燃烧产物辐射特性的误差对炉内辐射传热计算精度的影响

本文用离散坐标法对含吸收散射性介质矩形空腔内的３维辐射传递过程进行了模拟，并编写了相应的数值计算程序。利用该程序分析了介质的吸收系数、散射系数、相函数、光谱特性及壁面灰渣沉积层黑度的不确定性对矩形燃烧室内烟气温度及热流计算精度的影响。结果表明计算精度很大程度上取决于燃烧产物辐射特性的取值精度，特别是壁面灰渣沉积层黑度的取值精度。在煤粉燃烧室中，介质的散射不宜忽略。     

Extension of the zonal method to inhomogeneous non-grey semi-transparent medium

A radiation model is proposed to extend the zonal method of Hottel to semi-transparent inhomogeneous real combusting gas–soot mixture in a 2-D black-walled rectangular enclosure. The direct exchange areas are carried out by direct numerical integration and then adjusted to meet the conservation constraints using two smoothing processes namely the Larsen and Howell's least squares and generalized Lawson's improved smoothing methods, which has not been previously done to the best knowledge of the authors. The predicted net radiative heat flux distributions compare favorably with benchmark solutions for two test cases dealing with isothermal and non-isothermal homogeneous mediums. It is concluded from this investigation that there is no significant effect of the smoothing method on the computed wall heat fluxes for the homogeneous and inhomogeneous test cases using different grey gases number. The grid dependence study depicts that the numerical solutions fully achieve grid independence. It is worth noting that it can be proceeded with the present extended zonal method and computer code to more complex cases. The results based on the generalized Lawson's smoothing method compare favorably with those yielded by the popular least squares method and, consequently, can be considered as a benchmark solution for other investigations.     

NUMERICAL PREDICTION OF LAMINAR FORCED CONVECTION IN TRIANGULAR DUCTS WITH UNSTRUCTURED TRIANGULAR GRID METHOD

The flow and heat transfer characteristics of smooth triangular ducts with different apex angles of 15, 30, 60, and 90 under the fully developed laminar flow condition were predicted numerically using a finite volume method. The SIMPLE-like algorithm was employed together with an unstructured triangular grid method, where the grid was generated by a Delaunay method. The triangular grid was adopted instead of the traditional rectangular grid to fit better into the triangular cross section of the duct. Two kinds of boundary condition (uniform wall temperature and uniform wall heat flux) were considered. Comparison of the predictions with previous computational results indicated a very good agreement. Both the friction factor and Nusselt number (Nu) showed a strong dependence on apex angle of the triangular duct. When the apex angle was 60, the duct provided the highest steady-state forced convection from its inner surface to the airflow under the laminar flow condition.     

Local RBF meshless scheme for coupled radiative and conductive heat transfer

ABSTRACT

A local radial basis function meshless (LRBFM) method is developed to solve coupled radiative and conductive heat transfer problems in multidimensional participating media, in which compact support radial basis functions (RBFs) augmented on a polynomial basis are employed to construct the trial function, and the radiative transfer equation (RTE) and energy conservation equation are discretized directly at nodes by the collocation method. LRBFM belongs to a class of truly meshless methods which require no mesh or grid, and can be readily implemented in a set of uniform or irregular node distributions with no node connectivity. Performances of the LRBFM is compared to numerical results reported in the literature via a variety of coupled radiative and conductive heat transfer problems in 1D and 2D geometries. It is demonstrated that the local radial basis function meshless method provides high accuracy and great efficiency to solve coupled radiative and conductive heat transfer problems in multidimensional participating media with uniform and irregular node distribution, especially for coupled heat transfer problems in irregular geometry with Cartesian coordinates. In addition, it is extremely simple to implement.     

Finite volume method in 3-D curvilinear coordinates with multiblocking procedure for radiative transport problems

The finite volume method of radiation is implemented for complex 3-D problems in order to use it for combined heat transfer problems in connection with CFD codes. The method is applied for a 3-D block structured grid in a radiatively participating medium. The method is implemented in non-orthogonal curvilinear coordinates so that it can handle irregular structure with a body-fitted structured grid. The multiblocking is performed with overlapping blocks to exchange the information between the blocks. Five test problems are considered in this work. In the first problem, present work is validated with the results of the literature. To check the accuracy of multiblocking, a single block is divided into four blocks and results are validated against the results of the single block simulated alone in the second problem. Complicated geometries are considered to show the applicability of the present procedure in the last three problems. Both radiative and non-radiative equilibrium situations are considered along with an absorbing, emitting and scattering medium.     

