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A transient, three-dimensional, thermal model of a billet reheating furnace Scholey, Kenneth Erwin


Situated between the casting and rolling operations, the reheating process ensures steel billets or slabs are at temperatures high enough (~1200°C) to enable subsequent deformation pro-cesses to be carried out economically. Industrial reheating furnaces have varying designs, utilize different fuel mixtures and employ top, side or bottom firing. Under steady-state operating cond-itions, the challenge is to achieve good temperature homogenization while minimizing fuel con-sumption and maximising furnace throughput. During furnace stoppages, which are caused by delays in therolling mill, there is a need to minimise fuel consumption and maintain discharge temperatures. To gain better insight into the operation of a billet reheating furnace, a transient, three-dimen-sional thermal model has been developed. Radiative heat transfer in three-dimensions is solved using Hottel's "Zone Method", employing a clear-plus-three-grey gas model to represent the furnace atmosphere. In this method, the geometrical aspects of the problem are treated sepa-rately to produce total exchange areas that can be stored for repeated use. The main module then calculates the energy released through combustion, the heat transferred to the steel and the move-ment of the charge during each time step. Gas temperatures are determined from energy balances using a Newton-Raphson iterative technique. Conduction in the billets is solved in three-dimensions by taking into account heat transfer in the gaps between and underneath the billets. The model further evaluates heat losses through the furnace roof, walls and hearth. The mathematical model was verified using industrial data obtained from plant trials con-ducted at two Canadian steel mini-mills. Results from the plant trials indicated that the billets con-tinued to increase in temperature during furnace stoppages. The model suggests that this is due to continuous burner firing during these stoppages even with lower firing levels. For one of the furnaces, the model predicts the thermal efficiency to be 31% for the heating of 0.15 m (6") billets, with 68% of the combustion energy lost in the flue gases and the remainder lost through the refractory. Improved performance could be realized through better control of the furnace atom-sphere, with the air/fuel ratios maintained at levels closer to stoichiometric, as well as the installa- tion of a recuperator to preheat the combustion air. Different delay firing strategies that focussed on the recovery of the furnace were examined with the model and it was found that the sequential return to steady-state firing reduces the extent of billet over-heating while ensuring newly charged billets reached adequate rolling temperatures. The model was also used to examine the effect of air/fuel ratios in each of the furnace control zones and the benefits of recuperatively preheating the combustion air or hot-charging, where the billets are charged into the furnace soon after casting.

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