ΕΞΕΤΑΣΗ ΦΑΙΝΟΜΕΝΩΝ ΘΕΡΜΙΚΗΣ ΑΚΤΙΝΟΒΟΛΙΑΣ ΣΕ ΕΣΤΙΕΣ ΣΤΕΡΕΟΥ ΚΑΥΣΙΜΟΥ

1998 ◽  
Author(s):  
Ιωάννης Μαράκης
Keyword(s):  
Heat Transfer ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Operating Conditions ◽  
Radiative Properties ◽  
Band Model ◽  
Combustion Chambers ◽  
Practical Applications

THEMATIC AREA OF THIS THESIS IS THE HEAT TRANSFER IN COMBUSTION CHAMBERS. THE ORIGINALITY ITEMS ARE CONCERNED WITH THE DEVELOPMENT OF ACCURATE METHODS BOTH FOR THE CALCULATION OF THE FLUE GAS AND COMBUSTION PARTICLE RADIATIVE PROPERTIES, AS WELL AS THE SOLUTION OF THE RADIATIVE TRANSFER EQUATION IN FURNACE - LIKE ENCLOSURES. SPECIFICALLY, THIS WORK CONTRIBUTES TO THE EXACT DETERMINATION OF THE INFLUENCE THAT THE TEMPERATURE AND PRESSURE OPERATING CONDITIONS HAVE ON THE RADIATIVE FLUXES AND SOURCE TERMS, THE LATTER BEING THE NET THERMAL ENERGY EMITTED OR ABSORBED PER UNIT VOLUME. THE THESIS INCLUDES THE DEVELOPMENT OF TWO METHODS FOR THE SOLUTION OF THE RADIATIVE TRANSFER EQUATION (A MONTE CARLO VARIANT AND A NEW INTEGRAL METHOD NAMED DIRECT NUMERICAL INTEGRATION),TWO STATISTICAL NARROW BAND AND A WIDE BAND MODEL FOR THE CALCULATION OF THE NON - GRAY GAS SPECTRAL TRANSMISSIVITY, AN ALGORITHM BASED ON MIE THEORY FOR THE DETERMINATION OF THE ABSORPTION AND SCATTERING COEFFICIENTS, THE PHASE FUNCTION AND THE ASYMMETRY PARAMETER OF COAL, CHAR, FLY - ASH AND SOOT PARTICLES AND CORRELATIONS FOR THE RESPECTIVE SPECTRAL OPTICAL PROPERTIES. THE EXACT SOLUTION OF THE THERMAL RADIATION TRANSFER HAS SIGNIFICANT PRACTICAL APPLICATIONS, SUCH AS: 1) DESIGN OF COMBUSTION CHAMBERS AND HEAT TRANSFER SURFACES, 2) DETERMINATION OF THE RADIATIVE FLUX AT THE BOUNDARIES OF A GIVEN GEOMETRY (ABSTRACT TRUNCATED)

Sphere-to-Sphere Radiative Transfer Coefficient for Packed Sphere System

2001 ◽  
Author(s):  
S. H.-K. Lee ◽  
S. C.-H. Ip ◽  
A. K. C. Wu
Keyword(s):  
Heat Transfer ◽  
Radiative Transfer ◽  
Transfer Coefficient ◽  
Radiative Heat Transfer ◽  
Transfer Equation ◽  
Radiative Heat ◽  
Radiative Transfer Equation ◽  
Radiative Properties ◽  
Equation Approach ◽  
Packed Sphere

Abstract Rapid sintering is one of the most attractive metalworking technologies due to its ability to fabricate the final product with different microstructure in an economical manner. During this process, the high heating rate would induce a great thermal gradient to the sintering part. Such temperature differences affect the microstructure of the product, which in turn leads to the occurrence of microstructure defects. However, for this non-isothermal sintering, the present Radiative Transfer Equation approach or Units/Cells approach cannot effectively compute the temperature distributions inside the porous media, so as to predict the part defects. Cumbersome computations are needed for the Radiative Transfer Equation approach. For the Units/Cells approach, the use of regular assembly in the model limits the analysis of complex packed sphere systems. This study seeks to simplify the entire computational process for different packed sphere systems. By introducing a Radiative Transfer Coefficient (RTC) approach, the computation of radiative heat transfer within the porous bed can be enhanced. The newly introduced Radiative Transfer Coefficient is defined as the ratio of radiative energy exchange, including direct and indirect exchange, from the emitting sphere to the receiving sphere, which is a function of the system microstructure and radiative properties. A set of energy-balanced algebraic equations can then be established. With an appropriate initial energy guess for each sphere, these equations can be solved by the Gauss-Seidel iteration scheme, thereby computing the radiative heat transfer in packed sphere systems with different microstructures and radiative properties. The temperature for each sphere can therefore be computed right away. This model has been validated in different perspectives. With this RTC approach, the overall computational time required is significantly shorter, providing a set of fine-resolution temperature solution.

scholarly journals Combining magnetohydrostatic constraints with Stokes profiles inversions

2019 ◽  
Vol 632 ◽  
pp. A111 ◽  
Author(s):  
J. M. Borrero ◽  
A. Pastor Yabar ◽  
M. Rempel ◽  
B. Ruiz Cobo
Keyword(s):  
Magnetic Field ◽  
Radiative Transfer ◽  
Boundary Conditions ◽  
Optical Depth ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Gas Pressure ◽  
Order Of Magnitude

