Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-04T21:36:29.947Z Has data issue: false hasContentIssue false
  • English
  • Français

A turbulence dissipation inhomogeneity scaling in the wake of two side-by-side square prisms

Published online by Cambridge University Press:  04 August 2021

J.G. Chen Open the ORCID record for J.G. Chen [Opens in a new window] ,
C. Cuvier Open the ORCID record for C. Cuvier [Opens in a new window] ,
J.-M. Foucaut ,
Y. Ostovan  and
J.C. Vassilicos Open the ORCID record for J.C. Vassilicos [Opens in a new window]
J.G. Chen
Affiliation:
Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology, Centrale Lille, UMR 9014 – LMFL – Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, F-59000 Lille, France
C. Cuvier
Affiliation:
Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology, Centrale Lille, UMR 9014 – LMFL – Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, F-59000 Lille, France
J.-M. Foucaut
Affiliation:
Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology, Centrale Lille, UMR 9014 – LMFL – Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, F-59000 Lille, France
Y. Ostovan
Affiliation:
Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology, Centrale Lille, UMR 9014 – LMFL – Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, F-59000 Lille, France
J.C. Vassilicos*
Affiliation:
Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology, Centrale Lille, UMR 9014 – LMFL – Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, F-59000 Lille, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We experimentally study how the turbulent energy dissipation rate scales in the cross-stream direction of turbulent wake flows generated by two side-by-side square prisms. We consider three different such turbulent flows with gap ratios $G/H=1.25$, $2.4$ and $3.5$, where $G$ is the distance between the prisms and $H$ is the prism width. These three flows have a very different dynamics, inhomogeneities and large-scale features. The measurements were taken with a multi-camera particle image velocimetry system at several streamwise locations between $2.5H$ and $20H$ downstream of the prisms. After removing the large-scale most energetic coherent structures, the normalised turbulence dissipation coefficient $C'_{\epsilon }$ of the remaining incoherent turbulence is found to scale as $C'_{\epsilon } \sim (\sqrt {Re_{L}}/Re'_{\lambda })^{3/2}$ along the highly inhomogeneous cross-stream direction for all streamwise locations tested in all three flows and for all three inlet Reynolds numbers considered; $Re'_{\lambda }$ and $Re_{L}$ are, respectively, a Taylor length-based and an integral length-based Reynolds number of the remaining incoherent turbulence.

JFM classification

Turbulent Flows: Turbulence theory Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 924 , 10 October 2021 , A4
Check for updates
Copyright
© The Author(s), 2021. 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

