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Entrainment in variable-density jets

Published online by Cambridge University Press:  20 September 2024

P. Salizzoni Open the ORCID record for P. Salizzoni [Opens in a new window] ,
S. Vaux Open the ORCID record for S. Vaux [Opens in a new window] ,
M. Creyssels Open the ORCID record for M. Creyssels [Opens in a new window] ,
J. Craske Open the ORCID record for J. Craske [Opens in a new window]  and
M. van Reeuwijk Open the ORCID record for M. van Reeuwijk [Opens in a new window]
P. Salizzoni*
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, University of Lyon, CNRS UMR 5509 Ecole Centrale de Lyon, INSA Lyon, Université Claude Bernard, 36 avenue Guy de Collongue, 69134 Ecully, France Department of Environmental, Land, and Infrastructure Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
S. Vaux
Affiliation:
Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PSN-RES, SA2I, LIE, Cadarache, 13115 St Paul-Lez-Durance, France
M. Creyssels
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, University of Lyon, CNRS UMR 5509 Ecole Centrale de Lyon, INSA Lyon, Université Claude Bernard, 36 avenue Guy de Collongue, 69134 Ecully, France
J. Craske
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, Imperial College Road, London SW7 2AZ, UK
M. van Reeuwijk
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, Imperial College Road, London SW7 2AZ, UK
*
†Email address for correspondence: pietro.salizzoni@ec-lyon.fr
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Abstract

The entrainment of ambient fluid into a variable-density jet is typically quantified using an entrainment coefficient $\alpha$. Here, we investigate the dependence of $\alpha$ on the ratio of the jet's density $\rho _m$ and that of the ambient fluid $\rho _0$. Current parametrisations of $\alpha$ rely on a scaling inferred from early laboratory experiments (Ricou & Spalding, J. Fluid Mech., vol. 11, 1961, pp. 21–32). We demonstrate analytically that the experiments preclude definitive conclusions regarding the dependence of $\alpha$ on $\rho _m / \rho _0$ and that the underlying physical processes therefore warrant closer attention. To investigate the physics behind the dependence of entrainment on the density ratio we use a Favre-averaged entrainment decomposition. The decomposition is applied to data from large-eddy simulations of jets characterised by density ratios $\rho _m / \rho _0$ spanning over two orders of magnitude that have been verified against experimental data. Changes in the shape of the velocity profile are a significant contributor to entrainment in the near field due to the breakdown of the potential core, and persist over larger streamwise distances in heavy releases than in light releases. Therefore, to focus exclusively on the effects of density ratio, we study the region where the shape changes have become small but the density ratio is still significant. We show that the dimensionless turbulent kinetic energy production and mean kinetic energy flux depend strongly on the density ratio, both for our large-eddy simulation data and for recent experiments. Despite this, the entrainment coefficient is practically constant in this region and has value $\alpha \approx 0.07$ for all simulations.

JFM classification

Mixing: Turbulent mixing Turbulent Flows: Shear layer turbulence Wakes/Jets: Jets

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 995 , 25 September 2024 , A11
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© The Author(s), 2024. Published by Cambridge University Press

