Single Relaxation Time Research Articles

Viscoelastic Effects on the Response of Electroelastic Materials.

Electroelastic materials, as for example, 3M VHB 4910, are attracting attention as actuators or generators in some developments and applications. This is due to their capacity of being deformed when submitted to an electric field. Some models of their actuation are available, but recently, viscoelastic models have been proposed to give an account of the dissipative behaviour of these materials. Their response to an external mechanical or electrical force field implies a relaxation process towards a new state of thermodynamic equilibrium, which can be described by a relaxation time. However, it is well known that viscoelastic and dielectric materials, as for example, polymers, exhibit a distribution of relaxation times instead of a single relaxation time. In the present approach, a continuous distribution of relaxation times is proposed via the introduction of fractional derivatives of the stress and strain, which gives a better account of the material behaviour. The application of fractional derivatives is described and a comparison with former results is made. Then, a double generalisation is carried out: the first one is referred to the viscoelastic or dielectric models and is addressed to obtain a nonsymmetric spectrum of relaxation times, and the second one is the adoption of the more realistic Mooney–Rivlin equation for the stress–strain relationship of the elastomeric material. A modified Mooney–Rivlin model for the free energy density of a hyperelastic material, VHB 4910 has been used based on experimental results of previous authors. This last proposal ensures the appearance of the bifurcation phenomena which is analysed for equibiaxial dead loads; time-dependent bifurcation phenomena are predicted by the extended Mooney–Rivlin equations.

Development of a coupled simplified lattice Boltzmann method for thermal flows

The simplified lattice Boltzmann method (SLBM) is relatively new in the LBM community, which lowers the cost in virtual memories significantly and has better numerical stability compared with the single-relaxation-time (SRT) LBM. Recently, SLBM has been extended to simulate thermal flows based on the simplified thermal energy distribution function model. However, the existing thermal models developed for SLBM are not strict in theory. In this work, a coupled simplified lattice Boltzmann method (CSLBM) for thermal flows and its boundary treatment are proposed, where the Navier-Stokes equations for the hydrodynamic field and the convection-diffusion equation for the temperature field are solved independently by two sets of SLBM equations. The consistent forcing scheme is adopted to couple the contribution of the temperature field to the hydrodynamic field. The boundary treatment for temperature field proposed in this work offers an analytical interpretation of the no-slip boundary condition. To validate the accuracy, efficiency, and stability of the present CSLBM, several canonical test cases, including the porous plate problem, the Rayleigh-Bénard convection, and the natural convection in a square cavity are conducted. The numerical results agree well with the analytical solutions or numerical results in the literatures, which shows the present algorithm is of second-order accuracy in space and demonstrates the robustness of CSLBM in practical simulations.

Ultra-low lattice thermal conductivity and high thermoelectric efficiency in Cs2SnX6 (X=Br, I): A DFT study

High-performance thermoelectric materials provide an environmentally friendly route for future large-scale electricity production from waste heat recovery. In this work, we present an in-depth analysis of electronic, phononic, and thermoelectric properties of vacancy-ordered double perovskite Cs2SnX6 (X = Br, I) compounds based on generalized gradient approximations (GGA) and post-density functional theory treatments. We find that the optical phonon scattering mechanism plays a more critical role than the acoustical phonon and impurity scattering in both materials' transport properties. These materials also exhibit a relatively large Seebeck coefficient and ultra-low lattice thermal conductivity about 0.123/0.062 W/mK for Cs2SnBr6/Cs2SnI6 at room temperature calculated by single relaxation time model (SMRT). Such ultra-low lattice thermal conductivity arises from significant phonon-phonon scattering due to highly overlapped acoustic and optical phonon branches around ~1 THz. This occurrence introduces the Cs atom's rattling motion inside [SnX6]2- (X = Br, I) cages. The most considerable ZT values with the SMRT method at 300/500 K are about 0.32/0.82 for Cs2SnBr6 and 0.9/1.96 for Cs2SnI6. Our theoretical results suggest that both compounds have a great potential to be good candidates for thermoelectric materials and can be used to guide experimental investigation to obtain the optimal ZT performance.

