Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-17T09:17:39.679Z Has data issue: false hasContentIssue false
  • English
  • Français

Kinematics of local entrainment and detrainment in a turbulent jet

Published online by Cambridge University Press:  30 May 2019

Dhiren Mistry Open the ORCID record for Dhiren Mistry [Opens in a new window] ,
Jimmy Philip  and
James R. Dawson Open the ORCID record for James R. Dawson [Opens in a new window]
Dhiren Mistry*
Affiliation:
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
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we investigate the continuous, local exchange of fluid elements as they are entrained and detrained across the turbulent/non-turbulent interface (TNTI) in a high Reynolds number axisymmetric jet. To elucidate characteristic kinematic features of local entrainment and detrainment processes, simultaneous high-speed particle image velocimetry and planar laser-induced fluorescence measurements were undertaken. Using an interface-tracking technique, we evaluate and analyse the conditional dependence of local entrainment velocity in a frame of reference moving with the TNTI in terms of the interface geometry and the local flow field. We find that the local entrainment velocity is intermittent with a characteristic length scale of the order of the Taylor micro-scale and that the contribution to the net entrainment rate arises from the imbalance between local entrainment and detrainment rates that occurs with a ratio of two parts of entrainment to one part detrainment. On average, an increase in local entrainment is correlated with excursions of the TNTI towards jet centreline into regions of higher streamwise momentum, convex surface curvature facing the turbulent side of the jet and along the leading edges of the interface. In contrast, detrainment is correlated with excursions of the TNTI away from the jet centreline into regions of lower streamwise momentum, concave surface curvature and along the trailing edge. We find that strong entrainment is characterised by a local counterflow velocity field in the frame of reference moving with the TNTI which enhances the transport of rotational and irrotational fluid elements. On the other hand, detrainment is characterised by locally uniform flow fields with the local fluid velocity on either side of the TNTI advecting in the same direction. These local flow patterns and the strength of entrainment or detrainment rates are also observed to be strongly influenced by the presence and relative strength of vortical structures which are of the order of the Taylor micro-scale that populate the turbulent region along the jet boundary.

