We report the results of an experimental study of the transition to turbulence in a pipe under the condition of constant mass flux. The transition behaviour and structures observed in this experiment were qualitatively the same as those described in previous reported studies performed in pressure-driven systems. A variety of jet and suction devices were used to create repeatable disturbances which were then used to test the stability of developed Poiseuille flow. The Reynolds number ( Re ) and the parameters governing the disturbances were varied and the outcome, whether or not transition occurred some distance downstream of the injection point, was recorded. It was found that a critical amplitude of disturbance was required to cause transition at a given Re and that this amplitude varied in a systematic way with Re . This finite, critical level was found to be a robust feature, and was relatively insensitive to the form of disturbance. We interpret this as evidence for disconnected solutions which may provide a pointer for making progress in this fundamental, and as yet unresolved, problem in fluid mechanics.

Transition to turbulence in constant-mass-flux pipe flow

The authors’ research work into fully developed pulsating and oscillating laminar pipe and channel flows raised questions regarding the development length of the corresponding steady flow. For this development length, i.e., the distance from the entrance of the pipe to the axial position where the flow reaches the parabolic velocity profile of the Hagen-Poiseuille flow, a wide range of contradictory data exists. This is shown through a short review of the existing literature. Superimposed diffusion and convection, together with order of magnitude considerations, suggest that the normalized development length can be expressed as L∕D=C0+C1Re and for Re→0 one obtains C0=0.619, whereas for Re→∞ one obtains C1=0.0567. This relationship is given only once in the literature and it is presumed to be valid for all Reynolds numbers. Numerical studies show that it is only valid for Re→0 and Re→∞. The development length of laminar, plane channel flow was also investigated. The authors obtained similar results to those for the pipe flow: L∕D=C0′+C1′; Re, where C0′=0.631 and C1′=0.044. Finally, correlations are given to express L∕D analytically for the entire Re range for both laminar pipe and channel flows.

The Development Lengths of Laminar Pipe and Channel Flows

In his landmark paper of 1883, Reynolds addressed the question of why the fluid motion along a pipe changes from a laminar to a turbulent state at modest flow rates. His discoveries have remained a focus of hydrodynamic stability for the intervening 125 years, and the central puzzle of why the transition takes place at all remains unresolved. It is an enigma as all theoretical and numerical evidence suggests that the base state of fully developed flow, Hagen-Poiseuille flow, is linearly stable. The transition to turbulence is abrupt, mysterious, and largely dependent on the quality of the facility used in any experimental investigation. It is therefore not an example of transition via a sequence of instabilities or bifurcations in which considerable success has been achieved over the same period. Despite wide-ranging research activity that has uncovered many important pieces of the jigsaw, the central puzzle remains unresolved. The purpose of this review is to bring together the available experimental evidence and attempt to extract a set of accepted facts about this important problem.

Experimental Studies of Transition to Turbulence in a Pipe

https://www.washingtonpost.com/wp-srv/nation/pdfs/Sharkfeedingpaper.pdf

Feeding anatomy, filter-feeding rate, and diet of whale sharks Rhincodon typus during surface ram filter feeding off the Yucatan Peninsula, Mexico.

An experimental investigation was carried out of the development of steady, laminar, incompressible flow of a Newtonian fluid in the entry region of a curved pipe for the entry condition of uniform motion. Two semicircular pipes of radius ratios 1/20 and 1/7 were investigated, covering a Dean number range from 138 to 679. The axial velocity and the component of secondary velocity parallel to the plane of curvature of the pipe were measured using laser anemometry. It was observed that, in the upstream region where the boundary layers are thin compared with the pipe radius, the axial velocity within the irrotational core first develops to form a vortex-like flow. In the downstream region, characterized by viscous layers of thickness comparable with the pipe radius, there appears to be three-dimensional separation at the inner wall. There is also an indication of an additional vortex structure embedded within the Dean-type secondary motion. The experimental axial velocity profiles are compared with those constructed from the theoretical analyses of Singh and Yao & Berger. The quantitative agreement between theory and experiment is found to be poor; however, some of the features observed in the experiment are in qualitative agreement with the theoretical solution of Yao & Berger.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112078000762

Laser anemometer study of flow development in curved circular pipes

A method is described of predicting flow development and pressure drop in the inlet of a uniform pipe of circular cross-section for the incompressible isothermal laminar flow of a Newtonian fluid. Employment of both the differential and integral momentum equations leads to greater simplicity of expression than is found in other theoretical treatments, though the solutions obtained compare equally favourably with the limited experimental measurements available; those reported herein suggest the need for a more generalized analytical approach which covers non-isothermal flow and the effect on flow development of temperature-dependent viscosity.

D. Fargie

Papers

Developing Laminar Flow in a Pipe of Circular Cross-Section