Abstract
Hot-wire measurements of the full mapping of the velocity and Reynolds stress components are reported for developing turbulent flow in a strongly curved 180 deg pipe and its tangents. A slanted wire is rotated into 6 orientations and the voltage outputs from wires are combined to obtain the mean velocity and Reynolds stress components. The strength of secondary flow reaches up to the 28% of bulk mean velocity. The strong counter-rotating vortex pair induced by the transverse pressure gradient and centrifugal force imbalance grows up to Θ = 67.5° into the bend. But the vortex pair breaks down into two cell pattern after Θ=90° Core vortex formation and reversal of secondary flow direction along the bend symmetry plane is cleanly found in the secondary vector plot. At Θ=67.5° and Θ = 90° into bend a large “trough” develops in the longitudinal velocity toward the inside of the bend due to the breakdown of secondary flow. In the bend, the mean longitudinal velocity component changes little after Θ=90°, but secondary flow never achieves fully-developed state. Similar behaviors are observed in the radial and circumferential stresses.
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Abbreviations
- D:
-
Diameter of pipe
- D n :
-
Dean number =Re(D/Rc)1/2
- E:
-
Instantaneous voltage of hot-wire
- e:
-
Fluctuating voltage of hot-wire
- \(k_{\theta _i } \) :
-
Coefficient of hot-wire orientatation
- \(K_{E_i E_j } \) :
-
Covariance between wiresi andj
- K s :
-
Coefficient of hot-wire characteristics
- R c :
-
Radius of duct curvature
- Re:
-
Reynolds number (=WBDH/v)
- u:
-
Circumferential fluctuating velocity
- U:
-
Circumferential mean velocity component
- U e :
-
Effective velocity
- Ū i Ū j :
-
Reynolds stress tensor
- V:
-
Radial mean velocity component
- v:
-
Radial fluctuating velocity
- V λ :
-
Resultant velocity vector
- W:
-
Stream-wise mean velocity component
- W B :
-
Stream-wise bulk velocity
- w:
-
Stream-wise fluctuating velocity
- X:
-
Stream-wise coordinate
- \(\bar X_\theta \) :
-
Mean effective velocity
- r:
-
Radial coordinate
- \(\gamma _{E_i E_J } \) :
-
Correlation coefficient between cooling velocities of adjacent wire orientations
- Θ:
-
Rotation angle of hot-wire, bend angle from entrance
- k:
-
Experimental constant
- ν:
-
Kinetic viscosity
- ξ:
-
Angle between Vλ and a wire
- ρ:
-
Density
- σ2 :
-
Variance of a given quantity
- φ:
-
Circumferential angle from outer most radius of bend curvature, circumferential coordinate
- l, m :
-
Dummy indices which take the valves 1 to 3
- 1,2,3,4,5,6:
-
Refers to the six probe measuring positions
- Θ:
-
Rotation angle of hot-wire, bend angle
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Lee, G.H., Choi, Y.D. & Han, S.H. Measurement of developing turbulent flow in a U-bend of circular cross-section. J Mech Sci Technol 21, 348–359 (2007). https://doi.org/10.1007/BF02916295
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DOI: https://doi.org/10.1007/BF02916295