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Effect of buoyancy on the wakes of circular and square cylinders: a schlieren-interferometric study

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Abstract

Wakes behind heated cylinders, circular, and square have been experimentally investigated at low-Reynolds numbers. The electrically heated cylinder is mounted in a vertical airflow facility such that buoyancy aids the inertia of main flow. The operating parameters, i.e., Reynolds number and Richardson number are varied to examine flow behavior over a range of experimental conditions from forced to mixed convection regime. Laser schlieren-interferometry has been used for visualization and analysis of flow structures. Complete vortex shedding sequence has been recorded using a high-speed camera. The results on detailed dynamical characteristics of vortical structures, i.e., their size, shape and phase, Strouhal number, power spectra, convection velocity, phase shift, vortex inception length, and fluctuations are reported. On heating, alteration of organized (coherent) structures with respect to shape, size and their movement is readily perceived from instantaneous Schlieren images before they reduce to a steady plume. For both cylinders, Strouhal number shows a slow increase with an increase in Richardson number. At a critical value, there is complete disappearance of vortex shedding and a drop in Strouhal number to zero. The corresponding spectra evolve from being highly peaked at the vortex shedding frequency to a broadband appearance when vortex shedding is suppressed. The geometry of vortex structures transforms to a slender shape before shedding is suppressed. At this heating level, absence of multiple peaks in power spectra at cylinder centerline indicates absence of interaction between opposite shear layers. The convection velocity of vortices increases in stream wise direction to an asymptotic value and its variation is a function of Richardson number. The convection speed abruptly falls to zero at critical Richardson number. The phase difference of shed vortices between upstream and downstream location increases with an increase in Richardson number. Velocity profiles show an increase in fluid speed and beyond the critical point, buoyancy forces add enough momentum to cancel momentum deficit due to the cylinder. Overall, the combined effect of temperature gradient on the separating shear layer velocity profile in near field and vortical structures interaction in far field influences wake instability of a heated cylinder.

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Abbreviations

C p :

specific heat of the fluid, kJ/kg °C

d :

representative dimension of the cylinder (diameter for circular cylinder, edge for square cylinder), m

f o :

frequency of vortex shedding, Hz

g :

gravitational acceleration, m/s2

I :

gray scale intensity value of the image

k :

thermal conductivity of the fluid, W/m °C

L f :

formation length, m

L :

length of the cylinder, m

n :

refractive index of the working medium (air)

Pr :

prandtl number (μC p /k)

Re :

Reynolds number (U ∞ d/ν)

Ri :

Richardson number (dgβΔT/U 2∞ )

St :

Strouhal number (f o d/U ∞)

t :

time, s

T :

temperature, °C

T w :

cylinder surface temperature, °C

T ∞ :

free-stream temperature, °C

T eff :

effective temperature, (T ∞ + 0.28(T w − T ∞)) °C

T film :

film temperature, (T w + T ∞)/2 °C

T* :

temperature ratio [(T w + 273)/(T ∞ + 273)]

ΔT :

T w − T ∞, °C

ΔT ε :

temperature change per fringe shift, °C

u :

stream wise velocity, m/s

v :

cross-stream velocity, m/s

U ∞ :

uniform free-stream velocity, m/s

u c :

stream wise convection velocity, m/s

x :

stream wise dimension of coordinates, m

y :

transverse dimension of coordinates, m

z :

span wise dimension of coordinates, m

ν :

kinematic viscosity of the fluid, m2/s

β :

volume coefficient of thermal expansion, °C−1

θ :

non-dimensional temperature (T − T ∞)/(T w − T ∞)

ρ :

density of the fluid, kg/m3

λ :

wavelength of the laser beam, m

Φ:

phase difference

crit:

critical

w:

cylinder surface

rms:

root mean square

eff:

refers to conditions at effective temperature

film:

refers to conditions at arithmatic mean film temperature

∞:

free stream

References

  • Anderson RC, Milton JE (1989) A large aperture inexpensive interferometer for routine flow measurements. In: IEEE Conference Proceedings on Instrumentation in aerospace simulation facilities, 18–21 September 1989, ICIASF’89 record 10.1109/ICIASF, 1989, 77693, pp 394–399

  • Badr HM (1984) Laminar combined convection from a horizontal cylinder-parallel and contra flow regimes. Int J Heat Mass Transf 27(1):15–27

    Article  MATH  MathSciNet  Google Scholar 

  • Ben-yaker A, Hanson RK (2002) Ultra-fast-framing schlieren system for studies of the time evolution of jets in supersonic cross flows. Exp Fluids 32:652–666

    Google Scholar 

  • Brackenridge JB, Peterka J (1967) Criteria for quantitative schlieren interferometry. App Opt 6(4):731–735

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Dumouchel F, Lecordier JC, Paranthoen P (1998) The effective Reynolds number of a heated cylinder. Int J Heat Mass Transf 41(12):1787–1794

    Article  Google Scholar 

  • Gerrard JH (1966) The mechanics of the formation region of vortices behind bluff bodies. J Fluid Mech 25:401–413

