The Kernel Function of the Integral Equation Relating the Lift and Downwash Distributions of Oscillating Finite Wings in Subsonic Flow

1954 ◽  
Vol 21 (9) ◽  
pp. 635-636 ◽  
Author(s):  
G. N. Lance
Keyword(s):  
Integral Equation ◽  
Kernel Function ◽  
Subsonic Flow

A Comparison of Two Integral Equation Methods for High Subsonic Lifting Flows

1975 ◽  
Vol 26 (1) ◽  
pp. 56-58 ◽  
Author(s):  
D Nixon
Keyword(s):  
Integral Equation ◽  
Unique Solution ◽  
Subsonic Flow ◽  
Integral Equation Methods ◽  
High Subsonic Flow

SummaryA comparison is made of two recently published integral equation methods for calculating the high subsonic flow around lifting and non-lifting aerofoils. It is shown that one method leads to a non-unique solution.

Kernel Function for Nonplanar Oscillating Surfaces in a Subsonic Flow

AIAA Journal ◽  
1967 ◽  
Vol 5 (5) ◽  
pp. 1045-1046 ◽  
Author(s):  
M. T. LANDAHL
Keyword(s):  
Kernel Function ◽  
Subsonic Flow

scholarly journals APPROXIMATE FUNCTION FOR UNSTEADY AERODYNAMIC KERNEL FUNCTION OF AEROELASTIC LIFTING SURFACES

2014 ◽  
Vol 15 (1) ◽  
Author(s):  
Erwin Sulaeman ◽  
Layeeq Ahmed
Keyword(s):  
Integral Equation ◽  
Kernel Function ◽  
Numerical Estimation ◽  
Aerodynamic Pressure ◽  
Unsteady Aerodynamic ◽  
Cylindrical Function ◽  
Aeroelastic Analysis ◽  
Approximate Function ◽  
Lifting Surfaces ◽  
Previous Approximation

ABSTRACT: Prediction of unsteady aerodynamic loads is still the most challenging task in flutter aeroelastic analysis. Generally the numerical estimation of steady and unsteady aerodynamic of thin lifting surface is conducted based on an integral equation relating aerodynamic pressure and normal wash velocity. The present work attempts to increase the accuracy of the prediction by using an approximate approach to evaluate kernel function occurring in the integral equation in the form of cylindrical function.  Following previous approximation approach by other researchers to solve the cylindrical function for planar lifting surfaces, in the present work such approach is extended to non planar lifting surfaces.  To increase the accuracy of the method, the integration region of the kernel function is divided into two parts namely near and far regions, where a nonlinear regression curve fitting technique is adapted to approximate the denominator part of the cylindrical function of each region.ABSTRAK: Penelahan daya aerodinamik tidak stabil merupakan satu tugas yang mencabar dalam menganalisis getaran aeroanjalan. Umumnya, anggaran berangka untuk daya aerodinamik stabil dan tidak stabil pada permukaan mengangkat yang nipis, adalah berdasarkan kepada persamaan kamiran di antara tekanan aerodinamik dan halaju aliran udara pada garis normal yang terhasil di bawah sayap pesawat. Kajian ini adalah bertujuan untuk menghasilkan penelahan daya aerodinamik yang lebih tepat dengan menggunakan pendekatan kira hampir untuk menilai fungsi Kernel yang terdapat dalam persamaan kamiran dalam bentuk fungsi silinder. Dengan menggunakan pendekatan kira hampir yang digunakan oleh penyelidik sebelumnya untuk menyelesaikan fungsi silinder pada permukaan mengangkat satah, kajian ini mengembangkan pendekatan tersebut kepada permukaan mengangkat tak sesatah. Untuk meningkatkan lagi ketepatan penelahan, kawasan pengamiran fungsi Kernel dibahagikan kepada dua bahagian, kawasan hampir dan kawasan jauh, di mana penyuaian lengkung regresi tak linear digunakan untuk kiraan hampir penyebut pada fungsi silinder pada setiap kawasan.

Lifting Surface Theory for the Problem of an Arbitrarily Yawed Sinusoidal Gust Incident on a Thin Aerofoil in Incompressible Flow

1970 ◽  
Vol 21 (2) ◽  
pp. 182-198 ◽  
Author(s):  
J. M. R. Graham
Keyword(s):  
Integral Equation ◽  
Kernel Function ◽  
Incompressible Flow ◽  
Velocity Component ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Surface Theory ◽  
Equation Solution ◽  
Chebyshev Expansion ◽  
Dimensional Integral

SummaryThe solution to the problem of the loading generated on a two-dimensional thin aerofoil by an incompressible flow whose normal velocity component is of the general form exp [i(λx+/μy — ωt)] is calculated. The method used extends the two-dimensional integral equation solution for the induced vorticity by means of a Chebyshev expansion of part of the kernel function. Thin aerofoil approximations are made throughout, but no collocation procedure, as such, is required.

scholarly journals Numerical Solution of the Cauchy-Type Singular Integral Equation with a Highly Oscillatory Kernel Function

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 872 ◽  
Author(s):  
◽  
Shuhuang Xiang ◽  
Guidong Liu
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Numerical Solution ◽  
Integral Equations ◽  
Kernel Function ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Cauchy Type ◽  
Error Analyses ◽  
Highly Oscillatory

This paper aims to present a Clenshaw–Curtis–Filon quadrature to approximate thesolution of various cases of Cauchy-type singular integral equations (CSIEs) of the second kind witha highly oscillatory kernel function. We adduce that the zero case oscillation (k = 0) proposed methodgives more accurate results than the scheme introduced in Dezhbord at el. (2016) and Eshkuvatovat el. (2009) for small values of N. Finally, this paper illustrates some error analyses and numericalresults for CSIEs.

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