Two-dimensional axisymmetric formulation of high order spherical harmonics methods for radiative heat transfer

Ge, Wenjun; Modest, Michael F.; Marquez, Ricardo

doi:10.1016/j.jqsrt.2015.01.013

Cited by 24 publications

(5 citation statements)

References 21 publications

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“…It was found that while the P3 approximation is significantly more accurate than P1, the P5 approximation yields only a slight improvement in accuracy over P3, which is hardly justifiable regarding the increased computational effort. A simplified formulation for 2D axisymmetric problems, which also involves 2( + 1) 4 ⁄ simultaneous partial differential equations, was presented by Ge et al [50], and also implemented in OpenFOAM. Additional refinements of this work were reported by Ge et al [51] who derived a 2D Cartesian version of the higher-order PN method, extended the boundary conditions to allow for nonblack and mixed diffuse-specular surfaces, and to deal with specified radiative flux at the walls and for symmetry/specular reflection boundaries.…”

Section: Spherical Harmonic Methodsmentioning

confidence: 99%

The impact of radiative heat transfer in combustion processes and its modeling – with a focus on turbulent flames

Liu

Consalvi

Coelho

et al. 2020

Fuel

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Radiative heat transfer (RHT) is often the dominant mode of heat transfer in flames, fires, and combustion systems and affects significantly temperature distributions directly and kinetically controlled chemical processes indirectly. Modeling RHT accurately in multidimensional flames and combustion systems is challenging mainly due to the highly spectral dependence of radiative properties of combustion products, the high computational cost of solving the radiative transfer equation (RTE), and the strong turbulence and radiation interactions (TRI). Significant progress has been made in all the three aspects in the last three decades and the state-of-the-art models and methods have been incorporated into CFD practice for modeling fires, turbulent jet flames, and turbulent combustion in combustion systems. In this article, we first discuss the coupling between RHT and combustion and the important role played by RHT in some fundamental flame phenomena. Then we discuss the state-of-the-art radiation models with a focus on RTE solvers, radiative property models and TRI. Next, we review the recent simulations of turbulent combustion systems involving these state-of-the-art radiation models. Finally, we provide concluding remarks and some potential research areas to advance RHT modeling in multiphase reacting flows. Nomenclature, , area normal to directions x, y and z [m 2 ] non-grey stretching factor for WSGG, SLW, and FSK methods absorption cross-section of a soot primary particle [m 2 ] absorption cross-section of a soot aggregate [m 2 ] diameter [m] , , integral over a control angle of the direction cosines relative to x, y and z-axis particle size parameter [-] radiant fraction [-] array of variables defining the absorption coefficient, = { , , , } Ω solid angle [sr] Subscript Fuel direction j spectral line S soot at a given wavenumber Superscript aggregate lth direction (DOM) or lth control angle (FVM) mth direction (DOM) or mth control angle (FVM) primary particle Operators 〈 〉 Reynolds averaged quantity ′ Reynolds fluctuating quantity ̅ filtered (or resolved) quantity ′′ subgrid-scale (or residual) fluctuation Recently, quasi-MC methods [43], [44] were employed to solve RHT problems in 3D participating media, aimed at the improvement of the convergence rate, and therefore the computational efficiency. In these methods, the random numbers are replaced by low-

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Section: Spherical Harmonic Methodsmentioning

confidence: 99%

The impact of radiative heat transfer in combustion processes and its modeling – with a focus on turbulent flames

Liu

Consalvi

Coelho

et al. 2020

Fuel

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“…1a, FEF was produced by extruding ink in the syringe through the nozzle into the air with the piston movement. Dimensions of the geometrical model of FEF in DIW include: the inner diameter of syringe OpenFOAM is designed as a code for 3D space and defines all meshes as 3D meshes, but wedge type meshes are used for 2D axisymmetric problems specifically [34]. Thus, wedge type meshes were used for the simplified 2D axisymmetric model as shown in Fig.…”

Section: Meshes and Boundary Conditionsmentioning

confidence: 99%

Modeling and evaluation of freeform extruded filament based on numerical simulation method for direct ink writing

