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Entrainment at multi-scales across the turbulent/non-turbulent interface in an axisymmetric jet

Published online by Cambridge University Press:  10 August 2016

Dhiren Mistry ,
Jimmy Philip ,
James R. Dawson  and
Ivan Marusic
Dhiren Mistry*
Affiliation:
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
Jimmy Philip
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, VIC 3010, Australia
James R. Dawson
Affiliation:
Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
Ivan Marusic
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, VIC 3010, Australia
*
†Email address for correspondence: dhiren.v.mistry@ntnu.no
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Abstract

We consider the scaling of the mass flux and entrainment velocity across the turbulent/non-turbulent interface (TNTI) in the far field of an axisymmetric jet at high Reynolds number. Time-resolved, simultaneous multi-scale particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) are used to identify and track the TNTI, and directly measure the local entrainment velocity along it. Application of box-counting and spatial-filtering methods, with filter sizes $\unicode[STIX]{x1D6E5}$ spanning over two decades in length, show that the mean length of the TNTI exhibits a power-law behaviour with a fractal dimension $D\approx 0.31{-}0.33$. More importantly, we invoke a multi-scale methodology to confirm that the mean mass flux, which is equal to the product of the entrainment velocity and the surface area, remains constant across the range of filter sizes. The results, within experimental uncertainty, also show that the entrainment velocity along the TNTI exhibits a power-law behaviour with $\unicode[STIX]{x1D6E5}$, such that the entrainment velocity increases with increasing $\unicode[STIX]{x1D6E5}$. In fact, the mean entrainment velocity scales at a rate that balances the scaling of the TNTI length such that the mass flux remains independent of the coarse-grain filter size, as first suggested by Meneveau & Sreenivasan (Phys. Rev. A, vol. 41, no. 4, 1990, pp. 2246–2248). Hence, at the smallest scales the entrainment velocity is small but is balanced by the presence of a very large surface area, whilst at the largest scales the entrainment velocity is large but is balanced by a smaller (smoother) surface area.

JFM classification

Wakes/Jets: Jets Turbulent Flows: Turbulent Flows Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 802 , 10 September 2016 , pp. 690 - 725
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© 2016 Cambridge University Press 

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