Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-12-01T03:57:28.461Z Has data issue: false hasContentIssue false
  • English
  • Français

Momentum and heat transport in a three-dimensional transitional wake of a heated square cylinder

Published online by Cambridge University Press:  27 October 2009

L. DJENIDI  and
R. A. ANTONIA
L. DJENIDI*
Affiliation:
Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle 2308 NSW, Australia
R. A. ANTONIA
Affiliation:
Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle 2308 NSW, Australia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The transport of momentum and a passive scalar (temperature) in a three-dimensional transitional wake of a heated square cylinder has been carried out through direct numerical simulations using the lattice Boltzmann method at a Reynolds number Rd = 200 (d is the cylinder diameter) and a Prandlt number of 0.7. The simulations shows that while momentum and heat are transported by vortical structures, heat is in general more effectively transported than momentum. It is argued that the nature of the structural flow is responsible for the longitudinal heat flux uθ being larger than the lateral one vθ in the wake region extending up to 45d. It was shown that a gradient transport model could, to a first-order approximation, be used to model uv but would be less accurate for modelling vθ. Also the Reynolds analogy between momentum and heat transports is not verified in this flow. The fluctuating temperature field presents thermal structures similar to the velocity structures with, however, a different spatial organization. In addition the analogy between fluctuating turbulent kinetic energy and the temperature variance is relatively well satisfied throughout the wake flow.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 640 , 10 December 2009 , pp. 109 - 129
Copyright
Copyright © Cambridge University Press 2009

