Abstract:
Porous media flows are encountered in many natural and man-made systems such as gas adsorption, filtration, heat exchangers, combustion, catalytic reactors and groundwater hydrology. This study experimentally investigates these flows as function of pore Reynolds number, Re[subscript pore]. The pore Reynolds number is based on the porous bed hydraulic diameter, D[subscript H] =φD[subscript Β]/(1−φ) where φ is bed porosity and D[subscript B] is solid phase bead diameter and average bed interstitial velocity, V[subscript int]= V[subscript Darcy]/φ, where VDarcy= Q/A[subscript bed], with Q being the volumetric flow rate and A[subscript bed] the bed cross section normal to the flow. The flow characteristics are studied through application of a particle displacement technique called particle image velocimetry, PIV. In the case of PIV, flow fields are estimated by seeding the flow with tracer particles and then evaluating their displacements.
Application of quantitative imaging technique such as PIV to a complex flow domain like porous bed requires matching refractive index of liquid phase to that of the solid phase.
Firstly, the effect of slight index mismatch, due to experimental uncertainties, on obtaining highly accurate PIV measurements as expressed as an experimental uncertainty was explored. Mismatch of refractive indices leads to error in estimation of particle positions and their displacements due to refraction at solid-liquid interfaces. Slight mismatch, in order of 10⁻³, in refractive indices also leads to reduction in particle density, particle signal peak intensity and degrade the particle image. These effects on velocity field estimation using PIV is studied experimentally and numerically. The numerical model, after validating against experimental results, is used to generate an expression for the error in PIV measurements as a function of refractive index mismatch for a range of bead diameters, bed widths, bed porosity, and optical magnification.
After refractive index matching, planar PIV measurements were taken at discrete locations throughout a randomly packed bed with aspect ratio (bed width to bead diameter) of 4.67 for steady, low pore Reynolds number flows, Re[subscript pore] ~ 6, intermediate Re[subscript pore] of 54 and unsteady flow with high Re[subscript pore] ranging from 400-4000. Details of the measurement uncertainties as well as methods to determine local magnification and determination of the dynamic velocity range are presented. The data are analyzed using the PIV correlation averaging method for steady flows and multigrid and multipass correlation methods for unsteady turbulent flows with the largest velocity uncertainties arising from in plane image loss and out of plane motion.
Results for low Re[subscript pore] flows show the correspondence of the geometric and velocity correlation functions across the bed, and that the centerline of the bed shows a random-like distribution of velocity with an integral length scale on the order of one hydraulic diameter (or 0.38 bead diameters based on the porosity for this bed). The velocity variance is shown to increase by a factor of 1.8 when comparing the center plane data versus using data across the entire bed. It is shown that the large velocity variance contributes strongly to increased dispersion estimates, and that based on the center plane data of the variance and integral length scales, the dispersion coefficient matches well with that measured in high aspect ratio beds using global data.
For unsteady and turbulent flow, velocity data were used to determine the following turbulence measures: (i) turbulent kinetic energy components, (ii) turbulent shear production rate, (iii) integral Eulerian length and time scales, and (iv) energy spectra all for a range of pore Reynolds numbers, Re[subscript pore], from 418 to 3964. These measures, when scaled with the bed hydraulic diameter, DH, and average interstitial velocity, V[subscript int], all collapse for Re[subscript pore], beyond approximately 2800, except that the integral scales collapse at a lower value near 1300-1800. The results show that the pore turbulence characteristics are remarkably similar from pore to pore and that scaling based on bed averaged variables like D[subscript H] and V[subscript int] characterizes their magnitudes despite very different local mean flow conditions.
In the case of high Re[subscript pore] flows, large scale structures such as stationary and convected vortices and structures resembling jets were also identified. These structures were analyzed in detail using decomposition techniques like Large Eddy Scale decomposition and critical point analysis like swirl strength analysis. Direct velocity measurements were used to estimate Lagrangian statistics through Eulerian measures and then estimate contribution of flow structures to turbulent mechanical dispersion. Results agree well with those in the literature obtained using global measurements in very high aspect ratio, long test beds. Stationary vortical or recirculation regions were seen to play a dominant role in contributing to overall dispersion in porous beds.