The paper presents a computational model and the corresponding algorithm for estimating the arc energy distribution to conductive, convective and radiative heat transfer in an electric arc furnace (EAF). The proposed algorithm uses channel arc model (CAM) in order to compute the distribution of the arc energy through empirical equations (to approximate arc radius), ideal gas law (to approximate arc density) and results of magneto-hydro-dynamic (MHD) models (to approximate arc pressure, temperature and velocity). Results obtained using the proposed algorithm are comparable with other similar studies; however, in contrast to other arc-energy distribution models, this model requires only two input variables (arc length and arc current) in order to calculate the energy distribution. Furthermore, simple algebraic equations used in the algorithm ensure minimal computational load and consequently lead to short calculation times which are approximately one hundred thousand (100 000) times smaller than solving the MHD model equations, making the algorithm suitable for real-time applications, such as smart monitoring and model-based control. The algorithm has been validated by two different approaches. First, the simulation results have been compared to a study dealing with arc-heat distribution in plasma arc furnace; and second, the proposed arc module has been integrated into the frame of a comprehensive EAF model in order to estimate the EAF temperature levels and compare them with operational EAF measurements. Both validations show high levels of similarity with the comparing data.KEY WORDS: arc current; arc heat distribution; arc length; channel arc model; EAF.approximately 75-85% of the total energy in low to medium power furnaces and approximately 50-60% of the total energy in ultra-high power furnaces (UHP).3) Implementing an accurate arc module in a comprehensive model-based EAF control, which ensures optimal control of arc length and slag height can lead to substantial energy saving and associated cost reduction. If a total energy reduction in a 200 ton UHP EAF with approximate annual production of 675 000 tones is 50 kWh/ton, with an assumption of 25 kWh/ton being the electrical energy, with the price of 10 $Cent/kWh, total annual energy savings will be equivalent to 1.7 million $ per year.It is known that the heat generated by the arcs is dissipated into the furnace by all three mechanisms of heat transfer (convection, conduction and radiation); however, the amount of the heat, transferred by each mechanism varies according to several factors, such as arc length, arc current, slag height, stage of melting etc. Development of a computational model of the arc, which allows estimation of the arc-heat distribution should therefore include all three types of heat transfer mechanisms, which can also be used to obtain the overall energy balance of the EAF. Application of such models may provide appropriate tools for optimizing the energy flow or use of model-based control systems in the EAFs.

The paper presents a comprehensive electric arc furnace (EAF) model, developed for simulation and model-based control of the EAF processes. The model consists of three sub models, i.e., (i) arc model; (ii) chemical and slag model; and (iii) heat-transfer model. Arc model predicts the amount of energy dissipated from the arcs using arc currents and arc lengths; chemical and slag model calculates chemical energy and changes of elements/compounds, slag height and slag quality; while the heat-transfer model uses calculations of the other two models in order to establish a reference energy system (RES) for each zone in the EAF due to the variations in arc length, slag height, and bath height. The overall EAF model is based on fundamental thermodynamic and heat-transfer laws, reaction kinetics, and experimental equations. Governing equations describing the processes inside the EAF are of the first order. The validation of the model has shown that the model provides accurate estimation of the EAF process values, such as bath temperature as well as steel and slag compositions. The estimations made by the model are comparable to the measured EAF data, which allows the model to be used for comprehensive analysis of the EAF operation, process monitoring, establishing energy, and mass balance or model-based control of several process variables.

No abstract

The paper studies the effects of solid and liquid steel properties on the heat transfer coefficient (HTC) in electric arc furnaces (EAFs). Mathematically speaking, the HTC is a function of solid and liquid steel properties. Different velocities of the bath cause different flow paths around the solid particles and therefore different HTCs-a computational issue that has not been addressed yet. Therefore, a simplified calculation model is proposed, intended for HTC estimation according to the EAF conditions. Although many studies investigated this topic, most of them either assume unconventional conditions for the EAF operation, are computationally complex or focus on a specific case; and are, therefore, hard to implement in general EAF models. The algorithm proposed in this paper introduces simplified, yet accurate equations for calculating the HTC between solid and liquid steels as a function of their properties. Due to simplicity of the algorithm, the computational times are very short; thus, the procedure can be used in online model environments in order to perform different heat-transfer-related calculations. The obtained results show high similarity with other practical and theoretical studies. Furthermore, implementation of the HTC calculation submodule in a comprehensive EAF model yielded high accuracy in steelbath temperature prediction.

No abstract