbulence. The geometry is quantified with the principal curvatures of the surface. A large part of the surface has an approximately flat saddle shape, while elliptic concave and convex shapes with a large curvature intermittently appear on the shock surface. The pressure–dilatation correlation in the governing equation of pressure is investigated at the shock wave with the decomposition into three terms associated with the velocity gradients in the two directions of the principal curvatures and the normal direction of the shock wave. Fluid expansion in the tangential direction occurs at the shock wave with a convex shape in the direction of the shock propagation, resulting in a smaller pressure jump across the shock wave. For a concave shape, compression in the tangential direction can amplify the pressure jump. Consistently, small and large shock Mach numbers are observed for convex and concave shapes, respectively. The geometric influences are the most significant for elliptic concave and convex shapes with approximately equal curvatures in the two principal directions because the compression or expansion occurs in all tangential directions. These relations between the shock surface geometry and shock Mach number observed in turbulence are consistent with the theory of deformed shock waves, suggesting that the three-dimensional geometrical features of the shock surface are important in the modulation of shock waves due to turbulence.

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Impacts of grid turbulence on the side projection of planar shock waves

Cited by 5 publications

References 33 publications

Nearly homogeneous and isotropic turbulence generated by the interaction of supersonic jets

Nearly homogeneous and isotropic turbulence generated by the interaction of supersonic jets

Linear analysis on pressure-dilatation behind shock waves

Local geometry of a weak normal shock wave interacting with turbulence

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