G.H. Tang

LATTICE BOLTZMANN METHOD FOR SIMULATING GAS FLOW IN MICROCHANNELS

Isothermal gas flows in microchannels is studied using the lattice Boltzmann method. A novel equation relating Knudsen number with relaxation time is derived. The slip-velocity on the solid boundaries is reasonably realized by combining the bounce-back reflection with specular reflection in a certain proportion. Predicted characteristics in a two-dimensional microchannel flow, including slip-velocity, nonlinear pressure drop, friction factors, velocity distribution along the streamwise direction and mass flow rate, are compared with available analytical and experimental results and good agreement is achieved.

Improved axisymmetric lattice Boltzmann scheme.

This paper proposes an improved lattice Boltzmann scheme for incompressible axisymmetric flows. The scheme has the following features. First, it is still within the framework of the standard lattice Boltzmann method using the single-particle density distribution function and consistent with the philosophy of the lattice Boltzmann method. Second, the source term of the scheme is simple and contains no velocity gradient terms. Owing to this feature, the scheme is easy to implement. In addition, the singularity problem at the axis can be appropriately handled without affecting an important advantage of the lattice Boltzmann method: the easy treatment of boundary conditions. The scheme is tested by simulating Hagen-Poiseuille flow, three-dimensional Womersley flow, Wheeler benchmark problem in crystal growth, and lid-driven rotational flow in cylindrical cavities. It is found that the numerical results agree well with the analytical solutions and/or the results reported in previous studies.

IMPLICIT-EXPLICIT FINITE-DIFFERENCE LATTICE BOLTZMANN METHOD FOR COMPRESSIBLE FLOWS

We propose an implicit-explicit finite-difference lattice Boltzmann method for compressible flows in this work. The implicit-explicit Runge–Kutta scheme, which solves the relaxation term of the discrete velocity Boltzmann equation implicitly and other terms explicitly, is adopted for the time discretization. Owing to the characteristic of the collision invariants in the lattice Boltzmann method, the implicitness can be completely eliminated, and thus no iteration is needed in practice. In this fashion, problems (no matter stiff or not) can be integrated quickly with large Courant–Friedriche–Lewy numbers. As a result, with our implicit-explicit finite-difference scheme the computational convergence rate can be significantly improved compared with previous finite-difference and standard lattice Boltzmann methods. Numerical simulations of the Riemann problem, Taylor vortex flow, Couette flow, and oscillatory compressible flows with shock waves show that our implicit-explicit finite-difference lattice Boltzmann method is accurate and efficient. In addition, it is demonstrated that with the proposed scheme non-uniform meshes can also be implemented with ease.

Electroosmotic flow and mixing in microchannels with the lattice Boltzmann method

Understanding the electroosmotic flow in microchannels is of both fundamental and practical significance for the design and optimization of various microfluidic devices to control fluid motion. In this paper, a lattice Boltzmann equation, which recovers the nonlinear Poisson-Boltzmann equation, is used to solve the electric potential distribution in the electrolytes, and another lattice Boltzmann equation, which recovers the Navier-Stokes equation including the external force term, is used to solve the velocity fields. The method is validated by the electric potential distribution in the electrolytes and the pressure driven pulsating flow. Steady-state and pulsating electroosmotic flows in two-dimensional parallel uniform and nonuniform charged microchannels are studied with this lattice Boltzmann method. The simulation results show that the heterogeneous surface potential distribution and the electroosmotic pulsating flow can induce chaotic advection and thus enhance the mixing in microfluidic systems ef...

SIMULATION OF FLUID FLOW AND HEAT TRANSFER IN A PLANE CHANNEL USING THE LATTICE BOLTZMANN METHOD

Forced convective flow and heat transfer between two parallel plates are studied using the lattice Boltzmann method (LBM) in this paper. Three kinds of thermal boundary conditions at the top and bottom plates are studied. The velocity field is simulated using density distribution function while a separate internal energy distribution function is introduced to simulate the temperature field. The results agree well with data from traditional finite volume method (FVM) and analytical solutions. The present work indicates that LBM may be developed as a promising method for predicting convective heat transfer because of its many inherent advantages.

