Marcel Lacroix

Prediction of a 2-D Solidification Front in High Temperature Furnaces by an Inverse Analysis

This study presents an inverse heat transfer method for predicting the two-dimensional time-varying shape of the phase change protective bank on the inside surface of a wall of a high temperature furnace filled with molten material. The method rests on the Levenberg-Marquardt least-square minimization technique and it relies on non-intrusive temperature measurements. Results indicate that under typical melting furnace operating conditions, the 2-D inverse methodology provides accurate predictions of the moving boundary. For these real time industrial applications however, a simpler yet accurate quasi-2-D inverse method that is nearly 10 times faster than the full 2-D inverse model is proposed.

Control of the ledge thickness in high-temperature metallurgical reactors using a virtual sensor

A non-intrusive inverse heat transfer procedure for predicting the time-varying thickness of the phase change ledge on the inside surface of the walls of a high-temperature metallurgical reactor is presented. A Kalman filter, based on a state-space representation of the reactor, is coupled with a recursive least-square estimator in order to estimate online the position of the phase front. The data are collected by a heat flux sensor located inside or outside of the reactor wall. The inverse method, used here as a virtual sensor, is coupled to a classic proportional–integral controller in order to control the ledge thickness by regulating the air cooling applied on the outside surface of the reactor wall. The virtual sensor and the control strategy are thoroughly tested for typical phase change conditions that prevail inside industrial facilities. Results show that a virtual sensor that relies on a heat flux sensor embedded inside the reactor wall provides more accurate and stable information, but at a price of a more complicated installation. In that case, it is shown that the discrepancy between the exact and the estimated ledge thicknesses remains smaller than 3% at all times, and that the control strategy ensures a null steady-state tracking error, a maximum tracking error less than 10%, no overshoot and no significant time lag.

Prediction of the Bank Formation in High Temperature Furnaces by a Sequential Inverse Analysis with Overlaps

This article presents a simple sequential inverse method for predicting time-varying thickness of the phase change protective bank found on the inside surface of a wall of a high temperature furnace. The main feature of the proposed overlapping procedure is its unique capability to increase the diagnostic frequency for phase change processes with large thermal inertia. The inverse method rests on the adjoint problem and the conjugate gradient method, and it relies on nonintrusive temperature measurements. Results also indicate that under typical melting furnace operating conditions, the proposed overlapping procedure doubles the allowable diagnostic frequency for predicting the time-varying bank thickness.

Is the performance of a virtual sensor employed for the prediction of the ledge thickness inside a metallurgical reactor affected by the thermal contact resistance

A virtual sensor is developed for predicting the time-varying thickness of the ledge on the inside surface of a wall of a high-temperature metallurgical reactor. The virtual sensor tracks the position of the solid-liquid phase front using thermal measurements taken from a heat flux sensor embedded in the reactor wall. The virtual sensor comprises a state observer coupled to a reduced model of the reactor. It also accounts for the thermal contact resistance of the wall structure. Results indicate that the virtual sensor is increasingly accurate as the magnitude of the thermal contact resistance augments. Moreover, the predictions of the virtual sensor remain accurate even when the contact resistance is poorly known.

Prediction of the Time-Varying Ledge Profile inside a High-Temperature Metallurgical Reactor with an Unscented Kalman Filter-Based Virtual Sensor

A non-intrusive inverse heat transfer procedure for predicting the two-dimensional time-varying profile of the protective phase-change ledge on the inside surface of the walls of a high-temperature metallurgical reactor is presented. The inverse method, used here as a virtual sensor, enables the on-line estimation of the position of the solid-liquid phase front using thermal sensors embedded in the reactor wall. The virtual sensor comprises a state observer coupled to a reduced model of the reactor. Results show that the virtual sensor that yields the best prediction comprises an unscented Kalman filter, a nonlinear state-space model of thereactor, and two heat flux sensors located at the wall/ledge interface.

On the Prediction of the Crust Evolution inside Aluminum Electrolysis Cells

A model for predicting the evolution of the crust inside aluminum electrolysis cells is presented. The model takes into account the effects of heat transfer, solid/liquid phase-change, and chemical transformation of anode covering material (ACM). The model predicts: 1) the temperature field inside the cell, 2) the evolution of the ACM conversion into crust, 3) the melting/solidification processes inside the cell and, 4) the time-varying heat losses at the top of the cell. The model is validated with experimental data taken on an industrial electrolysis cell. Results show that the model captures the essential behavioral features of the industrial cell. However, further experiments must be performed in order to provide reliable data on the crust formation. These experimental data are needed for a thorough validation of the mathematical model.

Energy Savings in Aluminum Electrolysis Cells: Effect of the Cathode Design

Non uniform current distribution inside aluminum electrolysis cells is responsible for energy losses, a phenomena impacting on both the economy and the environment. Indeed, non uniform distribution induces premature wear of the cathode surface and triggers magneto-hydro-dynamic instabilities in the molten aluminum of the cell. The present study addresses this problem by examining the effect of the cathode shape and design on the current distribution. A computational methodology based on a finite element method is developed. It is then employed to determine the optimal cathode design, i.e., the design that minimizes the energy losses and maximizes the lifetime of the cell. The effect of various design parameters on the current distribution is highlighted. Their economic impacts on the operation of the cell are also assessed.