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Development of the high-efficiency technology of a [CO.sub.2] two-stage rotary expander.

INTRODUCTION

Since the Kyoto protocol to the United Nations Framework Convention on Climate Change was adopted by the Conference of Parties (COP-3) (UN 1997), the need for energy conservation in the household sector has increased. In Japan, energy conservation of heat-related home appliances has become an important issue, because approximately 50% of [CO.sub.2] emissions have been generated by space heating (28%) and water heating (23%). In 2001, a heat pump water heater operating with [CO.sub.2] refrigerant was introduced into the market. Because it uses low-cost, off-peak power to heat water, and it can reduce [CO.sub.2] emissions by using atmospheric thermal energy, the sales of this water heater have increased at a rate of more than 50% annually. The rated coefficient of performance (COP) has improved from 3.46 to 4.90, marking a performance improvement of 20% or more.

The state of [CO.sub.2] refrigerant during the heat pump cycle is supercritical between the single phase in the high-pressure side and the gas-liquid two-phase state in the low-pressure side, as there is a difference of more than 6 MPa (870 psi). Previous attempts to improve COP were limited to improving the efficiency of compressors and heat exchangers and the configuration of the cycle. This study focused on an expansion valve that wasted a large amount of pressure difference energy. Replacing the expansion valve with an expander is an effective means for recovering the drive power from the large pressure differential. Nagatomo et al. (1999a, 1999b) investigated scroll expanders for R-134a and concluded that the total efficiency of the expander was about 70%. Nagatomo et al. (2003) also investigated rotary expanders for R-22. The isentropic efficiency of the expander was measured to be about 80%. The New Energy and Industrial Technology Development Organization (2002, 2003, 2004) investigated two-stage swing expanders for [CO.sub.2] refrigerant. A total efficiency of 59% was achieved. Fukuta et al. (2006) investigated scroll expanders for [CO.sub.2] refrigerant and concluded that the total efficiency was measured to be about 55%. Fukuta et al. (2008) also investigated vane expanders for [CO.sub.2] refrigerant. A total efficiency of 50% or more was acheived.

An expander can operate by reverse-rotating a compressor, but it will face problems including those related to the suction control mechanism and the drastic change of the [CO.sub.2] refrigerant state from the supercritical single phase to the gas-liquid two-phase. A two-stage rotary expander was chosen for this study because it requires no suction control mechanism. Analytical technologies for optimizing the design parameters of the expander in the development process were used. The performance analysis model for predicting the expander performance was developed by combining the dynamic mechanical analysis and the refrigerant pressure analysis, which takes refrigerant leakage from clearances in the expansion chamber into consideration. By using refrigerant pressure analysis, the [CO.sub.2] property in the expansion chamber could be noted at every increment of the rotational angle by linking it with the Reference Fluid Thermodynamic and Transport Properties Database (REFPROP) (NIST 2002). This method yielded an accurate calculation of the [CO.sub.2] refrigerant expansion process from the supercritical single phase to the gas-liquid two-phase.

To optimize the design parameters of a two-stage rotary expander, the effect of each design parameter on the expander performance was examined by changing sets of parameters, based on an orthogonal array, and applying the calculation results to the "design of experiments" (Taguchi 1993).

STRUCTURE OF A TWO-STAGE ROTARY EXPANDER

Outline of a Compressor Combined with an Expander

The two-stage rotary expander used in this study was designed to combine its shaft with another shaft of a commercial scroll compressor in a [CO.sub.2] heat pump water heater by using a coupling connector. For this purpose, a commercial scroll compressor was remodeled into the compressor combined with the expander. The structure of the scroll compressor was not changed much aside from where the lower edge of the shaft was splined to join the coupling connector. The scroll compressor was located at the top, while the two-stage rotary expander was located under the compressor and the motor. The structure of the compressor combined with the expander is shown in Figure 1.

[FIGURE 1 OMITTED]

The refrigerant discharged from the scroll compressor filled the shell like a commercial scroll compressor. Therefore, the pressure in the shell was as high as the discharge pressure, and temperature around the compressor was as high as the discharge temperature. The suction tube of the two-stage rotary expander was directly connected with the expander (the expander discharged refrigerant directly out of the shell through the discharge tube). To thermally isolate the expander from the compressor, an isolation structure was set up between the motor and the expander. (An intermediate oil pump between the oil pool and the scroll compressor was set up in the isolation structure.) This structure kept the temperature around the expander low.

