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On swirl development in a square cross-sectioned, S-shaped duct

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Abstract

The flow in a uniform square cross-sectioned, S-shaped duct was investigated experimentally, at Reynolds number (Re) = 4.73 × 104 and 1.47 × 105, using three S-ducts of different curvature and turning angle. The hydraulic diameter (D) for each S-duct is 150 mm. Besides studying the square cross-sectioned S-duct flow at moderately higher Re than current literature, the S-ducts’ geometry used in this study also have larger curvatures and higher turning angles than those reported in the literature. With surface pressure measurement and smoke wire flow visualization, flow separation at the inside wall of the first bend was detected. Using surface oil flow visualization on the bottom wall of the S-duct and cross-wires measurement at the duct exit, it is shown here that the swirl developed in the first bend was partly attenuated in the second bend due to the formation of swirl of opposite direction. The swirl of an opposite sign results in the formation of a clear dividing or separation line on the bottom wall (and top wall) of the duct. Additional flow features include the formation of streamwise vortices on the outer-wall of the second bend. These streamwise vortices can either be a pair of counter-rotating vortices or a single vortex. The formation mechanism of these streamwise vortices is explained using the Squire and Winter [J Aeronaut Sci 18(4):271–277, 1951] formula and it is shown that the said mechanism is applicable to both Re in the present study.

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Abbreviations

C p :

pressure coefficient =  \( \frac{{P - P_{{\text{s}}} }} {{\frac{1} {2}\rho U^{2}_{m } }} \)

D :

hydraulic diameter = 0.150 ± 0.001 m

f i and g i :

yaw function for cross hot wire, i = 1 or 2

k 2 i :

yaw coefficient for cross hot wire, i = 1 or 2

L d :

length of S-duct test section = 0.400 ± 0.001 m

L o :

overall length of S-duct test section = 0.800 ± 0.001 m

L S :

length of straight inlet and outlet of S-duct test section = 0.200 ± 0.001 m

P :

side wall pressure (N/m2)

P S :

static pressure (N/m2)

P T :

total Pressure (N/m2)

R C :

radius of curvature of S-duct = 0.363 m (test section 1); 0.290 m (test section 2); 0.250 m (test section 3)

RC/D:

curvature ratio of S-duct = 2.422 (test section 1); 1.933 (test section 2); 1.667 (test section 3)

Re :

Reynolds number = 4.73 × 104 and 1.47 × 105

s, y, z :

streamwise, transverse and vertical coordinate direction

u, v, w :

velocity component in s-, y-, and z-direction, respectively (m/s)

U m :

mean free stream velocity = 5.00 ± 0.05 m/s, 15.00 ± 0.15 m/s

U :

velocity component parallel to cross wire probe axis

V :

velocity component normal to cross wire probe axis

V ei :

effective velocity measured by cross hot wire probe, i = 1 or 2

\( \ifmmode\expandafter\bar\else\expandafter\=\fi{\alpha }_{i} \) :

wire angle of cross hot wire probe, i = 1 or 2

θ :

duct turning angle = 33.4° (test section 1); 43.6° (test section 2); 53.1° (test section 3)

ρ :

density of air = 1.184 ± 0.012 kg/m3

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Acknowledgments

This work was supported partially by the Defense Science Organization (DSO) National Laboratories, Singapore.

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Author notes

  1. Q. W. Ho

    Present address: Defense Science and Technology Agency, 71 Science Park Drive, #02-05, Singapore, Singapore, 118253

Authors and Affiliations

  1. Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore, Singapore, 117576

    Y. T. Ng, S. C. Luo & T. T. Lim

  2. DSO National Laboratories, 20 Science Park Drive, Singapore, Singapore, 118230

    Q. W. Ho

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  1. Y. T. Ng
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  2. S. C. Luo
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  3. T. T. Lim
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Correspondence to Y. T. Ng.

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Ng, Y.T., Luo, S.C., Lim, T.T. et al. On swirl development in a square cross-sectioned, S-shaped duct. Exp Fluids 41, 975–989 (2006). https://doi.org/10.1007/s00348-006-0216-8

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  • DOI: https://doi.org/10.1007/s00348-006-0216-8

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