Development and Flow Modes of Vertical Taylor-Couette System with Free Surface

Affiliation(s)

Graduate School of Information Science, Nagoya University, Nagoya, Japan.

Department of Mechanical Engineering, Nagano National College of Technology, Nagano, Japan.

Graduate School of Information Science, Nagoya University, Nagoya, Japan.

Department of Mechanical Engineering, Nagano National College of Technology, Nagano, Japan.

ABSTRACT

We have numerically and experimentally investigated the flow modes of Taylor-Couette system consisting of coaxial two cylinders with vertical axes. The inner cylinder rotates and the outer cylinder and the bottom end of the cylinders remain stationary. The upper top boundary is the free surface of the working liquid between the inner and outer cylinders and it contacts with the air. While this flow appears in fluid machinery and chemical reactors and includes industrial interests, it also contains problems of fluid mechanics, which is about the behavior of the free surface in the rotating field. In this paper, we concretely show the developments of the one cell mode flow and the three cell mode flow at a small aspect ratio. We also represent the bifurcation diagram of the flow at the moderate aspect ratio about 5.5. In the numerical simulation, the flow is rest in the initial state, and the inner cylinder is linearly or suddenly accelerated to attain a flow with a prescribed Reynolds number. When the acceleration of the inner cylinder is high, an imperfect bifurcation occurs and the flows of the secondary modes emerge. At high Reynolds numbers, the flow first has many vortices and then some of the vortices collapse and the final stable flow arises. The loci of the normal five cell mode, the anomalous six cell mode and the secondary seven cell mode are determined.

KEYWORDS

Taylor-Couette System; Vertical Cylinders; Free Surface; Flow Mode; Mode Transition; Bifurcation

Taylor-Couette System; Vertical Cylinders; Free Surface; Flow Mode; Mode Transition; Bifurcation

Cite this paper

Watanabe, T. , Toya, Y. and Hara, S. (2014) Development and Flow Modes of Vertical Taylor-Couette System with Free Surface.*World Journal of Mechanics*, **4**, 90-96. doi: 10.4236/wjm.2014.43010.

Watanabe, T. , Toya, Y. and Hara, S. (2014) Development and Flow Modes of Vertical Taylor-Couette System with Free Surface.

References

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[2] Benjamin, T.B. (1978) Bifurcation Phenomena in Steady Flows of a Viscous Fluid: II. Experiments. Proceedings of the Royal Society A, 359, 27-43. http://dx.doi.org/10.1098/rspa.1978.0030

[3] Cole, J.A. (1976) Taylor-vortex Instability and Annulus-Length Effects. Journal of Fluid Mechanics, 75, 1-15.

http://dx.doi.org/10.1017/S0022112076000098

[4] Ammar, M., Ahcène, B. and Eddine, S.S. (2005) écoulement de Taylor-Couette en Géométrie Fine et à Surface Libre. The Canadian Journal of Chemical Engineering, 83, 652-657.

[5] Deng, R., Arifin, D.Y., Mak, Y.C. and Wang, C.-H. (2009) Characterization of Taylor Vortex Flow in a Short Liquid Column. AIChE Journal, 55, 3056-3064. http://dx.doi.org/10.1002/aic.11919

[6] Caton, F., Jniaud, B. and Hopfinger, E.J. (2000) Stability and Bifurcations in Stratified Taylor-Couette Flow. Journal of Fluid Mechanics, 419, 93-124. http://dx.doi.org/10.1017/S0022112000001348

[7] Ermanyuk, E.V. and Flór, J.-B. (2005) Taylor-Couette Flow in a Two-layer Stratified Fluid: Instabilities and Mixing. Dynamics of Atmospheres and Oceans, 40, 57-69. http://dx.doi.org/10.1016/j.dynatmoce.2004.10.005

[8] Woods, A.W., Caulfield, C.P., Landel, J.R. and Kuesters, A. (2010) Non-Invasive Turbulent Mixing across a Density Interface in a Turbulent Taylor-Couette Flow. Journal of Fluid Mechanics, 663, 347-357.

http://dx.doi.org/10.1017/S0022112010004295

[9] Oglethorpe, R.L.F., Caulfield, C.P. and Woods, A.W. (2013) Spontaneous Layering in Stratified Turbulent Taylor-Couette Flow. Journal of Fluid Mechanics, 721, R3-1-12.

