Skip to main content
SpringerLink
Log in

Vortex shedding around a heated square cylinder under the influence of buoyancy

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

The influence of buoyancy on vortex shedding and heat transfer from a cylinder of square cross-section exposed to a horizontal stream has been studied.Unsteady Navier-Stokes and energy equations are solved numerically using a control volume approach. Flow field has been analysed for a wide range of Reynolds number (which is based on the cross-sectional height of the cylinder) and Grashof number with Richardson number between 0 to 1. Our results show that the centerline symmetry of the wake is lost and the cylinder experiences a downwards lift when the buoyancy effect is considered. Vortex shedding suppression doesn’t occur in the present case in which the cylinder is exposed to a horizontal cross-flow. Heat transfer from the cylinder increases due to increase in Reynolds number and Grashof number.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Abbreviations

C L :

Lift coefficient

C p :

Pressure coefficient

c p :

Specific heat at constant pressure

\(\overline {C_{\text {L}}} \) :

Time-averaged lift coefficient

\(\overline {C_{\text{D}}} \) :

Time-averaged drag coefficient

\(\overline {C_{\text {p}}} \) :

Time-averaged pressure coefficient

g :

Gravitational acceleration

Gr:

Grashof number =gβ (Tw - T_0)H3/ν 2

H :

Height of the cylinder

Nu(t):

Local Nusselt number

Nu M (t):

Surface average heat transfer at each face of the cylinder

Nutotal(t):

Total heat transfer from the cylinder

\(\overline {{\text {Nu}}} \) :

Time-average local Nusselt number on the surface of the cylinder

\(\overline {{\text{Nu}}_{{\text {total}}}} \) :

Total mean Nusselt number on the cylinder

p :

Dimensionless pressure

Pr :

Prandtl number =μ c p /κ

Re:

Reynolds number = UH/ν

Ri:

Raichardson number = Gr/Re 2

St:

Strouhal number = fH/U

T :

Period of vortex shedding/dimensional temperature

T 0 :

Dimensional lower temperature

T w :

Dimensional higher temperature

t :

Dimensionless time

\(\overline t \) :

Dimensional time

U :

Reference horizontal velocity

u :

x-component of velocity

y :

Vertical distance

β:

Thermal coefficient of volume expansion

ε:

A small positive quentity

θ:

Dimensionless temperature

ν:

Kinematic viscosity coefficient

κ:

Thermal conductivity

μ:

Co-efficient of viscosity

ρ:

Fluid density

0:

In the undisturbed fluid

w :

At the wall

−:

Dimensional quentity

References

  1. Bearman PW (1984) Vortex Shedding from oscillating bluff bodies. Annu Rev Fluid Mech 16:195–222

    Google Scholar 

  2. Williamson CHK (1996) Vortex dynamics in the cylinder wake. Annu Rev Fluid Mech 28:447–539

    Google Scholar 

  3. Davis RW, Moore EF (1982) A numerical study of vortex shedding from rectangles. J Fluid Mech 116:475–506

    Google Scholar 

  4. Franke R, Rodi W, Schonung B (1990) Numerical calculation of laminar vortex shedding flow past cylinders. J Wind Eng Ind Aerodyns 35:237–257

    Google Scholar 

  5. Okajima A (1982) Strouhal numbers of rectangular cylinders. J Fluid Mech 123:379–398

    Google Scholar 

  6. Okajima A (1990) Numerical simulation of flow around rectangular cylinders. J Wind Eng Ind Aerodyns 33:171–180

    Google Scholar 

  7. Arnal MP, Georing DJ, Humphery JAC (1991) Vortex shedding from a bluff body on a sliding wall. J Fluids Eng 113:384–398

    Google Scholar 

  8. Okajima A, Ueno H, Sakai H (1992) Numerical simulation of laminar and turbulent flow around rectangular cylinders. Int J Numer Meth Fluids 15:999–1012

    Google Scholar 

  9. Kelkar KM, Patankar SV (1992) Numerical prediction of vertex shedding behind a square cylinder. Int J Numer Meth Fluids 14:327–341

