Thermal Lattice Boltzmann Method Research Articles

Thermal lattice Boltzmann approach-based numerical study of nanofluid magnetohydrodynamic forced convection in a back-facing stepped porous channel

Unsteady laminar magnetohydrodynamic forced convection and entropy generation inside a backward-facing step (BFS) porous channel with Cu-H2O nanofluid under a tilted magnetic field is numerically handled using a thermal lattice Boltzmann method (TLBM) with two distribution functions. The Darcy-Brinkman-Forchheimer (DBF) equations filled up with the energy equation (with local thermal equilibrium assumption) have been drawn up as the governing equations model. Their numerical solutions unveiled streamlines, Nusselt number, pumping power, performance index and entropy generation, and impacts of influential parameters (Hartmann number (Ha = 0; 10; 20; 100, 200), Darcy number (Da = 10−3; 10−2; 10−1), magnetic tilt angle (γ = 0, π∕4, π∕2), nanoparticles’ volume fraction (φ = 1 − 4%), medium porosity (ε = 0.6, 0.7, 0.8). The irreversibility analysis is also addressed to highlight the flow behavior. Regarding the validation of the modeling approach deemed, a consensus has been achieved with results available in the literature. Computations revealed that the volume fraction provides a fair performance rating with moderate pumping power. Likewise, the average Nusselt number, the average entropy generation, the pumping power and the performance index have a direct relationship with the Hartmann number, the nanoparticles volume fraction and the magnetic field tilt. Moreover, it can be stated the Cu-H2O nanofluid that seems worthwhile in terms of heat transfer efficiency compared to other examined nanofluids. Entropy generation due to the magnetic field was identified as the main source of irreversibility processes in all cases. Based on the outcomes, it is thought that applying a magnetic field can help minimize entropy generation in practical applications.

Effect of partitions on flow mechanism and heat transfer in thermal convection

The effect of gap width and partition thickness on the flow mechanism and heat transfer of partitioned thermal convection is investigated using a thermal lattice Boltzmann method from Ra = 8 × 106 to Ra = 1 × 108. Partitioning effects on the heat transfer and the physical mechanism of flow are analyzed using the velocity field and temperature field of the convection. Numerical simulation results show that the optimal gap width decreases and that the optimal partition thickness increases with increasing Rayleigh number (Ra). Gap width and partition thickness have a joint effect on the heat transfer. We have counted the comprehensive influence of dimensionless gap width (D*) and dimensionless partition thickness (S*) on diaphragm heat on Nu under Ra = 108. The results show that the global maximum of Nu appears in the regions of 0.004<D*<0.006 and 0.02<S*<0.035. Two important factors affecting the partitioned thermal convection have been found. In addition, an interesting relationship between the average Nusselt number and the presence of leakage vortices is also discussed in this study.

Numerical Investigation of Natural Convection in a Partially Heated Square Cavity and at Different Inclinations Filled by (Water-Al2O3) Nanofluid, Using the Thermal Lattice Boltzmann Method

Numerical Investigation of Natural Convection in a Partially Heated Square Cavity and at Different Inclinations Filled by (Water-Al2O3) Nanofluid, Using the Thermal Lattice Boltzmann Method

Direct numerical simulation of three-dimensional particle-laden thermal convection using the Lattice Boltzmann Method

In thermal multiphase flows, the modulation in the heat transfer rate due to the presence of finite-size solid particles attract growing interest in recent years. This study focuses on developing a robust and efficient simulation method for particle-laden Rayleigh-Bénard convection. The present work utilizes the double distribution function-based Thermal Lattice-Boltzmann method (TLBM), which enables successful simulations of multiphase fluid-thermal interactions. The no-slip boundary of the moving solid particles is handled by the interpolated bounce-back scheme. Additionally, Galilean invariant momentum exchange and heat exchange approaches are employed for hydrodynamic force and heat transfer calculation at the solid boundaries. The accuracy of the current method is verified with several benchmark cases, including three-dimensional single-phase Rayleigh-Bénard convection, as well as the settling of hot and cold spherical particles in a three-dimensional enclosure. Furthermore, we explore the modulation of Rayleigh-Bénard flows due to the presence of freely moving finite-size particles. The simulations are conducted on a distributed memory cluster with a 3D domain decomposition technique facilitated by the MPI library. A brief discussion on the parallel performance of the simulations is provided for both particle-laden and single-phase flow scenarios. Finally, the effects of finite-size solid particles on the overall heat transfer efficiency and modulation to the flow field in three-dimensional particle-laden turbulent Rayleigh-Bénard convection are discussed. The results show that addition of solid particles results in a moderate increase in the overall Nusselt number, and this enhancement is mainly due to the increased heat flux transported by the particles.

