A Numerical Study on Static and Dynamic Characteristics of Electromagnetic Air Compressor used in Household Refrigerators

Transcription

1 Journal of Experimental & Applied Mechanics ISSN: (online), ISSN: X (print) Volume 5, Issue 3 A Numerical Study on Static and Dynamic Characteristics of Electromagnetic Air Compressor used in Household Refrigerators Soutrik Bose*, Suvanjan Bhattacharyya Department of Mechanical Engineering, MCKV Institute of Engineering, Liluah, Howrah, West Bengal, India Abstract With the development of high-strength magnetic material, moving magnet linear compressors have been gradually introduced in the fields of refrigeration and cryogenic engineering, especially in Stirling. This paper presents computational investigations on the static and dynamic characteristics of a moving magnet. Equivalent magnetic circuits and finite element approaches have been used to model the moving magnet linear motor. In this paper an electromagnetic air compressor is used, where the piston which is a permanent magnet makes a suction stroke by the use of two electro magnets which is positioned at both inner and outer dead centers, and sucks air into the cylinder which is made by non-ferromagnetic material. The variation of force verses piston displacement and the Von Mises stress verses piston displacement is reported and results obtained. Finally, the method to identify optimal points of the linear compressor has been described, which is indispensable to the design and operation of moving magnet linear compressors. Keywords: Computational mechanics, refrigerator, Von-Mises, piston displacement *Author for Correspondence suvanjanr@gmail.com INTRODUCTION Refrigeration and heating systems are widely used in our society, with many diverse applications, from food conservation to ambient temperature control, enabling life quality and thermal comfort. One of the principal methods of heat exchange is through a fluid phase change. This kind of system has four main parts: evaporator, compressor, condenser and throttle valve, according to Figure 1. The refrigerant fluid, while passing through the throttle valve, has its pressure and temperature reduced, entering the evaporator as a liquid in a temperature lower than the environment. Then this fluid evaporates, taking the heat off the place to be refrigerated (Q E ). In the gaseous condition, the refrigerant is sucked off the evaporator and compressed in the compressor, reaching a raised pressure and a temperature higher than the environment. In the condenser, the refrigerant goes into the liquid condition, releasing the heat to the outside environment (Q C ), and it returns to the evaporator through the throttle valve. This closed cycle repeats constantly. In the field of mechanical engineering air compressor is a very commonly used machine. It delivers compressed pressurized air. An electromagnetic air compressor is a device where the piston which is a permanent magnet makes a suction stroke by the use of two electro magnets (positioned at both inner and outer dead centers) and sucks air into the cylinder which is made by non-ferromagnetic material (diamagnetic material). After that when the piston completes the suction stroke and reaches the inner dead centre, by the use of a sensor the direction of the current is reversed in both the electro magnets. By this due to the same action (at first repulsion by the 1st electro magnet and then attraction by 2nd electromagnet) the piston compressed the air to a suitable pressure ratio when it reaches the outer dead centre the same sensor reverse the current and the procedure continue. JoEAM (2014) 8-15 STM Journals All Rights Reserved Page 8

2 A Numerical Study on Static & Dynamic Characteristics Bose and Bhattacharyya The numerical study of H. Mohtar et al. [1] showed that the modification of the volute tongue location affects the compressor efficiency and pressure lines at high speed. The asymmetric influence of the volute on the flow in a transonic, high-pressure ratio centrifugal compressor at off-design conditions was investigated by X. Q. Zheng et al. [2] when the inter-passage variations in performance quantities and the influence of the volute tongue region are discussed in detail. The circumferential variations of incidence angle correlate with rotational speed, which, in combination with the higher sensitivity to incidence angle at transonic inflow conditions, seems to deteriorate stability when transonic inflow conditions are reached. A. S. Hassan [3] investigated theoretically and experimentally the effect of the volute design parameters on the centrifugal compressor range of stable operation and pressure rise coefficient, especially the theory is devoted to the effect of the area ratio on the stability, while the experience is made for understanding the effect of the gap between the diffuser and the volute casing. The study of the flow structure for different volute tongue geometries has been made by Cheng Xu et al. [4] and confirmed that the design of the volute tongue impacts the compressor operating range. The numerical and experimental analysis of different volutes, elaborated by A. Reunanen [5] showed that the change of the cross section, and the location of the volute inlet affect not only the compressor performance but even the non uniformity of pressure and force related to it at high flow rates. H. Rezaei [6] has investigated the flow structure and loss mechanism in a centrifugal compressor volute, when the results of experience show that the non-uniform circumferential static pressure distribution was observed in all cases, and revealed that this is due to the effect of the tongue on the compressor performance. Fig 1: Refrigeration Cycle by Vapor Compression. THE GEOMETRICAL AND NUMERICAL PROCESS An electromagnetic air compressor helps in compressing and pressurizing the air in suitable proportion by the use of two electromagnets and a permanent magnet which itself works as the piston. The piston moves inside the chamber applying the principle of magnetic pole attraction and repulsion methods. In this paper a designed of probable model of the electromagnetic compressor in CATIA V5 R19 version and calculated the probable force acting on the permanent magnet piston Ansys 13 is used for meshing in Figure 2 and analysis. In this paper a single cycle of operation is analyzed by means of single stroke of the piston. As it is a double acting compressor, in single complete stroke both air will be taken as suction air and also it compressed at other side. Fig. 2: Meshing of the Model. JoEAM (2014) 8-15 STM Journals All Rights Reserved Page 9