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References

Ai, J., Law, A.W.-K. & Yu, S.C.M. 2006 On Boussinesq and non-Boussinesq starting forced plumes. J. Fluid Mech. 558, 357–386.CrossRefGoogle Scholar
Amielh, M., Djeridane, T., Anselmet, F. & Fulachier, L. 1996 Velocity near-field of variable density turbulent jets. Intl J. Heat Mass Transfer 39 (10), 2149–2164.CrossRefGoogle Scholar
van den Bremer, T.S. & Hunt, G.R. 2010 Universal solutions for Boussinesq and non-Boussinesq plumes. J. Fluid Mech. 644, 165–192.CrossRefGoogle Scholar
Bruneau, C.-H. 2000 Boundary conditions on artificial frontiers for incompressible and compressible Navier–Stokes equations. Math. Model. Numer. Anal. 34, 303–314.CrossRefGoogle Scholar
Bruneau, C.-H. & Fabrie, P. 1994 Effective downstream boundary conditions for incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 19, 693–705.CrossRefGoogle Scholar
Bruneau, C.-H. & Fabrie, P. 1996 New efficient boundary conditions for incompressible Navier–Stokes equations: a well-posedness result. Math. Model. Numer. Anal. 30, 815–840.CrossRefGoogle Scholar
Charonko, J. & Prestridge, K. 2017 Variable-density mixing in turbulent jets with coflow. J. Fluid Mech. 825, 887–921.CrossRefGoogle Scholar
Cimarelli, A., Mollicone, J.-P., van Reeuwijk, M. & De Angelis, E. 2021 Spatially evolving cascades in temporal planar jets. J. Fluid Mech. 910, A19.CrossRefGoogle Scholar
Craske, J., Salizzoni, P. & van Reeuwijk, M. 2017 The turbulent Prandtl number in a pure plume is 3/5. J. Fluid Mech. 822, 774–790.CrossRefGoogle Scholar
Djeridane, T., Amielh, M., Anselmet, F. & Fulachier, L. 1996 Velocity turbulence properties in the near-field region of axisymmetric variable density jets. Phys. Fluids 8 (6), 1614–1630.CrossRefGoogle Scholar
Ezzamel, A., Salizzoni, P. & Hunt, G.R. 2015 Dynamic variability of axisymmetric buoyant plumes. J. Fluid Mech. 765, 576–611.CrossRefGoogle Scholar
García-Villalba, M., Fröhlich, J. & Rodi, W. 2006 Identification and analysis of coherent structures in the near field of a turbulent unconfined annular swirling jet using Large Eddy Simulation. Phys. Fluids 18 (5), 055103.CrossRefGoogle Scholar
Gerashchenko, S. & Prestridge, K. 2015 Density and velocity statistics in variable density turbulent mixing. J. Turbul. 16 (11), 1011–1035.CrossRefGoogle Scholar
Gharbi, A., Amielh, M. & Anselmet, F. 1995 Experimental investigation of turbulence properties in the interface region of variable density jets. Phys. Fluids 7 (10), 2444–2454.CrossRefGoogle Scholar
Gharbi, A., Ruffin, E., Anselmet, F. & Schiestel, R. 1996 Numerical modelling of variable density turbulent jets. Intl J. Heat Mass Transfer 39 (9), 1865–1882.CrossRefGoogle Scholar
Jarrin, N., Benhamadouche, S., Laurence, D. & Prosser, R. 2006 A synthetic-eddy-method for generating inflow conditions for large-eddy simulations. Intl J. Heat Fluid Flow 27 (4), 585–593.CrossRefGoogle Scholar
Jiang, L., Creyssels, M., Hunt, G.R. & Salizzoni, P. 2019 Control of light gas releases in ventilated tunnels. J. Fluid Mech. 872, 515–531.CrossRefGoogle Scholar
Kaminski, E., Tait, S. & Carazzo, G. 2005 Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech. 526, 361.CrossRefGoogle Scholar
Lanzini, S., Marro, M., Creyssels, M. & Salizzoni, P. 2024 Helium plumes at moderate Reynolds number. Phys. Rev. Fluids 9 (6), 064501.CrossRefGoogle Scholar
Mehaddi, R., Boulet, P., Koutaiba, M., Vauquelin, O. & Candelier, F. 2021 Emptying-filling boxes with non-Boussinesq plumes and fountains. Phys. Rev. Fluids 6, 083801.CrossRefGoogle Scholar
Morton, B.R. 1965 Modeling fire plumes. In Tenth Symposium (International) on Combustion, pp. 973–982. The Combustion Institute, Pittsburgh.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, 1–23.Google Scholar
O'Hern, T.J., Weckman, E.J., Gerhart, A.L., Tieszen, S.R. & Schefer, R.W. 2005 Experimental study of a turbulent buoyant helium plume. J. Fluid Mech. 544, 143–171.CrossRefGoogle Scholar
Panchapakesan, N.R. & Lumley, J.L. 1993 Turbulence measurements in axisymmetric jets of air and helium. Part 2. Helium jet. J. Fluid Mech. 246, 225–247.CrossRefGoogle Scholar
Papanicolaou, P.N. & List, E.J. 1988 Investigations of round vertical turbulent buoyant jets. J. Fluid Mech. 195, 341–391.CrossRefGoogle Scholar
Pietri, L., Amielh, M. & Anselmet, F. 2000 Simultaneous measurements of temperature and velocity fluctuations in a slightly heated jet combining a cold wire and laser doppler anemometry. Intl J. Heat Fluid Flow 21 (1), 22–36.CrossRefGoogle 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
van Reeuwijk, M., Salizzoni, P., Hunt, G.R. & Craske, J. 2016 Turbulent transport and entrainment in jets and plumes: a DNS study. Phys. Rev. Fluids 1, 074301.CrossRefGoogle Scholar
Ricou, F.P. & Spalding, D.B. 1961 Measurements of entrainment by axisymmetrical turbulent jets. J. Fluid Mech. 11, 21–32.CrossRefGoogle Scholar
Rooney, G.G. & Linden, P.F. 1996 Similarity considerations for non-Boussinesq plumes in an unstratfied environment. J. Fluid Mech. 318, 237–250.CrossRefGoogle Scholar
Salizzoni, P., Vaux, S., Creyssels, M., Amielh, M., Pietri, L. & Anselmet, F. 2023 Turbulent transfer and entrainment in a low-density jet. J. Fluid Mech. 968, A27.CrossRefGoogle Scholar
Vauquelin, O. 2015 Oscillatory behaviour in an emptying filling box. J. Fluid Mech. 781, 712–726.CrossRefGoogle Scholar
Vaux, S., Mehaddi, R., Vauquelin, O. & Candelier, F. 2019 Upward versus downward non-Boussinesq turbulent fountains. J. Fluid Mech. 867, 374–391.CrossRefGoogle Scholar
Viggiano, B., Dib, T., Ali, N., Mastin, L.G., Cal, R.B. & Solovitz, S.A. 2018 Turbulence, entrainment and low-order description of a transitional variable-density jet. J. Fluid Mech. 836, 1009–1049.CrossRefGoogle Scholar
Vreman, A.W. 2004 An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications. Phys. Fluids 16 (10), 3670–3681.CrossRefGoogle Scholar
Wang, H. & Law, A.W-K. 2002 Second-order integral model for round turbulent jet. J. Fluid Mech. 459, 397–428.CrossRefGoogle Scholar
Wang, P., Frohlich, J., Michelassi, V. & Rodi, W. 2008 Large-eddy simulation of variable-density turbulent axisymmetric jets. Intl J. Heat Fluid Flow 29 (3), 654–664.CrossRefGoogle Scholar
Woods, A.W. 1997 A note on non-Boussinesq plumes in an incompressible stratified environment. J. Fluid Mech. 345, 347–356.CrossRefGoogle Scholar