# An Improved Mathematical Model to Simulate the Stock in Pulse Fired Reheating Furnaces

• Alexander Matthew

Student thesis: Master's Thesis

### Abstract

The zone method of radiation analysis has been widely used in the steel industry to develop mathematical models to simulate the temperature performance of furnaces.

The zone method can provide an accurate calculation of the radiation exchanges, which are the main mode of heat transfer in the furnace. The zone method solves the radiant heat exchanges in the enclosure by splitting the furnace into a number of isothermal surface and volume zones. Applications of this method in the past have generally used a simplified representation of the furnace geometry and have not investigated the modelling of pulse fired burners.

This study aims to overcome the limitations of previous models by simulating transient furnace behaviour using long furnace models (LFM) and three-dimensional mathematical models, based on the zone method of radiation analysis. The zone model is an iterative technique that formulates a series of non linear energy balance equations.

A zone model was developed to simulate the transient thermal performance of a large continuous top and bottom fired steel re-heating furnace at Tata Steel that heats steel blooms to 1200°C at discharge. A new radiative exchange calculation program was developed called REFORM that uses ray tracing to evaluate the exchange factors between pairs of zones. REFORM also represents the furnace in a single model and allows for individual 3D blooms to be represented. The furnace contains 75 burners in total. A temperature controller and a plug-flow assumption were used to represent the opposing pulse fired burner flows.

The effect of 2D and 3D zone arrangements were investigated, the results for the 3D model was compared to a trial bloom measured data, the existing level-2 model predictions supplied by Tata steel as well as previous models. A simplified 2D LFM using a temperature controller and pulse firing technique was also used to simulate a 160 t/hr throughput rate with a short delay. The model was then validated using 74 t/hr throughput rate results. It was found that the 3D zone model has a significantly increased running time than the LFM with no obvious improvement in accuracy.

When comparing the 2D and 3D models at 160 t/hr throughput rate to measured data, the zone models' predictions did not give an exact match to the data, however, a similar temperature profile was produced. The zone models did provide a closer estimation of the measured data than the level-2 models predictions, however, the inclusion of modelling the pulse fired behaviour of the burners provided no further improvement on the accuracy of the results.

Comparing the LFM at 74 t/hr throughput rate, to Tata Steel's level-2 model predictions, the zone model provided a similarly accurate prediction. Therefore this model was employed to examine the influence of a range of parameters on the thermal behaviour of the furnace.

All simulations were conducted with the same initial conditions with the desire to reach a discharge bloom temperature of 1200°C with good temperature uniformity.

This study has demonstrated the use of multi-dimensional mathematical zone models running under transient operating conditions that represents the entire furnace in one simulation and fully models each individual steel bloom. The REFORM program is highly flexible and can handle a range of geometries and combined with a transient zone model can be used for reheating process control.
Date of Award Dec 2015 English CK Tan (Supervisor) & Paul Roach (Supervisor)

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