Optimisation of Acoustic Silencer for the Screw Compressor System

Transcription

1 Optimisation o Acoustic Silencer or the Screw Compressor System M. Swamy* 1, L.J van Lier 2, and J. Smeulers 3 TNO Heat Transer and Fluid Dynamics *Correspondg author: Stieltjesweg 1, 2628 CK Delt, maharudrayya.swamy@tno.nl Abstract: In one o the screw compressor system, designed silencer was not optimal. A great challenge was the large variation operatg conditions, especially the variation o the molecular weight o the gas. There was need to optimize the silencer. This paper describes the acoustic modellg tools to optimize the acoustic perormance o the silencer. Optimization steps carried out are based on the process parameters (molecular weight and speed o sound o the gas) and geometric parameters (size o silencer, thickness and length o the absorption core). For this acoustic modellg COMSOL has been used extensively. A 3-D model o the silencer has been used the present vestigation. Transmission losses and pressure pulsation reduction ratios were calculated or each case. Results are presented below. Keywords: Acoustic silencer, screw compressor, meral wool, transmission loss, pressure reduction actor. 1. Introduction Screw compressors are becomg more common stallations o the process dustries due to creased needs or gas compression applications. Normally these compressors generate signiicant pulsations at the lobe passg requencies and its multiples. The requency o the source, the range o Hz, aects a strong couplg o this acoustical power to the mechanical structure and it can cause vibrations that are diicult to control. These high pulsations can transmit to the upstream or downstream pipg o the system and aects the tegrity o the system. Oten, one badly designed silencer can underscore the importance o reliable design and the need or a complete system acoustic/mechanical evaluation. A careul analysis o the system design is mandatory to avoid issues due to excessive pulsations and pulsation-duced vibrations. Industrial standards such as the API 619 standard (or screw compressors) stipulate a design approach to identiy and resolve pulsation issues the design phase, as will be discussed section 2. A careul speciication and evaluation o the ull operatg envelope is essential. This is especially true or systems with an extreme operatg envelope such as collective vent and lare gas compressor systems. The variance the gas composition has an important impact on the pulsation behavior or several reasons. In one case it appeared that an origal design o pulsation silencer was not acceptable due to the high pressure pulsations that occurred at certa process conditions. It appeared that the perormance o the silencers was suicient to cover the ull range o process conditions, speciically molecular weights. Thereore the analysis o the silencer perormance over the entire range o molecular weights. As especially the perormance o the absorption material changes with molecular weight, the ocus o this paper is on the acoustic dampg. 2. Pulsation analysis o screw compressor systems 2.1 Pulsation sources For the waste gas application a screw compressor appeared to be the best choice. For screw compressor systems the pulsation problem is hardly recognized, which has proven to lead to vibration problems especially or the larger screw compressors. In spite o the act that the pulsation phenomenon is more complex screw compressors, the API 619 standard recommends only a relatively simple criterion or allowable pulsations. The generated pulsations have a much higher requency than pulsations generated by reciprocatg compressors. The high requency causes that, especially or the larger compressors, the propagation o pulsations three dimensional (3D) modes play a role and prohibit the commonly used one dimensional

