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

Simulating flows with moving rigid boundary using immersed-boundary method

Boundary conditions for thermal lattice Boltzmann equation method

Lattice Boltzmann methods for single-phase and solid-liquid phase-change heat transfer in porous media: A review

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.

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Consistent 2D and 3D thermal boundary conditions for thermal lattice Boltzmann simulations are proposed. The boundary unknown energy distribution functions are made functions of known energy distribution functions and correctors, where the correctors at the boundary nodes are obtained directly from the definition of internal energy density. This boundary condition can be easily implemented on the wall and corner boundary using the same formulation. The discrete macroscopic energy equation is also derived for a steady and fully developed channel flow to assess the effect of the boundary condition on the solutions, where the resulting second order accurate central difference equation predicts continuous energy distribution across the boundary, provided the boundary unknown energy distribution functions satisfy the macroscopic energy level. Four different local known energy distribution functions are experimented with to assess both this observation and the applicability of the present formulation, and are scrutinized by calculating the 2D thermal Poiseuille flow, thermal Couette flow, thermal Couette flow with wall injection, natural convection in a square cavity, and 3D thermal Poiseuille flow in a square duct. Numerical simulations indicate that the present formulation is second order accurate and the difference of adopting different local known energy distribution functions is, as expected, negligible, which are consistent with the results from the derived discrete macroscopic energy equation.

Thermal boundary conditions for thermal lattice Boltzmann simulations

Boundary conditions of lattice Boltzmann method to simulate flows embedded with a solid object is proposed. The closest nodes adjacent to the boundary in the fluid domain are used as boundary nodes of the flow domain. The fluid velocity of the boundary node is obtained by linear interpolation between the velocities of the solid object and the second fluid node further away. Then, distribution functions originating from the solid domain at the boundary nodes are modified using known distribution functions and correctors to satisfy the momentum. This boundary condition is an extended form of a method proposed by Hou et al. [C.F. Hou, C. Chang, C.A. Lin, Consistent boundary conditions for 2D and 3D Lattice Boltzmann simulations (submitted for publication)] for plane wall and regular geometry. The technique is examined by simulating decaying vortex, transient flow induced by an abruptly rotating ring and flow over an asymmetrically placed cylinder. Numerical simulations indicate that this method is second order accurate, and all the numerical results are compatible with the benchmark solutions.

Chih-Hao Liu

Papers

Thermal boundary conditions for thermal lattice Boltzmann simulations

Boundary conditions for lattice Boltzmann simulations with complex geometry flows