JFM classification

Wakes/Jets: Jets Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 871 , 25 July 2019 , pp. 896 - 924
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Bisset, D. K., Hunt, J. C. R. & Rogers, M. M. 2002 The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383–410.Google Scholar
Borrell, G. & Jiménez, J. 2016 Properties of the turbulent/non-turbulent interface in boundary layers. J. Fluid Mech. 801, 554–596.Google Scholar
Buxton, O. R. H. & Ganapathisubramani, B. 2010 Amplification of enstrophy in the far field of an axisymmetric turbulent jet. J. Fluid Mech. 651, 483–502.Google Scholar
Chauhan, K., Philip, J. & Marusic, I. 2014a Scaling of the turbulent/non-turbulent interface in boundary layers. J. Fluid Mech. 751, 298–328.Google Scholar
Chauhan, K., Philip, J., de Silva, C., Hutchins, N. & Marusic, I. 2014b The turbulent/non-turbulent interface and entrainment in a boundary layer. J. Fluid Mech. 742, 119–151.Google Scholar
Corrsin, S. & Kistler, A.1955 Free-stream boundaries of turbulent flows. NASA Tech. Rep. TN-1244.Google Scholar
Crimaldi, J. P. 2008 Planar laser induced fluorescence in aqueous flows. Exp. Fluids 44, 851–863.Google Scholar
Dimotakis, P. E. 2005 Turbulent mixing. Annu. Rev. Fluid Mech. 37, 329–356.Google Scholar
Dopazo, C., Martin, J. & Hierro, J. 2007 Local geometry of isoscalar surfaces. Phys. Rev. E 76, 056316.Google Scholar
Gampert, M., Boschung, J., Hennig, F., Gauding, M. & Peters, N. 2014 The vorticity versus the scalar criterion for the detection of the turbulent/non-turbulent interface. J. Fluid Mech. 750, 578–596.Google Scholar
Holzner, M. & Lüthi, B. 2011 Laminar superlayer at the turbulence boundary. Phys. Rev. Lett. 106, 134503.Google Scholar
Jahanbakhshi, R. & Madnia, C. K. 2016 Entrainment in a compressible turbulent shear layer. J. Fluid Mech. 797, 564–603.Google Scholar
Krug, D., Chung, D., Philip, J. & Marusic, I. 2017 Global and local aspects of entrainment in temporal plumes. J. Fluid Mech. 812, 222–250.Google Scholar
Krug, D., Holzner, M., Lüthi, B., Wolf, M., Kinzelbach, W. & Tsinober, A. 2015 The turbulent/non-turbulent interface in an inclined dense gravity current. J. Fluid Mech. 765, 303–324.Google Scholar
Meneveau, C. & Sreenivasan, K. R. 1990 Interface dimension in intermittent turbulence. Phys. Rev. A 41 (4), 2246–2248.Google Scholar
Mistry, D., Dawson, J. R. & Kerstein, A. R. 2018 The multi-scale geometry of the near field in an axisymmetric jet. J. Fluid Mech. 838, 501–515.Google Scholar
Mistry, D., Philip, J., Dawson, J. R. & Marusic, I. 2016 Entrainment at multi-scales across the turbulent/non-turbulent interface in an axisymmetric jet. J. Fluid Mech. 802, 690–725.Google Scholar
Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 1–23.Google Scholar
Philip, J., Bermejo-Moreno, I., Chung, D. & Marusic, I. 2015 Characteristics of the entrainment velocity in a developing wake. In International Symposium on Turbulence and Shear Flow Phenomena, TSFP-9, Melbourne, Australia.Google Scholar
Philip, J., Meneveau, C., de Silva, C. & Marusic, I. 2014 Multiscale analysis of fluxes at the turbulent/non-turbulent interface in high Reynolds number boundary layers. Phys. Fluids 26, 015105.Google Scholar
Prasad, R. R. & Sreenivasan, K. R. 1989 Scalar interfaces in digital images of turbulent flows. Exp. Fluids 7, 259–264.Google Scholar
Raffel, M., Willert, C., Wereley, S. & Kompenhans, J. 1998 Particle Image Velocimetry, 2nd edn. Springer.Google Scholar
van Reeuwijk, M. & Holzner, M. 2014 The turbulence boundary of a temporal jet. J. Fluid Mech. 739, 254–275.Google Scholar
da Silva, C., Hunt, J. C. R., Eames, I. & Westerweel, J. 2014a Interfacial layers between regions of different turbulence intensity. Annu. Rev. Fluid Mech. 46 (1), 567–590.Google Scholar
da Silva, C. & Pereira, J. 2008 Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets. Phys. Fluids 20, 055101.Google Scholar
de Silva, C. M., Philip, J., Chauhan, K., Meneveau, C. & Marusic, I. 2013 Multiscale geometry and scaling of the turbulent-nonturbulent interface in high Reynolds number boundary layers. Phys. Rev. Lett. 111, 044501.Google Scholar
da Silva, C. & Taveira, R. 2010 The thickness of the turbulent/nonturbulent interface is equal to the radius of the large vorticity structures near the edge of the shear layer. Phys. Fluids 22, 121702.Google Scholar
da Silva, C., Taveira, R. & Borrell, G. 2014b Characteristics of the turbulent/nonturbulent interface in boundary layers, jets and shear-free turbulence. J. Phys.: Conf. Series 506 (1), 012015.Google Scholar
Silva, T., Zecchetto, M. & da Silva, C. 2018 The scaling of the turbulent/non-turbulent interface at high Reynolds numbers. J. Fluid Mech. 843, 156–179.Google Scholar
Sreenivasan, K. R., Ramshankar, R. & Meneveau, C. 1989 Mixing, entrainment and fractal dimensions of surfaces in turbulent flows. Proc. R. Soc. Lond. A 421, 79–108.Google Scholar
Taveira, R. R. & da Silva, C. B. 2014 Characteristics of the viscous superlayer in shear free turbulence and in planar turbulent jets. Phys. Fluids 26, 021702.Google Scholar
Taveira, R. R., da Silva, C. B. & Pereira, C. F. 2011 The dynamics of turbulent scalar mixing near the edge of a shear layer. J. Phys. Conf. Ser. 318, 052049.Google Scholar
Tritton, D. J. 1988 Physical Fluid Dynamics. Clarendon Press.Google Scholar
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431–471.Google Scholar
Watanabe, T., Jaulino, R., Taveira, R. R., da Silva, C. B., Nagata, K. & Sakai, Y. 2017a Role of an isolated eddy near the turbulent/non-turbulent interface layer. Phys. Rev. Fluids 2, 094607.Google Scholar
Watanabe, T., Sakai, Y., Nagata, K., Ito, Y. & Hayase, T. 2014a Enstrophy and passive scalar transport near the turbulent/non-turbulent interface in a turbulent planar jet flow. Phys. Fluids 26, 105103.Google Scholar
Watanabe, T., Sakai, Y., Nagata, K., Ito, Y. & Hayase, T. 2014b Vortex stretching and compression near the turbulent/non-turbulent interface in a planar jet. J. Fluid Mech. 758, 754–785.Google Scholar
Watanabe, T., Sakai, Y., Nagata, K., Ito, Y. & Hayase, T. 2015 Turbulent mixing of passive scalar near turbulent and non-turbulent interface in mixing layers. Phys. Fluids 27, 085109.Google Scholar
Watanabe, T., da Silva, C. B., Nagata, K. & Sakai, Y. 2017b Geometrical aspects of turbulent/non-turbulent interfaces with and without mean shear. Phys. Fluids 29, 085105.Google Scholar
Westerweel, J., Fukushima, C., Pedersen, J. & Hunt, J. C. R. 2005 Mechanics of the turbulent-nonturbulent interface of a jet. Phys. Rev. Lett. 95, 174501.Google Scholar
Westerweel, J., Fukushima, C., Pedersen, J. & Hunt, J. C. R. 2009 Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631, 199–230.Google Scholar
Westerweel, J., Hofmann, T., Fukushima, C. & Hunt, J. C. R. 2002 The turbulent/non-turbulent interface at the outer boundary of a self-similar turbulent jet. Exp. Fluids 33, 873–878.Google Scholar
Wolf, M., Holzner, M., Lüthi, B., Krug, D., Kinzelbach, W. & Tsinober, A. 2013a Effects of mean shear on the local turbulent entrainment process. J. Fluid Mech. 731, 95–116.Google Scholar
Wolf, M., Lüthi, B., Holzner, M., Krug, D., Kinzelbach, W. & Tsinober, A. 2012 Investigations on the local entrainment velocity in a turbulent jet. Phys. Fluids 24, 105110.Google Scholar
Wolf, M., Lüthi, B., Holzner, M., Krug, D., Kinzelbach, W. & Tsinober, A. 2013b Erratum: investigations on the local entrainment velocity in a turbulent jet [2012 Phys. Fluids 24, 105110]. Phys. Fluids 25, 019901.Google Scholar