Mesoscopic Methods in Engineering and Science

(First paragraph) Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the macroscopic dynamics is usually insensitive to the details of the underlying microscopic interactions

Thermal lattice boltzmann simulation of diffusion/ forced convection using a double mrt model

The Lattice-Boltzmann method (LBM) is an alternative and flexible approach for computational fluid dynamics (CFD). Unlike many other direct numerical simulation (DNS) techniques, LBM is not solving the Navier-Stokes equations but is based on the kinetic theory and the discrete Boltzmann equation. LBM utilizes a Cartesian mesh and hence does not require a complex mesh derivation or a re-meshing in case of moving boundaries. Thermal LBM (TLBM) which is capable of solving thermal convection/diffusion problems relies on a set of two distribution functions, the so called double distribution function (DDF) approach; one for the fluid density and one for the internal energy. For the carried out numerical investigations a 3D TLBM framework is derived involving a multiple-relaxation-time (MRT) collision operator for both, the fluid and the temperature field which is yet not applied widely. Hydrodynamic and thermal boundary conditions are represented by interpolated bounce back schemes. The derived TLBM framework is applied to diffusion and convection-diffusion problems (e.g. forced convection) for plane and curved boundaries and is validated against analytical solutions, when available or compared to established correlations. The thermal MRT operator is further compared against an existing LBM model based on a thermal Bhatnagar-Gross-Krook (BGK) operator regarding accuracy and numerical stability. Averaged and local heat transfer coefficients are presented. The findings indicate that the double MRT framework with interpolated boundary conditions offers a highly accurate and efficient approach for the analysis of heat transfer problems especially for particle/fluid systems under detailed resolved flow

Development of the Single-Relaxation-Time Lattice Boltzmann Method for Application to Thermal Fluid Flows

This work investigates the single-relaxation-time Lattice Boltzmann Method and how to develop it into a full hydrodynamic and thermal modeling scheme. First the single-relaxation time isothermal Lattice Boltzmann Method is outlined, beginning with the fundamentals of the lattice model and then proceeding through the necessary governingequations for the two-dimensional, nine-directional lattice. The governing equations are then presented in a discretized form to be used for simulation, followed by treatment ofboundary conditions. Fluid and dimensional properties are explained in terms of both lattice units and physical units via conversion factors. Next is an introduction to thermalLattice Boltzmann, discussing the changes as well as going through new governing equations pertaining to the internal energy density distribution function. Then the thermalscheme is shown in discretized form along with thermal boundary conditions and updated hydrodynamic boundary conditions. Fluid properties are reviewed alongside thermal properties, as they are essential to know when designing a simulation. Finally, results are shown for some two-dimensional channel flow geometries with hot and cold surfaces: a uniform-width channel, a channel that undergoes sudden expansion, and a channel featuring sudden contraction. The flow within the channel could be dominated by the density stratification or the forced flow introduced at the inlet. These mixed flows of natural and forced convection are characterized by the Reynolds and Rayleigh numbers, the Rayleigh numbers above critical value to allow for formation of natural convection 2 cells when experiencing low-Reynolds flows. The results are presented as contour plots of temperature and stream function

Gas Seperation through Hollow Fiber and Spiral Wound Membranes

Computational fluid dynamics simulations are conducted for multicomponent fluid flows over banks of hollow fiber membranes. The hollow fiber membrane systems is considered here for gas separation applications. Separation of carbon dioxide (CO2) from methane (CH4) is studied using hollow fiber membranes packed in different arrangements. The membrane surface is considered as a functional surface where the mass flux and concentration of each species are coupled and are determined as a function of the local partial pressures, the permeability, and the selectivity of the membrane. k-ω Shear Stress Transport (k-ω SST) turbulent model is employed to study the mixture flow over banks of hollow fiber membrane for values of the Reynolds number up to 1000. The flow structure around the hollow fiber membranes dominates the performance of the separation process. This study demonstrates clearly that good mixing in the bank of hollow fiber membranes enhances the separation performance. The results show that hollow fiber membrane module with staggered arrangement performs much better than that with inline arrangement. For the spiral wound membrane, it has been shown that membrane performance could be greatly enhanced by momentum mixing in the feed channel induced by spacers. Square shaped spacer will be considered in the inline arrangement for values of the Reynolds number up to 500. In order to validate the turbulence model transient flow simulations are conducted using lattice Boltzmann method. The lattice Boltzmann method to simulate flow in the geometries related to the spiral wound membrane modules is developed by our research group at Lehigh. Two dimensional nine velocity directional, D2Q9, lattice arrangement with multi-relaxation time (MRT) lattice Boltzmann method is used to simulate transient flow field while single relaxation time (SRT) lattice Boltzmann method. Simulations are performed to determine concentration field for values of Re up to 300. The bounding surfaces are treated as impermeable walls for simulations conducted using the lattice Boltzmann method. The results predicted by the lattice Boltzmann method and the SST turbulence model agree well, validating the turbulence model and the numerical method

