Man Young Kim

Unstructured finite-volume method for radiative heat transfer in a complex two-dimensional geometry with obstacles

The radiative heat transfer in a complex two-dimensional enclosure with obstacles with participating medium is very important in practical engineering applications. In order to deal with this problem, in this study the enite-volume method (FVM) for radiation has been derived using the unstructured grid system. A general discretization equation was formulated by introducing the directional weight and the step scheme for spatial differencing. For its comparison and validation, two test cases, an equilateral triangular enclosure and a square enclosure with bafe e, were chosen. Then, more complex and practical cases, such as a semicircular enclosure with cylinder hole, a square enclosure withe nned internal cylinder, anda furnacewithembeddedcoolingpipes, were investigated. All the results obtained by the unstructured FVM agreed very well with the exact solutions as well as the results obtained by the zone method. Furthermore, the wiggling behavior occurring in the blocked-off FVM was not produced by the unstructured FVM. Three types of manipulation of control angle overlap were also examined here. It was found that the solutions depended on the type of manipulation of control angle overlap, especially when the number of control angles was small. Usually, both the pixelation method and exact treatment introduced here yielded better solutions than the bold approximation.The radiative heat transfer in a complex two-dimensional enclosure with obstacles with participating medium is very important in practical engineering applications. In order to deal with this problem, in this study the finite-volume method (FVM) for radiation has been derived using the unstructured grid system. A general discretization equation was formulated by introducing the directional weight and the step scheme for spatial differencing. For its comparison and validation, two test cases, an equilateral triangular enclosure and a square enclosure with baffle, were chosen. Then, more complex and practical cases, such as a semicircular enclosure with cylinder hole, a square enclosure with finned internal cylinder, and a furnace with embedded cooling pipes, were investigated. All the results obtained by the unstructured FVM agreed very well with the exact solutions as well as the results obtained by the zone method. Furthermore, the wiggling behavior occurring in the blocked-off FVM was not produced by the unstructured FVM. Three types of manipulation of control angle overlap were also examined here. It was found that the solutions depended on the type of manipulation of control angle overlap, especially when the number of control angles was small. Usually, both the pixelation method and exact treatment introduced here yielded better solutions than the bold approximation.

Nonorthogonal finite-volume solutions of radiative heat transfer in a three-dimensional enclosure

A finite-volume solution procedure for radiative heat transfer in a three-dimensional nonorthogonal enclosure containing participating medium is proposed with geometric relations commonly adopted in computational fluid dynamics. A general discretization equation is formulated by using the directional weight and the step scheme for spatial differencing. The present approach is validated through comparison with the problems of hexahedral enclosure, annular sector, and three-dimensional combustion chamber, in which the solution accuracy as well as computation efficiency required have been examined for various cases. Alt of the results presented here support its accuracy as well as moderate efficiency in computation time in the nonorthogonai three-dimensional radiation calculation. Finally, the present method is applied to a kidney-shaped combustion chamber as a three-dimensional test case.

Analysis of Radiative Transfer in Cylindrical Enclosures Using the Finite Volume Method

Radiative heat transfer in a cylindrical enclosure with or without a concentric cylinder containing absorbing-, emitting-, and isotropically- or anisotropically-scattering media is studied by using the finite volume method (FVM) for radiation. Since the unit direction vector is defined with respect to the Cartesian base vectors, the intrinsic difficulty in treating an angular derivative encountered in the discrete ordinates method (DOM) does not arise in the FVM. For the special case of an axisymmetric cylinder, a mapping, which transforms the dependence of intensity on two-spatial and two-angular to three-spatial and one-angular variables, was adopted. The scattering phase function is approximated by a finite series of Legendre polynomials. Several solutions are obtained in axisymmetric as well as three-dimensional cylindrical geometries with participating media and compared with others obtained by different methods, which are unique in this work. The computational efficiency of the FVM is discussed by comparison with the DOM. The problem of control angle overlaps is also examined in the last example by changing the angular grid systems.

MODIFICATION OF THE DISCRETE-ORDINATES METHOD IN AN AXISYMMETRIC CYLINDRICAL GEOMETRY

The conventional discrete-ordinates method is modified and developed for the analysis of two-dimensional axisymmetric cylindrical enclosure with absorbing, emitting, and either isotropiclly or anisotropically scattering gray medium. The main characteristic of the present method Is that the control angles can be arbitrarily specified pertaining to each problem dealt with. The scattering phase Junction is approximated by a finite series of Legendre polynomials. In order to validate the formulations, four benchmark problems are considered and their results are compared with other predictions or experimental data. It is shown that the present method is quite accurate, computationally efficient, and easy to use for the analysis of axisymmetric radiation heat transfer.

NUMERICAL ANALYSIS OF CONDUCTION. CONVECTION, AND RADIATION IN A GRADUALLY EXPANDING CHANNEL

The problem with simultaneous conductive, connective, and radiative heat transfer is analyzed in a two-dimensional gradual expansion channel flow. The main objective is to generate a program to attack the radiation in a curvilinear coordinate system with momentum and energy equations involved. The governing equations are transformed into generalized coordinates. Whereas the SIMPLE algorithm developed in a body-fitted coordinate system is used to obtain the flow field solution, the finite volume method is applied to solve the radiative transfer equation. The accuracy and performance of the finite volume method for the radiation are validated in a well-known combined heat transfer problem by using a curvilinear grid system. Then detailed thermal characteristics are investigated in a gradually expanding channel through various parameters such as Prandtl number, conduction to radiation parameter, wall emissivity, and scattering albedo. Results show that radiation plays a significant role in the gradually expa...

