NUMERICAL SIMULATION OF THE GAS FLOW AND MASS TRANSFER BETWEEN TWO COAXIALLY ROTATING DISKS

A problem of combined conductive and two-phase radiative heat transfer in a two-dimensional rectangular enclosure with two-phase (gas-particles) media is analyzed. A two-phase radiative transfer equation (RTE) considering radiation by both gas and particles is studied. Its nonlinear integrodifferential RTE is solved using the discrete ordinates method (DOM, or so-called S N method). To validate the program, we compare the solution in a two-dimensional rectangular black enclosure with others. The DOM is then applied to the unsteady thermal development in two-phase media contained in a rectangular enclosure. A parametric study is performed by changing the gas and particle absorption coefficients, particle number density, particle emissivity, wall emissivity, and aspect ratio of the enclosure. The results confirm a significant effect of the two-phase radiation on the thermal development in the geometry. However, it is found that the conduction is predominant near the hot wall.     

Numerical investigation of combustion with non-gray thermal radiation and soot formation effect in a liquid rocket engine

A numerical analysis was carried out in order to investigate the combustion and heat transfer characteristics in a liquid rocket engine in terms of non-gray thermal radiation and soot formation. Governing gas and droplet phase equations with PSIC model, turbulent combustion model with liquid kerosene fuel, soot formation, and non-gray thermal radiative equations are introduced. A radiation model was implemented in a compressible flow solver in order to investigate the effects of thermal radiation. The finite-volume method (FVM) was employed to solve the radiative transfer equation, and the weighted-sum-of-gray-gases model (WSGGM) was applied to model the radiation effect by a mixture of non-gray gases and gray soot particulates. After confirming the two-phase combustion behavior with soot distribution, the effects of the O/F ratio, wall temperature, and wall emissivity on the wall heat flux were investigated. It was found that the effects of soot formation and radiation are significant; as the O/F ratio increases, the wall temperature decreases. In addition, as the wall emissivity increases, the radiative heat flux on the wall increases.     

EFFECT OF RADIATIVE TRANSFER ON THE THERMOPHORETIC PARTICLE DEPOSITION AROUND A CIRCULAR CYLINDER IN A UNIFORM CROSS FLOW

We investigated the effects of radiative transfer on the particle deposition around a circular cylinder in a cross flow. The fluid is transparent to radiation, and radiating particles are suspended in flow. The finite volume method was applied to analyze radiative transfer in the flow utilizing the nonorthogonal coordinate system. The radiative transfer coupled with convection and mass transfer is reasonably predicted by the method. The results are in good agreement with those of boundary layer analysis and available experimental data. We discuss the effects of the conduction-to-radiation parameter, optical thickness, scattering albedo, and wall emissivity on the heat transfer and particle deposition.     

A formal averaging procedure for radiation heat transfer in particulate media

Radiative heat transfer in participating particulate media is modeled using a formal volume averaging procedure. The multiphase medium is composed of emitting-absorbing-scattering phases, i.e., a gas phase and several particle phases. Each particle phase contains large, opaque, gray, diffuse, and spherical particles having locally the same geometrical, thermophysical, and radiative properties. The resulting multiphase radiative transfer equation (MRTE) is solved using the discrete ordinates method. The present computed results are found to be in good agreement with those obtained using the Monte-Carlo theory and with the available experimental results. The coupling effect of the MRTE with the averaged energy equations in a three-dimensional cavity which is differentially heated or which contains a volumetric heat source is studied. A parametric study is performed for particle-phase and gas properties, and wall emissivity.     

Coupled radiation‐convection heat transfer of high‐temperature participating medium in heated/cooled tubes

The coupled radiation‐convection heat transfer of high‐temperature participating medium in heated/cooled tubes is investigated numerically. The medium flows in a laminar and fully developed state with a Poiseuille velocity distribution, but the thermal status is developing. By the discrete ordinate method, the nonlinear integrodifferential radiative transfer equation in a cylindrical coordinate form is solved to give the radiative source term in the energy equation of coupled heat transfer. The energy equation is solved by the control volume method. The local Nusselt number and wall heat flux of convection as well as the total wall heat flux are employed to evaluate the influence of radiation heat transfer on convection. The analysis shows that the radiation heat transfer weakens the convection effect, promotes the temperature development, and significantly shortens the tube length with obvious heated/cooled effect. There is an obvious difference between the coupled heat transfer in a heated tube and that in a cooled tube, even though the medium properties are kept constant. The wall emissivity, the medium thermal conductivity and scattering albedo have significant influences on the coupled heat transfer, but the effect of medium scattering phase function is small. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(1): 64–72, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10137     

