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Lösung von Randwertproblemen der Schwingungsgleichung für ein Modell eines Triebwerkeinlaufs
Author(s) -
Friedrich N.,
Meister E
Publication year - 1979
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670010203
Subject(s) - mathematics , cylinder , eigenfunction , inlet , mathematical analysis , geometry , physics , mechanical engineering , eigenvalues and eigenvectors , quantum mechanics , engineering
We consider a simple model of a jet engine inlet consisting of two coaxial cylinders. The inner cylinder extends in both directions to infinity and represents the hub of a jet engine. The outer cylinder is assumed to be semiinfinite representing the engine's jacket. This arrangement is approached by a compressible and invisced gas moving at a velocity U less than the speed of sound. Two problems are formulated. In problem A a normal speed distribution is given in the compressor‐inlet plane, in problem B we are given a pressure distribution. We look for the induced pressure and velocity fields. Using the acoustical approximation of the fundamental equations the Wiener‐Hopf‐method is applied then leading, after a multiplicative and additive decomposition procedure, to an infinite system of linear equations. These involve the expansion coefficients of the solution with respect to the eigenfunctions of the concentric cylindrical duct. Applying arguements from perturbation theory it is possible to extract the essential information from this system of equations. Apart from the possible exception of a denumerable set of values of the distance L of the blade‐row from the inlet the problem has a unique solution.