Structure and Operation of a Two-Stage Rotary Expander

The two-stage rotary expander consisted of two stacked rotary-type fluid machines and an intermediate plate separating the first and the second stage with a connecting hole. Each stage had an independent cylinder, piston, vane, and crankpin that was part of the crankshaft and engaged with the piston.

The operation of the two-stage rotary expander is shown in Figure 2. It was designed so that the expansion chamber surrounded by the piston and the cylinder in the second stage is larger than that in the first stage. In Figures 2a through 2d, the first stage is shown on the left, while the second stage is on the right. The shaft rotation is in a clockwise direction. Figure 2a shows the pistons during the first and the second stages are at the top dead centers. The expansion of [CO.sub.2] refrigerant starts when the shaft rotation [theta] angle reaches the suction process end angle [[theta].sub.s1]. At this angle, the first stage operation chamber has shut off the suction hole (between 2a and 2b). [CO.sub.2] refrigerant expands as the volume of the expansion chamber--formed by the first stage operation chamber, connecting hole, and second stage operation chamber--increases with the shaft rotation. The expansion process continues until the shaft rotation angle [theta] reaches the discharge process starting angle [[theta].sub.s2] (between 2d and 2a) and the refrigerant discharge starts from the discharge hole.

[FIGURE 2 OMITTED]

ANALYSIS METHOD

By combining the dynamic mechanical analysis and the refrigerant pressure analysis of the expansion chamber with leakage analysis, friction loss of each component of the expander; mechanical efficiency; and volumetric efficiency, which represents expander performance, can be calculated.

Method of Analyzing Refrigerant Pressure in the Expansion Chamber

The accurate calculation of refrigerant pressure in the expansion chamber is important when carrying out the dynamic mechanical analysis (to be discussed below). Two problems exist when calculating refrigerant pressure in the expansion process. The first is that it's difficult to develop a technique to analyze the expansion process of [CO.sub.2] refrigerant, because it drastically changes itself from the supercritical single phase to the gas-liquid two-phase. The other issue is figuring out how to analyze refrigerant leakage from the suction hole to the expansion chamber, and from the expansion chamber to the discharge hole.

Nagatomo et al. (1999) analyzed the performance of a scroll expander for R-134a. In the analysis, it was assumed that R-134a refrigerant expands in the gas single phase, and the heat capacity ratio is constant during the expansion process. To calculate pressure in the expansion chamber, the formula [PV.sup.[kappa]] = const (P: pressure, V: volume) was applied. However, in the expansion process of [CO.sub.2] refrigerant, which changes from the supercritical single phase to the gas-liquid two-phase, [kappa] in the supercritical single phase cannot be assumed as constant, because the value of [kappa] substantially changes with a small change of pressure, and [kappa] is indefinite in the gas-liquid two-phase. So, the above formula cannot be used during the expansion process of [CO.sub.2] refrigerant. For this reason, the refrigerant pressure analysis developed for this study uses the reference database of [CO.sub.2] refrigerant. That is, for each analysis time step, the refrigerant pressure analysis gets properties of [CO.sub.2] refrigerant from the standard reference database (REFPROP) of NIST (2002) and updates them in the expansion chamber.

On the other hand, the flow rate of [CO.sub.2] refrigerant--which leaks from each clearance due to the pressure difference between the suction hole and expansion chamber, or between the expansion chamber and discharge hole--is calculated at each analysis time step by using the experimental formula (Oku et al. 2005) of the pipe friction coefficient, which regards [CO.sub.2] refrigerant as a noncompressive fluid. In addition, the leakage flow rate calculated at a specific analysis time step (shaft rotation angle [theta]) is assumed to affect the change of the properties of [CO.sub.2] refrigerant in the expansion chamber in the next analysis step (shaft rotation angle [theta] + d[theta]). In the refrigerant pressure analysis, the calculation process is divided into two steps.

STEP1: Only the leakage effect is examined without considering the volume increase of the expansion chamber. In other words, the refrigerant, which leaks into the expansion chamber, is assumed to mix into the refrigerant in the expansion chamber, with the specific internal energy [u.sub.in]([theta]) being kept constant during the leak-in process. After mixing at the shaft rotation angle [theta], the refrigerant density [rho]'([theta]) and specific internal energy u'([theta]) are calculated using the following equations, when the temperature difference between the expansion chamber and the surroundings is small enough for ignoring heat transfer:

[rho]'([theta]) = [[M([theta]) + [M.sub.in]([theta]) - [M.sub.out]([theta])]/[VOL([theta])]] (1)

u'([theta]) = [[M([theta]) x u([theta]) x [M.sub.in]([theta]) x [u.sub.in]([theta]) - [M.sub.out]([theta]) x u([theta])]/[M([theta]) + [M.sub.in]([theta]) - [M.sub.out]([theta])]] (2)

