A Numerical Estimate of Flexible Short-Tube Flow and Deformation with R-134a and R-410a

Transcription

1 For personal use only. Additional reproduction, distribution, or transmission SL A Numerical Estimate of Flexible Short-Tube Flow and Deformation with R-134a and R-410a Ramadan Bassiouny, PhD Dennis L. O Neal, PhD, PE Fellow ASHRAE ABSTRACT A finite element model was used to estimate the refrigerant flow through flexible short-tubes for two refrigerants and three moduli of elasticity. The short-tubes were 14.5 mm (0.57 in.) in length with an inlet diameter of 2.06 mm (0.081 in.) and an outlet diameter of 2.46 mm (0.097 in.). The study included two refrigerants: R-134a and R-410a, and short-tubes with three moduli of elasticity: 5513, 7084, and 9889 kpa (800, 1025, and 1434 psi). A finite element model was developed using a commercially available software package. The model captured deformation by coupling the fluid/short-tube structural interaction in the shorttube. Upstream pressures were set to correspond to typical condensing temperatures for each refrigerant. The upstream subcooling was held at a constant value of 16.7 C (30 F). The model estimated tube deformation and refrigerant flow as a result of upstream pressure changes. The internal short-tube shape resembled the shape of a converging-diverging nozzle. A chamfered-like shape was seen at both the inlet and outlet of the short-tube. This shape reduced the large pressure drop at the vena contracta downstream of the tube inlet found in rigid short-tubes. However, flexible short-tubes showed a second pressure drop at approximately 4 mm (0.157 in.) from the inlet of the tubes. This second pressure drop was a consequence of the tube deformation and increased as the modulus of elasticity decreased. For a condensing temperature of 46 C (129 F), the operating upstream pressure of R-410a was 140% higher than that of R-134a. R-410a had a larger tube deformation than that of R-134a. INTRODUCTION Flexible short-tubes offer a potential replacement for existing rigid short-tubes as an expansion device in air conditioners and heat pumps. The main function of the short-tube is to control refrigerant mass flow into the evaporator. When the condenser pressure increases due to an increase in the ambient temperature above the system-design point, a rigid short-tube can allow enough refrigerant flow to flood the compressor with saturated refrigerant. On the other hand, when the condenser pressure decreases due to a decrease in the ambient temperature, a rigid short-tube passes a lower quantity of refrigerant. At low-condensing pressures, the flow rate can produce a high superheat leaving the evaporator, which can reduce performance and efficiency of the system. Compared to a rigid short-tube, a flexible short-tube can change shape in response to changes in condensing (upstream) pressure. With an increase in condensing pressure, the crosssectional area of the flow opening of a flexible short-tube decreases, which helps restrict refrigerant flow through the tube and maintain higher subcooling upstream of the shorttube. The advantage of short-tubes over other thermal or electronic expansion valves is their low cost. The flexible short-tubes (Figure 1) used in this study were made of an elastomeric material that deformed in response to an increased pressure differential across it. This deformation resulted in a variation of the tube s inner cross-sectional area. A full description of the original design of the flexible shorttube is presented in Drucker and Cann (1991), Drucker (1992), and Drucker and Abbott (1993). LITERATURE REVIEW Much of the previous work on short-tubes has focused on rigid short-tubes. This has included studies of R-22 (Aaron and Domanski 1990; Kim and O Neal 1994a), R-134a (Kim and O Neal 1994b), and R-410a (Payne and O Neal 1999). Three recent studies have focused on flexible short-tubes: Kim et al. (2002), Bassiouny and O Neal (2002), and Bassiouny Ramadan Bassiouny is an assistant professions in the Department of Mechanical Power Engineering and Energy, Minia University, Minia, Egypt. Dennis L. O Neal is a Holdredge-Paul professor and department head of the Department of Mechanical Engineering, Texas A&M University, College Station, TX ASHRAE