Melting evolution of phase change material in square cavity by lattice Boltzmann method

Most numerical simulations for solid–liquid phase change problems are based on the melting point of phase change materials (PCMs) as the initial condition, while research with an initial temperature below the melting point is relatively scarce. In this paper, an enthalpy-based thermal lattice Boltzmann method is employed to investigate the solid–liquid melting process in a square cavity, and various factors including ambient temperature (θa= 0.0, 0.1, and 0.2), saturation temperature (θs = 0.0–0.9), Rayleigh number (Ra = 103, 104, and 105), Stefan number (Ste= 0.025, 0.05, and 0.1), and Prandtl number (Pr= 0.025, 0.05, and 0.1) of the PCMs are systematically examined for their effects on the phase change process at saturated and unsaturated conditions. The simulation results indicate that, first, increasing the ambient temperature or decreasing the saturation temperature results in an accelerated melting rate. Moreover, when the system approaches the saturated condition, achieving complete melting becomes easier. Second, an increase in the Rayleigh number has a dual effect: it enhances convective heat transfer and simultaneously accelerates the melting rate. This effect is particularly pronounced under saturated conditions. Similarly, the Stefan number plays a crucial role in promoting the melting rate, although its impact on convective intensity is minimal. Finally, increasing the Prandtl number not only intensifies convective heat transfer and accelerates the melting rate but also reduces convective disturbances.

Expression of Concern: Heat Transfer and Fluid Flow around Starfish-Inspired Cylinder by Immersed Boundary-Simplified Thermal Lattice Boltzmann Method

Expression of Concern: Heat Transfer and Fluid Flow around Starfish-Inspired Cylinder by Immersed Boundary-Simplified Thermal Lattice Boltzmann Method

Cooling effects of the derived coolant-film layer from partitioned porous injectors for transpiration cooling

This study aims to reveal the cooling benefits of the derived coolant film from partitioned porous injectors for transpiration cooling. The near-wall flow development and the cooling performance are investigated based on various layouts of porous injectors. The numerical investigation is conducted using an in-house recursive regularized thermal lattice Boltzmann method (RR-TLBM). The validated RR-TLBM solver is accelerated by three Tesla V100 graphic processing units (GPUs) for the simulation of incompressible and coupled-domain transpiration cooling at high Reynolds numbers, based on high-resolution grids with 2.65 × 108 nodes. The results indicate that the near-wall flow shows high momentum with the partitioned porous injectors. And the mean velocity increases by more than 23 % with the same coolant consumption per unit blowing area, which contributes to the coolant-film development and cooling uniformity downstream. Moreover, the partitioned porous layout shows the possibilities of coolant reduction as compared to the single continuous porous injector in Case 1. A reduction of 43 % in total coolant consumption with the partitioned porous layout only results in a decrease of 6 % in cooling performance downstream. Additionally, the partitioned coolant injection improves local cooling performance by roughly 22 %, with better cooling homogeneity at the same total coolant consumption. Turbulent fluctuations are weakened in the partitioned coolant injection zones, which contributes to an improvement in cooling evenness. The partitioned porous layout can be an appropriate choice for transpiration cooling systems.

