The Use of Inverse Heat Conduction Models for Estimation of Transient Surface Heat Flux in Electroslag Remelting

Abstract

Three inverse heat conduction models were evaluated for their ability to predict the tran sient heat flux at the interior surface of the copper mold in the electroslag remelting (ESR) process for use in validating numerical ESR simulations and real-time control sys tems. The models were evaluated numerically using a simple one-dimensional (ID) test case and a 2D pseudo-ESR test case as a function of the thermocouple locations and sam ple frequency. The sensitivity of the models to measurement errors was then tested by applying random error to the numerically calculated temperature fields prior to the application of the inverse models. This error caused large fluctuations in the results of the inverse models, but these could be mitigated by implementing a simple SavitzkyGolay filter for data smoothing. Finally, the three inverse methods were applied to a fully transient ESR simulation to demonstrate their applicability to the industrial process. Based on these results, the authors recommend that the 2D control volume method described here be applied to industrial ESR trials.

A Sequence‐Coupled Mathematical Model of Magneto‐Hydrodynamic Two‐Phase Flow and Heat Transfer in a Triplex‐Electrode Electroslag Remelting Furnace

“…Other physical properties of slag and metal are assumed to be constant. [27] The configuration and insert depth of the electrode are fixed.…”

“…[26] Moreover, three inverse heat conduction models were evaluated to predict the transient heat flux at the interior surface of the copper mold in the ESR process. [27] Based on these results, the authors recommended that the 2D control volume method described can be applied to industrial ESR trials. Wang et al [28][29][30][31][32] developed a transient 3D coupled mathematical model to explore electromagnetic phenomena, flow, and temperature fields, solidification, inclusion motion behavior, desulfurization and oxygen transfer in the ESR process.…”

“…Later, the same research group established a numerical model of ESR used to examine the effects of ingot diameter, process current levels, and initial composition on macrosegregation in alloy 625 . Moreover, three inverse heat conduction models were evaluated to predict the transient heat flux at the interior surface of the copper mold in the ESR process . Based on these results, the authors recommended that the 2D control volume method described can be applied to industrial ESR trials.…”

Investigation on the effect of electrode tip on formation of metal droplets and temperature profile in a vibrating electrode electroslag remelting process

“…The heat transfer and solidification feature in the ESR process are described by the energy conservation equation based on the enthalpy-formulation [16]:…”

Time-Dependent Heat Flux Estimation in Multi-Layer Systems by Inverse Method

“…They make use of the conjugate gradient method to improve the estimation of the distribution of the surface temperature and heat flux for a two-dimensional cylindrical coordinate problem and solve the governing equation using finite element method. More recently, Plotkowski et al [11] evaluated three models of inverse heat conduction to prognosticate the transient heat flux at the interior surface of the copper mold in the electroslag remelting (ESR) process to validate numerical ESR simulations and real-time control systems. Eventually they applied the three inverse methods to a fully transient ESR simulation in order to demonstrate their applicability to the industrial process.…”