Research Papers: Flows in Complex Systems

Analysis of the Airfoil Stall With a Modification of Viscous-Inviscid Interaction Concept

[+] Author and Article Information
E. L. Amromin

Mechmath LLC,
Prior Lake, MN 55372

Manuscript received January 11, 2012; final manuscript received February 7, 2013; published online April 8, 2013. Assoc. Editor: Meng Wang.

J. Fluids Eng 135(5), 051105 (Apr 08, 2013) (7 pages) Paper No: FE-12-1008; doi: 10.1115/1.4023784 History: Received January 11, 2012; Revised February 07, 2013

A modification of the viscous-inviscid interaction concept with the employment of coupled vortices around the airfoil wake is introduced for analyzing the airfoil stall. The analyzed flow includes the laminar boundary layers, laminar separation bubble, laminar-turbulent transition zone, turbulent boundary layers, turbulent separation zone, wake, and outer inviscid flow. Integral methods are employed for the boundary layers. The boundaries of separation zones are analyzed as free surfaces, however, their lengths and shapes depend on the Reynolds number. The described modification is validated by a comparison of the numerical results with the previously published experimental data for various airfoils and Reynolds numbers at low Mach numbers. This modification achieves a reasonably good agreement of the computed lift and moment coefficients with their measured values.

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Fig. 1

Comparison of the lift and drag prediction with the RANS codes (OVERFLOW and FLUENT) and the viscous-inviscid interaction code (PROFIL07) with the experimental data for airfoils S406 and E387

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Fig. 2

Measured [2] and computed results with a RANS code pressure coefficient Cp on the airfoil at α = 18° and M = 0.3

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Fig. 3

Foil separated flows. (top) Flow around the plate with a constant pressure zone behind it, computed using the Tulin scheme with coupled spiral vortices. (bottom) Suggested scheme of the foil separated flow. The solid line is the foil contour; the dashed line is the computed section of the displacement body surface S that is the effective boundary of the outer inviscid flow. The dotted line shows the upper section of the turbulent separation zone.

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Fig. 4

Scheme of the separated flow behind a step: the dashed line is the displacement body section. The dash-dotted line is the boundary between the inviscid flow and the viscous flow.

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Fig. 5

Effect of dL/L on the computed pressure distribution in comparison with the experimental data [17]

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Fig. 6

Effect of the second vortex location on the intensity of the vortex pair behind the foil S805

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Fig. 7

Computed velocity along S for a NACA foil with the trailing edge separation at Re = 3 × 106

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Fig. 8

Comparison of the computed and measured [14] length of the separation zones behind the backward steps

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Fig. 9

Normalized pressure distribution: comparison between the presented computations and the experimental data [18] for separation zones behind the backward steps in channels. The numbers in the legend show the ratio of H to the channel width.

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Fig. 10

Effects of the Reynolds number and angle of attack on the computed thickness displacement on NACA0021

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Fig. 11

Comparison of the computed and measured [19] points of the boundary layer reattachment behind a laminar bubble over the NACA0021

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Fig. 12

Lift coefficient of the NACA 0021 airfoil; the curves show our computations and the symbols show the experimental data [19]

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Fig. 13

Lift coefficient of the NACA651-213 a = 0.50 airfoil. The curves show the numerical results and the symbols show the experimental data [20]. The numbers in the legend show the values of Re/106.

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Fig. 14

Lift coefficient of the NACA0012 airfoil at Re = 3.9 × 106; the curve shows the numerical results and the symbols show the experimental data [21]

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Fig. 15

Comparison between the computed and the experimental [21] moment coefficient of the airfoil NACA0012 at Re = 3.9 × 106

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Fig. 16

Comparison between the computed (solid line) and measured [23] (rhombs) lift coefficient of the Clark-Y airfoil. At the highest lift Re = 4.2 × 106; Re rises to 4.8 × 106 at low lift. The dashed line shows the ideal fluid asymptote.

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Fig. 17

Computed (solid line) and measured [1] (rhombs) lift coefficient of the S805 airfoil at Re = 106



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