Wall Emissivity Research Articles

A Narrow Band-Based Multiscale Multigroup Full-Spectrum k-Distribution Method for Radiative Transfer in Nonhomogeneous Gas-Soot Mixtures

The full-spectrum k-distribution (FSK) approach has become a promising method for radiative heat transfer calculations in strongly nongray participating media, due to its ability to achieve high accuracy at a tiny fraction of the line-by-line (LBL) computational cost. However, inhomogeneities in temperature, total pressure, and component mole fractions severely challenge the accuracy of the FSK approach. The objective of this paper is to develop a narrow band-based hybrid FSK model that is accurate for radiation calculations in combustion systems containing both molecular gases and nongray particles such as soot with strong temperature and mole fraction inhomogeneities. This method combines the advantages of the multigroup FSK method for temperature inhomogeneities in a single species, and the modified multiscale FSK method for concentration inhomogeneities in gas-soot mixtures. In this new method, each species is considered as one scale; the absorption coefficients within each narrow band of every gas scale are divided into M exclusive spectral groups, depending on their temperature dependence. Accurate and compact narrow band multigroup databases are constructed for combustion gases such as CO2 and H2O. Sample calculations are performed for a 1D medium and also for a 2D axisymmetric combustion flame. The narrow band-based hybrid method is observed to accurately predict heat transfer from extremely inhomogeneous gas-soot mixtures with/without wall emission, yielding close-to-LBL accuracy.

A Numerical Simulation of Combined Radiation and Natural Convection in a Differential Heated Cubic Cavity

This article presents a numerical simulation of combined radiation and natural convection in a three-dimensional differentially heated rectangular cavity with two opposite side walls kept at a temperature ratio Th/Tc=2.0 and Tc=500 K, with others walls insulated. A non-Boussinesq variable density approach is used to incorporate density changes due to temperature variation. The Navier–Stokes (NSE), temperature, as well as the radiative transfer (RTE) equations are solved numerically by a finite volume method, with constant thermophysical fluid properties (except density) for Rayleigh number Ra=105 and Prandtl number Pr=0.71. The convective, radiative, and total heat transfer on the isothermal and adiabatic walls is studied along with the flow phenomena. The results reveal an extraordinarily complex flow field, wherein, along with the main flow, many secondary flow regions and singular points exist at the different planes and are affected by the optical properties of the fluid. The heat transfer decreases with increase in optical thickness and the pure convection Nusselt number is approached as the optical thickness τ>100, but with substantially different velocity field. The wall emissivity has a strong influence on the heat transfer but the scattering albedo does not.

Modelling of combined surface radiation and natural convection in a vented “T” form cavity

In this paper, a numerical study of heat transfer and fluid flow in a “T” form cavity is carried out. The cavity contains two symmetrically identical isothermal blocks and is vented by two opening located in a vertical median axis at the top and the bottom parts of the cavity. A specifically developed numerical model, based on the finite-volume method, is used for the solutions of the governing differential-equations. The coupling of the velocity–pressure is treated by the Simpler algorithm. A special attention is given to study the effects of block height, opening size, Rayleigh number and surface emissivity of blocks and walls. Effects of different parameters on streamlines, temperature fields and average Nusselt-number are discussed. It is found that the radiative exchanges produce an increase of the average Nusselt-number. This one increases almost linearly with increasing the Rayleigh number Ra, and it becomes more important when the solid blocks heights are large.

Entropy production analysis of swirling diffusion combustion processes

A critical factor in the design of combustion systems for optimum fuel economy and emission performance lies in adequately predicting thermodynamic irreversibilities associated with transport and chemical processes. The objective of this study is to map these irreversibilities in terms of entropy production for methane combustion. The numerical solution of the combustion process is conducted with the help of a Fluent 6.1.22 computer code, and the volumetric entropy production rate due to chemical reaction, viscous dissipation, and mass and heat transfer are calculated as post-processed quantities with the computed data of the reaction rates, fluid velocity, temperature and radiative intensity. This paper shows that radiative heat transfer, which is an important source of entropy production, cannot be omitted for combustion systems. The study is extended by conducting a parametric investigation to include the effects of wall emissivity, optical thickness, swirl number, and Boltzmann number on entropy production. Global entropy production rates decrease with the increase in swirl velocity, wall emissivity and optical thickness. Introducing swirling air into the combustion system and operations with the appropriate Boltzmann number reduces the irreversibility affected regions and improves energy utilization efficiency.