The Effect of Radiation on Flow in a Conical Diffuser

The effect of thermal radiation on the flow in a conical diffuser of half-cone angle 2.5° is studied numerically for constant thermophysical properties. The finite-volume method (FVM) is employed to solve both the Navier-Stokes equation (NSE) and the integro-differential radiative transfer equation (RTE). The effect of radiative parameters, e.g., optical diameter, scattering albedo and wall emissivity at two Reynolds numbers (Re = 500 and 1000) and Pr = 1 has been investigated for constant wall temperature of 1000 K and inlet temperature of 2000 K. The results show that radiation in a transparent or in a purely scattering medium does not affect the flow temperature profile and bulk mean temperature variation, whereas it increases the total Nusselt number; however, radiation in a absorbing-emitting participating medium significantly affects the temperature profile as well as Nusselt number, when compared with the pure convection case.     

Analysis of combined mode heat transfer in a porous medium using the lattice Boltzmann method

ABSTRACT

Application of the lattice Boltzmann method (LBM) in solving a combined mode conduction, convection, and radiation heat transfer problem in a porous medium is extended. Consideration is given to a 1-D planar porous medium with a localized volumetric heat generation zone. Three particle distribution functions, one each for the solid temperature, the gas temperature, and the intensity of radiation, are simultaneously used to solve the gas- and the solid-phase energy equations. The volumetric radiation source term appears in the solid-phase energy equation, and it is also computed using the LBM. To check the accuracy of the LBM results, the same problem is also solved using the finite volume method (FVM). Effects of convective coupling, flow enthalpy, solid-phase conductivity, scattering albedo porosity, and emissivity on axial temperature distribution are studied and compared with the FVM results. Effects of flow enthalpy, solid-phase conductivity, and emissivity are also studied on radiative output. LBM results are in excellent agreement with those of the FVM.     

Particle–gas reacting flow under concentrated solar irradiation

A transient heat transfer model is developed for a reacting flow of CH₄ laden with carbon particles directly exposed to concentrated solar radiation and undergoing thermal decomposition into carbon and hydrogen. The unsteady mass and energy conservation equations, coupling convective heat and mass transfer, radiative heat transfer, and chemical kinetics for a two-phase solid–gas flow, are formulated and solved numerically for both phases by Monte Carlo and finite volume methods using the explicit Euler time integration scheme. Parametric study is performed with respect to the initial particle diameter, volume fraction, gas composition, and velocity. Validation is accomplished by comparing temperatures and reaction extent with those measured experimentally using a particle-flow solar reactor prototype subjected to concentrated solar radiation. Smaller particles and/or high volume fractions increase the optical thickness of the medium, its radiative absorption and extinction coefficients, and lead to higher steady-state temperatures, reaction rates, and consequently, higher extent of chemical conversion.     

Prediction of radiative heat transfer between two concentric spherical enclosures with the finite volume method

The radiative heat transfer between two concentric spheres separated by an absorbing, emitting, and isotropically scattering gray medium is investigated by using the finite volume method (FVM). Especially, a mapping that simplifies the solution of spherically symmetric radiative heat transfer problems is introduced, thereby, the intensity depending on spatial one-dimension and angular one-dimension is transformed into spatial two-dimensional one. By adopting this mapping process, angular redistribution, which appears in such curvilinear coordinates as cylindrical or spherical ones, is treated efficiently without any artifice usually introduced in the conventional discrete ordinates method (DOM). After a mathematical formulation and corresponding discretization equation for the radiative transfer equation (RTE) are derived, final discretization equation is introduced by using the directional weight, which is the key parameter in the FVM since it represents the inflow or outflow of radiant energy across the control volume faces depending on its sign. The present approach is then validated by comparing the present results with those of previous works by changing such various parameters as temperature ratio between inner and outer spherical enclosure, wall emissivity, and optical thickness of the participating medium. All the results presented in this work show that the present method is accurate and valuable for the analysis of spherically symmetric radiative heat transfer problems between two concentric spheres.     

Lattice Boltzmann Method and Modified Discrete Ordinate Method Applied to Radiative Transport in a Spherical Medium with and without Conduction

This article deals with the application of the modified discrete ordinate method (MDOM) to calculate volumetric radiative information with and without conduction in a concentric spherical enclosure containing a participating medium. With radiative information known from the MDOM, the energy equation of the combined mode transient conduction and radiation heat transfer is formulated and solved using the lattice Boltzmann method (LBM). Without conduction, for pure radiation case, two benchmark problems, representing nonradiative and radiative equilibrium situations are taken up. In the case of non-radiative equilibrium, an isothermal medium is bounded by cold walls and medium is the source of radiation, while in the case of radiative equilibrium, nonisothermal medium is confined between a hot and a cold wall, and the hot (inner sphere) wall is the radiation source. Depending upon the problem, heat flux, energy flow rate, emissive power, and temperature distributions in the medium are calculated for different values of parameters such as the extinction coefficient, the scattering albedo, the conduction-radiation parameter, the boundary emissivity, and the radius ratio. To validate the MDOM and the LBM-MDOM formulations, problems are also solved using the finite volume method (FVM) and the finite-difference method (FDM)–FVM approach, in which the FVM is used to calculate the volumetric radiation and the energy equation is also solved using the FDM. Results of the MDOM, LBM–MDOM, FVM and FDM–FVM are also benchmarked against those available in the literature. MDOM and LBM–MDOM have been found to provide accurate results.     