In-Plane Liquid Electrolyte Permeability of Porous Electrode in Vanadium Redox Flow Battery

Vanadium redox flow batteries (VRFBs) have received broad recognition due to their attractive characteristics, i.e., flexibility and scalability, high coulombic efficiency, and long cycle life. However, rapid market penetration of this technology is still restrained by high system capital cost and relatively low energy and power density compared to other energy storage technologies. At the cell level, mass transport contributes significantly to performance losses, limiting VRFB performance, especially for cells operating at high power densities [1]. Improving mass transport in the VRFB electrodes can lower system cost by enabling higher power densities and larger depth of discharge windows. In these systems, convective mass transport in the electrode is directly proportional to the electrochemical performance of the cell [2]. Permeability and diffusivity of the vanadium active species are also significant mass transport parameters affecting electrochemical performance [3]. In this study, the in-plane electrolyte permeability of the porous electrode is investigated computationally and experimentally as a function of electrode compression.Lattice Boltzmann models (LBMs) are a class of numerical methods which can be used to simulate fluid flows, mass transfer, heat transfer and many relevant physical phenomena which occur in these fields. The implementation of boundary conditions combined with the ease of parallelization make LBMs attractive for modeling mass transfer in geometrically complex domains such as porous media. A three-dimensional single-relaxation-time (SRT) LBM is employed (utilizing the Palabos library written in C++) to simulate the liquid electrolyte in the porous electrode [4]. Pressure-driven flow in porous media is achieved by imposing a constant pressure at the inlet and a constant lower pressure at the outlet. A computational domain (100 x 100 x 100 lattice unit) created within Python (Porespy module) [5] consists of randomly-generated fibers, having uniform diameter to simulate the carbon paper electrode pore structure as seen in Figure 1. Porosity of the unit structure is achieved by controlling the number of fibers in the domain. Permeability parameters are calculated for generated pore structures as functions of the electrode porosity.The in-plane electrolyte permeability of porous electrodes was measured to compare with computational predictions. The sample electrode was placed between two plates as shown in Figure 2. Various electrode thicknesses were tested using an incompressible PTFE gasket. The end plates were secured by eight bolts to a torque of 10 N m each to ensure uniform compression and tight sealing. The electrode thickness during compression was converted to porosity to compare experimental measurements with mathematical model predictions [6]. The inlet pressure was measured via pressure transducer (Omega Engineering Inc, 0-50 psi, 0.25% accuracy, Norwalk, CT, USA) for a range of flow rates from 10 mL min-1 up to 50 mL min-1 at each electrode thickness. The permeability was then calculated using Darcy’s law for incompressible fluid flow.Good agreement was achieved between experimental measurements and computational predictions. The result of this study will provide useful data for three-dimensional multi-physics VRFB models. References Ertugrul, T. Y., Clement, J. T., Gandomi, Y. A., Aaron, D. S., and Mench, M. M. “In-Situ Current Distribution and Mass Transport Analysis via Strip Cell Architecture for a Vanadium Redox Flow Battery” Journal of Power Sources 437, (2019): 226920. doi:10.1016/j.jpowsour.2019.226920Ertugrul, T. Y., Daugherty, M. C., Houser, J. R., Aaron, D. S., and Mench, M. M. “Computational and Experimental Study of Convection in a Vanadium Redox Flow Battery Strip Cell Architecture” Energies 13, no. 18 (2020): 4767. doi:10.3390/en13184767Ertugrul, T. Y., Daugherty, M., Aaron, D., and Mench, M. M. “Vanadium Flow Battery Electrochemistry and Fluid Dynamics Model with In-Situ Current Distribution Validation” ECS Meeting s MA2020-01, no. 3 (2020): 473–473. doi:10.1149/ma2020-013473mtgabsChopard, J. L. and O. M. and D. K. and A. P. and D. L. and F. B. and M. B. B. and Y. T. and S. L. and S. L. and F. M. and J. L. and C. K. “Palabos: Parallel Lattice Boltzmann Solver” Computers & Mathematics with Applications no. 0898–1221 (2020): doi:https://doi.org/10.1016/j.camwa.2020.03.022Gostick J, Khan ZA, Tranter TG, Kok MDR, Agnaou M, Sadeghi MA, J. R. “A Python Toolkit for Quantitative Analysis of Porous Media Images. Journal of Open Source Software” (2019): doi:10.5281/zenodo.2633284Mench, M. M. “Fuel Cell Engines” Fuel Cell Engines (2008): doi:10.1002/9780470209769 Figure 1

Convective Boundary Conditions Effect on Cylindrical Media with Transient Heat Transfer

