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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.

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References

Figures

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Fig. 1

Outline of the numerical setup

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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.

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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.

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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.

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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.

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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.

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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

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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)

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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

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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

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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

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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

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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

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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

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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

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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

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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.

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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

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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)

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