Non-dimensional Lattice Boltzmann Method Research Articles

Bridging pore scale and macroscopic scale foam structure enhanced channel flow cooling with three-dimensional mesoscale simulations

Metal foams with larger interface areas and higher effective conductivities are widely used to increase heat transfer in engineering applications. To reveal the quantitative relation between the pore scale and the macroscale convective thermal transport, foams immersed in a water cooling channel for two high temperature flat plates were simulated by the mesoscale non-dimensional lattice Boltzmann method. The generated structure parameters are global porosities from 0.70 to 0.95 and pore sizes from 6% to 16% of the square channel height. The flow simulation parameters are macroscopic Reynolds numbers from 50 to 1500 and pore scale Reynolds numbers from 3 to 240. Three-dimensional spirals inside foam pores and behind foam structures, which induce the third spatial direction convection, are observed to be positively related to pore sizes, Reynolds numbers, and the volume fractions of fluid and solid phases, respectively. The pore scale drag and heat transfer coefficient constants are inversely correlated from the pressure drop and heat flux of mesoscale simulation results with deviations of 13.2% and 12.5%, respectively. Together with the pore scale geometry factor and the global porosity, the correlations of pore scale and macroscopic scale drag and heat transfer are bridged by microscopic coefficient constants (0.0004, 4.59, 0.47) and (0.0001, 0.096, 0.50, 0.33), respectively. The cross scale correlations provide a practical tool for further engineering applications of enhancing convective cooling through porous structures.

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.

Sparse scattered high performance computing data driven artificial neural networks for multi-dimensional optimization of buoyancy driven heat and mass transfer in porous structures

An artificial intelligence (AI) enhanced optimization framework is developed to reduce computational costs for evaluating transport performance of buoyancy driven heat and mass transfer in porous structures. The present optimization framework integrates prediction with artificial neural networks (ANNs), optimization with the weighted objective function, and physics-based simulations with high performance computing (HPC). Multi-dimensional governing parameters and objectives are investigated by ANNs with sparse scattered training data obtained from HPC with controllable structure generation scheme (CSGS) and parallel non-dimensional lattice Boltzmann method (P-NDLBM). The macroscopic prediction results based on ANNs are validated by comparison with HPC results. Full maps of the objective function values versus structure and physical parameters are illustrated. The maximum objective function value subjected to constraints is obtained together with the corresponding optimal structure and physical parameters. The optimal parameters are further applied in HPC to obtain mesoscopic physical fields. The underlying mechanism is also revealed by comparing the physical fields with optimal and off-optimal parameters.

Three dimensional mesoscopic scale simulations of buoyancy driven flow and heat mass transfer through randomly packed fiber boards

Three dimensional (3D) buoyancy driven fluid flow, heat and mass transfer through a vertical board with structures of randomly packed fibers are simulated by a non-dimensional lattice Boltzmann method (NDLBM). The two outside walls in the board transverse direction are fixed with opposing constant temperature and species concentration. The outside walls in the longitudinal directions are adiabatic. Varying board porosities, fiber diameters, and board thicknesses are generated by a controllable structure generation scheme (CSGS). The NDLBM simulations with D3Q27 grids show 3D velocity, temperature and concentration fields in the mesoscopic scale. The effects of board porosity, fiber diameter, and board thickness are quantified. The results show that the trends of macroscopic Nusselt, Sherwood, and Biot numbers with macroscopic porosity are similar to previous 2D random structure simulations, but the 3D fiber structures are more effective for both heat and mass transfer compared to 2D random structures with equivalent governing parameters. The difference in transfer properties is attributed to mesoscopic flow patterns. The mesoscopic 3D spiral flow is due to the 3D vortex generated by local fiber boundaries. The stagnation points of the 3D spiral structures usually appear at relative higher local porosity positions. The 3D spirals enhance the pore scale heat mass transfer.

Three dimensional thermal conduction of randomly packed beds of porous cylindrical ceria pellets immersed in carbon dioxide with effects of deviations of pellet porosities and sizes

Structures of randomly packed beds of cylindrical shape porous pellets composed of tiny ceria (CeO2) particles with wide ranges of pellet porosities and number density probabilities are generated by an improved controllable structure generation scheme (CSGS) including deviations of both pellet porosities and sizes. Three dimensional (3D) mesoscopic scale thermal conduction through the structures immersed in carbon dioxide (CO2) gas is simulated by a parallel non-dimensional lattice Boltzmann method (P-NDLBM). Effective thermal conductivity (ETC) in each direction and 3D temperature distributions with effects of pellet number density probabilities, porosities, and deviations are illustrated. Although the pellet number density probability and pellet porosity are equivalently important for changing of macroscopic global porosity, they have different effects on temperature distribution patterns and the overall ETC. A new form of ETC correlation related to the pellet number density probability and pellet porosity is proposed. The present ETC correlation based on the two pellet parameters shows a slight improvement comparing to conventional forms based on the macroscopic global porosity.

