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Numerical Analysis of Turbulent Natural Convection in a Square Cavity using Large Eddy Simulation in Lattice Boltzmann Method
"... Abstract—In this paper Lattice Boltzmann simulation of turbulent natural convection with largeeddy simulations (LES) in a square cavity which is filled by water has been investigated. The present results are validated by finds of other investigations which have been done with different numerical me ..."
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Abstract—In this paper Lattice Boltzmann simulation of turbulent natural convection with largeeddy simulations (LES) in a square cavity which is filled by water has been investigated. The present results are validated by finds of other investigations which have been done with different numerical methods. Calculations were performed for high Rayleigh numbers of Ra=10 8 and 10 9. The results confirm that this method is in acceptable agreement with other verifications of such a flow. In this investigation is tried to present Largeeddy turbulence flow model by Lattice Boltzmann Method (LBM) with a clear and simple statement. Effects of increase in Rayleigh number are displayed on streamlines, isotherm counters and average Nusselt number. Result shows that the average Nusselt number enhances with growth of the Rayleigh numbers. Keywords—Turbulent natural convection, Large Eddy
EFFECT OF DISCRETE HEATER AT THE VERTICAL WALL OF THE CAVITY OVER THE HEAT TRANSFER AND ENTROPY GENERATION USING LATTICE BOLZMANN METHOD
"... In this paper lattice Boltzmann method was employed for investigation the effect of the heater location on flow pattern, heat transfer and entropy generation in a cavity. A 2D thermal lattice Boltzmann model with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations were pe ..."
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In this paper lattice Boltzmann method was employed for investigation the effect of the heater location on flow pattern, heat transfer and entropy generation in a cavity. A 2D thermal lattice Boltzmann model with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations were performed for Rayleigh numbers from 10 3 to 10 6 at Pr = 0.71. The study was carried out for heater length of 0.4 side wall length which is located at the right side wall. Results are presented in the form of streamlines, temperature contours, Nusselt number, and entropy generation curves. Results show that the location of heater has a great effect on the flow pattern and temperature fields in the enclosure and subsequently on entropy generation. The dimensionless entropy generation decreases at high Rayleigh number for all heater positions. The ratio of averaged Nusselt number and dimensionless entropy generation for heater located on vertical and horizontal walls was calculated. Results show that higher heat transfer was observed from the cold walls when the heater located on vertical wall. On the other hand, heat transfer increases from the heater surface when it is located on the horizontal wall. Key words: natural convection, cavity, entropy generation, lattice Boltzmann method
MIXED CONVECTION SIMULATION OF INCLINED LID DRIVEN CAVITY USING LATTICE BOLTZMANN METHOD*
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3D MODELING OF FLUIDSTRUCTURE INTERCATION WITH EXTERNAL FLOW USING COUPLED LBM AND FEM
"... ABSTRACT Three dimensional fluidstructure interaction was modeled using the coupled lattice Boltzmann and finite element methods. The latter technique was applied to model the structural behavior while the former was used to model the fluid field. For computationally efficient modeling of external ..."