In Equations 1 and 2, VOL([theta]) is the volume of the expansion chamber, u([theta]) is the specific internal energy of refrigerant, and [u.sub.in]([theta]) is the specific internal energy of the refrigerant that leaks into the expansion chamber. Further, [M.sub.in]([theta]) is the refrigerant mass that leaks into the expansion chamber, and [M.sub.out]([theta]) is the refrigerant mass that leaks out of the expansion chamber. [M.sub.in]([theta]) and [M.sub.out]([theta]) are calculated by using the experimental formula (Oku et al. 2005) of the pipe friction coefficient. The refrigerant mass M([theta]) in the expansion chamber is based on the refrigerant mass [M.sub.s] in the expansion chamber at the end of the suction process and is calculated using the following equation:

M([theta]) = [M.sub.s] + [[theta].[integral].[[theta].sub.s1]][M.sub.in]([theta])d[theta] - [[theta].[integral].[[theta].sub.s1]][M.sub.out]([theta])d[theta] (3)

When the values p'([theta])and u'([theta]) are provided to the reference database, the specific entropy s'([theta]), which considers the influence of leakage, is obtained.

STEP2: Under the isentropic expansion process, the volume of [CO.sub.2] refrigerant in the expansion chamber expands by the tiny shaft rotational angle d[theta]. That is, the specific entropy s'([theta]) assumes to be maintained in this expansion process. When two properties of [CO.sub.2] refrigerant at rotation angle [theta] + d[theta] (i.e., the refrigerant density [rho][[theta] + d[theta]), as expressed in the following equation, and the specific entropy s([theta] + d[theta]) = s'([theta]) are provided to the reference database, the pressure P([theta] + d[theta]) and other properties (i.e., specific enthalpy h[[theta] + d[theta]], specific internal energy h[[theta] + d[theta]], etc.) can be obtained:

[rho]([theta] + d[theta]) = [[M([theta]) + [M.sub.in]([theta]) - [M.sub.out]([theta])]/[VOL([theta] + d[theta])]] (4)

Dynamic Mechanical Analysis Method

The dynamic mechanical analysis solves the motion equation using the numerical analysis method, which is derived from the balance of forces and moments acting on the shaft, pistons, and vanes. The results of the refrigerant pressure analysis described in the previous subsection are input in the dynamic model. This analysis calculates an approximate solution of the shaft rotation of the scroll compressor combined with the two-stage rotary expander and then calculates inertia forces acting on the pistons and vanes with the fluctuation of the shaft rotational speed. Thus, the load and friction loss on each part can be calculated. When motion equations were derived, the technique proposed by Imaichi et al. (1982) was used. To calculate the frictional forces acting on surfaces between the vane and piston, between the piston and crankpin, and of main bearing, Coulomb's friction law is applied. Forces acting on the piston (first stage) and the shaft are shown in Figure 3. The motion equation of the shaft rotation of the scroll compressor combined with the two-stage rotary expander is shown here:

[FIGURE 3 OMITTED]

([I.sub.comp] + [I.sub.s] + [2.summation over (j = 1)][m.sub.pj][e.sub.j.sup.2])[theta] = [T.sub.comp]([theta], [theta]) + [2.summation over (j = 1)][[e.sub.j]{[F.sub.pj]sin([[theta] + [[xi].sub.j]]/2) - [F.sub.aj] - [F.sub.ctj] + [F.sub.vnj]sin([theta] + [[xi].sub.j]) - [F.sub.vtj]cos([theta] + [[xi].sub.j])} - [R.sub.pej][F.sub.etj]] - [R.sub.s][F.sub.bt] (5)

The suffix j refers to stage number j = 1, 2.

Efficiency of the Expander

Frictional losses of each component of the expander can be calculated as follows:

* Expansion work of [CO.sub.2] refrigerant [W.sub.co2j]:

[W.sub.co2j] = [2[pi].[integral].0][2.summation over (j = 1)][e.sub.j][F.sub.pj]sin([[theta] + [[xi].sub.j]]/2)d[theta] (6)

* Frictional loss of oil film between pistons and cylinder headers or the intermediate plate [W.sub.aj]:

[W.sub.aj] = [2[pi].[integral].0][2.summation over (j = 1)][e.sub.j][F.sub.aj]d[theta] (7)

* Frictional loss of oil film between pistons and cylinders [W.sub.ctj]:

