Frank Kushner is an independent Consulting Engineer specializing in dynamics and acoustics testing and analysis. He has had 42 years of experience with industrial turbomachinery, mostly with the Elliott Company, and four years previous experience with the jet engine combustion section development group at Pratt & Whitney Aircraft. Mr. Kushner holds patents for a blade damping mechanism and a method to prevent a one-cell rotating stall in centrifugal compressors.

Frank Kushner

This article applies to centrifugal and axial compressors. Reciprocating, screw, and scroll compressors and ejectors have different considerations. For “dynamic” radial or axial gas compressors the predominant noise source is rotating blade passing frequency. There is also noise due to flow turbulence and vortex shedding from stationary vanes and rotating blades. The blade passing frequency is due to interaction of non-uniform flow. Noise levels increase as power increases, but especially as equivalent tip speed goes higher. Operating far from design point can also increase noise levels due to poor blade incidence angles.

Upstream inlet and return channel vane wakes do not cause high interaction noise in centrifugal compressors as there typically is fairly high separation and thus upstream wake reduction. However, downstream diffusers can sometimes have vanes that are close to impeller tips.

Potential flow interaction is a mandatory design consideration for structural vibration of both the rotating impeller and diffuser vanes. In addition, the interaction can greatly increase acoustic pulsations with noise increase up to 10 dB at rotating blade passing frequency. The acoustic pulsations rotate with diametral patterns depending on numbers of upstream and downstream vanes, and can excite acoustic modes of the gas within the compressor – see previous blog article: "

Can High Noise Levels Cause Fatigue of Covered Impellers?

Most compressor casings for process plants are not treated for noise unless there is a low noise guarantee especially for residential boundary limits. Removable, reusable, weather and oil-proof acoustic blankets are an option. For very low noise cases noise barriers are an alternative to high-maintenance enclosures especially for hazardous gases, thus avoiding fire detection and suppression. There is no need to treat the casing if inlet and discharge piping is not treated with insulation and jacketing, overlapping and banding in-place as described in references.

For centrifugal compressors discharge piping noise can have a large increase due to resonance of acoustic modes of the gas within the pipe.

Piping Noise Resonance - Transverse Gas Modes Inside Pipes

Figure 1 has a plot for modes using the constants plotted with sonic velocity Vs blade passing frequency.

In Figure 2 the 2-diameter mode shape is shown.

Figure 1. Lines of Resonance for Gas Transverse Modes Within Long Circular Pipes.

Figure 2. Two-diameter Gas Mode Shape - Four Radial Node Lines

Figure 3. One-Circle Mode Resonance for Discharge Pipe from Compressor Handling Low Mol Weight Gas.

Lower mol weight gases are more likely to have resonance of the lower modes that are more easily excited by blade passing frequency.

In addition there can be resonance of piping structural modes with blade passing frequency.

 is natural frequency in Hz for mode with "n"-diameters

 = speed of sound in pipe   (17,100 ft/sec for steel at normal temperatures)

Common modes shapes for both the gas inside the pipes and the shell modes are possible and can lead to even higher noise and potential fatigue of pipes. A case of high noise causing piping stub out failures from operating on the verge of compressor surge is described in Reference 3. The last stage impeller revision changed the modes to much higher order and greatly reduced noise, along with not running at flow rate very near surge, the initial cause of piping failures.

For axial compressor typically with many more blades frequencies are much higher and resonance of higher-order modes is not an issue. For industrial axial compressors as for gas turbines, open-air inlets filters that reduce noise somewhat along with dissipative silencers are needed. Orientation for inlet silencers must assure the insulation cannot become wetted from rain.

Discharge silencers are an option as well if the gas is clean. Some centrifugal compressors utilize standard discharge dissipative silencers using insulation within perforated walls, or the Helmholtz resonator method, patterned after US Patent 4411592 - Pressure Variation Absorber. However, the process gas must be clean such as for natural gas pipeline compressors as both types utilize small holes that can become fouled from particulates and thus blocked from allowing sound waves to enter the device.