Lattice Boltzmann method is used to solve inside a cylindrical cavity with convective boundary condition is highlighted in this paper. Because of its simple, stable, accurate, efficient and ease for parallelization, we use the thermal Single Relaxation Time Bhatnagar Gross Krook (SRT BGK) mesoscopic approach in order to solve the energy equation. Thermal fields are simulated using D2Q9 scheme. We introduce and demonstrate numerically some usual cases (Dirichlet, Newmann) of Boundary conditions (Bcs). After validation, we extend the present work to the convective case. At the wall of the cavity, the unknown Thermal Distribution Functions (TDF) are exposed to the bounce back concept which is determined consistently by one of the imposed BCs. An in-house Fortran 90 code is used to analyze a variety of BCs inside a two-dimensional cavity. In validation, obtained results highlight a good agreement with literature. The present study is extended to deal with convective boundary condition for conduction transfer problems inside an axisymmetric cylindrical media subjected to heat generation and Newman boundary conditions.

Algorithmic augmentation in the pseudopotential-based lattice Boltzmann method for simulating the pool boiling phenomenon with high-density ratio.

The pseudopotential-based lattice Boltzmann method (LBM), despite enormous potential in facilitating natural development and migration of interfaces during multiphase simulation, remains restricted to low-density ratios, owing to inherent thermodynamic inconsistency. The present paper focuses on augmenting the basic algorithm by enhancing the isotropy of the discrete equation and thermodynamic consistency of the overall formulation, to expedite simulation of pool boiling at higher-density ratios. Accordingly, modification is suggested in the discrete form of the updated interparticle interaction term, by expanding the discretization to the eighth order. The proposed amendment is successful in substantially reducing the spurious velocity in the vicinity of a static droplet, while allowing stable simulation at a much higher-density ratio under identical conditions, which is a noteworthy improvement over existing Single Relaxation Time (SRT)-LBM algorithms. Various pool boiling scenarios have been explored for a reduced temperature of 0.75, which itself is significantly lower than reported in comparable literature, in both rectangular and cylindrical domains, and also with micro- and distributed heaters. All three regimes of pool boiling have aptly been captured with both plain and structured heaters, allowing the development of the boiling curve. The predicted value of critical heat flux for the plain heater agrees with Zuber correlation within 10%, illustrating both quantitative and qualitative capability of the proposed algorithm.

Linear viscoelastic properties of adhesive soft particle glasses

A model is presented to predict the linear viscoelastic rheology of hydrophobically modified adhesive soft particle glasses in an aqueous solution. The hydrophobes on the surfaces of particles in contact preferentially associate with each other, creating an adhesive force between particles. The extent of this adhesive force depends on the number of associating or physically bonded hydrophobes and the strain on the bonds. The model is first presented for two horizontal surfaces with hydrophobes attached to them. The force required for oscillatory movement between these adhesive surfaces exhibits a Maxwellian behavior with a single relaxation time that is about the time for hydrophobe dissociation. The model is extended to predict the storage and loss moduli of adhesive soft particle glasses in ordered cubic lattices. In addition to the adhesive force, the particles also exhibit repulsive elastic and elastohydrodynamic interparticle forces. For situations where there is no adhesive force between particles, the storage modulus is independent of frequency, and the loss modulus is a linear function of frequency. The storage and loss moduli as functions of frequency are richer with adhesive forces. The storage modulus exhibits two plateaus, one at low and one at high frequency. The loss modulus exhibits a local maximum in frequency that occurs at approximately the dissociation rate of the hydrophobes.

Extended lattice Boltzmann model for gas dynamics

We propose a two-population lattice Boltzmann model on standard lattices for the simulation of compressible flows. The model is fully on-lattice and uses the single relaxation time Bhatnagar–Gross–Krook kinetic equations along with appropriate correction terms to recover the Navier–Stokes–Fourier equations. The accuracy and performance of the model are analyzed through simulations of compressible benchmark cases including Sod shock tube, sound generation in shock–vortex interaction, and compressible decaying turbulence in a box with eddy shocklets. It is demonstrated that the present model provides an accurate representation of compressible flows, even in the presence of turbulence and shock waves.

Equivalent finite difference and partial differential equations for the lattice Boltzmann method

A general method for the derivation of equivalent finite difference equations (EFDEs) and subsequent equivalent partial differential equations (EPDEs) is presented for a general matrix lattice Boltzmann method (LBM). The method can be used for both the advection diffusion equations and Navier–Stokes equations in all dimensions.In principle, the EFDEs are derived using a recurrence formula. A computational algorithm is proposed for generating sequences of matrices and vectors that are used to obtain EFDEs coefficients. For all DdQq velocity models, the algorithm is proven to be finite and all coefficients are obtained after q iterations. The resulting EFDEs and EPDEs are derived for selected velocity models and include the single relaxation time, multiple relaxation times, and cascaded LBM collision operators.The algorithm for the derivation of EFDEs and EPDEs is implemented in C++ using the GiNaC library for symbolic algebraic computations. Its implementation is available under the terms and conditions of the GNU general public license (GPL).