[W.sub.ctj] = [2[pi].[integral].0][2.summation over (j = 1)][e.sub.j][F.sub.ctj]d[theta] (8)

* Frictional loss of vanes [W.sub.vj]:

[W.sub.vj] = [2[pi].[integral].0][2.summation over (j = 1)][e.sub.j](-[F.sub.vnj]sin([theta] + [[xi].sub.j]) + [F.sub.vtj]cos([theta] + [[xi].sub.j]))d[theta] (9)

* Frictional loss of crankpins [W.sub.ej]:

[W.sub.ej] = [2[pi].[integral].0][2.summation over (j = 1)][R.sub.pej][F.sub.etj]d[theta] (10)

* Frictional loss of bearing [W.sub.b]:

[W.sub.b] = [2[pi].[integral].0][R.sub.s][F.sub.btj]d[theta] (11)

Ideal recovered power [W.sub.ideal] of the expander is calculated here:

[W.sub.ideal] = ([h.sub.s] - [h.sub.d]) * [[rho].sub.s] * [V.sub.s] * Rps (12)

Here, [h.sub.s] and [h.sub.d] are the enthalpy of suction and discharge refrigerant, [[rho].sub.s] is the density of suction refrigerant, [V.sub.s] is the suction volume of the expander, and Rps is rotation speed. Mechanical efficiency and volumetric efficiency can be calculated as follows:

* Mechanical efficiency [[eta].sub.m]:

[[eta].sub.m] = [2.summation over (j = 1)]{[W.sub.co2j] - ([W.sub.aj] + [W.sub.ctj] + [W.sub.vj] + [W.sub.ej] + [W.sub.b])}/[W.sub.co2j] (13)

* Volumetric efficiency [[eta].sub.v]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)

Verification of the Model

To determine the coefficient of friction of each rubbing part used in the dynamic mechanical analysis, a two-stage rotary expander was manufactured (zeroth prototype) by setting design parameters of the expander (e.g., the cylinder radius, piston radius, cylinder height, etc.) with no reliable reason, testing its performance, and measuring the pressure in the expansion chamber (P-v measurement experiment).

To carry out the P-v measurement experiment, a the test rig was built to measure the performance of the independent expander. The scroll compressor was removed from the compressor-expander unit, and the motor was replaced by a generator, which changed the recovered power of the two-stage rotary expander to electric power. The efficiency of the generator had been previously measured.

To measure pressure in the expansion chamber, six pressure sensors were used. Three pressure sensors were installed at each stage of the two-stage rotary expander. In the first stage, one sensor was set near the suction port, near the bottom dead point (-x direction in Figure 2) and near the connection port. In the second stage, one sensor was set near the connection port, near the bottom dead point and near discharge port, respectively. By combining the data from the six pressure sensors, the change of pressure in the expansion chamber was obtained. On the other hand, to measure the rotation angle of the shaft at the specified time, a gap sensor attached at the edge of the shaft was used. A P-v diagram could be created by combining the data from the six pressure sensors and the gap sensor. When the P-v diagram was analyzed in detail, the suction loss, discharge loss, expansion loss (including heat transfer loss), and leakage loss were calculated. The total friction loss of the initial (zeroth) prototype was obtained by subtracting the generator loss, suction loss, discharge loss, expansion loss, and leakage loss from the ideal recovered power.

An error analysis was conducted to estimate the experimental uncertainty of this test rig for measuring expander efficiency. In this test rig, a power meter, pressure sensors, temperature sensors, mass flow meters, and a tachometer were installed. The accuracy of the power meter, the pressure sensor for the suction port, the pressure sensor for the discharge port, the temperature sensor for the suction port, and the mass flow meter were [+ or -]0.2%, [+ or -]11.25 kPa (1.63 psi), [+ or -]7.5 kPa (1.09 psi), [+ or -]0.1K, and [+ or -]0.5%, respectively. The calculation error of the efficiency of the generator was calculated by using the tachometer to measure rotation speed and was estimated to be [+ or -]0.5%. By using these values, the experimental uncertainty for measuring expander efficiency was estimated to be [+ or -]1.2% of the efficiency.

While referring to a study on a rotary compressor (Shintaku et al. 2000), the coefficients of friction were determined for ensuring that the error between the friction loss obtained by the P-v measurement experiment and by the dynamic mechanical analysis is 1% or less of the ideal collectable power (collectable power at 100% expander efficiency). The error was small when compared with that of the test rig.

