• Journal of computational fluids engineering
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• v.16 no.4
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• pp.7-13
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• 2011

A comparative analysis of thermal models in the lattice Boltzmann method(LBM) for the simulation of laminar natural convection in a square cavity is presented. A HYBRID method, in which the thermal equation is solved by the Navier-Stokes equation method while the mass and momentum conservation are resolved by the lattice Boltzmann method, is introduced and its merits are explained. All the governing equations are discretized on a cell-centered, non-uniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with a deferred correction method to ensure stability of the solutions. The HYBRID method and the double-population method are applied to the simulation of natural convection in a square cavity and the predicted results are compared with the benchmark solutions given in the literatures. The predicted results are also compared with those by the conventional Navier-Stokes equation method. In general, the present HYBRID method is as accurate as the Navier-Stokes equation method and the double-population method. The HYBRID method shows better convergence and stability than the double-population method. These observations indicate that this HYBRID method is an efficient and economic method for the simulation of incompressible fluid flow and heat transfer problem with the LBM.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.7 s.262
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• pp.620-627
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• 2007

In this paper, we adapt a modified internal energy non-equilibrium first-order extrapolation thermal boundary condition to the thermal lattice Boltzmann model (TLBM). This model is the double populations approach to simulate hydrodynamic and thermal fields. The bounce-back boundary condition which is a traditional boundary condition of lattice Boltzmann method has only a first order in numerical accuracy at the boundary and numerical instability. A non-equilibrium first-order extrapolation boundary condition has been verified to be of better numerical stability than the bounce-back boundary condition and this boundary condition is proved to be of second-order accuracy for the flat boundaries. The two-dimensional natural convection flow in a square cavity with Pr=0.71 and various Rayleigh numbers are simulated. The results are found to be in good agreement with those of previous studies.

• Journal of Mechanical Science and Technology
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• v.17 no.12
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• pp.2034-2041
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• 2003

This study introduced a lattice Boltzmann computational scheme capable of modeling thermo hydrodynamic flows with simpler equilibrium particle distribution function compared with other models. The equilibrium particle distribution function is the local Maxwelian equilibrium function in this model, with all the constants uniquely determined. The characteristics of the proposed model is verified by calculation of the sound speeds, and the shock tube problem. In the lattice Boltzmann method, a thermal fluid or compressible fluid model simulates the reflection of a weak shock wave colliding with a sharp wedge having various angles $\theta$$\sub$w/. Theoretical results using LBM are satisfactory compared with the experimental result or the TVD.

• Journal of Advanced Marine Engineering and Technology
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• v.34 no.1
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• pp.53-61
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• 2010

In the present study, a laminar natural convection flow of $H_2O$-Cu nanofluid in a two dimensional enclosure has been investigated using a thermal lattice Boltzmann approach with the Bhatnagar-Gross-Krook (BGK) model. The effect of suspended nanoparticles on the fluid flow and heat transfer process have been studied for different controlling parameters such as particle volume fraction ($\Phi$), Rayleigh number (Ra). For this investigation the Rayleigh number changes from 104 to 106 and volume fraction varied from 0 to 10% with three different particle diameters (dp), say 10 nm, 20 nm and 40 nm. It is shown that increasing the Rayleigh number (Ra) and the volume fraction of nanofluid causes an increase of the effective heat transfer rate in terms of average Nusselt number (Nu) as well as the thermal conductivity of nanofluid. On the other hand, increasing the particle diameter causes the decrease of the heat transfer rate and thermal conductivity. The result of the analysis are compared with experimental and numerical data both for pure and nanofluids and it is seen a relatively good agreement.

• The KSFM Journal of Fluid Machinery
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• v.14 no.6
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• pp.45-53
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• 2011

Multiphase lattice Boltzmann method (LBM) has been used to simulate the nucleate pool boiling directly. For the phase change model, the thermal model and the Stefan boundary condition were introduced to the isothermal LBM. The phase change model was validated by the bubble growth in a superheated liquid under no gravity. The bubble growth on and departure from a superheated wall has been simulated successfully. The preliminary results showed that the detail process of nucleate pool boiling was in good agreement with the experimental results.