3 Journal of Experimental & Applied Mechanics Volume 5, Issue 3 ISSN: (online), ISSN: X (print) Material-1: Aluminium Table 1: Material Properties. Material-2: Iron Yield Strength = 7 11 Mpa ρ = 2770 Specific heat = 0.91 (kj/kg K) Young s Modulus = 7.3E10 Poisson s ratio = 0.33 Thermal expansion = 2.27E-5 (m/m K) Thermal conductivity = 190 Yield Strength Mpa ρ = 7860 Specific heat = 0.45 (kj/kg K) Young s Modulus = 2.10E11 Poisson s ratio = 0.27 Thermal expansion = 1.2E-5 (m/m K) Thermal conductivity = 55 The high complexity of the flow in the compressor volute makes the CFD modeling very difficult, only steady state flow is investigated; the governing equations implemented in a commercial CFD code stress analysis are solved using the finite volume method. A fine meshing is done. For outside cylinder, a triangular 10-node element is taken and for the inner piston, tetrahedral element having four nodes is obtained. The outside cylinder is made of Aluminum which is a material of diamagnetic properties (Table 1). The inner piston material is made of Iron. The total length of the cylinder portion is 300 mm. Radius of piston is 50 mm. Working Procedure A diamagnetic material made tube is taken. Two electromagnets are placed at both extreme ends of the tube. In between them a permanent magnet is placed which will act as a piston. At first when the compressor will be started, Priming is required; means when the piston is at outer dead centre some air may be entrapped in the chamber before the start of the compressor. So, this air has to be pumped out once for smooth working. After that the procedure will be as follows: 1) Current is passed through both electro magnets and pole will be generated at the electro-magnets as given in the picture below. The poles of permanent magnets are shown in Figure 3(a). So repulsion will take place between outer centered electromagnet and the permanent magnet, followed by the attraction between the inner centered electro magnet and permanent magnet. This will be the suction stroke in which air will enter into the cylinder. When the pressure into the cylinder will fall below atmosphere pressure the inlet valve will open. 2) After that when the piston heads towards inner dead centre, some distance before the inner dead centre, there is a sensor which senses the incoming piston and changes the direction of current in both electromagnets which causes pole reversion in both electro magnets. Collision between electro magnet and piston (permanent magnet) will not be happened as it will decrease the power of permanent magnet. 3) When the poles are changed opposite action will happen in which the piston will go towards outer dead centre which is shown in the Figure 3(b). This is the compression stroke. In which when the pressure in the cylinder will cross a certain limit mentioned in pressure regulator the outlet valve opens and during the remaining stroke it supplies high pressure air in the receiver (pressure vessel). 4) When the piston comes close to inner dead centre same sensor is installed there which will perform the same act of reversing current. In this way the electromagnetic compressor works. STRESS ANALYSIS In this paper two types (element solution and nodal solution) of stress solutions available for analysis. Both of them are quite important in their respect. It follows directly from the theory of finite elements that discrete values of the degrees of freedom are calculated and available only at the nodes of the model. Hence, they can only be displayed with the nodal solution option of Ansys. Derived quantities - such as; element strains and stresses - are calculated at the integration points which are located somewhere inside each element and values are extrapolated to the nodes. Strains and stresses are displayed with the element solution option of Ansys. The non-smoothness of the strain and stress field can only be recognized if strains and stresses are shown in Figure 4 with the element JoEAM (2014) 8-15 STM Journals All Rights Reserved Page 10

4 A Numerical Study on Static & Dynamic Characteristics Bose and Bhattacharyya solution option. However, it is possible to post process strains and stresses also with the nodal solution option which simply means that the extrapolated element values of the integration points are averaged at the nodes. It can be recognized that the stress field is not smooth in the element solution as it is characteristic for finite element solutions. From the Figure 5; same quantity with nodal solution results in a smooth contour distribution due to the averaging process. The element solution is useful to identify high result gradients within single elements. In those areas a finer mesh is required. In these work two planes of geometry is analyzed. One is the global plane and another is the working plane and applying compressive force in working plane (piston) in negative Z direction as shown in Figure 6. It gives the direction constraints as zero displacement having only three degrees of freedom in the three translation axes X, Y, Z. In this paper basically, the stress analysis follows Von Mises Stress Criterion (Figure 7). Von Mises Stress Criterion is an equation that gives the equivalent stress at a point in a body acted upon normal and shear stress in all three directions. This equivalent stress is used to design a component. Consider a cube, acted on by stresses σ1, σ2 and σ3. Fig. 3: (a) and (b) Piston Cylinder Assembly with Electromagnets. Fig. 4: Element Solution of the Model. JoEAM (2014) 8-15 STM Journals All Rights Reserved Page 11

