Zur Theorie der ebenen, instationären Unterschallströmung um ein schwingendes Profil im Kanal

Abstract

The mixed boundary value problem for the determination of the velocity potential of an unsteady perturbation flow past an oscillating thin profile in an inviscid compressible gas at subsonic speeds is treated. After the separation of the wave-like terms in the Fourier expansions of the reduced potential, satisfying the Helmholtz wave equation, the boundary value problem for the remaining potential is transformed into a functional equation of the generalized Wiener-Hopf type by means of the Laplace transform. The familiar Wiener-Hopf technique leads to a linear system of infinitely many unknowns which can be solved by iteration for not too small profile lengths. Finally, two analytic expressions for the reduced potential in terms of different kernel functions and formulae for the lift and moment acting on the profile are written down.