The comparisons of the analysis results and the P-v measurement results are shown in Figures 4 and 5. Figure 4 shows the pressure of [CO.sub.2] refrigerant in the expansion chamber, with the volume (suction volume of the expansion chamber normalized as 1) of the expansion chamber on the horizontal axis, and the pressure (suction pressure normalized as 1) in the expansion chamber on the vertical axis. This figure indicates that this analysis can calculate the change in [CO.sub.2] refrigerant state from the supercritical single phase to the gas-liquid two-phase and also indicates a good agreement between the analysis result and the P-v measurement result. Figure 5 shows the rotation speed variation of the two-stage rotary expander with time on the horizontal axis and rotation speed (average speed normalized as 1) on the vertical axis. Again, the figure indicates good agreement between the dynamic mechanical analysis result and the experimental result. Therefore, the analysis method is deemed appropriate.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

THE OPTIMUM DESIGN PARAMETERS OF THE FIRST PROTOTYPE

Design Concept of the First Prototype

There are various losses that lower the expander's performance besides frictional losses such as suction, discharge, and heat transfer loss. In order to improve the expander's performance, it is necessary to reduce these losses, but it is preferable that the losses should be measured individually. For example, to reduce the suction and discharge loss, the suction and discharge passage should be optimized. To reduce the heat transfer loss, the temperature difference between the expander chamber and the expander surroundings should be reduced. As described above, the temperature difference between the expander and its surroundings is actually small enough because of the thermal isolation structure. Therefore, the influence of heat transfer loss is assumed to be ignored. On the other hand, in case of the friction loss, it is possible to reduce this by changing the expander design parameters.

For this reason, in the first prototype, by ignoring suction, discharge, and heat transfer loss, the design parameters of the two-stage rotary expander were optimized to maximize the isentropic efficiency [[eta].sub.s], which is defined in the following equation (for the purpose of mainly reducing friction losses by using the developed model):

[[eta].sub.s] = [[eta].sub.m] * [[eta].sub.v] (15)

In the compressor combined with expander, the compressor and expander rotate at the same speed. When the suction volume of the compressor is set, the suction volume of the expander is automatically set according to the specific cycle condition. In Japan, there are roughly three operating conditions during a year (JRAIA 2005), and the suction volume that suits each condition is different. Table 1 indicates the density ratio of the suction refrigerant of the compressor and that of the expander. Table 1 also shows the indispensable suction volume ratio of the suction volume of the expander in each condition, when the suction volume in the winter condition is set as 1.0. In the first prototype, the suction volume of the two-stage rotary expander was set as the minimum, or the volume in winter condition.
Table 1. Operating Conditions of Water Heaters in Japan

                      Winter  Intermediate  Summer

Density ratio          10.4       8.7         6.7
Suction volume ratio    1.0       1.3         1.6


To find the optimal design parameters of the expander, the design of experiments with an orthogonal array was applied (Taguchi 1993). This method allows for the examination of the sensitivity of each design parameter to the objective variable (by eliminating the effects of other parameters). In this study, the developed model was used for experiments, and [[eta].sub.s] was selected as the objective variable.

The eight design parameters to be examined this time are shown in Table 2. (The values of each level are shown by normalizing the second level as 1.0.) A total of 18 parameters (eight design parameters were decided upon based on the orthogonal array L18) were analyzed for the two-stage rotary expander by using the developed model, and [[eta].sub.s] of each expander was estimated in the winter condition. The sensitivity of each design parameter to [[eta].sub.s] is shown in Figure 6. In this figure, each value is normalized by the average efficiency of 18 parameters. From this figure, it is clear that the following design guidelines are effective for improving the performance of the two-stage rotary expander after appropriately determining A (i.e., the expansion ratio):
Table 2. Design Parameters of the Two-Stage Rotary Expander

                                 First Level  Second Level  Third Level

A  Expansion ratio                   0.7          1.0           --

B  Eccentricity of the first         0.8          1.0           1.2
   stage

C  Cylinder height of the first      0.9          1.0           1.1
   stage

D  Eccentricity of the second        0.8          1.0           1.2
   stage

E  Cylinder height of the            0.7          1.0           1.3
   second stage

F  Radius of crankpin of the         0.9          1.0           1.1
   first stage

G  Radius of crankpin of the         0.9          1.0           1.1
   second stage

H  Radius of the main bearing        0.9          1.0           1.1


[FIGURE 6 OMITTED]

* increase B (eccentricity of the first stage)

* decrease E (cylinder height of the second stage)

A two-stage rotary expander has been designed and manufactured based on these design guidelines. With the first prototype, a total of four types of expanders were designed to verify the validity of the guidelines by varying the values of design parameters B and E, which have been assessed as having a higher sensitivity, in consideration of restrictions of manufacturing. The value of the design parameter B was taken at 1.0 and 1.2, and the value of E was taken at 0.7 and 1.0 (these values are normalized by the value of the second level in Table 1).

