Turbulent heat transfer was studied by direct numerical simulation (DNS) in conjunction with the Lagrangian scalar tracking method (LST) for plane channel flow and plane Couette flow. 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 marker motion was decomposed into a convective part and a molecular diffusion part. The effects of the convective motion were simulated by moving the markers in every time step under the assumption that they follow the velocity field. The diffusion effect was simulated by adding a 3D random walk on the particle motion at the end of every convection step. This random jump followed a normal distribution with a zero mean and a standard deviation the depended on the diffusivity (i.e., the Prandtl number, Pr) of the scalar. In this manner fluids with Pr between 0.1 and 50000 were studied (i.e., liquid metals to electrochemical fluids), which is a range that cannot be simulated with other existing methodologies. This methodology has been used previously to determine the dependence of the heat transfer coefficient and turbulent dispersion of plane channel flow and plane Couette flow on Pr [1-3]. The focus of the present work is to explore the effects of turbulent structure on the mechanism of turbulent heat transport from the conductive wall sublayer to the logarithmic region of the flow.

The presence of high and low temperature streaks close to the wall, similar to the high and low Reynolds stress streaks for the velocity field, has been observed for low Pr fluids in turbulent channel flow [4, 5]. These previous studies have found that the velocity and the temperature streaks show a strong resemblance to each other. In fact, turbulence producing streaks are correlated to flow structures that produce temperature fluctuations. The streaks play a very important role in the generation of temperature fluctuations, and in the mechanism of turbulent heat transfer, because they are responsible for moving fluid of different temperature to different regions of the flow. The effect of the Prandtl number on the temperature streaky structures has not been explored, however, even though it can be quite significant within the viscous wall sublayer. The presentation will focus on medium and high Pr fluids in plane channel and plane Couette flows, using the data from DNS/LST method. The instantaneous velocity field and thermal fields can be visualized with this method, and the correlation between the flow structure and the thermal field structure as a function of Pr will be discussed. The connection between the turbulent flow structure close to the wall and the mechanism of turbulent heat transport in wall turbulence will be explored. As the Pr increases, turbulent heat transfer is more and more the result of strong fluid motions either away or towards the channel wall. These structures are spaced several hundred wall length units from each other. For low Pr, however, smaller flow structures contribute to the transport of heat. These results can have implications for the development of a model for the prediction of the turbulent Prandtl number in wall turbulence as a function of the molecular Prandtl number.

References

[1] B.M. Mitrovic, P.M. Le, D.V. Papavassiliou, On the Prandtl or Schmidt number dependence of the turbulence heat or mass transfer coefficient, Chemical Engineering Science 59(3) (2004) 543-555.

[2] P.M. Le, D.V. Papavassiliou, Turbulent dispersion from elevated sources in channel and Couette flow, AIChE Journal 51(9) (2005) 2402-2414.

[3] P.M. Le, D.V. Papavassiliou, Turbulent heat transfer in plane Couette flow, Journal of Heat Transfer – Transactions of ASME 128 (2006) 53-62.

[4] H. Kawamura, H. Abe, Y. Matsuo, DNS of turbulent heat transfer in channel flow with respect to Reynolds and Prandtl number effects, International Journal of Heat and Fluid Flow 20 (1999) 196-207.

[5] H. Abe, H. Kawamura, Y. Matsuo, Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence, Hournal of Fluids Engineering – Transactions of ASME 123 (2001) 382-393.