Calculable blackbody radiation as a source for the determination of the spectral responsivity of THz detectors

The spectral responsivity of the detector is important for the layout and quantitative interpretation of spectroscopic experiments. In the terahertz (THz) spectral range the knowledge of the total (integral) responsivity of a detector, as well as its spectral distribution, is often insufficient. PTB determined the spectral irradiance responsivity of two THz detectors, a pyroelectric DLATGS detector working at room temperature and a silicon-composite bolometer working at 4 K, in the wavelength range from 62 µm (4.82 THz) to 1340 µm (0.22 THz) with temperature radiation from blackbody radiators. Our approach is to use two THz cavity radiators in combination with THz bandpass filters to provide calculable spectral irradiances, according to Planck's law of radiation, at several wavelength bands in the THz spectral range. One cavity radiator is working at an adjustable fixed temperature in the range from 15 °C to 90 °C while the other cavity radiator operates at LN2 temperature. The radiation of the two cavity radiators is alternately imaged on the detector via a gold-coated chopper wheel. Hereby the background radiation is cancelled and also the necessary modulation for the lock-in detection is provided. The cavity of the high temperature radiator is coated with a dedicated paint providing high wall emissivity in the FIR and THz spectral range to ensure true blackbody behaviour of the radiator. The bottom of the low temperature radiator consists of THz absorber foam providing hereby also nearly blackbody behaviour. All individual filters and, additionally, the employed filter combinations are characterized for their transmittance in the entire wavelength range from 0.8 µm to 1700 µm to obtain a precise knowledge of the transmitted blackbody spectrum. The very reproducible results indicate that this setup allows a fast, simple and reliable determination of the spectral responsivity of THz detectors. In a next step, the uncertainty of this technique will be further evaluated and investigations will be extended to other types of detectors (e.g. LiTaO3 detectors and Golay cells).

Optimization of rapid thermal processing for uniform temperature distribution on wafer surface

An optimization of rapid thermal processing (RTP) was conducted to obtain uniform temperature distribution on a wafer surface by using linear programming and radiative heat transfer modeling. The results show that two heating lamp zones are needed to maintain uniform wafer temperature and the optimal lamp positions are unique for a given geometry and not affected by wafer temperatures. The radii of heating lamps, which were obtained by optimization, are 45 mm and 108 mm. The emissivity and temperature of the chamber wall do not significantly affect the optimal condition. With obtained optimum geometry of the RTP chamber and lamp positions, the wafer surface temperatures were calculated. The uniformity allowance of the wafer surface is less than ±1°C when the mean temperature of the wafer surface is 1000°C.

The heating sources of spots on the vacuum arc cathodes

We have considered two stages in the development of a spot on the surface of a vacuum arc cathode: the stage of ignition and the stage of the remaining arc lifetime which consists of arc spot operation until ultimately it is extinguished. A model for the near cathode region of electric arc has been applied to obtain different parameters involved in the cathode spot region during the spot ignition stage. This model is based on the construction of a thin sheath near the cathode wall and electron emission upon the thermo-field theory of electron emission. The model is time-dependent and hence the different parameters of the cathode, plasma and sheath can be derived as a function of time. In particular, we determine the required values of the plasma and sheath parameters for spot ignition on the smooth cathode surface. Based on these calculations and taking into consideration the fluctuation in plasma and sheath parameters, the contribution of different heating mechanisms at the spot initiation stage is evaluated. After spot ignition, some spot parameters such as temperature and mass density of spot material, electron current density and vapour pressure considerably increase. High values of the electron current density and low values of the electrical conductivity of the dense plasma in the spot region significantly increase Joule heating during the evolution stage of spot operation.

Combustion development of a Bi-Fuel engine

Environmental improvement and energy issues are increasingly becoming more important as worldwide concerns. Natural gas is a good alternative fuel that can help to improve these issues because of its large quantity and clean burning characteristics. This paper provides the experimental performance results of a Bi-Fuel engine that uses Compressed Natural Gas as its Primary fuel and gasoline as its secondary fuel. This engine is a modification of the basic 1.4-liter gasoline engine. Generally, on the unmodified base engine, torque and power for CNG fuel are considerably lower than gasoline fuel. In this paper, the influence of fuels on wall temperature, performance and emissions are investigated.

