This brief note describes a method for calculating the eigenfrequencies of a rotating acoustic air column inside labyrinth seals in turbomachinery. The method is applied to nonrotating air columns as well as to rotating air columns considering a body fixed and a spatial fixed coordinate system.

Issue Section:
Gas Turbines: Structures and Dynamics
Keywords:
acoustic resonance, turbogenerators, eigenvalues and eigenfunctions, rotors
Topics:
Acoustics, Annulus, Equations of motion, Turbomachinery
1.
Kwanka
,
K.
,
1997
, “
Improving the Stability of Labyrinth Gas Seals
,”
ASME J. Eng. Gas Turbines Power
,
123
(
2
), pp.
383
–
387
.
2.
Childs, D. W., 1993, Turbomachinery Rotordynamics, Wiley, New York.
3.
Gasch, R., Nordmann, R., and Pfu¨tzner, H., 2002, Rotordynamik, Springer, Berlin.
4.
Stetter, H., 1994, Thermische Stro¨mungsmaschinen, Manuskript zur Vorlesung, Institut fu¨r Thermische Stro¨mungsmaschinen, Universita¨t Stuttgart.
5.
Schuck, G., and Nordmann, R., 2002, “Investigation of Self-Excited Vibration in Flexible Labyrinth Seals due to Instationary Pressure Fields,” in Proceedings IFToMM International Conference on Rotor Dynamics, pp. 995–1002, Sydney, Australia.
6.
Childs
,
D. W.
, and
Scharrer
,
J.
,
1986
, “
An Iwatsubo-Based Solution for Labyrinth Seals—Comparison to Experimental Results
,”
ASME J. Eng. Gas Turbines Power
,
108
, pp.
325
–
331
.
7.
Benckert, H., 1980, “Stro¨mungsbedingte Federkennwerte in Labyrinthdichtungen,” Dissertation, Institut fu¨r Stro¨mungsmaschinen und Maschinenlaboratorium, Universita¨t Stuttgart, Stuttgart, Germany.
8.
Thieleke, H., 1991, “Experimentelle und Theoretische Untersuchungen der Stro¨mungskra¨fte in Labyrinthdichtungen von Turbomaschinen,” Dissertation, Institut fu¨r Stro¨mungsmaschinen und Maschinenlaboratorium, Universita¨t Stuttgart, Stuttgart, Germany.
9.
Nackenhorst, U., Wiesemann, S., and Lammering, R., 2000, “Zur Schallabstrahlung Rotierender Strukturen,” in Anwendungen der Akustik in der Wehrtechnik, Deutsche Gesellschaft fu¨r Wehrtechnik.
10.
Gaul, L., Nackenhorst, U., and Nolte, B., 2000, “Numerical Simulation of Noise Radiation From Rolling Tires,” in W. Wendland, editor, Multified Problems in Solid and Fluid Mechanics, Springer, Berlin, pp. 262–269.
11.
Gaul, L., Fischer, M., and Nackenhorst, U., 2002, “Vibrations and Sound Radiation Generated by Contact Between a Rotating Wheel and a Plane,” in Proceedings of ISROMAC-9, pp. DD-ABS-006:1–6.
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 by ASME
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