Experimental Results of the First Prototype

The sensitivity of design parameters B and E to the expander efficiency obtained by the performance examinations of the four types of expanders is shown in Figure 7. To measure these performances, the test rig for zeroth prototype was used again, and the experimental uncertainty for measuring expander efficiency was [+ or -]1.2% of the efficiency. Figure 7 also shows the sensitivity of design parameters B and E to [[eta].sub.s] the obtained by the developed model. In Figure 7, the sensitivity of B and E to the efficiency indicates the same tendency between the analysis and experiment, but there's a substantial difference in the value. The cause of the difference in the value of the efficiency between the analysis and experiment has been investigated in detail. First, the rubbing traces on the piston of the second stage and the intermediate plate separating the first and the second stage were identified. These traces showed that a large friction loss was generated between the piston and intermediate plate that had not been considered in the zeroth prototype. Second, the shape of the suction hole was changed in the first prototype from that of the zeroth prototype and would result in generating large suction loss.

[FIGURE 7 OMITTED]

THE OPTIMUM DESIGN PARAMETERS OF THE SECOND PROTOTYPE

Design Concept of the Second Prototype

The suction volume of the second prototype expander was set at the same volume as the first prototype, that is, it was set to the suitable volume in the winter condition. Then, the second prototype was designed to maximize the annual COP of the cycle. First of all, it was necessary to establish a structure to change the suction volume so that it was suitable for each operating condition. In this study, the two-port injection method, as shown in Figure 8, was adopted, which could change the rotational position once the suction process finished. Port A and B were set beside the suction hole to supply refrigerant to the expansion chamber in the first cylinder header so that the suction volume could be changed by opening or closing these ports. The positions of these ports were designed to match the suction volume in the intermediate condition when only port A was open and in the summer condition when both port A and B were open.

[FIGURE 8 OMITTED]

The four design parameters to be examined in the second prototype were selected as shown in Table 3. The expansion chamber volume when the expansion process finished (design parameter I) was added as a new evaluation parameter. This volume was constant regardless of the state of port A and B, and it decides the expansion ratio in each operating condition. If this expansion ratio matched the winter condition, refrigerant in the expansion chamber could not expand fully in the intermediate and summer conditions. On the other hand, if this ratio matched the summer condition, refrigerant in the expansion chamber expanded excessively and an over-expansion loss occurred in the intermediate and winter conditions. Therefore, design parameter I was changed three steps from suitable volume for the intermediate condition to that for the summer condition.
Table 3. Design Parameters of the Two-Stage Rotary Expander

                                 First Level  Second Level  Third Level

I  The expansion chamber volume      0.9          1.0           1.1
   when the expansion process
   finished

B  Eccentricity of the first         0.8          1.0           1.2
   stage

D  Eccentricity of the second        0.8          1.0           1.2
   stage

E  Cylinder height of the            0.6          0.9           1.2
   second stage


Other design parameters were selected to optimize the second stage. This was because the time when the suction process (started the expansion process) finished in the intermediate and summer conditions was later than the time this occurred in the winter conditions, so the main stage that [CO.sub.2] refrigerant worked was predicted to be the second stage. The eccentricity of the second stage (design parameter D) and the height of the second stage (E) were investigated again. To confirm the sensitivity of the design parameters of the first stage, the eccentricity of the first stage (B) that indicated the highest sensitivity to [[eta].sub.s] in the first prototype development process was selected. In Table 3, the value of each level of I is normalized by the second level, and the standard of each level of B, D, and E is the same as that in Table 1.

A total of nine parameters (four design parameters were decided upon based on the orthogonal array L9) were analyzed for the two-stage rotary expander by using the developed model and the COP improvement ratio of each expander compared with the conventional water heater cycle (in which the expansion valve was used) was estimated in each operating condition. The annual COP of each expander was calculated based on Japanese standard JRA4050 (2005), which considered both the period of each operating condition and the heat load of the heat pump cycle in each condition, and the sensitivity of each design parameter to the annual COP improvement was investigated. Figure 9 shows the result. In this figure, each value shows the annual COP improvement as compared to the average annual COP of the nine parameters. It is clear that all four evaluated parameters have high sensitivity to COP improvement. The following design guidelines were obtained:

[FIGURE 9 OMITTED]

* decrease I (the expansion chamber volume when the expansion process was finished)

* increase B (eccentricity of the first stage)

* increase D (eccentricity of the second stage)

* decrease E (cylinder height of the second stage)

A two-stage rotary expander was designed and manufactured based on the design guidelines. The value of the design parameter I was taken at 0.9 compared to the second level in Table 3, the value of B was 1.2, the value of D was 1.2 and the value of E was 1.0. The reason why the value of E was kept at 1.0 was due to the difficulties associated with manufacturing and pressure drop loss, which was caused by the long diagonal connection hole in the intermediate plate.

