Lösung von Randwertproblemen der Schwingungsgleichung für ein Modell eines TriebwerkeinlaufsHerrn Prof. Dr. H. Söhngen zu seinem 70. Geburtstag am 30. November 1978 gewidmet

0170-4214

Mathematics and Statistics ; Applied Mathematics

Wiley InterScience Backfile Collection 1832-2000

Mathematics

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.

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