Simulation of Natural Convection in the Presence of Volumetric Radiation Using the Lattice Boltzmann Method

Mondal, Bittagopal; Mishra, Subhash C.

doi:10.1080/10407780802603121

Cited by 90 publications

(52 citation statements)

References 40 publications

(74 reference statements)

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“…(34), the 4th order Wendland's function, 50 given by Eq. (35), is chosen that is compactly supported and continuous up to the 4th order derivatives.…”

Section: B Moving Least-squares Approximationmentioning

confidence: 99%

“…30 Besides, LBM can be coupled to a conventional numerical scheme to provide a convenient way to simulate multifield coupling problems such as the thermo-convective problems, thermo-magnetic systems, double diffusion models, coupled convection and radiation heat transfer problems, etc. In recent years, three different combinations have been proposed, namely, the combination of lattice-Boltzmann and finite difference method (LB-FDM), 13,14,31 the hybrid technique of lattice-Boltzmann and finite volume method (LB-FVM) [32][33][34][35] and the combination of lattice-Boltzmann and finite element method (LB-FEM). 36 One of the main advantages of LBM is that it is easy and robust to deal with the natural convection problems in complex geometries.…”

Section: Introductionmentioning

confidence: 99%

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Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Luo

Tan

2014

AIP Advances

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Transitions and bifurcations of transient natural convection in a horizontal annulus with radiatively participating medium are numerically investigated using the coupled lattice Boltzmann and direct collocation meshless (LB-DCM) method. As a hybrid approach based on a common multi-scale Boltzmann-type model, the LB-DCM scheme is easy to implement and has an excellent flexibility in dealing with the irregular geometries. Separate particle distribution functions in the LBM are used to calculate the density field, the velocity field and the thermal field. In the radiatively participating medium, the contribution of thermal radiation to natural convection must be taken into account, and it is considered as a radiative term in the energy equation that is solved by the meshless method with moving least-squares (MLS) approximation. The occurrence of various instabilities and bifurcative phenomena is analyzed for different Rayleigh number Ra and Prandtl number Pr with and without radiation. Then, bifurcation diagrams and dual solutions are presented for relevant radiative parameters, such as convection-radiation parameter Rc and optical thickness τ. Numerical results show that the presence of volumetric radiation changes the static temperature gradient of the fluid, and generally results in an increase in the flow critical value. Besides, the existence and development of dual solutions of transient convection in the presence of radiation are greatly affected by radiative parameters. Finally, the advantage of LB-DCM combination is discussed, and the potential benefits of applying the LB-DCM method to multi-field coupling problems are demonstrated.

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“…(34), the 4th order Wendland's function, 50 given by Eq. (35), is chosen that is compactly supported and continuous up to the 4th order derivatives.…”

Section: B Moving Least-squares Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Luo

Tan

2014

AIP Advances

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“…The usage of the LBM to formulate and solve different types of heat transfer problems involving volumetric radiation in different geometries has been extended (Mishra et al, 2014a, Chen and Zhang, 1999, Succi, 2001, Wang et al, 2013, Jiaung et al, 2001, Lankadasu and Mishra, 2005, Chaabane et al, 2011a, 2011b, Mishra and Mondal, 2009, Chaabane et al, 2011c. However, in all such problems, although the radiative information was computed using the conventional RTE solvers and in terms of formulation and computational time, the solution of the energy equation by the LBM was encouraging.…”

Section: Introductionmentioning

confidence: 99%

“…So, efforts toward development of efficient methods continue. In the recent past, the lattice Boltzmann method (LBM) has emerged as an efficient method to analyze a vast range of problems in fluid flow and heat transfer (Chen and Zhang, 1999, Succi, 2001, Wang et al, 2013, Jiaung et al, 2001, Lankadasu and Mishra, 2005, Chaabane et al, 2011a, 2011b, Mishra and Mondal, 2009, Chaabane et al, 2011c, Asinari et al, 2010and Di Rienzo et al, 2011. Unlike conventional methods, which solve the discretized macroscopic Navier-Stokes equations, the LBM uses simple microscopic kinetic models to stimulate complex transport phenomena.…”

Section: Introductionmentioning

confidence: 99%

“…In the recent past, the lattice Boltzmann method (LBM) has emerged as an efficient method to analyze a vast range of problems in fluid flow and heat transfer (Chen and Zhang, 1999, Succi, 2001, Wang et al, 2013, Jiaung et al, 2001, Lankadasu and Mishra, 2005, Chaabane et al, 2011a, 2011b, Mishra and Mondal, 2009, Chaabane et al, 2011c, Asinari et al, 2010and Di Rienzo et al, 2011. Unlike conventional methods, which solve the discretized macroscopic Navier-Stokes equations, the LBM uses simple microscopic kinetic models to stimulate complex transport phenomena.So, this surge in applications of the LBM, compared to existing CFD solvers, is owing to its simple calculation procedure, mesoscopic nature, simple and efficient implementation for parallel computation, easy, robust straight forward and efficient handing of complex geometry and boundary conditions, high computational performance with regard to stability, accuracy and precision and memory overhead over other methods (Succi, 2001).The usage of the LBM to formulate and solve different types of heat transfer problems involving volumetric radiation in different geometries has been extended (Mishra et al, 2014a, Chen and Zhang, 1999, Succi, 2001, Wang et al, 2013, Jiaung et al, 2001, Lankadasu and Mishra, 2005, Chaabane et al, 2011a, 2011b, Mishra and Mondal, 2009, Chaabane et al, 2011c. However, in all such problems, although the radiative information was computed using the conventional RTE solvers and in terms of formulation and computational time, the solution of the energy equation by the LBM was encouraging.…”

