Pulsation fluid models for reciprocating and screw compressor piping have become more sophisticated as the horsepower and speed ranges for the compressors have increased. This is due, in large part, to the need to more reliably predict system responses for control of high vibrations.
Using more advanced computational models, fluid system designers at Southwest Research Institute (SwRI) have been able to more accurately determine expected fluid pulsation levels and corresponding response frequencies and mode shapes, resulting in more efficient and reliable pulsation bottle designs with lower horsepower consumption.
This article highlights some examples of the use of advanced fluid system models at SwRI to provide integrated fluid mechanical design solutions for reciprocating compressor systems and screw compressor silencers.
Pulsation models of reciprocating compressor systems commonly utilize a one-dimensional (1D) representation with acoustic length modifications to represent the three-dimensional (3D) system, given the simplicity and cost-effectiveness of this approach. One-dimensional transient fluid models are generally accurate for pulsating flow piping systems where the dominant physical length is in the flow direction. In the areas near the compressor cylinder, very close to the fluid force excitation from the piston, the 1D assumptions break down since many of the high-frequency energy components have not diminished.
For new high-speed reciprocating compressor cylinder designs, certain 1D representations of the gas passage may not be valid and could lead to incorrect predictions.
Uncontrolled responses associated with the cylinder gas passage system are primarily evident as higher frequency vibrations and high cycle fatigue failures at the compressor valves, cylinder body, and in the cylinder nozzles. Inaccurate designs will lead to use of cylinder nozzle orifice plates, poor valve life, and low compressor efficiency due to high dynamic pressure drop.
SwRI conducted an investigation comparing field data on installed high-speed units to predicted 1D and 3D acoustic responses near the compressor cylinder gas passageways. The combination of a 3D acoustic response model and a 1D fluid representation model was used to provide accurate predictions of all gas passage system responses in a cost effective manner. The testing discussed herein validated the new integrated approach and refined the SwRI transient fluid modeling methods.
In order to characterize the responses in the system, pulsation data from the field site was recorded during a speed sweep of the reciprocating compressor unit which spanned the speeds from 825 -1,000 RPM. (This meant that the primary first order of excitation occurred at 13.75-16.6 Hz and the dominant energy at 2x spanned frequencies from 27.5-33.2 Hz). The four-cylinder compressor with the instrumentation installed is shown from its instrumented side in Figure 1. In this design, the two cylinders on each side of the machine fed into a three-chamber discharge pulsation filter bottle. Suction-side filtering was accomplished with a two-bottle system.
The speed sweep in the field allowed the responses in the gas passage system to be fully traced out, showing the exact location of pulsation maximums. The field data showed a fairly broad discharge cylinder nozzle resonance at 65-75 Hz with pulsation amplitudes as high as 85 psi peak-to-peak near the closed end of the acoustic response (valve cap data). Crank end pulsation levels recorded at the discharge valve cap are shown in Figure 2.
Figure 2: Pulsation Levels At The Discharge Valve Measured For Reciprocating Compressor Field Site (Double Acting Operation).
Lower amplitude responses were evident at 250 Hz and around 270 Hz on both ends of the cylinder. These responses were attributed to valve-to-valve length responses across the cylinder in the piston direction. The nozzle resonant pulsations were causing high vibrations and were the primary cause of concern, although the high frequency responses above 200 Hz were likely complicating the valve motion and may have been coincident with valve mechanical responses, which limited valve life. The vibration issue was later rectified with orifice plate installation at the nozzle cylinder flange. Although the orifice plate dampened the pulsations and brought down the vibrations, it also was costly in terms of compressor horsepower.
3D Acoustic Response Model
The 3D response analysis was performed using a combination of Solidworks and ANSYS finite element models to analyze the fluid space of the cylinder gas passage, nozzle, and filter bottle system. Acoustic modal analysis aims at determining the acoustic natural frequencies of a volumetric model. While all responses in a desired frequency range are determined using this type of analysis, not all responses are necessarily excited and are dependent on operating conditions. The outputs from the acoustic modal analysis are the natural frequencies and their corresponding mode shapes.
The acoustic modal analysis tool is an effective means of determining the natural responses of a solid or fluid domain, but when used by itself, this type of analysis will not determine the amplification of the various responses. It is a true 3D model and provides a means of visualizing the acoustic response, which can be beneficial in determining means of attenuating, altering, or shifting the acoustic response. In determining the significance of the various responses, the designer must review the dimensions, acoustic node, and anti-node points in the response plots.
