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Turbulent flows in porous media occur in a wide variety of applications, from catalysis in packed beds to heat exchange in nuclear reactor vessels. In this review, we summarize the current state of the literature on methods to model such flows. We focus on a range of Reynolds numbers, covering the inertial regime through the asymptotic turbulent regime. The review emphasizes both numerical modeling and the development of averaged (spatially filtered) balances over representative volumes of media. For modeling the pore scale, we examine the recent literature on Reynolds-averaged Navier–Stokes (RANS) models, large-eddy simulation (LES) models, and direct numerical simulations (DNS). We focus on the role of DNS and discuss how spatially averaged models might be closed using data computed from DNS simulations. A Darcy–Forchheimer-type law is derived, and a prior computation of the permeability and Forchheimer coefficient is presented and compared with existing data.
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Download Supplemental Appendix (PDF).
Supplemental Video 1: Animation illustrating the dynamics of a vortex in a single pore (extracted from the random packing illustrated in Figure 3 of the manuscript) for Rep=676. The stream ribbons represent the (tangent to the) instantaneous velocity. Ribbon color is the value of the second eigenvalue, λ2, of S2+Ω2.
Supplemental Video 2: Animation illustrating a set of two counter-rotating vortecies in a single pore (extracted from the random packing illustrated in Figure 3 of the manuscript) for Rep=676. The stream ribbons represent the (tangent to the) instantaneous velocity. Ribbon color is proportional to the pressure (where red is high and blue is low).
Supplemental Video 3: Animation illustrating the large scale motions captured from PIV experiments (described in section 2.2.2 and Figure 4) for Rep=510. The vectors indicate the local velocity field, where length is proportional to velocity. The color scale indicates the local vorticity magnitude. These values were found by applying and LES filter; in this case, averaging was accomplished using a spatial top-hat filter with dimensions dp/10 in each direction.
Supplemental Video 4: Animation illustrating the small scale motions (residuals) captured from PIV experiments (described in section 2.2.2 and Figure 4) for Rep=510. The vectors indicate the local deviation velocity field, where length is proportional to velocity. The color scale indicates the local deviation of the vorticity magnitude. Deviations were computed by subtracting the LES-filtered velocity values from the instantaneous measured velocity values.
Supplemental Video 5: Animation illustrating the large scale motions captured from PIV experiments (described in section 2.2.2 and Figure 4) for Rep=1612. The vectors indicate the local velocity field, where length is proportional to velocity. The color scale indicates the local vorticity magnitude. These values were found by applying and LES filter; in this case, averaging was accomplished using a spatial top-hat filter with dimensions dp/10 in each direction.
Supplemental Video 6: Animation illustrating the small scale motions (residuals) captured from PIV experiments (described in section 2.2.2 and Figure 4) for Rep=1612. The vectors indicate the local deviation velocity field, where length is proportional to velocity. The color scale indicates the local deviation of the vorticity magnitude. Deviations were computed by subtracting the LES-filtered velocity values from the instantaneous measured velocity values.
Supplemental Video 7: Animation illustrating the large scale motions captured from PIV experiments (described in section 2.2.2 and Figure 4) for Rep=4834. The vectors indicate the local velocity field, where length is proportional to velocity. The color scale indicates the local vorticity magnitude. These values were found by applying and LES filter; in this case, averaging was accomplished using a spatial top-hat filter with dimensions dp/10 in each direction.
Supplemental Video 8: Animation illustrating the small scale motions (residuals) captured from PIV experiments (described in section 2.2.2 and Figure 4) for Rep=4834. The vectors indicate the local deviation velocity field, where length is proportional to velocity. The color scale indicates the local deviation of the vorticity magnitude. Deviations were computed by subtracting the LES-filtered velocity values from the instantaneous measured velocity values.