    Article  Google Scholar 

  • Goldstein RJ (ed) (1996) Fluid mechanics measurements, 2nd edn. Taylor and Francis, New York

  • Jain PC, Lohar BL (1979) Unsteady mixed convection heat transfer from a horizontal circular cylinder. Trans ASME J Heat Transf 101:126–131

    Google Scholar 

  • Konstantinidis E, Balabani S, Yianneskis M (2003) The effect of flow perturbations on the near wake characteristics of a circular cylinder. J Fluids Struct 18:367–386

    Article  Google Scholar 

  • Lecordier JC, Browne LWB, Masson SL, Dumouchel F, Paranthoen P (2000) Control of vortex shedding by thermal effect at low Reynolds numbers. Exp Th Fluid Sc 21:227–237

    Article  Google Scholar 

  • Lin C, Hsieh SC (2003) Convection velocity of vortex structures in the near wake of a circular cylinder. ASCE J Eng mech 129(10):1108–1118

    Article  MathSciNet  Google Scholar 

  • Luo SC, Chew YT, Ng YT (2003) Characteristics of square cylinder wake transition flow. Phys Fluids 15(9):2549–2559

    Article  Google Scholar 

  • Maas WJPM, Rindt CCM, van Steenhoven AA (2003) The influence of heat on the 3D-transition of the von Karman vortex street. Int J Heat Mass Transf 46:3069–3081

    Google Scholar 

  • Merkin JH (1977) Mixed convection from a horizontal circular cylinder. Int J Heat Mass Transf 20:73–77

    Article  Google Scholar 

  • Michaux-Leblond N, Belorgey M (1997) Near wake behavior of a heated circular cylinder: viscosity-buoyancy duality. Exp Therm Fluid Sci 15:91–100

    Article  Google Scholar 

  • Muralidhar K (2001) Temperature field measurement in buoyancy-driven flows using interferometric tomography. Annu Rev Heat Transf 12:265–376

    Google Scholar 

  • Noto K, Ishida H, Matsumoto R (1985) A breakdown of the Karman vortex street due to natural convection. Flow visualization III. Springer, Berlin, pp 348–352

    Google Scholar 

  • Oosthuizen PH, Madan S (1971) The effect of flow direction on combined convective heat transfer from cylinders to air. Trans ASME C J Heat Transf 93:240–242

    Google Scholar 

  • Robichaux J, Balachandar S, Vanka SP (1999) Three-dimensional Floquet instability of the wake of a square cylinder. Phys Fluids 11(3):560–578

    Article  MATH  MathSciNet  Google Scholar 

  • Schumm M, Berger E, Monkewitz PA (1994) Self-excited oscillations in the wake of two-dimensional bluff bodies and their control. J Fluid Mech 271:17–53

    Article  Google Scholar 

  • Settles GS (2001) Schlieren and shadowgraph techniques: visualizing phenomenon in transparent media. Springer, New York

    Google Scholar 

  • Sharma A, Eswaran V (2004) Effect of aiding and opposing buoyancy on the heat and fluid flow across a square cylinder at Re = 100. Num Heat Transf A 45:601–624

    Article  Google Scholar 

  • Shi JM, Gerlach D, Breuer M, Biswas G, Durst F (2004) Heating effect on steady and unsteady horizontal laminar flow of air past a circular cylinder. Phys Fluids 16(12):4331–4345

    Article  Google Scholar 

  • Smith KM, Dutton JC (1999) A procedure for turbulent structure convection velocity measurements using time-correlated images. Exp Fluids 27:244–250

    Article  Google Scholar 

  • Sohankar A, Norberg C, Davidson L (1999) Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers. Phys Fluids 11(2):288–306

    Article  MATH  Google Scholar 

  • Vit T, Ren M, Travnicek Z, Marsik F, Rindt CCM (2006) The influence of temperature gradient on the Strouhal-Reynolds number relationship for water and air. Exp Therm Fluid Sci. doi:10.1016/j.exptthermflusci.2006.08.002

  • Wang A, Travnicek Z, Chia KC (2000) On the relationship of effective Reynolds number and Strouhal number for the laminar vortex shedding of a heated circular cylinder. Phys Fluids 12(6):1401–1410

    Article  MATH  Google Scholar 

  • Yu MH, Monkewitz PA (1990) The effect of nonuniform density on the absolute instability of two-dimensional inertial jets and wakes. Phys Fluids A 2(7):1175–1181

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    S. K. Singh, P. K. Panigrahi & K. Muralidhar

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  1. S. K. Singh
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  2. P. K. Panigrahi
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  3. K. Muralidhar
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Correspondence to P. K. Panigrahi.

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Singh, S.K., Panigrahi, P.K. & Muralidhar, K. Effect of buoyancy on the wakes of circular and square cylinders: a schlieren-interferometric study. Exp Fluids 43, 101–123 (2007). https://doi.org/10.1007/s00348-007-0329-8

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