0
Research Papers: Natural and Mixed Convection

Buoyancy Effect on the Flow Pattern and the Thermal Performance of an Array of Circular Cylinders

[+] Author and Article Information
Francesco Fornarelli

Department of Mechanics, Mathematics
and Management,
Polytechnic of Bari,
via Orabona 4,
Bari 70125, Italy;
INFN sez. Lecce,
Lecce 73100, Italy
e-mail: francesco.fornarelli@poliba.it

Antonio Lippolis

Professor
Department of Mechanics,
Mathematics and Management,
Polytechnic of Bari,
via Orabona 4,
Bari 70125, Italy
e-mail: antonio.lippolis@poliba.it

Paolo Oresta

Assistant Professor
Department of Mechanics,
Mathematics and Management,
Polytechnic of Bari,
via Orabona 4,
Bari 70125, Italy;
INFN sez. Lecce,
Lecce 73100, Italy
e-mail: paolo.oresta@poliba.it

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 10, 2016; final manuscript received August 22, 2016; published online October 4, 2016. Assoc. Editor: Dr. Antonio Barletta.

J. Heat Transfer 139(2), 022501 (Oct 04, 2016) (10 pages) Paper No: HT-16-1373; doi: 10.1115/1.4034794 History: Received June 10, 2016; Revised August 22, 2016

