Abstract
This experimental study concerns the characteristics of vortex flow in a concentric annulus with a diameter ratio of 0.52, whose outer cylinder is stationary and inner one is rotating. Pressure losses and skin friction coefficients have been measured for fully developed flows of water and of 0.4% aqueous solution of sodium carboxymethyl cellulose (CMC), respectively, when the inner cylinder rotates at the speed of 0-600 rpm. Also, the visualization of vortex flows has been performed to observe the unstable waves. The results of present study reveal the relation of the bulk flow Reynolds number Re and Rossby number Ro with respect to the skin friction coefficients. In somehow, they show the existence of flow instability mechanism. The effect of rotation on the skin friction coefficient is significantly dependent on the flow regime. The change of skin friction coefficient corresponding to the variation of rotating speed is large for the laminar flow regime, whereas it becomes smaller as Re increases for the transitional flow regime and, then, it gradually approach to zero for the turbulent flow regime. Consequently, the critical (bulk flow) Reynolds number Rec decreases as the rotational speed increases. Thus, the rotation of the inner cylinder promotes the onset of transition due to the excitation of Taylor vortices.
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Abbreviations
- Cf :
-
Skin friction coefficient
- Cf,R :
-
Skin friction coefficient with rotation
- Cf,s :
-
Skin friction coefficient without rotation
- C* f :
-
Relative skin friction coefficient (see Eq.(6))
- Dn :
-
Hydraulic diameter, 2(R2-R1)
- dp/dz:
-
Pressure loss (Pa/m)
- e:
-
Eccentricity (mm)
- m:
-
Ratio of the eccentricity to the difference of radius
- N:
-
Rotational speed (rpm)
- △P:
-
Difference of pressure (Pa)
- R1 :
-
Radius of inner cylinder (mm)
- R2 :
-
Radius of outer cylinder (mm)
- Re:
-
Bulk flow Reynolds number, v―zDn/v
- Rec :
-
Critical Reynolds number
- Rel,t :
-
Reynolds number discriminating laminar-Taylor vortex regime and pure laminar regime
- Reω :
-
Rotational Reynolds number, ωR1(R2-R1)/v
- Ro:
-
Rossby number, 2v―z/ωR1
- vz :
-
Velocity in the z-direction (m/s)
- △z:
-
Distance between pressure taps (mm)
- η:
-
Ratio of radius, R1/R2
- λ:
-
Wavelength (mm)
- μ:
-
Absolute viscosity (Pa⋅s)
- υ:
-
Kinematic viscosity (m2/s)
- ρ:
-
Density of fluid (kg/m3)
- ω:
-
Angular velocity of rotating cylinder (rad/s)
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Kim, YJ., Hwang, YK. Experimental study on the vortex flow in a concentric annulus with a rotating inner cylinder. KSME International Journal 17, 562–570 (2003). https://doi.org/10.1007/BF02984457
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DOI: https://doi.org/10.1007/BF02984457