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A rolling piston-type two-phase expander in the transcritical [CO.sub.2] cycle.

INTRODUCTION

Because of ozone depletion potential and the global warming potential of chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs), researchers been extremely interested in finding more environmentally friendly refrigerants that can be used in the air conditioning and refrigeration field. Technologies that use various kinds of natural refrigerants have been developed in many countries, especially Europe and Japan. [CO.sub.2] is considered to be one of the most popular natural refrigerants because of its nontoxic, nonflammable, and good thermodynamic properties (Lorentzen 1995). However, the disadvantage of the [CO.sub.2] transcritical cycle is that its coefficient of performance (COP) is lower than that of a conventional subcritical cycle with refrigerants such as R-22 or R-134a. However, theoretical researches and analyses show that the COP of a transcritical [CO.sub.2] cycle that employs an expander instead of an expansion valve could be equal to or even higher than that of conventional refrigerant cycles (Robinson and Groll 1998; Ma et al. 1999). Therefore, the development of a highly efficient expander is of great interest to researchers.

Preissner (2001) experimented with a prototype of [CO.sub.2] scroll expander that was modified from a scroll compressor of R-134a. The inner leakage loss of the prototype was quite serious, in spite of many reconstructions. It was thought that an optimized structure was necessary for the expander to be more efficient. Based on Preissner's research, Huff et al. (2003) studied the [CO.sub.2] scroll expander further. Some sealing mechanisms were adopted to reduce the leakage. The isentropic efficiency of the new prototype of the [CO.sub.2] scroll expander was 20% to 42%. A piston cylinder expander was developed by Baek et al. (2005a, 2005b). This device consisted of two cylinders, two piston groups, connecting levers, a quick response inlet, and exhaust solenoid valves. It could drive a water pump in the experimental system. The adiabatic efficiency of this device was about 10%. Sakitani et al. (2005) chose the two-stage swing rotary geometry as their first expander. The first cylinder acted as the suction control valve. The isentropic efficiency of the expander was 59%, and its volumetric efficiency was 98%. Yang et.al. (2007) studied the rotary vane of the [CO.sub.2] expander and tested three kinds of vanes with different materials. Their results showed that the internal leakage was great during the expansion process, which was the challenge they looked to resolve in future work. Fukuta et al. (2007) also chose to develop a vane-type expander and combined it with a vane-type compressor. This compressor was driven by the expander that operates as the second-stage compressor in the system. Their test results indicated that the balance point of the mass flow rate and the shaft torque between the compressor and expander was very important for the expander and compressor's performance. Matsui et al. (2008) developed a two-stage rolling piston-type expander that was similar to the structure of Sakitani et al. (2006). An expander isentropic efficiency of 60% was achieved by optimizing clearances between the parts. Their results showed that the heat pump cycle with the expander combined with the main compressor demonstrated a 6% COP improvement. Kohsokabe et al. (2008) took a scroll-type expander and combined it with a rolling piston-type rotary subcompressor by a crankshaft in a [CO.sub.2] chiller cycle. Their test results indicated that there was a 30% improvement from the base transcritical [CO.sub.2] cycle for both cooling and heating conditions to the [CO.sub.2] cycle with the expander and subcompressor.

This study presents the investigation results of the prototype of a [CO.sub.2] rolling piston-type expander. Unlike the two-stage cylinder concept, this expander has only one cylinder and a special suction mechanical control system.

THE EXPANDER'S OPERATING CONDITIONS

When an expander replaces an expansion valve in the [CO.sub.2] transcritical cycle, the isentropic expansion process (state point 3-5) takes place instead of the isenthalpic expansion process (state point 3-6). The specific cooling capacity increases, which can be seen in the shaded area shown in Figure 1. Meanwhile, output energy generated by the expander can be recovered to drive other machines. The operating condition of the expander is different from the compressor. The fluid expands and the expander inside temperature decreases. The inlet of the expander is at a supercritical state under high pressure and the outlet is at two-phase state under low pressure. The expansion process occurs from state point 3 to state point 5, as shown in Figure 1. During the expansion process, the fluid at high pressure (state point 3) becomes saturated liquid (state point 4), and then turns into two-phase state (state point 5) while continuously producing vapor. The expanding fluid will produce work in this process. The work from the expander can drive a fan or a water pump in the system. Furthermore, the expander can be installed in the cycle to drive a subcompressor, similar to the concept highlighted in Kohsokabe et al. (2008). The expander can also be connected to a main compressor shaft to supply energy for the compressor, similar to what was done in Matsui et al. (2008).

