Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-25T22:41:06.117Z Has data issue: false hasContentIssue false
  • English
  • Français

Energy transfer in turbulent flows behind two side-by-side square cylinders

Published online by Cambridge University Press:  18 September 2020

Yi Zhou Open the ORCID record for Yi Zhou [Opens in a new window] ,
Koji Nagata Open the ORCID record for Koji Nagata [Opens in a new window] ,
Yasuhiko Sakai ,
Tomoaki Watanabe Open the ORCID record for Tomoaki Watanabe [Opens in a new window] ,
Yasumasa Ito  and
Toshiyuki Hayase
Yi Zhou*
Affiliation:
School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing210094, PR China
Koji Nagata
Affiliation:
Department of Aerospace Engineering, Nagoya University, Nagoya464-8603, Japan
Yasuhiko Sakai
Affiliation:
Department of Mechanical Systems Engineering, Nagoya University, Nagoya464-8603, Japan
Tomoaki Watanabe
Affiliation:
Department of Aerospace Engineering, Nagoya University, Nagoya464-8603, Japan
Yasumasa Ito
Affiliation:
Department of Mechanical Systems Engineering, Nagoya University, Nagoya464-8603, Japan
Toshiyuki Hayase
Affiliation:
Institute of Fluid Science, Tohoku University, Sendai980-8577, Japan
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Our previous study (J. Fluid Mech., vol. 874, 2019, pp. 677–698) confirmed that two different types of $-5/3$ energy spectra (i.e. non-Kolmogorov and quasi-Kolmogorov $-5/3$ spectra) can be found in turbulent flows behind two side-by-side square cylinders. In the upstream region (i.e. $X/T_0=6$ with $T_0$ being the cylinder thickness), albeit the turbulent flow is highly inhomogeneous and intermittent and Kolmogorov's hypothesis does not hold, the energy spectrum exhibits a well-defined $-5/3$ power-law range for over one decade. Meanwhile, the power-law exponent of the corresponding second-order structure function is 1, which is significantly larger than the expected value, i.e. $2/3$. At the downstream location, i.e. $X/T_0=26$, in contrast, the quasi-Kolmogorov $-5/3$ energy spectrum (and also the 2/3 scaling of the second-order structure) can be identified. Through decomposing the streamwise velocity fluctuations into the spanwise average of instantaneous velocity and the turbulent residual, we demonstrate that the non-Kolmogorov $-5/3$ spectrum at $X/T_0=6$ is caused by the turbulent residual part. To shed light on the physics of the scale-by-scale energy transfer, we resort to the Kármán–Howarth–Monin–Hill equation. At $X/T_0=6$, the expected balance between the nonlinear term and the dissipation term cannot be detected. Instead, the contributions from the non-local pressure, advection, nonlinear transport and turbulent transport terms are dominant. Moreover, because the corresponding flow field is highly intermittent, the magnitudes of the non-local pressure, advection, nonlinear transport and turbulent transport terms are significantly larger than that of the dissipation term. At a far downstream location, i.e. $X/T_0=26$, where the dual-wake flow is fully turbulent and becomes much more homogeneous and isotropic, within a short intermediate range the two dominant terms in the two-point turbulent kinetic energy budget are the nonlinear transport term and the dissipation term, which to some extent echoes Kolmogorov's scenario, albeit the contribution from the large-scale advection term cannot be ignored. By comparing the behaviour of the one-point and two-point energy transfer, it can be seen that the two different energy transfer processes are actually closely related, that is, the similar relative importance of the viscous dissipation and the same role of the non-negligible terms in terms of being a source or sink term.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulence theory Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , A4
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

