Y. L. He

Lattice Boltzmann methods for multiphase flow and phase-change heat transfer

Over the past few decades, tremendous progress has been made in the development of particle-based discrete simulation methods versus the conventional continuum-based methods. In particular, the lattice Boltzmann (LB) method has evolved from a theoretical novelty to a ubiquitous, versatile and powerful computational methodology for both fundamental research and engineering applications. It is a kinetic-based mesoscopic approach that bridges the microscales and macroscales, which offers distinctive advantages in simulation fidelity and computational efficiency. Applications of the LB method have been found in a wide range of disciplines including physics, chemistry, materials, biomedicine and various branches of engineering. The present work provides a comprehensive review of the LB method for thermofluids and energy applications, focusing on multiphase flows, thermal flows and thermal multiphase flows with phase change. The review first covers the theoretical framework of the LB method, revealing the existing inconsistencies and defects as well as common features of multiphase and thermal LB models. Recent developments in improving the thermodynamic and hydrodynamic consistency, reducing the spurious currents, enhancing the numerical stability, etc., are highlighted. These efforts have put the LB method on a firmer theoretical foundation with enhanced LB models that can achieve larger liquid-gas density ratio, higher Reynolds number and flexible surface tension. Examples of applications are provided in fuel cells and batteries, droplet collision, boiling heat transfer and evaporation, and energy storage. Finally, further developments and future prospect of the LB method are outlined for thermofluids and energy applications.

Lattice Boltzmann modeling of boiling heat transfer: The boiling curve and the effects of wettability

A hybrid thermal lattice Boltzmann (LB) model is presented to simulate thermal multiphase flows with phase change based on an improved pseudopotential LB approach (Li et al., 2013). The present model does not suffer from the spurious term caused by the forcing-term effect, which was encountered in some previous thermal LB models for liquid–vapor phase change. Using the model, the liquid–vapor boiling process is simulated. The boiling curve together with the three boiling stages (nucleate boiling, transition boiling, and film boiling) is numerically reproduced in the LB community for the first time. The numerical results show that the basic features and the fundamental characteristics of boiling heat transfer are well captured, such as the severe fluctuation of transient heat flux in the transition boiling and the feature that the maximum heat transfer coefficient lies at a lower wall superheat than that of the maximum heat flux. Furthermore, the effects of the heating surface wettability on boiling heat transfer are investigated. It is found that an increase in contact angle promotes the onset of boiling but reduces the critical heat flux, and makes the boiling process enter into the film boiling regime at a lower wall superheat, which is consistent with the findings from experimental studies.

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.

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.

Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices.

In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal flows on the standard two-dimensional nine-velocity (D2Q9) lattice is developed in the framework of the double-distribution-function (DDF) approach in which the viscous heat dissipation and compression work are considered. In the model, a density distribution function is used to simulate the flow field, while a total energy distribution function is employed to simulate the temperature field. The discrete equilibrium density and total energy distribution functions are obtained from the Hermite expansions of the corresponding continuous equilibrium distribution functions. The pressure given by the equation of state of perfect gases is recovered in the macroscopic momentum and energy equations. The coupling between the momentum and energy transports makes the model applicable for general thermal flows such as non-Boussinesq flows, while the existing DDF LB models on standard lattices are usually limited to Boussinesq flows in which the temperature variation is small. Meanwhile, the simple structure and general features of the DDF LB approach are retained. The model is tested by numerical simulations of thermal Couette flow, attenuation-driven acoustic streaming, and natural convection in a square cavity with small and large temperature differences. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature.

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.

An Efficient Segregated Algorithm for Incompressible Fluid Flow and Heat Transfer Problems—IDEAL (Inner Doubly Iterative Efficient Algorithm for Linked Equations) Part II: Application Examples

In this article, comprehensive comparisons are made between the SIMPLER and IDEAL algorithms for four application examples. It is found that the IDEAL algorithm is efficient and stable not only for the simple, low-Re/Ra or coarse-mesh flow cases, but also for the complex, high-Re/Ra or fine-mesh flow cases. For the low-Re/Ra, coarse-mesh flow cases, the ratio of CPU time of IDEAL to that of SIMPLER ranges from 0.029 to 0.7. For the high-Re/Ra, fine-mesh flow cases, the IDEAL algorithm can obtain convergent results but the SIMPLER algorithm cannot, even though the underrelaxation factors are adjusted.

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.