Ahmad, Riaz; (1996) Three-dimensional vortex flows in distorted pipes: Theory and computation. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Three related pipeflow problems are studied analytically and computationally. Firstly the development of an arbitrary three-dimensional (starting) velocity profile is addressed for flow in a straight pipe. Results are presented for different values of initial disturbance. A Hagen-Poiseulle starting condition is also considered for this geometry with the addition of forcing terms which then set up a three-dimensional flow field downstream. Secondly, the influence of curvature on a pipeflow is discussed for a pipe that starts bending uniformly after an initial straight section. The motion depends on a parameter, the alternative Dean number K. The relative curvature [delta] is taken to be small. Thirdly, the fluid motion through a straight pipe which experiences an abrupt small angular bend or corner is considered. In all three cases the pipe is of circular cross-section, and the Reynolds number is taken to be large. The starting condition for the distorted pipes is that of Hagen-Poiseulle flow, which then becomes three-dimensional however due to the pipes' distortions. Two numerical techniques are developed to solve the three-dimensional vortex equations, making use of a forward marching scheme in the streamwise direction, x. In all three geometries, the flow starts in a boundary-layer fashion for small values of x. The results are presented for different values of K for the curved pipe and different angle values of the normalized pipe bend a. for the cornered pipe. Both short-scale and long-scale adjustments of the pipe flow, due to the presence of the abrupt curving or cornering, are examined, yielding upstream- and downstream-influence properties. Although this work covers flow characteristics arising from curvature and cornering, the computational scheme(s) derived can be used to study flow in pipes of a general cross-section. The equations of motion are developed and use of con- formal mappings is suggested to obtain the flow field arising from pipeflows of any general cross-sectional area, as a starting point for future work.

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