Mathematical modeling of an aluminum casting furnace combustion chamber
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I.
THE CASTING FURNACE
THE aluminum
casting furnace plays a central role in the fabrication of aluminum. It receives a solid charge of ingots, logs, extrusion butts to be melted, and the liquid metal from the electrolytic cells, then brings it to the appropriate temperature and composition through heating, stirring, fluxing, and alloying as preparation for casting. Casting furnaces vary in capacity, size, geometry, number, and type of burners and type of fuel. However, most basic characteristics are common. Figure 1 shows the main components of a typical casting furnace: the metal load, combustion chamber, and the gas exhaust system. The metal is the payload. Before it can be cast, it must satisfy conditions in temperature and chemical composition. The chamber plays the critical role of providing the heat required to melt the solid and of bringing the, metal temperature to the desired value in a given time in an economical way. The gas exhaust system is equipped with dampers to adjust the internal pressure of the chamber, which is kept slightly above the ambient pressure to avoid air inleakage. A detailed description of a complete batch of a typical casting furnace can be found in a recent publication. ~2] In that work, a one-dimensional model was built to simulate and analyze the global operation of an existing furnace. It is furnace specific and gives the overall performance, but it does not provide any detailed information needed to study different operational and design parameters. A three-dimensional model for the aluminum casting furnace is being developed to fulfill this need. The present work on the chamber is a part of this effort. II.
THE C O M B U S T I O N C H A M B E R
The phenomena encountered in the combustion chamber of a casting furnace are: T. BOURGEOIS, formerly Graduate Student, is Research Engineer; R.T. BUI and A. CHARETTE are Professors of Engineering; Y.S. KOCAEFE is Postdoctoral Fellow, Department of Applied Sciences, Universit6 du Qu6bec ~t Chicoutimi, Chicoutimi, PQ, G7H 2B1, Canada. Manuscript submitted January 4, 1988. METALLURGICAL TRANSACTIONS B
(1) momentum transfer by natural and forced convection; (2) heat transfer by convection, conduction, and, more importantly, by radiation between the gas, refractories, and the metal surface; (3) turbulence; (4) heat generation by the combustion of fuel; (5) inleakage of air or exleakage of hot gas; (6) heat loss to the environment. A detailed mathematical analysis of such an enclosure requires modeling all these interacting phenomena, resuiting in a complex set of equations which have to be solved by a numerical technique. Radiation, which is the dominant mode of heat transfer, is represented by integrodifferential equations, while all other transport phenomena are represented by nonlinear partial differential equations. For the calculation of radiative transfer, two methods are most commonly used, the zone method t51 and the flux method, till The zone method which treats radiation as a global phenomenon is the most reliable method avail
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