Context. Inversion codes for the polarized radiative transfer equation, when applied to spectropolarimetric observations (i.e., Stokes vector) in spectral lines, can be used to infer the temperature T, line-of-sight velocity vlos, and magnetic field B as a function of the continuum optical-depth τc. However, they do not directly provide the gas pressure Pg or density ρ. In order to obtain these latter parameters, inversion codes rely instead on the assumption of hydrostatic equilibrium (HE) in addition to the equation of state (EOS). Unfortunately, the assumption of HE is rather unrealistic across magnetic field lines, causing estimations of Pg and ρ to be unreliable. This is because the role of the Lorentz force, among other factors, is neglected. Unreliable gas pressure and density also translate into an inaccurate conversion from optical depth τc to geometrical height z. Aims. We aim at improving the determination of the gas pressure and density via the application of magnetohydrostatic (MHS) equilibrium instead of HE. Methods. We develop a method to solve the momentum equation under MHS equilibrium (i.e., taking the Lorentz force into account) in three dimensions. The method is based on the iterative solution of a Poisson-like equation. Considering the gas pressure Pg and density ρ from three-dimensional magnetohydrodynamic (MHD) simulations of sunspots as a benchmark, we compare the results from the application of HE and MHS equilibrium using boundary conditions with different degrees of realism. Employing boundary conditions that can be applied to actual observations, we find that HE retrieves the gas pressure and density with an error smaller than one order of magnitude (compared to the MHD values) in only about 47% of the grid points in the three-dimensional domain. Moreover, the inferred values are within a factor of two of the MHD values in only about 23% of the domain. This translates into an error of about 160 − 200 km in the determination of the z − τc conversion (i.e., Wilson depression). On the other hand, the application of MHS equilibrium with similar boundary conditions allows determination of Pg and ρ with an error smaller than an order of magnitude in 84% of the domain. The inferred values are within a factor of two in more than 55% of the domain. In this latter case, the z − τc conversion is obtained with an accuracy of 30 − 70 km. Inaccuracies are due in equal part to deviations from MHS equilibrium and to inaccuracies in the boundary conditions. Results. Compared to HE, our new method, based on MHS equilibrium, significantly improves the reliability in the determination of the density, gas pressure, and conversion between geometrical height z and continuum optical depth τc. This method could be used in conjunction with the inversion of the radiative transfer equation for polarized light in order to determine the thermodynamic, kinematic, and magnetic parameters of the solar atmosphere.

Correlation of Measured and Computed Radiation Intensity Exiting a Packed Bed

1996 ◽  
Vol 118 (1) ◽  
pp. 94-102 ◽  
Author(s):  
P. D. Jones ◽  
D. G. McLeod ◽  
D. E. Dorai-Raj
Keyword(s):  
Radiative Transfer ◽  
Radiation Intensity ◽  
Transfer Equation ◽  
Scattering Theory ◽  
Radiative Transfer Equation ◽  
Packed Bed ◽  
Radiative Properties ◽  
Discrete Ordinates ◽  
Measured Intensity ◽  
Participating Media

The spectral and directional distribution of radiation intensity is measured, using a direct radiometric technique, at the exposed boundary of a packed bed of stainless steel spheres. The purpose of these measurements is to provide an experimental data base of radiation intensity with which to correlate intensity field solutions of the radiative transfer equation in participating media. The bed is considered to be one-dimensional, is optically thick, and has measured constant-temperature boundary conditions. Intensity exiting the bed is numerically simulated using a discrete ordinates solution to the radiative transfer equation, with combined mode radiation-conduction solution of the coupled energy conservation equation. Radiative properties for the bed are computed using the large size parameter correlated scattering theory derived by Kamiuto from the general theory of dependent scattering by Tien and others. The measured intensity results show good agreement with computed results in near-normal directions, though agreement in near-grazing directions is poor. This suggests that either radiative transfer near the boundaries of this medium might not be adequately represented by a continuous form of the radiative transfer equation, or that the properties derived from correlated scattering theory are insufficient. In either case, development of a more detailed radiation model for spherical packed beds appears warranted.

An Acceleration Technique for the Computation of Participating Radiative Heat Transfer

2009 ◽  
Author(s):  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Heat Transfer ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Radiation Heat Transfer ◽  
Solution Procedure ◽  
Discrete Ordinates ◽  
Average Intensity ◽  
Scattering Media ◽  
Acceleration Techniques

It is known that the finite volume and discrete ordinates methods for computing participating radiation are slow to converge when the optical thickness of the medium becomes large. This is a result of the sequential solution procedure usually employed to solve the directional intensities, which couples the ordinate directions and the energy equation loosely. Previously published acceleration techniques have sought to employ a governing equation for the angular-average of the radiation intensity to promote inter-directional coupling. These techniques have not always been successful, and even where successful, have been found to destroy the conservation properties of the radiative transfer equation. In this paper, we develop an algorithm called Multigrid Acceleration using Global Intensity Correction (MAGIC) which employs a multigrid solution of the average intensity and energy equations to significantly accelerate convergence, while ensuring that the conservative property of the radiative transfer equation is preserved. The method is shown to perform well for radiation heat transfer problems in absorbing, emitting and scattering media, both and without radiative equilibrium, and across a range of optical thicknesses.

Sign in / Sign up

Export Citation Format

Share Document