TY - JOUR

T1 - The decay of suddenly blocked flow in a curved pipe

AU - Clarke, Richard J.

AU - Denier, James P.

PY - 2009

Y1 - 2009

N2 - Pressure-driven viscous flow through a rigid curved pipe of uniform circular cross-section which is suddenly stopped, for example through the instantaneous closure of a valve, is considered here. The profile of the flow at early times after the stoppage is analysed asymptotically, by matching diffusive boundary layers to a core flow that is driven by an axial pressure gradient. This pressure gradient is unknown a priori and, furthermore, exhibits singular behaviour immediately after the stoppage. This analysis therefore provides the flow information at small but finite times that is required for numerical determination of the flow at later times. The limiting case of weak curvature is also considered, where linearization of the governing flow equations is possible. The results illustrate some novel features of the flow which result solely from the pipe's curvature and the consequences for the flow's rate of decay are discussed.

AB - Pressure-driven viscous flow through a rigid curved pipe of uniform circular cross-section which is suddenly stopped, for example through the instantaneous closure of a valve, is considered here. The profile of the flow at early times after the stoppage is analysed asymptotically, by matching diffusive boundary layers to a core flow that is driven by an axial pressure gradient. This pressure gradient is unknown a priori and, furthermore, exhibits singular behaviour immediately after the stoppage. This analysis therefore provides the flow information at small but finite times that is required for numerical determination of the flow at later times. The limiting case of weak curvature is also considered, where linearization of the governing flow equations is possible. The results illustrate some novel features of the flow which result solely from the pipe's curvature and the consequences for the flow's rate of decay are discussed.

UR - http://www.scopus.com/inward/record.url?scp=62149104392&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/DP0556360

U2 - 10.1007/s10665-007-9210-2

DO - 10.1007/s10665-007-9210-2

M3 - Article

AN - SCOPUS:62149104392

VL - 63

SP - 241

EP - 257

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

SN - 0022-0833

IS - 2-4

ER -