Robert S. Bernard

Boundary conditions for the lattice Boltzmann method

When the Lattice Boltzmann Method (LBM) is used for simulating continuum fluid flow, the discrete mass distribution must satisfy imposed constraints for density and momentum along the boundaries of the lattice. These constraints uniquely determine the three‐dimensional (3‐D) mass distribution for boundary nodes only when the number of external (inward‐pointing) lattice links does not exceed four. We propose supplementary rules for computing the boundary distribution where the number of external links does exceed four, which is the case for all except simple rectangular lattices. Results obtained with 3‐D body‐centered‐cubic lattices are presented for Poiseuille flow, porous‐plate Couette flow, pipe flow, and rectangular duct flow. The accuracy of the two‐dimensional (2‐D) Poiseuille and Couette flows persists even when the mean free path between collisions is large, but that of the 3‐D duct flow deteriorates markedly when the mean free path exceeds the lattice spacing. Accuracy in general decreases with K...

Simulation of flow through bead packs using the lattice Boltzmann method

The lattice Boltzmann method (LBM) is used to simulate viscous fluid flow through a column of glass beads. The results suggest that the normalized velocity distribution is sensitive to the spatial resolution but not the details of the packing. With increasing spatial resolution, simulation results converge to a velocity distribution with a sharp peak near zero. A simple argument is presented to explain this result. Changes in the shape of the distribution as a function of flow rate are determined for low Reynolds numbers, and the large-velocity tail of the distribution is shown to depend on the packing geometry. The effect of a finite Reynolds number on the apparent permeability is demonstrated and discussed in relation to previous results in the literature. Comparison with velocity distributions from NMR (nuclear magnetic resonance) spectroscopy finds qualitative agreement after adjusting for diffusion effects in the NMR distributions.

Pore-scale simulation of dispersion

Tracer dispersion has been simulated in three-dimensional models of regular and random sphere packings for a range of Peclet numbers. A random-walk particle-tracking (PT) method was used to simulate tracer movement within pore-scale flow fields computed with the lattice-Boltzmann (LB) method. The simulation results illustrate the time evolution of dispersion, and they corroborate a number of theoretical and empirical results for the scaling of asymptotic longitudinal and transverse dispersion with Peclet number. Comparisons with nuclear magnetic resonance (NMR) spectroscopy experiments show agreement on transient, as well as asymptotic, dispersion rates. These results support both NMR findings that longitudinal dispersion rates are significantly lower than reported in earlier experimental literature, as well as the fact that asymptotic rates are observed in relatively short times by techniques that employ a uniform initial distribution of tracers, like NMR.

Hydrodynamic dispersion in confined packed beds

Pore-scale simulations of monodisperse sphere packing and fluid flow in cylinders have reproduced heterogeneities in packing density and velocity previously observed in experiment. Simulations of tracer dispersion demonstrate that these heterogeneities enhance hydrodynamic dispersion, and that the degree of enhancement is related to the cylinder radius, R. The time scale for asymptotic dispersion in a packed cylinder is proportional to R2/DT, where DT represents an average rate of spreading transverse to the direction of flow. A generalization of the Taylor–Aris model of dispersion in a tube provides qualitative predictions of the long-time dispersion behavior in packed cylinders.

Pore-Scale Flow and Dispersion

Pore-scale simulations of fluid flow and mass transport offer a direct means to reproduce and verify laboratory measurements in porous media. We have compared lattice-Boltzmann (LB) flow simulations with the results of NMR spectroscopy from several published flow experiments. Although there is qualitative agreement, the differences highlight numerical and experimental issues, including the rate of spatial convergence, and the effect of signal attenuation near solid surfaces. For the range of Reynolds numbers relevant to groundwater investigations, the normalized distribution of fluid velocities in random sphere packings collapse onto a single curve, when scaled with the mean velocity. Random-walk particle simulations in the LB flow fields have also been performed to study the dispersion of an ideal tracer. These simulations show an encouraging degree of quantitative agreement with published NMR measurements of hydrodynamic and molecular dispersion, and the simulated dispersivities scale in accordance with published experimental and theoretical results for the Peclet number rangek 1 ≤Pe≤1500. Experience with the random-walk method indicates that the mean properties of conservative transport, such as the first and second moments of the particle displacement distribution, can be estimated with a number of particles comparable to the spatial discretization of the velocity field. However, the accurate approximation of local concentrations, at a resolution comparable to that of the velocity field, requires significantly more particles. This requirement presents a significant computational burden and hence a numerical challenge to the simulation of non-conservative transport processes.

A simple computational model for bubble plumes

Abstract A simple approximation is proposed for the buoyant force in a bubble plume. Assuming a uniform radius and slip velocity for the entire bubble column, an expression is derived for the vertical acceleration of liquid in the column, which is directly proportional to the injected gas flow-rate and inversely proportional to depth and velocity. This bubble-induced acceleration has been implemented with a k – ϵ turbulence model in a three-dimensional, single-phase computational fluid dynamics (CFD) code, whose numerical predictions indicate that the velocity outside the plume is relatively insensitive to the column radius and the bubble slip velocity. Using a median observed value of 25 cm/s for the bubble slip velocity, and a column radius given by an empirical formula based on the work of Cedarwall and Ditmars, the model renders predictions for velocity that compare favorably with experimental data taken outside single and double plumes in water. Predicted velocity increases in less-than-linear fashion with the gas flow-rate, and the flow-rate exponent approaches 1/2 in the lower limit, and 1/3 in the upper limit. In the range of flow-rates (200–22,000 cm 3 /s) for which the model is validated herein, the exponent is roughly 2/5.

Accuracy of the Lattice-Boltzmann Method

The accuracy of the lattice-Boltzmann method (LBM) is moderated by several factors, including Mach number, spatial resolution, boundary conditions, and the lattice mean free path. Results obtained with 3D lattices suggest that the accuracy of certain two-dimensional (2D) flows, such as Poiseuille and Couette flow, persist even when the mean free path between collisions is large, but that of the 3D duct flow deteriorates markedly when the mean free path exceeds the lattice spacing. Accuracy in general decreases with Knudsen number and Mach number, and the product of these two quantities is a useful index for the applicability of LBM to 3D low-Reynolds-number flow. The influence of boundary representations on LBM accuracy is captured by the proposed index, when the accuracy of the prescribed boundary conditions is consistent with that of LBM.

Airflow Simulation over a Vegetated Soil Surface

The performance of infrared sensors under various meteorological and soil-surface conditions is a perennial concern for remote characterization of local environments. To aid in the testing and improvement of these sensors, computational fluid dynamics (CFD) models can provide realistic simulations of ambient airflow and temperature conditions. High CFD grid resolution is generally required for capturing the physical properties of a given region of interest, which may contain rocks, bushes, grasses, and other vegetation. In this study, the PAR3D model is used to compute spatially variable wind speeds and air temperatures, which will be coupled (in future work) with surface heat-exchange functions in ground-water and vegetation models. The resulting soil, rock, and vegetation temperatures can then be used to compute infrared images for these features, and the synthetic images can ultimately be used to test sensor performance. Thus, the eventual aim of the airflow, heat-transfer, and infrared computations is the production of high-resolution, synthetic infrared imagery for realistic surface environments.