Computation of aerodynamic interference effects on oscillating airfoils with controls in ventilated subsonic wind tunnels

Fromme, J. A.; Golberg, Michael A.

doi:10.2514/6.1979-346

Cited by 4 publications

(11 citation statements)

References 11 publications

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“…From our remarks above and well-known results for the Possio equation, 25 it is reasonable to consider polynomial expansion methods for solving Eq. (17), ones utilizing the airfoil polynomials behig of particular importance.…”

Section: Fourier Theory Of Airfoil Polynomialsmentioning

confidence: 99%

“…The airfoil polynomial pairs can be shown to represent infinitely many linearly independent solutions to the steady free air problem^y n =a nt n = l,2,... (25) and to be orthonormal with respect to reciprocal downwash and pressure weighting functions; i.e.,…”

Section: Fourier Theory Of Airfoil Polynomialsmentioning

confidence: 99%

“…Define two complex Hilbert spaces of square integrable functions, Once the Fourier coefficients of the pressure factor have been determined, the pressure jump may be computed from 4 rr= (30) Defining section coefficients and the aerodynamic work matrix in the usual way, 27 h m (x)*p n (x)dx (32) where Ap n is the pressure jump due to displacement mode h n , it then follows 25 easily that…”

Section: Fourier Theory Of Airfoil Polynomialsmentioning

confidence: 99%

“…While this assumption produces simple and useful engineering approximations to angle-of-attack and Mach number "corrections," it suffers by neglecting the truly coupled nature of interference between the walls and the Presented as Paper 79-0346 at the AIAA 17th Aerospace Sciences Meeting, New Orleans, La., Jan. [15][16][17]1979; submitted Jail. 30,1979; revision received July 16,1979 model. Thus, any rational theory of wind tunnel interference must be based on an appropriate formulation in which this aerodynamic coupling is explicitly present.…”

Section: Introductionmentioning

confidence: 99%

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Aerodynamic Interference Effects on Oscillating Airfoils with Controls in Ventilated Wind Tunnels

Fromme

Golberg

1980

AIAA Journal

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Lift interference effects are discussed based on Bland's integral equation. A mathematical existence theory is utilized for which convergence of the numerical method has been proved for general (square-integrable) downwashes. Airloads are computed using orthogonal airfoil polynomial pairs in conjunction with a collocation method which is numerically equivalent to Galerkin's method and complex least squares. Convergence exhibits exponentially decreasing error with the number n of collocation points for smooth downwashes, whereas errors are proportional to l/n for discontinuous downwashes. The latter is reduced to l//i m+/ with /nth order extrapolation to the limit (using m-1 we obtain hundredfold error reductions with only a 13 % increase of computer time). Numerical results are presented showing acoustic resonance, and the effect of Mach number, ventilation, height to chord ratio, and mode shape on wind tunnel interference. Excellent agreement with experiment is obtained in steady flow, and good agreement is obtained for unsteady flow.

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Section: Fourier Theory Of Airfoil Polynomialsmentioning

confidence: 99%

Section: Fourier Theory Of Airfoil Polynomialsmentioning

confidence: 99%

Section: Fourier Theory Of Airfoil Polynomialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Aerodynamic Interference Effects on Oscillating Airfoils with Controls in Ventilated Wind Tunnels

Fromme

Golberg

1980

AIAA Journal

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“…The mathematical formulation of physical phenomena often involves Cauchy-type (or more severe) singular integral equations. Integral and integrodifferential equations containing strongly singular kernels appear in studies involving elastic contact [1], stress analysis [1], fracture mechanics [2][3][4], airfoil theory [5][6][7][8][9][10], and combined infrared radiation and molecular conduction [11,12]. Owing to their common appearance in practice, there exists a growing need to develop accurate approximate analytical and numerical solutions to a large variety of singular integral and integro-differential equations.…”

mentioning

confidence: 99%

A Galerkin solution to a regularized Cauchy singular integro-differential equation

Frankel¹

1995

Quart. Appl. Math.

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Abstract. This paper presents a Galerkin approach for solving a regularized version of the Cauchy singular, linear integro-differential equation• Jy=o x-y subject to 0(0) = 0(1) = 0. This equation has appeared in both combined infrared gaseous radiation and molecular conduction, and elastic contact studies. A regularized formulation is produced which suggests the use of an expansion technique where the orthogonal basis functions are chosen as the Chebychev polynomials of the first kind. Accurate results, requiring a minimal computational cost, are formally documented and compared to a purely numerical solution.

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Reformulation of Possio's kernel with application to unsteady wind tunnel interference

Fromme

Golberg

1980

AIAA Journal

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An efficient. method for computing the Possio kernel has remained elusive up to the present time. In this paper we reformulate the Possio kernel so that it can be computed accurately using existing high precision numerical quadrature techniques. Convergence to the correct values is demonstrated and optimization of the integration procedures is discussed. Since more general kernels such as those associated with unsteady flows in ventilated wind tunnels are analytic perturbations of the Possio free air kernel, a more accurate evaluation of their collocation matrices results with an exponential improvement in convergence. An application to predicting frequency response of an airfoil-trailing edge control system in a wind tunnel compared with that in free air is given showing strong interference effects.

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Computation of aerodynamic interference effects on oscillating airfoils with controls in ventilated subsonic wind tunnels

Cited by 4 publications

References 11 publications

Aerodynamic Interference Effects on Oscillating Airfoils with Controls in Ventilated Wind Tunnels

Aerodynamic Interference Effects on Oscillating Airfoils with Controls in Ventilated Wind Tunnels

A Galerkin solution to a regularized Cauchy singular integro-differential equation

Reformulation of Possio's kernel with application to unsteady wind tunnel interference

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