Global stability analysis of axisymmetric boundary layer over a circular cylinder
- 77 Downloads
This paper presents a linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inflow boundary. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier–Stokes (LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi’s iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes is negative, and hence, the flow is temporally stable. The spatial structure of the eigenmodes shows that the disturbance amplitudes grow in size and magnitude while they are moving towards downstream. The global modes of axisymmetric boundary layer are more stable than that of 2D flat-plate boundary layer at low Reynolds number. However, at higher Reynolds number they approach 2D flat-plate boundary layer. Thus, the damping effect of transverse curvature is significant at low Reynolds number. The wave-like nature of the disturbance amplitudes is found in the streamwise direction for the least stable eigenmodes.
KeywordsAxisymmetric boundary layer Global stability Transverse curvature
Unable to display preview. Download preview PDF.
- 5.Costa, B., Don, W., Simas, A.: Spatial resolution properties of mapped spectral Chebyshev methods. In: Proceedings SCPDE: Recent Progress in Scientific Computing, pp. 179–188 (2007)Google Scholar
- 21.Mack, L.M.: Stability of axisymmetric boundary layers on sharp cones at hypersonic mach numbers. In: 19th AIAA, Fluid Dynamics, Plasma Dynamics, and Lasers Conference, p. 1413 (1987)Google Scholar
- 30.Roache, P.J.: A method for uniform reporting of grid refinment study. J. Fluids Eng. 116, 405413 (1994)Google Scholar
- 41.Vinod, N.: Stability and transition in boundary layers: effect of transverse curvature and pressure gradient. Ph.D. Thesis, Jawaharlal Nehru Center for Advanced Scientific Research (2005)Google Scholar