Finite Element Analysis for Acoustic Behavior of a Refrigeration Compressor

Swapan Kumar Nandi Tata Consultancy Services

GEDC, 185 LR, Chennai 600086, India

Abstract When structures in contact with a fluid vibrate there will be an interaction between the two systems. Geometry and motion of structure induce fluid dynamic forces, which in turn alter the structural behavior. A variety of such problems occurs in several engineering applications and is collectively called as Fluid-Structure-Interaction (FSI) problems. Analysis of fluid-structure-interaction problem, assuming fluid to be compressible, is highly useful in the study of acoustic behavior of such structures. Refrigeration compressor is a perfect example of such structure. In refrigeration compressor due to reciprocating motion of piston cylinder mechanism, pressure pulsations occur in acoustic cavity present between the shell and the rigid block which houses the motor and piston-cylinder mechanism. Due to high density associated with the fluids in the cavity, fluid loading on the structure is likely to occur; this will in turn influence the dynamic behavior of the shell. This present work deals with shell-cavity systems of a compressor, comprising fluids like lubricating oil, refrigerant and bubble in between oil and refrigerant. The objective of the present work is to analyze the acoustic behavior of such FSI problems. First, eigenvalue analysis is performed on the structure and fluid separately. Subsequently FSI is defined and eigenvalue problem is solved for the coupled system. Harmonic response analyses have been performed imposing disturbances on the rigid block at different interfaces with oil and refrigerant. Far field acoustic analysis of the compressor is performed and results are analyzed. Validation of this result is done using Boundary Element (BE) Method based software, SYSNOISE. Influence of location of disturbance on sound pressure level (dB) is studied and discussed.

Introduction Refrigeration compressors are widely used in domestic appliances, sound characteristics of this equipment is of prime importance. This equipment has several sources of disturbances like gas pulsations at suction and discharge part of compressor, reciprocating motion of piston cylinder mechanism etc. All these disturbance acts as sources of noise. However all these sources are not equally important. In the present analysis disturbances at the suction and discharge section of a compressor has been considered and analyses are performed to investigate which source produces more noise. This paper presents an implementation of finite element (FE) analysis method on a typical hermetically sealed refrigeration compressor comprising three fluids namely, the refrigerant, lubricating oil and bubble trapped in between these two mediums. The three dimensional model is developed in ANSYS with SOLID45, FLUID30 and FLUID130 elements. FSI between solid and fluid within the cavity and outside of cavity are defined. Disturbances on the rigid block at oil and refrigerant interfaces, which represents suction and discharge of the compressor, are applied separately and harmonic analyses are carried out to determine the sound pressure level (dB) produced by these disturbances. Contribution of each source of disturbance has been examined and results are discussed.

Literature Review Fluid structure interaction problems find wide application in many engineering disciplines and diverse technological processes. A brief review of literature related to this area has been done. Pritchard (1966) [1] had analyzed the transmission of sound through a finite, closed cylindrical shell. From his analysis he found two important frequencies for noise radiation; the ring frequency, where the wavelength of a longitudinal wave in the material is equal to circumference and the coincidence frequency, where the trace

wavelength of the incident wave is equal to the bending wavelength in the shell wall. Au-yang (1979) [2] had presented an analytical method for estimating the coolant pump induced acoustic pressure distribution in the inlet annulus of a pressurized water reactor. The phenomenon of beating due to slight difference in the pump blade passing frequencies is included in this analysis. Results are compared with those of experimental ones. Kung and Singh (1985) [3] have developed FE technique to find the natural frequencies and mode shapes of un-damped three-dimensional acoustic cavities. Zhou and Kim (1996) [4] have predicted the noise radiation of hermetic compressors by FE and Boundary Element (BE) methods. A numerical procedure combining the computer simulation program for the compressor and FE/BE methods has been developed to calculate the unsteady flow inputs to the cavity of the compressor. Prasad [5] studied structural acoustic interaction in shell cavity system in 2000. For compressor, presence of bubble in between oil and refrigerant may alter acoustic characteristic. Sound absorptivity of bubble has been studied and reported by Preston [6] in 2002.

There are several studies on prediction of noise from fluid coupled shell systems, yet noise radiation from refrigeration compressor taking into account the presence of multiple fluids in the acoustic cavity using FE technique are few.

Motivation and Objectives Since literature on coupled shell fluid system with multiple fluids using general purpose FE software is generally not available, the present work attempts to use ANSYS for finding natural frequencies and prediction of noise radiation with multiple fluids inside the cavity as well as outside of cavity.