[FIGURE 1 OMITTED]

The high-side pressure of the [CO.sub.2] transcritical cycle system is higher than its critical pressure, which is 7384 kPa. Its operating range can be between 8000 and 12,000 kPa. The outlet pressure and temperature of the [CO.sub.2] gas cooler have plenty of influence over the COP. The pressure and temperature of expander inlet are almost the same as the pressure and temperature of the gas cooler outlet. Therefore, the inlet condition of an expander should be optimized to maximize the COP of the system. Since the revolution speed of the compressor is 1450 rpm, 1450 rpm is assumed to be the revolution speed of the expander when it is combined with the compressor in the next step. Table 1 shows the design conditions of the expander.
Table 1. The Design Conditions

Parameter                                  Value

Inlet pressure of expander, kPa             9000
Inlet temperature of expander, [degrees]C    35
Discharge pressure of expander, kPa         3969
Refrigerant mass flow rate, kg/s           0.0727
Revolution speed, rpm                       1500
Pressure ratio                              2.267


PROTOTYPE OF A ROLLING PISTON-TYPE EXPANDER

A rolling piston-type geometry was chosen for the prototype expander design, since it was easy for fabrication purposes. Figure 2 shows the schematic of a rolling piston-type expander. There are three processes that occur during one rotation of the piston: intake, expansion, and discharge. During the intake process, the intake valve opens and [CO.sub.2] at the supercritical pressure flows into the cylinder and drives the piston to rotate. When the piston reaches a certain angle, the intake valve closes and the expansion process begins. Expansion work created by the fluid will keep the piston rotating. As the piston reaches the discharge port, the two-phase fluid is discharged. A suction control valve is essential for the expander to control the mass flow rate of [CO.sub.2]. In order to recover the energy from the expander, a generator is combined with the expander.

[FIGURE 2 OMITTED]

Design of the Cylinder Volume

The cylinder volume of an expander can be computed by the mass flow rate of the compressor as shown in the following equations:

[V.sub.e] = [[60[m.sub.c][v.sub.5]]/[n[[eta].sub.ev]]] (1)

[m.sub.c] = [[eta].sub.cv]*[V.sub.c]/[v.sub.1] (2)

The displacemental volume of the expander can also be calculated as

[V.sub.e] = [pi]([R.sup.2]-[r.sup.2])H = [V.sub.s] + [V.sub.d]. (3)

After considering the vane thickness, the volume of the cylinder at a certain rotation angle is

V = A([theta])H-[1/2]h * B * H. (4)

Lastly, the discharge volume, [V.sub.d], is obtained by using the following equation:

[V.sub.d] = [V.sub.e]-V (5)

Suction and Discharge Angle

The rolling piston-type expander is in a specific angle to control the mass flow rate of the fluid in the suction process, unlike the suction angle of the compressor, which is 360[degrees]. In light of the size of the suction and discharge ports, the primary suction angle ([[theta].sub.s0]) cannot be less than 10[degrees], and the exhaust angle ([[theta].sub.d]) should be less than 350[degrees]. The volume of suction can also be defined using the following equation, which determines the closed angle of suction ([[theta].sub.s]):

V([[theta].sub.s]) = 60[m.sub.e][v.sub.3]/n (6)

In Equation 6, the volume of the cylinder at the closed angle of suction is related to the mass flow rate of [CO.sub.2].

The volume of the cylinder at the exhaust angle ([[theta].sub.d]), shown in the following equation, is relevant to the volume of the cylinder at the closed angle of suction and the ratio of expansion ([epsilon]):

V([[theta].sub.d]) = [epsilon]V([[theta].sub.s]) (7)

Then, the suction duration ([[tau].sub.s]) can be calculated with this equation:

[[tau].sub.s] = [[[[theta].sub.s]-[[theta].sub.s0]]/[omega]]*[[pi]/180] (8)

According to Equations 6 and 7, the closed angle of suction and the discharge angle can be determined when the designed mass flow rate and ratio of expansion are known. As shown in Figure 3, for example, the closed angle of suction ([[theta].sub.S]) is 163[degrees] when the design mass flow rate is 0.071 kg/s. Assuming the designed expansion ratio is 2.516, the exhaust angle ([[theta].sub.d]) is 294[degrees] from Figure 4.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

