Stall Onset on Airfoils at Moderately High Reynolds Number Flows

Abstract

The inception of leading-edge stall on two-dimensional smooth thin airfoils at moderately high Reynolds number flows [in the range O(104) to O(106)] is investigated by an asymptotic approach and numerical simulations. The asymptotic theory is based on the work of Rusak (1994) and demonstrates that a subsonic flow about a thin airfoil can be described in terms of an outer region, around most of the airfoil 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 airfoil theory. Scaled (magnified) coordinates and a modified (smaller) Reynolds number are used to correctly account for the nonlinear behavior and extreme velocity changes in the inner region, where both the near stagnation and high suction areas occur. It results in a model (simplified) problem of a uniform flow past a semi-infinite parabola with a far-field circulation governed by a parameter à that is related to the airfoil’s angle of attack, nose radius of curvature, and camber and to the flow Mach number. The model parabola problem consists of a compressible and viscous flow described by the steady Navier-Stokes equations. This problem is solved numerically for various values of à using a Reynolds-averaged Navier-Stokes flow solver, and utilizing the Spalart-Allmaras viscous turbulent model to account for near-wall turbulence. The value Ãs where a large separation zone first appears in the nose flow concurrent with a sudden increase in the minimum pressure coefficient is determined. The change of Ãs with the modified Reynolds number is determined. These values indicate the stall onset on the airfoil at various flow conditions. The predictions according to this approach show good agreement with results from both numerical simulations and available experimental data of the stall of thin airfoils. This simplified approach provides a criterion to determine the stall angle of airfoils with a parabolic nose and the effect of airfoil’s thickness ratio, nose radius of curvature, camber and flaps, and flow compressibility on the onset of stall. This approach also presents an analysis method that can be used to predict the stall of airfoils with alternative nose geometry.

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

“…A similar identification of stall with unsteady flow situations is shown later on for Re M = 700. Note that in the range of Re M studies in this paper the loss of suction and stall is moderate compared to the abrupt stall that occurs at high Re M : see figures 2 and 6 in Rusak & Morris (2011) for comparison.…”

“…This means that the theory is limited to aerofoils with small thickness ratio, and as the thickness increases the error of this prediction also increases. Our numerical studies, presented in Rusak & Morris (2011), indicate that for practical aerofoils the theory provides relevant predictions when δ < 0.15 and |α s | < 15 • .…”

“…In a recent paper (Rusak & Morris 2011) we studied the leading-edge stall of thin aerofoils at subsonic speeds and moderately high Reynolds numbers, and we accounted for the interactions between the near-wall viscous flow and the outer inviscid flow. The analysis resulted in a model (simplified) problem of a uniform, compressible, steady stream at Re M past a semi-infinite, stationary, canonic parabola with a far-field circulation governed by a parameterÃ.…”

“…This paper extends the model problem in Rusak & Morris (2011) to investigate the onset of leading-edge stall on stationary, thin aerofoils at low to moderately high Reynolds numbers (Re M in the range 50 to 2100). This work also seeks to illuminate the flow physics in this range as well as establish an overlap region with the previously investigated stall at moderately high to high Re M .…”

Semi-Empirical Prediction of Airfoil Hysteresis

“…Table 1 contains α Re´ATT estimates from both theory and experiment. Theoretical predictions include the present method and estimates from the method of Rusak and Morris [13]. Agreement between the current method and that of Rusak and Morris is seen to be good.…”