(128d) Mechanism of Heat Transfer Away from the Wall and Turbulent Prandtl Numbers for Plane Channel and Plane Couette Flow
Previous investigation of the correlation between the velocity structure and the temperature field in turbulent flow has shown a strong resemblance to each other. In the present work, this matter was investigated using direct numerical simulation (DNS) in conjunction with the Lagrangian scalar tracking (LST) method. In the case of channel flow, the flow was driven by a constant mean pressure gradient, and for the case of plane Couette flow it was driven by the shear motion of the two moving walls of the channel. The transport of a passive scalar was simulated with LST, which involves the tracking of the trajectories of scalar markers in the flow field generated by the DNS. The Pr ranges from 0.1 to 100. The instantaneous velocity field and the thermal fields are visualized in a plane normal to the direction of the flow to investigate the connection between the turbulent structure and the mechanism of turbulent heat transport. A single line source was used to investigate the mechanism of particles moving away from the wall.
Length scales are calculated for the available range of Prandtl numbers at different locations across the channel. It appears that larger scales are contributing to the transport of heat as the distance from the wall increases, as is the case for momentum transfer. Turbulent Prandtl numbers can then be predicted by finding the ratio of the turbulent length scales for flow divided by the turbulent transport length scales, and compared to available models for the turbulent Prandtl number. Five runs were studied for the same set of Prandtl number for better statistics. The results show that the turbulent Prandtl number has no dependence on Prandtl number for high Prandtl number.