In this paper, we found, by means of numerical simulations, a transition in the oscillatory character of the flow field for a particular combination of buoyancy and spacing in an array of six circular cylinders at a Reynolds number of 100 and Prandtl number of 0.7. The cylinders are isothermal and they are aligned with the earth acceleration (g). According to the array orientation, an aiding or an opposing buoyancy is considered. The effect of natural convection with respect to the forced convection is modulated with the Richardson number, Ri, ranging between −1 and 1. Two values of center-to-center spacing (s = 3.6d–4d) are considered. The effects of buoyancy and spacing on the flow pattern in the near and far field are described. Several transitions in the flow patterns are found, and a parametric analysis of the dependence of the force coefficients and Nusselt number with respect to the Richardson number is reported. For Ri=−1, the change of spacing ratio from 3.6 to 4 induces a transition in the standard deviation of the force coefficients and heat flux. In fact, the transition occurs due to rearrangement of the near-field flow in a more ordered wake pattern. Therefore, attention is focused on the influence of geometrical and buoyancy parameters on the heat and momentum exchange and their fluctuations. The available heat exchange models for cylinders array provide a not accurate prediction of the Nusselt number in the cases here studied.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Ye, Y. , Saw, L. H. , Shi, Y. , and Tay, A. A. , 2015, “ Numerical Analyses on Optimizing a Heat Pipe Thermal Management System for Lithium-Ion Batteries During Fast Charging,” Appl. Therm. Eng., 86, pp. 281–291. [CrossRef]
Wan, Y. , Tamuly, D. , Allen, P. B. , Kim, Y.-T. , Bachoo, R. , Ellington, A. D. , and Iqbal, S. M. , 2013, “ Proliferation and Migration of Tumor Cells in Tapered Channels,” Biomed. Microdevices, 15(4), pp. 635–643. [CrossRef] [PubMed]
Wang, S.-y. , Tian, F.-b. , Jia, L.-b. , Lu, X.-y. , and Yin, X.-z. , 2010, “ Secondary Vortex Street in the Wake of Two Tandem Circular Cylinders at Low Reynolds Number,” Phys. Rev. E, 81(3), p. 036305. [CrossRef]
Duryodhan, V . S. , Singh, A. , Singh, S. G. , and Agrawal, A. , 2016, “ A Simple and Novel Way of Maintaining Constant Wall Temperature in Microdevices,” Sci. Rep., 6(18230), pp. 1–15.
Selimefendigil, F. , and Oztop, H. , 2014, “ Control of Laminar Pulsating Flow and Heat Transfer in Backward-Facing Step by Using a Square Obstacle,” ASME J. Heat Transfer, 136(8), p. 081701. [CrossRef]
Fornarelli, F. , Oresta, P. , and Lippolis, A. , 2015, “ Flow Patterns and Heat Transfer Around Six In-Line Circular Cylinders at Low Reynolds Number,” JP J. Heat Mass Transfer, 11(1), pp. 1–28. [CrossRef]
Chatterjee, D. , 2014, “ Dual Role of Thermal Buoyancy in Controlling Boundary Layer Separation Around Bluff Obstacles,” Int. Commun. Heat Mass Transfer, 56, pp. 152–158. [CrossRef]
Clifford, C. , and Kimber, M. , 2014, “ Optimizing Laminar Natural Convection for a Heat Generating Cylinder in a Channel,” ASME J. Heat Transfer, 136(11), p. 112502. [CrossRef]
Patnaik, B. , Narayana, P. , and Seetharamu, K. , 2000, “ Finite Element Simulation of Transient Laminar Flow Past a Circular Cylinder and Two Cylinders in Tandem,” Int. J. Numer. Methods Heat Fluid Flow, 10(6), pp. 560–580. [CrossRef]
Khan, W. , Culham, J. , and Yovanovich, M. , 2006, “ Convection Heat Transfer From Tube Banks in Crossflow: Analytical Approach,” Int. J. Heat Mass Transfer, 49(25–26), pp. 4831–4838. [CrossRef]
Wang, Y. , Penner, L. , and Ormiston, S. , 2000, “ Analysis of Laminar Forced Convection of Air for Crossflow in Banks of Staggered Tubes,” Numer. Heat Transfer, Part A, 38(8), pp. 819–845. [CrossRef]
Gowda, Y. , Narayana, P. , and Seetharamu, K. , 1998, “ Finite Element Analysis of Mixed Convection Over In-Line Tube Bundles,” Int. J. Heat Mass Transfer, 41(11), pp. 1613–1619. [CrossRef]
Zukauskas, A. , 1972, “ Heat Transfer From Tubes in Crossflow,” Adv. Heat Transfer, 8, pp. 93–160.
Gnielinski, V. , 1975, “ Berechnung mittlerer wärme- und stoffübergangskoeffizienten an laminar und turbulent überströmten einzelkörpern mit hilfe einer einheitlichen gleichung,” Forsch. Ingenieurwes., 41(5), pp. 145–153. [CrossRef]
Barkley, D. , and Henderson, R. , 1996, “ Three-Dimensional Floquet Stability Analysis of the Wake of a Circular Cylinder,” J. Fluid Mech., 322, pp. 215–241. [CrossRef]
Carmo, B. S. , Meneghini, J. R. , and Sherwin, S. J. , 2010, “ Secondary Instabilities in the Flow Around Two Circular Cylinders in Tandem,” J. Fluid Mech., 644, pp. 395–431. [CrossRef]
Carmo, B. , Meneghini, J. , and Sherwin, S. , 2010, “ Possible States in the Flow Around Two Circular Cylinders in Tandem With Separations in the Vicinity of the Drag Inversion Spacing,” Phys. Fluids, 22(5), p. 054101. [CrossRef]
Maas, W. , Rindt, C. , and van Steenhoven, A. , 2003, “ The Influence of Heat on the 3D-Transition of the von Kármán Vortex Street,” Int. J. Heat Mass Transfer, 46(16), pp. 3069–3081. [CrossRef]
Ren, M. , Rindt, C. , and van Steenhoven, A. , 2004, “ Experimental and Numerical Investigation of the Vortex Formation Process Behind a Heated Cylinder,” Phys. Fluids, 16(8), pp. 3103–3114. [CrossRef]
Boirlaud, M. , Couton, D. , and Plourde, F. , 2012, “ Direct Numerical Simulation of the Turbulent Wake Behind a Heated Cylinder,” Int. J. Heat Fluid Flow, 38, pp. 82–93. [CrossRef]
Popinet, S. , 2003, “ Gerris: A Tree-Based Adaptive Solver for the Incompressible Euler Equations in Complex Geometries,” J. Comput. Phys., 190(2), pp. 572–600. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Outline of the numerical setup

Grahic Jump Location
Fig. 2

Comparison of the dimensionless temperature distribution at t = 1800 for opposing buoyancy Ri < 0. The domain is placed in vertical position with the freestream velocity oriented downward.