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confidence: 99%

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Analysis of Rayleigh-Bénard convection with thermal volumetric radiation using Lattice Boltzmann Formulation

Chaabane

Askri

Jemni

et al. 2017

JTST

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The interactions between Transient Rayleigh-Bénard convection and volumetric radiation are investigated by means of the lattice Boltzmann method (LBM) performed for a two dimensional participating Rayleigh-Bénard cell. Given that, the analysis of the transient convection-radiation finds applications in combustion chambers, rocket propulsion systems, the design of reactors, heat pipes, etc. in this paper, we extended the mesoscopic Lattice Boltzmann model for analyzing the coupled engineering problem Rayleigh-Bénard Convection with thermal radiation. In order to highlight and assess the aim and the computational advantage of computing the radiative information too using the LBM and to demonstrate the workability of the LBM to a such coupled problem in two dimensional media, first, transient Rayleigh-Bénard convection is solved using the lattice Boltzmann method (LBM) and then are compared with those available in the literature. The coupled transient case, Rayleigh-Bénard convection-radiation in participating media is extended, where LBM, is used, both to calculate the volumetric radiative information needed for the energy equation, which is solved using the LBM. Results of this recent approach LBM-LBM work are compared with those available in the literature. In all cases, good agreement has been obtained. Indeed, the recent numerical approach is found to be efficient, accurate, and numerically stable for the simulation of fluid flows with heat and mass transfer in presence of volumetric radiation in participating medium. The steady state stream-functions, isotherms and pressure distribution were compared with results available in the literature. It is found that the recent approach provides accurate results and it is computationally more efficient than others CFD numerical methods which approve the workability of this recent approach and this make it a new potential computational tool for solving a large class of engineering problems. Chaabane, Askri, Jemni and Ben Nasrallah, Journal of Thermal Science and Technology, Vol.12, No.2 (2017) 20 computing the different dependent variables. Thus, development of methods, remain an ongoing phenomenon in the field of radiative heat transfer. For example, in a combined mode transient convection-radiation problem, the radiative information, which appears in the form of the divergence of radiative heat flux in the energy equation can be computed using various methods such as the Monte Carlo method (MCM) (Modest, 2003), the discrete transfer method (DTM) (Cumber, 1995, Mishra et al., 2003, the discrete ordinates method (DOM) (Jamaluddin and Smith, 1988), the finite-volume method (FVM) (Mishra et al., 2014a, Chui et al., 1992, Patankar and Chai, 2000, Mathur and Murthy, 1998, Kim, 2008, Kim and Baek, 2005, the collapsed dimension method (CDM) (Mishra et al., 2003), etc.However, in multi-dimensional geometry, in a combined mode problem, even with the FVM, the computational time becomes exorbitant (Mishra et al., 2014b). So, efforts toward development of efficient met...

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Two‐dimensional lattice Boltzmann simulation of natural convection in differentially heated square cavity: Effect of Prandtl and Rayleigh numbers

2015

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A thermal lattice Boltzmann method is utilized for the numerical simulation of the natural convection heat transfer phenomena inside a differentially heated square cavity. Numerical simulations are performed to elucidate the combined effects of Prandtl number (0.71 ≤ Pr ≤ 100) and Rayleigh number (104 ≤ Ra ≤ 106) on heat transfer and fluid flow characteristics inside the cavity. Detailed insights are gained by the evaluation of isotherms, stream functions and vorticity profiles. For higher Prandtl and Rayleigh numbers, streamlines become more confined to hot wall with the loss of symmetry. Similarly, isotherms patterns become more stratified towards the hot wall. The centre‐line velocity and temperature profiles are also analyzed. Further, the heat transfer rate is estimated in terms of average Nusselt number. It suggests a proportional increase in the average Nusselt number with the increasing values of Prandtl number for considered range of Rayleigh numbers. Finally, the numerical data for the average Nusselt number are presented in the form of a correlation for their best utilization in design and engineering practices.

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Simulation of Natural Convection in the Presence of Volumetric Radiation Using the Lattice Boltzmann Method

Cited by 90 publications

References 40 publications

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Analysis of Rayleigh-Bénard convection with thermal volumetric radiation using Lattice Boltzmann Formulation

Two‐dimensional lattice Boltzmann simulation of natural convection in differentially heated square cavity: Effect of Prandtl and Rayleigh numbers

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