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On an analytical explanation of the phenomena observed in accelerated turbulent pipe flow

Published online by Cambridge University Press:  24 October 2019

F. Javier García García Open the ORCID record for F. Javier García García [Opens in a new window]  and
Pablo Fariñas Alvariño
F. Javier García García*
Affiliation:
Department of Naval and Industrial Engineering, Higher Polytechnic School, University of A Coruña, Campus de Esteiro, C/Mendizábal s/n, 15403 Ferrol, Spain Integraciones Técnicas de Seguridad, S.A., C/Nobel 15, 15650 Cambre, A Coruña, Spain
Pablo Fariñas Alvariño
Affiliation:
Department of Naval and Industrial Engineering, Higher Polytechnic School, University of A Coruña, Campus de Esteiro, C/Mendizábal s/n, 15403 Ferrol, Spain
*
†Email address for correspondence: f.javier.garcia.garcia@udc.es
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Abstract

This research presents a new theory that explains analytically the behaviour of any fully developed incompressible turbulent pipe flow, steady or unsteady. We propose the name of theory of underlying laminar flow (TULF), because its main consequence is the description of any turbulent pipe flow as the sum of two components: the underlying laminar flow (ULF) and the purely turbulent component (PTC). We use the framework of the TULF to explain analytically most of the important and interesting phenomena reported in He & Jackson (J. Fluid Mech., vol. 408, 2000, pp. 1–38). To do so, we develop a simple model for the pressure gradient and Reynolds shear stress that could be applied to the linearly accelerated pipe flow described by He & Jackson (2000). The following features of the unsteady flow are explained: the deformation undergone by the mean velocity profiles during the transient, the velocity overshoot observed in the more rapid excursions, the dual deformation of mean velocity profiles when overshoots are present, the laminarisation effects described during acceleration, the rapid decrease of the Reynolds shear stress upon approaching the wall that brings forth the laminar sublayer, and some other minor effects. A new field is defined to characterise the degree of turbulence within the flow, directly calculable from the theory itself. Arguably, this new field would describe the degree of turbulence in a pipe flow more accurately than the familiar turbulence intensity parameter. Finally, a paradox is found in the deformation of the unsteady mean velocity profiles with respect to equal-Reynolds-number steady profiles, which is duly explained. The research also predicts the occurrence of mean velocity undershoots if the flow is decreased rapidly enough.

JFM classification

Mathematical Foundations: General fluid mechanics Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 881 , 25 December 2019 , pp. 420 - 461
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Copyright
© 2019 Cambridge University Press 

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