Aleksandr Vladimirovich Obabko

On the ejection-induced instability in Navier-Stokes solutions of unsteady separation

Numerical solutions of the flow induced by a thick-core vortex have been obtained using the unsteady, two-dimensional Navier–Stokes equations. The presence of the vortex causes an adverse pressure gradient along the surface, which leads to unsteady separation. The calculations by Brinckman and Walker for a similar flow identify a possible instability, purported to be an inviscid Rayleigh instability, in the region where ejection of near-wall vorticity occurs during the unsteady separation process. In results for a range of Reynolds numbers in the present investigation, the oscillations are also found to occur. However, they can be eliminated with increased grid resolution. Despite this behaviour, the instability may be physical but requires a sufficient amplitude of disturbances to be realized.

Detachment of the Dynamic-Stall Vortex Above a Moving Surface

Dynamic stall occurs on helicopter blades and pitching airfoils when the dynamic-stall vortex, which forms as a result of an unsteady boundary-layer eruption near the leading edge, detaches from the surface and convects into the wake of the airfoil. The dynamic-stall vortex is modeled as a thick-core vortex above an infinite plane surface. Numerical solutions of the unsteady Navier-Stokes equations are obtained to determine the nature of the unsteady separation and vortex detachment processes and the influence of a moving wall. Whereas the unsteady separation process evolves very differently within two Reynolds number regimes, the detachment process is observed to be very similar over the range of Reynolds numbers considered. A moving wall has a significant influence on both processes

Unsteady Natural Convection in a Horizontal Cylinder With Internal Heat Generation

The unsteady natural convection of a fluid within a horizontal cylinder with internal heat generation is considered. The unsteady Navier-Stokes equations in the Boussinesq approximation are computed numerically for Rayleigh numbers in the range from 106 to 1010 to determine the fluid flow and heat transfer characteristics. For Rayleigh numbers below a critical value, RaR ≈ 108 , the unsteady solutions approach a steady-state solution that is symmetric about the vertical center line. Above the critical Rayleigh number, however, the flow becomes highly unsteady and evolves toward a quasi-periodic asymmetric oscillation.Copyright

A Rayleigh Instability in Navier-Stokes Solutions of an Unsteady Boundary Layer

Numerical solutions of the unsteady, two-dimensional Navier-Stokes equations are considered for the flow induced by a thick-core vortex. The adverse pressure gradient imposed on the surface by the vortex leads to unsteady separation. The presence and nature of an instability that may arise during the unsteady separation process is considered. The instability arises in the form of small-scale oscillations in vorticity and streamwise pressure gradient along the wall, and the dominant wavenumber of the instability is O(Re), consistent with a Rayleigh-type instability. The existence of a Rayleigh instability is confirmed through evaluation of the Rayleigh equation for velocity profiles obtained from a boundary-layer calculation, and the dominant wavenumber of the instability agrees very closely with that predicted by the Rayleigh solutions.

Instabilities and Vorticity Shedding in Wall-Bounded Flows

Numerical solutions of the unsteady, twodimensional Navier-Stokes equations are considered for the flow induced by a thick-core vortex. The adverse pressure gradient imposed on the surface by the vortex leads to unsteady separation. In this investigation the presence and nature of two possible instabilities are considered that may arise during the unsteady separation process. The calculations by Brinckman & Walker (2001) 1 identify a possible instability in the region where unsteady separation occurs. Although the instability is likely physical, it appears to be removable with increased grid resolution. A second type of instability, which occurs earlier in time but at higher Reynolds numbers, is also observed. This instability appears to be of the Rayleigh type and requires viscous-inviscid interaction. The present results also suggest a mechanism of initiating vortex shedding in wall-bounded flows that is distinctly dierent from the inviscid mechanism observed in free-shear layers. This viscous mechanism involves periodic ejection of secondary vorticity from within the boundary layer, with each ejection shedding a vortex.