A manufacturer of pulsation dampers requested Dynaflow Research Group to verify the performance of one of its discharge silencer designs in combination with a double rotary lobe gas blower by means of a pulsation study. The scope of the study consisted of a connecting straight pipe spool and the silencer itself. The silencer was checked to conform to the API 619 code for rotary-type positive displacement compressors.
Rotary Lobe Blower
As the client did not have access to the specific flow data of the blower, its flow profile had to be estimated. Based on the dimension and the shape of the impellers, an Excel model was designed to compute the displaced volume of gas per rotation. Additional complexity was created by the presence of the WhispairTM opening.
The Whispair™ opening is a small port located just before the main discharge side of the blower. It is connected to the discharge opening by a small pipe. As a low-pressure gas pocket passes by the Whispair™ opening, its pressure is gradually increased. This helps reduce the pressure difference between the gas pocket on the inlet side and the discharge side. Additionally, it lessens the impact of the rapid expansion of discharge gas into the impeller pocket, minimizing shockwaves and promoting smoother operation.
Figure 1 | The movement of the rotary lobe blower.
Figure 2 | The flow profile obtained from the impeller dimensions.
Figure 3 | The blower causes four blows per revolution.
Silencer Model
Now the flow profile is known, the silencer could be modeled. Particular attention is paid to its interior. The silencer consists of two chambers that are connected through choke tubes. These cause a reduction in flow area, which is accounted for by the reduced volume and the gradual decrease in diameter and explains the conundrum shapes. The reduced diameter of the rings on the inside of the damper are taken into account as well in order to properly capture the pressure waves. The outlet of the silencer is connected to other piping with an unknown routing and therefore it contains an anechoic boundary condition. This ensures that the pressure is fixed, but pressure waves are not reflected back into the system from this point.
Figure 4 | BOSpulse model of the silencer with an attached spool piece. The rotary lobe impeller is modeled as a flow boundary condition.
Analysis
The analysis was performed using the pulsation analysis software BOSpulse. This software package assumes 1D pressure waves. For the silencer, the calculated pressure pulsations at the first three pocket passing frequencies (PPF) of the blower were assessed. The cut-on frequency of 3D acoustic waves was calculated to be around 179 Hz for the silencer, which is higher than 3x PPF. Therefore, the analysis using plane-wave pressure pulsations was found to be reliable, and three-dimensional acoustics were deemed unnecessary.
To account for any uncertainties in gas composition, temperature, and pressure, a sweep of ± 20% was applied to the wave speed. Within this range of wave speeds, it was found that the pressure pulsation allowable of 2% of the line pressure was exceeded. It showed that the length of the spool piece leads to a resonance frequency that matches with the first harmonic of the blower system, which leads to resonance. This can be prevented by changing the length of the connected spool piece.
Conclusions and Recommendations
The silencer and its connecting spool piece were analyzed following the API 619 code. Based on the results of this analysis the following conclusions can be drawn:
- With the design location of the silencer with respect to the blower, pulsation levels at the process side of the outlet silencer were found to be within the API 619 allowable values of 2%-line pressure. This excludes the wave speed variation.
- When the wave speed variation of ±20% is applied, the maximum pulsation levels are found to be 123.4% of the API 619 allowable value.
- With the design location of the silencer with respect to the blower no interference is expected.
Based on the above outcome it is advised to increase the distance between the blower outlet and the silencer inlet by 260 mm to mitigate the maximum pulsation levels. The team at DRG estimates that by doing so, the acoustical behavior of the complete blower-silencer system will improve and a reduction of the maximum pulsation levels to 77.5% of the API 619 allowable, thereby complying to the code.
