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As shown in previous articles it is stationary vane numbers that can cause significant interaction resonance of disk modes. Direct pressure loads at rotating blade passing frequency and harmonics in turn excite stationary vane natural frequencies. Downstream diffuser vanes for compressor stages are of prime importance to consider for resonance avoidance with number of rotating blades times speed. But there is some confusion in that some investigators have said to also avoid direct resonance where rotating blade passing frequency is equal to a disk mode frequency.
In the 1960’s there began much insight into jet engine blade passing frequency noise by Pratt & Whitney’s Tyler & Sofrin’s widely referenced paper (Ref. 1). They showed that tonal noise has inherent number of circumferential lobes based on phase analysis of numbers of rotating blades and stationary vanes; acoustic waves spin with modal patterns equal to sum and differences of rotating and stationary blade numbers, including harmonics that can also be important.
Besides this interaction there is concern for vortex shedding exciting acoustic modes within the annulus that contains axial compressor cantilevered blades. A case of blade failures was analyzed for excitation due to vortex shedding from inlet struts. It was shown not to be the cause but cracks were initiated by excessive surging of the system with an undersized blowoff valve. (See Case A-2 in Ref. 2). However treatment of the inlet vane shapes greatly reduced noise. Jet engine designers must guard against acoustic resonance for cantilevered blades.
Turning now to impellers for centrifugal gas compressors, there has been some concern that past fatigue failures had acoustic pressure pulsations as the excitation source. Eisinger (Ref. 3) described a case due to excessive turbulence at the inlet of a centrifugal fan. Price & Smith (Ref. 4) showed that noise caused by an inlet valve was eliminated, as it was the acoustic source for a covered impeller failure, albeit it may have been a different mode that what was described. Another source of high noise within machinery is flow past casing cavities, exciting modes within the cavity, but would be an extremely rare cause of structural fatigue for rotor components.
Normally the highest noise source in compressors is found to be at rotating blade passing frequency. The wavelengths are typically small enough to have little attenuation as the sound travels up and down piping, thus exciting acoustic modes within the pipes. Resonance can be a concern for piping walls with matching structural modes, but even more importantly have caused cracks at protruding take-offs for instrumentation, etc.
The question under consideration herein is whether rotating blade passing frequency noise – the predominant source - can actually cause self-excitation of impellers. It appears so but only in rare cases and likely only for high-pressure compressors where noise levels are much higher.
Excerpts from Ref. 5:
Where: B = Number of Blades V = Number of Vanes m = Circumferential mode order
w (omega) = Angular velocity (radians / second) f = frequency (Hz)
Subscripts: p – pressure abs – absolute rel – relative esc – excitation s - shaft
A paper by Richards et al, Ref. 6, utilized strain gauges to confirm disk mode acoustic resonance. This report did not show a resonance at the rotating blade passing frequency but rather found the resonance was due to a combination of upstream vane wakes and downstream vane acoustic reflections. In their case there was not a corresponding acoustic resonance coincident with Tyler/Sofrin modes so that dynamic strains were not of concern.
Two other recent papers by Siemens brought the potential of acoustic interaction with impeller structural modes to full understanding with conclusive proof. (Refs. 7 and 8). The Siemens 2010 paper confirmed Root Cause Failure Analysis given in their 2009 Texas A&M paper.
The two papers give analytical and confirming test results for two actual high-pressure compressor cases where modes of failed impellers were resonant at harmonics of stationary vanes – not at rotating blade passing frequency. It was concluded there was resonance for 17 bladed impellers, 5-diameter disk mode with resonance at 22 times speed from downstream vanes, along with side cavity acoustic 5-diameter mode at 17 per rev resonance deemed to cause a failure. The fix for both cases was to change number of stationary vanes, from 22 to 25 for Case A and from 22 to 19 for Case B. For both modifications disk modes did not change and blade passing frequency remained the same, leaving the number of impeller blades at 17.
Marked-up figure from the 2009 Siemens paper below shows triple coincidence:
1. Tyler/Sofrin mode with 5-diameter as 22-17 = 5
2. 5-Diameter Disk Mode at 22 X speed
3. Acoustic mode with 5 diameters = 17X
In summary, coupling of matching modes, acoustic and structural, is necessary at traveling wave resonance at operating speed. A triple coincidence is needed, the same structural and acoustic mode, along with the correct number of stationary vanes for Tyler / Sofrin spinning acoustic modes.
The GE and Siemens’ papers are conclusive proof that rotating blade passing frequency does not give concern if it matches frequency of a disk mode, but noise rather excites at traveling wave frequency. Whenever there is an impeller failure especially for a high pressure “dry” gas compressor acoustic analysis of gas modes at the sides of the cover and hub disk should be considered as explained by Siemens' papers.
1. Tyler, J.M., and Sofrin, T.G., 1962, “Axial Flow Compressor Noise Studies”, SAE Transactions, Vol.70, pp.309-332.
2. Kushner, F., 2004, "Rotating Component Modal Analysis And Resonance Avoidance Recommendations", Tutorial, Proceedings of the 33rd Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, TX. Pp. 143-161.
3. Frantisek L. Eisinger and Robert E. Sullivan, “Vibration Fatigue of Centrifugal Fan Impeller Due to Structural-Acoustic Coupling and Its Prevention: A Case Study”, PVP2006-ICPVT-11-93049; pp. 47-53 ASME Proceedings - 2006 Pressure Vessels and Piping/ICPVT-11, 2006, Vancouver, BC, Canada
4. S.M. Price and D.R. Smith, 1999, “Sources and Remedies of High-Frequency Piping Vibration and Noise”, Proceedings of the 28th Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, TX.
5. Petry, N., Benra, F. K., Konig, S., and Woiczinski, C., 2009. “Interaction between aerodynamic phenomena and impeller structure of high pressure radial compressors”. In 8th European Turbomachinery Conference, no. C71.
6. S. Richards, K. Ramakrishnan, C. Shieh, et al, “Unsteady Acoustic Forcing On an Impeller Due to Coupled Blade Row Interactions” Proceedings of ASME Turbo Expo 2010: June 14-18, 2010, Glasgow, UK
7. S. Konig, N. Petry, N.G. Wagner; 2009, “Aeroacoustic Phenomenon in High-Pressure Centrifugal Compressors- A Possible Root Cause For Impeller Failures”; Proceedings of the 38th Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, TX.
8. N. Petry, F. Benra, S. Koenig, 2010, “Experimental Study of Acoustic Resonances in the Side Cavities of a High-Pressure Centrifugal Compressor Excited by Rotor/Stator Interaction” Proceedings of ASME Turbo Expo 2010: June 14-18, 2010, Glasgow, UK