5 Journal of Experimental & Applied Mechanics Volume 5, Issue 3 ISSN: (online), ISSN: X (print) Fig. 5: Nodal Solution of the Model. Fig. 6: Load Applied on the Model. Fig. 7: Von Mises Stress Criterion. JoEAM (2014) 8-15 STM Journals All Rights Reserved Page 12

6 A Numerical Study on Static & Dynamic Characteristics Bose and Bhattacharyya The average of these three acting in all three directions; causes the cube to change volume. This average stress is also called Hydrostatic stress. Under this theory as stated by Von Mises, this stress does not cause the material to fail, rather it s the difference between the average and individual stress acting on it that causes an angular distortion causing the failure. (1) where, τ is Shear stress, σ is Normal Stress and σ is the Von Mises Stress. RESULT AND DISCUSSION A finite element (FE) model of the crankshaft was developed using for stress analyses. The model was meshed using a four-node tetraedric solid element, which is well suited to model irregular meshes. The whole model has 62,990 elements and 17,172 nodes. Develop radial forces only when both surfaces are compressed (Figure 8). the required magnetic force (recorded by the load cell) has to be adequate and the alternation of flux direction has to be sufficiently fast. The axial position of the rod and the corresponding applied control current at EM poles are shown in Figure 10. A constant stroke can be easily achieved because of the cooperation of the PM Halbach array and EM poles around the cylindrical frame. In other words, the stroke can be fixed once the number of PMs (i.e., the length of Halbach array) and the number of EM poles are both fixed and also from Figure 9 and Table 3, we can see that Von-Mises stress regions at different displacement positions. Table 2: Values of Force against Various Piston Displacements. Piston Displacement (mm) FORCE (N) Fig. 8: Electromagnetic Compressor Modeled in CATIA V5. The axial thrust force is measured by a load cell. For linear compressors, the linear actuator has to mainly present the properties of retaining a constant stroke and superior servo capability. In order to achieve high-frequency, Fig. 9: Von-Mises Stress vs. Piston Displacement Curve. JoEAM (2014) 8-15 STM Journals All Rights Reserved Page 13

7 Journal of Experimental & Applied Mechanics Volume 5, Issue 3 ISSN: (online), ISSN: X (print) Fig. 10: Axial Displacement of Rod and Applied Control Current. Table 3: Stress Displacement Value. Piston Displacement (mm) ELEMENT Von-Mises Stress (N/m 2 ) NODAL Von-Mises Stress (N/m 2 ) E E E E E E E E E E E E E E E E E E E E E E E E E E+09 Fig. 11: Force vs. Piston Displacement Graph. JoEAM (2014) 8-15 STM Journals All Rights Reserved Page 14

8 A Numerical Study on Static & Dynamic Characteristics Bose and Bhattacharyya CONCLUSION In this article, a model of the electromagnetic air compressor composed of a linear actuator nonlinear force was shown. The computational analysis on the static and dynamic characteristics of a moving magnet is also done. Equivalent magnetic circuits and finite element approaches have been used to model the moving magnet linear motor. The dynamic behavior of the system, composed of the linear actuator and the gas pressure nonlinear force, was analyzed, and the major effects caused by the gas pressure force were discussed. Axial displacement with time is also reported. Force and Von Mises stress is also plotted against piston displacement (Figure 11 and Table 2). Thus, since the part of the gas spring is nonlinear and variable throughout the operation, it is difficult to calculate the resonance frequency with the required precision to optimize the efficiency of the compressor. REFERENCES 1. Mohtar H., Chesse P., Chalet D., et al. Effect of Diffuser and Volute on Turbocharger Centrifugal Compressor Stability and Performance: Experimental Study, Oil & Gas Science and Technology Rev. IFP Energies nouvelles 2011; 66(5): p. 2. Zheng XQ, Huenteler J, Yang MY, et al. Influence of the Volute on the Flow in a Centrifugal Compressor of a Highpressure Ratio Turbocharger, Proc. IMechE, J. Power Energy 224 Part A: p. 3. Hassan AS, Influence of the Volute Design Parameters on the Performance of a Centrifugal Compressor of an Aircraft Turbocharger, Proc. IMechE, J. Power Energ 2007; 221 Part A: p. 4. Cheng Xu, Michael Muller, Development and Design of a Centrifugal Compressor Volute, Int J Rotat Mach 2005; 3: p. 5. Arttu Reunanen, Experimental and Numerical Analysis of Different Volutes in a Centrifugal Compressor, [Thesis of the Degree of Doctor Science], Lappeenranta University of Technology, Lappeenranta, Finland, Rezaei, Hooman, Investigation of the Flow Structure and Loss Mechanism in a Centrifugal Compressor Volute. Dissertation Abstr Int 2001; B: 1544p. JoEAM (2014) 8-15 STM Journals All Rights Reserved Page 15