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Research Papers: Radiative Heat Transfer

Implementation of High-Order Spherical Harmonics Methods for Radiative Heat Transfer on openfoam

[+] Author and Article Information
Wenjun Ge

School of Engineering,
University of California,
Merced, CA 95343
e-mail: wge@ucmerced.edu

Ricardo Marquez

School of Engineering,
University of California,
Merced, CA 95343
e-mail: rmarquez3@ucmerced.edu

Michael F. Modest

Professor
Fellow ASME
School of Engineering,
University of California,
Merced, CA 95343
e-mail: mmodest@ucmerced.edu

Somesh P. Roy

School of Engineering,
University of California,
Merced, CA 95343
e-mail: sroy3@ucmerced.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 19, 2014; final manuscript received December 29, 2014; published online February 10, 2015. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 137(5), 052701 (May 01, 2015) (9 pages) Paper No: HT-14-1548; doi: 10.1115/1.4029546 History: Received August 19, 2014; Revised December 29, 2014; Online February 10, 2015

A general formulation of the spherical harmonics (PN) methods was developed recently to expand the method to high orders of PN. The set of N(N + 1)/2 three-dimensional second-order elliptic PDEs formulation and their Marshak boundary conditions for arbitrary geometries are implemented in the openfoam finite volume based cfd software. The results are verified for four cases, including a 1D slab, a 2D square enclosure, a 3D cylindrical enclosure, and an axisymmetric flame. All cases have strongly varying radiative properties, and the results are compared with exact solutions and solutions from the photon Monte Carlo method (PMC).

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Figures

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Fig. 1

Definition of Euler angles for an arbitrary rotation

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Fig. 5

Incident radiation for a cylinder enclosure at two axial locations with various PN approximations. (a) z = 0.71 and (b) z = 1.20.

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Fig. 6

Cylinder mesh of scaled Flame D in the analysis

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Fig. 7

Mean temperature and mass fraction fields for scaled Sandia Flame D

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Fig. 8

Radiative source for Sandia Flame D × 4 at two axial locations as calculated with various PN approximations. (a) z = 1.00 m and (b) z = 1.43 m.

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Fig. 2

Rotations of 1D slab at angles φ=0,45 deg,-45 deg in the x-y plane. The medium properties increase with low values at the lower wall to higher values at the upper wall.

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Fig. 3

Comparing incident radiation and radiative heat source with analytical solutions of PN and exact solution of 1D slab. (a) Incident radiation G and (b) radiative heat source ∇·q.

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Fig. 4

Incident radiation and radiative source for a square enclosure with various PN approximations. (a) Ck = 1, (b) Ck = 0.1, and (c) Ck = 0.01.

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