Xin-Lin Xia

Temperature field of radiative equilibrium in a semitransparent slab with a linear refractive index and gray walls

Abstract The temperature field in a semitransparent slab of absorbing–emitting gray medium at radiative equilibrium is solved in this paper. The medium has a linear refractive index and the two boundaries are diffuse gray walls. A curved ray tracing technique is combined with a pseudo-source adding method to deduce the radiative intensities on the gray walls. And on the basis of the previous work done by Ben Abdallah and Le Dez, the discrete temperature field in the slab is deduced. The influences of refractive index distribution, boundary wall emissivities and optical thickness on the radiative equilibrium temperature field are examined. The results display the significant influences of the refractive index distribution and the boundary wall emissivities.

Radiative intensity solution and thermal emission analysis of a semitransparent medium layer with a sinusoidal refractive index

The radiative intensity in a sinusoidal refractive index semitransparent medium layer is solved by the curved ray-tracing method in combination with the pseudo-source adding method. One boundary of the medium layer is an opaque diffuse substrate wall. The other boundary is a semitransparent specular or diffuse surface, from which the medium thermal emission emerges. With considering a linear temperature distribution, the radiative intensity formulae are, respectively, deduced under the two boundary conditions. On the basis of the radiative intensity solutions, the directional and hemispherical emission of the medium layer with a specular surface as well as the hemispherical emission of that with a diffuse surface are calculated. The influences of the optical thickness, sinusoidal refractive index distribution and linear temperature distribution on the thermal emission are investigated. The results show that the effects of refractive index and temperature distribution are significant and are different under the two reflecting modes of the surface.

Simultaneous radiation and conduction heat transfer in a graded index semitransparent slab with gray boundaries

Abstract The simultaneous radiation and conduction heat transfer in a semitransparent slab of absorbing–emitting gray medium is solved in this paper. The refractive index of the medium spatially varies in a linear relationship, and the two boundary walls are diffuse and gray. A curved ray tracing technique in combination with a pseudo-source adding method is employed to deduce the radiative intensities on gray walls. Resorting to some of the results presented by Ben Abdallah and Le Dez, an exact expression of the radiative flux in medium is deduced. The influences on the temperature and radiative flux fields are examined, which are caused by the refractive index distribution, absorbing coefficient, thermal conductivity and the boundary wall emissivities. The results display the significant influences of the refractive index distribution and boundary wall emissivities on the radiative flux and temperature in medium.

Comparison of two methods for solving radiative heat transfer in a gradient index semitransparent slab

Two numerical methods for solving the radiative heat transfer in a gradient index semitransparent slab are compared. The slab is discretized into many sublayers. The constant refractive index assumption in a sublayer and the ray splitting and tracing technique are used in the first method, and the linear approximation of refractive index in a sublayer and the curved ray tracing technique are adopted in the second method. The heat transfer at radiative equilibrium and coupled radiation-conduction are involved in the comparison. The results of the two methods show good agreement, but their calculating efficiencies are found to be quite different.

Implementation of density-based solver for all speeds in the framework of OpenFOAM ☆

Abstract In the framework of open source CFD code OpenFOAM, a density-based solver for all speeds flow field is developed. In this solver the preconditioned all speeds AUSM+(P) scheme is adopted and the dual time scheme is implemented to complete the unsteady process. Parallel computation could be implemented to accelerate the solving process. Different interface reconstruction algorithms are implemented, and their accuracy with respect to convection is compared. Three benchmark tests of lid-driven cavity flow, flow crossing over a bump, and flow over a forward-facing step are presented to show the accuracy of the AUSM+(P) solver for low-speed incompressible flow, transonic flow, and supersonic/hypersonic flow. Firstly, for the lid driven cavity flow, the computational results obtained by different interface reconstruction algorithms are compared. It is indicated that the one dimensional reconstruction scheme adopted in this solver possesses high accuracy and the solver developed in this paper can effectively catch the features of low incompressible flow. Then via the test cases regarding the flow crossing over bump and over forward step, the ability to capture characteristics of the transonic and supersonic/hypersonic flows are confirmed. The forward-facing step proves to be the most challenging for the preconditioned solvers with and without the dual time scheme. Nonetheless, the solvers described in this paper reproduce the main features of this flow, including the evolution of the initial transient. Program summary Program title: allSpeedUnsteadFoam/allSpeedUnsteadFoam_dualtime Catalogue identifier: AETK_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AETK_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License No. of lines in distributed program, including test data, etc.: 255467 No. of bytes in distributed program, including test data, etc.: 971156 Distribution format: tar.gz Programming language: C++. Computer: All capable of running Linux. Operating system: Linux. Has the code been vectorized or parallelized?: Yes Parallelized RAM: 500 MB or more Classification: 12. External routines: OpenFOAM ( http://www.openfoam.org ) Nature of problem: This software provides a library of models for the simulation of steady and unsteady all speeds flow field (all Mach number flow field including incompressible and compressible flow). Combining this library with other libraries within OpenFOAM, such as turbulence, radiation, solid conduction, etc., the more complex multi-physics model including all speeds flow field could be established conveniently. Solution method: Standard finite volume method (FVM) is used for solving all the preconditioned conservation governing equations. The preconditioned all speeds AUSM+(P) scheme is adopted to discretize the convective term in the governing equations. The total variation diminishing (TVD) scheme with interface reconstruction is used to improve the accuracy of this solver. The dual time scheme is used to solve the unsteady problem. Restrictions: The limiter functions have obvious effect on the accuracy of the numerical result and according to actual situation, so the selection of limiter functions should be focused on. Running time: It can vary from minutes to days to weeks depending on the size of the system, length of time simulated and number of processors used.