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ABSTRACT Three dimensional fluidstructure interaction was modeled using the coupled lattice Boltzmann and finite element methods. The latter technique was applied to model the structural behavior while the former was used to model the fluid field. For computationally efficient modeling of external flow over embedded pipes with their interaction, the pipes were modeled using 3D beam elements rather than shell elements. This paper presents an algorithm for how to couple 3D beam finite elements with the lattice Boltzmann grids so that the fluidstructure interaction can be properly modeled at the outer surfaces of pipes. Some numerical examples were analyzed using the developed technique, and the fluidstructure interaction characteristics were examined through the examples. IN Fluidstructure interaction is a very common and critical problem in power plants and heat exchangers. Such interaction is a complex problem and requires numerical analyses. Historically, the Finite Element Method (FEM) has been used dominantly for structural analysis while the Computational Fluid Dynamics (CFD) has been used mostly for flow analysis. As a result, coupling techniques were developed between FEM and CFD so that fluidstructure interaction can be solved TRODUCTION The Lattice Boltzmann Method (LBM) is a newer method than other techniques such as CFD, FEM and BEM. It has been developed and applied to mainly fluid flow problems since 1980's. As a result, the present paper was to develop a 3D fluidstructure interaction model using the lattice Boltzmann and finite element methods. The latter technique was applied to model the structural behavior while the former was used to model the fluid field. For computationally efficient modeling of external flow over embedded pipes with their interaction, the pipes were modeled using 3D beam elements rather than shell elements. This paper presents an algorithm for how to couple 3D beam finite elements with the lattice Boltzmann grids so that the fluidstructure interaction can be properly modeled at the outer surfaces of pipes. The next section describes the development of the LBM. Then, the procedure to couple the fluidstructure interface using LBM and 3D bean finite elements is presented. Finally, some numerical examples are presented to demonstrate the coupled technique, and the summary is followed. 1
A 3D Lattice BGK Scheme for Simulation of Thermal Flow in Cubic Cavity
, 2009
"... Abstract In this paper, a 3D doublepopulation thermal lattice Boltzmann BGK scheme is applied to solve threedimensional, incompressible thermal fluid flow problem. The simplest lattice BGK D3Q6 model, developed based on passivescalar approach, is proposed to represent the energy distribution fun ..."
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Abstract In this paper, a 3D doublepopulation thermal lattice Boltzmann BGK scheme is applied to solve threedimensional, incompressible thermal fluid flow problem. The simplest lattice BGK D3Q6 model, developed based on passivescalar approach, is proposed to represent the energy distribution function. While the D3Q19 lattice model is chosen to represent density distribution function in order to calculate the density and velocity fields. The simulation of natural convection in a cubic cavity with Prandtl number 0.71 and Rayleigh number ranging from 10 3 to 10 5 are carried out to test the validity of the proposed approach. The flow patterns are observed and the heat transfer rate is estimated in terms of Nusselt number. The dependence of the hear transfer mechanism on the Rayleigh number is shown to agree well with that obtained by the calculations of 3D NavierStokes equation. It is observed that the combination of D3Q6 and D3Q19 give excellent numerical stability and accuracy for the simulation at wide range of Rayleigh numbers.
PARTICULATE FLOW SIMULATION BY THE IMMERSED BOUNDARY LATTICE BOLTZMANN METHOD
"... ABSTRACT We demonstrate the applicability of the immersed boundary lattice Boltzmann method (IBLBM) based on the implicit correction method to the simulation of rigid body motion in a viscous fluid and to the natural convection calculation. We compare the accuracy of the IBLBM based on the implic ..."
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ABSTRACT We demonstrate the applicability of the immersed boundary lattice Boltzmann method (IBLBM) based on the implicit correction method to the simulation of rigid body motion in a viscous fluid and to the natural convection calculation. We compare the accuracy of the IBLBM based on the implicit correction method with one of the IBLBM based on the direct forcing method that eliminates the necessity of the determination of free parameters. In the simulations of the cylindrical Couette flow and of the heat transfer between two concentric cylinders, the implicit correction method indicates the firstorder accuracy in the number of Lagrangian points. The accuracy of the IBLBM based on the direct forcing method is independent of the number of the boundary points. The IBLBM based on the implicit correction method is more accurate than one based on the direct forcing method.
A THERMAL LATTICE BOLTZMANN MODEL FOR MICRO/NANOFLOWS
"... ABSTRACT With the development of micro/nanodevices, low speed rarefied gas flows have attracted significant research interest where successful numerical methods for traditional high speed flows, including the direct simulation Monte Carlo method, become computationally too expensive. As the Knudse ..."
