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https://hdl.handle.net/2440/36180
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Type: | Journal article |
Title: | The instability of the flow in a suddenly blocked pipe |
Author: | Jewell, N. Denier, J. |
Citation: | Quarterly Journal of Mechanics and Applied Mathematics, 2006; 59(PN Part 4):651-673 |
Publisher: | Oxford Univ Press |
Issue Date: | 2006 |
ISSN: | 0033-5614 1464-3855 |
Abstract: | This paper considers the decay of Poiseuille flow within a suddenly blocked pipe. For small to moderate times the flow is shown to consist of an inviscid core flow coupled with a boundary layer at the pipe wall. A small-time asymptotic solution is developed and it is shown that this solution is valid for times up to the point at which the boundary layer fills the whole pipe. A small-time composite solution is used to initiate a numerical marching procedure which overcomes the small-time singularity that arises in the flow and so allows us to describe the ultimate decay of the flow within a blocked pipe. The stability of this flow is then considered using both a quasi-steady approximation and a transient-growth analysis based upon marching solutions of the linearized Navier–Stokes equations. Our transient stability analysis predicts a critical Reynolds number, for transition to turbulence, in the range 970 < Re < 1370. |
DOI: | 10.1093/qjmam/hbl021 |
Published version: | http://dx.doi.org/10.1093/qjmam/hbl021 |
Appears in Collections: | Applied Mathematics publications Aurora harvest 6 Environment Institute publications |
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