[10] Djéridi, H., Favé, J.-F., Billard, J.-Y. and Fruman, D.H. (1999) Bubble Capture and Migrationin Couette-Taylor Flow. Experiments in Fluids, 26, 233-239. http://dx.doi.org/10.1007/s003480050284

[11] Djéridi, H., Gabillet, C. and Billard, J.Y. (2004) Two-phase Couette-Taylor Flow: Arrangement of the Dispersed Phase and Effects on the Flow Structures. Physics of Fluids, 16, 128-139. http://dx.doi.org/10.1063/1.1630323

[12] Atkhen, K., Fontaine, J. and Wesfreid, J.E. (2000) Highly Turbulent Couette-Taylor Bubbly Flow Patterns, Journal of Fluid Mechanics, 442, 55-68. http://dx.doi.org/10.1017/S0022112000001592

[13] Sugiyama, K., Calzavarini, E. and Lohse, D. (2008) Microbubbly Drag Reduction in Taylor-Couette Flow in the Wavy Vortex Regime. Journal of Fluid Mechanics, 608, 21-41. http://dx.doi.org/10.1017/S0022112008001183

[14] Nakamura, I., Toya, Y., Yamashita, S. and Ueki, Y. (1990) An Experiment on a Taylor Vortex Flow in a Gap with a Small Aspect Ratio (Bifurcation of Flows in a Symmetric System). JSME International Journal. Series II, 33, 685-691.

[15] Nakamura, I., Toya, Y., Yamashita, S. and Ueki, S. (1989) An experiment on a Taylor Vortex Flow in a Gap with a Small Aspect Ratio (Instability of Taylor Vortex Flows). JSME International Journal. Series II, 23, 388-394.

[16] Toya, Y., Nakamura, I., Yamashita, S. and Ueki, S. (1994) An Experiment on a Taylor Vortex Flow in a Gap with a Small Aspect Ratio: Bifuration of Flows in an Asymmetric system. Acta Mechanica, 102, 137-148.

http://dx.doi.org/10.1007/BF01178523

[17] Linek, M. and Ahlers, G. (1998) Boundary Limitation of Wave Numbers in Taylor-vortex Flow. Physical Review E, 58, 3168-3174. http://dx.doi.org/10.1103/PhysRevE.58.3168

[18] Watanabe, T. and Toya, Y. (2012) Vertical Taylor-Couette Flow with Free Surface at Small Aspect Ratio. Acta Mechanica, 222, 347-353. http://dx.doi.org/10.1007/s00707-011-0569-9

[19] Nakase, M., Makabe, R. and Takeshita, K. (2013) Relation between Oil-Water Flow and Extraction Performance in Liquid-Liquid Countercurrrent Centrifugal Extractor with Taylor Vortices. Journal of Nuclear Science and Technology, 50, 287-295. http://dx.doi.org/10.1080/00223131.2013.772445

[20] Watanabe, T., Furukawa, H. and Nakamura, I. (2002) Nonlinear Development of Flow Patterns in an Annulus with Decelerating Inner Cylinder. Physics of Fluids, 14, 333-341. http://dx.doi.org/10.1063/1.1416498

[1] Benjamin, T.B. (1978) Bifurcation Phenomena in Steady Flows of a Viscous Fluid: I. Theory. Proceedings of the Royal Society A, 359, 1-26. http://dx.doi.org/10.1098/rspa.1978.0028

[2] Benjamin, T.B. (1978) Bifurcation Phenomena in Steady Flows of a Viscous Fluid: II. Experiments. Proceedings of the Royal Society A, 359, 27-43. http://dx.doi.org/10.1098/rspa.1978.0030

[3] Cole, J.A. (1976) Taylor-vortex Instability and Annulus-Length Effects. Journal of Fluid Mechanics, 75, 1-15.

http://dx.doi.org/10.1017/S0022112076000098

[4] Ammar, M., Ahcène, B. and Eddine, S.S. (2005) écoulement de Taylor-Couette en Géométrie Fine et à Surface Libre. The Canadian Journal of Chemical Engineering, 83, 652-657.

