Angular multiscale statistics of turbulence in a porous bed
Résumé
Direct numerical simulation of pore-scale turbulence is performed in a unit cell of a face-centered cubic lattice at three different pore Reynolds numbers (300, 500, and 1000). The pore-geometry gives rise to very low porosity resulting in rapid acceleration and deceleration of the flow in different regions. Eulerian statistics of mean velocity and turbulent kinetic energy are first described to provide a good understanding of the overall flow topology. In addition, the spatial variances and probability density functions for the instantaneous and temporal fluctuation velocities are computed to assess the higher-order statistics. The flow field is then analyzed using angular Lagrangian multiscale statistics of fluid particles to study their directional change at different timescales. Two power laws are observed for the evolution of the mean absolute angle as a function of time lag, demarking the early time and an intermediate, inertial range. The effect of the geometric confinement on the asymptotic behavior of the angular statistics is examined in detail. An asymptotic limit different than π/2 (corresponding to equidistribution of the mean angle, observed for three-dimensional isotropic turbulence with periodic boundaries) or 2 3 π (observed for two-dimensional wall-bounded turbulence) is obtained, representing the strong effect of geometric confinement on turbulence. Besides, the probability density functions (PDFs) for the instantaneous curvature angles are computed and the normalized PDFs are fit to a Fisher distribution. Furthermore, a Monte Carlo-based stochastic model is developed to predict the asymptotic curvature angle.
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