Grahic Jump Location
Fig. 3

Near field comparison of the dimensionless temperature distribution at t = 1800 for opposing buoyancy Ri < 0. The domain is placed in vertical position with the freestream velocity oriented downward.

Grahic Jump Location
Fig. 4

Comparison of the dimensionless temperature distribution at t = 1800 for aiding buoyancy Ri ≥ 0. The domain is placed in vertical position with the freestream velocity oriented upward.

Grahic Jump Location
Fig. 5

Snapshots of the dimensionless temperature distribution over one oscillation cycle in case of forced convection Ri = 0, for s/d = 3.6 at t = 1800.0 (a), t = 1802.5 (b), t = 1805.0 (c), t = 1807.5 (d), and t = 1810.0 (e), and s/d = 4.0 at t = 1800.0 (f), t = 1802.5 (g), t = 1805.0 (h), and t = 1807.5 (i). The domain is placed in vertical position with the freestream velocity oriented upward.

Grahic Jump Location
Fig. 6

Time-averaged drag coefficient (〈Cd〉) of the array withrespect to the Richardson number (Ri) for s/d = 3.6 and s/d = 4.0. The linear fitting of the aiding buoyancy cases (0 ≤ Ri ≤ 1) is reported.

Grahic Jump Location
Fig. 19

Standard deviation of the Nusselt number (σ(Nu)) of each cylinder respect to the Richardson number (Ri) for s/d = 3.6 (a) and s/d = 4.0 (b)

Grahic Jump Location
Fig. 18

Standard deviation of the Nusselt number (σ(Nu)) of the array with respect to the Richardson number (Ri) for s/d = 3.6 and s/d = 4.0

Grahic Jump Location
Fig. 17

Time-averaged Nusselt number (〈Nu〉) of the array with respect to the Richardson number (Ri) for s/d = 3.6 and s/d = 4.0. The predictions of Zukauskas [13] in two different Reynolds ranges, 0–100 and 100–1000, and three values of Gnielinski [14] for a single line of six cylinders (s/q = 0), and two configurations of an infinite array of six cylinders (s/d = 3.6–4 and q/d = 40) are reported.

Grahic Jump Location
Fig. 16

Surface-averaged Nusselt number (Nu) of each cylinder with respect to the dimensionless time t, for s/d = 4.0 and Ri = 1

Grahic Jump Location
Fig. 15

Surface-averaged Nusselt number (Nu) of each cylinder with respect to the dimensionless time t, for s/d = 3.6 and Ri = 1

Grahic Jump Location
Fig. 14

Surface-averaged Nusselt number (Nu) of each cylinder with respect to the dimensionless time t, for s/d = 4.0 and Ri = −1

Grahic Jump Location
Fig. 13

Surface-averaged Nusselt number (Nu) of each cylinder with respect to the dimensionless time t, for s/d = 3.6 and Ri=−1

Grahic Jump Location
Fig. 12

Surface-averaged Nusselt number (Nu) of each cylinder with respect to the dimensionless time t, for s/d = 4.0 and Ri = 0

Grahic Jump Location
Fig. 11

Surface-averaged Nusselt number (Nu) of each cylinder with respect to the dimensionless time t, for s/d = 3.6 and Ri = 0

Grahic Jump Location
Fig. 10

Strouhal number (St) of the first cylinder with respect to the Richardson number (Ri) for s/d = 3.6 and s/d = 4.0

Grahic Jump Location
Fig. 9

Standard deviation of the lift coefficient (σ(Cl)) averaged over six cylinders with respect to the Richardson number (Ri) for s/d = 3.6 and s/d = 4.0

Grahic Jump Location
Fig. 8

Standard deviation of the drag coefficient (σ(Cd)) of each cylinder with respect to the Richardson number (Ri) for s/d = 3.6 (a) and s/d = 4.0 (b)

Grahic Jump Location
Fig. 7

Standard deviation of the drag coefficient (σ(Cd)) averaged over six cylinders with respect to the Richardson number (Ri) for s/d = 3.6 and s/d = 4.0

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In