Suction Control System

To control the beginning and ending of the suction process, a valve is needed at the inlet pipeline. When the valve opens, the high-pressure fluid enters the cylinder and drives the eccentric shaft. When the piston reaches the closed angle of suction, the valve shuts down. Then, the suction process stops, and the expansion process starts. In each rotation, the valve opens at the beginning angle of suction and closes at the ending angle of suction. If the rotation speed of the expander is 1500 rpm, the on-off time of the valve is about 0.02 s. For such short cycle time, the mechanical control valve is thought to be more reliable and more cost efficient than solenoid valves. A mechanical cam device was adopted to act as the control valve (Wei 2002). Its biggest advantage is that its motion is regulated once the curve profile of the cam is designed. It is also simple and compact. The suction control system is composed of a disk cam and a control valve. The disk cam rotates with the main shaft of the expander, and the control valve shifts with the cam's up and down movement. Figure 5 shows the mechanical control valve, including the valve body and an inlet valve rod with a rectangular hole (Zha and Ma 2003). The inlet valve rod, pushed by the cam, reciprocates vertically to the inlet channel. When the rectangular hole coincides with the inlet channel, the suction valve is open. In order to overcome the problem at the start-up, a start-up motor is used. For the targeted control valve motion, the cam's curve shape can be designed to open the suction valve when the rotary angle of the rolling piston reaches the primary suction angle ([[theta].sub.s0]) and to close the suction valve at the closed angle of suction ([[theta].sub.s]). If the control valve follows sinusoidal motion, as shown in the following equation, and the period of motion is [t.sub.0], the maximum stroke of the valve can be the length of the suction port in the control valve ([s.sub.0]):

[FIGURE 5 OMITTED]

s = [s.sub.0]sin[[pi]/[t.sub.0]]t (9)

One disadvantage of this device is that additional friction loss of the control valve will cause a decrease in the recovery work of the expander. Another disadvantage is that there is a clearance volume between the suction control valve and the cylinder of about 0.09 x [10.sup.-6][m.sup.3].

TEST ENVIRONMENT

The test environment for the [CO.sub.2] transcritical cycle with an expander consisted of the transcritical [CO.sub.2] cycle, the prototype expander, the chilling water system, and the cooling water system. The [CO.sub.2] cycle included a compressor, a gas cooler, an expansion valve, an evaporator, and a gas-liquid separator as shown in Figure 6. The prototype expander was installed parallel to the expansion valve. In this environment, the [CO.sub.2] compressor was the reciprocating type. The gas cooler and the evaporator were two shell-tube heat exchangers, and [CO.sub.2] flowed inside the tube and water was in the shell side. The data acquisition system focused on taking pressure, temperature, power, and rotation speed measurements.

[FIGURE 6 OMITTED]

The generating efficiency ([[eta].sub.ex]) of the expander, described as the ratio of the generating power and the ideal expansion work, can be determined using the following equation (generating power [[W.sub.out]] is measured by the power meter):

[[eta].sub.ex] = [[W.sub.out]/[m([h.sub.in]-[h.sub.out])]] (10)

The isentropic efficiency ([[eta].sub.isex]) of the expander can be calculated as follows:

[W.sub.exp] = [W.sub.out]/[[eta].sub.ge] (11)

[[eta].sub.isex] = [[W.sub.exp]/[m([h.sub.in]-[h.sub.out])]] (12)

[[eta].sub.ge] is the mechanical efficiency of the generator, which was measured at different revolution speeds before the generator was combined with the expander. The mechanical efficiency of the generator ranges from 0.8 to 0.92, corresponding to rotary speeds from 800 to 1600 rpm. [h.sub.in]-[h.sub.out] is the difference of inlet enthalpy and the outlet of the expander during the isentropic expansion process; [W.sub.exp] is the recovered energy by the expander.

The COPs are calculated as follows:

COP = [Q/[W.sub.com]] (13)

[COP.sub.exp] = [Q/[[W.sub.com]-[W.sub.out]]] (14)

Q = [m.sub.w]Cp([T.sub.win]-[T.sub.wout]) (15)

Q represents the cooling capacity of the evaporator, which can be calculated by the mass flow rate of chilling water and the temperature difference of chilling water inlet and outlet, as shown in Equation 15. The symbols [W.sub.com] and [W.sub.out] illustrate the compressor work and the work produced from the generator driven by the expander. [COP.sub.exp] are the COPs of the system, considering the recovery work of the expander.

