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Title: Stabilized finite element methods for natural and forced convection-radiation heat transfer
Author: Albadr, Jaafar
ISNI:       0000 0004 9354 9536
Awarding Body: Durham University
Current Institution: Durham University
Date of Award: 2020
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Thermal radiation in forced and natural convection can be an important mode of heat transfer in high temperature chambers, such as industrial furnaces and boilers, even under non-soot conditions. Growing concern with high temperature processes has emphasized the need for an evaluation of the eect of radiative heat transfer. Nevertheless, the modelling of radiation is often neglected in combustion analysis, mainly because it involves tedious mathematics, which increase the computation time, and also because of the lack of detailed information on the optical properties of the participating media and surfaces. Ignoring radiative transfer may introduce signicant errors in the overall predictions. The most accurate procedures available for computing radiation transfer in furnaces are the Zonal and Monte Carlo methods. However, these methods are not widely applied in comprehensive combustion calculations due to their large computational time and storage requirements. Also, the equations of the radiation transfer are in non-dierential form, a signicant inconvenience when solved in conjunction with the dierential equations of ow and combustion. For this reason, numerous investigations are currently being carried out worldwide to assess computationally ecient methods. In addition ecient modelling of forced and natural convection-radiation would help to simulate and understand heat transfer appearing in various engineering applications, especially in the case of the heat treatment of high-alloy steel or glass by a continuously heating process inside industrial furnaces, ovens or even smaller applications like microwaves. This thesis deals with the design of such methods and shows that a class of simplied approximations provides advantages that should be utilized in treating radiative transfer problems with or without ow convection. Much of the current work on modelling energy transport in high-temperature gas furnaces or chemically reacting ows, uses computational uid dynamics (CFD) codes. Therefore, the models for solving the radiative transfer equations must be compatible with the numerical methods employed to solve the transport equations. The Zonal and Monte Carlo methods for solving the radiative transfer problem are incompatible with the mathematical formulations used in CFD codes, and require prohibitive computational times for spatial resolution desired. The main objectives of this thesis is then to understand and better model the heat treatment at the same time in the furnace/oven chamber and within the workpieces under specied furnace geometry, thermal schedule, parts loading design, initial operation conditions, and performance requirements. Nowadays, there is a strong need either for appropriate fast and accurate algorithms for the mixed and natural convection-radiation or for reduced models which still incorporate its main radiative transfer physics. During the last decade, a lot of research was focused on the derivation of approximate models allowing for an accurate description of the important physical phenomena at reasonable numerical costs. Hence, a whole hierarchy of approximative equations is available, ranging from half-space moment approximations over full-space moment systems to the diusion-type simplied PN approximations. The latter were developed and extensively tested for various radiative transfer problems, where they proved to be suciently accurate. Although they were derived in the asymptotic regime for a large optical thickness of the material, these approximations yield encouraging even results in the optically thin regime. The main advantage of considering simplied PN approximations is the fact that the integro-dierential radiative transfer equation is transformed into a set of elliptic equations independent of the angular direction which are easy to solve. The simplied PN models are proposed in this thesis for modelling radiative heat transfer for both forced and natural convection-radiation applications. There exists a variety of computational methods available in the literature for solving coupled convection-radiation problems. For instance, applied to convection-dominated ows, Eulerian methods incorporate some upstream weighting in their formulations to stabilize the numerical procedure. The most popular Eulerian methods, in nite element framework, are the streamline upwind Petrov-Galerkin, Galerkin/least-squares and Taylor-Galerkin methods. All these Eulerian methods are easy to formulate and implement. However, time truncation errors dominate their solutions and are subjected to Courant-Friedrichs-Lewy (CFL) stability conditions, which put a restriction on the size of time steps taken in numerical simulations. Galerkin-characteristic methods (also known by semi-Lagrangian methods in meteorological community) on the other hand, make use of the transport nature of the governing equations. The idea in these methods is to rewrite the governing equations in term of Lagrangian co-ordinates as dened by the particle trajectories (or characteristics) associated with the problem. Then, the Lagrangian total derivative is approximated, thanks to a divided dierence operator. The Lagrangian treatment in these methods greatly reduces the time truncation errors in the Eulerian methods. In addition, these methods are known to be unconditionally stable, independent of the diusion coecient, and optimally accurate at least when the inner products in the Galerkin procedure are calculated exactly. In Galerkin-characteristic methods, the time derivative and the advection term are combined as a directional derivative along the characteristics, leading to a characteristic time-stepping procedure. Consequently, the Galerkin-characteristic methods symmetrize and stabilize the governing equations, allow for large time steps in a simulation without loss of accuracy, and eliminate the excessive numerical dispersion and grid orientation eects present in many upwind methods. This class of numerical methods have been implemented in this thesis to solve the developed models for mixed and natural convection-radiation applications. Extensive validations for the numerical simulations have been carried out and full comparisons with other published numerical results (obtained using commercial softwares) and experimental results are illustrated for natural and forced radiative heat transfer. The obtained convectionradiation results have been studied under the eect of dierent heat transfer characteristics to improve the existing applications and to help in the furnace designs.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available