Effects of finite thickness on crack propagation in viscoelastic materials

Crack propagation in viscoelastic materials is a problem of considerable importance, now relatively well understood after early paradoxical results have been addressed with the use of cohesive models. However, finite size effects have received limited theoretical attention so far. Here, following suggestions of Persson (2017), we derive simple results for a crack propagating in a finite size specimen for a model of a single relaxation time material (but extension to many relaxation times is trivial). We show results for the maximum velocity above which the crack may become unstable and the toughness enhancement reduction with respect to that of the infinite system, which corresponds to the ratio of instantaneous to relaxed elastic moduli. Agreement with the literature is dubious, since de Gennes (1996) predicts instability but same amplification as the infinite system, whereas a more recent theory of Persson (2021) suggests same amplification of that of the infinite system, but without instability. A clarification of these qualitative differences is hoped for the future.

Gray Phonon Transport Prediction of Thermal Conductivity in Lithium Aluminate with Higher-Order Finite Elements on Meshes with Curved Surfaces

We present a method for predicting thermal conductivity by deterministically solving the Boltzmann transport equation for gray phonons by utilizing arbitrary higher-order continuous finite elements on meshes which may also be unstructured and utilize curved surfaces. The self-adjoint angular flux (SAAF) formulation of the gray, steady-state, single relaxation time, phonon radiative transport (PRT) equation was spatially discretized using the continuous finite element method and angularly discretized using the discrete ordinates method. The solution discretization methodology was verified using a method of manufactured solution (MMS) spatial convergence test case and compared favorably to previous work. The angular phonon radiances, heat flux, and temperatures computed in this work compare favorably to previous literature in silicon thin films. Using local values of the temperature gradient and heat flux, the thermal conductivity as a function of position in a one-dimensional perfect crystal was evaluated using a Fourier’s Law representation and compared to kinetic theory. Our results show that in the interior of the simulation domain, our transport-based prediction of thermal conductivity converged on the kinetic theory estimation. We also find that near isothermal boundaries, the transport solution deviated from kinetic theory, implying non-equilibrium behavior in the thin-film limit and agreed with previous studies.

Numerical analysis of mixed convection heat transfer and laminar flow in a rectangular inclined micro-channel totally filled with Water/Al2O3 Nano fluid

A numerical analysis was carried out of mixed convection heat transfer for a laminar flow in a rectangular inclined microchannel totally filled with a water/Al2O3 nanofluid. The governing conservation equations are translated into a dimensionless form using the thermal single relaxation time and they modify the lattice Boltzmann method with double distribution functions. The viscous dissipation effects are adapted to the energy equation. The effects of nanoparticle volume fractions ϕ (0 ≤ ϕ ≤ 0.04) and inclination angles γ (0° ≤ γ ≤ 60°) on the flow of the nanofluid and the heat transfer are investigated. The obtained results are presented in terms of streamlines, isotherms, slip velocity, wall temperature and Nusselt number. The results show that the higher values of the volume fraction of Al2O3 and the large values of inclination angles improve the heat transfer rate.

Fluid Viscoelasticity Triggers Fast Transitions of a Brownian Particle in a Double Well Optical Potential.

Thermally activated transitions are ubiquitous in nature, occurring in complex environments which are typically conceived as ideal viscous fluids. We report the first direct observations of a Brownian bead transiting between the wells of a bistable optical potential in a viscoelastic fluid with a single long relaxation time. We precisely characterize both the potential and the fluid, thus enabling a neat comparison between our experimental results and a theoretical model based on the generalized Langevin equation. Our findings reveal a drastic amplification of the transition rates compared to those in a Newtonian fluid, stemming from the relaxation of the fluid during the particle crossing events.