[5] Deng, R., Arifin, D.Y., Mak, Y.C. and Wang, C.-H. (2009) Characterization of Taylor Vortex Flow in a Short Liquid Column. AIChE Journal, 55, 3056-3064. http://dx.doi.org/10.1002/aic.11919

[6] Caton, F., Jniaud, B. and Hopfinger, E.J. (2000) Stability and Bifurcations in Stratified Taylor-Couette Flow. Journal of Fluid Mechanics, 419, 93-124. http://dx.doi.org/10.1017/S0022112000001348

[7] Ermanyuk, E.V. and Flór, J.-B. (2005) Taylor-Couette Flow in a Two-layer Stratified Fluid: Instabilities and Mixing. Dynamics of Atmospheres and Oceans, 40, 57-69. http://dx.doi.org/10.1016/j.dynatmoce.2004.10.005

[8] Woods, A.W., Caulfield, C.P., Landel, J.R. and Kuesters, A. (2010) Non-Invasive Turbulent Mixing across a Density Interface in a Turbulent Taylor-Couette Flow. Journal of Fluid Mechanics, 663, 347-357.

http://dx.doi.org/10.1017/S0022112010004295

[9] Oglethorpe, R.L.F., Caulfield, C.P. and Woods, A.W. (2013) Spontaneous Layering in Stratified Turbulent Taylor-Couette Flow. Journal of Fluid Mechanics, 721, R3-1-12.

[10] Djéridi, H., Favé, J.-F., Billard, J.-Y. and Fruman, D.H. (1999) Bubble Capture and Migrationin Couette-Taylor Flow. Experiments in Fluids, 26, 233-239. http://dx.doi.org/10.1007/s003480050284

[11] Djéridi, H., Gabillet, C. and Billard, J.Y. (2004) Two-phase Couette-Taylor Flow: Arrangement of the Dispersed Phase and Effects on the Flow Structures. Physics of Fluids, 16, 128-139. http://dx.doi.org/10.1063/1.1630323

[12] Atkhen, K., Fontaine, J. and Wesfreid, J.E. (2000) Highly Turbulent Couette-Taylor Bubbly Flow Patterns, Journal of Fluid Mechanics, 442, 55-68. http://dx.doi.org/10.1017/S0022112000001592

[13] Sugiyama, K., Calzavarini, E. and Lohse, D. (2008) Microbubbly Drag Reduction in Taylor-Couette Flow in the Wavy Vortex Regime. Journal of Fluid Mechanics, 608, 21-41. http://dx.doi.org/10.1017/S0022112008001183

[14] Nakamura, I., Toya, Y., Yamashita, S. and Ueki, Y. (1990) An Experiment on a Taylor Vortex Flow in a Gap with a Small Aspect Ratio (Bifurcation of Flows in a Symmetric System). JSME International Journal. Series II, 33, 685-691.

[15] Nakamura, I., Toya, Y., Yamashita, S. and Ueki, S. (1989) An experiment on a Taylor Vortex Flow in a Gap with a Small Aspect Ratio (Instability of Taylor Vortex Flows). JSME International Journal. Series II, 23, 388-394.

[16] Toya, Y., Nakamura, I., Yamashita, S. and Ueki, S. (1994) An Experiment on a Taylor Vortex Flow in a Gap with a Small Aspect Ratio: Bifuration of Flows in an Asymmetric system. Acta Mechanica, 102, 137-148.

http://dx.doi.org/10.1007/BF01178523

[17] Linek, M. and Ahlers, G. (1998) Boundary Limitation of Wave Numbers in Taylor-vortex Flow. Physical Review E, 58, 3168-3174. http://dx.doi.org/10.1103/PhysRevE.58.3168

[18] Watanabe, T. and Toya, Y. (2012) Vertical Taylor-Couette Flow with Free Surface at Small Aspect Ratio. Acta Mechanica, 222, 347-353. http://dx.doi.org/10.1007/s00707-011-0569-9

[19] Nakase, M., Makabe, R. and Takeshita, K. (2013) Relation between Oil-Water Flow and Extraction Performance in Liquid-Liquid Countercurrrent Centrifugal Extractor with Taylor Vortices. Journal of Nuclear Science and Technology, 50, 287-295. http://dx.doi.org/10.1080/00223131.2013.772445

[20] Watanabe, T., Furukawa, H. and Nakamura, I. (2002) Nonlinear Development of Flow Patterns in an Annulus with Decelerating Inner Cylinder. Physics of Fluids, 14, 333-341. http://dx.doi.org/10.1063/1.1416498