Contact-point analysis of attached-wall cavitation evolution on chemically patterned surfaces using the lattice Boltzmann method

In this study, we aim to investigate the contact-point characteristics of cavitation bubble evolution on different chemically patterned surfaces using the thermal pseudopotential lattice Boltzmann method (LBM). The local temperature variation is considered in the contact-point dynamics simulation. Force analysis is performed on the contact points, and two main controlling factors for contact-point dynamics are identified, namely, the local pressure difference and the unbalanced Young’s force. A dimensionless temperature is used to describe the heat exchange efficiency between the wall and fluids for different wall wettability and temperatures. The attached-wall bubble on the wet wall has an unbalanced Young’s force, which is directed toward the inside of the bubble throughout the entire growth and collapse stages at the contact point, resulting in a smaller contact radius and stronger collapse intensity and making the wet wall more suitable for wall cooling. Significant pressure differences are observed at the contact points owing to local momentum concentration. In contrast, the non-wetting wall surface is more suitable for wall heating because of its smaller collapse intensity and larger contact radius on the wall.

Lattice-Boltzmann modeling of centrifugal buoyancy-induced flows in rotating compressor cavities

Turbofan compressor cooling circuits exhibit inherent unsteadiness within their cavities due to the interplay of forced and natural convection phenomena. This dynamic is fueled by axial cooling throughflow, centrifugal forces, and large temperature gradients. This paper introduces an extended compressible lattice-Boltzmann approach tailored for accurately modeling centrifugal buoyancy-driven flows in such cavities. The approach integrates a local rotating reference frame model into a hybrid thermal lattice Boltzmann method, facilitating the simulation of rotating flows of perfect gases. Moreover, a new mass-conserving boundary treatment, based on the reconstruction of distribution functions, enhances precision in predicting rotor disk heat transfer. Finally, an adapted direct-coupling mesh-refinement strategy, accounting for source terms at grid transitions, enables efficient high buoyancy flow simulations. The proposed approach effectively recovers flow and heat transfer mechanisms on sealed and open rotating compressor cavity rigs, spanning a large range of Rayleigh numbers (up to 109). Through an analysis of the compressibility effects, adjustments to the adiabatic exponent and Eckert number allow for a significant boost in computational speed without undermining the reliability of the flow and heat transfer dynamics, aligning well with established theoretical models and numerical studies. With computational efficiency that outperforms conventional compressible finite volume solvers, the proposed approach stands as a promising method for industrial-scale modeling of turbomachinery cooling circuits.

Improving leading edge cooling through transpiration with partitioned porous injectors and a jet

This study proposes a novel transpiration cooling layout that improves the cooling effect in the stagnation region and downstream zones for a sharp leading edge. Large-eddy simulation is conducted using our in-house recursive-regularized thermal lattice Boltzmann method (RR-TLBM) and high-resolution grids with 2.33 × 108 nodes. The RR-TLBM method shows low numerical dissipation, which is crucial in studying the transpiration-cooled leading edge with small-scale flow structures. A proper size of transpiration area in a single porous injector can extend the effective cooling area, with about 62.2 % of the wall area cooled at the same coolant consumption. Moreover, the opposing jet can reduce the local heat flux in the stagnation region, especially for the sharp leading edges. The proposed combinational cooling method shows an improvement of about 20 % in the cooling performance of the stagnation zone, while there is a 25 % improvement downstream of the stagnation region when compared to that of the porous layout with partitioned injectors. Furthermore, turbulent mixing can impair the improvement in cooling performance downstream, and the extended effective cooling area is related to low turbulent fluctuation. The RR-TLBM solver shows great potential in capturing the 3D coherent structures in the transpiration-cooled leading edge, based on high-resolution grids and a desktop-level computer with three Tesla V100 graphics processing units (GPUs).

Numerical investigation of droplet impact dynamics on Janus-textured heated substrates

Janus-textured substrates refer to surfaces with heterogeneous topographies, which have received particular attention recently due to their potential application in manipulating droplet-bouncing behaviors [Li et al., Nat. Phys. 12, 606–612 (2016)]. In this paper, the droplet impact dynamics on the Janus-textured heated substrates are numerically investigated with an improved thermal lattice Boltzmann method. A comprehensive parametric study is conducted by varying the wettability, the Jakob number, the Weber number, and the surface topographies. With different control parameters, three distinct boiling regimes are observed, i.e., the contact boiling regime, the transition boiling regime, and the film boiling regime (Leidenfrost state). To reveal the underlying physics, the distributions of the unbalance Young's force, the thermophoretic force, and the vapor pressure difference in the system are theoretically analyzed. As for the self-propulsion behaviors, it is find that the droplet tends to move toward the denser side (area with more pillar arrays) for the contact boiling regime. However, when the droplet is under the Leidenfrost state, its bouncing dynamics depend on the combined effects of the Weber number and the wettability, and a decrease in wettability induces the droplet to migrate toward the sparser side (area with fewer pillar arrays). These physical insights enrich the fundamental understanding of the droplet-bouncing dynamics on heated substrates and also provide guidelines for designing advanced surfaces to manipulate the droplet-bouncing behavior.

