In glass production, flanges are used for the electric heating of platinum pipes through which the glass melt flows. The electric current produces a Joule effect in the pipe wall, which can influence the temperature of the glass melt. The flange should heat the pipe homogeneously and should not have any local influence on the glass, otherwise cristallizations could occur at certain points. Such inhomogeneities have a very decisive influence on the quality of the glass.
Optimal Shape Design
The control of the flange temperature exclusively by the induced electrical current is not sufficient in order to avoid local effects. Therefore, the flange geometry must additionally be optimized. This optimum shape design is an inverse problem where, apart from a homogeneous temperature transfer from the flange to the pipe, further conditions must be accounted for:
- the electric potential satisfies the potential equation,
- the temperature satisfies the heat conduction equation,
- and economic aspects must also be considered.
The flange thickness is very small compared to the other dimensions, therefore the three-dimensional shape design problem can be reduced to a two-dimensional parameter identification problem by asymptotic expansion. The parameter function to be determined is the thickness of the flange.
This problem - which is also inverse - was solved by Lagrange multipliers, and the respective software was developed. Thus, our industrial cooperation partner received a tool which allows an essentially simpler development of flanges according to the respective technical requirements.
Type of Project: Industry Project
Project Partner: Schott Glas, Mainz