Solution of radiative heat transfer in a semitransparent slab with an arbitrary refractive index distribution and diffuse gray boundaries

Abstract On the basis of medium discretization and local linear approximation of refractive index distribution, the curved ray tracing technique is used in combination with the pseudo source adding method to numerically solve the radiative heat transfer in a semitransparent slab with an arbitrary refractive index distribution and two diffuse gray walls. The radiative equilibrium temperature field of a linear refractive index distribution is evaluated by this method and the results show excellent agreement with that of the previous research. For two types of sinusoidal refractive index distributions, the radiative equilibrium temperature field as well as the temperature and heat flux fields of coupled radiation–conduction are investigated in detail. The results show considerable significance of the gradient refractive index effect, and some important conclusions are to be obtained.

Transient coupled heat transfer in multilayer composite with one specular boundary coated

Abstract By the ray tracing⧹node method, the transient coupled radiative and conductive heat transfer in absorbing, scattering multilayer composite is investigated with one surface of the composite being opaque and specular, and the others being semitransparent and specular. The effect of Fresnel’s reflective law and Snell’s refractive law on coupled heat transfer are analyzed. By using ray tracing method in combination with Hottel and Sarofim’s zonal method and spectral band model, the radiative intensity transfer model have been put forward. The difficulty for integration to solve radiative transfer coefficients (RTCs) is overcame by arranging critical angles according to their magnitudes. The RTCs are used to calculated radiative heat source term, and the transient energy equation is discretized by control volume method. The study shows that, for intensive scattering medium, if the refractive indexes are arranged decreasingly from the inner part of the composite to both side directions respectively, then, the total reflection phenomenon in the composite is advantageous for the scattered energy to be absorbed by the layer with the biggest refractive index, so at transient beginning a maximum temperature peak may appear in the layer with the biggest refractive index.

Numerical Study of Radiation Characteristics in a Dish Solar Collector System

This paper aims at predicting radiation characteristics of the solar collector system by the Monte Carlo method with respect to the corresponding optical properties. Several probability models were introduced to analyze the effects of sunshape and surface roughness. Directional characteristics of radiative flux in the focal region and flux distribution of the cavity receiver were considered. An equivalent radiation flux method is presented for designing the shape of the cavity receiver. Based on the relative numerical simulation results, a new shape cavity receiver called “upside-down tear drop” is proposed to meet an almost uniform radiation flux field. Radiation effects due to multiple reflections and thermal emission in the cavity are parametrized by using the radiative exchange factor. The calculation results can be a valuable reference for the design and assemblage of the dish solar collector system. DOI: 10.1115/1.2840570

A Curve Monte Carlo Method for Radiative Heat Transfer in Absorbing and Scattering Gradient-Index Medium

By discretizing the medium into many sublayers and employing a linear refractive index approximation for each sublayer, a curve Monte Carlo method is developed to solve the radiative heat transfer in an absorbing and scattering gradient-index medium. The probability models for emission point and radiation transfer path samplings are derived. For an absorbing and isotropic scattering medium with a sinusoidal refractive index distribution, the effects of optical thickness, boundary characteristics, and isotropic scattering on radiative equilibrium temperature and radiative heat flux in the medium are investigated by the method. From the analysis, some valuable information is obtained.

Determined Optical Constants of ZnSe Glass from 0.83 to 21 µm by Transmittance Spectra: Methods and Measurements

Based on the transmittance spectra modeling, spectroscopic methods were developed to determine the optical constants of glass materials including extinction coefficient and refractive index. The transmittance spectrograms of ZnSe glass slabs at normal incidence with different thicknesses in the infrared wavelength 0.83?21 ?m were measured by a Bruke V70 Fourier transform infrared (FTIR) spectrometer. These values were introduced into spectroscopic methods to calculate the optical constants of ZnSe glass. The results showed most of the optical constants of ZnSe determined by the new method had a good agreement with previously data, indicating that the spectroscopic methods can be used to determine the optical constants of glass materials in most infrared spectra.