Alam, M.M. & Zhou, Y. 2013 Intrinsic features of flow around two side-by-side square cylinders. Phys. Fluids 25 (8), 085106.CrossRefGoogle Scholar
Alam, M.M., Zhou, Y. & Wang, X.W. 2011 The wake of two side-by-side square cylinders. J. Fluid Mech. 669, 432–471.CrossRefGoogle Scholar
Alves Portela, F., 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
Avelar, M. 2019 Spatial evolution of wakes generated by side by side cylinders. PhD thesis, Department of Aeronautics, Imperial College London.Google Scholar
Batchelor, G.K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Beaulac, S. & Mydlarski, L. 2004 Dependence on the initial conditions of scalar mixing in the turbulent wake of a circular cylinder. Phys. Fluids 16 (8), 3161–3172.CrossRefGoogle Scholar
Berkooz, G., Holmes, P. & Lumley, J.L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539–575.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
Cafiero, G. & Vassilicos, J.C. 2020 Non-equilibrium scaling of the turbulent-nonturbulent interface speed in planar jets. Phys. Rev. Lett. 125 (17), 174501.CrossRefGoogle Scholar
Carlier, J. & Stanislas, M. 2005 Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry. J. Fluid Mech. 535, 143–188.CrossRefGoogle Scholar
Chen, J.G., Zhou, Y., Antonia, R.A. & Zhou, T.M. 2018 Characteristics of the turbulent energy dissipation rate in a cylinder wake. J. Fluid Mech. 835, 271–300.CrossRefGoogle Scholar
Chen, J.G., Zhou, Y., Antonia, R.A. & Zhou, T.M. 2019 The turbulent Kármán vortex. J. Fluid Mech. 871, 92–112.CrossRefGoogle Scholar
Chen, J.G., Zhou, Y., Antonia, R.A. & Zhou, T.M. 2020 Temperature correlations with vorticity and velocity in a turbulent cylinder wake. Intl J. Heat Fluid Flow 84, 108606.CrossRefGoogle Scholar
Chongsiripinyo, K. & Sarkar, S. 2020 Decay of turbulent wakes behind a disk in homogeneous and stratified fluids. J. Fluid Mech. 885, A31.CrossRefGoogle Scholar
Dairay, T., Obligado, M. & Vassilicos, J.C. 2015 Non-equilibrium scaling laws in axisymmetric turbulent wakes. J. Fluid Mech. 781, 166–195.CrossRefGoogle Scholar
Foucaut, J.-M., Cuvier, C., Coudert, S. & Stanislas, M. 2016 3D spatial correlation tensor from an l-shaped spiv experiment in the vear wall region. In Progress in Wall Turbulence (ed. M. Stanislas, J. Jimenez & I. Marusic), vol. 2, pp. 405–417. Springer.CrossRefGoogle Scholar
Foucaut, J.-M., George, W.K., Stanislas, M. & Cuvier, C. 2020 Velocity derivatives in a high Reynolds number turbulent boundary layer. Part III: optimization of an SPIV experiment for derivative moments assessment. arXiv:2010.09364.Google Scholar
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
George, W.K. & Hussein, H.J. 1991 Locally axisymmetric turbulence. J. Fluid Mech. 233, 1–23.CrossRefGoogle Scholar
Goto, S. & Vassilicos, J.C. 2015 Energy dissipation and flux laws for unsteady turbulence. Phys. Lett. A 379 (16), 1144–1148.CrossRefGoogle Scholar
Goto, S. & Vassilicos, J.C. 2016 a Local equilibrium hypothesis and Taylor's dissipation law. Fluid Dyn. Res. 48 (2), 021402.CrossRefGoogle Scholar
Goto, S. & Vassilicos, J.C. 2016 b Unsteady turbulence cascades. Phys. Rev. E 94 (5), 053108.CrossRefGoogle ScholarPubMed
Hayakawa, M. & Hussain, F. 1989 Three-dimensionality of organized structures in a plane turbulent wake. J. Fluid Mech. 206, 375–404.CrossRefGoogle Scholar
Hearst, R.J. & Lavoie, P. 2014 Decay of turbulence generated by a square-fractal-element grid. J. Fluid Mech. 741, 567–584.CrossRefGoogle Scholar
Holmes, P., Lumley, J.L., Berkooz, G. & Rowley, C.W. 2012 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.CrossRefGoogle Scholar
Isaza, J.C., Salazar, R. & Warhaft, Z. 2014 On grid-generated turbulence in the near-and far field regions. J. Fluid Mech. 753, 402–426.CrossRefGoogle Scholar
Ishigai, S. & Nishikawa, E. 1975 Experimental study of structure of gas flow in tube banks with tube axes normal to flow part ii; on the structure of gas flow in single-column, single-row, and double-rows tube banks. Bull. JSME 18 (119), 528–535.CrossRefGoogle Scholar
Kim, J. & Durbin, P.A. 1988 Investigation of the flow between a pair of circular cylinders in the flopping regime. J. Fluid Mech. 196, 431–448.CrossRefGoogle Scholar
Kolář, V., Lyn, D.A. & Rodi, W. 1997 Ensemble-averaged measurements in the turbulent near wake of two side-by-side square cylinders. J. Fluid Mech. 346, 201–237.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 a Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 16–18.Google Scholar
Kolmogorov, A.N. 1941 b The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301–305.Google Scholar
Kolmogorov, A.N. 1941 c On degeneration (decay) of isotropic turbulence in an incompressible viscous liquid. Dokl. Akad. Nauk SSSR 31, 538–540.Google 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