2 For personal use only. Additional reproduction, distribution, or transmission and O Neal (2004). The study by Kim et al. (2002) was an experimental study of the performance of flexible short-tubes with R-22. Bassiouny and O Neal (2002) developed a numerical model for the flow of R-22 through flexible short-tubes. Kim et al. (2002) evaluated the overall performance of two flexible short-tubes with two different moduli of elasticity: 7084 and 9889 kpa (1025 and 1434 psia). The tests included a range of operating variables such as inlet subcooling/quality, upstream pressure, and downstream pressure. They observed that the mass flow rate through the flexible short-tubes was strongly dependent on the modulus of elasticity of the material and on upstream pressure. For short-tubes with the same undeformed diameter, they observed that the lower modulus (more flexible) short-tubes had a smaller refrigerant flow than the higher modulus (less flexible) short-tubes. Their study focused on mass flow. No data were collected or observations made about how the tube deformed as the upstream pressure was increased, nor were data collected on the pressure distribution in the short-tube. Bassiouny and O'Neal (2004) focused on predicting the tube deformation for different moduli of elasticity under different upstream pressures for R-22. They found that the tube s inner area, upon deformation, resembled a converging-diverging nozzle. The model captured the sharp pressure drop at the tube inlet and the pressure recovery after the vena-contracta zone. It was expected that the pressure would drop sharply due to the sudden contraction at the entrance. Another dip in the axial pressure variation was seen corresponding to the tube throat caused by the deformation of the tube. A semi-empirical correlation was developed by Kim et al. (2002) to predict the mass flow rate through flexible short-tubes before flashing. This correlation was based on the single-phase, single-component orifice equation. The form of this correlation along with its regression constants was given in Kim et al. (2002). This correlation was used by Bassiouny and O Neal (2004) to validate the numerical model for R-22. The model showed the same flow trends with respect to upstream pressure as the experimental data and estimated flow within 14% of the experimental data over a range of upstream pressures. The tube s inner cross-sectional area plays an important role in controlling the refrigerant flow rate. Thus, to estimate mass flow through a flexible short-tube, it is important to be able to estimate the change in inner diameter as the upstream Figure 1 A schematic of the flexible short-tube orifice configuration. conditions change. A numerical model that includes interaction between the flow and short-tube may provide insights into how the tube is deforming and how different material properties can be used to better optimize the design that can efficiently perform in the system application. NUMERICAL MODEL Because refrigerant flow through a short-tube is dependent on the size and shape of the opening of the short-tube, modeling refrigerant flow requires a methodology that can predict the shape change under upstream pressure conditions. Due to its capability to handle fluid-structure interaction and flexibility of having different element shapes, the finite element method (FEM) was used in this study to handle this problem. A similar fluid-structure interaction problem was carried out by Erbay and Demiray (1995). They developed a model with assumptions to predict the deformation of an elastic tube under axial and tangential loads. They mentioned that the problem of viscous flow inside an elastic tube must take into account both the tangential stress and the axial varying internal pressure acting on the inner surface. The pressure also varies along any streamline, even on the tube wall, due to viscous drag. An axisymmetric analysis was adopted due to the assumptions of having a tube constructed of a homogeneous elastomer material and axisymmetric boundary conditions. The mesh configuration for the axisymmetric computational domain of the flexible tube is shown in Figure 2. A commercially available finite element code (Swanson 1995) was chosen to model the flow through the short-tube. This code had the capability to model the fluid/structure interaction required to estimate the change in shape of the short-tube as the upstream pressure changed. The continuity and momentum equations for the fluid-flow side, and the stress-strain relations for the structure side and their discretization method are discussed comprehensively in Swanson (1995). Applying the Galarkin's method, the partial differential equations are transformed into algebraic or matrix form. This matrix was iteratively solved. To show a grid-independent solution, the analysis started with a relatively coarse mesh for a rigid shorttube. The pressure distribution inside the short- tube was then estimated with the finite element model. A finer mesh was then applied to the geometry until there was no significant change Figure 2 The axisymmetric computational domain of the flexible short-tube orifice. 441

