R. T. Bui

Performance analysis of the aluminum casting furnace

The casting furnace plays a central role in the production of aluminum. Its design and operation are complex and involve some 450 parameters. There is a need for a model to predict and analyze its performance. We propose a simplified model in which each main component of the furnace is treated as a 1-D heat conduction medium. Based on the equations of conservation of mass, energy, and chemical species, complemented by the equations of conduction and the Hottel’s formulation of radiative heat transfer, this dynamic model can simulate any sequence of operations such as loading, heating, stirring, skimming … that constitutes a batch, and can take into account other operational details such as the opening of doors. It is validated on a real furnace, then used to predict furnace performance in other modes of operation, and also to determine an optimal fuel flow that minimizes a chosen cost function.

Model-based optimization of the operation of the coke calcining kiln

A mathematical model was recently developed to simulate the calcination process of regular petroleum coke suitable for aluminum industry applications. The model is made of 14 ordinary differential equations describing energy and mass conservation in the gas and in the coke bed, and complemented by correlations and algebraic equations. It calculates temperature and concentration profiles in the kiln, and also yields other information important to kiln operation, such as calcined coke recovery factor and coke loss through the generation of dust. In this paper it is demonstrated that the model is an efficient tool for the optimization of kiln operation. The model is used to study the effect of key control variables upon kiln operation and productivity. Further, it is shown that higher kiln productivity may be obtained with optimized kiln control and without loss of satisfactory kiln operating condition.

Simulating the process of carbon anode baking used in the aluminum industry

A simulation scheme for the baking process of carbon anodes as practiced in the aluminum industry is presented. Despite the very complex nature of the process, the proposed scheme is simple enough to be readily implemented on the computer yet takes into account all the important aspects of anode baking: the infiltration of air, the control of depression in the flues, the release and burning of volatiles, and the heat loss to the atmosphere and to the furnace foundation. Emphasis in this paper is laid on the design of the simulation algorithm, more than on the detailed arguments behind the development of the model equations. Two interesting features are worth mentioning. First, the modular structure adopted for the algorithm helps increase its clarity. Second, in executing a simulation run on the computer, the analyst actually “adjusts” the depression in the flues and the fuel flow at the burners the same way a human operator does in the real process. Test runs are made, first to reproduce the existing operating conditions, then to study the effects of various parameter changes on the process. Most of the time this cannot be done on the real facility due to the costs and risks involved. Results show that the proposed model is a reliable tool for process evaluation and improvement.

Optimal control of an aluminum casting furnace: Part I. The control model

This is a series of two articles on the control of an aluminum casting furnace to bring a mass of liquid aluminum from a known initial temperature to a desired final temperature in a given time with minimal fuel cost. An analytic model of the furnace already exists but is too complex for control purposes. Here in Part I, a simplified nonlinear control model is derived from the analytic model. In Part II, an optimization of the fuel flow is performed on the control model using Pontryagin’s maximum principle. The first article shows that despite the complexity of the analytic model, a tenth-order nonlinear control model with good representativity can be obtained. The second article shows that the maximum principle applied to this problem leads to a solution with optimal fuel cost. If modeling industrial processes is a complex problem in itself, obtaining a control model therefrom is just as delicate. This series of articles proposes an approach that works for the casting furnace and is indeed applicable to other industrial processes as well. In the existing analytic model, the casting furnace is treated as two one-dimensional conducting media (metal and refractories), while its chamber is seen as a well-stirred reactor. In this article, a control model is derived therefrom by a statistical method. The analytic model is run several times to obtain a set of predicted data on which a least-squares approximation is performed to determine the best parameter values to be used for the control model equations. The conduction equations in the two media are linear. The expressions for heat generation in the chamber and for radiative-convective heat transfer from the chamber to the two media are nonlinear and are kept to ensure maximum representativity. The result is a highly representative tenth-order control model, the degree of representativity being assessed by comparing the temperature outputs and the energy balances obtained from the analytic model with those obtained from the control model.