Non-dimensional lattice Boltzmann simulations on pore scale double diffusive natural convection in an enclosure filled with random porous media

Double diffusive natural convection in an enclosure filled with random porous media has been simulated by a Non-dimensional Lattice Boltzmann method (NDLBM). The random structures with different porosities are generated by a Controllable Structure Generation Scheme (CSGS). The NDLBM and the CSGS with mesoscopic scale governing parameters enable the direct simulations of transient velocity, temperature and concentration fields in pore scale for random media of a wide range of porosities. Validations of the parallel codes have been done by comparing to natural convection in a pure fluid filled enclosure obtained by various methods. Distributions of pore scale velocities, temperatures, and concentrations are quantitatively shown. Effects of the governing parameters on the macroscopic Nusselt, Sherwood and Biot numbers are presented. The changes of physical properties including solid fluid interface effects are also discussed.

A three-dimensional phonon energy transport model based on the non-dimensional lattice Boltzmann method

A new three-dimensional phonon energy transport model based on the non-dimensional lattice Boltzmann method (NDLBM) is developed to be applicable in the sub-continuum regime for diffusive and ballistic phonon transport. Two Knudsen numbers based on the base frequency and variable frequency, Knω0 and Knω, are defined in order to isolate the effects of material size and phonon transfer frequency. Both the relaxation time and boundary conditions of the phonon Boltzmann transport equation are modeled in dimensionless form. The physical meaning of each component in the relaxation time and discontinuous boundary models is interpreted. By introducing the Boltzmann constant and Planck’s constant, all other coefficients can be simplified into order of one. The transient dimensionless phonon probability distribution functions are solved by the Parallel NDLBM with D3Q27 grids. The dimensionless temperature distributions, i.e. the dimensionless phonon energy density distributions, compare favorably with previous experimental and numerical results for various Knω0. The effects of material size, temperature, and phonon transfer frequency are investigated.

A comparative study of permeable and semipermeable membranes constructed multiple layer water filters by non-dimensional lattice Boltzmann simulations

A Non-Dimensional Lattice Boltzmann Method (NDLBM) based on a multiple zone porous medium model is extended to simulate fluid flow and mass transfer inside multiple layer water filters. Comparative studies based on two basic design models (permeable and semipermeable membrane model) are carried out to investigate the flow and mass transport inside cylindrical multiple layer water filters. In the permeable membrane design model, the water is purified by passing multiple units with sandwich like structures. In the semipermeable membrane model, macromolecules such as suspended particulates cannot pass the semipermeable membranes, while micromolecules can pass the porous semipermeable membranes. The quasi-steady state velocity distributions are obtained. The transient concentrations of suspended particulates captured by porous solid structures and left in water are compared for the two design models. Different dimensionless governing parameters and the porosities for the membranes are studied to understand the underlying mechanism of the purification procedure and to compare performance of the two models.

A mesoscopic model for transient mass transfer of volatile organic compounds from porous walls of different structures

Transient mass diffusion and convection of volatile organic compounds (VOCs) from walls is an important issue for air quality in buildings. In the present work, a new model of these processes that captures mass transport within the wall structure is presented and applied for a ventilated enclosure. Porous wall structures composed of two solid phases (one carrying the VOC and one inert) and one fluid phase air are generated by the Controllable Structure Generation Scheme (CSGS) based on discrete Gaussian quadrature space and velocity. Mesoscopic scale parallel non-dimensional lattice Boltzmann method (P-NDLBM) simulations are performed for relevant ranges of wall porosity, Reynolds and Schmidt numbers for a two-dimensional enclosure with a top inlet and bottom outlets. The effect of the wall structure on mass transfer in the enclosure is investigated for two wall structures: type (A) a wall with randomly immersed particles, and type (B) a shape-separated wall structure. Results include transient VOC concentration and streamlines in the porous wall and the enclosure for a vary of porosities and diffusivities for each phase. The pore structure and porosity of the wall have significant impact on mass transfer. Type (B) structures are more favorable for rapid mass transfer within the wall.

Three dimensional thermal diffusion in anisotropic heterogeneous structures simulated by a non-dimensional lattice Boltzmann method with a controllable structure generation scheme based on discrete Gaussian quadrature space and velocity

A new Controllable Structure Generation Scheme (CSGS) based on discrete Gaussian quadrature space and velocity is presented and used to generate multiple-phase random isotropic homogenous and shape-constrained anisotropic heterogeneous structures. The primary advantage of the new CSGS over the existing random structure generation growth method is the ability to model a wide variety of structures by controlling the shape through relatively simple constraint indexes. The growth speed probability function is introduced to control the mesoscopic porosities and mixture/separation of material phases. The model is applied to generate four packed structure types (shapeless random, separated solid shapes, separated random-filled shapes, and random-mixture-filled shapes). Three-dimensional steady and transient thermal diffusion are simulated by Non-Dimensional Lattice Boltzmann Method (NDLBM). The steady state results are compared to measured data available in the published literature. The transient results reveal how the mesoscopic shape of a structure impacts thermal diffusion. With equivalent macroscopic volume fractions, structures with higher mesoscopic volume fractions of high conductivity phases possess higher effective thermal conductivity/diffusivity because there is greater connectivity of the higher conductive material at mesoscopic scale.