3 For personal use only. Additional reproduction, distribution, or transmission in the pressure distribution inside the short-tube. This process resulted in a mesh size of 3885 elements needed for the model: 2010 for the fluid domain and 1875 for the structural domain. This mesh size was used for all calculations. The technique used for the solution is known as the sequential coupled-field analysis. In this procedure, the nonlinear fluid equations are solved first. This solution provided a pressure-distribution estimate inside the shorttube. This pressure distribution was then transferred, as an internal-area boundary condition, to the structure model, which was used to solve for the tube deformation. The deformation was then used to specify the new flow boundary in the flow model. The pressure and flow were then recalculated in the flow model. This process was repeated until there was no change in the pressure profile or shape. RESULTS AND DISCUSSION The pressure profiles for flow of R-134a and R-410a along the length of the flexible short-tubes at different tube moduli of elasticity and at the same condensing temperature are shown in Figures 3 and 4, respectively. The short-tubes were 14.5 mm (0.57 in.) in length, had an undeformed inlet diameter of 2.06 mm (0.081 in.), and an outlet diameter of 2.46 mm (0.097 in.). The pressure profile, represented by the solid lines in both figures, corresponds to that of an undeformed rigid tube. Both figures illustrate two regions of pressure drop. The first is a sharp pressure drop immediately downstream of the inlet, which is commonly called the vena contracta. This pressure drop was due to a rapid acceleration of the flow due to the sudden contraction from the larger-diameter refrigerant tube to the smaller-diameter short-tube. The drop in pressure at the vena contracta was largest for the rigid short-tube and decreased as the modulus of elasticity decreased (flexibility increased). The more flexible the short-tube, the more the Figure Axial pressure profiles for R-134a single phase flow through a flexible short-tube orifice. deformation (Figures 5 and 6). This deformation produced a more gradual (or less sharp) entrance, which produced less pressure drop at the vena contracta. A second pressure drop was observed in the flexible shorttube at approximately 4 mm (0.157 in.) from the entrance. No second pressure drop was seen in the rigid short-tube. The pressure profile of the rigid short-tube showed a drop at the vena contracta and a gradual recovery toward the exit of the shorttube. The second pressure drop at 4 mm (0.157 in.) in the flexible short-tubes appears to correspond to the location in the flexible short-tube where the cross-sectional area is smallest (Figures 5 and 6). The lowest modulus, 5513 kpa (800 psi) material showed the most deformation (Figure 5) of the three flexible short-tubes. Downstream of the second pressure drop, the pressure recovered over the rest of the length of the short-tube. Similar qualitative trends are shown in Figure 4. The condensing pressure of R-410a is almost 140% higher than that of R-134a when operating at the same condenser temperature. The figure shows a larger dip in the pressure profiles downstream of the tube inlet compared to R-134a (Figure 3) for the same subcooling. The pressure drop at the tube inlet was smaller as the tube deformed more for the higher-pressure refrigerant, R-410a. As the tube deformed, the inlet edge buckled more, increased the chamfering angle, and decreased the pressure drop at the tube inlet. An unrealistic negative pressure was obtained for the lower modulus short-tube with R-410a. This would indicate a limit to the accuracy of the numerical scheme for large deformations for the high upstream pressure. A gradual pressure recovery downstream of the dip is shown in Figure 4 due to the larger diverging angle of the exit section of the tube upon deformation. The flexible short-tube deforms as a result of the net forces exerted on its internal and external sides. Because of the design, the fluid surrounding the external length of the short- Figure 4 Axial pressure profiles for R-410A single phase flow through a flexible short-tube orifice.

4 For personal use only. Additional reproduction, distribution, or transmission tube is near the upstream (condensing) pressure. The internal pressure distribution would be the same as shown in Figures 3 and 4. The larger the difference between these internal and external pressures, the larger the expected deformation of a flexible short- tube. Figures 5 and 6 illustrate the deformation of the tube diameter along the tube length for R-134a and R410a, respectively. Figure 5 shows the gradual change in the tube shape from the inlet to the outlet as the modulus of elasticity is decreased. The inner area for a rigid short-tube had a gradual taper from the entrance to the exit. In contrast, the flexible short-tube resembled more of a converging/diverging nozzle. The entrance of the flexible short-tube showed a more gradual transition than the rigid short-tube. This transition at the entrance was similar to chamfering that is used in some rigid short-tubes. The minimum tube diameter was approximately 1.7 mm (0.067 in.) for R-134a and occurred at an axial Figure 5 Short-tube inner radius variation as a result of R-134a single phase flow. Figure 6 Short-tube inner radius variation as a result of R-410A single phase flow. distance at almost 4.0 mm (0.157 in.) from the tube inlet. The flow would be expected to accelerate through this smaller opening, which would produce an area of low pressure. The maximum deformed flow area was 36% less than that of the undeformed flow area at the 4.0 mm (0.157 in.) location. Figure 6 shows changes in the tube diameter when R-410a was used as the refrigerant. Thus, the chamfered-like inlet, as well as the converging-diverging shape, was larger with R410a compared to R-134a because of the higher operating pressures. The minimum tube diameter was approximately 1.4 mm (0.039 in.) and occurred at an axial distance of 4.0 mm (0.157 in.) from the tube inlet. The larger tube deformation produced a larger pressure drop near the 4.0 mm (0.157 in.) location from the tube inlet (Figure 4). The upstream pressure is an important operating variable when considering the performance of a flexible short-tube. The pressure variation along the flexible short-tube as the upstream pressure changed for the same evaporator temperature, 29.5 C (85 F) is presented in Figures 7 and 8 for R-134a and R-410a, respectively. The downstream pressure was held constant and equal to or above the saturation pressure corresponding to the inlet temperature. Figure 7 shows that as the inlet upstream pressure increased, the pressure drop at the vena contracta (immediately downstream of the inlet) increased for the same evaporating (downstream saturation) temperature. Increasing the pressure differential across the short-tube would increase the mass flow rate. The tube inlet loss is directly proportional to the mass flow rate. Therefore, increasing the pressure differential across the orifice increased the inlet loss and, accordingly, increased the pressure drop at the inlet. After the vena contracta, the pressure recovered in the short-tube. At 4 mm (0.157 in.), there was a slight drop in pressure that was noticeable at 1197 and 1302 kpa (175 and 190 psia) upstream pressures. This may be attributed Figure 7 Axial pressure profiles at different condensing temperatures for R-134a single phase flow through a flexible short-tube orifice. 443

