Multiscale Lagrangian Statistics of Curvature Angle in Pore-Scale Turbulence

Porescale turbulent flow physics are investigated using Direct Numeric Simulation (DNS) of flow through a periodic face centered cubic (FCC) unit cell at Reynolds numbers of 300, 500 and 1000. The simulations are performed using a fictitious domain approach [Apte et al, J. Comp. Physics 2009], which uses non-body conforming Cartesian grids. Lagrangian statistics of scale dependent curvature angle and acceleration are calculated by tracking a large number of fluid particle trajectories. For isotropic turbulence, it has been shown [Bos et al. 2015, PRL] that the mean curvature angle varies linearly with time initially, reaches an inertial range and asymptotes to a value of $\pi/2$ at long times, corresponding to the decorrelation and equipartition of the cosine of the curvature angle. Similar trends are observed at early times for turbulence in porous medium; however, the mean curvature angle asymptotes to a value larger than $\pi/2$, due to the effect of confinement on the fluid particle trajectories that result in preferred directions at large times. A Monte-Carlo based stochastic model to predict the long-time behavior of curvature angles is developed and shown to correctly predicts an angle larger than $\pi/2$ at large times.