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Experimental investigation of turbulent characteristics in pore-scale regions of porous media

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Abstract

The study of flow dynamics in porous media or randomly packed beds is essential because these systems are commonly applied in a wide array of engineering applications, such as thermal energy storage, catalytic reactors for processing and distillation, oil recovery, fuel cells, and pebble bed nuclear reactor cores. The flow mixing and turbulence characteristics in pore-scale regions of an experimental facility composed of randomly packed spheres with an aspect ratio of 4.4 were experimentally investigated in this study. Velocity measurements at several pores in the test facility were conducted by combining the matched-index-of-refraction and time-resolved particle image velocimetry techniques, and these measurements were performed at Reynolds numbers of 490, 1023, and 1555. The results obtained from the velocity measurements in the pore regions revealed different and complex flow patterns depending on the pore geometries. In pore region 1, it was found that a strong axial flow entered the pore and impinged into the sphere’s surface when it encountered another flow entering laterally. These dynamic interactions created a high level of turbulent mixing, a recirculation flow region, and a shear layer, as observed in the computed statistical results for \(u^{\prime }_\mathrm{{rms}}\), \(v^{\prime }_\mathrm{{rms}}\), and \(u^{\prime }v^{\prime }\). In other pore regions, the flow field results exhibited complex interactions among jet flows discharging into the pores from various flow gaps created by neighboring spheres. These mutual interactions between the entering jet flows were found to create highly turbulent mixing regions at the pore’ centers and low-velocity or stagnation-flow regions in the vicinity of the sphere surfaces. Flapping shear layers were also observed when two jet flows with unequal strengths entered the pores. The characteristics of turbulent flow mixing in different pore regions were investigated via the spatiotemporal two-point correlation of fluctuating velocities along the velocity streamlines. This approach mitigated the constraints of the random geometries of pore regions on the extent of spatial separation lengths in the two-point velocity correlations. Using this approach, spatial distributions of integral length scales and convection velocities were estimated along the streamlines within the random geometries of pore regions. It was found that the estimated values of the integral length scales and convection velocities were spatially dependent on the localized flow characteristics within the pores. The integral length scales were found to be less than \(0.4D_\mathrm{{sp}}\), experimentally confirming the pore-scale prevalence hypothesis that turbulent structures in porous media are restricted by the pore sizes. In addition, the ratio of the convection velocity to the interstitial velocity (or local velocity magnitude) decreased as the Reynolds number increased.

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Abbreviations

\(\langle .\rangle \) :

Time-averaged operator

\(\epsilon _N\) :

Absolute difference between the statistics

\(\eta _\mathrm{s}\) :

Separation length along the streamline (mm)

\(\gamma \) :

Slope of the fitted straight line

\(\mu _\mathrm{{pcy}}\) :

Dynamic viscosity of p-cymene (\(\hbox {Pa} \times \hbox {s}\))

\(\nu _\mathrm{{pcy}}\) :

Kinematic viscosity of p-cymene (\(\hbox {m}^2\)/s)

\(\varOmega \) :

Vorticity (\(\hbox {s}^{-1}\))

\(\rho _\mathrm{{pcy}}\) :

Density of p-cymene (kg/\(\hbox {m}^{3}\))

\(\tau \) :

Time delay (s)

\(R_{uu0},R_{vv0}\) :

Velocity–velocity spatial correlation coefficients

\(R_{uu},R_{vv}\) :

Velocity–velocity spatial-temporal correlation coefficients

\(\mathrm{{Re}}\) :

Reynolds number

\(\epsilon _\mathrm{b}\) :

Porosity

\(^sL_u,^sL_v\) :

Integral length scales (mm)

\(A_\mathrm{{bed}}\) :

Total cross-sectional area of the bed (\(\hbox {m}^2\))

D :

Bed diameter (mm)

\(d_\mathrm{h}\) :

Effective hydraulic diameter (mm)

\(D_\mathrm{{sp}}\) :

Sphere diameter (mm)

f :

Sampling frequency (Hz)

N :

Number of samples

Q :

Volumetric flow rate (\(\hbox {m}^3\)/s)

U, V :

Horizontal and vertical time-averaged velocities (m/s)

\(u^{\prime },v^{\prime }\) :

Horizontal and vertical fluctuating velocities (m/s)

\(u^{\prime }_\mathrm{{rms}},v^{\prime }_\mathrm{{rms}}\) :

Horizontal and vertical root-mean-square fluctuating velocities (m/s)

\(u^{\prime }v^{\prime }\) :

Reynolds stress (\(\hbox {m}^2\)/\(\hbox {s}^2\))

\(U_\mathrm{c}\) :

Convection velocity vector (m/s)

\(u_i(t),v_i(t)\) :

Instantaneous horizontal and vertical velocities at point i (m/s)

\(U_{c,\mathrm{{mag}}}\) :

Convection velocity magnitude computed as \(U_{c,\mathrm{{mag}}}=\sqrt{U_{c-u}^{2}+U_{c-v}^{2}}\) (m/s)

\(U_{c-u},U_{c-v}\) :

Convection velocity components estimated using the two-point cross-correlations \(R_{uu}\) and \(R_{vv}\), respectively (m/s)

\(U_\mathrm{g}\) :

Superficial velocity (m/s)

\(U_\mathrm{{int}}\) :

Interstitial velocity (m/s)

\(U_\mathrm{{loc,mag}}\) :

Local velocity spatially averaged along the streamline (m/s)

\(U_\mathrm{m}\) :

Free stream velocity (m/s) considered in flows over bluff bodies

x, y :

Horizontal (traversal), vertical (axial) directions

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Acknowledgements

This research was partially funded by the U.S. Department of Energy, NEAMS project, under Contract No. DE-NE0008983. The authors also thank the support from the U.S. Argonne National Laboratory.

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  1. Thermal-Hydraulic Research Laboratory, Texas A&M University, College Station, TX, 77845, USA

    Thien Nguyen, Stephen King & Yassin Hassan

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  1. Thien Nguyen
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Nguyen, T., King, S. & Hassan, Y. Experimental investigation of turbulent characteristics in pore-scale regions of porous media. Exp Fluids 62, 72 (2021). https://doi.org/10.1007/s00348-021-03171-1

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