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.

Gust Loading on a Thin Aerofoil

1971 ◽  
Vol 22 (3) ◽  
pp. 301-310 ◽  
Author(s):  
B. D. Mugridge
Keyword(s):  
Approximate Solution ◽  
Closed Form ◽  
Incompressible Flow ◽  
Velocity Component ◽  
Closed Form Expression ◽  
Sound Power ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Form Expression ◽  
Final Expression

SummaryA closed-form expression is derived which gives an approximate solution to the lift generated on a two-dimensional thin aerofoil in incompressible flow with a normal velocity component of the form exp [i(ωt–xx+yy)]. The inaccuracy of the solution when compared with other published work is compensated by the simplicity of the final expression, particularly if the result is required for the calculation of the sound power radiated by an aerofoil in a turbulent flow.

Nonaxisymmetric Annular Punch Problem

1991 ◽  
Vol 58 (4) ◽  
pp. 947-953
Author(s):  
V. I. Fabrikant
Keyword(s):  
Integral Equation ◽  
Potential Theory ◽  
Two Dimensional ◽  
Title Problem ◽  
Annular Punch ◽  
First Time ◽  
Dimensional Integral ◽  
Punch Problem

A general formulation is given for the first time to the title problem. The method is based on the new results in potential theory obtained by the author earlier. The problem is reduced to a two-dimensional integral equation with an elementary kernel. Several specific examples are considered.

Three-Dimensional Lifting-Surface Theory for an Annular Blade Row

1979 ◽  
Author(s):  
G. F. Homicz ◽  
J. A. Lordi
Keyword(s):  
Integral Equation ◽  
Three Dimensional ◽  
Computer Time ◽  
Two Dimensional ◽  
Blade Loading ◽  
Surface Theory ◽  
Lifting Surface ◽  
Strip Theory ◽  
Blade Row ◽  
Flow Through

A lifting-surface analysis is presented for the steady, three-dimensional, compressible flow through an annular blade row. A kernel-function procedure is used to solve the linearized integral equation which relates the unknown blade loading to a specified camber line. The unknown loading is expanded in a finite series of prescribed loading functions which allows the required integrations to be performed analytically, leading to a great savings in computer time. Numerical results are reported for a range of solidities and hub-to-tip ratios; comparisons are made with both two-dimensional strip theory and other three-dimensional results.

The effect of a fixed vertical barrier on surface waves in deep water

1947 ◽  
Vol 43 (3) ◽  
pp. 374-382 ◽  
Author(s):  
F. Ursell
Keyword(s):  
Integral Equation ◽  
Surface Waves ◽  
Deep Water ◽  
Vertical Plane ◽  
Standing Waves ◽  
Simple Type ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Vertical Barrier ◽  
The Mean

In this paper the two-dimensional reflection of surface waves from a vertical barrier in deep water is studied theoretically.It can be shown that when the normal velocity is prescribed at each point of an infinite vertical plane extending from the surface, the motion on each side of the plane is completely determined, apart from a motion consisting of simple standing waves. In the cases considered here the normal velocity is prescribed on a part of the vertical plane and is taken to be unknown elsewhere. From the condition of continuity of the motion above and below the barrier an integral equation for the normal velocity can be derived, which is of a simple type, in the case of deep water. We begin by considering in detail the reflection from a fixed vertical barrier extending from depth a to some point above the mean surface.

Sign in / Sign up

Export Citation Format

Share Document