DNS of turbulent flow and heat transfer in a channel with surface mounted cubes

The turbulent flow and heat transfer in a channel with surface mounted cubical obstacles forms a generic example of a problem that occurs in many engineering applications, for instance in the design of cooling devices. We have performed a numerical simulation of it without using any turbulence models. This approach is the most accurate - but also the most expensive - way of computing complex turbulent flows since all dynamically significant scales of motion are to be solved numerically from the unsteady, incompressible Navier-Stokes equations and the energy equation. In view of the computational complexity, our first concern is to reduce the computational cost as far as we can get. We discretise convective and diffusive operators such that their spectral properties are preserved, i.e. convection ↔ skew-symmetric; diffusion ↔ symmetric, positive definite. Such a symmetry-preserving discretisation is stable on any grid and conserves mass, momentum and kinetic energy if the dissipation is turned off. First, the results of a second-order and a fourth-order, symmetry-preserving discretisation are compared for a fully developed, turbulent flow in a plane channel. The more accurate fourth-order method is applied to perform a numerical simulation of turbulent flow and heat transfer in a channel, where a matrix of cubes is mounted at one wall. Here, the temperature is treated as a passive scalar. The Reynolds number (based on the channel width and the mean bulk velocity) is equal to Re = 13, 000. The results of the numerical simulation agree well with the available experimental data.