Previous |  Up |  Next

Article

Full entry | Fulltext not available (moving wall 24 months)      Feedback
Keywords:
shape optimization; heat-conducting fluid; energy transfer
Summary:
In this contribution, we present the problem of shape optimization of the plunger cooling which comes from the forming process in the glass industry. We look for a shape of the inner surface of the insulation barrier located in the plunger cavity so as to achieve a constant predetermined temperature on the outward surface of the plunger. A rotationally symmetric system, composed of the mould, the glass piece, the plunger, the insulation barrier and the plunger cavity, is considered. The state problem is given as a multiphysics problem where solidifying molten glass is cooled from the inside by water flowing through the plunger cavity and from the outside by the environment surrounding the mould. \endgraf The cost functional is defined as the squared $ L^2_r $ norm of the difference between a prescribed constant and the temperature on the outward boundary of the plunger. The temperature distribution is controlled by changing the insulation barrier wall thickness. \endgraf The numerical results of the optimization to the required target temperature 800 $^{\circ } $C of the outward plunger surface together with the distribution of temperatures along the interface between the plunger and the glass piece before, during and after the optimization process are presented.
References:
[1] Haslinger, J., Neittaanmäki, P.: Finite Element Approximation for Optimal Shape Design: Theory and Applications. John Wiley & Sons, Chichester (1988). MR 0982710 | Zbl 0713.73062
[2] Kufner, A.: Weighted Sobolev Spaces. A Wiley-Interscience Publication, John Wiley & Sons, New York (1985). MR 0802206 | Zbl 0567.46009
[3] Matoušek, I., Cibulka, J.: Analýza tvarovacího cyklu na karuselovém lisu NOVA. TU v Liberci, Liberec (1999), Czech.
[4] Salač, P.: Optimal design of the cooling plunger cavity. Appl. Math., Praha 58 (2013), 405-422. DOI 10.1007/s10492-013-0020-8 | MR 3083521 | Zbl 1289.49043
[5] Salač, P.: Optimization of plunger cavity. Programs and Algorithms of Numerical Mathematics 16, 2012 Academy of Sciences of the Czech Republic, Institute of Mathematics, Praha J. Chleboun et al. (2013), 174-180. MR 3203817 | Zbl 1340.80025
[6] Salač, P., Starý, M.: The cooling of the pressing device in the glass industry. Internat. J. Multiphysics 7 (2013), 207-218. DOI 10.1260/1750-9548.7.3.207
[7] Šorin, S. N.: Sdílení Tepla. SNTL, Praha (1968), Czech.
Partner of
EuDML logo