Lattice Boltzmann model for axisymmetric thermal flows.

A thermal lattice Boltzmann (LB) model is presented for axisymmetric thermal flows in the incompressible limit. The model is based on the double-distribution-function LB method, which has attracted much attention since its emergence for its excellent numerical stability over the multispeed LB method. Compared with the existing axisymmetric thermal LB models, the present model is simpler and retains the inherent features of the standard LB method. Numerical simulations are carried out for the thermally developing laminar flows in circular ducts and the natural convection in an annulus between two coaxial vertical cylinders. The Nusselt number obtained from the simulations agrees well with the analytical solutions and/or the results reported in previous studies.

Three-dimensional lattice Boltzmann model for gaseous flow in rectangular microducts and microscale porous media

Microscale fluid dynamics has received intensive interest due to the rapid advances in microelectromechanical systems. In this work, the lattice Boltzmann method is applied to simulate isothermal gaseous slip flow in three-dimensional (3D) rectangular microducts and microscale porous structures. The flow characteristics in 3D microducts—including velocity profile, nonlinear pressure distribution, friction factor, and mass flow rate—are compared with analytical solutions, and the agreement is good. The flow-rate results show that due to the slip-velocity emergence at the walls, the lateral wall influence on the flow rate in 3D rectangular microducts is decreased. The predicted transport characteristics in 3D microscale porous media show that the rarefaction influence increases the gas permeability. The Klinkenberg effect is confirmed and the predicted gas permeability is qualitatively consistent with the experimental results. Furthermore, the nonlinear behavior of the porous flow at relatively higher Reynolds number is also observed. This study demonstrates that the lattice Boltzmann method can be employed to efficiently predict transport characteristics in microducts and microscale porous media.

Experimental observations and lattice Boltzmann method study of the electroviscous effect for liquid flow in microchannels

The existing experimental data in the literature on hydrodynamics for liquid flow in microchannels are analyzed and the reasons causing the diversities are discussed and summarized. The present experimental data for deionized water flow in glass microtubes with diameters ranging from 50 to 530 µm show that the friction factors and transition Reynolds numbers from laminar to turbulent flow are in good agreement with the conventional theoretical predictions. However, the friction factors in stainless steel microtubes with diameters of 119 and 172 µm are much higher than the conventional theoretical predictions. This discrepancy is attributed to the large surface relative roughness or dense roughness distribution in the stainless steel tubes. Numerical simulations taking into account the electroviscous effect are carried out by using the lattice Boltzmann method. The simulation results show that the electroviscous effect does not play a significant role in the flow characteristics for channel dimensions of the order of microns and hence it can be neglected in engineering applications for moderate electrical conductivity of the liquid and conductivity of the walls. From the literature review and the present test data, it is validated that for liquid flow in smooth microchannels the conventional theoretical prediction for flow characteristics should still be applied.

Thermal conduction in nano-porous silicon thin film

Controlling the thermal conductivity of thermoelectric materials continues to be a goal for energy conversion applications. The Phonon Boltzmann Transport Equation is solved by using the Discrete Ordinates Method to numerically study the phonon thermal conductivity of nano-structured silicon thin film with pores in this study. The effects of the film thickness, film porosity, and porous structure are concerned. The numerical results show that the nano-pores are able to reduce the thermal conductivity of the silicon thin film sharply by the phonon boundary scattering, and the scattering boundary area has significant effect on the thermal conductivity. The method of local angle distribution between heat fluxes is introduced for the first time to optimize the pore placement for reducing the thermal conductivity.

Phonon boundary scattering effect on thermal conductivity of thin films

In the study, we introduced the local mean free path of phonons with boundary effects. The local thermal conductivity distribution from boundary to film bulk region was obtained, and the boundary scattering effect was examined by introducing a phonon Knudsen layer thickness. We calculated the ratio of effective thermal conductivity to the bulk one and the results are in agreement with available data.