Use of direct numerical simulation to study the effect of Prandtl number on temperature fields

The influence of Prandtl number on statistical parameters characterizing tu rbulent transport and the spatial variation of the mean-square of the tempe rature fluctuations, <(theta(2))over bar>, is described. The system conside red is fully developed flow in a channel for which the bottom wall is heate d and the top wall is cooled. Results from direct numerical solutions of th e Euler balance equations for Pr = 0.3, 1, 3, 10 and Lagrangian studies, in a DNS, of the dispersion of heat markers from wall sources for Pr = 0.1-24 00 are used. The Eulerian results for Pr = 10 are new and of particular int erest. A time scale se can be defined from the dissipation of k(theta) = <( theta(2))over bar>/2, as tau(theta) = k(theta)/epsilon(theta). This is anal ogous to the time scale defined from the dissipation of turbulent kinetic e nergy, tau = k/epsilon. Prandtl number is found to strongly affect rb and t he correlation, <(u(i)theta)over bar>/<(u(i)(2))over bar>(1/2)<(theta(2))ov er bar>(1/2). These results can be understood by recognizing that the spect ral density function for temperature fluctuations extends over an increasin gly larger range of wavenumbers as Pr increases. The observed effect of Pr on tau(theta), suggests fundamental problems in developing relations for th e turbulent diffusivity by a k(theta)tau tau(theta) approach analogous to t he k tau approach used to describe momentum transport. The use of a gradien t transport model to represent the turbulent transport of k(theta) also has fundamental problems. (C) 1999 Elsevier Science Inc. All rights reserved.