Modeling inception and evolution of near-wall vapor thermo-cavitation bubbles via a lattice Boltzmann method

The proposed method simulates the growth and collapse mechanisms of lasers or sparks cavitation bubbles based on a double-distributed pseudo-potential thermal lattice Boltzmann method, which gives a high-temperature spot equal to or larger than the critical temperature of the fluid. This technique offers valuable insights into both the hydro- and the thermodynamics evolution of near-wall bulk bubbles. Our findings indicate that the dimensionless bubble-wall distance and the maximum radius share a correlative relationship, expressible via a piecewise function. The critical radius required for bubble inception exhibits a direct correlation with surface tension. We also observe a power-law relationship between surface tension and the maximum radius: lower surface tension results in increased deformation and a larger jet volume. The simulation results reveal the significant influence of initial input temperature on the pressure dynamics within the gas nucleus, leading to varied surface expansion velocities. However, this factor only marginally affects the surface wall expansion velocities. An increased input temperature results in intensified collapse mechanisms. Nevertheless, the elevated temperature during the initial collapse may cause an increase in pressure within the remaining bubble components, potentially leading to oscillations in the bubble radius.

Laminar rarefied flow analysis in a microchannel with H2O-Cu nanofluid: A thermal lattice Boltzmann study

This research paper presents an investigation into the behavior of rarefied flow and heat transfer in a rectangular microchannel utilizing a Cu-water nanofluid. The study employs the thermal lattice Boltzmann method (LBM) with a lattice featuring a double distribution function and a BGK collision model. The simulations are performed using Python software, incorporating slip velocity and temperature jump effects. The primary objective is to analyze the influence of various thermophysical parameters of the coolant fluid on the microchannel, specifically focusing on the characteristics of the Cu-water nanofluid. The study considers laminar flow conditions with nanofluid volume fractions of 2%, 4% and 6%. The findings reveal that both rarefaction effect and Reynolds numbers, as well as the nanoparticle volume fraction, significantly impact the system. Moreover, the investigation evaluates key parameters such as the Nusselt number, skin friction coefficient, temperature jump slip velocity and velocity and temperature profiles. Notably, the nanoparticle volume fraction exhibits minimal influence on the velocity distribution or temperature field, whereas the Nusselt number increases with higher nanoparticle volume fractions. Additionally, the rarefaction effect leads to a reduction in velocity and temperature. At a nanoparticle volume fraction of 2%, increasing the Reynolds number results in elevated velocities and lower temperatures. The skin friction coefficient displays a decreasing trend along the microchannel with increasing Reynolds numbers. Furthermore, an increase in Knudsen numbers corresponds to a decrease in the skin friction coefficient. Finally, an increase in the nanoparticle volume fraction is associated with a decrease in the skin friction coefficient.

A Novel Thermal Lattice Boltzmann Method for Numerical Simulation of Natural Convection of Non-Newtonian Fluids

A modified thermal Bhatnagar–Gross–Krook Lattice Boltzmann (BGK-LB) model was developed to study the convection phenomenon of non-Newtonian fluids (NNFs). This model integrates the local shear rate into the equilibrium distribution function (EDF) of the flow field and keeps the relaxation time from varying with fluid viscosity by introducing an additional parameter. In addition, a modified temperature EDF was constructed for the evolution equation of the temperature field to ensure the precise recovery of the convection–diffusion equation. To validate the accuracy and effectiveness of the proposed model, numerical simulations of benchmark problems were performed. Subsequently, we investigated the natural convection of power–law (PL) fluids and examined the impact of the PL index (n = 0.7–1.3) and Rayleigh number (Ra = 103–5 × 105) on the flow and temperature fields while holding the Prandtl number (Pr = 7) constant. The obtained results indicate that, for a given value of n, the convective intensity exhibits a positive correlation with Ra, which is illustrated by the rising trend in the average Nusselt number (Nu¯) with increasing Ra. Additionally, shear-thinning fluid (n &lt; 1) exhibited increased Nu¯ values compared to the Newtonian case, indicating an enhanced convection effect. Conversely, shear-thickening fluid (n &gt; 1) exhibits reduced Nu¯ values, indicating weakened convective behavior.

