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Experimental observation and empirical estimation of formation of solid carbon dioxide in safety valves for Refrigerating system.

Safety valves are used to guarantee refrigeration system safety under abnormal overpressure. For the safety valve of a C[O.sub.2] refrigeration system, the tendency to form solid C[O.sub.2] and to block the release path of the safety valve during release may endanger the entire system. This problem is unique for C[O.sub.2] refrigeration systems and has never been studied before. In order to fill in the blank, the blockage characteristics of the different types of safety valves were experimentally studied by constructing glass tubes with different geometries similar to the flow channel in safety valves and building them into an experimental rig. And the effect of other parameters on the formation of solid C[O.sub.2] was studied by theoretical analysis of the pressures along the release path based on a much simplified model. These studies showed that severe blockage will occur in the downstream line and endanger the protected system after the valve house is partly blocked by solid C[O.sub.2]. To avoid the blockage of solid C[O.sub.2] in safety valves, a simple structure of the safety valve, high fluid velocity, and long downstream pipe are preferred. But this preference will cause high pressure in the downstream line and might further lead to blockage in the downstream line. So the downstream line should be able to tolerate high pressure, and measures such as heating or blowing should be simultaneously taken to prevent the blockage in the downstream line.

INTRODUCTION

Since Lorentzen (1993a, 1993b) has proposed the reuse of C[O.sub.2] as a refrigerant, C[O.sub.2] is receiving increasing interest for various refrigeration and heat pump applications. Kim et al. (2004) reviewed over 200 documents in the open literature from all over the world on C[O.sub.2] refrigeration systems. Among these refrigeration systems, the transcritical C[O.sub.2] automotive air conditioners/heat pumps and subcritical C[O.sub.2] cascade food processing/conservation systems are two of the most promising, where C[O.sub.2] is under much higher pressures (2.8-12 MPa or 406-1740 lbf x [in..sup.-2]) than conventional refrigerants.

Safety valves are used to protect the system from an abnormal overpressure probably caused by power failure or malfunction of the compressor and throttling part. If an abnormal overpressure occurs and the safety valve cannot achieve timely release of some refrigerant to reduce the system pressure, the safety operation of the entire system will be influenced to an unacceptable level. More importantly, the damage of the high pressure will be much more severe than that of a lower pressure. Thus, the safety valve is very important for a C[O.sub.2] refrigeration system.

But the normal function of the safety valve will be destroyed by the blockage of its release path in C[O.sub.2] systems. The reason is that the C[O.sub.2] triple-point pressure of 0.52 MPa (75 lbf x [in..sup.-2]) lies between the system pressure and the atmospheric pressure of 0.101325 MPa (15 lbf x [in..sup.2]). Solid C[O.sub.2] may be formed and block the safety valve when C[O.sub.2] expands through the safety valve from the system pressure to the atmospheric pressure.

This problem is unique for C[O.sub.2] safety valves and has never been studied before. Only Krings (1997) noted it in his experiments, but he has not studied it in detail. To study it is difficult because safety valves are normally not transparent and made of metal due to the high working pressure. So the conditions for the occurrence of this problem and its characteristics are unknown so far. This work will focus on them.

DESCRIPTION OF THE FLOW THROUGH C[O.sub.2] SAFETY VALVE

The safety valve normally does not release C[O.sub.2] directly into the atmosphere, partly because of the low temperature (195 K) of the formed, solid C[O.sub.2] and partly because such installations will cause other freezing problems, i.e., the steam in the ambient air will be condensed and solidified in the safety valve. So a downstream pipe is required for the path of release. Figure 1 is a schematic view of the release path, including the safety valve and the downstream line. C[O.sub.2] flows into the inlet pipe of the safety valve and raises the disc when an overpressure occurs. Then the fluid flows through the gap between the seat and disc, inducing larger pressure drop and producing a mixture of vapor-solid C[O.sub.2] or vapor-liquid C[O.sub.2]. This mixture expands into the valve house, inducing another larger pressure drop, and finally flows through the outlet pipe into the downstream line.

Solid C[O.sub.2] will be formed when the pressure is dropped down to the triple-point pressure. So whether the solid C[O.sub.2] is formed in the safety valve or in the downstream line depends on the pressure drop at the outlet of the safety valve and in the downstream line. The pressure drop is determined by the mass flow rate and the geometry of the outlet of the safety valve and the downstream line. The mass flow rate is decided by the upstream thermodynamic properties and the geometry of the disc and seat. In all, the upstream thermodynamic properties and the geometry of the release path decide the formation of solid C[O.sub.2] and will further decide the location of the blockage.

Safety valves under such a high working pressure are usually made of metal, and the flow in it is vapor-liquid-solid three-phase flow. Therefore, the blockage in it can neither be directly observed nor numerically calculated. Thus, the influence of the different inner shapes of the safety valves was experimentally observed by constructing glass tubes with different geometries similar to the flow channels in safety valves and building them into an experimental rig. The effect of other parameters was studied by theoretical analysis of the pressures along the release path based on a much simplified model.

