Bulk viscosity effects in compressible turbulent Couette flow

Abstract

This work investigates the effect of bulk viscosity in one-, two-, and three{dimensional compressible fows via direct numerical simulation. The role of bulk viscosity in compressible turbulence is of increasing importance due to three applications: spacecraft descending through the Martian atmosphere, the thermodynamic cycle of solar-thermal power plant, and carbon capture and storage compressors. All three rely on the accurate description of turbulence in carbon dioxide, a gas with a bulk-to-shear viscosity ratio three orders of magnitude larger than for air. In these applications, invoking Stokes's hypothesis is questioned as the divergence of velocity is non-zero, implying a significant difference between mechanical and thermodynamic pressures. Results of a constantly forced velocity perturbation follow the same trend as that predicted by Landau's acoustic absorption coeffcient for suffciently high Reynolds numbers. Below an optimum Reynolds number, the damping effectiveness reduces by a different mechanism to that of Landau. Maximum damping is achieved at an acoustic Reynolds number equal to unity. Two-dimensional decaying turbulence at the bulk-to-shear viscosity ratio of carbon dioxide demonstrates that the magnitude of the dilatational production term is greatly enhanced and is strongly biased to negative values, reducing the generation of velocity dilatation compared to the zero bulk viscosity case. Compressible Couette flow at two Reynolds numbers and two bulk-to-shear viscosity ratios show minimal changes to mean flow quantities and the main terms of interest in the turbulence kinetic energy budget. Instantaneous views of the dilatational velocity field show that an intermediate range of scales are damped in accordance with Landau's acoustic damping coeffcient. At small scales, however, damping reduces and turbulent patterns are preserved.