Heat flux characteristics of a single droplet splashing on the liquid film obtained with a thermal lattice Boltzmann method

The double-distribution-function thermal lattice Boltzmann method is employed to investigate the heat flux characteristics of single droplet impact on a liquid film above a heated wall. The effects of impact velocity, liquid film thickness, droplet radius, and viscosity coefficient on the average and instant heat flux distribution are analyzed. The droplet impact first breaks the steady-state thermal boundary layer in the impact region, causing the heat flux in the wall impact region to increase. This is because the temperature gradient between the liquid film and the wall increases as the droplet dives downward and expands. The velocity discontinuity at the liquid jet sheet prevents the transfer of the transverse velocity in the liquid film to the static region, yielding a transition region. Convective heat transfer is dominant in the impact and transition regions, while conductive heat transfer is dominant in the static region. Moreover, a large impact velocity promotes the synergy between the temperature and flow velocity fields, enhancing the heat transfer efficiency. The kinetic energy consumption of the droplet increases with the liquid film thickness, which causes the heat flux to decrease. The effect of droplet radius on the heat flux at the wall is minimal. Furthermore, an increased liquid viscosity is not beneficial for wall heat dissipation.

Heat transfer mechanism in vibrational turbulent Rayleigh–Bénard convection with rough plates

The joint effect of rectangular-type roughness and horizontal vibration on two-dimensional (2D) turbulent Rayleigh–Bénard convection (RBC) is investigated by using the thermal lattice Boltzmann method (LBM) in this article. The present work focuses on the Nusselt number and plume dynamics of the convection in the range of dimensionless vibration frequency 0 ≤ ω* ≤ 1000 and the range of dimensionless roughness height 0 ≤ h* ≤ 0.05. The Rayleigh number is 108 and Prandtl number is 4.38. Our numerical results indicate that the relationship between the Nusselt number and roughness height is mostly proportional, and the relationship between the Nusselt number and the vibration frequency is exponential. It is further found that heat transfer enhances by 3.06 times under the joint effect of horizontal vibration and rectangular roughness on turbulent RBC. It provides significant physical insight into the mechanism of cooperative heat transfer enhancement.

Investigation of microparticle deposition and removal behavior using hybrid thermal Lattice Boltzmann method

A numerical method for deposition evolution is proposed by incorporating mechanistic sticking and melt faction sticking model. The hybrid thermal Lattice Boltzmann method is developed to simulate thermal fluid flow, and the particle trajectory is tracked by probabilistic cellular automata model. The proposed model has been validated by experiment and proven to be a promising approach for predicting deposition rate at high–temperature. The contribution of the thermophoresis and Brownian forces to deposition mass is <10% in total. Noteworthily, coarse particles do not necessarily possess higher deposition efficiency. The critical impact velocity (vel = 0.084e–0.48lnStp) and critical shear velocity (vsh,cr = 8.29e–0.46lnStp) are negatively correlated with Stokes number. The average of Nusselt number decreases from 6.94 to 6.17, 5.91, and 5.78 with an increase in eccentricity. The result shows that increasing the tube ellipticity is conducive for reducing deposition at the expense of heat transfer efficiency.

