Chairman: S.H. Chan


Institute of Thermal Engineering, Technical University of Vienna,
Getreidemarkt 9/302, A-1060 Vienna, Austria

Abstract. A mathematical model for description of heat transfer under Circulating Fluidized Bed (CFB)-conditions is proposed. According to the dominating heat transfer mechanisms (particle convection and particle radiation) the model is based on two modules describing radiative and convective part. The shielding effect of the dense and cool wall layer is included and demonstrated. Due to the variation of particles concentration in the wall layer the radiation behaviour changes between optical thin and optical thick. The development of a wall layer close to wall and platen heat exchangers in CFBs was investigated in experimental way. In a further step bed to wall heat transfer coefficients were measured and are compared to data from literature.


Alejandro F. Romero,
Instituto de Ingeniería,
UNAM Universidad Nacional Autónoma de México
Tel. (52)(5) 622-8142, Fax (52)(5) 616-2894 & 1514

ABSTRACT.- A particulate aggregate model which takes place during the incomplete combustion of Diesel fuel in heavy duty engines is presented. An approximate analytical solution for the temperature field in a filter ceramic porous wall is presented. Ceramic monoliths are being used for filtration of particulate matter (or soot). An alternative approach covering essential engineering problems is presented by means of a numerical simulation, which shows safety operational features of the proposed scheme. Some predicted performance of the filter ceramic traps are also presented.


Shawn P. Burns, Russell D. Skocypec, Bruce L. Bainbridge,
Dean Dobranich, Louis A. Gritzo, Micheal W. Glass, James H. Strickland
Engineering Sciences Center
Sandia National Laboratories, Albuquerque, New Mexico, USA

One of the goals of the Engineering Sciences Center at Sandia National Laboratories is to provide heat transfer solutions for engineering systems. Solutions are sought for a wide range of applications in manufacturing and defense programs including industrial furnace, combustion, and fire safety applications. Applications often involve transient and steady state, multiphysics solutions characterized by complex multidimensional geometries and nonlinear material properties and boundary conditions. Radiative transport plays an important role in many of the applications of interest to the Center which supports a number of existing computational tools as well as an active research program to develop advanced computational techniques. The objective of this paper is to describe the numerical algorithms currently in use and under development at the Engineering Sciences Center and provide some details regarding the formulations used and their implementation.

Radiative exchange between gray, diffuse surfaces is the most fundamental radiative transport mode and plays an important role in industrial furnace applications. The CHAPARRAL software developed in the Engineering Sciences Center employs the hemicube algorithm to provide surface-to-surface view factors in a general three dimensional geometry. Spatial discretization is provided using an unstructured finite element mesh in which the surface emissivity may vary. Successive refinement is employed to improve the view factor calculation when surfaces are close compared to their effective diameter. This is an important capability for many engineering systems in which radiative exchange may take place across narrow gaps.

Applications such as glass furnaces and fire safety also involve radiative transport within absorbing, emitting, and scattering materials. The Engineering Sciences Center currently employs the MYST package, a descendant of the NIKE/ATHENA neutron transport software originally developed at Los Alamos National Laboratories, for this class of application. The NIKE/ATHENA software employs either a discrete ordinate or a simplified spherical harmonics formulation with the even/odd parity form of the Boltzmann transport equation on an unstructured tetrahedral finite element mesh. The NIKE/ATHENA software is capable of evaluating nongray (multiple energy group) radiative transport with anisotropic scattering. The MYST package also provides material property submodels for a number of gases as well as Mie scattering phase functions for spherical particles with specified diameter complex index of refraction.

In most engineering systems radiative transport is coupled to other heat transport modes requiring a simultaneous solution of the radiative transport and conservation of energy. For enclosure radiation applications, the COYOTE conduction heat transfer package employs the viewfactors developed by the CHAPARRAL software to provide the necessary heat flux values at the boundaries of radiation enclosures. For many applications Picard iteration is employed in which the radiative fluxes are calculated at the enclosure surfaces and are then included as source terms for the conservation of energy equation resulting in a segregated or uncoupled formulation. A Newton iteration scheme may be employed for steady state applications involving solid regions which are not in direct contact and exchange energy purely through radiation. Each step of the Newton iteration scheme involves a solution of the fully coupled or unsegregated conservation of energy and radiative transport system.

A segregated approach is also employed for applications involving combined conduction and participating media radiative transport. During each nonlinear iteration the temperature solution is passed to the participating media radiation solver which provides volumetric source terms and boundary heat flux values for the subsequent iteration.

Hydrocarbon pool fire modeling is currently one of the most challenging areas of research underway at the Engineering Sciences Center. Fire modeling requires the simultaneous solution of the turbulent fluid flow, species, and energy transport and chemical reaction equations. Furthermore, to resolve the length and time scales of importance in a complex three dimensional geometry requires the use of high resolution computational grids on the order of 106 to 108 computational cells.

Radiative transport is a dominant heat transport mode in hydrocarbon pool fires. For heavily sooting fires, the radiative material properties are dominated by the soat phase which may be modeled as gray and nonscattering to a good first approximation. The SYRINX software under development at the Engineering Sciences Center employs a parallel discrete ordinate formulation of the gray, nonscattering radiative transport equation on an unstructured finite element spatial grid. The SYRINX software employs spatial domain based parallelism to achieve the spatial resolution required on a distributed memory, massively parallel architecture. As a consequence of the global nature of the radiative transport, however, spatial decomposition results in relatively poor parallel efficiency although useful parallel speedup is still achieved. To improve parallel efficiency, the SYRINX software also allows the use of angular domain based parallelism in combination with spatial decomposition.

Other areas of research at the Engineering Sciences Center include the development of a gridless Lagrangian formulation of the radiative transport equation which utilizes a fast multipole algorithm to solve the resulting N body problem. The natural adaptivity of the Lagrangian formulation allows the concentration of computational effort in regions where radiative transport is most important. Such adaptivity has great potential for fire modeling applications which are characterized by high temperature flame sheets within the optically thick plume region. Additionally, improving the spatial resolution in this manner may allow the inclusion of nongray material properties and scattering within the fire model.

This paper has provided formulation and implementation details for a number of numerical modeling packages employed by the Engineering Sciences Center to address modeling needs involving thermal radiative transport. In developing these analysis tools the center recognizes that it is not possible to select a single optimum algorithm or formulation which can treat the wide variety of radiative transport applications. Continuing research will be conducted to develop robust and accurate solutions for engineering systems using state of the art technology.

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