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 the input data, but the third order moments are not specified due to the lack of reliable data. First, we checked on the consistency condition for the simulated velocity field. Second, the long time dispersion was examined. The Eulerian velocity statistics show good agreement with the specified data to the second order. With regard to long time dispersion, the longitudinal distributions of a cross-sectional mean concentration agree well with experiments. It is also found that the proper value of the Kolmogorov constant C0 is 1.9 for this problem.
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