Statistical features of heat transfer in grid-generated turbulence: constant-gradient case

Abstract

Turbulence produced by a grid which simultaneously imparts a mean temperature profile varying linearly with height was investigated in a specially constructed wind tunnel. While the mean temperature profile is preserved downstream of the grid in accordance with the theory of Corrsin (1952), the downstream evolution of the r.m.s. temperature fluctuation is at variance with his prediction. The reason for this discrepancy is shown to lie in the neglect of molecular diffusivity, which leads to unbounded growth of the fluctuations. Along with conventional correlations and spectra, the filtered heat-transfer correlation is presented. About 60% of the heat transport is accomplished by the low wavenumber components having length scales equal to or larger than the integral scale. An intriguing feature of the present experiments is the presence of an inertial-convective subrange for the temperature field notwithstanding the low Reynolds number and the consequent absence of an inertial subrange for the velocity field. Experimental results show that the temperature has a positive skewness everywhere in contrast to the velocity components, which are symmetrically distributed. Measurements of the joint probability density function of the vertical component of the velocity and the temperature indicate that, while the assumption of joint normality is not uniformly valid, the conditional expectations nearly follow the normal law. Marginal and joint moments of up to fourth order are presented. Odd-order joint moments are clearly sensitive to the skewness of the temperature.