Francis Henrique Ramos França

Comparison of Methods for Inverse Design of Radiant Enclosures

A particular inverse design problem is proposed as a benchmark for comparison of five solution techniques used in design of enclosures with radiating sources. The enclosure is three-dimensional and includes some surfaces that are diffuse and others that are specular diffuse. Two aspect ratios are treated. The problem is completely described, and solutions are presented as obtained by the Tikhonov method, truncated singular value decomposition, conjugate gradient regularization, quasi-Newton minimization, and simulated annealing. All of the solutions use a common set of exchange factors computed by Monte Carlo, and smoothed by a constrained maximum likelihood estimation technique that imposes conservation, reciprocity, and non-negativity. Solutions obtained by the various methods are presented and compared, and the relative advantages and disadvantages of these methods are summarized.

ANALYSIS OF THE TURBULENT, NON-PREMIXED COMBUSTION OF NATURAL GAS IN A CYLINDRICAL CHAMBER WITH AND WITHOUT THERMAL RADIATION

Abstract This work presents a numerical simulation of the non-premixed combustion of natural gas in atmospheric air in an axis-symmetric cylindrical chamber, focusing on the effect of thermal radiation on the temperature and chemical species concentration fields and the heat transfer. The simulation is based on the solution of the mass, energy, momentum and the chemical species conservation equations. Thermal radiation exchanges in the combustion chamber is computed through the zonal method, and the gas absorption coefficient dependence on the wavelength is resolved by the weighted-sum-of-gray-gases model. The turbulence is modeled by the standard k − ϵ model, and the chemical reactions are described by the E–A (Eddy Breakup–Arrhenius model). The finite volume method is employed to treat the differential equations. Among other results, the solution of the governing equations allows the determination of the region where combustion takes place, the distribution of the chemical species, the velocity fields and the heat transfer rate by convection and radiation. The results indicate that while thermal radiation has a strong effect on the temperature field and heat transfer, its effect on the chemical reactions rates is of less importance. The numerical results are compared to experimental results obtained by Garréton and Simonin (1994).

Transient inverse design of radiative enclosures for thermal processing of materials

This work presents a methodology to solve transient inverse design of radiative enclosures for heating processes that require refined temperature control. The proposed methodology is applied to find the heat input to a heater located at the top of a three-dimensional enclosure that can satisfy a prescribed time-dependent temperature curve on a surface located at the base of the enclosure. The process is governed by radiative exchanges between diffuse, gray surfaces. This problem is described by an ill-conditioned system of linear equations, which is regularized by the truncated singular value decomposition (TSVD) method. The inverse analysis led to a heat input in the heater that assured, within an error less than 1.0%, both uniformity and the correct magnitude of the design surface temperature in every instant of the process.

Inverse design of thermal systems with dominant radiative transfer

Abstract The design of thermal systems often involves the specification of two conditions, typically both temperature and heat flux distributions on some surfaces or within media to perform particular tasks. Examples are in annealing ovens, dryers, chambers for rapid thermal processing of semiconductor wafers, utility and chemical furnaces, infrared ovens, and many others. Conventional design techniques require specification of one and only one boundary condition on each surface of a system, requiring trial-and-error solutions to achieve a design that satisfies the second specified condition. Here, the methods of inverse analysis are applied to the ill-conditioned equations that result when two conditions are specified for a particular surface. It is demonstrated that the use of inverse methods can result in multiple designs that each provide the required conditions; that designs are generated that might not be found through the conventional approach; and that the use of inverse design can lead the designer to efficient and novel designs for thermal systems.

Application of inverse analysis to illumination design

This work investigates the application of the inverse analysis to the illumination design of a three-dimensional rectangular enclosure. The illumination design is inherently an inverse problem, in which the design surface is subjected to two conditions–the prescribed luminous flux and null luminous power–while the light sources are left unconstrained. It is considered that all surfaces emit and reflect diffusely, and that the hemispheric spectral emissivities are wavelength independent in the visible region of the spectrum. The illumination design is treated by two different approaches: by an explicit formulation that is regularized by the truncated singular value decomposition due to its ill-conditioned nature; and by an implicit formulation that is treated as an optimization problem using the generalized extremal optimization method, a stochastic algorithm. Both approaches are capable of providing design solutions that satisfy the prescribed luminous flux on the design surface with maximum errors that are less than 3.0%. † Preliminary versions of this work were presented in the 10th Brazilian Congress of Thermal Sciences and Engineering (ENCIT 2004) and in the 19th International Congress of Mechanical Engineering (COBEM 2007).