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

Abe, H., Antonia, R. A. & Kawamura, H. 2009 Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow. J. Fluid Mech. 627, 1–32.CrossRefGoogle Scholar
Antonia, R. A., Abe, H. & Kawamura, H. 2009 Analogy between velocity and scalar fields in a turbulent channel flow. J. Fluid Mech. 628, 241–268.CrossRefGoogle Scholar
Antonia, R. A., Chambers, A. J., Britz, D. & Browne, L. W. B. 1986 Organized structures in a turbulent plane jet: topology and contribution to momentum and heat transport. J. Fluid Mech. 172, 211–229.CrossRefGoogle Scholar
Antonia, R. A. & Mi, J. 1993 Vorticity and temperature distributions for an isolated viscous vortex. Tech. Rep. T.N. -FM 93/02. University of Newcastle.Google Scholar
Antonia, R. A., Zhou, Y. & Matsumura, M. 1993 Spectral characteristics of momentum and heat transfer in the turbulent wake of a circular cylinder. Exp. Therm. Fluid Sci. 6, 371–375.CrossRefGoogle Scholar
Benzi, R., Succi, S. & Vergassola, M. 1992 Lattice Boltzmann equation: theory and applications. Phys. Rep. 222, 145–197.CrossRefGoogle Scholar
Braza, M. 1999 The three-dimensional transition to turbulence in wake flows by means of direct numerical simulation. Flow Turbul. Combust. 63, 315–341.CrossRefGoogle Scholar
Chen, S. & Doolen, G. D. 1998 Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364.CrossRefGoogle Scholar
Djenidi, L. 2006 Lattice Boltzmann simulation of grid-generated turbulence. J. Fluid Mech. 552, 13–35.CrossRefGoogle Scholar
Djenidi, L. & Antonia, R. A. 2008 Lattice Boltzmann prediction of three-dimensional natural transition to turbulence. In Seventeenth Intl Conf. on Discrete Simulation of Fluid Dynamics, Florianopolis, Brazil.Google Scholar
Djenidi, L. & Moghtaderi, B. 2006 Numerical investigation of laminar mixing in a coaxial microreactor. J. Fluid Mech. 568, 223–242.CrossRefGoogle Scholar
Durão, D. F. G, Heitor, M. V. & Pereira, J. C. F. 1988 Measurements of turbulent and periodic flows around a square cross-section cylinder. Exp. Fluids 6, 298–304.CrossRefGoogle Scholar
Ezersky, A. B, Lecordier, J. C., Paranthoën, P & Soustov, P. L. 2000 Structure of vortices in a Kármán street behind a heated cylinder. Phys. Rev. E 61, 2107–2110.CrossRefGoogle Scholar
Frisch, U., Hasslacher, B. & Pomeau, Y. 1986 Lattice gas automata for the Navier–Stokes equations. Phys. Rev. Lett. 56, 1505–1508.CrossRefGoogle Scholar
Godard, G. 2001 Experimental study of a passive scalar field in a Bénard–Kármán street. PhD Thesis, University of Rouen, France.Google Scholar
Godard, G., Weiss, F., Gonzalez, M. & Paranthoën, P. 2005 Heat transfer from a line source located in the periodic laminar near wake of a circular cylinder. Exp. Therm. Fluid Sci. 29, 947–956.CrossRefGoogle Scholar
Green, R. B. & Gerrard, J. H. 1991 An optical interferometric study of the wake of a bluff body. J. Fluid Mech. 226, 219–242.CrossRefGoogle Scholar
Liou, T.-M., Chen, S.-H., & Hwang, P.-W. 2002 Large eddy simulation of turbulent wake behind a square cylinder with a nearby wall. J. Fluid Engng 124, 81–90.CrossRefGoogle Scholar
Massaioli, F., Benzi, R. & Succi, S. 1993 Exponential tails in two-dimensional Rayleigh–Bénard convection. Europhys. Lett. 21, 305–310.CrossRefGoogle Scholar
Matsumura, M. & Antonia, R. A. 1993 Momentum and heat transport in the turbulent intermediate wake of a circular cylinder. J. Fluid Mech. 250, 651–668.CrossRefGoogle Scholar
Mi, J. & Antonia, R. A. 1993 Thermal characteristics of turbulent vortices in the wake of a circular cylinder. In Proceedings of the Nineth Symposium on Turbulent Shear Flows, Kyoto, Japan.Google Scholar
Mi, J. & Antonia, R. A. 1994 Temperature distribution within vortices in the wake of a cylinder. Intl J. Heat Mass Transfer 37, 1048–1050.CrossRefGoogle Scholar
Mydlarski, L. & Warhaft, Z. 1998 Passive scalar statistics in high-Péclet-number grid turbulence. J. Fluid Mech. 358, 135–175.CrossRefGoogle Scholar
Okude, M. & Matsui, T. 1987 a Correspondance of velocity fluctuations to flow patterns in a Kármán vortex street at low Reynolds numbers. Trans. Japan Soc. Aeronaut. Space Sci. 30 (88), 80–90.Google Scholar
Okude, M. & Matsui, T. 1987 b Vorticity distribution of vortex street in the wake of a circular cylinder. Trans. Japan Soc. Aeronaut. Space Sci. 33 (99), 1–13.Google Scholar
Paranthoën, P., Godard, G., Weiss, F. & Gonzalez, M. 2004 Counter gradient diffusion vs counter diffusion temperature profile. Intl J. Heat Mass Transfer 47, 819–825.CrossRefGoogle Scholar
Persillon, H. & Braza, M. 1998 Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier–Stokes simulation. J. Fluid Mech. 365, 23–88.CrossRefGoogle Scholar
Rehab, H., Antonia, R. A., Djenidi, L. & Mi, J. 2000 Characteristics of fluorescein dye and temperature fluctuations in a turbulent near-wake. Exp. Fluids 28, 462–470.CrossRefGoogle Scholar
Shadaram, A., Fard, M. A. & Rostamy, N. 2008 Experimental study of near-wake flow behind a rectangular cylinder. Am. J. Appl. Sci. 5 (8), 917–926.Google Scholar
Sreenivasan, K. R. 1996 The passive scalar spectrum and the Obukhov–Corrsin constant. Phys. Fluids 8, 189–196.CrossRefGoogle Scholar
Succi, S. 2001 The lattice Boltzmann equation for fluid dynamics and Beyond. Numer. Math. Sci. Comput. Oxford University Press.Google Scholar
Warhaft, Z. 2000 Passive scalar in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240.CrossRefGoogle Scholar
Watanabe, T. & Gotoh, T. 2004 Statistics of a passive scalar in homogeneous turbulence. New J. Phys 6, 40 (http://www.njp.org/).CrossRefGoogle Scholar
Williamsom, C. H. K. 1996 a Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539.CrossRefGoogle Scholar
Williamsom, C. H. K. 1996 b Three-dimensional wake transition. J. Fluid Mech. 328, 345–407.CrossRefGoogle Scholar
Yuan, P. & Schaefer, L. 2006 A thermal lattice Boltzmann two-phase flow model and its application to heat transfer problems. Part 1. Theoretical foundation, J. Fluid Engng 128, 142–150.CrossRefGoogle Scholar