Estimation of power of heaters in a radiant furnace for uniform thermal conditions on 3-D irregular shaped objects

For uniform thermal conditions on 3-D irregular shaped design objects, this paper reports estimation of optimal power of the panel heaters placed along the walls of a 3-D radiant furnace. Hemispherical, cylindrical, conical, and a combination of cylindrical and conical, and finally a case study of a car body model are considered as the design objects (DOs). The entire surface areas of the furnace walls and that of the DO are divided into surface elements. The surface elements of the furnace walls are made of the panel heaters. In this boundary design problem, the objective function is developed as an error function of estimated and the desired heat fluxes on the surfaces of DO. The radiative exchange among the surface elements is computed using the radiation element method by ray emission model (REM²), and the objective function is minimized using the micro-genetic algorithm (MGA). Power of the panel heaters are estimated for different sizes of the DOs. Although the panel heaters have been placed along the furnace walls, for uniform thermal conditions, for a given DO, not all are required. Having known that not all are required, to ease the control, estimations have also been shown by grouping the heaters along the furnace walls. This study provides a guideline for a priori knowing the heater setting and their corresponding power requirement in heating of 3-D irregular shaped objects.     

Heat transfer analysis of a two-dimensional rectangular porous radiant burner

In the present work, a 2-D rectangular porous burner is considered for investigation. Methane–air combustion with detailed chemical kinetics is used to model the combustion part. 164 chemical reactions with 20 species are considered. Separate energy equations for gas and solid phases are solved. The radiative part of the energy equation is modeled using the collapsed dimension method. The effects of the power density, equivalence ratio, extinction coefficient and volumetric heat transfer coefficient on temperature and concentration profiles are studied.     

THREE-DIMENSIONAL ANALYSIS OF THE WALKING-BEAM-TYPE SLAB REHEATING FURNACE IN HOT STRIP MILLS

Three-dimensional analysis is performed for the turbulent reactive flow and radiative heat transfer in the walking-beam-type slab reheating furnace by FLUENT. A simplified burner is validated against the results of the actual burner with the detailed grid resolution to avoid an excessive number of grids. The predicted temperature distribution in the furnace and global energy flow fractions are in reasonable agreement with available data. Distribution of the heat flux to the slabs, velocity vectors, and all major scalar variables in the furnace also are predicted. This study shows that three-dimensional analysis may be a useful tool to understand quantitatively the complicated combustion and heat transfer characteristics in the furnace.     

Efficiency analysis of radiative slab heating in a walking-beam-type reheating furnace

The thermal efficiency of a reheating furnace was predicted by considering radiative heat transfer to the slabs and the furnace wall. The entire furnace was divided into fourteen sub-zones, and each sub-zone was assumed to be homogeneous in temperature distribution with one medium temperature and wall temperature, which were computed on the basis of the overall heat balance for all of the sub-zones. The thermal energy inflow, thermal energy outflow, heat generation by fuel combustion, heat loss by the skid system, and heat loss by radiation through the boundary of each sub-zone were considered to give the two temperatures of each sub-zone. The radiative heat transfer was solved by the FVM radiation method, and a blocked-off procedure was applied to the treatment of the slabs. The temperature field of a slab was calculated by solving the transient heat conduction equation with the boundary condition of impinging radiation heat flux from the hot combustion gas and furnace wall. Additionally, the slab heating characteristics and thermal behavior of the furnace were analyzed for various fuel feed conditions.     

Chebyshev collocation spectral domain decomposition method for coupled conductive and radiative heat transfer in a 3D L-shaped enclosure

ABSTRACT

This paper presents a Chebyshev collocation spectral domain decomposition method (CSDDM) to study the coupled conductive and radiative heat transfer in a 3D L-shaped enclosure. The partitioned 3D L-shaped enclosure is subdivided into rectangular subdomains based on the concept of domain decomposition. The radiative transfer equation is angularly discretized by the discrete ordinate method with the SRAP_N quadrature scheme and then solved by the CSDDM using the same grid system as in solving the conduction. The effects of the conduction–radiation parameter, the optical thickness, the scattering albedo, and the aspect ratio on thermal behavior of the system are investigated. The results indicate that the 3D CSDDM has a good accuracy and can be considered as a good alternative approach for the solution of the coupled conduction and radiation problems in 3D partitioned domains.     

