Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-19T01:10:33.163Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulence structure of neutral and negatively buoyant jets

Published online by Cambridge University Press:  29 December 2020

K. M. Talluru Open the ORCID record for K. M. Talluru [Opens in a new window] ,
S. Armfield ,
N. Williamson Open the ORCID record for N. Williamson [Opens in a new window] ,
M. P. Kirkpatrick Open the ORCID record for M. P. Kirkpatrick [Opens in a new window]  and
L. Milton-McGurk Open the ORCID record for L. Milton-McGurk [Opens in a new window]
K. M. Talluru*
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW2006, Australia
S. Armfield
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW2006, Australia
N. Williamson
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW2006, Australia
M. P. Kirkpatrick
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW2006, Australia
L. Milton-McGurk
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW2006, Australia
*
†Email address for correspondence: murali.talluru@sydney.edu.au
Get access Rights & Permissions [Opens in a new window]

Abstract

High-fidelity measurements of velocity and concentration are carried out in a neutral jet (NJ) and a negatively buoyant jet (NBJ) by injecting a jet of fresh water vertically downwards into ambient fresh and saline water, respectively. The Reynolds number ($Re$) based on the pipe inlet diameter ($d$) and the source velocity ($W_o$) is approximately 5900 in all the experiments, while the source Froude number based on density difference is approximately 30 in the NBJ experiments. Velocity and concentration measurements are obtained in the region $17 \leq z/d \leq 40$ ($z$ being the axial coordinate) using particle image velocimetry and planar laser induced fluorescence techniques, respectively. Consistent with the literature on jets, the centreline velocity ($W_c$) decays as $z^{-1}$ in the NJ, but in the NBJ, $W_c$ decays faster along $z$ due to the action of negative buoyancy. Nonetheless, the mean velocity ($W$) and concentration ($C$) profiles in both the flows exhibit self-similar Gaussian form, when scaled by the local centreline parameters ($W_c,C_c$) and the jet half-widths ($r^\ast _{W},r^\ast _{C}$). On the other hand, the turbulence statistics and Reynolds stress in the NBJ do not scale with $W_c$. The results of autocorrelation functions, integral length scales and two-dimensional correlation maps show the similarity of turbulence structure in the NJ and the NBJ when the axial and radial distances are normalised by the local jet half-width. Further, the spectra and probability density functions are similar on the axis and only minor differences are seen near the jet interface. The above findings are fundamentally consistent with our recent analysis (Milton-McGurk et al., J. Fluid Mech., 2020b), where we observed that the mean and turbulence statistics in the NBJ have different development characteristics. Overall, we find that the turbulence structure of the NBJ (when scaled by local velocity and length scales) is very similar to the momentum-driven NJ, and the differences (e.g. spreading rate, scaling of turbulence intensities, etc.) between the NJ and the NBJ seem to be of secondary importance.

JFM classification

Wakes/Jets: Jets Convection: Plumes/thermals
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 909 , 25 February 2021 , A14
Check for updates
Copyright
© The Author(s), 2020. Published by 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