Optimal control of an aluminum casting furnace: Part II. Fuel optimization

In this second of a two-article series, the simplified model of the aluminum casting furnace presented in Part I is used to solve a fuel-optimal control problem. Basically a Lagrange problem with equality and inequality constraints, it is formulated through variational calculus into a two-point boundary-value problem with known initial and final conditions and specified final time. It yields an optimal solution with a time-vary ing fuel flow rate that gives 10.9 pct fuel economy over the conventional nonoptimal constant fuel flow rate. This shows that variational calculus can be used to solve optimal control problems for the aluminum casting furnace and for other similar thermal systems commonly encountered in the metallurgical industry.

Numerical simulation of a casting furnace

Industrial furnaces constitute a complex, nonlinear, distributed- parameter thermal system. The usual way to model them is to write the equations describing the physical phenomena. The analytic model thus obtained is often too complex to be useful for control and optimization purposes. We propose to build a linear model by running the analytic model to obtain the simulated data, then apply the least square approximation to those data to obtain the linearizing coefficients. This statistical approach is simple to implement and yields linear models with good representativity. The annoying aspect is that some of the coefficients thus obtained may not lend themselves to a direct interpre tation of the physical process. But with proper consideration, this is no obstacle to the use of the model.

3D-simulation of the thermal performance of a coke calcining kiln

This is the first time ever a fully three-dimensional model of the rotary coke calcining kiln is built, to include all the important phenomena occurring therein. The overall kiln model consists of two separate models, one for the freeboard gas and one for the coke bed, coupled together with intermittent information exchange. The phenomena treated by the model include heat transfer, fluid flow, turbulence, volatiles combustion, third air, effect of kiln rotation. The model, based on the general equations of conservation is solved with the help of the CFD general-purpose code PHOENICS. Due to the huge dimensions of the real kiln, the model is validated on a laboratory size pilot kiln. Results are presented and the potential use of the model is discussed.

Mathematical modeling of an aluminum casting furnace combustion chamber

A mathematical model has been developed for the combustion chambers of aluminum casting furnaces by combining the fluid flow code PHOENICS with a zone model for the radiative heat transfer analysis and a simplified flame model. It offers flexibility in specifying the size and the combustion and heat transfer characteristics of the furnace. Thus, the model can be used to study a combustion chamber under different operating conditions and for different design op-tions. This paper presents the model and describes the coupling mechanism between PHOENICS and the zone method. Various case studies have been carried out for a 72-ton melter-holder. Results are presented which show the negative effect of ambient air inleakage on furnace per-formance as an application example.

Performance prediction of the aluminum casting furnace

ABSTRACT A comprehensive three-dimensional overall transient model has been built for the aluminum casting furnace. It results from the coupling of two models, representing the combustion chamber and the metal respectively. The chamber model takes account of gas flow, combustion and heat transfer, mainly radiative. The metal model includes the melting of a solid charge. The overall model can readily accommodate the various operational procedures and can be used to study furnace performance as well as solve design problems.

The paramount importance of thermal properties and coefficients in thermal process modelling

Abstract For a long time the progress made in the quantitative description of complex industrial processes had been slow due to the lack of means to solve the appropriate mathematical models. Although the difficulties associated with the handling of mathematical models for arbitrary 3D geometries, complicated boundary conditions, nonlinearities etc. have not yet been eliminated, it becomes more and more evident, that significant research efforts have to be made to strengthen physical modelling, for providing reliable input data base. While - using advanced computer technology and sophisticated numerical methods - we can solve our basic set of equations with an accuracy of say 0.1 percent or less, the input data like thermal conductivities, specific heats, emissivities, surface heat transfer coefficients, contact resistances etc. are known only with large uncertainties like ±20% - if available at all. A review is given to demonstrate the efforts to reach a well-balanced situation between the accuracy of numerical solving methods and that of the input data which describe the physical behaviour of substances in the system, and the interactions between the system and its environment. Aspects of various problems that will be touched upon in this article include: critical evaluation of literature data, discovering the sources of scatter in results due to deviations in model concepts; the use of sensitivity analysis to clarify the effect of various input data on the overall performance of the simulation; the proper selection of set of properties to characterize the behaviour of matter under given load patterns; and finally, the efforts to develop new measurement methods and devices using microcomputer control and evaluation, making possible the study of thermal properties even in factory environments.