Li-Ming Ruan

On the discrete ordinates method for radiative heat transfer in anisotropically scattering media

Abstract In the discrete ordinates method (DOM), the normalized condition for the numerical quadrature of some complex scattering phase functions may not be satisfied. In this paper, a revised discrete ordinates method (RDOM) is developed to overcome this problem, in which a renormalizing factor is added into the numerical quadrature of in-scattering term. The RDOM is used to solve the radiative transfer problem in one-dimensional anisotropically scattering media with complex phase function. The radiative heat fluxes obtained by the RDOM are compared with those obtained by the conventional discrete ordinates method (CDOM) and Monte Carlo method. The results show the RDOM can overcome the false scattering resulted from the numerical quadrature of in-scattering term and improve largely the accuracy of solution of the radiative transfer equation by comparison with the CDOM.

Transient coupled radiative and conductive heat transfer in an absorbing, emitting and scattering medium

Abstract On the basis of our previous papers, the redistribution of radiative energy in the case of isotropic scattering is investigated and the radiative transfer coefficient (RTC) under specular reflection in an absorbing, emitting and isotropic scattering parallel slab is derived. Considering both multi-reflection and multi-scattering in the derivation, the RTC can accommodate various boundary conditions under specular reflection. By accumulating the RTC for specular reflection boundary and that for diffuse reflection boundary linearly, the RTC are calculated. The validity and high precision of the formula for the RTC are confirmed by comparing with references. The effects of single-scattering albedo ω, Planck number Np and refractive index of STM nm on the transient coupled heat transfer in a one-dimensional isotropic scattering medium are reviewed for: (a) two semi-transparent boundaries; and (b) one semi-transparent boundary and one opaque boundary. The presented calculation and formula for the redistribution of the scattering energy can also be applied to other radiative calculations, such as total radiative exchange area or total radiative transfer coefficient in multi-dimensional isotropic scattering media.

Temperature response in absorbing, isotropic scattering medium caused by laser pulse

Abstract On the basis of our previous papers (H.P. Tan, B. Maestre, M. Lallemand, Journal of Heat Transfer 113 (1) (1991) 166–173; H.P. Tan, T.W. Tong, L.M. Ruan, X.L. Xia, Q.Z. Yu, Int. J. Heat Mass Transfer 42 (1999) 2967–2980), the radiative source term in absorbing, emitting, isotropic scattering medium, caused by collimated incidence through semitransparent boundary, is deduced in this paper. With some different sorts of boundary conditions, optical, spectral, and scattering characters, the transient temperature response, produced by a short-time laser pulse irradiating the surface of a semitransparent medium is simulated. The simulating results show that coating the non-incident side of medium with strongly absorbing material and selecting suitable incident wavelength, can increase the excess temperature of the non-incident surface, or can reduce the incident radiative intensity if keeping the excess temperature identical to that without coating or with coating both sides of the medium, and so, the probability of producing non-Fourier effect may be reduced.

Simultaneous retrieval of the complex refractive index and particle size distribution.

A secondary optimization technique is proposed that allows the complex refractive index and particle size distribution (PSD) to be retrieved simultaneously by using the diffuse transmittance (T), diffuse reflectance (R), and collimated transmittance (T(c)) of a 1-D spherical particle systems as measured values. In the proposed method, two 1-D experimental samples of different thicknesses were exposed to continuous wave lasers of two different wavelengths. First, T, R, and T(c) were calculated by solving the radiative transfer equation. Then, the complex refractive index and PSDs were retrieved simultaneously by applying the inversion technique, quantum particle swarm optimization. However, the estimated results of the PSDs proved to be inaccurate. Hence, a secondary optimization was performed to improve the accuracy of the PSDs on the basis of the first optimization process. The results showed that the proposed technique can estimate the complex refractive index and particle size distribution accurately.

Inverse Transient Radiative Analysis in Two-Dimensional Turbid Media by Particle Swarm Optimizations

Three intelligent optimization algorithms, namely, the standard Particle Swarm Optimization (PSO), the Stochastic Particle Swarm Optimization (SPSO), and the hybrid Differential Evolution-Particle Swarm Optimization (DE-PSO), were applied to solve the inverse transient radiation problem in two-dimensional (2D) turbid media irradiated by the short pulse laser. The time-resolved radiative intensity signals simulated by finite volume method (FVM) were served as input for the inverse analysis. The sensitivities of the time-resolved radiation signals to the geometric parameters of the circular inclusions were also investigated. To illustrate the performance of these PSO algorithms, the optical properties, the size, and location of the circular inclusion were retrieved, respectively. The results showed that all these radiative parameters could be estimated accurately, even with noisy data. Compared with the PSO algorithm with inertia weights, the SPSO and DE-PSO algorithm were demonstrated to be more effective and robust, which had the potential to be implemented in 2D transient radiative transfer inverse problems.

