Effects of Orbital Motion on the Boundary Layer Flow on a Spinning Disk

Affiliation(s)

Graduate School of Science and Technology, Kumamoto University, Kumamoto, Japan.

Mechanical Engineering Department, Kumamoto University, Kumamoto, Japan.

Graduate School of Science and Technology, Kumamoto University, Kumamoto, Japan.

Mechanical Engineering Department, Kumamoto University, Kumamoto, Japan.

ABSTRACT

The objective of this study is to experimentally examine the effects of orbital motion on the boundary layer flow on a spinning disk. The boundary layer flow on the disk is visualized by the oil flow method, and velocity in the boundary layer is measured by the hot-wire method. For the oil flow pattern in the case of spinning motion only, streaks are clearly observed on the disk as transient vortices, but by adding orbital motion to the spinning motion, we find that streaks are not observed in a certain range of orbital conditions. With increasing orbital motion speed, the laminar re- gion becomes narrower and transition is promoted from the inward region of the disk, regardless of the direction of ro- tation. Also, with the addition of orbital motion, the velocity profile in the boundary layer becomes more asymmetric with respect to the spin axis of the disk. Furthermore, stationary vortices do not appear on the disk when the orbital speed is beyond a certain critical value. Therefore, the lack of streaks in the oil film pattern when orbital motion is added is due to the spatiotemporal unsteadiness of the flow field on the disk.

The objective of this study is to experimentally examine the effects of orbital motion on the boundary layer flow on a spinning disk. The boundary layer flow on the disk is visualized by the oil flow method, and velocity in the boundary layer is measured by the hot-wire method. For the oil flow pattern in the case of spinning motion only, streaks are clearly observed on the disk as transient vortices, but by adding orbital motion to the spinning motion, we find that streaks are not observed in a certain range of orbital conditions. With increasing orbital motion speed, the laminar re- gion becomes narrower and transition is promoted from the inward region of the disk, regardless of the direction of ro- tation. Also, with the addition of orbital motion, the velocity profile in the boundary layer becomes more asymmetric with respect to the spin axis of the disk. Furthermore, stationary vortices do not appear on the disk when the orbital speed is beyond a certain critical value. Therefore, the lack of streaks in the oil film pattern when orbital motion is added is due to the spatiotemporal unsteadiness of the flow field on the disk.

Cite this paper

M. Munekata, N. Jobi, K. Ikebe and H. Yoshikawa, "Effects of Orbital Motion on the Boundary Layer Flow on a Spinning Disk,"*Open Journal of Fluid Dynamics*, Vol. 2 No. 4, 2012, pp. 187-194. doi: 10.4236/ojfd.2012.24A020.

M. Munekata, N. Jobi, K. Ikebe and H. Yoshikawa, "Effects of Orbital Motion on the Boundary Layer Flow on a Spinning Disk,"

References

[1] H. L. Reed and W. S. Saric, “Stability of Three-Dimensional Boundary Layers,” Annual Review of Fluid Mechanics, Vol. 21, No. 1, 1989, pp. 235-284. doi:10.1146/annurev.fl.21.010189.001315

[2] N. Gregory, J. T. Stuart and W. S. Walker, “On the Stability of Three-Dimensional Boundary Layers with Application to the Flow Due to a Rotating Disk,” Philosophical Transactions of the Royal Society, Vol. 248, No. 943, 1955, pp. 155-199. doi:10.1098/rsta.1955.0013

[3] Y. Kohama, “Study on Boundary Layer Transition of a Rotating Disk,” Acta Mechanica, Vol. 50, No. 3-4, 1984, pp. 193-199. doi:10.1007/BF01170959

[4] Y. Kohama, “Turbulent Transition Process of the Spiral Vortices Appearing in the Laminar Boundary Layer of a Rotating Cone,” PhysicoChemical Hydrodynamics, Vol. 6, No. 5-6, 1985, pp. 659-669.

