An Online Input Estimation Algorithm For A Coupled Inverse Heat Conduction-Microstructure Problem

Abstract

<p>This study focuses on developing a new online recursive numerical algorithm for a coupled nonlinear inverse heat conduction-microstructure problem. This algorithm is essential in identifying, designing and controlling many industrial applications such as the quenching process for heat treating of materials, chemical vapor deposition and industrial baking. In order to develop the above algorithm, a systematic four stage research plan has been conducted. </P> <p> The first and second stages were devoted to thoroughly reviewing the existing inverse heat conduction techniques. Unlike most inverse heat conduction solution methods that are batch form techniques, the online input estimation algorithm can be used for controlling the process in real time. Therefore, in the first stage, the effect of different parameters of the online input estimation algorithm on the estimate bias has been investigated. These parameters are the stabilizing parameter, the measurement errors standard deviation, the temporal step size, the spatial step size, the location of the thermocouple as well as the initial assumption of the state error covariance and error covariance of the input estimate. Furthermore, three different discretization schemes; namely: explicit, implicit and Crank-Nicholson have been employed in the input estimation algorithm to evaluate their effect on the algorithm performance. </p> <p> The effect of changing the stabilizing parameter has been investigated using three different forms of boundary conditions covering most practical boundary heat flux conditions. These cases are: square, triangular and mixed function heat fluxes. The most important finding of this investigation is that a robust range of the stabilizing parameter has been found which achieves the desired trade-off between the filter tracking ability and its sensitivity to measurement errors. For the three considered cases, it has been found that there is a common optimal value of the stabilizing parameter at which the estimate bias is minimal. This finding is important for practical applications since this parameter is usually unknown. Therefore, this study provides a needed guidance for assuming this parameter. </p> <p> In stage three of this study, a new, more efficient direct numerical algorithm has been developed to predict the thermal and microstructure fields during quenching of steel rods. The present algorithm solves the full nonlinear heat conduction equation using a central finite-difference scheme coupled with a fourth-order Runge-Kutta nonlinear solver. Numerical results obtained using the present algorithm have been validated using experimental data and numerical results available in the literature. In addition to its accurate predictions, the present algorithm does not require iterations; hence, it is computationally more efficient than previous numerical algorithms. </p> <p> The work performed in stage four of this research focused on developing and applying an inverse algorithm to estimate the surface temperatures and surface heat flux of a steel cylinder during the quenching process. The conventional online input estimation algorithm has been modified and used for the first time to handle this coupled nonlinear problem. The nonlinearity of the problem has been treated explicitly which resulted in a non-iterative algorithm suitable for real-time control of the quenching process. The obtained results have been validated using experimental data and numerical results obtained by solving the direct problem using the direct solver developed in stage three of this work. These results showed that the algorithm is efficiently reconstructing the shape of the convective surface heat flux. </P>