Besides compressor noise, vortex shedding and other acoustic pulsations such as from valves are potential causes of piping fatigue. In Reference 7 is a quotation from a technical group covering aspects of piping failures. “Failures of piping in the hydrocarbon industry represent a potential for catastrophic accidents in terms of both lives and dollars lost. It has been reported that over 20% of the piping failures in the UK sector of the North Sea were due to piping vibration and fatigue failures. It is clear that AIV is a serious risk since a single failure will often shut down a facility for hours or days, resulting in lost production, at a minimum.”

1. Jungbauer and Eckhardt, “Flow-induced Turbocompressor and Piping Noise and Vibration Problems—Identification, Diagnosis, and Solution”, 26

 Texas A&M Turbomachinery Symposium Proceedings, 1997, pp. 79-86.

2. Price and Smith, “Sources and Remedies of High-Frequency Piping Vibration and Noise”, 28

 Texas A&M Turbomachinery Symposium Proceedings, 1999, pp. 189-212.

3. Kushner, Walker, and Hohlweg, “Compressor Discharge Pipe Failure Investigation with a Review of Surge, Rotating Stall” and Piping Resonance”, 31

 Texas A&M Turbomachinery Symposium Proceedings, 2002, pp. 49-60.

4. Badini, John and Brown, Paul A., “Guidelines For Reducing the Noise Level of a Centrifugal Air Compressor Installation”, Proceedings of the Second Middle East Turbomachinery Symposium, 2013, Doha, Qatar.

5. Stein, Thomas, "Analyzing and Controlling Noise in Process Plants", Chemical Engineering, March 10, 1980, PP 129-137.

      6. “The Role of Insulation in Noise Control - Acoustical Lagging Systems for Reducing Pipe-Radiated Noise”

7. Linkedin: Acoustic-Induced Vibration Technical Group

Articles

Better design for less noise in compressors

Interference Diagrams” also termed by some as “Safe Diagrams" are utilized for fully-coupled rotating blades. In Reference No. 1 resonance where harmonic of speed is equal to nodal diameters is reviewed, along with when difference in numbers of blades and vanes equal to number of diameters.

An example of nodal diameter “critical speeds” is shown above where there are 60 interlocked blades with a speed range of 3600 to 4800 rpm.

Nozzle passing frequency is not of much concern for modern designs utilize continuous shrouded blades, termed Z-lock or Z-notch, where there is beneficial friction damping at the shrouds. For long tapered, twisted blades there will be vibratory motion for each direction, axial and tangential giving first and second families of modes shown in the plot above.

Many other designs for long turbine blade are not fully connected (one packet) but are assembled into separate packets that could be resonant with even lower harmonics of speed. For these the tuned “Safe Diagram” theory is more likely to apply than for short blades as described in the author’s previous article. Each packet of long blades could have individual frequencies very close to each other, just as assumed with models for finite element analyses. Tuned packets result in coupled modes where patterns produce diametral nodal lines with adjacent packets out-of-phase with each other. With 24 packets the highest in-phase mode would have 12 diameters as shown in the figure below for 120 blades, 24 tuned packets with five nearly identical last stage blades per packet.

12 Diameter Mode Shape: 12 packets In-Phase and 12 Packets Out-of Phase

Lower harmonic excitation can arise from non-uniformity of upstream nozzles as well as potential flow of non-uniform 90-degree exhaust casings. Can the 24-packet assembly respond for resonance with five times operating speed of the fundamental In-Phase mode? There would be response for this example as five is less than 24/2 = 12.

If this design has 10 or more packets it could respond with fairly high response at 5X. With 24 packets five times speed would excite the 5-diameter mode. But by changing to only  8 packets some claim it would not respond if it was tuned; i.e. the point 8 over 2 = 4 shown in the figure above is less than 5 times running speed. The five diameter mode would not exist for eight tuned packets. Due to phase cancellation five times speed also would not excite a 4-diameter mode if its frequency was at five time speed. Note that nodal diameter frequencies are close together in the figure above. In Reference 4 the authors Wagner and Griffin give an equation to use to check for other cases of tuned packet response where they say for a mode wirh "m" diameters:

It was shown in Part I that the condition required for an N group bladed disk to respond to an excitation harmonic h while constrained to mode harmonic m is given by h = jN ± m

where j = 0, 1, 2, . . . , with the further condition that h cannot be negative, and that negative values of m need not be considered.

