Determination of turbulent thermal diffusivities for flow of liquids in pipes

Abstract

Eddy thermal diffusivities as a function of radial position and Reynolds number were determined for turbulent flow of water in a tube with a constant wall heat flux. The temperature and velocity profiles were measured, and the eddy thermal diffusivities were calculated by solving the energy balance equation using a semi-numerical technique. Also, the eddy momentum diffusivities were determined so that analogies between heat and momentum transport could be tested. The eddy thermal and momentum diffusivities as a function of radial position were found to reach a maximum value at a position about midway between the center and the wall of the tube The eddy thermal diffusivities were correlated with Reynolds number and radial position. The turbulent Prandtl number was found to vary with radial position from a value less than unity at the center to a value greater than unity at the wall. These results agree with previous mass transfer work and with theoretical models. The space-averaged thermal and momentum diffusivities were found to be roughly linear in Reynolds number. Also, the space-averaged turbulent Prandtl number decreased with increasing Reynolds number approaching the value of unity. The ratio of the average flow velocity and space-averaged thermal diffusivity, expressed inmore » terms of a Peclet number, was found to decrease slightly with Reynolds number. The momentum and thermal position Peclet numbers both varied similarly with position Reynolds number. Both position numbers increased near the wall, increasing faster than values given by correlations which have been previously proposed for eddy momentum diffusivities. A comparison of the thermal and momentum diffusivity results with mass diffusivity results indicates that molecular properties of the fluid have an important influence on the turbulent properties. (auth)« less