Experimental Results of the Second Prototype

When the second prototype was designed, the problems of the first prototype were in the process of being solved. To set the optimal clearances between the pistons and the intermediate plate, the deformation of the intermediate plate was analyzed using the Integrated Design and Engineering Analysis Software (Siemens PLM Software 2004). The suction hole shape was also improved to reduce the suction loss. The performance test results of the second prototype are shown in Table 4. The test rig for the zeroth prototype was used again in this test, and the experimental uncertainty for measuring expander efficiency was [+ or -]1.2% of the efficiency. Though the efficiency in the intermediate condition was low, the efficiency of 60[+ or -]1.2% or more could be achieved in winter and summer conditions.
Table 4. Experimental Result of the Two-Stage Rotary Expander

              Expander Efficiency, %    [[eta].sub.s], %
              (Experimental Result)   (Simulation Result)

Winter            60[+ or -]1.2               58

Intermediate      54[+ or -]1.2               63

Summer            63[+ or -]1.2               66


CONCLUSION

The performance analysis model was developed by combining the refrigerant pressure analysis and the dynamic mechanical analysis. By using this model, the design of experiments based on an orthogonal array was applied and the sensitivity of the expander design parameters to the isentropic efficiency [[eta].sub.s] was examined to help with determining the optimum set of design parameters. The following results were obtained in the described development process.

1. The refrigerant pressure analysis that updates properties of [CO.sub.2] refrigerant from REFPROP (NIST 2002) and calculates the leakage flow rate of refrigerant in each clearance by using the experimental formula of the pipe friction coefficient at each analysis time step was established. This analysis allowed for the pressure in the expansion chamber to be calculated. It was deemed appropriate through comparing the pressure in the chamber with the P-v experiment results.

2. The dynamic mechanical analysis that solves the rotational motion equation of the shaft of the scroll compressor combined with the two-stage rotary expander and calculates the friction loss in each rubbing part was made reliable by adjusting the coefficients of friction to fit the total friction loss obtained by the P-v measurement experiment.

3. The design parameters for the input data of the developed model were changed based on the orthogonal array, and the sensitivity of each design parameter to the expander performance was examined by using the developed model. The optimum set of design parameters was determined. As a result, an expander efficiency of 54[+ or -]1.2% or more during a year was achieved after two prototyping cycles.

NOMENCLATURE

[e.sub.j] = eccentricity

[F.sub.aj] = frictional force of the oil film on the top and bottom surfaces of the piston

[F.sub.bt] = frictional force of the main bearing

[F.sub.ctj] = frictional force of the oil film between the piston and cylinder

[F.sub.etj] = frictional force between the piston and crankpin

[F.sub.pj] = pressure differential force of [CO.sub.2] refrigerant

[F.sub.vnj] = frictional force between the vane and piston

[h.sub.d] = the specific enthalpy of discharge refrigerant

[h.sub.s] = the specific enthalpy of suction refrigerant

h([theta]) = the specific enthalpy of refrigerant in the expansion chamber

[I.sub.comp] = inertia moment of the scroll compressor

[I.sub.s] = inertial moment of the shaft

[m.sub.pj] = mass of the piston

M([theta]) = the refrigerant mass in the expansion chamber

[M.sub.in]([theta]) = the refrigerant mass that leaks into the expansion chamber

[M.sub.out]([theta]) = the refrigerant mass that leaks out of the expansion chamber

[M.sub.s] = refrigerant mass in the expansion chamber at the end of the suction process.

