# Development of Improved Mathematical Models for the Design and Control of Gas-Fired Furnaces

• Sara Correia

Student thesis: Doctoral Thesis

### Abstract

Mathematical models based on the zone method for radiation analysis have been frequently employed to evaluate the performance of a variety of furnaces and other high temperature systems. Generally in these systems the dominant mode of heat transfer is radiation so that prediction of the thermal performance requires accurate calculation of the radiative transfer. This can be achieved by using the zone method in which the furnace enclosure is subdivided into a number of zones. Applications of the zone method, however, have been generally confined to over-simplified furnace geometries and steadystate operating conditions. In addition combustion is usually simplified, for example, by assuming nozzle mix burners where combustion is virtually complete within the burner. Moreover, the combustion products flow patterns have generally been simplified due to lack of realistic data on the overall flow in the furnace chamber. Furthermore, little is known with regard to the effect of the number and arrangement of the gas zones, adopted to represent the enclosure, on the overall accuracy of the predictions. This present study aims to improve the applicability of zone models by overcoming some of the current limitations. For this reason both steady-state and transient operating conditions have been simulated using zoning arrangements ranging from simple long furnace models to more sophisticated multi-dimensional models. Information on the inter-zone mass flows and mixing patterns were obtained by means of an isothermal computational fluid dynamics (CFD) calculation and it was considered that this technique can provide sufficiently realistic representations of the overall flow of combustion products and heat release distribution inside the enclosure. The isothermal CFD simulations, which were tested for grid independence and compared where possible to data from closely related problems, were capable of simulating the furnace flow and mixing patterns for a variety of burner characteristics.

The zone models were then used to investigate both the transient and steady-state thermal performance of a metal reheating furnace producing steel bars at a nominal discharge temperature of 1250°C. The effect of different zone sizes was demonstrated by varying the number of gas zones from 7 to 50 with a corresponding variation in the number of surface zones from 37 to 147. It was found that changes in the number of zones employed in the calculation could significantly alter the model predictions. Results from simpler long furnace models were compared to those obtained from more complex two-dimensional arrangements and it was shown that the use of simplified versions can lead to substantial differences in the predictions. As a result relatively fine subdivisions should be employed in regions where the flow and temperature variations are likely to be important, for example, in the near burner region, hi general the use of finer zone subdivisions resulted in improved predictions albeit at the expense of additional computational time. Nevertheless, the computational effort remained competitive when compared with other alternative furnace simulation methods. The steady-state models were used to predict the discharge temperatures within the steel bars, as well as the furnace thermal performance, for a range of production rates. The transient models concentrated on predicting fuel usage, heating rates and load temperatures following a cold start-up of the furnace, hi addition the transient models were used to study a period of prolonged operation.

A two-dimensional (2D) zone model was then employed to assess the influence of changes to the burner geometry including burner diameter and orientation as well as position. Furnace control was investigated by studying the effects of changes in the roof set point temperature, which is used to control the thermal input to the burners as well as by varying the position of the control sensor relative to the burners. The effect of increasing the length of the furnace to provide stock preheating was also examined. The 2D zone model was also employed to simulate other changes in the design and operation of the furnace such as the use of alternative refractory constructions and combustion air preheating equipment. The zone models were then modified to incorporate diffusion flames where combustion progresses along the furnace length. CFD calculations were employed to determine mixing rates between gas and air streams and hence heat release rates. Two flames were studied corresponding to two different levels of excess air. Comparisons of the predictions with those for the equivalent nozzle mix cases illustrate the importance of modelling combustion heat release since it can lead to considerable variations in the heat flux profile and hence overall furnace behaviour. Overall the potential for the use of zone models for furnace design and control purposes has been demonstrated under both steady-state and transient operating conditions. The method is sufficiently flexible to handle a range of geometries and heating cycles. The relatively short computing times, even for a relatively large number of zones, means that they are potentially suitable for online process control.
Date of Award Dec 2001 English

### Keywords

• Gas furnaces Design
• Mathematical models
• Heat engineering

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