Direct numerical simulation of low Mach number turbulent wall bounded flow with favourable and adverse pressure gradients

Abstract

Direct numerical simulation (DNS) of turbulent isothermal-wall bounded flow subjected to favourable and adverse pressure gradient (FPG, APG) at low Mach number is investigated. The FPG/APG is obtained by imposing a concave/convex curvature on the top wall of a plane channel. The flows on the bottom and top walls are a tripped turbulent and laminar boundary layers, respectively. It is observed that the flow reaches equilibrium in the FPG region and the first and second order statistics are strongly influenced by the pressure gradients. For FPG/APG regions very near the bottom plane wall, the correlations between the streamwise pressure gradient and the spanwise vorticity flux and between the spanwise pressure gradient and the streamwise vorticity flux in the wall-normal direction are high on the wall and quickly drops to a negligible value within the viscous sublayer. Related flow physics and linkage to energy balance transport is discussed.

Keywords:

• direct numerical simulation
• Mach number
• turbulent flow
• adverse pressure gradient
• favourable pressure gradient
• discontinuous Galerkin method

Acknowledgments

The authors thank Dr. George Karniadakis and his CRUNCH group and Dr. Mike Kirby for providing the original discontinuous Galerkin code and for the related helpful email discussions. The research was funded through grants from NSERC Canada. Computing resources were provided by HPCVL (www.hpcvl.org). Queen’s ITS is acknowledged for providing access to an IBM server for the post-processing of some data.