Radiative and conductive transfer for a real gas in a cylindrical enclosure with gray walls

The purpose of this study is to examine the interaction of radiative and conductive transfer for a radiatively participating real gas stagnant in a cylindrical enclosure with gray diffuse walls. Consideration of reflecting boundaries represents an extension of previous black wall studies. Examination of radiative transfer was made by the zone method with gas radiative properties furnished by the weighted sum of gray gases model. Directed flux areas are expressed as the weighted sum of gray gas total exchange areas which are evaluated using the matrix formulation method from direct exchange areas. Axial and radial gas temperatures are examined along with wall heat flux or temperature for respective cases of either specified wall temperatures or heat fluxes. Emphasis is placed on examining results to show the effects of wall emittance and duct diameter. Results for heat generation within the gas are also presented.     

Spectrally correlated radiation and laminar forced convection in the entrance region of a circular duct

The two-dimensional combined radiative and convective transfer in emitting and absorbing real gases in the entrance region of a duct with a jump of wall temperature is studied. The axial propagation of radiation is taken into account in the analysis. The flow field and the energy equations are solved simultaneously and the radiative properties of the flowing gases, CO₂ or H₂O, are modeled by using either the narrow-band correlated-k model or the global absorption distribution function (ADF) model. The results are presented in terms of temperature and radiative power fields, and of the evolution of bulk temperatures and of heat transfer coefficients. Due to the axial component of the radiative flux, the gas is preheated or precooled before the change in wall temperature and this induces a persistent difference between the results of 1-D and 2-D radiation analyses. Some differences between CO₂ and H₂O temperature and radiative power profiles, due to the different structures of their spectra, are put in evidence. The ADF model, only suitable for gray walls, is shown to be less accurate when the gas is heated than when it is cooled.     

Numerical analysis of combined-mode dual-phase-lag heat conduction and radiation in an absorbing,emitting, and scattering cylindrical medium

Combined-mode dual-phase-lag (DPL) heat conduction and radiation heat transfer is analyzed in a concentric cylindrical enclosure filled with a radiatively absorbing, emitting, and scattering medium. The governing energy equation is incorporated with volumetric radiation as a source term, essentially to take the effect of radiative heat flux into account. While the energy equation is solved using the lattice Boltzmann method (LBM), the finite volume method (FVM) is used to calculate the radiative information. To establish the accuracy of the proposed LBM formulation, the governing energy equation is also solved with the finite difference method (FDM). Thermal perturbation is caused by suddenly changing the temperature at the boundaries. Radial temperature distributions during transience as well as steady state (SS) are presented for a wide range of parameters such as lag ratio, extinction coefficient, scattering albedo, conduction–radiation (C-R) parameter, boundary emissivity, and radius ratio. Sample results are benchmarked with those available in the literature, and a good agreement between the present and reported results is found.     

THERMOPHORESIS OF PARTICLES IN GAS-PARTICLE TWO-PHASE FLOW WITH RADIATION EFFECT

The radiation effect on the thermophoresis of particles is analyzed for a gas-particle twophase laminar flow. Two-phase radiation by both gas and particles is considered; in addition, the thermal nonequilibrium between gas and particle is taken into account. It is concluded that the particle diffusion velocity as well as particle concentration depends strongly on the optical radius of gas or particle. In general, the radiation was found to decrease the particle diffusion. In case that gas as well as particle radiation exists, the deposition of particle is mainly influenced by the gas. The effects of parameters such as the optical radius, conduction to radiation parameter, thermal loading ratio, and wall emissivity on the cumulative collection efficiency E ( x ) are also considered. As the optical radius and tube wall emissivity increase, E ( x ) decreases. The increase in conduction to radiation parameter N and thermal loading ratio CL leads to an increase in E ( x ).     