Scope of Work The FE technique is used to evaluate frequencies of acoustic cavity and structure. Coupled frequencies of structural-acoustic system have been evaluated using unsymmetric FE formulation. Far field acoustic problem is solved to investigate noise radiation outside domain of the compressor. A study has been made on the influence of presence of disturbance on noise radiation level at outside of compressor.

Procedure Acoustic analysis in ANSYS can be solved by performing harmonic analysis. The analysis calculates the pressure distribution in the fluid due to a harmonic load at the fluid-structure interface. Modal and transient acoustic analyses also may be performed.

The procedure for a harmonic acoustic analysis consists of three main steps:

• Building model

• Applying boundary conditions and loads and obtaining solution

• Review results

Computational Model Major dimensions of the compressor model considered for the present study are shown in Figure 1. Modeling actual 3D 360 degree compressor considering far field will results in large numbers of elements that require enormous resource and time to solve harmonic analyses. To reduce resource requirement and solution time approximation on the actual model is advisable.

For this analysis one 90-degree sector has been considered. To validate this approximation similar analysis is performed on a 2D cross section of the actual 3D model considering full 360 degree and 90-degree sector. Figure 2 and 3 shows these 360-degree and 90 degree models. For 90-degree model symmetry boundary condition (BC) are applied on solid structural part as shown in Figure 3 and no BC is defined on acoustic region. Harmonic analyses have been performed on both the models with similar loads and the sound pressure level (dB) outside cavity of these models is presented in Figure 4. One can infer from the

Figure 1. Schematic Diagram of Refrigeration Compressor results that 90-degree sector approximation of the 360-degree full model is a valid one. To reduce number of elements for far field analysis, 3D model is further approximated at outside of cavity and the final model of the compressor is shown in Figure 5. To validate this approximation, the 360-degree 3D model without the acoustic part outside of shell has been analyzed in ANSYS for a harmonic load of 1 mm with frequency of 2000 Hz, and then the far field analysis on full 3D model has been performed in SYSNOISE using BEM approach. Similar far field analysis on 90-degree sector model as shown in Figure 5 has been performed in ANSYS. Sound pressure level (dB) at far field of this 360-degree full model solved in SYSNOISE and similar results of 90-degree sector model solved in ANSYS are shown in Figure 6 and 7 respectively. The dB levels of these two figures match very closely with each other; though the contours are not matching exactly. This may be due to approximation on the 90-degree sector model, specially the symmetric BC; because in 3D 360-degree actual model disturbance is at only one place, which is not the case for the 3D 90-degree sector model. As this is a comparative study and we are mainly interested on the contribution of different sources towards noise production, and range of sound pressure level of this sector model is matching with that of full model this reduced model is acceptable for the present study. All other analyses are performed on the 3D 90-degree sector model in ANSYS.

Figure 2. 2D 360 degree Cross Sectional Model of Compressor

Figure 3. 2D 90 degree Cross Sectional Model of Compressor

Figure 4. Sound Pressure Level (dB) Plot of 2D Models

Figure 5. Computational Model of Refrigeration Compressor

Figure 6. Sound Pressure Level (dB) at Spherical Field Points from SYSNOISE Results

Figure 7. Sound Pressure Level (dB) at Spherical Field Points from ANSYS Results

Analysis For lubricating oil and refrigerant density and speed of sound are taken as 9e-10 tonne/mm3 & 1200000 mm/s, and 3e-11 tonne/mm3 & 180000 mm/s respectively. Bubble in between oil and refrigerant has density very close to that of oil and speed of sound close to bubble’s speed of sound, these values are taken as 8e-10 tonne/mm3 and 300000 mm/s respectively. Bubble boundary admittance at the interface has been considered as 0.075. This is the average of boundary admittance of bubble reported by Preston. While creating FE model for acoustic medium element sizes are calculated to have at least 10 elements per wavelength considering highest frequency of interest. KEYOPT (2) for acoustic elements that are in contact with solid elements is set to zero. This results in unsymmetric element matrices with UX, UY, UZ, and PRES as the degrees of freedom. For all other acoustic elements KEYOPT (2) is set to 1, which results in symmetric element matrices with the PRES degree of freedom as symmetric matrices require much less storage and computer time. To simulate far field acoustic behavior infinite acoustic elements are used. These infinite acoustic elements absorb the pressure waves, simulating the outgoing effects of a domain that extends to infinity beyond the acoustic elements. Infinite acoustic elements provide a second-order absorbing boundary condition so that an outgoing pressure wave reaching the boundary of the model is absorbed with minimal reflections back into the fluid domain. Fluid-structure interface (FSI) has been defined at all interfaces between solid and fluid, which will couple the structural motion and fluid pressure at interfaces. The surface load label IMPD with a value of unity has been used to include damping that is present at oil-bubble and bubble-refrigerant interfaces. Appropriate reference pressure (PREF) is defined to maintain consistent unit system.

