[Paper Review] Multiple-relaxation-time lattice Boltzmann model for convection heat transfer in porous media under local thermal non-equilibrium condition

Q. Liu, Yaling He|arXiv (Cornell University)|Aug 14, 2016

Lattice Boltzmann Simulation Studies49 references3 citations

TL;DR

This paper proposes a multiple-relaxation-time (MRT) lattice Boltzmann model for simulating convection heat transfer in porous media under local thermal non-equilibrium (LTNE) conditions. By employing three distribution functions—two for fluid and solid phase temperatures and one for velocity—along with source terms that account for thermal non-equilibrium and discrete lattice effects, the model achieves improved stability and accuracy over standard LB methods, as validated by numerical simulations showing excellent agreement with benchmark solutions.

ABSTRACT

In this paper, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for convection heat transfer in porous media under local thermal non-equilibrium (LTNE) condition. The model is constructed within the framework of the three-distribution-function approach: two temperature-based MRT-LB equations are proposed for the temperature fields of fluid and solid phases in addition to the MRT-LB equation of a density distribution function for the velocity field described by the generalized non-Darcy model. The thermal non-equilibrium effects are incorporated into the model by adding source terms into the temperature-based MRT-LB equations. Moreover, the discrete lattice effects are considered in the introduction of source terms into the temperature-based MRT-LB equations. The source terms accounting for the thermal non-equilibrium effects are simple and the model retains the inherent features of the standard LB method. Numerical results demonstrate that the proposed model can be served as an accurate and efficient numerical method for studying convection heat transfer in porous media under LTNE condition.

Motivation & Objective

• To develop a robust and accurate lattice Boltzmann method for modeling convection heat transfer in porous media under local thermal non-equilibrium (LTNE) conditions.
• To overcome limitations of single-relaxation-time (SRT) models in handling complex thermal coupling and anisotropic diffusion in porous media.
• To incorporate thermal non-equilibrium effects through physically meaningful source terms in the MRT framework.
• To ensure the model preserves the inherent advantages of the lattice Boltzmann method, such as simplicity and efficiency, while maintaining numerical stability.
• To validate the model against analytical and benchmark solutions for various flow and thermal configurations.

Proposed method

• The model uses a three-distribution-function approach: one for velocity (based on the generalized non-Darcy model), and two for the temperature fields of fluid and solid phases.
• Multiple-relaxation-time (MRT) collision schemes are applied to the velocity and temperature distribution functions to enhance numerical stability and reduce viscosity-dependent artifacts.
• Source terms are introduced into the temperature-based MRT-LB equations to model thermal non-equilibrium between fluid and solid phases.
• The source terms are derived to account for interphase heat transfer and are adjusted to include discrete lattice effects for improved accuracy.
• The model is constructed to be consistent with the underlying partial differential equations of the LTNE system, ensuring second-order accuracy in space.
• Boundary conditions are implemented using a bounce-back scheme with appropriate treatment for temperature and velocity at solid-fluid interfaces.

Experimental results

Research questions

• RQ1 Can an MRT lattice Boltzmann model accurately simulate convection heat transfer in porous media under local thermal non-equilibrium conditions?
• RQ2 How do source terms accounting for thermal non-equilibrium and lattice discretization effects influence model stability and accuracy?
• RQ3 Does the proposed MRT model outperform standard SRT-LB models in simulating complex thermal flows in porous media?
• RQ4 To what extent does the model reproduce benchmark solutions for natural convection in porous enclosures under LTNE?
• RQ5 How does the model handle varying thermal conductivity ratios and interphase heat transfer coefficients?

Key findings

• The proposed MRT-LB model demonstrates excellent agreement with analytical and benchmark numerical solutions for natural convection in a porous cavity under LTNE conditions.
• The model achieves second-order spatial accuracy, as confirmed by convergence rate analysis across multiple test cases.
• Incorporating source terms that account for both thermal non-equilibrium and discrete lattice effects significantly improves numerical stability and reduces spurious currents.
• The model successfully captures the temperature difference between fluid and solid phases, confirming the presence of LTNE, especially at high interphase heat transfer coefficients.
• The MRT formulation reduces the dependency on relaxation parameters and enhances stability compared to SRT-LB models, particularly in high-contrast thermal conductivity scenarios.
• Numerical results show that the model can efficiently simulate complex thermal flows with minimal numerical diffusion and high resolution of thermal gradients.