Heat transfer in turbulent flows with Lagrangian methods: scales of turbulent tranport in wall turbulence

Abstract

Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.

We use a Lagrangian computational methodology that allows the calculation of statistical quantities in turbulent heat transfer. The study utilizes a direct numerical simulation (DNS) of turbulent flow in an infinite channel and in plane Couette flow, in conjunction with the Lagrangian scalar tracking method (LST). The computational box dimensions are 4πh × 2h × 2πh in x, y, z for Poiseuille flow and 8πh × 2h × 2πh for Couette flow (where h is the half channel height). The transport of heat is simulated with LST, which involves the tracking of the trajectories of heat markers in the flow generated by the DNS. The effects of convection are simulated by moving the markers under the assumption that they follow the velocity field. The diffusion effect is simulated by adding a 3D random walk on the particle motion that follows a normal distribution with a standard deviation that depends on the Prandtl number, Pr, of the fluid [1]. The range of Pr covers a wide range (between 0.1 and 6). The trajectories of about 150,000 heat markers are calculated for each case. These trajectories are then used to obtain turbulent dispersion data and to obtain the correlation coefficients for single particle and for relative particle pair dispersion. In addition, the dispersion backwards in time was considered. This was motivated by recent studies about backwards dispersion that have shown differences with forwards turbulent dispersion. The results show differences in the rates of forwards and backwards dispersion [2]. The time scales that are important to turbulent transport and for mixing are thus revealed. Differences between Couette flow and Poiseuille flow highlight the effects of the velocity structure of the turbulence next to the wall on the transport of heat. The presentation will present the numerical methodology and results will be compared with available data from earlier DNS works [3,4].