UNCERTAINTY ANALYSIS FOR THE EXPERIMENTAL MEASUREMENT

In this experiment, the data accuracy is affected by many uncertainties, such as experimental conditions, the measurement instruments precision and calibration, repeatability, and so on. The existence of these uncertain factors is inevitable, and some measures can be taken to minimize the error. The uncertainties of the measured parameters are summarized in Table 2. An uncertainty analysis was conducted for the results of the experiments using the Kline and McClintock method (1953) based on these uncertainties of instruments. The following equation was used:
Table 2. Uncertainties of Instruments

Parameters                 Error Source              Error Band

Mass flow rate           [CO.sub.2] mass                0.15%
of [CO.sub.2]               flow meter

Volume flow rate        Turbine flow meter     [+ or -]0.1 [m.sup.3]/h
of water

[CO.sub.2]           Pt100 temperature sensor  [+ or -]0.15[degrees]C
temperature

Chilled-water        Pt100 temperature sensor  [+ or -]0.15[degrees]C
temperature

[CO.sub.2] pressure    Pressure transducer         [+ or -]40 kPa

Power                      Power meter                   0.2%

Revolution speed            Tachometer                  1 rpm


[w.sub.A] = [[[j.summation over (i = 1)]([[partial derivative]A]/[[partial derivative][z.sub.i]][w.sub.z]).sup.2].sup.[1/2]] (16)

where

[w.sub.A]= total uncertainty associated with the dependent variable A

[z.sub.i]= independent variable that affects the dependent variable A

[w.sub.z]= uncertainty of the variable Zi

While the uncertainty of COP ranges from 7% to 15%, most COP uncertainties are around 10%. The main contributor to the COP uncertainty is the temperature difference of chilling water. The uncertainty of expander isentropic efficiency is within 3%. It can be seen that the uncertainty has little influence on the expander efficiency.

RESULTS AND DISCUSSIONS

Performance of the System with the Expander Prototype

The efficiency of the expander was influenced by many operational parameters, such as inlet pressure, inlet temperature, mass flow rate, and refrigeration capacity. So, the rotational speed and the pressure ratio are discussed in the following results of the system performance. In order to vary the revolution speed of the expander and keep the inlet temperature and pressure of the expander constant, the loads of the generator and the temperature of the inlet water were regulated during the experiments.

Figure 7 and Figure 8 show that the isentropic efficiency of the expander was diversified at different inlet pressures and [CO.sub.2] temperatures. In Figure 7, it can be seen that when the inlet parameters of the expander are changed, the revolution speed is also varied. A maximum efficiency exists at the optimal revolution speed. The main reason for this is that the leakage losses will increase at the low revolution speed and the high revolution speed will cause large friction losses. So, the total loss (including leakage losses and friction losses) can keep the minimum value at the optimal revolution speed. The higher inlet pressure seems to be favorable to the higher efficiency of the expander when the inlet temperatures in two groups of experiments are the same. The main reason for this is that the theoretically recoverable energy of the expander at the high inlet pressure is lower than that of the low inlet pressure at the same inlet temperature, but the actual recovered energy of the former is higher than that of the latter at the same revolution speed of the expander, based on tested results. In Figure 7, the maximum isentropic efficiency of the expander reaches 57.4% at the optimal state (when the parameters are close to the design values).

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

In Figure 8, the maximum isentropic efficiency of the expander can reach 58.7% when the pressure ratio is close to the design ratio, but when the mass flow rate of [CO.sub.2] and the revolution speed are smaller than the design values. Although the temperature difference of the inlet temperature of the expander in two groups of data is only 1.5[degrees], the actual recovered energy of the expander at the high inlet temperature is almost the same or lower than that at the low inlet temperature. The ideal recoverable energy of the former is higher than that of the latter when the inlet pressure and the pressure ratio are same. Therefore, the isentropic efficiency of the expander is high at the lower inlet temperature of the expander, according to the results in this figure. It can also be seen from Figure 8 that the low-pressure ratio doesn't seem to benefit the efficiency of the expander, which indicates that the total loss of energy does not decrease too much under a low pressure ratio. The reason for this is that the high revolution speed of the expander at the low pressure ratio causes the increase in friction losses.

From the experiments, it was observed that the mechanical control valve operated smoothly and was able to control the mass flow rate effectively.

