The Influence of Two-Dimensional Stream Shear on Airfoil Maximum Lift

Vidal, R. J.; CURTIS, J. T.; HILTON, J. H.

doi:10.21236/ad0263597

Cited by 6 publications

(12 citation statements)

References 2 publications

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“…it follows that the lift increment due to the thicknessshear interaction, as given by the partial solution, is ACL = KPT^W] " wS (8) Comparing this with the lift increment given in Eqs. (1) and (5), AC L = (Tr/2)rk h it can be seen that the partial solution yields about 70 percent of the increment predicted by uniform-shear theory and other nonuniformshear theories.…”

Section: H/c « Y 4 (L + R)mentioning

confidence: 87%

“…In general, the treatments fall into two categories: exact solutions for airfoils in flows with uniform shear 2, 3 and approximate solutions for airfoils in flows with symmetric nonuniform shear. 4 ' 5 > 8 The literature treating uniform-shear flows 2 ' 3 shows that the stream shear interacts with the airfoil thickness and camber to produce an overall increase in lift, much like an increased effective camber, an overall increase in pitching moment analogous to a distorted camber distribution, and a small increase in lift-and moment-curve slopes analogous to an increase in airfoil thickness. The theory for thin airfoils in nonuniform shear 4 provides an approximate solution restricted to small values of stream shear to show that the first-order effect of the nonuniform shear is to increase markedly the slope of the lift and moment curves.…”

Section: H/c « Y 4 (L + R)mentioning

confidence: 99%

“…8 The formulas given in Eqs. (9) and (12) have been used to calculate the velocity distribution on the airfoil used in the experiments (r = 0.17).…”

Section: Pressure Distributionmentioning

confidence: 99%

See 2 more Smart Citations

The Influence of Two-Dimensional Stream Shear on Airfoil Maximum Lift

Vidal

1962

Journal of the Aerospace Sciences

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Section: H/c « Y 4 (L + R)mentioning

confidence: 87%

Section: H/c « Y 4 (L + R)mentioning

confidence: 99%

See 1 more Smart Citation

The Influence of Two-Dimensional Stream Shear on Airfoil Maximum Lift

Vidal

1962

Journal of the Aerospace Sciences

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“…Eq. (29) shows that the characteristic time depends on the value of the moment. This is a general feature of nonlinear problems, namely, the characteristic time depends on the integrals of the stress as well as on the distribution.…”

Section: V2)mentioning

confidence: 99%

Characteristic Times of Nonhomogeneous Maxwell Materials

Dillon

1962

Journal of the Aerospace Sciences

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This paper considers the transient stress distribution which exists in bars of nonlinear and nonhomogeneous viscoelastic (Maxwell) materials.The particular nonhomogeneity considered is an exponential variation of the fluidity in the thickness direction which is independent of time. It has previously been shown that this variation could be caused by a steady linear temperature gradient. Emphasis is given to the evaluation of the characteristic time of the stress-redistribution process.Five specific problems are solved by the Galerkin technique. In all of these problems the load remains constant. It is found that the characteristic time depends on the average stress for nonlinear problems and in a complicated way on the magnitude of the nonhomogeneity. Results are given in graphical form for a range of the nonhomogeneity parameter. The principal purpose of this paper is the qualitative determination of the time after which a Maxwell material can be considered as a viscous fluid for the determination of the state of stress. Symbols b = width of cross section, Fig. 1 h = thickness of cross section, Fig. 1 k = exponent in stress-strain-time relation, Eq. (1) n = center of rotation parameter t = time A = area of cross section E = Young's modulus or equation M = moment TV = temperature gradient (nonhomogeneity) parameter P = load e = strain f = nondimensional thickness coordinate, Fig. 1 f * = element which is characteristic of the cross section k = curvature rate A = fluidity Xo = fluidity at the cold face £ = 0 rj = characteristic parameter, Eq. (11)

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“…The pressure distribution along the foil may give some indication of the stalling characteristics of the foil. 5 In this paper, we first systematically expand the components of the disturbance velocity into a power series in e, which is a small parameter characterizing the size of small disturbances. The vorticity of the approaching stream need not be small, but must be of order 1.…”

Section: Introductionmentioning

confidence: 99%

Second-order theory for airfoils in uniform shear flow.

Chen

1966

AIAA Journal

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The first-and second-order problems for a uniform shear flow past an airfoil have been formulated and solved. It has been assumed that the stream shear, when properly nondimensionalized, must be of order 1. Expressions for the first-and second-order pressure coefficients have been obtained. The lift and moment coefficients are given in integral form. Once the airfoil shape is known, the force coefficients can be obtained by integration. Numerical calculations have been carried out to obtain lift coefficients on a symmetric Joukowsky airfoil, a circular arc, and a cambered Joukowsky airfoil for different values of stream vorticity. It is found that, in general, if the nondimensional stream vorticity (with respect to the airfoil chord and a reference velocity) is limited to 1 or less, the second-order theory will give lift coefficients within 5% of the exact theory up to 30° angle of attack. The uniformly valid pressure distributions correct to the second order along a symmetric Joukowsky airfoil at 10° incidence are presented to exhibit the effect of stream shear.

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The Influence of Two-Dimensional Stream Shear on Airfoil Maximum Lift

Cited by 6 publications

References 2 publications

The Influence of Two-Dimensional Stream Shear on Airfoil Maximum Lift

The Influence of Two-Dimensional Stream Shear on Airfoil Maximum Lift

Characteristic Times of Nonhomogeneous Maxwell Materials

Second-order theory for airfoils in uniform shear flow.

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