• 유체기계공업학회:학술대회논문집
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• 2006.08a
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• pp.391-394
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• 2006

In this paper, the thermal lattice Boltzmann method(TLBM) proposed by Guo et al.(2002) is applied to analyze the forced convective flow and heat transfer of 2-D micro channel. Nonequilibrium extrapolation boundary condition is adopted to simulate the velocity and temperature behavior at wall boundaries. Numerical results obtained by the present study give a good prediction of the micro fluidic characteristics with thermal effects.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.557-560
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• 2002

In this study, simulation of weak shock waves are peformed by a two-dimensional thermal fluid or compressible fluid model of the lattice Boltzmann method. The shock wave represents an abrupt change in fluids properties, in which finite variations in pressure, internal energies, and density occur over the shock thickness. The characteristics of the proposed model with a simple distribution function is verified by calculation of the sound speeds, and the shock tube problem. The reflection of a weak shock wave by wedge propagating in a channel is performed. The results agree well with those by finite difference method or by experiment. In the simulation of unsteady shock wave diffraction around a sharp corner, we show a flow field of vortical structure near the comer.

• Journal of computational fluids engineering
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• v.16 no.4
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• pp.39-46
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• 2011

A numerical study of a turbulent natural convection in an enclosure with the lattice Boltzmann method (LBM) is presented. The primary emphasis of the present study is placed on investigation of accuracy and numerical stability of the LBM for the turbulent natural convection flow. A HYBRID method in which the thermal equation is solved by the conventional Reynolds averaged Navier-Stokes equation method while the conservation of mass and momentum equations are resolved by the LBM is employed in the present study. The elliptic-relaxation model is employed for the turbulence model and the turbulent heat fluxes are treated by the algebraic flux model. All the governing equations are discretized on a cell-centered, non-uniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with the deferred correction way to ensure accuracy and stability of solutions. The present LBM is applied to the prediction of a turbulent natural convection in a rectangular cavity and the computed results are compared with the experimental data commonly used for the validation of turbulence models and those by the conventional finite-volume method. It is shown that the LBM with the present HYBRID thermal model predicts the mean velocity components and turbulent quantities which are as good as those by the conventional finite-volume method. It is also found that the accuracy and stability of the solution is significantly affected by the treatment of the convection term, especially near the wall.

• Computers and Concrete
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• v.32 no.6
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• pp.567-576
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• 2023

In this study, a 3D microstructure-based model is established to simulate the effective thermal conductivity of cement paste, covering varying influencing factors associated with microstructure and thermal transfer mechanisms. The virtual cement paste divided into colloidal C-S-H and heterogeneous paste are reconstructed based on its structural attributes. Using the two-level hierarchical cement pastes as inputs, a lattice Boltzmann model for heat conduction is presented to predict the thermal conductivity. The results suggest that due to the Knudsen effect induced by the nanoscale pore, the thermal conductivity of air in C-S-H gel pore is significantly decreased, maximumly accounting for 3.3% thermal conductivity of air at the macroscale. In the cement paste, the thermal conductivities of dried and saturated cement pastes are stable at the curing age larger than 100 h. The high water-to-cement ratio can decrease the thermal conductivity of cement paste.

• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.2032-2039
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• 2005

The lattice Boltzman method (LBM) and the finite difference-based lattice Boltzmann method (FDLBM) are quite recent approaches for simulating fluid flow, which have been proven as valid and efficient tools in a variety of complex flow problems. They are considered attractive alternatives to conventional finite-difference schemes because they recover the Navier-Stokes equations and are computationally more stable, and easily parallelizable. However, most models of the LBM or FDLBM are for incompressible fluids because of the simplicity of the structure of the model. Although some models for compressible thermal fluids have been introduced, these models are for monatomic gases, and suffer from the instability in calculations. A lattice BGK model based on a finite difference scheme with an internal degree of freedom is employed and it is shown that a diatomic gas such as air is successfully simulated. In this research we present a 2-dimensional edge tone to predict the frequency characteristics of discrete oscillations of a jet-edge feedback cycle by the FDLBM in which any specific heat ratio $\gamma$ can be chosen freely. The jet is chosen long enough in order to guarantee the parabolic velocity profile of a jet at the outlet, and the edge is of an angle of $\alpha$=23$^{o}$. At a stand-off distance w, the edge is inserted along the centerline of the jet, and a sinuous instability wave with real frequency is assumed to be created in the vicinity of the nozzle exit and to propagate towards the downstream. We have succeeded in capturing very small pressure fluctuations resulting from periodic oscillation of the jet around the edge.