Hostname: page-component-7c8c6479df-27gpq Total loading time: 0 Render date: 2024-03-28T16:18:01.282Z Has data issue: false hasContentIssue false

Flow past a rotating cylinder

Published online by Cambridge University Press:  10 March 2003

SANJAY MITTAL
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology, Kanpur, UP 208 016, Indiasmittal@iitk.ac.in
BHASKAR KUMAR
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology, Kanpur, UP 208 016, Indiasmittal@iitk.ac.in

Abstract

Flow past a spinning circular cylinder placed in a uniform stream is investigated via two-dimensional computations. A stabilized finite element method is utilized to solve the incompressible Navier–Stokes equations in the primitive variables formulation. The Reynolds number based on the cylinder diameter and free-stream speed of the flow is 200. The non-dimensional rotation rate, α (ratio of the surface speed and freestream speed), is varied between 0 and 5. The time integration of the flow equations is carried out for very large dimensionless time. Vortex shedding is observed for α < 1.91. For higher rotation rates the flow achieves a steady state except for 4.34 < α < 4:70 where the flow is unstable again. In the second region of instability, only one-sided vortex shedding takes place. To ascertain the instability of flow as a function of α a stabilized finite element formulation is proposed to carry out a global, non-parallel stability analysis of the two-dimensional steady-state flow for small disturbances. The formulation and its implementation are validated by predicting the Hopf bifurcation for flow past a non-rotating cylinder. The results from the stability analysis for the rotating cylinder are in very good agreement with those from direct numerical simulations. For large rotation rates, very large lift coefficients can be obtained via the Magnus effect. However, the power requirement for rotating the cylinder increases rapidly with rotation rate.

Type
Research Article
Copyright
© 2003 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)