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Acoustic Resonance in a High-Speed Axial Compressor

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Acoustic Resonance in a High-Speed Axial Compressor ACOUSTIC RESONANCE IN A HIGH -SPEED AXIAL COMPRESSOR ACOUSTIC RESONANCE IN A HIGH- SPEED AXIAL COMPRESSOR Der Fakultät für Maschinenbau der Gottfried Wilhelm Leibniz Universität Hannover zur Erlangung des akademischen Grades Doktor-Ingenieur genehmigte Dissertation von Dipl.-Phys. Bernd Hellmich geboren am 23.11.1970 in Rahden/Westfalen, Deutschland 2008 I ACOUSTIC RESONANCE IN A HIGH -SPEED AXIAL COMPRESSOR Referent: Prof. Dr.-Ing. Jörg Seume Korreferent: Prof. Dr.-Ing. Wolfgang Neise Vorsitzender: Prof. Dr.-Ing. Peter Nyhuis Tag der Promotion: 12.11.2007 II ACOUSTIC RESONANCE IN A HIGH -SPEED AXIAL COMPRESSOR „Das Chaos ist aufgebraucht, es war die beste Zeit“ B. Brecht Für Bettina III ACOUSTIC RESONANCE IN A HIGH -SPEED AXIAL COMPRESSOR IV ACOUSTIC RESONANCE IN A HIGH -SPEED AXIAL COMPRESSOR 1. Abstract 1. Abstract Non-harmonic acoustic resonance was detected in the static pressure and sound signals in a four-stage high-speed axial compressor when the compressor was operating close to the surge limit. The amplitudes of the resonant acoustic mode are in a range comparable to the normally dominating blade passing frequency. This has led to blade cracks in the inlet guided vanes of the compressor where the normal mechanical and aerodynamic load is low. The present measurements were obtained with a dynamic four-hole pneumatic probe and an array of dynamic pressure transducers in the compressor casing. For signal decomposition and analysis of signal components with high signal-to-noise ratio, estimator functions such as Auto Power Spectral Density and Cross Power Spectral Density were used. Based on measurements of the resonance frequency and the axial and circumferential phase shift of the pressure signal during resonance, it is shown that the acoustic resonance is an axial standing wave of a spinning acoustic mode with three periods around the circumference of the compressor. This phenomenon occurs only if the aerodynamic load in the compressor is high, because the mode needs a relative low axial Mach number at a high rotor speed for resonance conditions. The low Mach number is needed to fit the axial wave length of the acoustic mode to the axial spacing of the rotors in the compressor. The high rotor speed is needed to satisfy the reflection conditions at the rotor blades needed for the acoustic resonance. The present work provides suitable, physically based simplifications of the existing mathematical models which are applicable for modes with circumferential wavelengths of more than two blade pitches and resonance frequencies considerably higher than the rotor speed. The reflection and transmission of the acoustic waves at the blade rows is treated with a qualitative model. Reflection and transmission coefficients are calculated for certain angles of attack only, but qualitative results are shown for the modes of interest. Behind the rotor rows the transmission is high while in front of the rotor rows the reflection is dominating. Because the modes are trapped in each stage of the compressor by the rotor rows acoustic resonance like this could appear in multi stage axial machines only. Different actions taken on the compressor to shift the stability limit to lower mass flow like dihedral blades and air injection at the rotor tips did not succeed. Hence, it is assumed that the acoustic resonance is dominating the inception of rotating stall at high rotor speeds. A modal wave as rotating stall pre cursor was detected with a frequency related to the acoustic resonance frequency. In addition the acoustic resonance is modulated in amplitude by this modal wave. The acoustic waves are propagating nearly perpendicular to the mean flow, so that they are causing temporally an extra incidence of the mean flow on the highly loaded blades, but it could not be proved if this triggers the stall. A positive effect of the acoustic resonance on the stability limit due to the stabilization of the boundary layers on the blades by the acoustic field is also not excluded. Keywords: acoustic resonance, axial compressor, rotating stall V ACOUSTIC RESONANCE IN A HIGH -SPEED AXIAL COMPRESSOR 1. Abstract Kurzfassung Nicht drehzahlharmonische akustische Resonanzen sind in den statischen Drucksignalen in einem vierstufigen Hochgeschwindigkeitsaxialverdichter gemessen worden, als dieser nahe der Pumpgrenze betrieben worden ist. Die Amplituden der resonanten Moden lagen in derselben Größenordnung wie die Schaufelpassier- frequenz. Das führte zu Rissen in den Schaufeln im Vorleitapparat des Kompressors, wo die normale mechanisch und aerodynamisch Belastung niedrig ist. Die vorliegenden Messungen sind mit einer dynamischen Vierloch-Sonde und einem Feld von dynamischen Drucksensoren im Kompressorgehäuse