Validation and verification of a 2D lattice Boltzmann solver for incompressible fluid flow

The lattice Boltzmann method (LBM) is becoming increasingly popular in the fluid mechanics society because it provides a relatively easy implementation for an incompressible fluid flow solver. Furthermore the particle based LBM can be applied in microscale flows where the continuum based Navier-Stokes solvers fail. Here we present the validation and verification of a two-dimensional in-house lattice Boltzmann solver with two different collision models, namely the BGKW and the MRT models [1]. Five different cases were studied, namely: (i) a channel flow was investigated, the results were compared to the analytical solution, and the convergence properties of the collision models were determined; (ii) the lid-driven cavity problem was examined [2] and the flow features and the velocity profiles were compared to existing simulation results at three different Reynolds number; (iii) the flow in a backward-facing step geometry was validated against experimental data [3]; (iv) the flow in a sudden expansion geometry was compared to experimental data at two different Reynolds numbers [4]; and finally (v) the flow around a cylinder was studied at higher Reynolds number in the turbulent regime. The first four test cases showed that both the BGKW and the MRT models were capable of giving qualitatively and quantitatively good results for these laminar flow cases. The simulations around a cylinder highlighted that the BGKW model becomes unstable for high Reynolds numbers but the MRT model still remains suitable to capture the turbulent von Karman vortex street. The in-house LBM code has been developed in C and has also been parallelised for GPU architectures using CUDA [5] and for CPU architectures using the Partitioned Global Address Space model with UPC [6

Validation and verification of a 2D lattice Boltzmann solver for incompressible fluid flow

The lattice Boltzmann method (LBM) is becoming increasingly popular in the fluid mechanics society because it provides a relatively easy implementation for an incompressible fluid flow solver. Furthermore the particle based LBM can be applied in microscale flows where the continuum based Navier-Stokes solvers fail. Here we present the validation and verification of a two-dimensional in-house lattice Boltzmann solver with two different collision models, namely the BGKW and the MRT models [1]. Five different cases were studied, namely: (i) a channel flow was investigated, the results were compared to the analytical solution, and the convergence properties of the collision models were determined; (ii) the lid-driven cavity problem was examined [2] and the flow features and the velocity profiles were compared to existing simulation results at three different Reynolds number; (iii) the flow in a backward-facing step geometry was validated against experimental data [3]; (iv) the flow in a sudden expansion geometry was compared to experimental data at two different Reynolds numbers [4]; and finally (v) the flow around a cylinder was studied at higher Reynolds number in the turbulent regime. The first four test cases showed that both the BGKW and the MRT models were capable of giving qualitatively and quantitatively good results for these laminar flow cases. The simulations around a cylinder highlighted that the BGKW model becomes unstable for high Reynolds numbers but the MRT model still remains suitable to capture the turbulent von Karman vortex street. The in-house LBM code has been developed in C and has also been parallelised for GPU architectures using CUDA [5] and for CPU architectures using the Partitioned Global Address Space model with UPC [6

Lattice Boltzmann based discrete simulation for gas-solid fluidization

Discrete particle simulation, a combined approach of computational fluid dynamics and discrete methods such as DEM (Discrete Element Method), DSMC (Direct Simulation Monte Carlo), SPH (Smoothed Particle Hydrodynamics), PIC (Particle-In-Cell), etc., is becoming a practical tool for exploring lab-scale gas-solid systems owing to the fast development of parallel computation. However, gas-solid coupling and the corresponding fluid flow solver remain immature. In this work, we propose a modified lattice Boltzmann approach to consider the effect of both the local solid volume fraction and the local relative velocity between particles and fluid, which is different from the traditional volume-averaged Navier-Stokes equations. A time-driven hard sphere algorithm is combined to simulate the motion of individual particles, in which particles interact with each other via hard-sphere collisions, the collision detection and motion of particles are performed at constant time intervals. The EMMS (energy minimization multi-scale) drag is coupled with the lattice Boltzmann based discrete particle simulation to improve the accuracy. Two typical fluidization processes, namely, a single bubble injection at incipient fluidization and particle clustering in a fast fluidized bed riser, are simulated with this approach, with the results showing a good agreement with published correlations and experimental data. The capability of the approach to capture more detailed and intrinsic characteristics of particle-fluid systems is demonstrated. The method can also be used straightforward with other solid phase solvers.Comment: 15 pages, 11 figures, 2 tables. In Chemical Engineering Science, 201

