Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-01T13:27:32.834Z Has data issue: false hasContentIssue false
  • English
  • Français

A simple analytical model for turbulent kinetic energy dissipation for self-similar round turbulent jets

Published online by Cambridge University Press:  25 March 2024

Gagan Kewalramani Open the ORCID record for Gagan Kewalramani [Opens in a new window] ,
Bowen Ji ,
Yvan Dossmann Open the ORCID record for Yvan Dossmann [Opens in a new window] ,
Simon Becker ,
Michel Gradeck Open the ORCID record for Michel Gradeck [Opens in a new window]  and
Nicolas Rimbert Open the ORCID record for Nicolas Rimbert [Opens in a new window]
Gagan Kewalramani*
Affiliation:
Université de Lorraine, CNRS, LEMTA, F-54000, Nancy, France
Bowen Ji
Affiliation:
Université de Lorraine, CNRS, LEMTA, F-54000, Nancy, France
Yvan Dossmann
Affiliation:
Université de Lorraine, CNRS, LEMTA, F-54000, Nancy, France
Simon Becker
Affiliation:
Université de Lorraine, CNRS, LEMTA, F-54000, Nancy, France
Michel Gradeck
Affiliation:
Université de Lorraine, CNRS, LEMTA, F-54000, Nancy, France
Nicolas Rimbert
Affiliation:
Université de Lorraine, CNRS, LEMTA, F-54000, Nancy, France
*
†Email address for correspondence: gagan.kewalramani@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

This work presents a simple analytical model for the streamwise and radial variations of turbulent kinetic energy dissipation in an incompressible round turbulent jet. The key assumptions in the model are: similarity in the axial velocity profile with a Gaussian shape, axisymmetric flow and the dominance of radial derivatives of the mean velocity over axial direction derivatives (similar to boundary layer theory). Initially, a simplified eddy-viscosity relation for turbulent stresses is derived using the algebraic stress model by Gatski & Speziale (J. Fluid Mech., vol. 254, 1993, pp. 59–78). Subsequently, with this eddy-viscosity relation, the relation for variations of turbulent kinetic energy dissipation is formulated using the conservation of turbulent kinetic energy. To extract the necessary constants of the model, experimental velocity statistics for round jets are obtained through particle image velocimetry measurements. The experimental results of the mean entrainment coefficient for turbulent jets are also analysed. When comparing the radial variation of turbulent kinetic energy dissipation from the model with experimental results at Reynolds number $1.4\times 10^5$ and numerical results at Reynolds number $1200$ from the available literature, we observe a maximum error of $10\,\%$ and $15\,\%$, respectively. Finally, using the validated model, we analyse the impact of mean velocity evolution parameters on the behaviour of turbulent kinetic energy dissipation and discuss its potential significance in future studies.

JFM classification

Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 983 , 25 March 2024 , A44
Check for updates
Copyright
© The Author(s), 2024. 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