Comparison of the System with and without the Expander Prototype

Since the objective of using an expander is to improve the COP of the [CO.sub.2] transcritical cycle, it is important to compare the performance of the system with and without an expander. For a fair comparison, operating conditions of the two systems were kept constant during the tests. The experimental results of systems with an expander and without an expander are compared in Table 3. In Table 3, there are three groups of data at three conditions.
Table 3. Experimental Results

Test Group                                          1

Expansion device                     [S.sub.exp]         [S.sub.exv]

Inlet temperature of chilling water     12.19               12.41
([T.sub.e,water,in]), [degrees]C

Inlet temperature of cooling water      33.74               33.74
([T.sub.g,water,in), [degrees]C

Discharge pressure of compressor         8490                8470
([P.sub.c,out]), kPa

Suction pressure of compressor           3850                3820
([P.sub.c,in]), kPa

Outlet pressure of gas cooler            8390                8380
([P.sub.g,out]), kPa

Inlet pressure of expander or            8260                8270
expansion valve ([P.sub.ex,in]),
kPa

Outlet pressure of expander or           3880                3840
expansion valve ([P.sub.ex,out),
kPa

Discharge temperature of compressor     56.86               65.17
([T.sub.c,out]), [degrees]C

Outlet temperature of gas cooler        36.24               36.93
([T.sub.g,out]), [degrees]C

Inlet temperature of expander or        35.84               36.71
expansion valve ([T.sub.ex,in]),
[degrees]C

Outlet temperature of evaporator         4.16               3.96
([T.sub.e,out), [degrees]C

Mass flow rate of [CO.sub.2]            0.066               0.060
([m.sub.CO2]), kg/s

Input power of compressor                3056               3056
([W.sub.com]), W

Pressure ratio                          2.129                --

Output power of expander                427.5                --
([W.sub.out]), W

Generating efficiency of expander       0.476                --
([[eta].sub.ev])

Isentropic efficiency of expander       0.541                --
([[eta].sub.isev])

Revolution speed of expander             1248                --
([n.sub.exp]), rpm

COP of [S.sub.exp] / COP of                       1.024
[S.sub.exv]

[COP.sub.exp] of [S.sub.exp] / COP                1.191
of [S.sub.exv]

Test Group                                          2

Expansion device                     [S.sub.exp]         [S.sub.exv]

Inlet temperature of chilling water     12.41               12.29
([T.sub.e,water,in]), [degrees]C

Inlet temperature of cooling water      33.74               33.88
([T.sub.g,water,in), [degrees]C

Discharge pressure of compressor         8530                8560
([P.sub.c,out]), kPa

Suction pressure of compressor           3810                3820
([P.sub.c,in]), kPa

Outlet pressure of gas cooler            8440                8480
([P.sub.g,out]), kPa

Inlet pressure of expander or            8300                8380
expansion valve ([P.sub.ex,in]),
kPa

Outlet pressure of expander or           3840                3820
expansion valve ([P.sub.ex,out),
kPa

Discharge temperature of compressor     58.42               62.99
([T.sub.c,out]), [degrees]C

Outlet temperature of gas cooler        36.53               37.33
([T.sub.g,out]), [degrees]C

Inlet temperature of expander or        36.12               37.10
expansion valve ([T.sub.ex,in]),
[degrees]C

Outlet temperature of evaporator         3.65               3.75
([T.sub.e,out), [degrees]C

Mass flow rate of [CO.sub.2]            0.064               0.061
([m.sub.CO2]), kg/s

Input power of compressor                3080               3136
([W.sub.com]), W

Pressure ratio                          2.172                --

Output power of expander                417.5                --
([W.sub.out]), W

Generating efficiency of expander       0.467                --
([[eta].sub.ev])

Isentropic efficiency of expander       0.531                --
([[eta].sub.isev])

Revolution speed of expander             1172                --
([n.sub.exp]), rpm

COP of [S.sub.exp] / COP of                       1.005
[S.sub.exv]

[COP.sub.exp] of [S.sub.exp] / COP                1.164
of [S.sub.exv]

Test Group                                          3

Expansion device                     [S.sub.exp]         [S.sub.exv]

Inlet temperature of chilling water     12.46               12.19
([T.sub.e,water,in]), [degrees]C

Inlet temperature of cooling water       33.8               33.95
([T.sub.g,water,in), [degrees]C

Discharge pressure of compressor         9010                9020
([P.sub.c,out]), kPa

Suction pressure of compressor           3790                3780
([P.sub.c,in]), kPa

Outlet pressure of gas cooler            8920                8940
([P.sub.g,out]), kPa

Inlet pressure of expander or            8820                8850
expansion valve ([P.sub.ex,in]),
kPa

Outlet pressure of expander or           3800                3800
expansion valve ([P.sub.ex,out),
kPa

Discharge temperature of compressor     62.38                64.1
([T.sub.c,out]), [degrees]C