An Investigation of the Lattice Boltzmann Method for Large Eddy Simulation of Complex Turbulent Separated Flow

Lattice Boltzmann method (LBM) is a relatively recent computational technique for fluid dynamics that derives its basis from a mesoscopic physics involving particle motion. While the approach has been studied for different types of fluid flow problems, its application to eddy-capturing simulations of building block complex turbulent flows of engineering interest has not yet received sufficient attention. In particular, there is a need to investigate its ability to compute turbulent flow involving separation and reattachment. Thus, in this work, large eddy simulation (LES) of turbulent flow over a backward facing step, a canonical benchmark problem which is characterized by complex flow features, is performed using the LBM. Multiple relaxation time formulation of the LBM is considered to maintain enhanced numerical stability in a locally refined, conservative multiblock gridding strategy, which allows efficient implementation. Dynamic procedure is used to adapt the proportionality constant in the Smagorinsky eddy viscosity subgrid scale model with the local features of the flow. With a suitable reconstruction procedure to represent inflow turbulence, computation is carried out for a Reynolds number of 5100 based on the maximum inlet velocity and step height and an expansion ratio of 1.2. It is found that various turbulence statistics, among other flow features, in both the recirculation and reattachment regions are in good agreement with direct numerical simulation and experimental data

TURBULENT TRANSITION SIMULATION AND PARTICULATE CAPTURE MODELING WITH AN INCOMPRESSIBLE LATTICE BOLTZMANN METHOD

Derivation of an unambiguous incompressible form of the lattice Boltzmann equation is pursued in this dissertation. Further, parallelized implementation in developing application areas is researched. In order to achieve a unique incompressible form which clarifies the algorithm implementation, appropriate ansatzes are utilized. Through the Chapman-Enskog expansion, the exact incompressible Navier-Stokes equations are recovered. In initial studies, fundamental 2D and 3D canonical simulations are used to evaluate the validity and application, and test the required boundary condition modifications. Several unique advantages over the standard equation and alternative forms found in literature are found, including faster convergence, greater stability, and higher fidelity for relevant flows. Direct numerical simulation and large eddy simulation of transitional and chaotic flows are one application area explored with the derived incompressible form. A multiple relaxation time derivation is performed and implemented in a 2D cavity (direct simulation) and a 3D cavity (large eddy simulation). The Kolmogorov length scale, a function of Reynolds number, determines grid resolution in the 2D case. Comparison is made to the extensive literature on laminar flows and the Hopf bifurcation, and final transition to chaos is predicted. Steady and statistical properties in all cases are in good agreement with literature. In the 3D case the relatively new Vreman subgrid model provides eddy viscosity modeling. By comparing the center plane to the direct numerical simulation case, both steady and unsteady flows are found to be in good agreement, with a coarse grid, including prediction of the Hopf bifurcation. Multiphysics pore scale flow is the other main application researched here. In order to provide the substrate geometry, a straightforward algorithm is developed to generate random blockages producing realistic porosities and passages. Combined with advection-diffusion equations for conjugate heat transfer and soot particle transport, critical diesel particulate filtration phenomena are simulated. To introduce additional fidelity, a model is added which accounts for deposition caused by a variety of molecular and atomic forces. Detailed conclusions are presented to lay the groundwork for future extensions and improvements. Predominantly, higher lattice velocity large eddy simulation, improved parallelization, and filter regeneration