durchgeführt worden. Zur Signalzerlegung und Analyse mit hohem Signal zu Rauschverhältnis sind Schätzfunktionen wie Autospektrale Leistungsdichte und Kreuzspektrale Leistungsdichte verwendet worden. Aufgrund von Messungen der Resonanzfrequenz sowie des axialen und peripheren Phasenversatzes der Drucksignale unter resonanten Bedingungen ist gezeigt worden, dass die akustische Resonanz in axialer Richtung eine stehende Welle ist mit drei Perioden um den Umfang. Das Phänomen tritt nur auf, wenn die aerodynamische Belastung des Kompressors hoch ist, da die Resonanzbedingungen für die Mode eine niedrige axiale Machzahl bei hoher Rotordrehzahl erfordern. Die relativ niedrige axiale Machzahl ist nötig, damit die axiale Wellenlänge zum axialen Abstand der Rotoren passt. Die hohe Drehzahl ist notwendig, um die Reflektionsbedingungen an den Rotorschaufeln zu erfüllen. Die vorliegende Arbeit verwendet physikalisch basierte Vereinfachungen von existierenden Modellen, die anwendbar sind auf Moden mit einer Wellenlänge in Umfangsrichtung, die größer als zwei Schaufelteilungen sind und eine Resonanzfrequenz haben, die über der Rotordrehzahl liegt. Die Reflektion und Transmission von akustischen Wellen ist mit einem qualitativen Modell behandelt worden. Die Reflektions- und Transmissionskoeffizienten sind nur für bestimmte Einfallswinkel berechnet worden, aber die Ergebnisse zeigen, dass für die relevanten Moden die Transmission hinter den Rotoren hoch ist während vor den Rotoren die Reflexion dominiert. Weil die Moden zwischen den Rotoren eingeschlossen sind, können akustische Resonanzen wie diese nur in mehrstufigen Axialmaschinen auftreten. Verschiedene Maßnahmen, die an dem Kompressor durchgeführt worden sind, wie dreidimensionale Schaufelgeometrien oder Einblasung an den Rotorspitzen, haben zu keiner Verschiebung der Stabilitätsgrenze zu niedrigeren Massenströmen geführt. Deshalb wird angenommen, dass die akustische Resonanz die Entstehung einer rotierenden Ablösung (Rotating Stall) herbeiführt. Eine Modalwelle als Vorzeichen für den Rotating Stall ist gemessen worden, dessen Frequenz ein ganzzahliger Bruchteil der Frequenz der akustischen Resonanz ist. Außerdem ist die Amplitude der akustischen Resonanz von der Modalwelle moduliert. Die akustischen Wellen laufen nahezu senkrecht zur Strömungsrichtung, so dass sie kurzzeitig eine zusätzliche Fehlanströmung der hoch belasteten Schaufeln verursachen, aber es konnte nicht bewiesen werden, dass dies die Ablösung auslöst. Ein positiver Einfluss der akustischen Resonanz auf die Stabilität des Verdichters durch die Stabilisierung der Grenzschichten auf den Verdichterschaufeln ist ebenso nicht ausgeschlossen. Schlagwörter: Akustische Resonanz, Axialverdichter, Rotierende Ablösung VI ACOUSTIC RESONANCE IN A HIGH -SPEED AXIAL COMPRESSOR 2. Contents 2. Contents 1. Abstract...................................................................................................................V 2. Contents................................................................................................................VII 3. Nomenclature ........................................................................................................IX 4. Introduction ............................................................................................................ 1 4.1. Compressors...................................................................................................... 1 4.2. Flow distortions in compressors ......................................................................... 3 5. Literature Review ................................................................................................... 5 6. Test facility.............................................................................................................. 8 6.1. The test rig ......................................................................................................... 8 6.2. Sensors, Signal Conditioning and Data Acquisition.......................................... 10 7. Signal processing methods ................................................................................ 12 7.1. Auto Power Spectral Density (APSD)............................................................... 12 7.2. APSD estimation by periodogram averaging method....................................... 13 7.3. Cross power spectral density (CPSD), phase, and coherence......................... 15 7.4. Coherent transfer functions.............................................................................. 17 7.5. Statistical Errors of coherence, power and phase spectra ............................... 18 7.6. Spectral leakage............................................................................................... 20 8. The Phenomenon ................................................................................................
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