Inverse finite element techniques for the analysis of solidification processes

✍ Scribed by Nicholas Zabaras

• Publisher: John Wiley and Sons
• Year: 1990
• Tongue: English
• Weight: 882 KB
• Volume: 29
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620290713

✦ Synopsis

This paper provides a finite element methodology (FEM) for the solution of several one-dimensional inverse solidification problems. In particular two design related problems will be addressed. The first one uses an inverse technique to calculate the boundary heat flux history that will achieve a specified velocity and flux at the freezing front. This front velocity and flux history can be appropriately selected so that the cast structure is controlled. The second problem is the calculation of the boundary heat flux and freezing front position, given appropriate estimates of the temperature field in a specified number of sensor locations (thermocouples) inside a solidifying body.

Front fixing and front tracking FEM techniques are used for the solution of the first problem, while a fixed domain finite element formulation (enthalpy method) is used for the solution of the second one. The 'future information technique' is employed in both problems. A detailed analysis of the effect on the solution of the error in the data, amount of future information used, time step, number of sensors and their location and of other parameters in the solution will be examined via several numerical tests. Finally, further applications of such inverse methodologies on the control of casting processes will be mentioned.