Comparing to the field data for the reciprocating compressor system, the 3D acoustic response model predicted four responses in the gas passage system which matched the field data very closely, as seen in Figure 3. The primary responses of significance to the manifold system were the cylinder nozzle response predicted at 67 Hz and the valve-to-valve response at 258 Hz and 277 Hz.
The cylinder nozzle resonance predicted to be at 67 Hz in the 3D response model actually peaked at approximately 70 Hz in the field data. The small frequency shift from the field data was likely due to damping effects and the magnitude of excitation frequencies in the actual field system. This was also a fairly broad cylinder nozzle response which could be excited by multiple compressor orders, as shown by the field data speed sweep.
The gas passage responses at 258 and 277 Hz also matched the field data closely (Figure 2). Both of these responses were aligned with the piston direction, which served as the forcing excitation for the fluid system. The side-to-side gas passage response at 180 Hz was not as amplified in the actual system. One reason for the diminished amplification of this response is its direction conflicting with the piston direction. As such, this response was not as evident in the field data.
Figure 3: 3D Response Analysis for Case B – Primary Responses Shown at 66.7 Hz, 180 Hz, 258 Hz and 277.3 Hz.
The utilization of 3D acoustic modal response modeling resulted in a better means of determining source modes and causes of high pulsation for the reciprocating compressor system. Used in combination for 1D pulsation filter designs, the 3D response modeling can help to avoid the use of orifice plates in the cylinder nozzles and other problematic cylinder resonances that can lead to high vibrations and valve failures. This design approach can be used in combination with OEM cylinder designs and bottle design options to place the gas passage and cylinder nozzle responses at optimal frequencies for lower pressure drop compressor manifold systems.
The one-dimensional representations of the gas passage can influence the nozzle and gas passage responses. The current SwRI investigation showed that the representation affects the model predictions for the gas passage system responses. Using this methodology, the 3D fluid-side modal response model of the fluid system can be used to calibrate the 1D fluid model for correct nozzle frequency response and gas passage responses.
The response model will predict less important responses as well and must be reviewed by an experienced engineer or alongside field data to determine the relevant responses which can be excited by the compressor. Verification of the 1D model must still be performed to verify gas passage volume similarity in the 1D representation and correct damping due to the gas passage diameters and valve boundaries.
Screw Compressor Silencer
Another common analysis requiring an integrated 1D/ 3D pulsation analysis alongside the mechanical analysis is the design of screw compressor silencer bottles. Treatment for the screw compressor pulsation control is often in the form of silencer Helmholtz responses, exterior silencer wraps (which also keep noise levels low), and smaller vessel designs with less 3D modes to excite. A good silencer acoustic design should start with minimizing all fluid-side pulsations, which treats the root cause of most vibration issues and will also help to maintain low dynamic losses and high efficiency of the compression system.
As with reciprocating compressors, the acoustic analysis and design of the associated silencer (filter bottle) can help or hurt the overall reliability and efficiency of the compression system. The difficulty in the acoustic analysis of screw compressors comes with the complexity of the 3D acoustic modes, which can lead to severe pulsations and vibrations, but are also more difficult to analyze using traditional fluid analysis tools.
In this example, the running speed range of the four-lobed (primary rotor) screw compressor was 3,000-5,000 rpm which corresponded to a primary excitation frequency range of 200-333 Hz (second order of excitation ranged from 400-666 Hz.). Figure 4 shows the fluid volume occupied by the initial discharge silencer for the original design, which utilized a volume-choke-volume arrangement. A combination of 1D transient fluid models and 3D acoustic modal analysis was used to redesign the discharge silencer to better isolate acoustic modes and reduce the probability of excitation from the screw compressor. This design approach helped to reduce the overall pressure pulsation amplitudes in the discharge flow, which brought down the fluid-side forces causing high piping vibrations.
Figure 4: Cross Section View Of The Fluid Volume For The Original Silencer Design.
The compressor system had experienced many outages and downtime related to high cycle fatigue failures in the inlet and outlet piping. The re-design had been prompted by field test data showing that the silencer volume itself had relatively high pulsations at amplitudes of 15-20 psi peak-to-peak in the fundamental excitation range of interest. Vibrations on the discharge piping lines exceed 1.0 ips in some cases and corresponded to the 1x and 2x frequency range.
To study the existing silencer pulsation issues, a 3D acoustic modal analysis was performed to determine the natural frequencies and associated mode shapes. Since many of the responses were associated with 3D modes, a typical 1D transient fluid model was not sufficient in characterizing all of the possible responses. Based on the distribution of the modal amplitudes, the modes can be classified into: 1) the fundamental Helmholtz response; 2) bottle length responses; 3) choke tube length responses; 4) nozzle quarter-wave type response; and 5) other 3D cross modes, which primarily affected the first silencer chamber.
