Perspective on the Response of Turbulent Pipe Flows to Strong Perturbations

Liuyang Ding,Tyler Van Buren,Alexander J Smits,Ian E Gunady

doi:10.3390/fluids6060208

Liuyang Ding, Tyler Van Buren + Show 2 more

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https://doi.org/10.3390/fluids6060208

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Abstract

Pipe flow responds to strong perturbations in ways that are fundamentally different from the response exhibited by boundary layers undergoing a similar perturbation, primarily because of the confinement offered by the pipe wall, and the need to satisfy continuity. We review such differences by examining previous literature, with a particular focus on the response of pipe flow to three different kinds of disturbances: the abrupt change in surface condition from rough to smooth, the obstruction due to presence of a single square bar roughness elements of different sizes, and the flow downstream of a streamlined body-of-revolution placed on the centerline of the pipe. In each case, the initial response is strongly influenced by the pipe geometry, but far downstream all three flows display a common feature, which is the very slow, second-order recovery that can be explained using a model based on the Reynolds stress equations. Some future directions for research are also given.

Highlights

Bill Willmarth had a particular interest in turbulent boundary layers, especially the nature of the wall pressure fluctuations [1] and the scaling of the Reynolds stresses [2]
As noted by Blackwelder et al [3], he posed provocative questions regarding turbulent wall-layer structures, like “What are the effects of parameters, such as wall-roughness, pressure-gradients, surface-curvature, and three-dimensionality on the structure elements? How do the evolutionary histories of structures change with the above parameters?”
Saito and Pullin [29] performed a high Reynolds number large eddy simulation (LES) study of turbulent flow in a long channel that experienced repeated transitions between smooth and rough surfaces. They found that the friction velocity first overshot and undershot their equivalent equilibrium value before recovering over a stream-wise distance of order 10–30h, where h is the channel half-height, depending on both roughness and Reynolds number. These observations are in line with the response of boundary layers to a change in surface roughness [30,31], but they noted the important role played by confinement due to the channel geometry

Summary

Introduction

This paper is part of the Special Issue honoring the contributions of W. They found that the friction velocity first overshot and undershot their equivalent equilibrium value before recovering over a stream-wise distance of order 10–30h, where h is the channel half-height, depending on both roughness and Reynolds number These observations are in line with the response of boundary layers to a change in surface roughness [30,31], but they noted the important role played by confinement due to the channel geometry. Three cases are considered: the recovery from a step change in roughness from rough to smooth; the relaxation downstream of a single square bar roughness element of different heights; and the recovery of the wake downstream of a body-of-revolution placed on the centerline of the pipe This summary of recent work is more in the service of assessing our present knowledge of perturbed pipe flows, rather than an original research contribution, and so we are interested in drawing out the similarities observed in the more general flow response. Fluids 2021, 6, 208 by presenting brief summaries of the data for all three experiments, and discuss the modeling effort and how it can be used to unify the observational experience

Flow Past a Step-Change in Wall Roughness

Flow Downstream of a Square Bar Roughness Element

Flow Downstream of a Streamlined Body of Revolution

Modeling Non-Equilibrium Wall-Bounded Turbulence

Opportunities for Future Research