### Abstract

Language | English |
---|---|

Pages | 533-553 |

Number of pages | 20 |

Journal | International Journal of Numerical Methods in Fluids |

Volume | 38 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2002 |

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### Keywords

- thin viscous sheets
- windscreen sagging problem

### Cite this

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*International Journal of Numerical Methods in Fluids*, vol. 38, no. 6, pp. 533-553. https://doi.org/10.1002/fld.227

Research output: Contribution to journal › Article

TY - JOUR

T1 - Numerical solution of the flow of viscous sheets under gravity and the inverse windscreen sagging problem

AU - Hunt, R.

PY - 2002

Y1 - 2002

N2 - The slumping of a thin sheet of very viscous liquid glass is used in the manufacture of windscreens in the automotive industry. The governing equations for an asymptotically thin sheet with variable viscosity are derived in which the vertical coordinate forms the centre-line of the sheet. The time-dependant equations have been solved numerically using the backward Euler method to give results in both two and three dimensions. The flow of an initially flat sheet falls freely under gravity until it becomes curved and the flow becomes very slow in the slumped phase. Finally the sheet freefalls as the thickness becomes small at the boundaries. The inverse problem in which the viscosity profile is to be determined for a given shape can be solved as an embedding problem in which a search is made amongst the forward solutions. Possible shapes in the two-dimensional problem are very restrictive and are shown to be related to the sheet thickness. In three dimensions the range of shapes is much greater.

AB - The slumping of a thin sheet of very viscous liquid glass is used in the manufacture of windscreens in the automotive industry. The governing equations for an asymptotically thin sheet with variable viscosity are derived in which the vertical coordinate forms the centre-line of the sheet. The time-dependant equations have been solved numerically using the backward Euler method to give results in both two and three dimensions. The flow of an initially flat sheet falls freely under gravity until it becomes curved and the flow becomes very slow in the slumped phase. Finally the sheet freefalls as the thickness becomes small at the boundaries. The inverse problem in which the viscosity profile is to be determined for a given shape can be solved as an embedding problem in which a search is made amongst the forward solutions. Possible shapes in the two-dimensional problem are very restrictive and are shown to be related to the sheet thickness. In three dimensions the range of shapes is much greater.

KW - thin viscous sheets

KW - windscreen sagging problem

UR - http://dx.doi.org/10.1002/fld.227

U2 - 10.1002/fld.227

DO - 10.1002/fld.227

M3 - Article

VL - 38

SP - 533

EP - 553

JO - International Journal of Numerical Methods in Fluids

T2 - International Journal of Numerical Methods in Fluids

JF - International Journal of Numerical Methods in Fluids

SN - 0271-2091

IS - 6

ER -