Although there are several modes within the frequency range, not all may be necessarily excited. The modal analysis only serves as a guide to determine which modes may be important. Further work is needed to determine overall amplitudes and severity of the 3D modes, especially when field data is not available.
The Helmholtz response occurs at 77.41 Hz (Figure 5), which means that the silencer acts as low-pass filter to filter out higher frequency pulsations above the cut-off limit beyond the silencer outlet. Modes associated with the nozzle and the primary bottle can be most affected by pulsations from the compressor. These modes are evaluated to determine their proximity from the excitation orders. Figure 6 shows a length response of the primary bottle. Several choke tube responses also occur. One of them is illustrated in Figure 7.
Figure 5: Choke Tube Response At 124.48 Hz.
Figure 6: Quarter-Wave Nozzle Response At 207.60 Hz.
Figure 7: Nozzle Response At 320.34 Hz.
Through the analysis of the 3D modal responses, the field data pulsations were found to correspond with the second mode of the choke tube length response near 240 Hz and the nozzle quarter-wave mode near 320 Hz. Adjustments were needed to adjust the internal compressor cylinder volume, since the original OEM compressor design drawings were not available at the time of this study. This gas volume adjustment provided a more correct “calibrated” compressor gas volume, which brought the nozzle response down near 300 Hz to better match the field data frequencies.
The silencer redesign effort utilized a shift in the Helmholtz frequency upward slightly to open up the choke tubes and result in less pressure drop and more compressor through-put. The redesigned volume and its new Helmholtz response is 98.85 Hz. The new silencer design utilized an overall smaller volume to limit the 3D acoustic modes and thicker walls to the vessel for noise and vibration control.
Through the use of 3D acoustic modal analysis and field test data, the silencer redesign resulted in the following overall benefits:
1) A more compact silencer volume with less 3D acoustic modes in the primary excitation range and higher frequency length responses outside of the excitation range.
2) Avoidance of the choke tube length responses, compared with the previous design, which had shown severe pulsations due to a second mode of the choke tube length response.
3) A shift in the Helmholtz frequency upward (but still well below the necessary cut-off frequency), which provides less restrictive choke tubes and more throughput for the compressor.
4) Additional damping through the use of multi-hole orifice plates to attenuate shorter wavelength, high frequency pulsations which could still exist at the silencer outlet.
5) A smaller overall vessel size, which could be mechanically braced better and made more rigid with thicker vessel walls. This also resulted in a better mechanical solution for the discharge piping on the outlet, which was mounted on and supported by the silencer vessel.
Contact website: www.machinery.swri.org.
Marybeth G. Nored is the group leader for the Fluid Machinery Systems Group at Southwest Research Institute (SwRI) which investigates machinery related fluid dynamics in piping systems, surge modeling and control, pulsating flows and detailed aero / thermal studies for turbomachinery design. She is experienced in reciprocating and screw compressor pulsation analysis, thermodynamic power cycles, gas property determination, machinery performance, and natural gas flow measurement. She can be reached at email@example.com.
Stephen M. James is engineer in the rotating machinery dynamics group at SwRI. He holds a master’s degree in mechanical engineering from Texas A&M (2010). His research interests are in the areas of rotating machinery rotordynamics, structural dynamics, acoustic analysis, and finite element analysis. He evaluates and analyzes problems in fluids machinery and associated plant systems. He has a broad knowledge of programming languages and development platforms, and supports the group’s internal software applications..
Dr. Klaus Brun manages the Rotating Machinery Section at SwRI. His experience includes positions in engineering, project management, and management at Solar Turbines, GE and Alstom. He holds two patents (four patents pending), has authored over 80 papers and published a textbook on gas turbines. He won an R&D 100 award in 2007 for his Semi-Active Valve invention and ASME Oil & Gas Committee Best Paper awards in 1998, 2000, 2005, 2009, and 2010. He was chosen to the “40 under 40” by the San Antonio Business Journal.
Eugene L. (Buddy) Broerman, III, is a senior research engineer. He holds a B.S. degree in mechanical engineering (computer science minor) from Texas A&M, Kingsville. He has experience in the fields of acoustics, vibrations and piping design. He has performed more than 100 acoustic analyses of complex machinery piping systems with the aid of various acoustic simulation design analysis tools that range from the analog to digital tools. He has also performed a comparable number of mechanical design analyses with the aid of ANSYS (finite element software) and thermal design analyses with the aid of the COADE software package, CAESAR II.