Adrian, R.J. & Westerweel, J. 2011 Particle Image Velocimetry. Cambridge University Press.Google Scholar
Anghan, C., Dave, S., Saincher, S. & Banerjee, J. 2019 Direct numerical simulation of transitional and turbulent round jets: evolution of vortical structures and turbulence budget. Phys. Fluids 31 (6), 065105.CrossRefGoogle Scholar
Antonia, R.A., Satyaprakash, B.R. & Hussain, A.K.M.F. 1980 Measurements of dissipation rate and some other characteristics of turbulent plane and circular jets. Phys. Fluids 23 (4), 695–700.CrossRefGoogle Scholar
Ball, C.G., Fellouah, H. & Pollard, A. 2012 The flow field in turbulent round free jets. Prog. Aerosp. Sci. 50, 1–26.CrossRefGoogle Scholar
Breda, M. & Buxton, O.R.H. 2018 Influence of coherent structures on the evolution of an axisymmetric turbulent jet. Phys. Fluids 30 (3), 035109.CrossRefGoogle Scholar
Burattini, P., Antonia, R.A. & Danaila, L. 2005 Similarity in the far field of a turbulent round jet. Phys. Fluids 17 (2), 025101.CrossRefGoogle Scholar
Cafiero, G. & Vassilicos, J.C. 2019 Non-equilibrium turbulence scalings and self-similarity in turbulent planar jets. Proc. R. Soc. Lond. A 475 (2225), 20190038.Google ScholarPubMed
Chen, J.G., Cuvier, C., Foucaut, J.-M., Ostovan, Y. & Vassilicos, J.C. 2021 A turbulence dissipation inhomogeneity scaling in the wake of two side-by-side square prisms. J. Fluid Mech. 924, A4.CrossRefGoogle Scholar
Crow, S.C. & Champagne, F.H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48 (3), 547–591.CrossRefGoogle Scholar
Daly, B.J. & Harlow, F.H. 1970 Transport equations in turbulence. Phys. Fluids 13 (11), 2634–2649.CrossRefGoogle Scholar
Darisse, A., Lemay, J. & Benaïssa, A. 2015 Budgets of turbulent kinetic energy, Reynolds stresses, variance of temperature fluctuations and turbulent heat fluxes in a round jet. J. Fluid Mech. 774, 95–142.CrossRefGoogle Scholar
Ewing, D., Frohnapfel, B., George, W.K., Pedersen, J.M. & Westerweel, J. 2007 Two-point similarity in the round jet. J. Fluid Mech. 577, 309–330.CrossRefGoogle Scholar
Ezzamel, A., Salizzoni, P. & Hunt, G.R. 2015 Dynamical variability of axisymmetric buoyant plumes. J. Fluid Mech. 765, 576–611.CrossRefGoogle Scholar
Falchi, M. & Romano, G.P. 2009 Evaluation of the performance of high-speed PIV compared to standard PIV in a turbulent jet. Exp. Fluids 47, 509–526.CrossRefGoogle Scholar
Gatski, T.B. & Jongen, T. 2000 Nonlinear eddy viscosity and algebraic stress models for solving complex turbulent flows. Prog. Aerosp. Sci. 36 (8), 655–682.CrossRefGoogle Scholar
Gatski, T.B. & Speziale, C.G. 1993 On explicit algebraic stress models for complex turbulent flows. J. Fluid Mech. 254, 59–78.CrossRefGoogle Scholar
George, W.K. 1989 The self-preservation of turbulent flows and its relation to initial conditions and coherent structures. Adv. Turbul. 3973, 39–73.Google Scholar
Hussain, A.K.M.F. & Clark, A. 1977 Upstream influence on the near field of a plane turbulent jet. Phys. Fluids 20 (9), 1416–1426.CrossRefGoogle Scholar
Kaminski, E., Tait, S. & Carazzo, G. 2005 Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech. 526, 361–376.CrossRefGoogle Scholar
Kantharaju, J., Courtier, R., Leclaire, B. & Jacquin, L. 2020 Interactions of large-scale structures in the near field of round jets at high Reynolds numbers. J. Fluid Mech. 888, A8.CrossRefGoogle Scholar
Kewalramani, G. 2023 Experimental and theoretical analysis of a turbulent two-phase jet. PhD thesis, Université de Lorraine.Google Scholar
Kewalramani, G., Ji, B., Dossmann, Y., Gradeck, M. & Rimbert, N. 2022 a Experimental analysis of lagrangian paths of drops generated by liquid/liquid sprays. Exp. Fluids 63 (9), 147.CrossRefGoogle Scholar
Kewalramani, G., Pant, C.S. & Bhattacharya, A. 2022 b Energy consistent Gaussian integral model for jet with off-source heating. Phys. Rev. Fluids 7 (1), 013801.CrossRefGoogle Scholar
Lavoie, P., Avallone, G., De Gregorio, F., Romano, G.P. & Antonia, R.A. 2007 Spatial resolution of PIV for the measurement of turbulence. Exp. Fluids 43 (1), 39–51.CrossRefGoogle Scholar
Mi, J., Xu, M. & Zhou, T. 2013 Reynolds number influence on statistical behaviors of turbulence in a circular free jet. Phys. Fluids 25 (7), 075101.CrossRefGoogle Scholar
Miller, D.R. & Comings, E.W. 1957 Static pressure distribution in the free turbulent jet. J. Fluid Mech. 3 (1), 1–16.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
Pope, S. 1975 A more general effective-viscosity hypothesis. J. Fluid Mech. 72 (2), 331–340.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Portela, F.A., Papadakis, G. & Vassilicos, J.C. 2018 Turbulence dissipation and the role of coherent structures in the near wake of a square prism. Phys. Rev. Fluids 3 (12), 124609.CrossRefGoogle Scholar
van Reeuwijk, M. & Craske, J. 2015 Energy-consistent entrainment relations for jets and plumes. J. Fluid Mech. 782, 333–355.CrossRefGoogle Scholar
Ruffin, E., Schiestel, R., Anselmet, F., Amielh, M. & Fulachier, L. 1994 Investigation of characteristic scales in variable density turbulent jets using a second-order model. Phys. Fluids 6 (8), 2785–2799.CrossRefGoogle Scholar
Sadeghi, H., Lavoie, P. & Pollard, A. 2015 Equilibrium similarity solution of the turbulent transport equation along the centreline of a round jet. J. Fluid Mech. 772, 740–755.CrossRefGoogle Scholar
Schreyer, A.M., Lasserre, J.J. & Dupont, P. 2015 Development of a dual-PIV system for high-speed flow applications. Exp. Fluids 56 (10), 1–12.CrossRefGoogle Scholar
Shih, T.-H., Liou, W.W., Shabbir, A., Yang, Z. & Zhu, J. 1994 A new $k\textrm {-}\epsilon$ eddy viscosity model for high Reynolds number turbulent flows: model development and validation. NASA Tech. Rep. CMOTT-94-6.Google Scholar
Tang, S.L., Antonia, R.A. & Djenidi, L. 2022 Approach towards local isotropy in statistically stationary turbulent shear flows. J. Fluid Mech. 952, A17.CrossRefGoogle Scholar
Taylor, G.I. 1935 Statistical theory of turbulenc. Proc. R. Soc. Lond. A 151 (873), 421–444.CrossRefGoogle Scholar
Thiesset, F., Antonia, R.A. & Djenidi, L. 2014 Consequences of self-preservation on the axis of a turbulent round jet. J. Fluid Mech. 748, R2.CrossRefGoogle Scholar
Tokgoz, S., Elsinga, G.E., Delfos, R. & Westerweel, J. 2012 Spatial resolution and dissipation rate estimation in Taylor–Couette flow for tomographic PIV. Exp. Fluids 53, 561–583.CrossRefGoogle Scholar
Vassilicos, J.C. 2015 Dissipation in turbulent flows. Annu. Rev. Fluid Mech. 47 (1), 95–114.CrossRefGoogle Scholar
Viggiano, B., Basset, T., Solovitz, S., Barois, T., Gibert, M., Mordant, N., Chevillard, L., Volk, R., Bourgoin, M. & Cal, R.B. 2021 Lagrangian diffusion properties of a free shear turbulent jet. J. Fluid Mech. 918, A25.CrossRefGoogle Scholar
Xu, G. & Antonia, R.A. 2002 Effect of different initial conditions on a turbulent round free jet. Exp. Fluids 33 (5), 677–683.CrossRefGoogle Scholar