2 (1D) modelg. Moreover also the vibration response is more complicated, because addition to the axial bendg modes also circumerential modes are excited. 2.2 Pulsations generated by screw compressors Screw compressors are sources o pulsations. This can be explaed by considerg the mechanisms o the compression. The pressure o the gas is creased by transer o mechanical energy rom the rotation o 2 helical rotors (emale and male lobes) to the gas. At the suction side, a pocket o gas is haled and enclosed with a cavity between the lobes. By the design o the rotor geometry, the volume o the cavity is reduced while the gas pocket travels toward the discharge side, thus creasg the pressure. Upon openg o the pocket, the compressed gas is exhausted to the discharge pipg. This occurs on an termittent basis, and thus leads to a pulsatg low. In many screw compressor designs, 4 pockets per revolution (4 male lobes) are transported to the discharge side. In that case, the pulsation source spectrum is domated by the teger multiples o the pocketpassg requency (PPF). For example at the 4th harmonic o the compressor speed (1*PPF), the 8th harmonic (2*PPF), the 12th harmonic (3*PPF) etcetera. The typical pulse shapes are illustrated Figure 2. Note that these time signals are associated with 1 pocket contaed by the rotors. In reality, the signal will be repeated, 4 times each crank revolution, with a phase shit o 90 degrees. Figure 2. Typical discharge pulse shapes generated by one lobe, or ideal design, under-compression case and over-compression case. The propagation o the pockets rom suction to discharge side takes more than 1 revolution o the compressor axis; the example o Figure 1 nearly 700 degrees. It must be noted that, due to the geometrical layout o the rotors, multiple pockets can be exposed to the suction and discharge side. See or example Figure 1, the openg o a pocket at the suction side is nearly 360 degrees. Per revolution, 4 pockets (each pocket is shited 90 degrees relative to the previous one) are exposed at the same time. This has an important eect on the amplitude o the pulsations. When multiple pockets are exposed to the let our outlet pipg, the unsteady eect will tend to be more averaged. This is one o the reasons why pulsations at the suction side are generally less strong (multiple pockets are exposed, contrast to the discharge side where usually only one or 2 pockets are exposed simultaneously). Another reason is the absence o a pressure mismatch at the suction side, contrast to the discharge side. However, also the suction low will have an unsteady character, and thus the risk o pulsations shall be careully evaluated the design! 2.3 Pulsation analysis accordg to the API 619 standard Figure 1. Typical port area, outport area and pocket volume time unctions. Sce positive displacement machery can be signiicant sources o pulsations, dustry standards are developed that stipulate the design evaluation o these systems. or screw compressors, the API 619 standard [1] addresses some design considerations with respect to pulsations. The description is rather global, and ocusg on the pulsation suppressors/silencers.

3 Exact details on the approach are not cluded the standard. It is stated explicitly that the entire operatg range shall be considered. It is clear that or vent gas screw compressors this is an important and challengg statement. The API 619 standard provides the ollowg allowable level or pressure pulsations the system: 28.6 P allowable 1/ 3 P smaller, or 2%, whichever is (1) P allowable is the allowable pulsation level % peak-to-peak o the mean pressure. P is the le pressure kilopascal absolute. The criterion is illustrated Figure 3. With creasg requency, more and more higher-order acoustic modes will contribute to the propagation o the acoustic waves. The onset or the occurrence o 3D modes is the so-called cut-on requency c,i. For circular pipes, the cuton requency or the i th described by: k c acoustic mode is c, i i (2) Di k i is the cut-on coeicient or mode i, c is the speed o sound o the gas and Di is the ner diameter o the pipe. The irst higher order (3D) mode has k i =1.84. For example or a natural gas system with a speed o sound o 400 m/s, Error! Reerence source not ound. below illustrates the cut-on requencies o the irst higher order (3D) mode, or dierent pipe sizes. Table 1. Frequency limits or plane-wave propagation o pulsations. Pipe size Inner diameter [mm] Plane wave limit requency Hz Hz Hz Hz Hz Figure 3. Allowable pulsation level, accordg to API 619 standard. Furthermore, the standard addresses an important pot. Due to the relatively high rotation speed, the acoustic modes associated with the pulsations, are three-dimensional (3D). The propagation o low-requency pulsations can be conveniently described with plane-wave (onedimensional) theory. This is a simpliied approach that is valid or low-requency pulsation sources, such as reciprocatg compressors. Figure 4. Illustration o plane wave (k0) and higher order acoustic modes, rom [2]. Screw compressor systems with high rotational speed, large pipe sizes and heavy gases will readily violate the plane-wave assumption shown Table 1. Oten, the lowest order(s) o the Pocket Pass Frequency (PPF) are the 1Drange, but the higher orders, will trigger 3D acoustic eects. This is particularly true side the silencer, where general larger geometrical dimensions are ound, compared to the pipg. Includg 3D eects to the simulation model, requires an excessive crease modellg eort and calculation time.