Numerical simulation of the interaction between turbulence and radiation in reactive flows

The interaction between turbulence and radiation (TRI) in reactive flows has been demonstrated experimentally, theoretically and numerically, and results from the highly non-linear coupling between fluctuations of radiation intensity and fluctuations of temperature and chemical composition of the medium. The instantaneous and the time-averaged form of the radiative transfer equation (RTE) are presented, and the TRI effects resulting from time-averaging are discussed. Methods to account for TRI in practical calculations are surveyed, and works where such methods have been employed are reviewed. These include both decoupled and coupled fluid flow/radiative transfer calculations. It is shown that the solution of the RTE using instantaneous scalar data is the most accurate way to deal with TRI, but it is computationally prohibitive for coupled problems. Hence, this approach has been mainly used to calculate the radiation intensity along lines of sight. The generation of time series of instantaneous scalar data may be accomplished using stochastic or deterministic models, which are also surveyed. Coupled fluid flow/radiative transfer problems are generally solved using the time-averaged form of the RTE or the Monte Carlo method, and rely on the optically thin fluctuation approximation, which neglects the correlation between fluctuations of the absorption coefficient and fluctuations of the radiation intensity. Experimental data and numerical calculations demonstrate that turbulent fluctuations may significantly increase the mean spectral radiation intensity in both non-luminous and luminous flames. Turbulent fluctuations contribute to decrease the flame temperature below the level observed without fluctuations, particularly for optically thick flames. The net radiative power and the fraction of radiative heat loss increase due to TRI, particularly in the case of optically thin flames. Recent direct numerical simulations provide additional insight on the role of different correlations responsible for TRI, and on how they are influenced by the optical thickness of the medium.     

Study of two-dimensional and dynamic heat and mass transfer in a metal–hydrogen reactor

To analyse heat and mass transfer in a metal–hydrogen reactor, the hypothesis that disregards the radiative heat transfer in the reactor, is typically used. In this paper, we take into account the radiative heat transfer and we test the validity of this hypothesis in the case of the LaNi₅ and in the case of the magnesium. A theoretical model is conducted for the two-dimensional system where conduction, convection radiation and chemical reaction take place simultaneously. This model is solved by the finite volume method. The numerical simulation is used to present the time–space evolutions of the temperature and the hydride density in the reactor and to determinate the sensitivity to some parameters (absorption coefficient, scattering coefficient, reactor wall emissivity).     

Enhancement of heat transfer: Combined convection and radiation in the entrance region of circular ducts with porous inserts

Using porous ceramic inserts in high temperature equipment has been proven to be an effective means to enhance combined convective–radiative heat transfer. The porous ceramic insert was referred to as a convection-to-radiation converter (CRC) by previous investigators. We consider a novel application of CRC cores in a partial by pass flow system for heat transfer enhancement. Both hydrodynamically and thermally developing laminar flow is considered in the entrance region of a circular pipe with a porous insert located at the center. The momentum and Darcy–Brinkman equations are applied to the flow field in the annular gas layer and central porous layer respectively. The energy equation is coupled with the radiative transfer equation by the radiation source term. The radiative transfer is simulated by the newly developed integral equations [X.L. Chen, W. Sutton, Radiative transfer in finite cylindrical media using transformed integral equations, J. Quant. Spectrosc. Radiat. Transfer 77 (3) (2003) 233–271; W. Sutton, X.L. Chen, A general integration method for radiative transfer in 3-D non-homogeneous cylindrical media with anisotropic scattering, J. Quant. Spectrosc. Radiat. Transfer 84 (2004) 65–103] to avoid singularity problem and give high accuracy. The working fluid and porous medium are both considered as participating media. Finally, this highly non-linear system of equations is solved by a mixed iteration method. The results are compared between the cases with and without the porous insert. The porous insert enhances both convective and radiative transfer by about 35% and 105% respectively at the most. The effects of important parameters on this enhancement are discussed in detail.     

燃烧室内三维温度场的辐射反问题

本文提出了一种在介质辐射特性已知的条件下,由壁面入射辐射热流的测量值反演燃烧室内三维温度场的方法。该方法是在辐射传递方程离散坐标近似的基础上,用求目标函数极小值的共轭梯度法进行反演计算。通过对吸收系数、散射不对称因子、反照率、壁面黑度和燃烧室大小尺寸等参数对反演精度影响的分析,结果表明,即使存在随机测量误差,这些参数对温度场反演精度的影响也不大,本文所提出的方法可较精确地反演燃烧室内三维温度场。     

Numerical analysis of entropy generation through non-grey gas radiation in a cylindrical annulus

This study is devoted to analyze the radiative heat transfer of non-grey gas confined in a cylindrical annulus with isothermal walls. The radiative heat transfer equation is resolved through the Ray Tracing method, which is associated to the statistical narrow bands correlated–k (SNBcK) model to compute the medium radiative properties. Special focus is given on the components of radiative entropy generation and its dependency on geometrical and thermodynamic parameters. The results show that entropy generation is greatly affected by gas and wall temperatures. Moreover, the dominance between wall radiative entropy generation and the volumetric one depends mainly on differences between gas and wall temperatures.     

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.