A Two-Temperature Model for Predicting Heat and Fluid Flow by Natural Convection and Radiation within a Saturated Porous Vertical Channel

The present article deals with a numerical study of fluid flow and heat transfer by unsteady natural convection and thermal radiation in a vertical channel opened at both ends and filled with a fluid-saturated porous medium and adopts a two-temperature model of microscopic heat transfer. The bounding walls of the channel are gray and kept at a constant hot temperature. In the present study, we suppose the validity of the Darcy law for motion. For heat transfer, two energy conservation equations for both fluid and solid phases are derived. The radiative coupling problem is solved numerically by the finite volume method. Present solutions are compared with known results from previous published works. Excellent agreement was obtained between results that validate the used computer code. The numerical results have allowed us to represent the time-space variations of the different state variables. The effects of some influencing parameters (i.e., the internal Biot number Biint, the Planck number N, the optical thickness τ the wall's emissivity ε, and the single-scattering albedo ω) on the validity domain of the local thermal equilibrium assumption are checked.

Analysis of a Localized Fire in a 3-D Tunnel Using a Hybrid Solver: Lattice Boltzmann Method, Finite-Volume Method, and Fully Explicit Upwind Scheme

A localized fire in a 3-D tunnel is analyzed by solving a combined-mode natural-convection and radiation problem. Nonlocal thermal equilibrium between air and smoke is considered. Separate energy equations are used for the two species. The density and temperature fields required for the solution of the energy equation are computed using the lattice Boltzmann method. The finite-volume method is used to compute radiative information. The energy equations are solved using the fully explicit upwind scheme. The Boussinesq approximation is used to account for the buoyancy effect. Effects of the scattering albedo, the convection-radiation parameter, and the wall emissivities on temperature profiles in the tunnel have been studied.

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.

Performance of the Various Sn Approximations of DOM in a 3D Combustion Chamber

We have carried out a three-dimensional numerical study to investigate the radiative heat transfer in a model gas turbine combustor. The combustion chamber is a representative of the Rolls-Royce Tay engine combustor. The discrete ordinate method (Sn) in general body-fitted coordinate system is developed and then applied to solve the filtered radiative transfer equation for the radiation modeling, and this has been combined with a large eddy simulation of the flow, temperature, and composition fields within the combustion chamber. Various approximations of Sn have been considered and their performances in the investigation of the radiative heat transfer are presented in the paper. The radiation considered in this work is due only to the hot combustion gases, notably carbon dioxide (CO2) and water vapor (H2O) also known as nonluminous radiation. The instantaneous results of the radiation properties such as the incident radiation and the radiative energy source or sink as the divergence of the radiative heat fluxes are computed inside the combustion chamber and presented graphically. Effects of the wall emissivity on the incident radiation inside the combustion chamber have been examined, and it has been found that the radiative energy is enhanced with the increment of the wall emissivity.

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.

Radiation symmetry test and uncertainty analysis of Monte Carlo method based on radiative exchange factor

Using Monte Carlo method, the paper investigates the radiative heat transfer in participating media. Based on the radiative exchange factor, an uncertainty analysis of Monte Carlo method is undertaken and the corresponding mathematical expressions are deduced to predict its accuracy. Furthermore, randomness properties of pseudorandom number generators are investigated, and a model to test radiation symmetry is adopted to validate the performance of some generators. The paper studies the effects of energy bundle numbers, discretization schemes, emission location, optical thicknesses, wall emissivity and CPU time on the numerical accuracy. In addition, the simulation results are proved to give a reference for using Monte Carlo method, which is applicable for calculation of the radiative exchange factor.

Experimental investigation on heat loss and combustion in methane/oxygen micro-tube combustor

To understand working features of a micro-tube combustor, combustion of CH 4/O 2 was carried out in three types of micro-tubes with the same outer diameter of 3 mm. In the tests, combustion characteristics and heat loss in micro-tubes were studied. It is shown that when equivalence ratio was lower than unity, CH 4 was not completely oxidized and a great amount of gas H 2 and CO was produced, which lowered the combustion heat release. If equivalence ratio is a little larger than unity, CH 4 was completely oxidized to gas CO 2 and water vapor, and the reaction released the maximum combustion heat. Meanwhile, heat loss of the tube wall was the largest. Heat loss of the stainless steel tube occupied 22% of the heat release at most. Since the wall emissivity of stainless steel tube was larger than that of ceramic tube, radiative heat loss was very large and the most occupied 70% of the total heat loss. Additionally, because thermal conductivity of ceramic was less than that of stainless steel, temperature gradient along axis was larger than that of stainless steel tube, which was disadvantageous to axis heat transfer and flame stabilization.

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.

