Analytical Determination of Blockage Effects in a Perforated-Wall Transonic Wind Tunnel

Kraft, Edward; Lo, C. F.

doi:10.2514/3.60654

Cited by 12 publications

(2 citation statements)

References 12 publications

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“…This relation is a linearized version of Darcy's law [13], [18]; the factor R − (x) depends on the porosity of the surface. Again, the condition on the curvilinear surface can be replaced by…”

Section: Formulation Of the Problem Uniqueness Of The Solutionmentioning

confidence: 99%

Solvability of a problem for transonic flow with a local supersonic region

Kuzmin

2001

NoDEA, Nonlinear differ. equ. appl.

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A nonlinear perturbation problem for steady two-dimensional inviscid transonic flow with a local supersonic region is considered. A damping condition is prescribed on a portion of the boundary in order to prevent the arising of shock waves in the flow. The existence of a smooth solution to the problem is established. A proof is based on the Fredholm alternative and on a technique for uniqueness analysis worked out by and Cook (1978).2000 Mathematics Subject Classification: 35M10, 76H05.

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Section: Formulation Of the Problem Uniqueness Of The Solutionmentioning

confidence: 99%

Solvability of a problem for transonic flow with a local supersonic region

Kuzmin

2001

NoDEA, Nonlinear differ. equ. appl.

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“…Whereas integral equations are more difficult to formulate, they enjoy the advantage that the dimension of the space in which the problem must be solved is reduced by one. This undoubtedly accounts for their being a frequent method of choice in subsonic and supersonic flow, and there is now evidence 13 to suggest that in transonic flow as well, nonlinear integral equation methods may be an order of magnitude faster than PDE methods.…”

Section: Introductionmentioning

confidence: 95%

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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A Survey of Numerical Methods for Integral Equations

Golberg

1979

Solution Methods for Integral Equations

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Analytical Determination of Blockage Effects in a Perforated-Wall Transonic Wind Tunnel

Cited by 12 publications

References 12 publications

Solvability of a problem for transonic flow with a local supersonic region

Solvability of a problem for transonic flow with a local supersonic region

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

A Survey of Numerical Methods for Integral Equations

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