Acoustic diffraction by a flat airfoil in uniform flow
전원주

AIAA Journal
46/12
(2008)
Diffraction by a flat airfoil in uniform flow in analytically examined, g on the acquisition of an accurate series solution for both lowand highfrequency incident waves. formulation of integral equations is based on the use of the WienerHopf technique in the complex domain. As the kernels of the Integral equations are multivalued functions having a branch cut in the complex domain, the unknown in the integral operator is assumed to be a constant. Therefore, the solution is a zerothorder approximate solution adequate for a highfrequency problem. In this stury, the unknown is expanded by a Taylor series of an arbitrary order in the analytic region, and the solution is obtained in series form involving a special function called a generalized gamma function Gamma(m) (u,z). As the generalized gamma functions occuring in finite diffraction theroy have the specific argument u as "nonnegative Integer +1/2," the authors used their previously determined exact and closedform formulas of this special function to obtain the complete series solution. The present series solution exhibits faster convergence at a high frequency compared to a low frequency, whereas the Mathieu series solution in the elliptic coordinates converges faster at a low frequency relative to a higher frequency. Through exact and asymptotic evaluations of inverse Fourier transforms, the scattered and total acoustic fields are visualized in a physical domain and each term of the solution is physically interpreted as 1) semiinfinite leadingedge scattering, 2) trailingedge correction, and 3) interaction between leading and trailing edges, respectively.
 초록
Diffraction by a flat airfoil in uniform flow in analytically examined, g on the acquisition of an accurate series solution for both lowand highfrequency incident waves. formulation of integral equations is based on the use of the WienerHopf technique in the complex domain. As the kernels of the Integral equations are multivalued functions having a branch cut in the complex domain, the unknown in the integral operator is assumed to be a constant. Therefore, the solution is a zerothorder approximate solution adequate for a highfrequency problem. In this stury, the unknown is expanded by a Taylor series of an arbitrary order in the analytic region, and the solution is obtained in series form involving a special function called a generalized gamma function Gamma(m) (u,z). As the generalized gamma functions occuring in finite diffraction theroy have the specific argument u as "nonnegative Integer +1/2," the authors used their previously determined exact and closedform formulas of this special function to obtain the complete series solution. The present series solution exhibits faster convergence at a high frequency compared to a low frequency, whereas the Mathieu series solution in the elliptic coordinates converges faster at a low frequency relative to a higher frequency. Through exact and asymptotic evaluations of inverse Fourier transforms, the scattered and total acoustic fields are visualized in a physical domain and each term of the solution is physically interpreted as 1) semiinfinite leadingedge scattering, 2) trailingedge correction, and 3) interaction between leading and trailing edges, respectively.
 초록
Diffraction by a flat airfoil in uniform flow in analytically examined, g on the acquisition of an accurate series solution for both lowand highfrequency incident waves. formulation of integral equations is based on the use of the WienerHopf technique in the complex domain. As the kernels of the Integral equations are multivalued functions having a branch cut in the complex domain, the unknown in the integral operator is assumed to be a constant. Therefore, the solution is a zerothorder approximate solution adequate for a highfrequency problem. In this stury, the unknown is expanded by a Taylor series of an arbitrary order in the analytic region, and the solution is obtained in series form involving a special function called a generalized gamma function Gamma(m) (u,z). As the generalized gamma functions occuring in finite diffraction theroy have the specific argument u as "nonnegative Integer +1/2," the authors used their previously determined exact and closedform formulas of this special function to obtain the complete series solution. The present series solution exhibits faster convergence at a high frequency compared to a low frequency, whereas the Mathieu series solution in the elliptic coordinates converges faster at a low frequency relative to a higher frequency. Through exact and asymptotic evaluations of inverse Fourier transforms, the scattered and total acoustic fields are visualized in a physical domain and each term of the solution is physically interpreted as 1) semiinfinite leadingedge scattering, 2) trailingedge correction, and 3) interaction between leading and trailing edges, respectively.
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