4 2.4 Pulsation dampers used screw compressor system Generally, absorptive or a combation o absorptive and reactive type o silencers are used screw compressor systems. Absorption material core placed the middle o the silencer. Normally, glass wool, rock wool, meral wool or polymer oam is used as acoustic absorption material. They perorm very well at the higher requencies and dissipate the acoustic power. Sometimes, an additional absorptive material layer along the ner wall o the silencer shell is placed. The absorption ner core is made up o our layers, absorption material, th ibre layer, wire-mesh around and ally packed to the perorated sheet. This combation gives a good mechanical tegrity. I the acoustic attenuation is not suicient, an additional resonator, which is eective the lower requency range, can be stalled combation o the absorptive silencer. It is very important to note that API 619 [1] also stipulates the allowable pressure losses across the silencers. Thereore the absorption material should still allow a suicient low area. 3. COMSOL Multiphysics modelg The 3D modelg o the complete silencer has been done usg COMSOL version 4.3. The acoustic pressure requency doma module o the COMSOL has been used the present vestigation. Boundary conditions used are: Inlet: plane wave with cident pressure ield (1 Pa) Outlet: Relection ree boundary Walls: sound hard wall boundary Mesh dependency test has been carried out to see the mesh adequacy on the results. Typical geometry o design case silencer is shown Figure 5. Typical mesh o the geometry is shown Figure 6. It can be seen that there is a central core meral wool core and gas lows through the annulus (between core and the silencer wall). Fluid the open low path is modelled as lear elastic model. Absorption material core is modelled COMSOL through macroscopic empirical porous models which mimics the bulk losses certa porous/ibrous materials. The model represents a porous medium with the ollowg complex propagation constants: C2 C4 w 0 0 (3) kc 1 C1 ic 3 c R R C6 C8 0 0 (4) Z c 0c 1 C5 ic 7 R R Where k c is the complex wave number, Z c is the complex impedance, ρ 0 is the luid density (kg/m 3 ), is requency (Hz), c is the speed o sound (m/s), R is the low resistivity (Pa.s/m 2 ) the porous medium and C 1 -C 8 are constants. These constants are dierent or dierent absorption material. For the meral wool these values are not available the COMSOL tool so we used these constant rom text book by Beranek [2]. The constants used are: C 1 = 0.136, C 2 = 0.641, C 3 = 0.322, C 4 = C 5 = 0.081, C 6 = 0.699, C 7 = 0.191, C 8 = Flow resistivity o (Pa.s/m 2 ) is used or the calculations. Nevertheless, a sensitivity o the low resistivity (varied rom Pa.s/m 2 ) has been carried out and it has a signiicant impact on the perormance. Eigen mode analysis has been carried out or a design case to understand and ga sight on the type o 3-D acoustic modes present the silencer. Figure 5. Simulation model o the design case silencer. Figure 6. Mesh o the Simulation model o the design case silencer. 4. Results and discussions

5 The perormance o absorptive silencer depends on the geometry o the silencer and absorption material. Geometrical aspects o the silencer are: Length o the silencer Diameter o the silencer The perormance o the absorption material depends on the gas composition and on the ollowg aspects: Wave length versus thickness o the material (ner core and/or layer around the ner wall o the silencer) Operatg pressure and density. Porosity o the material, usually classiied as low resistance. Viscosity o the gas. Perormance o the silencer is measured by Transmission losses and pressure reduction ratio calculated or a the requency range o Hz. reduced at the 400 Hz (1 st order o the pocketpassg requency: compressor speed o 6000 rpm with 4/6 lobes layout). Figure 7. Transmission loss o the geometry. reerence The transmission loss o a silencer is deed as W log (5) Wout TL 10 Where W is the comg power at the let and Wout is the outgog power at the outlet. The comg power at the let is W A 2 P 2 c s da (6) Outgog power at the outlet is given by W out Aout 2 out P da 2 c s out (7) Where P is the average pressure at the let, Pout is the average pressure at the outlet, ρ is the gas density, c s is the speed o sound and A is the surace area. Pressure reduction ratio is deed as Pout Pred (8) P The transmission loss or the low molecular weight gas with is shown Figure 7. This gas has mol weight o 9.5 kg/kg-mol and speed o sound o 620 m/s. It can be observed that silencer perorms well at the higher requencies ( > 1200 Hz). Reduction pressure pulsation ratios is shown Figure 8. It can be observed that only 10 % o the pressure amplitude is Figure 8. Pressure pulsation ratio o the reerence geometry. The results o Eigen mode analysis are shown Figure 9 Figure 10. Higher order acoustic modes can be observed. Figure 9. Typical result o a COMSOL eigen mode calculation at 1250 Hz.