P([theta]) = the pressure of the refrigerant in the expansion chamber

[R.sub.pej] = radius of the crankpin

Rps = rotation speed

[R.sub.s] = radius of the shaft (bearing)

S([theta]) = the specific entropy of the refrigerant

[T.sub.comp] = all torques of the scroll compressor

u([theta]) = the specific internal energy of the refrigerant

[u.sub.in]([theta]) = the specific internal energy of the refrigerant that leaks into the expansion chamber

VOL([theta]) = volume of the expansion chamber

[V.sub.s] = suction volume of the expander

[W.sub.aj] = frictional loss of oil film between pistons and cylinder headers or intermediate plate

[W.sub.b] = frictional loss of bearing

[W.sub.co2j] = expansion work of CO2 refrigerant

[W.sub.ctj] = frictional loss of oil film between pistons and cylinders

[W.sub.ej] = frictional loss of crankpins

[W.sub.vj] = frictional loss of vanes

[W.sub.ideal] = ideal recovered power

[[eta].sub.m] = mechanical efficiency

[[eta].sub.s] = isentropic efficiency

[[eta].sub.v] = volumetric efficiency

[kappa] = the heat capacity ratio

[theta] = shaft rotation angle

[[theta].sub.e2] = discharge process starting angle

[[theta].sub.s1] = suction process end angle

[[rho].sub.s] = the density of suction refrigerant

[rho]([theta]) = the density of the refrigerant

[[xi].sub.j] = displacement angle at the vane-piston contact point

Suffix

j = stage number of two-stage rotary expander

REFERENCES

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Fukuta, M., T. Yanagisawa, O. Kosuda, and Y. Ogi. 2006. Performance of scroll expander for [CO.sub.2] refrigeration cycle. Proceedings of the Eighteenth International Compressor Engineering Conference at Purdue, West Lafayette, IN, C109.

Fukuta, M., M. Higasiyama, T. Yanagisawa, and Y. Ogi. 2008. Observation of [CO.sub.2] transcritical expansion process. Proceedings of the Twelveth International Refrigeration and Air Conditioning Conference at Purdue, West Lafayette, IN, 2374.

Imaichi, K., M. Fukushima, S. Muramatsu, and N. Ishii. 1982. Vibration analysis of rotary compressors. Proceedings of the Purdue Compressor Technology Conference, West Lafayette, IN, pp. 275-82.

JRAIA. 2005. Standard name, JRA4050. Tokyo, Japan: The Japan Refrigeration and Air Conditioning Industry Association.

Nagatomo, S., T. Ootaka, and A. Morishima. 1999a. Scroll expander first report: Effects of operating conditions on expander performance characteristics. Trans. of the JSRAE 16(1):59-66.

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Nagatomo, S., H. Hattori, and A. Morishima. 2003. Rolling piston type rotary expander first report: Experimental study of rotary expander performance. Trans. of the JSRAE 20(1):11-20.

NEDO. 2002. Development of two-phase flow compressor and expander for [CO.sub.2] air-conditioner. New Energy and Industrial Technology Development Organization, Kanagawa, Japan.

NEDO. 2003. Development of two-phase flow compressor and expander for [CO.sub.2] air-conditioner. New Energy and Industrial Technology Development Organization, Kanagawa, Japan.

NEDO. 2004. Development of two-phase flow compressor and expander for [CO.sub.2] air-conditioner. New Energy and Industrial Technology Development Organization, Kanagawa, Japan.

NIST. 2002. Reference Fluid Thermodynamic and Transport Properties Database (REFPROP), Version 7.0. National Institute of Standards and Technology, Gaithersburg, MD.

Oku, T., N. Ishii, K. Anami, K. Yasuda, K. Sawai, N. Iida, T. Morimoto, and A. Hiwata. 2005. Basic study of gas leakage flow through small clearances in scroll compressors. Proceedings of the 2005 JSRAE Annual Conference, Tokyo, Japan, C312.

Shintaku, H., T. Harada, M. Ikoma, H. Nakata, H. Hasegawa, and M. Kurimoto. 2000. Characteristics evaluation of new type rotary compressor. Proceedings of the 34th the federation conference of air-conditioning and refrigerating, Tokyo, Japan, pp. 57-60.

Siemens PLM Software. 2004. I-deas 11 NX. Siemens PLM Software, Plano, TX.

Taguchi, G. 1993. Taguchi On Robust Technology Development: Bringing Quality Engineering Upstream. New York: American Society of Mechanical Engineers.

Masara Matsui and Takeshi Ogata are staff engineers, Hiroshi Hasegawa is team leader, and Masanobu Wada is staff engineer in the Living Environment Development Center, Panasonic Corporation, Osaka, Japan.

Received December 15, 2008; accepted April 22, 2009
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Author:Matsui, Masaru; Hasegawa, Hiroshi; Ogata, Takeshi; Wada, Masanobu
Publication:HVAC & R Research
Article Type:Report
Geographic Code:9JAPA
Date:Jul 1, 2009
Words:6413
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