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Research Papers: Flows in Complex Systems

Stall Onset on Airfoils at Moderately High Reynolds Number Flows

[+] Author and Article Information
Zvi Rusak

Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute Troy, NY 12180-3590rusakz@rpi.edu

Wallace J. Morris

Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute Troy, NY 12180-3590morriw@rpi.edu

J. Fluids Eng. 133(11), 111104 (Nov 08, 2011) (12 pages) doi:10.1115/1.4005101 History: Received January 16, 2011; Accepted September 09, 2011; Revised September 09, 2011; Published November 08, 2011; Online November 08, 2011

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.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

The physical model of an attached flow around an airfoil showing the outer, inner, boundary-layer, and wake regions and relations between them

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Figure 2

The distribution of the pressure coefficient along the parabola upper and lower surfaces at various values of Ã. Here ReM  = 362 and Ma = 0.2.

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Figure 3

Contours of the axial velocity field around the parabola at circulation parameter Ã = 1.78. Here ReM  = 362 and Ma = 0.2.

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Figure 4

Contours of the axial velocity field around the parabola at circulation parameter Ã = 1.98. Here ReM  = 362 and Ma = 0.2.

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Figure 5

Contours of the axial velocity field around the parabola at circulation parameter Ã = 2.2. Here ReM  = 362 and Ma = 0.2.

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Figure 6

The distributions of the pressure coefficient along the parabola upper surface at various values of Ã. Here ReM  = 23,000 and Ma = 0.2.

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Figure 7

Contours of the axial velocity field around the parabola at circulation parameter Ã = 3.16. Here ReM  = 23,000 and Ma = 0.2.

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Figure 8

Contours of the axial velocity field around the parabola at circulation parameter Ã = 3.21. Here ReM  = 23,000 and Ma = 0.2.

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Figure 9

Contours of the axial velocity field around the parabola at circulation parameter Ã = 3.27. Here ReM  = 23,000 and Ma = 0.2.

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Figure 10

Modified turbulent viscosity of a laminar separation at Ã = 3.48. Here ReM  = 46,000 and Ma = 0.2.

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Figure 11

The circulation parameter at stall Ãs as function of ReM for Ma = 0.2

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Figure 12

Comparison of experimental data with theoretical prediction for Ãs as a function of log(ReM )

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Figure 13

(a) Comparison of experimental data and theoretical predictions for αs as function of Rc /c at Re = 3 × 106 and Ma = 0.2. (b) Comparison of experimental data and theoretical predictions for Cl max as function of Rc /c at Re = 3 × 106 and Ma = 0.2.

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Figure 14

(a) Comparison of experimental data and theoretical prediction for the increase in Cl max as function of flap deflection for various flap sizes of a NACA 23012 at Re = 3 × 106 . (b) Comparison of experimental data and theoretical prediction for the increase in Cl max as function of flap deflection for various flap sizes of a NACA 23030 at Re = 3 × 106 s, Ma = 0.2. (c) Comparison of experimental data and theoretical prediction for the slope dCl max /f as function of flap size at Re = 3 × 106 and Ma = 0.2.

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Figure 15

Comparison of experimental data and theoretical prediction for αs as function of Mach number for the NACA 66 ( 109 ) -210 airfoil

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Figure 16

Summary of experimental data and theoretical prediction for αs of the NACA 0012 as function of Reynolds number at Ma = 0.2

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