An Effective Calculation Method for Radiative Exchange in an Enclosure with Specular Surfaces

A new calculation method is proposed to determine the radiative heat transfer in enclosures composed of specularly reflecting surfaces. This method is based on the concept of the transition reflection in the context of the ray-tracing method, by which only two reflections of ray tracing are necessary to consider in the evaluation of net radiative transfer rate. This method can also be used not only for diffuse and specular surfaces but also for directional surfaces such as non-Lambert surface. Because the radiative exchange rate can be obtained by considering only two reflections of ray tracing, the matrix inversion is not required, and thus computational time can be reduced substantially. In order to validate the present method, the radiative exchange between two parallel plates is calculated, and the results are compared with those of previous methods including analytic solutions and stochastic methods. The parameters tested are the wall emissivity and the ratio of the distance between two plates to the length of plates. For all cases considered, the present results are in excellent agreement with exact solutions within 0.5% error, and show better accuracy than other methods. The new calculation method is also tested for nondiffusely emitting and reflecting surfaces of platinum and glass.

Natural convection‐radiation cooling of a vertical divided vented channel

PurposeThe purpose of this paper is to study the radiation‐natural convection interactions in a vertical divided vented channel. The effects of the surface emissivity, the vent opening position and size on the heat transfer and the flow structures inside the channel were studied.Design/methodology/approachThe governing differential equations are solved by a finite volume method, with adopting the SIMPLER algorithm for pressure‐velocity coupling. The view factors were determined by using a boundary elements approximation and a Monte Carlo method.FindingsThe effect of the radiation exchange is very important, it increases the average hot wall Nusselt number by more than 100 per cent. The contribution of the channel wall emissivity in the heat transfer is more important than that of the plate emissivity. The average hot wall Nusselt number increases with increasing the vent opening size, only in presence of the radiation exchange, and this increase is more pronounced, particularly when the vent opening is located near the channel inlet.Research limitations/implicationsThe flow is assumed to be incompressible, laminar and two dimensional. The radiative surfaces are assumed diffuse‐grey. The working fluid, air, is considered as transparent with respect to the radiation.Practical implicationsThe industrial applications of this study are solar collectors, thermal building, electronic cooling, aeronautics, chemical apparatus, nuclear engineering, etc.Originality/valueIn comparison to the preceding studies, the originality of this paper is the taking into account of the radiation exchange in a vented and divided channel.

Conjugate turbulent natural convection with surface radiation in air filled rectangular enclosures

Conjugate turbulent natural convection and surface radiation in rectangular enclosures heated from below and cooled from other walls, typically encountered in Liquid Metal Fast Breeder Reactor (LMFBR) subsystems, have been investigated by a finite volume method for various aspect ratios. The formulation comprises the standard two equation k– ε turbulence model with physical boundary conditions (no wall functions), along with the Boussinesq approximation, for the flow and heat transfer. As far as radiation is concerned, the radiosity – irradiation formulation for a transparent fluid of Prandtl number 0.7 has been employed. The conjugate coupling on the walls has been handled by using a fin type formulation. The Rayleigh number based on the width of the enclosure is varied from 10 8 to 10 12 and the aspect ratio is varied from 0.5 to 2.0. Detailed results including stream lines, temperature profiles, and convective, radiative and overall Nusselt numbers are presented. A correlation for the mean convection Nusselt number in terms of Rayleigh number and aspect ratio is proposed for design purposes. The influence of the wall emissivity and the external heat transfer coefficient on the heat transfer from the enclosure has also been investigated.

Treatment of Wall Emission in the Narrow-Band Based Multiscale Full-Spectrum k-Distribution Method

The multiscale full-spectrum k-distribution (MSFSK) method has become a promising method for radiative heat transfer in inhomogeneous media. In this paper a new scheme is proposed to extend the MSFSK’s ability in dealing with boundary wall emission by distributing this emission across the different gas scales. This scheme pursues the overlap concept of the MSFSK method and requires no changes in the original MSFSK formulation. A boundary emission distribution function is introduced and two approaches of evaluating the function are outlined. The first approach involves line-by-line integration of the spectral absorption coefficients and is, therefore, impractical. The second approach employs a narrow-band k-distribution database to calculate all parameters as in the original narrow-banded based MSFSK formulation and is, therefore, efficient. This distribution scheme of wall emission is evaluated and the two approaches are compared by conducting sample calculations for radiative heat transfer in strongly inhomogeneous media using both the MSFSK method and the line-by-line method.