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Heat transfer and flow behavior around four staggered elliptic cylinders in cross flow

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Abstract

Experimental and numerical studies were carried out to investigate forced convection heat transfer and flow features around the downstream elliptic cylinder in four staggered cylinders in cross flow. The elliptic cylinders examined had an axis ratio (b/c) of 1:2, and they were arranged with zero angle of attack to the upstream flow. The present heat transfer measurements were obtained by heating only the downstream elliptic cylinder (test cylinder) under the condition of constant heat flux. The testing fluid was air and the Reynolds number based on the major axis length (c) was ranged from 4,000 to 45,570. The tested longitudinal spacing ratio (Sx/c) and the transversal spacing ratio (Sy/b) were in the ranges of 1.5 ≤ Sx/c ≤ 4.0 and 1.5 ≤ Sy/b ≤ 4.0, respectively. The air flow pattern and temperature fields around the four staggered elliptic cylinders were predicted by using CFD software package. Also, a flow visualization study was made to show the flow features around the elliptic cylinders. It was observed that Num of the downstream elliptic cylinder in four staggered cylinders was higher than that of three in-line cylinders for all tested spacing ratios and Reynolds numbers except for Re = 4,000. It was clear that, at lower Reynolds number values (Re < 14,100), the average Nusselt number of the downstream elliptic cylinder in three staggered arrangement was higher than that of the downstream cylinder in four staggered arrangement for all tested spacing ratios. On the other hand, at Re > 14,100, the tested elliptic cylinder in four staggered arrangement had the higher values of the average Nusselt number. Moreover, in four staggered arrangement, the maximum average Nusselt number enhancement ratio (average Nusselt number of the tested downstream cylinder/average Nusselt number of a single elliptic cylinder) was found to be about 2.0, and was obtained for spacing ratios of Sx/c = 2.5, Sy/b = 2.5 and at Re = 32,000. Finally, the average Nusselt number of the tested cylinder in four staggered arrangement was correlated in terms of Reynolds number and cylinder spacing ratios.

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Abbreviations

b:

Minor axis length of elliptic cylinder (m)

c:

Major axis length of elliptic cylinder (m)

H:

Duct height (m)

h:

Local heat transfer coefficient (W/m2°C)

hm :

Average heat transfer coefficient to air stream (W/m2°C)

K:

Fluid thermal conductivity (W/m°C)

k:

Turbulent kinetic energy (m2/s2 or J/kg)

Nu:

Local Nusselt number

Num :

Average Nusselt number around the tested elliptic cylinder

Nus,m :

Average Nusselt number around a single elliptic cylinder

qw :

net heat flux (W/m2)

Re:

Reynolds number = Uo c/ν

Sx :

Longitudinal spacing distance (longitudinal distance between two cylinder centers) (m)

Sy :

Transversal spacing distance (transversal distance between the intermediate cylinders centers normal to the flow direction) (m)

s:

Circumferential distance from the leading edge, taken as positive along the upper side (m)

T:

Local surface temperature (°C)

To :

Average inlet air temperature (°C)

u:

Stream-wise velocity component (m/s)

Uo :

Upstream mean velocity (m/s)

v:

Transverse velocity component (m/s)

x:

Stream-wise coordinate (m)

y:

Normal coordinate (m)

ε:

Rate of dissipation of turbulent kinetic energy (m2/s3)

α:

Angle of attack

ν:

Kinematic viscosity (m2/s)

μt :

Turbulent dynamic viscosity (N s/m2)

Φ:

Viscous dissipation term (W/m3)

ρ:

Density (kg/m3)

θ:

Non-dimensional temperature, θ = [(T − To)K]/(qwc)

b:

Bulk

o:

Upstream flow

s:

Single cylinder

w:

Wall

x:

Local distance in the axial direction

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  1. Mechanical Engineering Department, Shoubra Faculty of Engineering, Benha University, Benha, Egypt

    Nabil S. Berbish

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Berbish, N.S. Heat transfer and flow behavior around four staggered elliptic cylinders in cross flow. Heat Mass Transfer 47, 287–300 (2011). https://doi.org/10.1007/s00231-010-0719-y

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