Abstract
The flow generated by the rotation of the disk in a stationary cylindrical casing is investigated by the numerical and experimental approaches. When the rotating disk has finite radius and thickness, there exists the axial gap between the disk surface and the end wall of the casing and the radial gap between the disk tip and the side wall of the casing. The flows in these gaps show complex flow structures depending on the geometric and kinetic parameters. In this study, five disks with different radii are introduced and the effects of the radial gap width and the Reynolds number on the flow structures are investigated. The flow with steady Taylor vortices emerges in the radial gap at relatively low Reynolds numbers. When the Reynolds number is moderate, Taylor vortices in the radial gap have the wavy structures in the azimuthal direction. The flow with the wavy structure is classified into two types: one is the normal mode and the other is the anomalous mode. The latter type has the extra vortices at the corner of the casing. At the higher Reynolds numbers, the turbulent Taylor vortices appear in the radial gap. In this case, the disturbances in the radial gap propagate inward along the end walls of the casing and the spiral vortices occur near the disk tip in the upper and lower axial gaps. The dependency of the flow structure on the radial gap width is clarified.
Graphical abstract
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- r, θ, z :
-
Cylindrical coordinates
- r d :
-
112, 117, 122, 127 and 132 mm, radius of the rotating disk
- r c :
-
142 mm, radius of the cylindrical casing
- r s :
-
10 mm, radius of the shaft
- h d :
-
30 mm, thickness of the rotating disk
- h c :
-
40 mm, height of the cylindrical casing
- h l :
-
5 mm, lower axial gap
- h u :
-
5 mm, upper axial gap
- Γ :
-
= h c/(r c−r d), aspect ratio of the radial gap
- ω :
-
Angular velocity of the rotating disk
- ν :
-
Kinematic viscosity of the fluid
- Re :
-
\(= \omega \,{{r_{\text{d}}^{2} } \mathord{\left/ {\vphantom {{r_{\text{d}}^{2} } \nu }} \right. \kern-0pt} \nu }\), rotational Reynolds number
- u :
-
= (u, v, w)T, flow velocity
- p :
-
Pressure
- t :
-
Time
- w mean :
-
Azimuthally averaged axial velocity component
- \(e_{r\theta } ,\,e_{\theta z} ,\,e_{zr}\) :
-
Components of the velocity strain rate
- Q :
-
Second invariant of the velocity gradient tensor
References
Aubry N, Chauve MP, Guyonnet R (1994) Transition to turbulence on a rotating flat disk. Phys Fluids 6(8):2800–2814. doi:10.1063/1.868168
Benjamin TB, Mullin T (1981) Anomalous Modes in the Taylor Experiment. Proc R Soc London Ser A Mathe Phys Sci 377(1770):221–249. doi:10.1098/rspa.1981.0122
Cros A, Le Gal P (2002) Spatiotemporal intermittency in the torsional Couette flow between a rotating and a stationary disk. Phys Fluids 14(11):3755–3765. doi:10.1063/1.1508796
Cros A, Floriani E, Le Gal P, Lima R (2005) Transition to turbulence of the batchelor flow in a rotor/stator device. Eur J Mech B/Fluids 24:409–424. doi:10.1016/j.euromechflu.2004.11.002
Dong S (2007) Direct numerical simulation of turbulent Taylor-Couette flow. J Fluid Mech 587:373–393. doi:10.1017/S0022112007007367
Guermond JL, Migeon C, Pineau G, Quartapelle L (2002) Start-up flows in a three-dimensional rectangular driven cavity of aspect ratio 1:1:2 at Re = 1000. J Fluid Mech 450:169–199. doi:10.1017/S0022112001006383
Hendriks F (2010) On Taylor vortices and Ekman layers in flow-induced vibration of hard disk drives. Microsyst Technol 16:93–101. doi:10.1007/s00542-008-0765-2
Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285:69–94. doi:10.1017/S0022112095000462
Launder B, Poncet S, Serre E (2010) Laminar, transitional and turbulent flows in rotor-stator Cavities. Annu Rev Fluid Mech 42:229–248. doi:10.1146/annurev-fluid-121108-145514
Meeuwse M, van der Schaaf J, Schouten JC (2012) Multistage rotor-stator spinning disc reactor. AIChE J 58(1):247–255. doi:10.1002/aic.12586
Nakamura I, Toya Y (1996) Existence of extra vortex and twin vortex of anomalous mode in Taylor vortex flow with a small aspect ratio. Acta Mech 117(1–4):33–46. doi:10.1007/BF01181035
Nakamura I, Toya Y, Yamashita S, Ueki Y (1989) An experiment on a Taylor vortex flow in a gap with a small aspect ratio (instability of Taylor vortex flows). JSME Int J Ser 2 32(3):388–394
Schouveiler L, Le Gal P, Chauve MP (1998) Stability of a traveling roll system in a rotating disk flow. Phys Fluids 10(11):2695–2697. doi:10.1063/1.869793
Schouveiler L, Le Gal P, Chauve MP (2001) Instabilities of the flow between a rotating and a stationary disk. J Fluid Mech 443:329–350. doi:10.1017/S0022112001005328
Washizu T, Lubisch F, Obi S (2013) LES study of flow between shrouded co-rotating disks. Flow Turbul Combust 91:607–621. doi:10.1007/s10494-013-9494-4
Watanabe T, Furukawa H (2010a) Flows around rotating disk with and without rim-shroud gap. Exp Fluids 45(4):631–636. doi:10.1007/s00348-009-0785-4
Watanabe T, Furukawa H (2010b) The effect of rim-shroud gap on the spiral rolls formed around a rotating disk. Phys Fluids 22(11):1140107. doi:10.1063/1.3493640
Wu SC (2009) A PIV study of co-rotating disks flow in a fixed cylindrical enclosure. Exp Thermal Fluid Sci 33:875–882. doi:10.1016/j.expthermflusci.2009.03.008
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hara, S., Watanabe, T., Furukawa, H. et al. Effects of a radial gap on vortical flow structures around a rotating disk in a cylindrical casing. J Vis 18, 501–510 (2015). https://doi.org/10.1007/s12650-015-0292-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12650-015-0292-z