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ABSTRACT With the development of micro/nanodevices, low speed rarefied gas flows have attracted significant research interest where successful numerical methods for traditional high speed flows, including the direct simulation Monte Carlo method, become computationally too expensive. As the Knudsen number can be up to the order of unity in a micro/nano flow, one approach is to use continuumbased methods including the NavierStokesFourier (NSF) equations, Burnett/super Burnett equations, and moment models. Limited success has been achieved because of theoretical difficulties and/or numerical problems. The recently developed lattice Boltzmann equation (LBE) offers a fundamentally different approach which is close to kinetic methods but with a significantly smaller computational cost. However, success of LBE methods for rarefied gas motion has been mainly on isothermal flows. In this paper, thermal rarefied gas flows are investigated. Due to the unique features of micro/nano flows, a simplified thermal lattice Boltzmann model with two distribution functions can be used. In addition, kinetic theory boundary conditions for the number density distribution function can be extended to construct a thermal boundary condition. The model has been validated in the slipflow regime against solutions of the NSF equations for shear and pressure driven flows between two planar plates. It is shown that the present thermal LBE model can capture some unique flow characteristics that the NSF equations fail to predict. The present work indicates that the thermal lattice Boltzmann model is a computationally economic method that is particularly suitable to simulate low speed thermal rarefied gas flows.
WSEAS TRANSACTIONS on MATHEMATICS C. S. Nor Azwadi, S. Syahrullail A ThreeDimension DoublePopulation Thermal Lattice BGK Model for Simulation of Natural Convection Heat Transfer in a Cubic Cavity
"... Abstract: In this paper, a doublepopulation thermal lattice Boltzmann was applied to solve three dimensional, incompressible, thermal fluid flow problem. The simplest lattice BGK D3Q6 model was proposed to determine the temperature field while D3Q15 or D3Q19 for the density and velocity fields. Th ..."
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Abstract: In this paper, a doublepopulation thermal lattice Boltzmann was applied to solve three dimensional, incompressible, thermal fluid flow problem. The simplest lattice BGK D3Q6 model was proposed to determine the temperature field while D3Q15 or D3Q19 for the density and velocity fields. The simulation of natural convection in a cubic cavity with Prandtl number 0.71 and Rayleigh number ranging from 10 3 to 10 5 were carried out and compared with the published results in literature. It was observed that the combination of D3Q6 and D3Q19 produces better numerical stability and accuracy compared to D3Q6 with D3Q15 for the simulation at high Rayleigh numbers. KeyWords: Double population, lattice Boltzmann, distribution function, BGK collision, natural convection 1
Thermal Lattice Boltzmann Models 1
"... Abstract In this paper, an incompressible twodimensional (2D) and threedimensional (3D) thermohydrodynamics for the lattice Boltzmann scheme are developed. The basic idea is to solve the velocity field and the temperature field using two different distribution functions. A derivation of the latti ..."
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Abstract In this paper, an incompressible twodimensional (2D) and threedimensional (3D) thermohydrodynamics for the lattice Boltzmann scheme are developed. The basic idea is to solve the velocity field and the temperature field using two different distribution functions. A derivation of the lattice Boltzmann scheme from the continuous Boltzmann equation for 2D is discussed in detail. By using the same procedure as in the derivation of the discretised density distribution function, it is found that new lattice of fourvelocity (2D) and eightvelocity (3D) models for internal energy density distribution function can be developed where the viscous and compressive heating effects are negligible. These models are validated by the numerical simulation of the 2D porous plate Couette flow problem where the analytical solution exists and the natural convection flows in a cubic cavity.
Lattice Boltzmann simulations of a timedependent natural convection problem
, 2013
"... A twodimensional double MultipleRelaxationTime thermal lattice Boltzmann method is used to simulate natural convection flows in differentially heated cavities. The buoyancy effects are considered under the Boussinesq assumption. Flow and temperature fields are respectively solved with nine and fi ..."
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A twodimensional double MultipleRelaxationTime thermal lattice Boltzmann method is used to simulate natural convection flows in differentially heated cavities. The buoyancy effects are considered under the Boussinesq assumption. Flow and temperature fields are respectively solved with nine and five discrete velocities models. Boundary conditions are implemented with the classical bounceback or a “onnode ” approach. The latter uses popular Zou and He and CounterSlip formulations. This paper evaluates the differences between the two implementations for steady and timedependent flows as well as the space and time convergence orders.