Analysis of radiative heating of a rocket plume base with the finite-volume method

The finite-volume method for radiation is applied to investigate a radiative heating of rocket base plane due to searchlight and plume emissions. The exhaust plume is assumed to absorb, emit and scatter the radiant energy isotropically, as well as anisotropically, while the medium between the plume boundary and the base plane is cold and nonparticipating. The scattering phase function is modeled by a finite series of Legendre polynomials. After validating the benchmark solution by comparison with that of previous works obtained by the Monte-Carlo method, further investigations have been done by changing various parameters, such as plume cone angle, scattering albedo, scattering phase function, optical radius and nozzle exit temperature. The results show that the base plane is predominantly heated by the plume emission, rather than the searchlight emission, when the nozzle exit temperature is the same as that of plume.

Unstructured Polygonal Finite-Volume Solutions of Radiative Heat Transfer in a Complex Axisymmetric Enclosure

Radiative heat transfer in a complex axisymmetric enclosure with participating medium is investigated by using the finite-volume method (FVM). In particular, an implementation of the unstructured polygonal meshes is adopted by connecting each center point of the unstructured triangular meshes rather than joining the centroids of the triangular elements to the midpoints of the corresponding sides to form a polygonal element. Also, typical considerations regarding application of the present polygonal mesh system to axisymmetric radiation are discussed. After a mathematical formulation and corresponding discretization equation for the radiative transfer equation (RTE) are derived, the final discretization equation is introduced with the conventional finite-volume approach by using the directional weights. For validation and comparison, three test examples with complex axisymmetric geometries have been accomplished. The present study shows that not only is the method flexible in treating radiative problems with complex geometries, it is also accurate and efficient for the analysis of axisymmetric radiative heat transfer.

ANALYSIS OF CONDUCTION AND RADIATION HEAT TRANSFER IN A 2-D CYLINDRICAL MEDIUM USING THE MODIFIED DISCRETE ORDINATE METHOD AND THE LATTICE BOLTZMANN METHOD

This article deals with the analysis of radiative transport with and without conduction in a finite concentric cylindrical enclosure containing absorbing, emitting, and scattering medium. Isothermal medium as the radiation source confined between the cold cylinders and a nonisothermal medium with the inner cylinder as the radiation source are the two nonradiative and radiative equilibrium problems. They involve only calculation of radiative information. In the third problem, a conducting-radiating medium is thermally perturbed by raising the temperature of the inner cylinder. In all problems, radiative information is computed using the modified discrete ordinate method (MDOM), and in the third problem, the lattice Boltzmann method (LBM) is used to formulate and solve the energy equation. Depending on the problems, effects of various parameters such as the extinction coefficient, the scattering albedo, the boundary emissivity, the conduction-radiation parameter, and the radius ratio are studied on temperature and heat flux distributions. The MDOM and the LBM-MDOM results are compared with those available in the literature. To further establish the accuracy of the MDOM and the LBM-MDOM results, in all problems, comparisons are made with the results obtained from the finite volume method (FVM) and the finite difference method-FVM approach, in which FVM provides the radiative information. The selection of the FDM-FVM for the third problem is also with the objective that for this problem, not much work is reported in which the FVM is used to calculate the radiative information. MDOM and LBM-MDOM results are found to compare well with those available in the literature, and in all cases they are in excellent agreement with FVM and FDM-FVM approaches.

Lattice Boltzmann Method Applied to the Analysis of Transient Conduction-Radiation Problems in a Cylindrical Medium

The lattice Boltzmann method (LBM) is applied to solve the energy equation of a transient conduction-radiation heat transfer problem in a 1-D concentric cylindrical participating medium. The finite-volume method (FVM) is used to obtain the radiative information. To study the effectiveness of the LBM-FVM combination to conduction-radiation problems in cylindrical media, the energy equation of the problem is also solved using the finite-difference method (FDM) in which the FVM is used to compute radiative information. The effects of different parameters, such as the conduction-radiation parameter, the scattering albedo, the extinction coefficient, and the radius ratio on temperature distributions in the medium are studied. Results of the present work are benchmarked against those available in the literature. LBM-FVM results are also compared with those obtained by the FDM-FVM combination. In all cases, excellent agreement has been obtained.

Inverse Natural Convection Problem with Radiation in Rectangular Enclosure

Inverse thermal problem is applied to natural convective flow with radiative heat transfer. The bottom wall temperature in the 2-D cavity domain is estimated by using gas temperature measurements in the flow field. The inverse problem is solved through a minimization of an objective function using the conjugate gradient method with adjoint problem. The effects of functional form of bottom wall temperature profile, the number and the position of measurement points, and the measurement errors are investigated and discussed. The conjugate gradient method is found to work well in estimating the bottom wall temperature, even when natural convection with radiation phenomena is involved.