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Numerical Instability Analysis of the Rotating Boundary-Layer flow Including Pre-Swirl

예선회가 존재하는 회전유동장의 불안정성 수치해석

  • 황영규 (성균관대학교 기계공학부) ;
  • 이윤용 (성균관대학교 기계기술연구소) ;
  • 이광원 (성균관대학교 대학원 기계공학부)
  • Published : 2003.04.01

Abstract

The hydrodynamic instability of the three-dimensional boundary-layer over a rotating disk has been numerically investigated for these flows; Ro = -1, -0.5, and 0, using linear stability theory. Detailed numerical values of the disturbance wave number. wave frequency. azimuth angle. radius (Reynolds number, Re) and other characteristics have been calculated for the pre-swirl flows. On the basis of Ekman and Karman boundary layer theory, the instability of the pre-swirl flows have been investigated for the unstable criteria. The disturbance will be relatively fast amplified at small fe and within wide bands of wave number compared with previously known Karman boundary-layer results. The flow (Ro =-0.5) is found to be always stable for a disturbance whose dimensionless wave number is greater than 0.9. It has a larger range of unstable interval than Karman boundary layer and can be unstable at smaller Re.

Keywords

References

  1. Faller, A. J., 1991, 'Instability and Transition of Disturbed Flow over a Rotationg Disk,' J. Fluid Mech., Vol. 230, pp. 245-269 https://doi.org/10.1017/S0022112091000782
  2. Lingwood, R. J., 1997, 'Absolute Instability of the Ekman Layer and Related Rotating Flows,' J. Fluid Mech., Vol. 331, pp. 405-428 https://doi.org/10.1017/S0022112096004144
  3. Malik, M. R., Wilkinson, S. P., Orszag, S. A., 1981, 'Instability and Transition in Rotating Disk Flow,' AIAA Journal, Vol. 19, No. 9, pp. 1131-1138 https://doi.org/10.2514/3.7849
  4. Kang, K., Kim, S.-C., Hwng,Y.-K., Park, E. T. and Kim, C. J., 1995, 'The Neutral Stability of Rotating Disk Flows,' Proceeding of the KSME Thermal & Fluid Engineering Division, KSME, pp. 146-150(in Korean)
  5. Hwang, Y.-K. and Lee, Y.-Y., 2000, 'Theoretical Flow Instability of the Kaman Boundary Layer,' KSME International J., Vol. 14, No. 3, pp.358-368 https://doi.org/10.1007/BF03186429
  6. Wilkinson, S. P., Blanchard, A. E., Selby, G., Gaster, M., Triz, T., and Gad-el-Hak, M., 1990, 'Flow Visualization of Wave-Packet in a Rotating Disk,' Instability and Transition, ed. Hussaini, M. Y. and Voigt, K. G., Vol. 1, Springer-Verlag, pp. 306-318
  7. Wimmer, M., 1989, 'Classification of Laminar-Turbulent Transition near Rotating Bodies,' Laminar-Turbulent Transition, in Proc. IUTAM Symposiuim on Laminar-Turbulent Transition, ed. Arnal, D. and Michel, R., Springer-Verlag, pp. 545-550
  8. Lingwood, R. J., 1996, 'An Experimental Study of Absolute Instability of the Rotationg Disk Boundary Layer Flow', J. Fluid Mech., Vol. 314, pp. 373-405 https://doi.org/10.1017/S0022112096000365
  9. Nino, H., 1988, 'Inertial instability of the Stewarson $E^{1/4}$-layer,' Fluid Dynamics Research, Vol.3, pp. 407-414 https://doi.org/10.1016/0169-5983(88)90101-3
  10. Bader, G. and Ascher, U., 1985, 'A New Basis Implementation for a Mixed Order Boundary O.D.E. Solver,' Tech. Rep. 85-11, Dept. of Computer Science, U. of British Columbia, Vancouver, Canada