Hassan

Arrieta‐Escobar

et al. 2022

Int J Adv Manuf Technol

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Direct ink writing (DIW) is an extrusion-based additive manufacturing (AM) technique. One of the required factors for printing quality in DIW is to extrude continuous and tubular freeform extruded filaments (FEF) with diameters close to the nozzle inner diameter. This paper established a simulation model of FEF with volume of fluid (VOF) method and then evaluated the FEF based on the simulation results. First, ink properties including density, surface tension coefficient and rheological properties were determined by properties tests. Then, the model of FEF was established using VOF simulation method with the software OpenFOAM and two evaluation indicators, mean diameter and stability, were proposed to evaluate the FEF. Two inks, a cellulose ink and a Nivea Crème, were used under three levels of piston velocity to verify the method universality for different inks and variable process parameters. The prediction accuracy of the established simulation model was verified as the relative error between simulation and experimental results of diameter was less than 10.22%. In this work, it was found that: (1) piston velocity needed to be set higher than a minimum value to overcome yield stress and surface tension to successfully extrude filaments; (2) mean diameter of FEF decreased while stability of FEF decreased firstly and then increased as piston velocity increased. The proposed model and evaluation indicators gave an accurate and effective framework to analyze effect of the piston velocity on FEF, characterize the ink printability and find suitable printable windows for process parameters in DIW.

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“…The spherical harmonics (P N ) approximation results from expanding the angular intensity as a series of spherical harmonics [5][6][7][8][9][10][11]. The series is then truncated at some point defining the order of the approximation.…”

Section: The Spherical Harmonics Approximationmentioning

confidence: 99%

Coupling radiative heat transfer in participating media with other heat transfer modes

Tencer

Howell

2015

J Braz. Soc. Mech. Sci. Eng.

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transfer modes are minimized or eliminated as in Dewar flasks and cryogenic storage systems. In this review, we discuss the common and not-so-common methods for treating radiation heat transfer in participating (absorbing/emitting and scattering) media, and how these methods are coupled with the overall energy equation for treating thermal transfer problems.Because radiation is almost inevitably coupled with other heat transfer modes, an overall thermal analysis requires solution of the energy equation, which is actually a balance of energy rates. Here, we follow the development in Howell et al. [1].The general form for the energy equation for a compressible fluid is where D/Dt is the substantial derivative, the left-hand side accounts for changes in stored energy within the medium, and the terms on the right-hand side account for changes in pressure work, contributions by conduction and radiation, internal sources (chemical, electrical, nuclear, etc.,), and viscous dissipation. In most practical thermal analysis problems, the pressure work and viscous dissipation terms can be neglected.Of greatest interest here is the evaluation of the local divergence of radiative flux, −∇ · q r . This is the difference in the local absorbed radiative energy minus the local emitted radiation, 4π ∞ =0 κ I b d , where κ λ is the local spectral absorptivity of the medium and I λb is the blackbody intensity given by the Planck distribution. In an absorbing-emitting-scattering medium, the absorbed radiative energy is found by first finding the local radiative intensity I λ (Ω), which is defined as the spectral energy propagating in a given direction Ω per unit solid angle, per unit area AbstractThe common methods for finding the local radiative flux divergence in participating media through solution of the radiative transfer equation are outlined. The pros and cons of each method are discussed in terms of their speed, ability to handle spectral properties and scattering phenomena, as well as their accuracy in different ranges of media transport properties. The suitability of each method for inclusion in the energy equation to efficiently solve multi-mode thermal transfer problems is discussed. Finally, remaining topics needing research are outlined.

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Two-dimensional axisymmetric formulation of high order spherical harmonics methods for radiative heat transfer

Cited by 24 publications

References 21 publications

The impact of radiative heat transfer in combustion processes and its modeling – with a focus on turbulent flames

The impact of radiative heat transfer in combustion processes and its modeling – with a focus on turbulent flames

Modeling and evaluation of freeform extruded filament based on numerical simulation method for direct ink writing

Coupling radiative heat transfer in participating media with other heat transfer modes

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