Pipe flow

About: Pipe flow is a research topic. Over the lifetime, 13826 publications have been published within this topic receiving 351605 citations.

On the effect of torsion on a helical pipe flow

Abstract: An orthogonal coordinate system along a generic spatial curve has been introduced, and the Navier-Stokes equations for a steady incompressible viscous flow have been explicitly written in this frame of reference. As an application the flow in a helical pipe has been studied, and, formdii 5f curvature and torsion small compared with the radius of the pipe, the flow has been considered as a perturbed Poiseuille flow. The result is that for curvatures and torsions of the same order and for low Reynolds number the curvature induces on the flow a first-order effect on the parameter e =κa, where κ is the curvature and a the radius of the pipe, while the effect of the torsion on the flow is of the second order in E. This last result disagrees with those of Wang (1981), who, adopting a non-orthogonal coordinate system, found a first-order effect of torsion on the flow.

Transition to shear-driven turbulence in Couette-Taylor flow.

Abstract: Turbulent flow between concentric cylinders is studied in experiments for Reynolds numbers 800R1.23\ifmmode\times\else\texttimes\fi{}${10}^{6}$ for a system with radius ratio \ensuremath{\eta}=0.7246. Despite predictions for the torque scaling as a power law of the Reynolds number, high-precision torque measurements reveal no Reynolds-number range with a fixed power law. A well-defined nonhysteretic transition at R=1.3\ifmmode\times\else\texttimes\fi{}${10}^{4}$ is marked by a change in the Reynolds-number dependence of the torque. Flow quantities such as the axial turbulent diffusivity, the time scales asociated with the fluctuations of the wall shear stress, and the root-mean-square fluctuations of the wall shear stress and its time derivative are all shown to be simply related to the global torque measurements. Above the transition, the torque measurements and observed time scales indicate a close correspondence between this closed-flow system and open-wall--bounded-shear flows such as pipe flow, duct flow, and flow over a flat plate.

Turbulence transition and the edge of chaos in pipe flow

Abstract: The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the edge of chaos which separates perturbations that decay towards the laminar profile and perturbations that trigger turbulence. Using the lifetime as an indicator and methods developed in Skufca et al., Phys. Rev. Lett. 96, 174101 (2006), we show that superimposed on an overall 1/Re scaling predicted and studied previously there are small, nonmonotonic variations reflecting folds in the edge of chaos. By tracing the motion in the edge we find that it is formed by the stable manifold of a unique flow field that is dominated by a pair of downstream vortices, asymmetrically placed towards the wall. The flow field that generates the edge of chaos shows intrinsic chaotic dynamics.

A connection between the Camassa–Holm equations and turbulent flows in channels and pipes

Abstract: In this paper we discuss recent progress in using the Camassa–Holm equations to model turbulent flows. The Camassa–Holm equations, given their special geometric and physical properties, appear particularly well suited for studying turbulent flows. We identify the steady solution of the Camassa–Holm equation with the mean flow of the Reynolds equation and compare the results with empirical data for turbulent flows in channels and pipes. The data suggest that the constant α version of the Camassa–Holm equations, derived under the assumptions that the fluctuation statistics are isotropic and homogeneous, holds to order α distance from the boundaries. Near a boundary, these assumptions are no longer valid and the length scale α is seen to depend on the distance to the nearest wall. Thus, a turbulent flow is divided into two regions: the constant α region away from boundaries, and the near wall region. In the near wall region, Reynolds number scaling conditions imply that α decreases as Reynolds number increas...