Abstract
The generation and evolution of small amplitude long wavelength traveling disturbances in rotating-disk flow is the subject of this paper. The steady rotational speed of the disk is perturbed so as to introduce high-frequency oscillations in the flow field. Secondly, we introduce surface imperfections on the disk such as roughness elements. The interaction of these two disturbances will generate the instability waves whose evolution is governed by parabolic partial differential equations which are solved numerically. It is found that, for the class of disturbances considered here (wavelength on the order of Reynolds number), eigensolutions exist which decay or grow algebraically in the radial direction. However, these solutions grow only for frequencies larger than 4.58 times the steady rotational speed of the disk. The computed receptivity coefficient shows that there is an optimum size of roughness for which these modes are preferentially excited. The width of these roughness elements in the radial direction is about 0.1r *0 where r *0 is the radial location of the roughness. It is also found that the receptivity coefficient is larger for a negative spanwise wave number than for a positive one. The cumulative wave pattern produced from the roughness site shows that the typical wave angles for these disturbances are about −26° with about seven waves around the circumference. This is in contrast with the wave angles of 10°–14° found for the 30 or so inviscid cross-flow vortices.
Similar content being viewed by others
References
Balakumar, P., and Malik, M.R.: Theoret. Comput. Fluid Dynamics 2, 125, 1990.
Balakumar, P., and Malik, M.R.: AIAA 26th Fluid Dynamics, Plasmadynamics and Lasers Conference, Honolulu, HI, June 1991, AIAA Paper 91-1646.
Denier, J.P., Hall P., and Seddougui S.: ICASE Report No. 90–31, 1990.
Faller, A.J., and Kaylor, R.E.: in Dynamics of Fluids and Plasmas, p. 309, Academic Press, New York, edited by S.I. Pai et al., 1966.
Gregory, N., Stuart, J.T., and Walker, W.S.: Proc. Roy. Soc. London Ser. A 248, 155, 1955.
Hall, P.: J. Fluid Mech. 124, 475, 1982.
Hall, P.: J. Fluid Mech. 130, 41, 1983.
Hall, P.: Proc. Roy. Soc. London Ser. A 406, 93, 1986.
Mack, L.M.: AIAA Paper 86-0490, 1985.
Malik, M.R.: J. Fluid Mech. 164, 275, 1986.
Spall, R.E., and Malik, M.R.: Phys. Fluids A1 11, 1822, 1989.
Wilkinson, S.P., and Malik M.R.: AIAA Paper 83-1760, 1983. (Also, AIAA J. 23, 588, 1985.)
Author information
Authors and Affiliations
Additional information
Communicated by M.Y. Hussaini
This work was sponsored by NASA Langley Research Center under Contracts NAS1-18240 (P.B. and M.R.M.) and NAS1-18605 (P.H.).
Rights and permissions
About this article
Cite this article
Balakumar, P., Malik, M.R. & Hall, P. On the receptivity and nonparallel stability of traveling disturbances in rotating-disk flow. Theoret. Comput. Fluid Dynamics 3, 125–140 (1991). https://doi.org/10.1007/BF00271798
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00271798