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

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 twodimensional enclosure. DOI: 10.1115/1.2430720

Transient coupled heat transfer in a multi-layer composite with opaque specular surfaces and semitransparent specular interfaces

Abstract In this paper, one-dimensional transient coupled radiative and conductive heat transfer in a multi-layer absorbing and isotropic scattering composite is investigated. The composite is considered to be of opaque specular boundaries and semitransparent specular interfaces. In combination with ray tracing method, spectral band model and the Hottel and Sarofims zonal method, the radiative transfer coefficients (RTCs) of the multi-layer composite are deduced. The RTCs are used to calculate the radiative heat source term in the transient energy control equation, which is solved by the fully implicit discrete control-volume method. The effects of refractive index and vacuum space on transient coupled heat transfer are analyzed. Except for refractive index, all the other parameters of each layer have been kept the same, and the total thickness also has been kept unchanged, then along the thickness of the composite when the decrement or the increment of refractive index decreases as layer number increases, the temperature profile becomes smoother and the steady heat flux increases.

Simultaneous retrieval of temperature-dependent absorption coefficient and conductivity of participating media

A secondary optimization technique was proposed to estimate the temperature-dependent thermal conductivity and absorption coefficient. In the proposed method, the stochastic particle swarm optimization was applied to solve the inverse problem. The coupled radiation and conduction problem was solved in a 1D absorbing, emitting, but non-scattering slab exposed to a pulse laser. It is found that in the coupled radiation and conduction problem, the temperature response is highly sensitive to conductivity but slightly sensitive to the optical properties. On the contrary, the radiative intensity is highly sensitive to optical properties but slightly sensitive to thermal conductivity. Therefore, the optical and thermal signals should both be considered in the inverse problem to estimate the temperature-dependent properties of the transparent media. On this basis, the temperature-dependent thermal conductivity and absorption coefficient were both estimated accurately by measuring the time-dependent temperature, and radiative response at the boundary of the slab.

Refractive Index Effects on Heat Transfer in Multilayer Scattering Composite

By the use of the ray tracing method, in combination with Hottel and Sarofims zonal method and spectral model, transient coupled radiative and conductive heat transfer in a multilayer absorbing, isotropically scattering composite with semitransparent and specular surfaces and interfaces is investigated. The specular reflectivities of all of the surfaces and interfaces are determined by Fresnels reflective law and Snells refractive law. For the ray tracing method, the complex total reflection problem of the multilayer composite is properly solved, and the radiative transfer coefficients (RTCs) of the multilayer composite are derived. The RTCs are used to calculate a radiative source term, and the transient energy equation is solved by the fully universal implicit discrete control volume method. Combined with extinction coefficient, conduction-radiation parameter, scattering albedo, layer thickness, and number of layers, the effects of refractive index on pure radiative and coupled radiative and conductive heat transfer are investigated

Fast method of retrieving the asymmetry factor and scattering albedo from the maximum time-resolved reflectance of participating media.

This research presents a parametric study of the time-resolved hemispherical reflectance of a semi-infinite plane-parallel slab of homogeneous, nonemitting, absorbing, and anisotropic scattering medium exposed to a collimated Gaussian pulse. The one-dimensional transient radiative transfer equation was solved by using the finite volume method. The internal reflection at the medium-air interface caused by the mismatch of the refractive indices was considered. In particular, this work focused on the maximum diffuse hemispherical reflectance. Three different optical regions were identified according to the dimensionless pulsewidth βctp. The correlation between the normalized maximum hemispherical reflectance and βctp was conformed to the Boltzmann function. The coefficients in the correlating functions of the match and mismatch refractive index cases were fitted as polynomial fitting functions of the single scattering albedo ω and Henyey-Greenstein asymmetric factor g. Thus, ω and g can be simultaneously reconstructed by the semi-empirical correlations without solving the forward model. In conclusion, the proposed method can potentially retrieve the asymmetry factor and single scattering albedo of participating media accurately and efficiently.