REFERENCES

Abraham, G. 1967 Jets with negative buoyancy in homogeneous fluid. J. Hydraul Res. 5 (4), 235–248.CrossRefGoogle Scholar
Baines, W. D., Turner, J. S. & Campbell, I. H. 1990 Turbulent fountains in an open chamber. J. Fluid Mech. 212, 557–592.CrossRefGoogle Scholar
Bloomfield, L. J. & Kerr, R. C. 1998 Turbulent fountains in a stratified fluid. J. Fluid Mech. 358, 335–356.CrossRefGoogle Scholar
Bloomfield, L. J. & Kerr, R. C. 2000 A theoretical model of a turbulent fountain. J. Fluid Mech. 424, 197–216.CrossRefGoogle Scholar
Browne, L. W. B., Antonia, R. A. & Chua, L. P. 1988 Calibration of x-probes for turbulent flow measurements. Exp. Fluids 7 (3), 201–208.CrossRefGoogle Scholar
Burridge, H. C. & Hunt, G. R. 2012 The rise heights of low-and high-Froude-number turbulent axisymmetric fountains. J. Fluid Mech. 691, 392–416.CrossRefGoogle Scholar
Burridge, H. C. & Hunt, G. R. 2013 The rhythm of fountains: the length and time scales of rise height fluctuations at low and high Froude numbers. J. Fluid Mech. 728, 91–119.CrossRefGoogle Scholar
Burridge, H. C. & Hunt, G. R. 2014 Scaling arguments for the fluxes in turbulent miscible fountains. J. Fluid Mech. 744, 273–285.CrossRefGoogle Scholar
Carazzo, G, Kaminski, E & Tait, S 2008 On the dynamics of volcanic columns: a comparison of field data with a new model of negatively buoyant jets. J. Volcanol. Geotherm. Res. 178 (1), 94–103.CrossRefGoogle Scholar
Cresswell, R. W. & Szczepura, R. T. 1993 Experimental investigation into a turbulent jet with negative buoyancy. Phys. Fluids A 5 (11), 2865–2878.CrossRefGoogle Scholar
Dowling, D. R. & Dimotakis, P. E. 1990 Similarity of the concentration field of gas-phase turbulent jets. J. Fluid Mech. 218, 109–141.CrossRefGoogle Scholar
Ezzamel, A., Salizzoni, P. & Hunt, G. R. 2015 Dynamical variability of axisymmetric buoyant plumes. J. Fluid Mech. 765, 576–611.CrossRefGoogle Scholar
de Gortari, J. C. & Goldschmidt, V. W. 1981 The apparent flapping motion of a turbulent plane jet—further experimental results. J. Fluids Engng 103, 119.CrossRefGoogle Scholar
Hunt, G. R. & Burridge, H. C. 2015 Fountains in industry and nature. Annu. Rev. Fluid Mech. 47, 195–220.CrossRefGoogle Scholar
Kaminski, E., Tait, S. & Carazzo, G. 2005 Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech. 526, 361–376.CrossRefGoogle Scholar
Kaye, N. B. & Hunt, G. R. 2006 Weak fountains. J. Fluid Mech. 558, 319–328.CrossRefGoogle Scholar
Lin, Y. J. P. & Linden, P. F. 2005 The entrainment due to a turbulent fountain at a density interface. J. Fluid Mech. 542, 25–52.CrossRefGoogle Scholar
List, E. J. 1982 Turbulent jets and plumes. Annu. Rev. Fluid Mech. 14 (1), 189–212.CrossRefGoogle Scholar
McDougall, T. J. 1981 Negatively buoyant vertical jets. Tellus 33 (3), 313–320.CrossRefGoogle Scholar
Milton-McGurk, L., Williamson, N., Armfield, S. W. & Kirkpatrick, M. P. 2020 a Experimental investigation into turbulent negatively buoyant jets using combined PIV and PLIF measurements. Intl J. Heat Fluid Flow 82, 108561.CrossRefGoogle Scholar
Milton-McGurk, L., Williamson, W., Armfield, S. W., Kirkpatrick, M. P. & Talluru, K. M. 2020 b Entrainment and structure of negatively buoyant jets. J. Fluid Mech. (submitted).Google Scholar
Mizushina, T., Ogino, F., Takeuchi, H. & Ikawa, H. 1982 An experimental study of vertical turbulent jet with negative buoyancy. Wärme-Stoffübertrag. 16 (1), 15–21.CrossRefGoogle Scholar
Morton, B. R. 1959 Forced plumes. J. Fluid Mech. 5 (1), 151–163.CrossRefGoogle 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 (1196), 1–23.Google Scholar
Panchapakesan, N. R. & Lumley, J. L. 1993 Turbulence measurements in axisymmetric jets of air and helium. Part 1. Air jet. J. Fluid Mech. 246, 197–223.CrossRefGoogle Scholar
Papanicolaou, P. N. & Kokkalis, T. J. 2008 Vertical buoyancy preserving and non-preserving fountains, in a homogeneous calm ambient. Intl J. Heat Mass Transfer 51 (15–16), 4109–4120.CrossRefGoogle Scholar
Papanicolaou, P. N., Papakonstantis, I. G. & Christodoulou, G. C. 2008 On the entrainment coefficient in negatively buoyant jets. J. Fluid Mech. 614, 447–470.CrossRefGoogle Scholar
Patel, R. P. 1974 A note on fully developed turbulent flow down a circular pipe. Aeronaut. J. 78 (758–759), 93–97.Google Scholar
Pincince, A. B. & List, E. J. 1973 Disposal of brine into an estuary. J. Water Pollut. Con. F. 45 (11), 2335–2344.Google Scholar
Priestley, C. H. B. & Ball, F. K. 1955 Continuous convection from an isolated source of heat. Q. J. R. Meteorol. Soc. 81 (348), 144–157.CrossRefGoogle Scholar
van Reeuwijk, M. & Craske, J. 2015 Energy-consistent entrainment relations for jets and plumes. J. Fluid Mech. 782, 333–355.CrossRefGoogle Scholar
Suzuki, Y. J., Koyaguchi, T., Ogawa, M. & Hachisu, I. 2005 A numerical study of turbulent mixing in eruption clouds using a three-dimensional fluid dynamics model. J. Geophys. Res. 110 (B8).Google Scholar
Turner, J. S. 1966 Jets and plumes with negative or reversing buoyancy. J. Fluid Mech. 26 (4), 779–792.CrossRefGoogle Scholar
Wang, H. & Law, A. W. 2002 Second-order integral model for a round turbulent buoyant jet. J. Fluid Mech. 459, 397.CrossRefGoogle Scholar
Weisgraber, T. H. & Liepmann, D. 1998 Turbulent structure during transition to self-similarity in a round jet. Exp. Fluids 24 (3), 210–224.CrossRefGoogle Scholar
Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. C. R. 2009 Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631, 199–230.CrossRefGoogle Scholar
Williamson, N., Armfield, S. W. & Lin, W. 2011 Forced turbulent fountain flow behaviour. J. Fluid Mech. 671, 535–558.CrossRefGoogle Scholar
Williamson, N., Srinarayana, N., Armfield, S. W., McBain, G. D. & Lin, W. 2008 Low-Reynolds-number fountain behaviour. J. Fluid Mech. 608, 297–317.CrossRefGoogle Scholar
Wygnanski, I & Fiedler, H. 1969 Some measurements in the self-preserving jet. J. Fluid Mech. 38 (3), 577–612.CrossRefGoogle Scholar
Zhang, H. & Baddour, R. E. 1998 Maximum penetration of vertical round dense jets at small and large Froude numbers. J. Hydraul Engng 124 (5), 550–553.CrossRefGoogle Scholar