DIFFUSION IN TURBULENT PIPE-FLOW USING A STOCHASTIC-MODEL

A generalized Langevin equation developed by Haworth and Pope [Phys. F luids, 29-2 (1986), 387] is applied to calculate the dispersion of a p assive contaminant in turbulent pipe flow. The model coefficients in t he equation are determined from an algebraic relation based on the con sistency condition for the second-order moments oi velocity, which inc ludes the third-order moments. In the present model, the first- and se cond-order moments are used as input data, but the third-order moments are not inputted due to lack of reliable data. First, we confirmed nu merically the consistency condition for a simulated velocity field. Se cond, the long-time diffusion mras examined. The Eulerian velocity sta tistics show good agreement with the prescribed data up to second orde r. With regard to long-time diffusion, the longitudinal distributions of a cross-sectional mean concentration agree well with experiments. I I is also found that the appropriate value for the Kolmogorov constant C-0 is 1.9 for this problem.