Lattice Boltzmann Modelling of Fluid Flow through Porous Media. A Comparison between Pore-Structure and Representative Elementary Volume Methods

In this study, we present a novel comparison between pore-structure (PS) and representative elementary volume (REV) methods for modelling fluid flow through porous media using a second-order lattice Boltzmann method (LBM). We employ the LBM to demonstrate the importance of the configuration of square obstacles in the PS method and compare the PS and the REV methods. This research provides new insights into fluid flow through porous media as a novel study. The behaviour of fluid flow through porous media has important applications in various engineering structures. The aim of this study is to compare two methods for simulating porous media: the PS method, which resolves the details of the solid matrix, and the REV method, which treats the porous medium as a continuum. Our research methodology involves using different arrangements of square obstacles in a channel including in-line, staggered and random for the PS method and a porosity factor and permeability value for the REV method. We found that the porosity and obstacle arrangement have significant effects on the pressure drop, permeability and flow patterns in the porous region. While the REV method cannot simulate the details of fluid flow through pore structures compared to the PS method, it is able to provide a better understanding of the flow field details around obstacles (Tortuosity). This study has important applications in improving our understanding of transport phenomena in porous media. Our results can be useful for designing and optimizing various engineering systems involving porous media

The Lattice Boltzmann Methods and Their Applications to Fluid Flows

The history of the Lattice Boltzmann Method and its application to fluid mechanics are investigated here. Detailed formulations are provided to form a basis for the Lattice Boltzmann Method and its many variations. These variations are designed to overcome shortcomings in the standard single relaxation time Lattice Boltzmann model. Presented here are: a model that utilizes the non-equilibrium parts of the stress tensor, the Regularized Lattice Boltzmann model; a model that converts over to momentum space, the Multi-Relaxation Time Lattice Boltzmann model; and a model that corrects itself using the entropy equation, the entropic Lattice Boltzmann model. Extensions for the Lattice Boltzmann method are derived that include: external forces, multiphase flows, and thermal flows. Various types of boundary conditions are modeled using different approaches. A detailed explanation on extracting common macroscopic flow properties in physical units is provided. These extracted properties can be used to check temporal and spatial convergence. A two dimensional, nine velocity model and a three dimensional, fifteen velocity model are used to provide examples of a number of the approaches mentioned. A two dimensional and three dimensional lid-driven cavity flow is used to illustrate these methods

A Ghost Fluid Approach for Thermal Lattice Boltzmann Method in Dealing with Heat Flux Boundary Condition in Thermal Problems with Complex Geometries

In this paper, the ghost fluid thermal lattice Boltzmann method is improved to properly impose the heat flux boundary condition on complex geometries [Khazaeli, R., S. Mortazavi and M. Ashrafizaadeh (2013). Application of a ghost fluid approach for a thermal lattice Boltzmann method, J. Comput. Phys. 250, 126– 140]. A double-population thermal lattice Boltzmann method is used to handle both the flow and temperature fields on a Cartesian grid and the boundary conditions are imposed using a ghost fluid method. The method is based on the decomposition of the unknown distribution functions into their equilibrium and non-equilibrium parts at every ghost point. The equilibrium parts are determined by performing an extrapolation of major quantities from the image points to the associated ghost points. The bounce-back scheme is then used to determine the non- equilibrium parts. The method benefits from some features such as easy implementation and second order accuracy. The method is applied to simulate natural convection within annuluses with different shapes and boundary conditions,. The obtained results are generally in a good agreement with those predicted by other numerical efforts

Application of an Immersed Boundary Treatment in Simulation of Natural Convection Problems with Complex Geometry via the Lattice Boltzmann Method

In this study, a version of thermal immersed boundary-Lattice Boltzmann method (TIB-LBM) is used to simulate thermal flow problems within complex geometries. The present approach is a combination of the immersed boundary method (IBM) and the thermal lattice Boltzmann method (TLBM) under the double population approach. The method combines two different grid systems, an Eulerian grid for the flow domain and a Lagrangian grid for the boundary points immersed in the flow. In the present method, an unknown velocity correction is considered on the boundary points to impose the no-slip boundary condition. As a similar approach, an unknown internal energy correction on the boundary points is applied to satisfy the constant temperature boundary condition. The advantages of this approach are its second-order accuracy and straightforward calculation of the Nusselt number. The natural convection in an annulus with various outer cylinder shapes for different Rayleigh numbers have been simulated to demonstrate the capability and the accuracy of present approach. In terms of accuracy, the predicted results show an excellent agreement with those predicted by other experimental and numerical approaches