Howell, P. D. (2001) *Fluid mechanical modelling of the scroll compressor.* In: Mathematical Modeling: Case Studies from Industry. Mathematics for Science and Engineering . Cambridge University Press, Cambridge, UK, pp. 32-56. ISBN 0521011736

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## Abstract

This case-study concerns the flow of gas in a so-called Scroll Compressor. In this device a number of chambers of gas at different temperatures and pressures are separated by narrow channels through which leakage can occur. Using compressible lubrication theory, an estimate for the leakage rate is found in terms of the material properties of the gas and the geometry of the compressor. Thus a simple functional is obtained which allows the efficiency of different compressor designs to be compared. Next we derive a set of ordinary differential equations for the temperature and pressure in each chamber; the coupling between them arises from the leakage. The numerical solution of these equations allows a realistic simulation of a working compressor, and suggests some interesting possibilities for future designs.

This problem arose at the 32nd European Study Group with Industry held in September 1998 at the Technical University of Denmark: the first ever to be held outside the United Kingdom. It was presented by Stig Helmer Jorgensen from DANFOSS, which is Denmark's largest industrial group and specialises in controls for refrigeration and heating. The Danish Study Group was a great success and is expected to be repeated annually henceforth. The feedback from DANFOSS has also been encouraging and hopefully this represents the start of a long-term collaboration.

Item Type: | Book Section |
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Subjects: | D - G > Fluid mechanics |

Research Groups: | Oxford Centre for Industrial and Applied Mathematics |

ID Code: | 131 |

Deposited By: | Peter Howell |

Deposited On: | 14 Sep 2004 |

Last Modified: | 20 Jul 2009 14:18 |

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