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KSME international journal v.17 no.9, 2003년, pp.1388 - 1396   피인용횟수: 2

The Flow Instability Over the Infinite Rotating Disk

Lee, Yun-Yong   (School of Mechanical Engineering, Sungkyunkwan UniversityUU0000759  ); Hwang, Young-Kyu   (School of Mechanical Engineering, Sungkyunkwan UniversityUU0000759  ); Lee, Kwang-Won   (School of Mechanical Engineering, Sungkyunkwan UniversityUU0000759  );
  • 초록

    The hydrodynamic instability of the three-dimensional boundary layer on a rotating disk introduces a periodic modulation of the mean flow in the form of stationary cross flow vortices. The instability labeled Type II by Faller occurs first at lower Reynolds number than that of well known Type I instability. Detailed numerical values of the amplification rates, neutral curves and other characteristics of the two instabilities have been calculated over a wide range of parameters. Presented are the neutral stability results concerning the two instability modes by solving the appropriate linear stability equations reformulated not only by considering whole convective terms but also by correcting some errors in the previous stability equations. The present stability results agree with the previously known ones within reasonable limit. Consequently, the flow is found to be always stable for a disturbance whose dimensionless wave number is greater than 0.75. Some spatial amplification contours have been computed for the stationary disturbance wave, whose azimuth angle $\varepsilon$ = 11.29<TEX>$ 11.29 $^{\circ}$ to 15 $^{\circ}$ and for the moving disturbance wave, whose azimuth angle $\varepsilon$ = 12.5<TEX>$^ 12.5 $^{\circ}$ to 15 $^{\circ}$ . Also, some temporal amplification contours have been computed for the stationary disturbance wave, whose azimuth angle $\varepsilon$ = 11.29<TEX>$ 11.29 $^{\circ}$ to 15 $^{\circ}$ and for the moving disturbance wave, whose azimuth angle $\varepsilon$ = 12<TEX>$^{\ 12 $^{\circ}$ to 15 $^{\circ}$ . The flow instability was observed by using a white titanium tetrachloride gas over rotating disk system. When the numerical results are compared to the present experimental data, the numerical results agree quantitatively, indicating the existence of the selective frequency mechanism.


  • 주제어

    Karman boundary-layer flow .   Flow Instability .   Rotating disk .   Spatial Amplification .   Temporal Amplification.  

  • 참고문헌 (18)

    1. Wilkinson, S. P. and Malik, M. R., 1985, 'Stability Experiments in the Flow over a Rotating Disk,' AIAA Journal, Vol. 23, No.4, pp.588-595 
    2. Sparrow, E. M. and Gregg, J. L., 1960, 'Mass Transfer, Flow and Heat Transfer about a Rotating Disk,' Transactions ASME, J. Heat Transfer, Vol. 82, pp.294-302 
    3. Smith, N. H., 1947, 'Exploratory Investigation of Boundary Layer Oscillations on a Rotating Disk,' NACA Tech. Note 1227 
    4. von Karman, T, 1921, 'Uber Laminare und Turbulente Reibung,' Z. Angew. Math. Mech., Vol. 1, pp.233-252 
    5. Lilly, D. K., 1966, 'On the Instability of Ekman Boundary Flow,' J. of the Atmospheric Science, Vol. 23, pp.481-494 
    6. Malik, M. R., Wilkinson, S. P. and Orszag, S. A., 1981, 'Instability and Transition in Rotating Disk Flow,' AIAA Journal, Vol. 19, No.9, pp.1131-1138 
    7. Malik, M. R., 1986, 'The Neutral Curve for Stationary Disturbances in Rotating Disk Flow,' J. Fluid Mech., Vol. 164, pp. 275-287 
    8. Rogers, M. G. and Lance, G. N., 1960, 'The Rotationally Symmetric Flow of a Viscous Fluid in the Presence of an Infinite Rotating Disk,' J. Fluid Mech., Vol. 7, pp.617-631 
    9. Kohama, Y. and Suda, K., 1993, 'Crossflow Instability in a Spinning Disk Boundary Layer,' AIAA Journal, Vol. 31, No.1, pp. 212-214 
    10. Kobayashi, R., Kohama, Y. and Takamadate, C., 1980, 'Spiral Vortices in Boundary Layer Transition Regime on a Rotating Disk,' Acta Mechanica, Vol. 35, pp. 71-82 
    11. Lingwood, R. J., 1997, 'Absolute Instability of the Ekman Layer and Related Rotating Flows,' J. Fluid Mech., Vol. 331, pp.405-428 
    12. Gregory, N., Stuart, J. T. and Walker, W. S., 1955, 'On the Stability of Three-dimensional Boundary Layers with Application to the Flow due to a Rotating Disk,' Phil. Trans. Roy. Soc., Vol. 248, pp. 155-199 
    13. Gregory, N. and Walker, W. S., 1960, 'Experiments on the Effect of Suction on the Flow due to a Rotating Disk,' J. Fluid Mech., Vol. 9, pp. 225-234 
    14. Hwang, Y. -K. and Lee, Y. -Y., 2000, 'Theoretical Flow Instability of the Karman Boundary Layer,' KSME J., Vol. 14, No.3, pp. 358-368     
    15. Faller, A. J., Yang, S. T. and Piomelli, U., 1989, 'Instability of the KEB Boundary Layers,' Tech. Note BN-1102, Inst. Phys. Sci. and Tech., U. of Maryland 
    16. Faller, A. J., 1991, 'Instability and Transition of Disturbed Flow over a Rotating Disk,' J. Fluid Mech., Vol. 230, pp.245-269 
    17. Chin, D. T. and Litt, M., 1972, 'An Electrochemical Study of Flow Instability on a Rotating Disk,' J. Fluid Mech., Vol. 54, pp. 613-625 
    18. 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 
  • 이 논문을 인용한 문헌 (2)

    1. 2007. "" Journal of mechanical science and technology, 21(1): 174~183     
    2. 2007. "" Journal of mechanical science and technology, 21(3): 518~524     

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