5 For personal use only. Additional reproduction, distribution, or transmission to more stress on the tube material as a result of increasing the upstream pressure, which led the tube to constrict more than at the lower upstream pressure. The effect of varying the condenser pressure on the tube diameter for the 9889 kpa (1434 psi) modulus of elasticity short-tube is shown in Figures 8 and 9 for R-134a and R-410a, respectively. The tube deformed more at the higher upstream pressure (Figure 9). The stiffer the material (higher modulus of elasticity), the smaller the deformation in shape and diameter for the lower upstream pressures. Nevertheless, at the operating pressures of R-410a (Figure 10), the deformation in shape and diameter was much larger. The effect of the upstream pres- sure on flow increased as the upstream pressure increased. This was experimentally observed by Kim et al. (2002). These results show that the impact of modulus of elasticity and upstream pressure can produce large changes in the diameter and shape of a flexible short-tube. The change in shape produced a much different axial pressure distribution in the flexible short-tube, compared to a rigid short-tube. Ultimately, the designer is interested in the change in flow produced by the short-tube. A variable that was developed to quantify the deformation of the flexible short-tubes is the diameter ratio, Dr, which is defined as follows: Dr = Ddef,avg/Dundef,avg Figure 8 Short-tube inner radius variation as a result of R-134a single-phase flow at different upstream pressures. Figure 9 Short-tube inner radius variation as a result of R-410A single-phase flow at different upstream pressures. 444 where Ddef,avg = average diameter under deformation Dundef,avg = average diameter without deformation Figure 10 shows the diameter ratio, Dr, as a function of the tube modulus of elasticity for R-134a, R-22, and R-410a. The values for R-22 were from a previous study (Bassiouny and O Neal 2002). Qualitatively, all three refrigerants exhibited a similar trend as the tube modulus increased. R-410a yielded the lowest diameter ratios, meaning the highest deformation of the three refrigerants. There was a steeper slope in Dr as the modulus decreased below about 7000 kpa (1015 psi) for R-410a. Figure 11 shows the effect of varying the tube elasticity on the refrigerant flow rate for three different refrigerants. The figure illustrates that when the tube modulus of elasticity was greater than 7000 kpa (1015 psi), the flow rate, in the case of using R-410a, was high compared to R-22 or R-134a. This was due to the fact that R-410a had the higher operating pressures at the given operating conditions. The flow rate of R-410a dropped rapidly as the modulus of elasticity decreased lower than 7000 kpa (1015 psi). In contrast, the flow rate appeared to slowly decrease, approaching constant values for both R-134a Figure 10 Diameter ratio variation at different modules of elasticity for three different refrigerants.