Outlet temperature of gas cooler        38.52               38.84
([T.sub.g,out]), [degrees]C

Inlet temperature of expander or        38.07               38.62
expansion valve ([T.sub.ex,in]),
[degrees]C

Outlet temperature of evaporator         3.62               3.52
([T.sub.e,out), [degrees]C

Mass flow rate of [CO.sub.2]            0.063               0.061
([m.sub.CO2]), kg/s

Input power of compressor                3320               3240
([W.sub.com]), W

Pressure ratio                          2.315                --

Output power of expander                302.5                --
([W.sub.out]), W

Generating efficiency of expander       0.322                --
([[eta].sub.ev])

Isentropic efficiency of expander       0.366                --
([[eta].sub.isev])

Revolution speed of expander             933                 --
([n.sub.exp]), rpm

COP of [S.sub.exp] / COP of                       0.948
[S.sub.exv]

[COP.sub.exp] of [S.sub.exp] / COP                1.044
of [S.sub.exv]

Notes:

[S.sub.exp] = the system with an expander

[S.sub.exv] = the system with a throttling valve


It can be seen from Table 3 that the COP of the system with an expander is almost the same as that of the system with an expansion valve. It indicates that the cooling capacity at the specific input power of the compressor in the system with the prototype expander is not increased, as was the case described in Figure 1. A possible reason for this is that the heat generated by the friction of the expander decreases a part of the cooling capacity. After considering the generating power of the expander ([W.sub.out]) as the recovered power, the [COP.sub.exp] of the system with the prototype expander is higher than the [COP.sub.exp] of the system with an expansion valve. In the first and second test groups, the of the system with the expander can increase up to 19% and 16%, respectively.

Although the inlet pressure and inlet temperature of the expander in the third test group are the highest, the efficiency enhancement by the expander is not higher than those in the first and second. A possible reason for this is that the revolution speed of the expander reduced by the increased loads will cause more leakage losses. Meanwhile, the input power of the compressor is increased, and the COP of the system decreases.

CONCLUSION

This study investigated the performance potential of a rolling piston-type expander. Based on prototype construction and experiments, the following conclusions were deduced:

a. The cylinder volume of an expander can be determined by the displacement of the compressor. The suction and discharge angle can be calculated as a function of the expansion ratio and the mass flow rate of [CO.sub.2]. A mechanical suction control mechanism was designed and demonstrated effective control for the on-off of suction angle.

b. The isentropic efficiency of the expander varies depending upon operating conditions. Inlet parameters, including inlet pressure, inlet temperature, and the operating revolution speed, affect the efficiency of the expander. In most cases, the isentropic efficiency of the prototype ranged from 23% to 58%. The highest isentropic efficiency of the prototype expander was 58.7%.

c. The expander does not seem to increase the cooling capacity. However, it can increase the COP of the system by at least 10% when the recovered power from the expander is taken into account.

ACKNOWLEDGMENT

The study presented in this paper is funded by Projects 50506019 and 50676064, which are supported by the Natural Science Fund of China.

NOMENCLATURE

Exp = expander

Exv = expansion valve

m = mass flow rate, kg/s

V = displacemental volume, [m.sup.3]/s

[eta] = efficiency

n = revolution speed of expander, rpm

v = specific volume, [m.sup.3]/kg

R = radius of cylinder, m

r = radius of piston, m

H = height of cylinder, m

B = thickness of vane, m

h = length of vane in the cylinder, m

V = working volume, [m.sup.3]

[epsilon] = expansion ratio

[theta] = angle of rolling piston

s = stork of the control valve, m

[[tau].sub.s] = time of suction, s

[t.sub.0] = period of control valve, s

t = time of motion of the control valve, s

T = temperature, [degrees]C

Subscripts

c = compressor

e = expander

v = volumetric

s = suction

d = discharge

w = water

1 = compressor suction

2 = compressor discharge

3 = expander inlet

4 = saturated liquid

5 = expansion process outlet under isentropic expansion process

6 = expansion process outlet under isenthalpic expansion process

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Minxia Li is an associate professor, Yitai Ma is a professor, and Hua Tian is a PhD student in the School of Mechanical Engineering, Tianjin University, Tianjin, China.

Received November 27, 2008; accepted March 25, 2009
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Author:Li, Minxia; Ma, Yitai; Tian, Hua
Publication:HVAC & R Research
Article Type:Report
Geographic Code:1USA
Date:Jul 1, 2009
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