Das Potential und das Geschwindigkeitsfeld der harmonisch schwingenden tragenden Fläche bei Unterschallströmung

Abstract

Für einen in Unterschallströmung senkrecht zu seiner Ebene harmonisch schwingenden Tragflügel wird das Potential und das Geschwindigkeitsfeld formuliert. Die zugehörigen Einflußfunktionen werden für einige besondere Fälle diskutiert.

Use of complex cross-flow representation in nonplanar oscillating-surface theory.

“…It may be more efficient to employ (13) instead of (17), however, since the integral involved in (13) contains only the comparatively simple kernel function (A'x,p)* The current and more complicated kernel A(x } p) in (17) also appears in the first term of (13), but in this case it is sufficient to evaluate it only at one point, located at the trailing edge, on each chord. We note that a slightly different formula but with similar favorable properties as (13) has been employed earlier by Davies. 2 We also note that (9) might be considered as another possible alternative for numerical evaluation.…”

“…The expression (13) represents an alternative formula that may be used instead of (17) for evaluation of J(v) for any loading function in a linear approximation to A$ x (x). The potential jump in (13) is to be replaced by streamwise integrals, usually obtainable in closed form, of the loading functions.…”

“…The expression (13) represents an alternative formula that may be used instead of (17) for evaluation of J(v) for any loading function in a linear approximation to A$ x (x). The potential jump in (13) is to be replaced by streamwise integrals, usually obtainable in closed form, of the loading functions. It may be more efficient to employ (13) instead of (17), however, since the integral involved in (13) contains only the comparatively simple kernel function (A'x,p)* The current and more complicated kernel A(x } p) in (17) also appears in the first term of (13), but in this case it is sufficient to evaluate it only at one point, located at the trailing edge, on each chord.…”

Self‐propulsion of oscillating wings in incompressible flow

“…In exchange for the limitations concerning the geometry of the airfoil, the lifting surface theory has a nice mathematical formulation which leads to an integral equation for the jump of the pressure across the airfoil. The problem of the oscillatory thin wings in subsonic flow (and implicitly in incompressible flow) was studied, among others by Watkins et al [1], Laschka [2], and Landahl [3]. In their theory, the integral equation, originally performed by Küssner [4] is obtained by determining the acceleration potential due to a continuous distribution of doublets on the wing.…”

Incompressible flow past oscillatory wings of low aspect ratio by the integral equations method

“…The camber problem for the oscillating wings in subsonic ow (and implicitly in incompressible ow) was studied, among others, by Watkins et al [1], Laschka [2] and Landahl [3]. In their theory the integral equation, originally performed by K ussner [4] is obtained by determining the acceleration potential due to a continuous distribution of doublets on the wing.…”