Central moments multiple relaxation time LBM for hemodynamic simulations in intracranial aneurysms: An in-vitro validation study using PIV and PC-MRI

The lattice Boltzmann method (LBM) has recently emerged as an efficient alternative to classical Navier-Stokes solvers. This is particularly true for hemodynamics in complex geometries. However, in its most basic formulation, i.e. with the so-called single relaxation time (SRT) collision operator, it has been observed to have a limited stability domain in the Courant/Fourier space, strongly constraining the minimum time-step and grid size. The development of improved collision models such as the multiple relaxation time (MRT) operator in central moments space has tremendously widened the stability domain, while allowing to overcome a number of other well-documented artifacts, therefore opening the door for simulations over a wider range of grid and time-step sizes. The present work focuses on implementing and validating a specific collision operator, the central Hermite moments multiple relaxation time model with the full expansion of the equilibrium distribution function, to simulate blood flows in intracranial aneurysms. The study further proceeds with a validation of the numerical model through different test-cases and against experimental measurements obtained via stereoscopic particle image velocimetry (PIV) and phase-contrast magnetic resonance imaging (PC-MRI). For a patient-specific aneurysm both PIV and PC-MRI agree fairly well with the simulation. Finally, low-resolution simulations were shown to be able to capture blood flow information with sufficient accuracy, as demonstrated through both qualitative and quantitative analysis of the flow field while leading to strongly reduced computation times. For instance in the case of the patient-specific configuration, increasing the grid-size by a factor of two led to a reduction of computation time by a factor of 14 with very good similarity indices still ranging from 0.83 to 0.88.

A non-uniform stretched mesh scheme for non-dimensional lattice Boltzmann simulations of natural convective flow and heat transfer

To increase the flexibility of the non-dimensional lattice Boltzmann method (NDLBM), a non-uniform stretched mesh scheme was developed for coupled flow and heat transfer simulations. Mesoscopic scale governing equations and parameters are obtained through coordinate transformation between the non-uniform and uniform mesh spaces. Different from conventional single relaxation time closure models of the collision process, which need space interpolations and momentum adjustments, the present collision model is related to transformed relaxation time and force matrixes. Additional interpolations and adjustments are not necessary because the effects of local grids and properties are included in each component of the matrixes. The components of the relaxation time matrixes are directly expressed by mesoscopic governing parameters, discrete directions and local stretch gradients. Natural convection in an enclosure is simulated with meshes of various global stretch ratios and grid numbers. The non-uniform stretched mesh scheme can capture the temperature and velocity distributions as well as Nusselt numbers with negligible deviations from the uniform grids. Deviations increase slightly with global stretched ratios and appear at larger local velocity and grid size positions. Effects of the tilt angle and key governing parameters from conduction to convection regimes are illustrated and compare favorably with previous studies.

FLOW DYNAMICS OF LID-DRIVEN CAVITIES WITH OBSTACLES OF VARIOUS SHAPES AND CONFIGURATIONS USING THE LATTICE BOLTZMANN METHOD

This work implements the emerging computational technique namely the Lattice Boltzmann Method (LBM) to a fluid flow problem of single sided lid-driven cavities with various shapes of obstacles placed in it. The numerical methodology employs the Single-Relaxation-Time (SRT) model applicable to low Mach number hydrodynamic problem for incompressible flow regime. Three geometrical shapes of the obstacles considered are circular, square, and elliptic. Cavity with obstacles exhibited remarkable circulation zones and structures in contrast to the classical lid driven cavity. The flow mechanics and the vortex dynamics are studied for various values of Reynolds Number (Re = 100, 400, and 1000). Due to the introduction of the obstacles, a strong induced vortex forms close to the obstacles and its size changes interestingly with the variation of Reynolds number, which is captured by LBM. Further the study is extended to examine the vortex phenomena induced by changing the position of the obstacles within the cavity. It is observed that the flow structures change dramatically with little change in the position of obstacle inside the cavity which helps to identify position with enhanced mixing characteristics.

Analysis of magnetic field effect in micro-beam resonators at distinct boundary conditions

The present study is concerned with the analysis of the existence of magnetic field in micro-beam resonators in the context of generalized thermoelasticity with single relaxation time. MEMS are mostly set in permanent magnetic fields. Two dissimilar cases, with different boundary conditions (First: simply supported and isothermal, Second: clamped and isothermal) of micro-beam resonators, have been discussed. In the first case, magneto-thermoelastic damping has been analyzed by the vibration responses of deflection and thermal moment, which are obtained by the Laplace transform method along with the finite Fourier sine transform method, while in the second case, the magneto-thermoelastic damping has been characterized by the vibration frequency through normal mode analysis. Therefore, the present study highlights the influence of magnetic field in the vibration responses of deflection as well as thermal moment of the micro-beam resonators in both cases separately. Size dependency of micro-beam resonators has been observed. The analytic result shows that the amplitude of deflection and thermal moment is attenuated for the coupled magneto-thermoelasticity.

