Direct numerical simulation of a fully developed compressible wall turbulence over a wavy wall

ABSTRACT

Compressible turbulent channel flow over a wavy surface is investigated by direct numerical simulations using high-resolution finite difference schemes. The Reynolds number considered in the present paper is 3380 based on the bulk velocity, the channel half-width and the kinetic viscosity at the wall. Four test cases are simulated and analysed at Ma_m = 0.33, 0.8, 1.2, 1.5 based on the bulk velocity and the speed of sound at the wall. We mainly focus on the curvature and the Mach number effects on the compressible turbulent flows. Numerical results show that although the wavy wall has effects on the mean and fluctuation quantities, log law still exists in the distribution of the wave-averaged streamwise velocity if the roughness effects are taken into consideration in the scaling of it. Near-wall streaks are broken by the wavy surface and near-wall quasi-streamwise vortices mostly begin at the upslope of the wave and pass over the crest of it. The wavy wall makes the turbulence more active and the flow easier to be blended. From the viewpoint of turbulent kinetic budgets, curvature effects strengthen both the diffusion terms and the dissipation terms. At the same time, they change the properties of the compressibility-related terms and promote more inner energy transferring into turbulent kinetic energy. As the Mach number increases, the reattachment of the mean flow is delayed, which indicates the mean separation bubble becomes larger. Concerning the near-wall coherent structures, the vortices are more sparsely distributed with the increasing of the Mach number. For the supersonic cases, shock waves appear. Though they have little effects on the mean turbulent quantities, they change the structures of the flow fields and induce local separations at the upper wall of the channel.

KEYWORDS:

• Compressible wall turbulence
• wavy surface
• compressibility effects
• curvature effects
• direct numerical simulation

Acknowledgments

The authors would like to thank Prof. Yuxin Ren in Tsinghua University for his valuable suggestions and discussions. We also thank supercomputer center in Tsinghua University for providing computer hours.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the project of Aeronautical Science Foundation of China [grant number 201514U8005]; National Natural Science Foundation of China [grant number 11302250]; Natural Science Foundation of Shaanxi Province [grant number 2015JQ1008].