Alam, M. M., Bai, H. L. & Zhou, Y. 2016 The wake of two staggered square cylinders. J. Fluid Mech. 801, 475–507.CrossRefGoogle Scholar
Alam, M. M. & Zhou, Y. 2013 Intrinsic features of flow around two side-by-side square cylinders. Phys. Fluids 25, 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
Cuypers, Y., Maurel, A. & Petitheans, P. 2003 Vortex bursts as a source of turbulence. Phys. Rev. Lett. 91, 194502.CrossRefGoogle Scholar
Davidson, P. A. 2004 Turbulence, An Introduction for Scientists and Engineers. Oxford University Press.Google Scholar
Gomes-Fernandes, R., Ganapathisubramani, B. & Vassilicos, J. C. 2014 Evolution of the velocity-gradient tensor in a spatially developing turbulent flow. J. Fluid Mech. 756, 252–292.CrossRefGoogle Scholar
Gomes-Fernandes, R., Ganapathisubramani, B. & Vassilicos, J. C. 2015 The energy cascade in near-field non-homogeneous non-isotropic turbulence. J. Fluid Mech. 771, 676–705.CrossRefGoogle Scholar
Goto, S. 2012 Coherent structures and energy cascade in homogeneous turbulence. Prog. Theor. Phys. Suppl. 195, 139–156.CrossRefGoogle Scholar
Goto, S. & Vassilicos, J. C. 2015 Energy dissipation and flux laws for unsteady turbulence. Phys. Lett. A 379, 1144–1148.CrossRefGoogle Scholar
Goto, S. & Vassilicos, J. C. 2016 Local equilibrium hypothesis and Taylor's dissipation law. Fluid Dyn. Res. 48, 021402.CrossRefGoogle Scholar
Hearst, R. J. & Lavoie, P. 2014 Scale-by-scale energy budget in fractal element grid-generated turbulence. J. Turbul. 15, 540–554.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
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 the 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 the degeneration of isotropic turbulence in an incompressible viscous fluid. Dokl. Akad. Nauk SSSR 31, 538–540.Google Scholar
Laizet, S. & Lamballais, E. 2009 High-order compact schemes for incompressible flows: a simple and efficient method with the quasi-spectral accuracy. J. Comput. Phys. 228, 5989–6015.CrossRefGoogle Scholar
Laizet, S., Lamballais, E. & Vassilicos, J. C. 2010 A numerical strategy to combine high-order schemes, complex geometry and parallel computing for high resolution DNS of fractal generated turbulence. Comput. Fluids 39, 471–484.CrossRefGoogle Scholar
Laizet, S. & Li, N. 2011 Incompact3d, a powerful tool to tackle turbulence problems with up to $O(10^5)$ computational cores. Intl J. Numer. Methods Fluids 67, 1735–1757.CrossRefGoogle Scholar
Laizet, S., Nedić, J. & Vassilicos, J. C. 2015 The spatial origin of $-5/3$ spectra in grid-generated turbulence. Phys. Fluids 27, 065115.CrossRefGoogle Scholar
Laizet, S., Vassilicos, J. C. & Cambon, C. 2013 Interscale energy transfer in decaying turbulence and vorticity-strain-rate dynamics in grid-generated turbulence. Fluid Dyn. Res. 45, 061408.CrossRefGoogle Scholar
Lumley, J. L. 1978 Computational modelling of turbulent flows. Adv. Appl. Mech. 18, 123–126.CrossRefGoogle Scholar
Lundgren, T. S. 1982 Strained spiral vortex model for turbulent fine structure. Phys. Fluids 25, 2193–3005.CrossRefGoogle Scholar
Marati, N., Casciola, C. M. & Piva, R. 2004 Energy cascade and spatial fluxes in wall turbulence. J. Fluid Mech. 521, 191–215.CrossRefGoogle Scholar
Melina, G., Bruce, P. J. K. & Vassilicos, J. C. 2016 Vortex shedding effects in grid-generated turbulence. Phys. Rev. Fluids 1, 044402.CrossRefGoogle 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, 015102.CrossRefGoogle Scholar
Nedić, J. & Tavoularis, S. 2016 Energy dissipation scaling in uniformly sheared turbulence. Phys. Rev. E 93, 033115.CrossRefGoogle ScholarPubMed
Obligado, M. & Vassilicos, J. C. 2019 The non-equilibrium part of the inertial range in decaying homogeneous turbulence. Europhys. Lett. 127, 64004.CrossRefGoogle Scholar
Parnaudeau, P., Carlier, J., Heitz, D. & Lamballais, E. 2008 Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900. Phys. Fluids 20, 085101.CrossRefGoogle Scholar
Paul, I., Papadakis, G & Vassilicos, J. C. 2017 Genesis and evolution of velocity gradients in near-field spatially developing turbulence. J. Fluid Mech. 815, 295–332.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Portela, F. A., Papadakis, G. & Vassilicos, J. C. 2017 The turbulence cascade in the near wake of a square prism. J. Fluid Mech. 825, 315–352.CrossRefGoogle Scholar
Richardson, L. F. 1922 Weather Prediction by Numerical Process. Cambridge University Press.Google Scholar
Thiesset, F., Danaila, L., Antonia, R. A. & Zhou, T. 2011 Scale-by-scale energy budgets which account for the coherent motion. J. Phys.: Conf. Ser. 318, 052040.Google Scholar
Tsinober, A. 2009 An Informal Conceptual Introduction to Turbulence, 2nd edn.Springer.CrossRefGoogle Scholar
Valente, P. C. & Vassilicos, J. C. 2012 Universal dissipation scaling for non-equilibrium turbulence. Phys. Rev. Lett. 108, 214503.CrossRefGoogle Scholar
Valente, P. C. & Vassilicos, J. C. 2015 The energy cascade in grid-generated non-equilibrium decaying turbulence. Phys. Fluids 27, 045103.CrossRefGoogle Scholar
Vassilicos, J. C. 2015 Dissipation in turbulent flows. Annu. Rev. Fluid Mech. 47, 95–114.CrossRefGoogle Scholar
Yasuda, T., Goto, S. & Vassilicos, J. C. 2019 Formation of power-law scalings of spectra and multiscale coherent structures in the near-field of grid-generated turbulence. Phys. Rev. Fluids 5, 014601.CrossRefGoogle Scholar
Yasuda, T. & Vassilicos, J. C. 2018 Spatio-temporal intermittency of the turbulent energy cascade. J. Fluid Mech. 853, 235–252.CrossRefGoogle Scholar
Zhou, Y., Nagata, K., Sakai, Y., Ito, Y. & Hayase, T. 2016 Spatial evolution of the helical behavior and the 2/3 power-law in single-square-grid-generated turbulence. Fluid Dyn. Res. 48, 021404.CrossRefGoogle Scholar
Zhou, Y., Nagata, K., Sakai, Y. & Watanabe, T. 2018 Dual-plane turbulent jets and their non-Gaussian velocity fluctuations. Phys. Rev. Fluids 3, 124604.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