Study on Performance of Laminar Taylor-Couette Flow with Different Developed Procedures

ABSTRACT

The performance of laminar Taylor-Couette flow with different developed procedures is studied by the way of computational fluid dynamics (CFD) in steady state. In order to gain a group of developed procedure in CFD, a set of convergent solutions are used as the initial value of next boundary condition, and the new set of convergent solutions are regarded as developing from the previous steady state. Three groups of developed procedures are gained from the rotating speed series of inner cylinder, respectively from the gradual increase procedure (GIP), the gradual decrease procedure (GDP) and the sudden increase procedure (SIP). It is proved that the convergent solutions of fluid control equations are different when they are solved from laminar state with the same boundary condition, the same fluid property, the same mesh grid in CFD and the same business software except that the flow states have developed from the procedures of GDP, GIP and SIP. It is shown that the developed procedure could leave behind some information in the performance of the flow. In other words, the flow between concentric rotating cylinders has somewhat memory for the procedure of its history.

The performance of laminar Taylor-Couette flow with different developed procedures is studied by the way of computational fluid dynamics (CFD) in steady state. In order to gain a group of developed procedure in CFD, a set of convergent solutions are used as the initial value of next boundary condition, and the new set of convergent solutions are regarded as developing from the previous steady state. Three groups of developed procedures are gained from the rotating speed series of inner cylinder, respectively from the gradual increase procedure (GIP), the gradual decrease procedure (GDP) and the sudden increase procedure (SIP). It is proved that the convergent solutions of fluid control equations are different when they are solved from laminar state with the same boundary condition, the same fluid property, the same mesh grid in CFD and the same business software except that the flow states have developed from the procedures of GDP, GIP and SIP. It is shown that the developed procedure could leave behind some information in the performance of the flow. In other words, the flow between concentric rotating cylinders has somewhat memory for the procedure of its history.

Cite this paper

X. Zhou, Y. Shi and Y. Kong, "Study on Performance of Laminar Taylor-Couette Flow with Different Developed Procedures,"*Modern Mechanical Engineering*, Vol. 2 No. 1, 2012, pp. 14-23. doi: 10.4236/mme.2012.21003.

X. Zhou, Y. Shi and Y. Kong, "Study on Performance of Laminar Taylor-Couette Flow with Different Developed Procedures,"

References

[1] G. I. Taylor, “Stability of a Viscous Liquid Contained Between Two Rotating Cylinders,” Philosophical Translations of the Royal Society A, Vol. 223, No. 605-615, 1923, pp. 289-343. doi:10.1098/rsta.1923.0008

[2] P. A. Drazin and W. H. Reid, “Hydrodynamic Stabilit,” Cambridge University Press, New York, 1981.

[3] M. Renardy, Y. Renardy, R. Sureshkumar and A. N. Beris, “Hopf-Hopf and Steady-Hopf Mode Interactions in Taylor-Couette Flow of an Upper Convected Maxwell Liquid,” Journal Non-Newtonian Fluid Mechanics, Vol. 63, No. 1, 1996, pp. 1-31. doi:10.1016/0377-0257(95)01415-2

[4] D. G. Thomas, B. Khomami and R. Sureshkumar, “Nonlinear Dynamics of Vis-coelastic Taylor-Couette Flow: Effect of Elasticity on Pattern Selection, Molecular Conformation and Drag,” Journal of Fluid Mechanics, Vol. 620, 2009, pp. 353-382. doi: 10.1017/S0022112008004710

[5] Andrew Hill and Ian Stewart, “Hopf-Steady-State Mode Interactions with O (2) Symmetry,” Dynamics and Stability of Systems, Vol. 6, No. 2, 1991, pp. 149-171. doi:10.1080/02681119108806113

[6] J. Parker and P. Merati, “Investigation of Turbulent Taylor-Couette Flow Using Laser Doppler Velocimetry in a Refractive Index Matched Facility,” Journal of Fluids Engineering, Vol. 118, No. 4, 1996, pp. 810-818. doi:10.1115/1.2835513

[7] H. A. Snyder, “Change in Wave-Form and Mean Flow Associated with Wavelength Variation in Rotating Couette Flow Part 1,” Journal of Fluid Mechanics, Vol. 35, No. 2, 1969, pp. 337-352. dio:10.1017/S0022112069001145

[8] V. Sobolik, B. Izrar, F. Lusseyran and S. Skali, “Interaction between the Ekman Layer and the Couette-Taylor Instability,” International Journal of Heat and Mass Transfer, Vol. 43, No. 24, 2000, pp. 4381-4393. doi:10.1016/S0017-9310(00)00067-3

[9] E. L. Koschmieder, “Turbulent Taylor Vortex Flow,” Journal Fluid Mechanics, Vol. 93, No. 3, 1979, pp. 515-527. doi:10.1017/S0022112079002639

