85b Prediction of Turbulent Prandtl Number In Wall Flows

Chiranth Srinivasan¹, Phuong M. Le¹, and Dimitrios V. Papavassiliou². (1) Chemical Engineering, University of Oklahoma, Sarkeys Energy Center, 100 East Boyd Street, Norman, OK 73019, (2) Chemical, Biological, and Materials Engineering, University of Oklahoma, Sarkeys Energy Center, 100 East Boyd Street, Norman, OK 73019

Abstract

The turbulent Prandtl number is an important parameter in the study of turbulent boundary layer flows or flow through ducts. The paper discusses three different methods by which we can determine turbulent Prandtl number. These are all based on a Lagrangian approach to study turbulent heat transfer. In the Lagrangian framework, heat markers are released instantaneously from point sources located on the wall of a numerically simulated turbulent channel flow. The channel essentially comprises of a computational block, which is 4πh × 2h × 2πh in the x, y, z dimensions (where h is the half channel height and h =150). In order to estimate turbulent Prandtl number we need to find out the eddy viscosity and the eddy conductivity in the turbulent channel. The first method of calculation involves determining the eddy viscosity for the channel flow by using the known values of the Reynolds stress and the mean velocity in the x direction. Values of eddy conductivity are obtained by the method proposed by Churchill(1). According to Churchill the eddy conductivity is just the ratio of the heat flux due to turbulence divided by the total heat flux. The second method involves finding the length scales that are proportional to the mixing length for momentum transfer and for heat transfer, comparing the scales and determining their ratio to find the turbulent Prandtl number. The third approach involves finding the eddy viscosity and the eddy conductivity using the turbulence scaling suggested by Churchill, and using the mean temperature profiles determined previously in our laboratory(2). Results obtained are compared with the existing direct numerical simulation data of Kasagi et al.(3) and with the data of Manhart et al(4). , which use an Eulerian framework.

1) S.W. Churchill, A reinterpretation of the turbulent Prandtl number, Industrial and Engineering Chemistry Research 41 (2002), pp. 6393–6401.

2) P.M. Le, D.V. Papavassiliou, On temperature prediction at low Re turbulent flows using the Churchill turbulent heat flux correlation, International Journal of Heat and Mass Transfer, 49, (2006), pp. 3681-3690.

3) Kasagi, N., and Shikazono, N., 1995, “Contribution of Direct Numerical Simulation to Understanding and Modeling Turbulent Transport,” Proc. R. Soc. Londonm Ser A, 451, pp. 257-292.

4) F. Schwertfirm, M. Manhart, DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers, International Journal of Heat and Fluid Flow, (2007).