    Google Scholar 

  10. Sohankar A, Norberg C, Davidson L (1999) Simulation of the three-dimension flow around a square cylinder at moderate Reynolds number. Phys Fluids 11:288–306

    Google Scholar 

  11. Karniadakis GM (1998) Numerical simulation of forced convection heat transfer from a circular cylinder in cross flow. Int J Heat Mass Transfer 31:107–118

    Google Scholar 

  12. Chen C, Weng F (1990) Heat transfer for incompressible and compressible flows over a heated cylinder. Num Heat Transfer 18:325–342

    Google Scholar 

  13. Lange CF, Durst F, Breuer M (1998) Momentum and heat transfer from cylinders in laminar cross flow at 10−4 ≤ Re ≤ 200. Int J Heat Mass Transfer 41:3409–3430

    Google Scholar 

  14. Shuja SZ, Yilbas BS, Iqbal MO (2000) Heat Transfer characteristics of flow past a rectangular protruding body. Num Heat Transfer 37:307–321

    Google Scholar 

  15. Yang RJ, Fu LM (2001) Thermal and flow analysis of a heated electronic component. Int J Heat Mass Transfer 44:2261–2275

    Google Scholar 

  16. Badar HM (1984) Laminar combined convection from a horizontal cylinder-parallel and contra flow regimes. Int J Heat Mass Transfer 27:15–17

    Google Scholar 

  17. Chang KS, Sa JY (1990) The effect of buoyancy on vortex shedding in the near wake of a circular cylinder. J Fluid Mech 220:253–266

    Google Scholar 

  18. Hatankara K, Kawahara M (1995) A numerical study of vortex shedding around a heated/cooled circular cylinder by the three-step Taylor-Galerkin Method. Int J Num Methods Fluids 21:857–867

    Google Scholar 

  19. Patnaik BSV, Narayana PSA, Seetharamu KN (1999) Numerical simulation of Vortex shedding past a circular cylinder under the influence of buoyancy. Int J Heat Mass Transfer 42:3495–3507

    Google Scholar 

  20. Noto K (1990) Computational investigation on wake behavior with buoyancy from heated elliptic cylinder: Effect of mainstream attack angle. In: 39th Japanese national congress of applied mechanics : Univ of Tokyo Press, pp 293–303

  21. Kieft RN, Rindt CCM, Steenhoven AAV, Heijst GJFN (2003) On the wake structure behind a heated horizontal cylinder in cross-flow. J Fluid Mech 486:189–211

    Google Scholar 

  22. Patankar SV (1980) Numerical heat transfer and fluid flow. Hemisphere Publishing Corporation, Washington DC

    Google Scholar 

  23. Triedler EB (1991) An experimental and numerical investigation of flow past ribs in channel. Ph D Thesis, Univ of California

  24. Li G, Humphrey JAC (1995) Numerical modelling of confined flow past a cylinder of square cross-section at various orientations. Int J Numer Methods Fluids 20:1215–1236

    Google Scholar 

  25. Hwang RR, Yao C (1997) A numerical study of vortex shedding from a square cylinder with ground effect. J Fluid Eng119:512–518

    Google Scholar 

  26. Mukhopadhyay A , Biswas G, Sundarajan T (1992) Numerical investigation of confined wakes behind a square cylinder in a channel. Int J Numer Methods Fluids 14:1473–1484

    Google Scholar 

Download references

Acknowledgments

One of the authors (S.B.) wish to thank CSIR, India for providing financial support.

Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, India

    S. Bhattacharyya & S. Mahapatra

Authors
  1. S. Bhattacharyya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Mahapatra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Bhattacharyya.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bhattacharyya, S., Mahapatra, S. Vortex shedding around a heated square cylinder under the influence of buoyancy. Heat Mass Transfer 41, 824–833 (2005). https://doi.org/10.1007/s00231-005-0626-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-005-0626-9

Keywords

Search

Navigation