A BAYESIAN APPROACH FOR THE SOLUTION OF INVERSE PROBLEMS TO ESTIMATE RADIATIVE PROPERTIES

The main objective of the present work is related to the formulation and solutionof inverse problems in radiative heat transfer phenomena. The analysis consists in estimating parameters and functions of a participanting medium, such as optical thickness, single scattering albedo, diffusive reflectivities and phase function coefficients. It is performed with the numerical application of a Bayesian framework, which includes “Maximum a Posteriori” (MAP) and "Markov Chains Monte Carlo"(MCMC), within the Metropolis-Hastings procedure. These methodologiesproved to be effective for solving such problems.

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A PDF/Photon Monte Carlo Method for Radiative Heat Transfer in Turbulent Flames

Heat Transfer: Volume 1 ◽

10.1115/ht2005-72748 ◽

2005 ◽

Cited By ~ 2

Author(s):

Liangyu Wang ◽

Daniel C. Haworth ◽

Michael F. Modest

Keyword(s):

Heat Transfer ◽

Monte Carlo ◽

Radiative Heat Transfer ◽

Radiative Heat ◽

Numerical Models ◽

Dominant Role ◽

Flame Temperature ◽

Turbulent Flames ◽

Radiative Properties ◽

Pollutant Emissions

Thermal radiation plays a dominant role in heat transfer for most combustion systems. Accurate predictions of radiative heat transfer are essential for the correct determination of flame temperature, flame structure, and pollutant emissions in combustion simulations. In turbulent flames, transported probability density function (PDF) methods provide a reliable treatment of nonlinear processes such as chemical reactions and radiative emission. Here a second statistical approach, a photon Monte Carlo (PMC) method, is employed to solve the radiative transfer equation (RTE). And a state-of-the-art model for spectral radiative properties, the full-spectrum k-distribution (FSK) method, is employed. The FSK method provides an efficient and accurate approach for spectral integration in radiation calculations. The resulting model is applied to simulate radiation and turbulence/radiation interactions in nonluminous turbulent non-premixed jet flames. The initial results reported here emphasize sensitivities of computed results to variations in the physical and numerical models. Results with versus without radiation, results obtained using two different RTE solvers, and results with a gray-gas approximation versus a spectral FSK method are compared.

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Backward Monte Carlo Simulations in Radiative Heat Transfer

Journal of Heat Transfer ◽

10.1115/1.1518491 ◽

2003 ◽

Vol 125 (1) ◽

pp. 57-62 ◽

Cited By ~ 65

Author(s):

Michael F. Modest

Keyword(s):

Heat Transfer ◽

Monte Carlo ◽

Monte Carlo Method ◽

Monte Carlo Simulations ◽

Optical Thickness ◽

Radiative Heat ◽

Forward Direction ◽

Point Sources ◽

Small Spot ◽

Radiation Sources

Standard Monte Carlo methods trace photon bundles in a forward direction, and may become extremely inefficient when radiation onto a small spot and/or onto a small direction cone is desired. Backward tracing of photon bundles is known to alleviate this problem if the source of radiation is large, but may also fail if the radiation source is collimated and/or very small. In this paper various implementations of the backward Monte Carlo method are discussed, allowing efficient Monte Carlo simulations for problems with arbitrary radiation sources, including small collimated beams, point sources, etc., in media of arbitrary optical thickness.

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

Journal of Heat Transfer ◽

10.1115/1.4029546 ◽

2015 ◽

Vol 137 (5) ◽

Cited By ~ 11

Author(s):

Wenjun Ge ◽

Ricardo Marquez ◽

Michael F. Modest ◽

Somesh P. Roy

Keyword(s):

Heat Transfer ◽

Monte Carlo ◽

Monte Carlo Method ◽

Spherical Harmonics ◽

Radiative Heat ◽

Three Dimensional ◽

Radiative Properties ◽

Elliptic Pdes ◽

Square Enclosure ◽

Arbitrary Geometries

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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Radiative Heat Transfer Through a Randomly Packed Bed of Spheres by the Monte Carlo Method

Journal of Heat Transfer ◽

10.1115/1.3245582 ◽

1983 ◽

Vol 105 (2) ◽

pp. 325-332 ◽

Cited By ~ 46

Author(s):

Y. S. Yang ◽

J. R. Howell ◽

D. E. Klein

Keyword(s):

Heat Transfer ◽

Monte Carlo ◽

Radiative Heat Transfer ◽

Radiative Heat ◽

Packed Bed ◽

Radiative Properties ◽

Packed Beds ◽

Rigid Spheres ◽

Scattering Coefficients ◽

Effective Absorption

Radiative heat transfer through evacuated randomly packed beds of uniform-diameter spheres is considered. A Monte Carlo technique is used to simulate the energy bundle traveling through the voids of the bed. The randomly packed bed is assumed to be an absorbing-scattering medium with effective absorption and scattering coefficients. The packing pattern is modeled by a numerical simulation of rigid spheres slowly settling into a randomly packed assemblage. The Monte Carlo simulation of radiant energy transport through the packed beds generates the transmission curve as a function of bed height and sphere emissivity. The effective absorption and scattering coefficients of the randomly packed bed are evaluated by using the solution of the two-flux equations and Monte Carlo transmission results. Results show a strong dependence of the thermal radiative properties on the packing structure and the size and emissivity of constitutent spheres. Qualitative agreement is shown in comparison with other work which used regular cubic packing, and with existing experimental data.

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