Gabriel Węcel

Absorption line black body distribution function evaluated with proper orthogonal decomposition for mixture of CO2 and H2O

Purpose – The purpose of this paper is to present a new approach of evaluation of the absorption line black body distribution function (ALBDF) for a mixture of gases. Currently published correlations, which are used to reproduce the ALBDF, treat only single gases. Design/methodology/approach – A discrete form of the ALBDF is generated using line by line (LBL) calculations. The latest spectroscopic database HITEMP 2010 is used for the generation of the absorption coefficient histogram, which is cumulated later in order to produce a tabulated form of the ALBDF. The proper orthogonal decomposition (POD) statistical method is employed for the reproduction of the ALBDF. Interpolation property of the POD allows to reproduce the ALBDF for arbitrary gas mixture parameters. Findings – POD proved to possess optimal interpolation properties. Results obtained by using POD are in very good agreement with LBL integration. Research limitations/implications – One have to be aware that the model generated with the POD met...

Simulations of the PC boiler equipped with complex swirling burners

Purpose – The purpose of this paper is to show possible approaches which can be used for modeling complex flow phenomena caused by swirl burners combined with simulating coal combustion process using air- and oxy-combustion technologies. Additionally, the response of exist boiler working parameter on changing the oxidizer composition from air to a mixture of the oxygen and recirculated flue gases is investigated. Moreover, the heat transfer in the superheaters section of the boiler was taken into account by modeling of the heat exchange process between continuum phase and three stages of the steam superheaters. Design/methodology/approach – An accurate solution of the flow field is required in order to predict combustion phenomena correctly for numerical simulations of the industrial pulverized coal (PC) boilers. Nevertheless, it is a very demanding task due to the complicated swirl burner construction and complex character of the flow. The presented simulations were performed using the discrete phase mod...

Coupling of conductive, convective and radiative heat transfer in Czochralski crystal growth process

Abstract This paper studies the conjugate problems of fluid flow and energy transport (involving conduction, convection and radiation heat transfer) within a material changing its phase. The analysis focuses on the Czochralski crystal growth process. The solidifying material is treated as a pure substance with constant material properties. The solution of the resulting 3-D, axisymmetric, non-linear problem is obtained iteratively using the commercial CFD package Fluent. The algorithm employed here treats each subdomain of the system separately, i.e. the liquid and solid phases of the solidified material, as well as the inertial gas surrounding both phases. Results of a test case shows the velocity field and temperature distribution within a simple system employed for the growth of a single silicon crystal.

CFD modelling of air and oxy-coal combustion

Purpose – The main goal of this work was the CFD analysis of air and oxy-coal combustion, in order to develop a validated with experimental measurements model of the combustion chamber. Moreover, the purpose of this paper is to provide information about limitations of the sub-models implemented in commercial CFD code ANSYS Fluent version 13.0 for the oxy-coal combustion simulations. The influence of implementation of the weighted sum of gray gas model (WSGGM) with coefficients updated to oxy-coal combustion environment has been investigated. Design/methodology/approach – The sub-models validated with experimental measurements model for the air combustion has been used to predict the oxy-coal combustion case and subsequently the numerical solutions have been compared with the experimental data, which enclose the surface incident radiation (SIR) and the flue gas temperature. To improve the numerical prediction of the oxy-coal combustion process the own routine for calculating properties of the oxy-combustio...

Analysis of fluid flow and energy transport in Czochralski's process

Abstract In this paper the conjugate fluid flow and energy transport problem (involving conduction–convection–radiation heat transfer) resulting from the Czochralski crystal growth process is analysed. The solidifying material is treated as a pure and semitransparent substance with material properties depending neither on temperature nor on the wavelength. The solution of the problem is obtained iteratively using two computer codes: FLUENT, a commercial CFD package, and BEM-based in-house code capable of analysing the radiative heat transfer in the entire computational domain. Obtained results not only show velocity field and temperature distribution within the bodies under consideration but also demonstrate the influence of thermal radiation on these quantities.

BEM SOLUTION OF THE RADIATIVE HEAT TRANSFER WITHIN NATURAL GAS FIRED COMBUSTION CHAMBER

Conjugate radiation-convection heat transfer in a combustion chamber is considered. Radiation in emitting absorbing medium is coupled with general heat convection problems. While the radiation solver is an in-house BEM (Boundary Element Method) based code, heat convection is modelled using a commercial package. A procedure of acceleration of the ray tracing in ortho cartesian and cylindrical meshes is developed, significantly increasing the numerical efficiency of the radiative solver. The developed procedure is compared with a series of benchmarks and applied to the simulation of the radiative heat transfer within combustion chamber fired with natural gas. Good agreement with standard Discrete Ordinates solvers is observed.

BEM-FVM solution of the conjugate radiative and convective heat transfer problem

SummaryThe problem addressed in the paper is the coupling between heat radiation and convection in participating media. While convection is modelled by finite volumes, heat radiation is solved using the boundary element method (BEM). The latter is a technique of solving the integral equations of radiation using weighted residuals.BEM can be seen as an alternative approach to the well established zoning method or FEM, its higher order generalization. When compared with these approaches, BEM offers substantial computing time economy due to the reduction of the integration dimension and lack of volume integrals.Coupling convection solution with heat radiation is accomplished in an iterative way. First the initial temperatures of the medium is computed by the convection solver for given walls temperature assuming no interaction with radiation. Using this temperature field the radiative heat fluxes and sources are computed and their values substituted to the corrected energy convection equation. The procedure is repeated until a required accuracy is reached. Mild underrelaxaction of the heat sources improves the convergence.BEM radiation procedure requires numerical integration over all discrete surface elements, and ray tracing of the Gaussian rays connecting the collocation point and the nodes of the Gaussian quadrature. The latter is the most time consuming operation. Numerical tests have shown that standard ray tracing on convection meshes leads to prohibitively long computing time. To accelerate the procedure the ray tracing is performed on a much coarser structural grid. This is an acceptable approximation as heat radiation volumetric grid does not need to capture small scale phenomena which is in contrast with the convection grid where the resolution of the resulting fields depends strongly on the mesh density. This assumption accelerates the ray tracing by at least two orders of magnitude. The transition between the radiative and convection nodes is accomplished using the radial basis function network concept.Several industrial problems have been solved using this model. Commercial CFD code Fluent has been used to solve the convection equations. The interaction between the in-house radiative code BERTA and Fluent was maintained by modifying source term of energy balance equation within latter. The coupling was programmed at a level of a script.The results have been compared with some available benchmark solutions and with the radiative transfer solvers (Discrete Ordinates and Discrete Transfer) installed in the CFD code. Very good agreement has been observed.The ray tracing concept has been extended to cylindrical coordinates systems to solve axisymmetric problems. The technique has been also used to model the interaction of radiation and conduction in semitransparent, non gray media.Numerical results of both some benchmark solutions and industrial problems are shown in the paper.