[10] C. D. Andereck, S. S. Liu and H. L. Swinney, “Flow Regimes in a Circular Couette System with Independently Rotating Cylinders,” Journal Fluid Mechanics, Vol. 164, No. 3, 1986, pp. 155-183. doi:10.1017/S0022112086002513

[11] R. J. Cornish, “Flow of Water Through Fine Clearance with Relative Motion of the Boundaries,” Proceedings of the Royal Society A, Vol. 140, No. 840, 1933, pp. 227-240. doi:10.1098/rspa.1933.0065

[12] T. W. Steven and M. L. Richard, “Spatio-Temporal Character of Non-Wavy and Wavy Taylor-Couette Flow,” Journal Fluid Mechanics, Vol. 364, 1998, pp. 59-80. doi:10.1017/S0022112076000098

[13] J. A. Cole, “Taylor Vortex Instability and Annulus-Length Effects,” Journal of Fluid Mechanics, Vol. 75, No. 1, 1976, pp. 1-15. doi:10.1017/S0022112076000098

[14] J. E. Burkhalter and E. L. Koschmieder, “Steady Supercritical Taylor Vortices after Sudden Starts,” Physics of Fluids, Vol. 17, No. 11, 1974, pp. 1929-1935. doi:10.1063/1.1694646

[1] G. I. Taylor, “Stability of a Viscous Liquid Contained Between Two Rotating Cylinders,” Philosophical Translations of the Royal Society A, Vol. 223, No. 605-615, 1923, pp. 289-343. doi:10.1098/rsta.1923.0008

[2] P. A. Drazin and W. H. Reid, “Hydrodynamic Stabilit,” Cambridge University Press, New York, 1981.

[3] M. Renardy, Y. Renardy, R. Sureshkumar and A. N. Beris, “Hopf-Hopf and Steady-Hopf Mode Interactions in Taylor-Couette Flow of an Upper Convected Maxwell Liquid,” Journal Non-Newtonian Fluid Mechanics, Vol. 63, No. 1, 1996, pp. 1-31. doi:10.1016/0377-0257(95)01415-2

[4] D. G. Thomas, B. Khomami and R. Sureshkumar, “Nonlinear Dynamics of Vis-coelastic Taylor-Couette Flow: Effect of Elasticity on Pattern Selection, Molecular Conformation and Drag,” Journal of Fluid Mechanics, Vol. 620, 2009, pp. 353-382. doi: 10.1017/S0022112008004710

[5] Andrew Hill and Ian Stewart, “Hopf-Steady-State Mode Interactions with O (2) Symmetry,” Dynamics and Stability of Systems, Vol. 6, No. 2, 1991, pp. 149-171. doi:10.1080/02681119108806113

[6] J. Parker and P. Merati, “Investigation of Turbulent Taylor-Couette Flow Using Laser Doppler Velocimetry in a Refractive Index Matched Facility,” Journal of Fluids Engineering, Vol. 118, No. 4, 1996, pp. 810-818. doi:10.1115/1.2835513

[7] H. A. Snyder, “Change in Wave-Form and Mean Flow Associated with Wavelength Variation in Rotating Couette Flow Part 1,” Journal of Fluid Mechanics, Vol. 35, No. 2, 1969, pp. 337-352. dio:10.1017/S0022112069001145

[8] V. Sobolik, B. Izrar, F. Lusseyran and S. Skali, “Interaction between the Ekman Layer and the Couette-Taylor Instability,” International Journal of Heat and Mass Transfer, Vol. 43, No. 24, 2000, pp. 4381-4393. doi:10.1016/S0017-9310(00)00067-3

[9] E. L. Koschmieder, “Turbulent Taylor Vortex Flow,” Journal Fluid Mechanics, Vol. 93, No. 3, 1979, pp. 515-527. doi:10.1017/S0022112079002639

[10] C. D. Andereck, S. S. Liu and H. L. Swinney, “Flow Regimes in a Circular Couette System with Independently Rotating Cylinders,” Journal Fluid Mechanics, Vol. 164, No. 3, 1986, pp. 155-183. doi:10.1017/S0022112086002513

[11] R. J. Cornish, “Flow of Water Through Fine Clearance with Relative Motion of the Boundaries,” Proceedings of the Royal Society A, Vol. 140, No. 840, 1933, pp. 227-240. doi:10.1098/rspa.1933.0065

[12] T. W. Steven and M. L. Richard, “Spatio-Temporal Character of Non-Wavy and Wavy Taylor-Couette Flow,” Journal Fluid Mechanics, Vol. 364, 1998, pp. 59-80. doi:10.1017/S0022112076000098

[13] J. A. Cole, “Taylor Vortex Instability and Annulus-Length Effects,” Journal of Fluid Mechanics, Vol. 75, No. 1, 1976, pp. 1-15. doi:10.1017/S0022112076000098

[14] J. E. Burkhalter and E. L. Koschmieder, “Steady Supercritical Taylor Vortices after Sudden Starts,” Physics of Fluids, Vol. 17, No. 11, 1974, pp. 1929-1935. doi:10.1063/1.1694646