Comparison of spectral models in the computation of radiative heat transfer in participating media composed of gases and soot

Accurate combustion models are necessary to predict, among other effects, the production of pollutant gases and the heat transfer. As an important part of the combustion modeling, thermal radiation is often the dominant heat transfer mechanism, involving absorption and emission from soot and participating gases, such as water vapor and carbon dioxides. If the radiative heat transfer is not accurately predicted, the solution can lead to poor prediction of the temperature field and of the formation and distribution of the gases and soot. The modeling of the absorption coefficient of the gases is a very complex task due to its highly irregular dependence on the wavenumber. On the other hand, the absorption coefficient of the soot is known to behave linearly with the wavenumber, allowing for a simpler approach. Depending on the amount of soot, the more sophisticated and expensive gas models can be replaced by simpler ones, without considerable loss of accuracy. In this study, the radiative heat transfer for a medium composed of water vapor, carbon dioxide and soot is computed with the gray gas (GG), the weighted-sum-of-gray-gases model (WSGG), and the cumulative wavenumber (CW) models. The results are compared to benchmark line-by-line (LBL) calculations.

Inverse Boundary Design in Heat Transfer Combining Turbulent Convection and Thermal Radiation

This work investigates the solutions of an inverse boundary design problem that has multimode (radiation and convection) heat transfer mechanisms. The problem consists of finding the heat flux distribution required on heaters located on the top and side walls of a two-dimensional enclosure that satisfies both the temperature and heat flux distributions prescribed on the design surface of the enclosure. A turbulent air flow is generated by a fan located inside the chamber. The walls are gray, diffuse emitters and absorbers. The combined heat transfer problem is described by a system of non-linear equations, which is expected to be ill-conditioned as an inverse analysis is involved. The system of equations is solved by an iterative procedure: the basic set of equations relates the radiation transferred between the heater and the design surface, while all the other terms involved in the energy exchange are found from the conditions of the previous iteration. This way, the ill-posed part of the problem (which arises from the design surfaces containing two conditions, and the heater elements being unconstrained) is isolated for a more effective treatment. The solution is obtained by regularizing the ill-conditioned system of equations by means of the truncated singular value decomposition (TSVD) method.

Radiative Heat Transfer Modeling Using the CW and SLW Models in Gas Mixtures With Soot

This paper presents the computation of radiative heat transfer in a slab filled with a participating medium composed of CO2, H2O, and soot. The HITEMP 2010 spectral database is employed to obtain the necessary parameters for the prediction of radiative transfer in the non-isothermal, homogeneous medium. The spectral integration is performed with the spectral line weighted-sum-of-gray-gases (SLW) and the cumulative wavenumber (CW) models and compared with the line-by-line (LBL) benchmark solution. Since radiation heat transfer can sometimes be the dominant heat transfer mechanism in combustion processes, it is important to understand how the predicted thermochemical state depends on the radiation model for the composition, taking into account the complex dependence of the properties with the spectrum. The contribution of this work is to compare two detailed spectral model that are available in the literature and determine advantages and disadvantages in some practical, illustrative examples.© 2012 ASME

A Numerical Study of the Influence of Temperature Fluctuations in the Thermal Radiation Field

The present paper performs a numerical study of the influence of fluctuations on the temperature field over the thermal radiation field with the purpose to simulate the effect of Turbulence-Radiation Interactions (TRI). To evaluate the behaviour of the divergence of radiative heat flux for a flame in a cylindrical cavity, four temperature profiles are imposed: an average temperature profile and other three with 10%, 20% and 30% of turbulence intensity. The radiative transfer equation is solved using the discrete ordinates method (DOM) and the participating medium is treated as a gray gas. The results achieved demonstrate that the fluctuations of temperature profiles increase significantly the mean divergence of the radiative heat flux in comparison with the average temperature profile, reaching to approximately 20% for the profile with 30% of turbulence intensity.

Assessment of combustion models for numerical simulations of a turbulent non-premixed natural gas flame inside a cylindrical chamber

ABSTRACT This work presents a Computational Fluid Dynamics (CFD) study of the non-premixed combustion of natural gas with air in an axisymmetric cylindrical chamber, focusing on the contribution of the chemical reaction modeling on the temperature and the chemical species concentration fields. Simulations are based on the solution of mass, momentum, energy and chemical species conservation equations. Thermal radiation heat transfer in the combustion chamber is computed through the Discrete Transfer Radiation Method, and the Weighted-Sum-of-Gray-Gases model solves the dependence of gas absorption coefficient on the wavelength. Turbulence is modeled by the standard k-ε model. Regarding the combustion modeling, it is performed a comparison of solutions obtained with the combined Eddy Break-Up/Arrhenius (EBU/Arrhenius) and the Steady Laminar Diffusion Flamelet (SLDF) models. The finite volume method is employed to treat the differential equations. Among other results, the solution of the governing equations allows for the determination of the region where combustion takes place, the distribution of the chemical species and the velocity fields. The numerical results are compared to experimental measurements, showing varied agreements. Results indicate that, in this case, the EBU/Arrhenius model can predict the flame temperature and the concentration of the most important species with better accuracy than the more sophisticated SLDF model.