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The self-similarity of wall-bounded temporally accelerating turbulent flows
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.ORCID iD: 0000-0002-3349-601X
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.ORCID iD: 0000-0002-6473-7090
2018 (English)In: Journal of turbulence, ISSN 1468-5248, E-ISSN 1468-5248, Vol. 19, no 1, p. 49-60Article in journal (Refereed) Published
Abstract [en]

From the study of viscous flow it is known that certain time-dependent laminar problems, such as the impulsively started flat plate and the diffusion of a vortex sheet, possess self-similar solutions. Previous studies of turbulent channel and pipe flows accelerating between two steady states have shown that the flow field evolves in three distinct stages. Furthermore, recent direct numerical simulations have shown that the perturbation velocity, i.e. the surplus velocity from the initial value, in an impulsively accelerating turbulent channel and pipe flow also possesses a self-similar distribution during the initial stage. In here, these results are developed analytically and it is shown that accelerating flows in which the centreline velocity develops as Uc(t) = U0(t/t0)m will possess a self-similar velocity distribution during the initial stage. The displacement thickness of the perturbation velocity is shown to be dependent only on the type of acceleration, and not on the initial Reynolds number, the acceleration rate or the change in Reynolds number. The derived formulas are verified with good agreement against measurements performed in a linearly accelerating turbulent pipe flow and with data from channel flow simulations.

Place, publisher, year, edition, pages
Taylor & Francis, 2018. Vol. 19, no 1, p. 49-60
National Category
Fluid Mechanics and Acoustics
Research subject
Fluid Mechanics
Identifiers
URN: urn:nbn:se:ltu:diva-66785DOI: 10.1080/14685248.2017.1390239ISI: 000427894200003OAI: oai:DiVA.org:ltu-66785DiVA, id: diva2:1160703
Note

Validerad;2018;Nivå 2;2017-12-15 (andbra)

Available from: 2017-11-28 Created: 2017-11-28 Last updated: 2018-04-06Bibliographically approved
In thesis
1. Studies of Transient and Pulsating flows with application to Hydropower
Open this publication in new window or tab >>Studies of Transient and Pulsating flows with application to Hydropower
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Studier av transient och pulserande strömning med applikation inom vattenkraft
Abstract [en]

The rotational motion of a hydraulic turbine runner makes pulsating flows ubiquitous in different locations of the machine. The cyclic loading thus induced may generate large pressure forces acting periodically on both stationary and rotating parts. In addition to the presence of pulsating flows in a turbine runner, transient flows are encountered at an increasingly higher rate due to the continual installation of intermittent sources of renewable energy, such as wind and solar power. To mitigate the imbalance that these unpredictable sources induce on the frequency of the electrical grid, hydropower turbines are enforced to regulate their power production, and consequently flow rate, thus leaving them to operate under transient conditions. In terms of wear and fatigue, a startup or shutdown of a hydraulic turbine corresponds to 10-20 hours of steady state operation at the design point. Transient operation of a hydraulic machine can, however, also be used in favour for measuring the discharge through the turbine using the pressure-time method. A better understanding of pulsating and transient flows thus has the potential both to mitigate problems associated with them, and to increase the accuracy with which the turbine flow rate can be measured; two great merits for the hydropower community. In light of this observation, the following work constitutes a fundamental investigation of transient and pulsating flows performed in a straight pipe.Studies have been performed experimentally using particle image velocimetry, hot-film anemometry, laser Doppler velocimetry and pressure sensors.

A chief finding is that the time-development of the wall shear stress and near-wall turbulence fields exhibit significant similarity between transient and pulsating flows, despite the different conditions of the mean flow. Whereas the former is initiated from a statistically steady state, the latter is constantly subjected to a time-varying forcing. Both types of unsteady flows have previously been investigated in detail; however, any potential similarity between them has, largely, been unexplored. An important implication of this finding, then, is that knowledge acquired in one type of unsteady flow can be used, if not interchangeably, at least as a guidance for the expected behaviour in the other type of flow. An example is the development of unsteady turbulence models. Another important finding is that the frictional losses arising during the late stage of a pressure-time flow rate measurement can be accurately modelled using an analytical laminar formulation of the wall shear stress, despite the bulk of the flow being turbulent. The formulation of the wall shear stress has potential to be further improved by incorporating a damping-function.

Place, publisher, year, edition, pages
Luleå: Luleå University of Technology, 2018
Series
Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544
Keywords
Turbulent flows, Pipe flow, Unsteadiness, Friction modeling
National Category
Fluid Mechanics and Acoustics
Research subject
Fluid Mechanics
Identifiers
urn:nbn:se:ltu:diva-67865 (URN)978-91-7790-065-8 (ISBN)978-91-7790-066-5 (ISBN)
Public defence
2018-04-20, E231, Luleå, 09:30 (English)
Opponent
Supervisors
Available from: 2018-03-07 Created: 2018-03-06 Last updated: 2018-04-05Bibliographically approved

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