[5] M. Munekata, S. Kimura, H. Kurishima, J. Tanaka, H., Yoshikawa, and H. Ohba, “Effect of the Catch Cup Geometry on the 3D Boundary Layer Flow over the Wafer Surface in a Spin Coating,” Journal of Thermal Science, Vol. 17, No. 1, 2008, pp. 56-60. doi:10.1007/s11630-008-0056-3

[6] S. Kimura, H. Yoshikawa, M. Munekata, H. Kurishima, S. Yamamoto and H. Ohba, “Effect of Spin-up Acceleration on Onset of Transient Vortices over Rotating Wafer,” Transactions of JSME, Series B, Vol. 74, No. 744, 2008, pp.1735-1740. doi: 10.1299/kikaib.74.1735

[7] I. Sawada, K. Matsuzaki, T. Tanaka, M. Iwashita and M. Munekata, “Spin Coater and Coating Method,” Japan Patent Kokai 2007-189185, 2007.

[8] M. R. Malik, S. P. Wilkinson and S. A. Orszag, “Instability and Transition in Rotating Disk Flow,” AIAA Journal, Vol. 19, No. 9, 1981, pp. 1131-1138.

[9] S. P. Wilkinson and M. R. Malik, “Stability Experiments in the Flow over a Rotating Disk,” AIAA Journal, Vol. 23, No. 4, 1983, pp. 588-595.

[10] H. Schlichting, “Boundary-Layer Theory,” McGraw-Hill, New York, 1955, pp. 83-89.

[11] S. Wahal, A. Oztekin, D. E. Bornside, R. A. Brown, P. K. Seidel, P. W. Ackmann and F. T. Geyling, “Visualization of a Gas Flow Instability in Spin Coating Systems,” Applied Physics Letters, Vol. 62, No. 20, 1993, pp. 25842586. doi:10.1063/1.109304.

[1] H. L. Reed and W. S. Saric, “Stability of Three-Dimensional Boundary Layers,” Annual Review of Fluid Mechanics, Vol. 21, No. 1, 1989, pp. 235-284. doi:10.1146/annurev.fl.21.010189.001315

[2] N. Gregory, J. T. Stuart and W. S. Walker, “On the Stability of Three-Dimensional Boundary Layers with Application to the Flow Due to a Rotating Disk,” Philosophical Transactions of the Royal Society, Vol. 248, No. 943, 1955, pp. 155-199. doi:10.1098/rsta.1955.0013

[3] Y. Kohama, “Study on Boundary Layer Transition of a Rotating Disk,” Acta Mechanica, Vol. 50, No. 3-4, 1984, pp. 193-199. doi:10.1007/BF01170959

[4] Y. Kohama, “Turbulent Transition Process of the Spiral Vortices Appearing in the Laminar Boundary Layer of a Rotating Cone,” PhysicoChemical Hydrodynamics, Vol. 6, No. 5-6, 1985, pp. 659-669.

[5] M. Munekata, S. Kimura, H. Kurishima, J. Tanaka, H., Yoshikawa, and H. Ohba, “Effect of the Catch Cup Geometry on the 3D Boundary Layer Flow over the Wafer Surface in a Spin Coating,” Journal of Thermal Science, Vol. 17, No. 1, 2008, pp. 56-60. doi:10.1007/s11630-008-0056-3

[6] S. Kimura, H. Yoshikawa, M. Munekata, H. Kurishima, S. Yamamoto and H. Ohba, “Effect of Spin-up Acceleration on Onset of Transient Vortices over Rotating Wafer,” Transactions of JSME, Series B, Vol. 74, No. 744, 2008, pp.1735-1740. doi: 10.1299/kikaib.74.1735

[7] I. Sawada, K. Matsuzaki, T. Tanaka, M. Iwashita and M. Munekata, “Spin Coater and Coating Method,” Japan Patent Kokai 2007-189185, 2007.

[8] M. R. Malik, S. P. Wilkinson and S. A. Orszag, “Instability and Transition in Rotating Disk Flow,” AIAA Journal, Vol. 19, No. 9, 1981, pp. 1131-1138.

[9] S. P. Wilkinson and M. R. Malik, “Stability Experiments in the Flow over a Rotating Disk,” AIAA Journal, Vol. 23, No. 4, 1983, pp. 588-595.

[10] H. Schlichting, “Boundary-Layer Theory,” McGraw-Hill, New York, 1955, pp. 83-89.

[11] S. Wahal, A. Oztekin, D. E. Bornside, R. A. Brown, P. K. Seidel, P. W. Ackmann and F. T. Geyling, “Visualization of a Gas Flow Instability in Spin Coating Systems,” Applied Physics Letters, Vol. 62, No. 20, 1993, pp. 25842586. doi:10.1063/1.109304.