Lecordier, B. & Trinite, M. 2004 Advanced PIV algorithms with image distortion validation and comparison using synthetic images of turbulent flow. In Particle Image Velocimetry: Recent Improvements (ed. M. Stanislas, J. Westerweel & J. Kompenhans), pp. 115–132. Springer.CrossRefGoogle Scholar
Lefeuvre, N., Thiesset, F., Djenidi, L. & Antonia, R.A. 2014 Statistics of the turbulent kinetic energy dissipation rate and its surrogates in a square cylinder wake flow. Phys. Fluids 26 (9), 095104.CrossRefGoogle Scholar
Lumley, J.L. 1967 The structure of inhomogeneous turbulence. In Atmospheric Turbulence and Radio Wave Propagation (ed. A.M. Yaglom & V.I. Tatarski), pp. 166–178.Google Scholar
Nagata, K., Saiki, T., Sakai, Y., Ito, Y. & Iwano, K. 2017 Effects of grid geometry on non-equilibrium dissipation in grid turbulence. Phys. Fluids 29 (1), 015102.CrossRefGoogle Scholar
Nagata, K., Sakai, Y., Inaba, T., Suzuki, H., Terashima, O. & Suzuki, H. 2013 Turbulence structure and turbulence kinetic energy transport in multiscale/fractal-generated turbulence. Phys. Fluids 25 (6), 065102.CrossRefGoogle Scholar
Nedić, J., Tavoularis, S. & Marusic, I. 2017 Dissipation scaling in constant-pressure turbulent boundary layers. Phys. Rev. Fluids 2 (3), 032601.CrossRefGoogle Scholar
Nedić, J, Vassilicos, J.C. & Ganapathisubramani, B. 2013 Axisymmetric turbulent wakes with new nonequilibrium similarity scalings. Phys. Rev. Lett. 111 (14), 144503.CrossRefGoogle ScholarPubMed
Obligado, M., Dairay, T. & Vassilicos, J.C. 2016 Nonequilibrium scalings of turbulent wakes. Phys. Rev. Fluids 1 (4), 044409.CrossRefGoogle Scholar
Ortiz-Tarin, J.L., Nidhan, S. & Sarkar, S. 2021 High-Reynolds-number wake of a slender body. J. Fluid Mech. 918, A30.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Rubinstein, R. & Clark, T.T. 2017 ‘Equilibrium’ and ‘non-equilibrium’ turbulence. Theor. Appl. Mech. Lett. 7 (5), 301–305.CrossRefGoogle Scholar
Scarano, F. 2001 Iterative image deformation methods in PIV. Meas. Sci. Technol. 13 (1), R1.CrossRefGoogle Scholar
Seoud, R.E. & Vassilicos, J.C. 2007 Dissipation and decay of fractal-generated turbulence. Phys. Fluids 19 (10), 105108.CrossRefGoogle Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. I. Coherent structures. Q. Appl. Maths 45 (3), 561–571.CrossRefGoogle Scholar
Soria, J. 1996 An investigation of the near wake of a circular cylinder using a video-based digital cross-correlation particle image velocimetry technique. J. Expl Therm. Fluid Sci. 12 (2), 221–233.CrossRefGoogle Scholar
Sumner, D., Wong, S.S.T., Price, S.J. & Paidoussis, M.P. 1999 Fluid behaviour of side-by-side circular cylinders in steady cross-flow. J. Fluids Struct. 13 (3), 309–338.CrossRefGoogle Scholar
Taylor, G.I. 1935 Statistical theory of turbulence IV-diffusion in a turbulent air stream. Proc. R. Soc. Lond. A 151 (873), 465–478.Google Scholar
Taylor, G.I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164 (919), 476–490.Google Scholar
Tennekes, H. & Lumley, J.L. 1972 A First Course in Turbulence. MIT.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 (3), 561–583.CrossRefGoogle Scholar
Valente, P.C. & Vassilicos, J.C. 2012 Universal dissipation scaling for nonequilibrium turbulence. Phys. Rev. Lett. 108 (21), 214503.CrossRefGoogle ScholarPubMed
Vassilicos, J.C. 2015 Dissipation in turbulent flows. Annu. Rev. Fluid Mech. 47, 95–114.CrossRefGoogle Scholar
Willert, C.E. & Gharib, M. 1991 Digital particle image velocimetry. Exp. Fluids 10 (4), 181–193.CrossRefGoogle Scholar
Xu, S.J., Zhou, Y. & So, R.M.C. 2003 Reynolds number effects on the flow structure behind two side-by-side cylinders. Phys. Fluids 15 (5), 1214–1219.CrossRefGoogle Scholar
Yasuda, T. & Vassilicos, J.C. 2018 Spatio-temporal intermittency of the turbulent energy cascade. J. Fluid Mech. 853, 235–252.CrossRefGoogle Scholar
Yen, S.C. & Liu, J.H. 2011 Wake flow behind two side-by-side square cylinders. Intl J. Heat Fluid Flow 32 (1), 41–51.CrossRefGoogle Scholar
Zhou, Y. & Antonia, R.A. 1993 A study of turbulent vortices in the near wake of a cylinder. J. Fluid Mech. 253, 643.CrossRefGoogle Scholar
Zhou, Y., Nagata, K., Sakai, Y. & Watanabe, T. 2019 Extreme events and non-Kolmogorov $-5/3$ spectra in turbulent flows behind two side-by-side square cylinders. J. Fluid Mech. 874, 677–698.CrossRefGoogle Scholar
Zhou, Y. & Vassilicos, J.C. 2017 Related self-similar statistics of the turbulent/non-turbulent interface and the turbulence dissipation. J. Fluid Mech. 821, 440–457.CrossRefGoogle Scholar
Zhou, Y., Zhang, H.J. & Yiu, M.W. 2002 The turbulent wake of two side-by-side circular cylinders. J. Fluid Mech. 458, 303–332.CrossRefGoogle Scholar