Direct Numerical Simulation of Turbulent Flow in a Porous, Face-centered Cubic Unit Cell

Abstract:

Turbulent flows through packed beds and porous media are encountered in a number
of natural and engineered systems, however our general understanding of moderate and
high Reynolds number flows is limited to mostly empirical and macroscale relationships.
In this work the porescale flow physics, which are important to properties such as bulk
mixing performance and permeability, are investigated using Direct Numeric Simulation
(DNS) of flow through a periodic face centered cubic (FCC) unit cell at pore Reynolds
number of 300, 500 and 1000.The simulations are performed using a fictitious domain
approach [Apte et al, J. Comp. Physics 2009], which uses non-body conformal Cartesian
grids, with resolution up to D/\Delta=250 (354^3 cells total). Early transition to turbulence
is obtained for the low porosity arrangement of packed beads involving rapid expansions,
contractions, as well as flow impingement on bead surfaces. The data are used to
calculate the distribution and budget of turbulent kinetic energy and energy spectra.
Turbulent kinetic energy is found to be large over the entire pore region. The structure
of turbulence along different path lines is characterized by using the Lumley triangle,
and it is observed that high production regions are characterized by rod-like turbulence
structures. Eulerian and Lagrangian correlations are obtained to find the integral length
and time scales. The integral length scales are found to be less than 10% of the bead
diameter for all Reynolds numbers. The Lagrangian time-scales are also estimated using
the Eulerian correlations based on the Tennekes and Lumley model (Tennekes and
Lumley, 1972) to evaluate the effectiveness of the model. Finally, the data obtained
is used to test the effectiveness and applicability of the standard two-equation
turbulence closure models based on the gradient diffusion hypothesis.