Cascaded lattice Boltzmann modeling and simulations of three-dimensional non-Newtonian fluid flows

Non-Newtonian fluid flows, especially in three dimensions (3D), arise in numerous settings of interest to physics. Prior studies using the lattice Boltzmann method (LBM) of such flows have so far been limited mainly to two dimensions and used less robust collision models. In this paper, we develop a new 3D cascaded LBM based on central moments and multiple relaxation times (MRT) on a three-dimensional, nineteen velocity (D3Q19) lattice for simulation of generalized Newtonian (power law) fluid flows. The relaxation times of the second order moments are varied locally based on the local shear rate and parameterized by the consistency coefficient and the power law index of the nonlinear constitutive relation of the power law fluid. Numerical validation study of the 3D cascaded LBM for various benchmark problems, including the complex 3D non-Newtonian flow in a cubic cavity at different Reynolds numbers and power law index magnitudes encompassing shear thinning and shear thickening fluids, are presented. Furthermore, in order to demonstrate the advantages of the proposed 3D cascaded LBM based on central moments, numerical stability comparisons against the LBMs based on a single relaxation time model and a MRT model using raw moments are made. Numerical results demonstrate the accuracy, second order grid convergence and significant improvements in numerical stability of the 3D cascaded LBM for simulation of 3D non-Newtonian flows of power law fluids.

Modeling and computation for non-equilibrium gas dynamics: Beyond single relaxation time kinetic models

Many kinetic relaxation models have been proposed for the study of rarefied flows. Based on the single relaxation time model, a discrete velocity method-based unified gas-kinetic scheme (UGKS) has been constructed. The UGKS models the gas dynamics on the discretized space directly on account of accumulating flow evolution from particle transport and collision within a time step. Under the UGKS framework, a unified gas-kinetic wave-particle (UGKWP) method has been further developed for non-equilibrium flow simulation, where the time evolution of the gas distribution function is composed of analytical wave and individual particles. In the highly rarefied regime, the flow evolution is mainly described by the particle transport and collision. Because of the use of single relaxation time for particle collision, there is a noticeable discrepancy between the UGKWP solution and the full Boltzmann or direct simulation Monte Carlo (DSMC) result, such as the temperature distribution inside a shock layer at high Mach numbers. In this Letter, a modification of the particle collision time according to the particle velocity will be implemented in the UGKWP. As a result, the new model greatly improves the performance of the UGKWP in the capturing of non-equilibrium flows. There is an excellent match between UGKWP and DSMC or Boltzmann solution in the highly rarefied regime. In the continuum flow regime, due to the absence of particles, the modification of the particle collision time will not take effect and the UGKWP will get back to the hydrodynamic Navier–Stokes flow solver with correct dissipative coefficients at small cell Knudsen numbers.

Advanced thermal lattice Boltzmann method for the simulation of latent heat thermal energy in a porous storage unit

The current research expounds numerical investigation of key parameters effects, namely porosity ( ε= 0.4, 0.6, 0.7 and 0.8), Reynolds number (Re = 100, 200, 400 and 600) and Eckert number (Ec= 0, 1, 5 and 10) on the forced convective laminar flow and heat transfer through a horizontal porous channel filled with a metal foam structure impregnated with paraffin as a phase change material (PCM). The Darcy-Brinkman-Forchheimer model under the local thermal non-equilibrium (LTNE) condition is deemed at the representative elementary volume (REV) scale. The fully coupled equations of Navier-Stokes, Poisson’s equation, energy equations, and continuity equation were handled numerically via a thermal single relaxation time lattice Boltzmann method (TSRT-LBM). To facilitate implementation, all LB equations are based on the same speed discretization scheme (D2Q9). Three-population distribution functions were applied to simulate the fluid flow, and temperatures of the fluid and solid phases. Previously, the numerical model was validated by available cases. Then, a comprehensive investigation has been performed to investigate the influence of the aforementioned dimensionless numbers. All LBM results are found to be highly consistent with other numerical works. The outcomes reported that at lower porosities, the energy and exergy efficiencies increased with increasing Re and Ec. However, for large porosity values, the efficiencies were optimum for a critical Re ~ 400. To sum up, it can be stated that the implemented thermal lattice Boltzmann method has been demonstrated as a suitable approach study the thermal sensible energy storage.