On the performance of the moment approximation for the numerical computation of fiber stress in turbulent channel flow

Abstract

Fiber-induced drag reduction can be studied in great detail by means of direct numerical simulation [J. S. Paschkewitz et al., J. Fluid Mech. 518, 281 (2004)]. To account for the effect of the fibers, the Navier-Stokes equations are supplemented by the fiber stress tensor, which depends on the distribution function of fiber orientation angles. We have computed this function in turbulent channel flow, by solving the Fokker-Planck equation numerically. The results are used to validate an approximate method for calculating fiber stress, in which the second moment of the orientation distribution is solved. Since the moment evolution equations contain higher-order moments, a closure relation is required to obtain as many equations as unknowns. We investigate the performance of the eigenvalue-based optimal fitted closure scheme [J. S. Cintra and C. L. Tucker, J. Rheol. 39, 1095 (1995)]. The closure-predicted stress and flow statistics in two-way coupled simulations are within 10% of the “exact” Fokker-Planck solution.