Thus for 120 blades with eight packets, a 3-diameter mode has response when at resonance with five times speed as: 5 = 8 packets – 3.

See Table 2 highlighted in red below showing positive participation factor.

For certain numbers of blades and packet selections even tuned assemblies will respond. With a change to 112 total blades and using seven packets with 16 blades there would be phase cancellation if the 3-diameter mode was resonant with 5 times speed. However the possibility of mistuned packets should also be considered, not only from design and manufacturing differences, but from changes during operation such as from erosion/corrosion. Using many more blades per packets than five or six is usually much better for phase cancellation. An example of experimental results for a case with 12 packets, resonant with 3X is shown in Figure 10 of Reference 5.

Let us again review a design with 120 rotating blades, but with mistuned packets, resonant with five times speed. Recommending a change from 24 packets to 8 packets will reduce the resonant response factor at 5X speed from 0.93 to 0.47 as shown in the table below. This may not be safe enough, especially if the stage is a transition stage with wet steam and corrodants in the steam. The optimum would be five packets of blades; the resonant response factor would be near zero for the fundamental mode. This is called the “long arc” or “harmonic shrouding” method of selecting blade packets for back-end stages. (Reference 6). Using Weaver & Prohl equations with excitation at the 5’Th harmonic:

Table: Resonant Response Variation with Packet Changes

              120 Blades : Resonance Of Fundamental IN-Phase Mode With 5 X Speed

                       4

                    0.96

                       5

                    0.93

                      15

                    0.47

                      24

                    0.00

It usually turns out where shrouds are attached with peened-on tangs that as many blades as possible should be used instead of only five or six per packet often found in practice. (Some older designs are welded into groups). However all designs should be checked with Weaver and Prohl equations for fundamental mode response. For some stages with very low “Goodman Factors” checking the next highest packet mode where half the blades vibrate out-of-phase with the other blades may also be needed as explained in References 1 and 4.

This review is for fundamental modes with vibration in tangential direction; similar analysis applies to fundamental axial direction in-phase modes. Again for long tapered, twisted blades there will be vibratory motion for each direction for the axial and tangential mode families. Failure analysis of high cycle fatigue of blades assembled into packets should review potential resonance, reduction in strength of excitation sources, and the benefit of change to an optimum number of blades per packet. In addition correct operating conditions and steam purity must be reviewed for root cause failure analysis.

 1. Kushner, F., 1979, “Disc Vibration - Rotating Blade and Stationary Vane Interaction,” ASME Paper No. 79-Det-83: 1980 ASME Transactions, Journal of Mechanical Design, 102, pp. 579-584.

2. Weaver, F. L., and Prohl, M. A., 1958, “High Frequency Vibration of Steam Turbine Buckets,” Trans. ASME, Vol. 78, pp. 181-189, 1958.

3. 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.

4. Wagner, L. F. and Griffin, J. H., 1996, “Forced Harmonic Response of Grouped Blade Systems: Part II—Application,” ASME Journal of Engineering for Gas Turbines and Power, 118, pp. 137-145.

5. Sanvito, M., Pesatori, E., Bachschmid, N., Chatterton, S., 2012, “Analysis of LP Steam Turbine Blade Vibrations: Experimental Results and Numerical Simulations”; 10th International Conference on Vibrations in Rotating Machinery, IMech, pp 189 – 197.

6. Ortolano, R.J., La Rosa J.A., and Welch W.P., 1981, "Long Arc Shrouding - A Reliability Improvement for Untuned Steam Turbine Blading," ASME J. Eng. Gas Turbines Power 103(3), pp. 522-527.