Fire dynamics simulations of a one-meter diameter methane fire

A one-meter diameter-methane fire was simulated to validate a fire dynamics simulation code for large-scale fires. A uniform grid size of 2.5 cm in the entire computational domain is used. Therefore, only large-scale motions of the fire are resolved. The subgrid-scale heat release is modeled using a mixture-fraction-based combustion model. The radiative heat loss is computed using two methods: a fixed radiative fraction method and a finite volume method. The computed puffing cycle frequency is affected very weakly by the radiation heat loss. The vertical velocity magnitudes without considering radiation heat loss are about 15% higher, particularly at locations farther away from the burner exit. Good agreement between the predictions and the recent data from Tieszen and co-workers at Sandia National Laboratory confirms the feasibility of fire dynamics simulations of relatively large fires.     

A heat transfer model for the analysis of transient heating of the slab in a direct-fired walking beam type reheating furnace

A mathematical heat transfer model for the prediction of heat flux on the slab surface and temperature distribution in the slab has been developed by considering the thermal radiation in the furnace chamber and transient heat conduction governing equations in the slab, respectively. The furnace is modeled as radiating medium with spatially varying temperature and constant absorption coefficient. The steel slabs are moved on the next fixed beam by the walking beam after being heated up through the non-firing, charging, preheating, heating, and soaking zones in the furnace. Radiative heat flux calculated from the radiative heat exchange within the furnace modeled using the FVM by considering the effect of furnace wall, slab, and combustion gases is introduced as the boundary condition of the transient conduction equation of the slab. Heat transfer characteristics and temperature behavior of the slab is investigated by changing such parameters as absorption coefficient and emissivity of the slab. Comparison with the experimental work show that the present heat transfer model works well for the prediction of thermal behavior of the slab in the reheating furnace.     

Thermal analysis of a 2-D heat recovery system using porous media including lattice Boltzmann simulation of fluid flow

The present work deals with the fluid flow simulation and thermal analysis of a two-dimensional heat recovery system using porous media. A basic high-temperature flow system is considered in which a high-temperature non-radiating gas flows through a random porous matrix. The porous medium, in addition to its convective heat exchange with the gas, may absorb, emit and scatter thermal radiation. It is desirable to have large amount of radiative heat flux from the porous segment in the upstream direction (towards the thermal system). The lattice Boltzmann method (LBM) is used to simulate fluid flow in the porous medium. The gas and solid phases are considered in non-local thermal equilibrium, and separate energy equations are applied to these phases. Convection, conduction and radiation heat transfers take place simultaneously in solid phase, but in the gas flow, heat transfer occurs by conduction and convection. In order to analyze the thermal characteristics of the heat recovery system, volume-averaged velocities through the porous matrix obtained by LBM are used in the gas energy equation and then the coupled energy equations for gas and porous medium are numerically solved using finite difference method. For computing of radiative heat flux in the porous medium, discrete ordinates method is used to solve the radiative transfer equation. Finally the effect of various parameters on the performance of porous heat recovery system is studied.     

有限体积法在电站锅炉炉膛辐射换热计算中的应用

辐射换热是大型锅炉炉膛内的主要换热形式,准确的计算炉膛内的辐射换热量对大型锅炉设计和优化有重要意义。本文将有限体积法推广用于求解和分析大型电站锅炉炉膛内的辐射换热。给出了有限体积法对辐射传递方程进行离散和求解的基本过程。评估了有限体积法求解大型电站锅炉炉膛辐射换热的可靠性。将有限体积法用于分析某电厂600MW锅炉炉膛内的辐射换热,结果表明有限体积法可以有效的求解大型电站锅炉炉膛内的复杂辐射换热过程。     

Estimation of slab surface radiative emissivities by solving an inverse coupled conduction,convection, and radiation problem

Slab surface radiative emissivities severely affect the radiative heat transfer in a reheating furnace, as well as the slabs’ coupled conduction, convection, and radiation. Accurate evaluation of these parameters is of significance to ensure the high accuracy of the mathematical model for a reheating furnace, which is beneficial to the energy saving. However, it is difficult to directly and accurately measure these parameters. In this article, slab surface radiative emissivities in a reheating furnace are estimated by solving a nonlinear inverse problem, which is an inverse coupled conduction, convection, and radiation problem. An efficient and accurate gradient method, i.e., Levenberg–Marquardt algorithm, is applied to obtain the solution of the inverse problem. First, a finite difference method and the complex-variable-differentiation method are used for sensitivity analysis, and the inversion accuracy coupled with the efficiency is demonstrated. Then, effects of initial guesses, measurement errors, and measurement locations on estimated slab surface radiative emissivities are investigated in detail. Finally, conclusions are drawn based on the results and analysis.     

