Diffusion in Turbulent Pipe Flow Using a Stochastic Model.

Abstract

A generalized Langevin equation developed by Haworth and Pope [Phys. Fluids, 29-2 (1986), 387] is applied to calculate the dispersion of a passive contaminant in turbulent pipe flow. The model coefficients in the equation are determined from an algebraic relation based on the consistency condition for the second-order moments of velocity, which includes the third-order moments. In the present model, the first-and second-order moments are used as input data, but the third-order moments are not inputted due to lack of reliable data. First, we confirmed numerically the consistency condition for a simulated velocity field. Second, the long-time diffusion was examined. The Eulerian velocity statistics show good agreement with the prescribed data up to second order. With regard to long-time diffusion, the longitudinal distributions of a cross-sectional mean concentration agree well with experiments. It is also found that the appropriate value for the Kolmogorov constant Co is 1.9 for this problem.