Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-30T20:42:33.786Z Has data issue: false hasContentIssue false
  • English
  • Français

Scaling of square-prism shear layers

Published online by Cambridge University Press:  28 June 2018

D. C. Lander Open the ORCID record for D. C. Lander [Opens in a new window] ,
D. M. Moore ,
C. W. Letchford  and
M. Amitay
D. C. Lander*
Affiliation:
Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
D. M. Moore
Affiliation:
Center for Flow Physics and Control, Department of Mechanical, Nuclear and Aerospace Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
C. W. Letchford
Affiliation:
Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
M. Amitay
Affiliation:
Center for Flow Physics and Control, Department of Mechanical, Nuclear and Aerospace Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Scaling characteristics, essential to the mechanisms of transition in square-prism shear layers, were explored experimentally. In particular, the evolution of the dominant instability modes as a function of Reynolds number were reported in the range $1.5\times 10^{4}\lesssim Re_{D}\lesssim 7.5\times 10^{4}$. It was found that the ratio between the shear layer frequency and the shedding frequency obeys a power-law scaling relation. Adherence to the power-law relationship, which was derived from hot-wire measurements, has been supported by two additional and independent scaling considerations, namely, by particle image velocimetry measurements to observe the evolution of length and velocity scales in the shear layer during transition, and by comparison to direct numerical simulations to illuminate the properties of the front-face boundary layer. The nonlinear dependence of the shear layer instability frequency is sustained by the influence of $Re_{D}$ on the thickness of the laminar front-face boundary layer. In corroboration with the original scaling argument for the circular cylinder, the length scale of the shear layer was the only source of nonlinearity in the frequency ratio scaling, within the range of Reynolds numbers reported. The frequency ratio scaling may therefore be understood by the influence of $Re_{D}$ on the appropriate length scale of the shear layer. This length scale was observed to be the momentum thickness evaluated at a transition point, defined where the Kelvin–Helmholtz instability saturates.

JFM classification

Wakes/Jets: Shear layers Instability: Transition to turbulence Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 849 , 25 August 2018 , pp. 1096 - 1119
Check for updates
Copyright
© 2018 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

Alves Portela, F., Papadakis, G. & Vassilicos, J. C. 2017 The turbulence cascade in the near wake of a square prism. J. Fluid Mech. 825, 315–352.Google Scholar
Blackburn, H. M. & Melbourne, W. H. 1996 The effect of free-stream turbulence on sectional lift forces on a circular cylinder. J. Fluid Mech. 306, 267–292.Google Scholar
Bloor, M. S. 1964 The transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 19 (2), 290–304.Google Scholar
Brown, G. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (4), 775–816.Google Scholar
Brun, C., Aubrun, S., Goossens, T. & Ravier, Ph. 2008 Coherent structures and their frequency signature in the separated shear layer on the sides of a square cylinder. Flow Turbul. Combust. 81 (1–2), 97–114.Google Scholar
Christensen, K. T. & Scarano, F. 2015 Uncertainty quantification in particle image velocimetry. Meas. Sci. Technol. 26 (7), 14–16.Google Scholar
Coleman, H. W. & Steele, W. G. 2009 Experimentation, Validation, and Uncertainty Analysis for Engineers. John Wiley & Sons.Google Scholar
Ho, C.-M. & Huerre, P. 1984 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16 (1), 365–422.Google Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in open shear layers. J. Fluid Mech. 159, 151–168.Google Scholar
Koenig, K.1978 Interaction effects on the drag of bluff bodies in tandem. PhD thesis, California Institute of Technology.Google Scholar
Lander, D. C., Letchford, C. W., Amitay, M. & Kopp, G. A. 2016 Influence of the bluff body shear layers on the wake of a square prism in a turbulent flow. Phys. Rev. Fluids 1 (4), 044406.Google Scholar
Liu, J. T. C. & Merkine, L. 1976 On the interactions between large-scale structure and fine-grained turbulence in a free shear flow I. The development of temporal interactions in the mean. Phil. Trans. R. Soc. Lond. A 352 (1669), 213–247.Google Scholar
Lyn, D & Rodi, W 1994 The flaping shear layer formed by flow separation from the forward corner of a square cylinder. J. Fluid Mech. 267, 353–376.Google Scholar
Michalke, A. 1965 On spatially growing disturbance in an inviscid shear layer. J. Fluid Mech. 23 (3), 521–544.Google Scholar
Mignot, E., Vinkovic, I., Doppler, D. & Riviere, N. 2014 Mixing layer in open-channel junction flows. Environ. Fluid Mech. 14 (5), 1027–1041.Google Scholar
Monkewitz, P. A. 1982 Influence of the velocity ratio on the spatial instability of mixing layers. Phys. Fluids 25 (7), 1137–1143.Google Scholar
Monkewitz, P. A. & Nguyen, L. N. 1987 Absolute instability in the near-wake of two-dimensional bluff bodies. J. Fluids Struct. 1 (2), 165–184.Google Scholar
Morton, B. R. 1984 The generation and decay of vorticity. Geophys. Astrophys. Fluid Dyn. 28, 277–308.Google Scholar
Neal, D. R., Sciacchitano, Andrea, Smith, B. L. & Scarano, Fulvio 2015 Collaborative framework for PIV uncertainty quantification: the experimental database. Meas. Sci. Technol. 26 (7), 74003.Google Scholar
Norberg, C. 1993 Flow around rectangular cylinders: pressure forces and wake frequencies. J. Wind Engng Ind. Aerodyn. 49, 187–196.Google Scholar
Prasad, A. & Williamson, C. H. K. 1997 The instability of the shear layer separating from a bluff body. J. Fluid Mech. 333, 375–402.Google Scholar
Rajagopalan, S. & Antonia, R. A. 2005 Flow around a circular cylinder – structure of the near wake shear layer. Exp. Fluids 38 (4), 393–402.Google Scholar
Roshko, A.1954 On the drag and shedding frequency of two-dimensional bluff bodies. Tech. Rep.Google Scholar
Roshko, A. 1955 On the wake and drag of bluff bodies. J. Aero. Sci. 22 (2), 124–132.Google Scholar
Sato, H. 1956 Experimental investigation on the transition of laminar separated layer. J. Phys. Soc. Japan 11 (6), 702–709.Google Scholar
Sciacchitano, A., Neal, D. R. & Smith, B. L. 2015 Collaborative framework for PIV uncertainty quantification: comparative assessment of methods. Meas. Sci. Technol. 26 (7), 074004.Google Scholar
Sigurdson, L. W.1986 The structure and control of a turbulent reattaching flow. PhD thesis, California Institute of Technology, Los Angeles.Google Scholar
Trias, F. X., Gorobets, A. & Oliva, A. 2015 Turbulent flow around a square cylinder at Reynolds number 22,000: a DNS study. Comput. Fluids 123 (22), 87–98.Google Scholar
Wieneke, B. 2015 PIV uncertainty quantification from correlation statistics. Meas. Sci. Technol. 26 (7), 074002.Google Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63 (2), 237–255.Google Scholar