Lattice Boltzmann Methods for Wind Energy Analysis

An estimate of the United States wind potential conducted in 2011 found that the energy available at an altitude of 80 meters is approximately triple the wind energy available 50 meters above ground. In 2012, 43% of all new electricity generation installed in the U.S. (13.1 GW) came from wind power. The majority of this power, 79%, comes from large utility scale turbines that are being manufactured at unprecedented sizes. Existing wind plants operate with a capacity factor of only approximately 30%. Measurements have shown that the turbulent wake of a turbine persists for many rotor diameters, inducing increased vibration and wear on downwind turbines. Power losses can be as high as 20-30% in operating wind plants, due solely to complex wake interactions occurring in wind plant arrays. It is my objective to accurately predict the generation and interaction of turbine wakes and their interaction with downwind turbines and topology by means of numerical simulation with high-performance parallel computer systems. Numerical simulation is already utilized to plan wind plant layouts. However, available computational tools employ severe geometric simplifications to model wake interactions and are geared to providing rough estimates on desktop PCs. A three dimensional simulation tool designed for modern parallel computers based upon lattice Boltzmann methods for fluid-dynamics, a general six-degree-of-freedom motion solver, and foundational beam solvers has been proposed to meet this simulation need. In this text, the software development, verification, and validation are detailed. Fundamental computational fluid dynamics issues of boundary conditions and turbulence modeling are examined through classic cases (Cavity, Jeffery-Hammel, Kelvin-Helmholtz, Pressure wave, Vorticity wave, Backward facing step, Cylinder in cross-flow, Airfoils, Tandem cylinders, and Turbulent flow over a hill) to asses the accuracy and computational cost of developed alternatives. Simulations of canonical motion (falling beam), fluid-structure-interaction cases (Hinged wing and Flexible pendulum), and realistic horizontal axis wind turbine geometries (Vestas v27, NREL 5MW, and MEXICO) are validated against benchmarks and experiments. Results from simulations of the three turbine array at the Scaled Wind Farm Test facility are presented for two steady wind conditions

Development of a multiblock solver utilizing the lattice Boltzmann and traditional finite difference methods for fluid flow problems

This dissertation develops the lattice Boltzmann method (LBM) as a strong alternative to traditional numerical methods for solving incompressible fluid flow problems. The LBM outperforms traditional methods on a standalone basis for certain problem cases while for other cases it can be coupled with the traditional methods using domain decomposition. This brings about a composite numerical scheme which associates the efficient numerical attributes of each individual method in the composite scheme with a particular region in the flow domain. Coupled lattice Boltzmann-traditional finite difference procedures are developed and evaluated for CPU time reduction and accuracy of standard test cases. The standard test cases are numerical solutions of the two-dimensional unsteady and steady convection-diffusion equations and two-dimensional steady laminar incompressible flows represented by the backward-facing step flow problem and the flow problem around a cylinder. Multiblock Cartesian grids and hybrid Cartesian-cylindrical grid systems are employed with the composite numerical scheme. A cache-optimized lattice Boltzmann technique is developed to utilize the full computational strength of the LBM. The LBM is an explicit time-marching method and therefore has a time step size limitation. The time step size is limited by the grid spacing and the Mach number. A lattice Boltzmann simulation necessarily requires a low Mach number since it relates to the incompressible Navier-Stokes equations in the low Mach number limit. For steady state problems, the smaller time step results in slow convergence. To improve the time step limitation imposed by the grid spacing, an improved LBM that adopts a new numerical discretization for the advection term has been developed and the results were computed for a convection-diffusion equation and compared with the original LBM. The performance of traditional finite difference methods based on the alternating direction implicit scheme for the convection-diffusion equation and the vorticity-stream function method for the laminar incompressible flow problems is evaluated against the composite numerical scheme. The composite numerical scheme is shown to take lesser CPU time for solving the given benchmark problems