Advanced numerical analysis of convective rarefied flows in microchannels: Studying the impact of multiple obstacle arrangements through LBM modeling

The investigation of fluid flow and forced convective heat transfer in microchannels with square barriers is the focus of this study. The positioning of obstacles was varied in three cases: at the top wall, bottom wall, and symmetrically distributed on both sides of the microchannel wall. The thermal Lattice Boltzmann Method in conjunction with the Double Distribution Function and Bhatnagar–Gross–Krook approach was used for simulation through computer code in Python. Slip velocity and temperature jump were considered in the boundary conditions for the walls of the microchannel and obstacles. The results demonstrate that the rarefaction effect, placement of barriers, and choice of square obstacles significantly impact fluid flow and heat transfer. An increase in Knudsen numbers (Kn) leads to a decrease in temperature and velocity. The presence of obstructions on both sides of the microchannel walls reduces the fluid’s velocity and cools the fluid at the microchannel’s exit. The third case, with obstacles on both sides, presents a practical approach for reducing the fluid’s temperature at the exit, resulting in the lowest level of skin friction (Cf) and a reduction in the Nusselt number (Nu). The proposed configurations can be utilized to enhance the geometry of microchannels and for cooling purposes in small-scale devices and systems with miniature mechanical and electrical components. The study’s findings suggest that the placement of obstacles at the bottom or on both sides, depending on the need for best cooling on both sides or only at the top to reduce material consumption, can achieve low temperature at the exit of a rectangular microchannel.

On the combined influence of Reynolds number and cylinder spacing for flow around a row of heated square cylinders

AbstractThe characteristics of forced convection heat transfer across a row of heated square cylinders kept in side‐by‐side arrangement are numerically investigated to examine the combined effects of Reynolds number and cylinder spacing for Ri = 0, 60 ≤ Re ≤ 160, Pr = .71, and s/d = 1.0–8.0, where the space between cylinder surfaces is s and the cylinder size is d. A numerical study was carried out using the thermal lattice Boltzmann method. The goal of this work is to explore the transitions in heat transfer phenomenon that occurs behind the cylinder and to report the corresponding regimes for heat transfer namely synchronous, quasiperiodic, and chaotic. The proposed regime of heat flow is a function of Reynolds number and spacing. The synchronous heat regime is obtained for s/d ≥ 5.0 and quasiperiodic, chaotic regimes are observed for 3.0 ≤ s/d &lt; 5.0, s/d &lt; 3.0, respectively at Re = 100. The instantaneous isotherms, the power spectra of the corresponding Nusselt number signals, and the significance of cylinder Nusselt number frequency are used to examine these heat flow regimes. The heat transfer regimes for a row of heated cylinders and flow regimes for a row of unheated cylinders both have comparable appearances except for the fact that the heat transfer regime is synchronous at s/d ≥ 5.0 and flow is synchronous at s/d ≥ 4.0. The chaotic or quasiperiodic heat transfer regimes occur due to merging and strong interactions between thermal blobs shed from the cylinders. Heat transfer is synchronous at a higher spacing and characterized by independent thermal blobs shedded from the cylinders. It is reported that as spacing reduces and Reynolds number increases, the mean value of the Nusselt number experienced by all cylinders increases. The important outcome of the present numerical work is that for understanding heat transfer from bluff body, the transitions that occur in heat transfer are useful.

Improved multi-relaxation time thermal pseudo-potential lattice Boltzmann method with multi-block grid and complete unit conversion for liquid–vapor phase transition

In recent years, the thermal pseudo-potential lattice Boltzmann method (LBM) has been widely adopted in numerical simulations of liquid–vapor phase transition systems. However, the unit conversion for thermal pseudo-potential LBM remains incomplete and elusive, and the numerical simulation efficiency is limited by the uniformly single-block grid. In this paper, the dimensionless evolution equations of thermal pseudo-potential LBM with multi-relaxation time operators are derived for the convenience of adopting real physical parameters and improvement of computational efficiency. The energy equation is re-derived and improved for enhanced accuracy and convenience of numerical calculation. Additionally, a more accurate Martin–Hou equation of state for cryogen is adopted and a modified term for surface tension coefficient is improved to confirm that the surface tension coefficient is grid independent. Moreover, a three-layer boundary structure for the coarse grid is proposed to introduce the multi-block grid into the thermal pseudo-potential LBM for taking into account the intermolecular force and internal heat source term. The aforementioned works improve the thermal pseudo-potential LBM and enable efficient and accurate simulation of the liquid–vapor phase transition within the three-dimensional structure with real physical parameters of a specific working fluid. Finally, numerical simulations are adopted to validate the efficiency and accuracy of the proposed improvements for simulating liquid–vapor phase transition.