In this analysis the full 360 degree model is approximated as a 90-degree sector model. Symmetry boundary condition was applied on appropriate areas of solid structures. On acoustic region no boundary conditions are applied; if no boundary conditions are applied on an acoustic domain, the default boundary condition is normal pressure gradient is zero. Pressure gradient is proportional to velocity; so by default zero velocity at acoustic domain is applied automatically. To fix the compressor shell all outer nodes on bottom part of the shell were arrested in UX, UY, and UZ directions. To simulate the pulsation at suction and discharge of compressor displacement of 1mm has been applied on outer node of block at different locations. First, this 1mm radial disturbance was applied on the outer node of block at oil region and harmonic analysis was performed; this will be referred as case A, then similar disturbance was applied on node at refrigerant region separately and harmonic analyses were performed; this is case B. For harmonic analyses sparse direct solver (SPARSE) was used and range of frequency was 0-2000 Hz in steps of 10. Constant damping of 2% was considered.

Results and Discussion Post processing of case A and case B for all frequencies are carried out and sound pressure level (dB) is calculated for similar elements for these cases. Sound pressure level at cavity and at a distance of 285 mm and 500 mm from center of compressor are plotted in Figure 8. Similar results of case B are presented in Figure 9. From these figure one can find that sound level at the near field (cavity) is more than that of far field, this is because of the fact that the disturbance which results in noise is present in the rigid block which is inside of cavity. The variations of dB level across the distance away from the source for case A for frequency of 2000 Hz are plotted in Figure 10. The sound pressure level in the near field is very high. In the far field the sound pressure is inversely proportional to the distance away from the source. Every doubling of the distance away from the source results in a halving of sound pressure or a doubling of distance away from the source results in a 6 dB decrease in the sound pressure level. This characteristic can be observed from Figure 10. Due to fluid structure interaction between rigid block and fluid within cavity dynamic forces are induced on outer shell, which again interacts with the acoustic medium (air) outside of the shell. Here shell acts as a filter to reduce the sound level at outside of cavity. To compare the contribution of two different sources results of Figure 8 and 9 are combined and presented in Figure 11. This figure shows that dB level for case A is in general more than dB level of case B. That is disturbance presents in interface of rigid block and oil produce more noise than disturbance present in refrigerant area. This is due to the high density of oil compared to that of refrigerant.

Figure 8. Sound Pressure Level (dB) at different location for Case A

Figure 9. Sound Pressure Level (dB) at different location for Case B

Figure 10. Sound Pressure Level (dB) across the distance from source

Figure 11. Sound Pressure Level (dB) at different location for Case A and Case B

Conclusion In this paper, acoustic analysis of a refrigeration compressor with multiple fluids using FE method has been presented. The disturbance due to pulsation of refrigerant at suction side of the pump, which exits at oil level of the compressor, is modeled by introducing a radial disturbance of 1mm. Similar disturbance present due to pulsation of refrigerant at delivery side of the pump is modeled by introducing 1 mm radial disturbance on rigid block at refrigerant level. Harmonic analysis has been performed and results are analyzed for both the cases. Validation of the FE method has been done by another software, SYSNOISE using BE method.

It has been found that the shell is acting as a filter to reduce the sound level at outside of compressor. The disturbance due to pulsation exists in suction side of the pump has predominant effect over the disturbance presents in delivery side. Currently investigations are being carried out for conclusion on effect of presence of bubble on sound level at outside of compressor.

References 1 Pritchard H. White (1966) Sound Transmission Through a Finite Closed Cylindrical Shell.

Journal of the Acoustical Society of America, 40(5), 1124-1130.

2 Au-Yang, M. K. (1979) Pump Induced Acoustic Pressure Distribution in an Annular Cavity Bounded by Rigid Walls. Journal of Sound and Vibration, 62, 577-591.

3 Singh, R. and Kung, C. H., (1985) Finite Element Modeling of Annular Like Acoustic Cavity, ASME Journal of Vibration, Acoustics, Stress and Reliability in Design, 107, 81-85.

4 Zhou, W. and Kim, J., (1996) Prediction of Noise radiation of Hermetic Compressors Utilizing the Compressor Simulation Program and FEM/BEM Analysis, Proceedings of 6th International Compressor Conference, Purdue University, I, 587-592.

5 Siva Prasad, Y. V., (2000) Structural Acoustic Interaction in Shell Cavity System, Master of Science Thesis, Indian Institute of Technology Madras, Chennai, India.

6 Preston, S. Wilson (2002) Sound Propagation and Scattering in Bubbly Liquid, Doctor of Philosophy Thesis, Boston University College of Engineering, USA.