A Study of the Radiant Heat Exchange within a Controlled-Atmosphere Furnace

Transient three-dimensional heat transfer between a traversing, structured, and rectangular object and an enclosure is studied. This study investigates the heat transfer process that occurs in brazing an aluminum heat exchanger in a controlled-atmosphere furnace. A model's development is discussed with prescribed enclosure temperature boundary conditions. The program determines the radiant heat exchange between gray diffuse surfaces, and solves the three-dimensional conduction equation for a solid with a radiant heat flux boundary condition using an implicit finite-difference method. The structured object's conduction and radiant thermal properties are described by effective values. It was shown that radiative thermal properties of the traversing object and the enclosure's temperature have a strong impact on the object's temperature history. The effective thermal emissivity was found to influence the object's rate of temperature change. The enclosure's temperatures influenced the object's equilibrium temperature. Also, it was shown that the object's position and rotation can alter its temperature distribution, but not as strong as the effect of boundary conditions and thermal properties. In addition to numerical methods, experiments were performed to further understand the process.     

炉内辐射换热过程的有限体积法

简要分析了含吸收散射性介质的三维空腔内辐射传递方程的有限体积法求解过程,应用该方法对四角切圆炉膛内的辐射换热过程进行模拟计算,得出了炉膛内温度分布,并将计算结果与实测值进行了比较。通过数值计算表明：有限体积法计算速度快,对不规则边界适应性强,具有很高的工程可用性。     

The Re-Plating Algorithm for Radiation Total Exchange Area Calculation

Great efforts have been made to date toward modeling nongray radiative heat transfer accurately. In this article, a new version of the plating algorithm, designated the re-plating algorithm, for total exchange areas (TEAs) calculation from direct exchange areas (DEAs) for nongray radiative problems is presented. The re-plating algorithm calculates TEAs for a given band number b from those of band number b ? 1 by performing successive re-plating procedures. The effectiveness of the new algorithm is demonstrated for thermal modeling of an aluminum brazing furnace and a glass treatment furnace. CPU requirements for TEA calculation were reduced significantly.     

马蹄形火焰玻璃熔窑燃烧空间流动与传热的数值模拟

对马蹄形火焰玻璃窑炉燃烧空间内的流动、燃烧及辐射传热等过程进行了数值模拟研究,得到了炉内燃烧空间的速度场、温度场、组分浓度分布及燃烧空间向玻璃液面传递的热流分布。探讨了燃烧空间入口的进气角度对炉内温度场和向玻璃面传递的热流的影响,模拟结果表明,当入口的进气角度在5°～10°之间时,传热效果较好。     

Simultaneous estimation of four parameters in a combined-mode heat transfer in a 2D porous matrix with heat generation

This article reports a study on simultaneous estimation of four parameters for combined-mode conduction and radiation heat transfer in a 2D rectangular porous matrix with a localized volumetric heat generation source. Air flows at uniform velocity through the conducting and radiating porous matrix. In the heat generation zone, and its downstream, the gas temperature is higher than that of the solid, and in the upstream the reverse situation occurs. This temperature difference between gas and the solid results in heat transfer by convection between the two phases, and the analysis thus requires consideration of separate energy equations for the two phases. The solid being involved radiatively, the volumetric radiative source term, in the form of the divergence of radiative heat flux, appears only in the solid-phase energy equation. The two equations are coupled through the convective heat transfer term. Four parameters—scattering albedo, emissivity, solid conductivity, and heat transfer coefficient—are simultaneously estimated based on the solid and gas temperature distributions, and convective and radiative heat fluxes at the outer surface of the porous matrix. In both direct and inverse approaches, the energy equations are solved using the finite volume method. For a test case, determining the genetic algorithm is much more time-consuming than the global search algorithm; in other cases, parameter estimations are done using the global search algorithm. Parameters are found to be estimated accurately.