6 Figure 11. Eect o gas composition on the perormance. Figure 10. Typical result o a COMSOL Eigen mode calculation at 2100 Hz. Optimization results are presented the sections below. 3.1 Eect o process conditions Well-designed silencer need to show good perormance or all the operatg gas compositions. Results o three dierent gas compositions are calculated or the reerence geometry. The pressure pulsation reduction as unction o requency is shown Figure 11. The heaviest gas has molecular weight o 40.4 kg/kg-mol and speed o sound o 285 m/s whereas lightest gas has molecular weight o 9.7 kg/kg-mol and speed o sound o 620 m/s respectively. The perormance o the silencer is best at the heavy gases (high Molecular Weight, low speed o sound c) while worst at the light gases. The perormance improves with creasg requency. Heavier gases can absorb the pulsation and dissipate the power better than the lighter gas requency range o Hz. In screw compressor applications, the domatg pressure pulsations are at one and two times the pocket-passg requencies. 3.2 Eect o core geometry The eect o meral wool core thickness has been vestigated. Core thickness varies rom 223 mm (reerence geometry) to 303 mm (see Figure 12). An additional layer o 50 mm around the meral wool core consists o wiremesh, knitted staless steel and perorated plate. The rest o the silencer geometry is kept same. This means that or the larger core thicknesses the low path is narrower and thus the pressure loss higher. The perormance o the silencer or three dierent meral wool cores is shown Figure 13. Results dicates that higher the core diameter better is the perormance. This better perormance is at the cost o pressure loss. There is a trade-o between the core thickness and low gap which is available or the gas to low, i.e. a trade-o between acoustic dampg and pressure loss. There is a API 619 guidele that speciies the allowable pressure loss across the silencer. It has been observed that creasg the silencer size (also core length creases) has a positive impact on the silencer perormance.

7 Figure 12. Variation o meral wool core thickness or the same silencer diameter. Figure 14. Results o optimized geometry 4. Conclusions Numerical modelg has been perormed to optimize the perormance o the absorptive silencer or screw compressor system. 3D modelg is necessary to capture higher order acoustic modes the silencer. Figure 13. Eect o core thickness on the perormance. 3.2 Optimized geometry The silencer geometry is optimized based on the easibility and the cost. Length o the silencer is creased by 20 % (eective core length rom 1350 mm -> 1600 mm), cross-sectional area o the silencer by o the silencer is reduced by 12 % (ner diameter orm 381 mm -> 362 mm). Meral wool core thickness is kept the same (223 mm (reerence geometry). The COMSOL s pressure acoustics requency doma module has been an excellent tool or the optimization. The silencer has been optimized with respect to geometry o silencer, meral wool core thickness and dierent operatg gases. These results were used the pulsation analysis o the ield pipg. 5. Reerences [1] API 619 standard, Rotary-type, Positivedisplacement compressors or Petroleum, Petrochemical and Natural Gas Industries, 4th edition, [2] VDI 3733 standard, Noise at pipes, [3] Leo L. Beranek (ed.), Noise and Vibration Control, McGraw-Hill Inc. (1971), ISBN X Results are shown Figure 14. It can be seen that or the lighter gas there is 30 % reduction pressure pulsations (amplitude) compared to the designed silencer (Pressure reduction ratio rom 0.9 to 0.6). same holds good or the other gas compositions. This optimized results and model has been the urther pulsation analysis the ield pipg.