A Parallel Non-Dimensional Lattice Boltzmann Method for fluid flow and heat transfer with solid–liquid phase change

A new mesoscopic scale Parallel Non-Dimensional Lattice Boltzmann Method (P-NDLBM) is developed to dramatically speed up the computation of transient fluid flow and heat transfer problems. The P-NDLBM code using message passing interface (MPI) was compiled in Fortran. The model is presented in dimensionless form to simplify application to a broad range of problems. The effective domain decomposition, data transfer between CPUs, and various boundary conditions based on the P-NDLBM are presented. The code is validated by comparison to prior experimental and single CPU computational studies of cavity flow and the Rayleigh–Bénard problem. The time costs of simulations with equal mesh size are compared for CPU numbers from 1 to 64 to show the effectiveness of the approach. To illustrate the utility of the code, simulations of the transient temperature and fluid velocity during charging and discharging of an integral collector storage solar system are presented. The modeled system has encapsulated phase change embedded in the water-filled enclosure. The results illustrate the capability of the code to capture the phase transition within the encapsulated phase change material as well as the details of the overall flow structure and temperature field.

A new mesoscopic scale timestep adjustable non-dimensional lattice Boltzmann method for melting and solidification heat transfer

A mesoscopic scale timestep adjustable non-dimensional lattice Boltzmann method (NDLBM) for fluid flow and heat transfer with solid–liquid phase change is developed using a scaling analysis based on the mesoscopic length and velocity scales. The interface between fluid and solid is treated as a mixture domain with transient porosity distributions and thickness. Timesteps are adjusted by using a transient mesoscopic Mach number independent of mesh size to speed up the computation. The code is validated by comparison of transient Nusselt numbers, isotherms, streamlines, and porosity with prior studies of natural convection in a square enclosure with and without phase change material. A benchmark problem is proposed to obtain the same equilibrium state for both melting and solidification procedures. Full maps of the flow and heat transfer patterns for both melting and solidification are presented based on the key dimensionless governing parameters. The effects of Mach, Stefan (0.01–10), Rayleigh (103–108), and Prandtl (0.1–10) numbers are discussed.

A Non-Dimensional Lattice Boltzmann Method for direct and porous medium model simulations of 240-tube bundle heat exchangers in a solar storage tank

An improved Non-Dimensional Lattice Boltzmann Method (NDLBM) is developed and a uniform computational code is compiled to fit into both direct and porous medium model simulations. Comparison studies based on natural convection of 240 cylindrical tube bundle heat exchangers immersed in a thin rectangular solar storage tank show the computational efficiency and accuracy of both direct simulations and porous medium model simulations achieved by using NDLBM. The governing parameters in the macroscopic, microscopic, and mesoscopic length scales corresponding to the enclosure width, tube diameter, and mesh size are obtained. Transient isotherms, streamlines, Nusselt numbers, and CPU time of nine models have been simulated for various pitch, porosity, and distributions of tubes. Given the same grid number and simulation time, the CPU time of the porous medium model simulations by using NDLBM is about 1/60 of that of porous medium simulations by using finite difference based on projection method, and 1/20 of that of the direct simulations with the uniform code based on NDLBM. The porous medium simulations can only obtain Darcy velocity and volume averaged temperature, while the direct simulations can obtain both macroscopic and microscopic velocity and temperature.

Experimental and numerical investigations on a solar tracking concentrated photovoltaic–thermal system with a novel non-dimensional lattice Boltzmann method

A small scale solar tracking concentrated photovoltaic–thermal (CPV–T) system was investigated to enhance the energy efficiency of photovoltaic systems. The experimental measurement was firstly done to obtain the environmental parameters and on site efficiencies of the system. A novel Non-Dimensional Lattice Boltzmann Method (NDLBM) was then developed to simulate the transient fluid flow and heat transfer of the CPV–T receiver. This NDLBM establishes a whole set of dimensionless form of lattice Boltzmann equations and boundary conditions with dimensionless governing parameters in both macroscopic and mesoscopic length scales. The relaxation time is expressed in form of the mesoscopic Reynolds number instead of the viscosity, making the relationship between the mesh size and simulation range clearer. The present physics-based dimensionless inlet/outlet flow and heat flux boundary conditions make it possible to simulate the present high solar irradiance, large temperature difference, and high velocity mixed convection heat transfer problem. The effects of the flow rate, inlet flow temperature and distributions of the inlet/outlet on the heat transfer are obtained with NDLBM simulations over a wide range of Reynolds number, Rayleigh number, and Richardson number. The results provide a full understanding of the mechanics of the efficiency enhancement of the CPV–T system due to water cooling.