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RESEARCH PAPERS: Radiative Heat Transfer

Finite Element Simulation for Short Pulse Light Radiative Transfer in Homogeneous and Nonhomogeneous Media

[+] Author and Article Information
W. An

School of Energy Science and Engineering, Harbin Institute of Technology, 150001 Harbin, P.R.C.anwei@hit.edu.cn

L. M. Ruan1

School of Energy Science and Engineering, Harbin Institute of Technology, 150001 Harbin, P.R.C.ruanlm@hit.edu.cn

H. P. Tan, H. Qi, Y. M. Lew

School of Energy Science and Engineering, Harbin Institute of Technology, 150001 Harbin, P.R.C.

1

Corresponding author.

J. Heat Transfer 129(3), 353-362 (Jun 26, 2006) (10 pages) doi:10.1115/1.2430720 History: Received November 22, 2005; Revised June 26, 2006

With the rapid progress on ultrashort pulse laser, the transient radiative transfer in absorbing and scattering media has attracted increasing attention. The temporal radiative signals from a medium irradiated by ultrashort pulses offer more useful information which reflects the internal structure and properties of media than that by the continuous light sources. In the present research, a finite element model, which is based on the discrete ordinates method and least-squares variational principle, is developed to simulate short-pulse light radiative transfer in homogeneous and nonhomogeneous media. The numerical formulations and detailed steps are given. The present models are verified by two benchmark cases, and several transient radiative transfer cases in two-layer and three-layer nonhomogeneous media are investigated and analyzed. The results indicate that the reflected signals can imply the break of optical properties profile and their location. Moreover, the investigation for uniqueness of temporal reflected and transmitted signals indicate that neither of these two kinds of signals can be solely taken as experimental measurements to predict the optical properties of medium. They should be measured simultaneously in the optical imaging application. The ability of the present model to deal with multi-dimensional problems is proved by the two cases in the two-dimensional enclosure.

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Figures

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Figure 1

The physical model of transient radiative transfer

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Figure 2

The dimensionless heat flux and incident radiation in one-dimensional slab at different time: (a) the dimensionless heat flux; and (b) the dimensionless incident radiation. The optical thickness is 1.0 and the albedo is 0.5.

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Figure 3

The structural and optical properties of the two-layer media: the optical thicknesses of the two-layer media are all 0.5; their albedoes are 0.1 and 0.9, respectively

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Figure 4

The reflectance in the two-layer inhomogenous media: the results of the left-incident and right-incident light

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Figure 5

The schematic diagram for Cases 1–3: the locations of the interface are 0.2, 0.5, and 0.8m, respectively. The optical thicknesses and albedos of two-layer media are equivalent in the three cases.

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Figure 6

The reflectance and transmittance in the two-layer media for Cases 1–3: (a) the reflectance; and (b) the transmittance

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Figure 7

The reflectance in the two-layer media for Cases 4–6: the “dual peak” phenomenon can be observed in Case 4, but cannot be founded in Cases 5 and 6

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Figure 8

The schematic diagram for the three-layer media: the absorbing and scattering coefficient of the two side layers are 0.25m−1 and 2.25m−1, that of the middle layer are 18.0m−1 and 2.0m−1 in Case 1. They become 8.0m−1 and 2.0m−1 in Case 2.

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Figure 9

The reflectance and transmittance in the three-layer media: (a) the reflectance; and (b) the transmittance. The reflected signals are very close in the majority of time for the two cases. The transmitted signals are obviously different.

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Figure 10

Effect of albedo in the optically thick media: the albedos are 0.9, 0.5, and 0.1, respectively

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Figure 11

The reflectance and transmittance in the two dimensional homogeneous media: (a) the reflectance; and (b) the transmittance. The optical thickness τx=τy=10 and the albedo is 0.998.

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Figure 12

The schematic diagram for the two-dimensional inhomogeneous media: the absorbing and isotropic scattering coefficients of background media are 0.01m−1 and 1.99m−1, respectively; they become 0.05m−1 and 9.95m−1 in the center core

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Figure 13

The detected signals on the boundary of 2D inhomogeneous media: (a) the reflectance at points 1–4; (b) the transmittance at points 5–9, and (c) the transmittance at points 10–14

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