6 For personal use only. Additional reproduction, distribution, or transmission Figure 11 Refrigerant flow rate variation at different tube modules of elasticity of three different refrigerants. and R-22. As the modulus of elasticity increased, the tube got stiffer, and the mass flow rate increased. Once the tube modulus decreased beyond about 7000 kpa (1015 psi), the tube could not resist the forces exerted by the higher pressure R-410a. The model showed a much larger deformation for R-410a, which caused the flow to decrease below that of R-134a and R-22. Figure 12 indicated the effect of condenser pressure on the refrigerant flow for the three refrigerants. The condensing temperature was constant and the tube geometry and modulus of elasticity were the same for all three refrigerants. The overall trends were similar for each refrigerant. However, there was a quantitative variation due to operating conditions of each refrigerant. For example, having a condensing temperature of 46 C (115 F) yielded upstream pressures of 1197, 1779, and 2804 kpa (174, 260, and 405 psia) for R-134a, R-22, and R-410a, respectively. If the condenser temperature increased, the upstream pressure increased. Keeping the evaporator pressure or the downstream pressure constant meant that the pressure differential across the short-tube increased as the upstream pressure increased. This would lead to increasing the refrigerant flow. The slope of the lines differed when the tube modulus of elasticity changed. CONCLUSIONS A finite element model was used to estimate the deformation, flow, and pressure distribution for flexible short-tubes over a range of operating conditions with two refrigerants (R-134a and R-410a). Because of the higher operating pressures for R-410a, the flexible tubes deformed more with R-134a than with R-410a. As a consequence, the pressure drop at the entrance to the shorttubes was greater with R-410a. For some larger deformations, the model estimated unrealistically low pressure drops near the entrance of the tube. This could have been caused by not having a fine enough grid right near the entrance of the tube. For combinations of the higher elasticity tubes and higher upstream pres Figure 12 Predicted refrigerant flow rate variation vs. upstream pressure for three different refrigerants. sures with R-410a, the model showed unrealistic pressure distribution results, particularly near the tube entrance. These results could be interpreted as a collapse of the tube. However, we did not have experimental results to verify that interpretation of the results. The results from the model showed that the operating shape of the flexible short-tube resembled a convergingdiverging nozzle upon deformation. The tube was more compressed with the higher pressure R-410a than with R-134a at the same condensing (upstream saturation) temperature of 46 C(115 F). For R-410a, the minimum tube diameter was almost 1.4 mm (0.055 in.) and occurred at an axial distance approximately 4 mm (0.157 in.) from the tube inlet. However, in the case of R-134a, the minimum diameter, which occurred at the same axial location as R-410a, was 1.7 mm (0.067 in.). While the mass flows for R-410a were higher for the stiffer short-tubes, the mass flow dropped more rapidly as the modulus of elasticity decreased. For the lower modulus of elasticity, 5513 kpa (810 psia), R-410a produced the lowest flow. These results indicate that flexible short-tubes could potentially be useful in a refrigeration or air-conditioning system for controlling flow. The fact that the flow crosssectional area reduces in size as the upstream pressure increases means that they provide a measure of control not found with conventional rigid short-tubes. This work does show that using the smaller modulus flexible short-tubes with a refrigerant like R-410a may require additional study because the predicted deformations were large enough that the model estimated unrealistic pressure distributions. REFERENCES Aaron, A.A., and P.A. Domanski Experimentation, analysis, and correlation of refrigerant-22 flow through 445

7 For personal use only. Additional reproduction, distribution, or transmission short tube restrictors. 96(1): Bassiouny, R., and D.L. O Neal A numerical study of pressure distribution and flow through rigid short-tube orifices. 108(1): Bassiouny, R., and D.L. O'Neal Analysis of refrigerant flow and deformation for a flexible short-tube using a finite element model. International Journal of Refrigeration 27(2): Drucker, A.S Variable area refrigerant expansion device having a flexible orifice. U.S. Patent Drucker, A.S., and A.D. Abbott Variable area refrigerant expansion device having a flexible orifice. U.S. Patent Drucker, A.S., and P.L. Cann Variable area refrigerant expansion device having a flexible orifice. U.S. Patent Erbay, H.A., and H. Demiray Finite axisymmetric deformations of elastic tubes: An approximation method. Journal of Engineering Mathematics 29(5): Kim Y., and D.L. O Neal. 1994a. Two-phase flow of Refrigerant-22 through short-tube orifices. 100(1): Kim Y., and D.L. O Neal. 1994b. The effect of oil on the two-phase critical flow of Refrigerant 134a through short tube orifices. International Journal of Heat and Mass Transfer 37(9): Kim, Y., D.L. O Neal, W.V. Payne, and M. Farzad Refrigerant flow through flexible short-tube orifices. International Journal of HVAC&R Research 8(2): Payne, W.V., and D.L. O Neal Multiphase flow of Refrigerant 410A through short tube orifices. ASHRAE Transactions 105(2): Swanson Analysis System, Inc Theory. Vol. IV, ANSYS User s Manual. Houston, PA. 446

8 ESL-PA Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.