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Stall onset on aerofoils at low to moderately high Reynolds number flows

Published online by Cambridge University Press:  24 September 2013

Wallace J. Morris II  and
Zvi Rusak
Wallace J. Morris II
Affiliation:
Department of Mechanical, Aerospace, and Nuclear Engineering Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
Zvi Rusak*
Affiliation:
Department of Mechanical, Aerospace, and Nuclear Engineering Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
*
†Email address for correspondence: rusakz@rpi.edu
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Abstract

The inception of leading-edge stall on stationary, two-dimensional, smooth, thin aerofoils at low to moderately high chord Reynolds number flows is investigated by a reduced-order, multiscale model problem via numerical simulations. The asymptotic theory demonstrates that a subsonic flow about a thin aerofoil can be described in terms of an outer region, around most of the aerofoil’s chord, and an inner region, around the nose, that asymptotically match each other. The flow in the outer region is dominated by the classical thin aerofoil theory. Scaled (magnified) coordinates and a modified (smaller) Reynolds number $(R{e}_{M} )$ are used to correctly account for the nonlinear behaviour and extreme velocity changes in the inner region, where both the near-stagnation and high suction areas occur. It results in a model problem of a uniform, incompressible and viscous flow past a semi-infinite parabola with a far-field circulation governed by a parameter $\tilde {A} $ that is related to the aerofoil’s angle of attack, nose radius of curvature, thickness ratio, and camber. The model flow problem is solved for various values of $\tilde {A} $ through numerical simulations based on the unsteady Navier–Stokes equations. The value ${\tilde {A} }_{s} $ where a global separation zone first erupts in the nose flow, accompanied by loss of peak streamwise velocity ahead of it and change in shedding frequency behind it, is determined as a function of $R{e}_{M} $. These values indicate the stall onset on the aerofoil at various flow conditions. It is found that ${\tilde {A} }_{s} $ decreases with $R{e}_{M} $ until some limit $R{e}_{M} $ (${\sim }300$) and then increases with further increase of Reynolds number. At low values of $R{e}_{M} $ the flow is laminar and steady, even when stall occurs. The flow in this regime is dominated by the increasing effect of the adverse pressure gradient, which eventually overcomes the ability of the viscous stress to keep the boundary layer attached to the aerofoil. The change in the nature of stall at the limit $R{e}_{M} $ is attributed to the appearance of downstream travelling waves in the boundary layer that shed from the marginal separation zone and grow in size with either $\tilde {A} $ or $R{e}_{M} $. These unsteady, convective vortical structures relax the effect of the adverse pressure gradient on the viscous boundary layer to delay the onset of stall in the mean flow to higher values of ${\tilde {A} }_{s} $. Computed results show agreement with marginal separation theory at low $R{e}_{M} $ and with available experimental data at higher $R{e}_{M} $. This simplified approach provides a universal criterion to determine the stall angle of stationary thin aerofoils with a parabolic nose.

JFM classification

Aerodynamics: Aerodynamics Boundary Layers: Boundary Layers Boundary Layers: Boundary layer separation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 733 , 25 October 2013 , pp. 439 - 472
Copyright
©2013 Cambridge University Press 

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