Shape optimization for a time-dependent model of a carousel press in glass production

Petr Salač; Jan Stebel

Applications of Mathematics (2019)

  • Volume: 64, Issue: 2, page 195-224
  • ISSN: 0862-7940

Abstract

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This contribution presents the shape optimization problem of the plunger cooling cavity for the time dependent model of pressing the glass products. The system of the mould, the glass piece, the plunger and the plunger cavity is considered in four consecutive time intervals during which the plunger moves between 6 glass moulds. The state problem is represented by the steady-state Navier-Stokes equations in the cavity and the doubly periodic energy equation in the whole system, under the assumption of rotational symmetry, supplemented by suitable boundary conditions. The cost functional is defined as the squared weighted L 2 norm of the difference between a prescribed constant and the temperature of the plunger surface layer at the moment before separation of the plunger and the glass piece. The existence and uniqueness of the solution to the state problem and the existence of a solution to the optimization problem are proved.

How to cite

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Salač, Petr, and Stebel, Jan. "Shape optimization for a time-dependent model of a carousel press in glass production." Applications of Mathematics 64.2 (2019): 195-224. <http://eudml.org/doc/294406>.

@article{Salač2019,
abstract = {This contribution presents the shape optimization problem of the plunger cooling cavity for the time dependent model of pressing the glass products. The system of the mould, the glass piece, the plunger and the plunger cavity is considered in four consecutive time intervals during which the plunger moves between 6 glass moulds. The state problem is represented by the steady-state Navier-Stokes equations in the cavity and the doubly periodic energy equation in the whole system, under the assumption of rotational symmetry, supplemented by suitable boundary conditions. The cost functional is defined as the squared weighted $ L^2 $ norm of the difference between a prescribed constant and the temperature of the plunger surface layer at the moment before separation of the plunger and the glass piece. The existence and uniqueness of the solution to the state problem and the existence of a solution to the optimization problem are proved.},
author = {Salač, Petr, Stebel, Jan},
journal = {Applications of Mathematics},
keywords = {shape optimization; Navier-Stokes equations; heat transfer},
language = {eng},
number = {2},
pages = {195-224},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Shape optimization for a time-dependent model of a carousel press in glass production},
url = {http://eudml.org/doc/294406},
volume = {64},
year = {2019},
}

TY - JOUR
AU - Salač, Petr
AU - Stebel, Jan
TI - Shape optimization for a time-dependent model of a carousel press in glass production
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 2
SP - 195
EP - 224
AB - This contribution presents the shape optimization problem of the plunger cooling cavity for the time dependent model of pressing the glass products. The system of the mould, the glass piece, the plunger and the plunger cavity is considered in four consecutive time intervals during which the plunger moves between 6 glass moulds. The state problem is represented by the steady-state Navier-Stokes equations in the cavity and the doubly periodic energy equation in the whole system, under the assumption of rotational symmetry, supplemented by suitable boundary conditions. The cost functional is defined as the squared weighted $ L^2 $ norm of the difference between a prescribed constant and the temperature of the plunger surface layer at the moment before separation of the plunger and the glass piece. The existence and uniqueness of the solution to the state problem and the existence of a solution to the optimization problem are proved.
LA - eng
KW - shape optimization; Navier-Stokes equations; heat transfer
UR - http://eudml.org/doc/294406
ER -

References

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