[FIGURE 1 OMITTED]

EXPERIMENTS

Experimental Setup

In order to observe the flow of C[O.sub.2] in geometrical structures similar to those in safety valves, various transparent configurations were designed to substitute for a real safety valve. Such configurations consisted of an outer glass tube and inner acrylic glass. The outer glass tube was made of five KPG tubes from Duran, which were fused with a special method. The inner diameter of the outer glass tube is 30 mm (1.18 in.), and the outer diameter is 90 mm (3.54 in.). The outer glass tube is reliable under an inner pressure of up to 8 MPa (1160 lbf x [in..sup.-2]). Inside the outer glass tube is an insert tube made of acrylic glass, which is used to simulate channels similar to those in safety valves. The acrylic glass tube is fixed in the outer glass tube by two flanges.

In order to size the channels for practical flow rates and pressure drop as they occur in safety valves, the mass flow rate of the designed glass tube should be comparable to a real safety valve.

The mass flow rate through the safety valve can be estimated as follows:

[dot.m.sub.sv] = K[rho]a(CZ)[pi][D.sub.0] (1)

where [rho] is the fluid density at the throat, a is the speed of sound, C is the lift percentage of the total lift, Z is the total lift, [D.sub.0] is the bore diameter, and K is the reduction rate of the flow cross section due to the flow separation at the gap between the disc and seat.

The mass flow rate through the glass tube can be calculated with the following equation:

[dot.m.sub.gt] = [rho]a[[pi]/4][d.sub.gt.sup.2] (2)

From Equations 1 and 2 we can get:

[dot.m.sub.gt]/[dot.m.sub.sv] = [[rho]a[[pi]/4][d.sub.gt.sup.2]]/[K[rho]aCZ[pi][D.sub.0]] = [1/[4KC(Z/[D.sub.0])]]([d.sub.gt]/[D.sub.0])[.sup.2] (3)

Safety valves are classified into full-lift safety valves (A), relief valves (B), and safety relief valves (C) according to DIN 3320 depending on the opening characteristics. Schematic views of safety valves are shown in Figure 2. Relief valves (B) have a disc diameter the same as the bore, and full-lift safety valves (A) and safety relief valves (C) have a disc with a diameter larger than the bore. The small structures on the disc of these two safety valves prevent the fluid directly flowing from the ring gap between the disc and seat into the valve house but lead the flow through the meander gap between the disc and seat. The small structures also determine the different opening characteristics. The relief valve (B) is a proportional valve, and the safety valves (A) and (C) have a proportional phase with 5%-20% of the total lift.

Considering that the safety valve is always opened to a small opening, a glass tube with a mass flow rate corresponding to about 10% of the mass flow rate through the fully opened safety valve is designed, i.e., [dot.m.sub.gt]/[dot.m.sub.sv] = 0.1. From the Leser (2002) catalog, we chose the smallest available safety valve with a bore diameter [D.sub.0] = 6 mm (0.24 in.), which is normally enough for a C[O.sub.2] refrigeration system. Its ratio of total lift to the diameter of the safety valve is Z/[D.sub.0] = 0.18, KC is taken as 0.4, and then from Equation 3 we get the smallest diameter of glass tubes, [d.sub.gt] = 1 mm (0.04 in.). The diameter of the inlet and outlet part is chosen to be four times the narrowest diameter, i.e., 4 mm (0.16 in.). The width of the part simulating the valve housing is 8 mm (0.32 in.).

In order to study the influence of different geometries of safety valves, three channels were built and their dimensions are shown in Figure 3. All three channels have a capillary 1 mm (0.04 in.) in diameter between the inlet and outlet part, which is used to simulate the ring gap between the disc and the seat. The throttling part of channel 1 in Figure 3a is used to simulate the flow channel in the safety relief valves (C) and the full-lift safety valves (A), when they are just slightly opened. Obstruction is built in the 8 mm wide valve house to simulate the meander gap between the disc and seat. The throttling part of channel 2 in Figure 3b is a capillary channel to simulate the relief valve (B) because fluid in relief valve (B) flows out directly through the ring gap between the disc and seat. Channel 3 in Figure 3c is designed to simulate the flow channel representing these three types of safety valves when their valve houses are partly blocked by solid C[O.sub.2].

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

A schematic view of the experimental setup is shown in Figure 4. Liquid C[O.sub.2] is drawn from the C[O.sub.2] storage cylinder, which is heated by a water loop. The water loop consists of a reservoir and a thermostat. The heat from the water loop is used to compensate the energy loss due to C[O.sub.2] release and to maintain temperature and pressure of C[O.sub.2] in the cylinder unchanged. The C[O.sub.2] cylinder and reservoir are placed over a supporting frame with which they can be moved onto and away from an electronic balance. The C[O.sub.2] stream from the cylinder is split into two streams. The distribution of the two C[O.sub.2] streams is controlled with two regulating valves. One of the streams flows through a coil-tube that is heated by another water loop. The water loop also consists of a reservoir and a thermostat. Then the stream merges with the other stream and both together flow into the glass tube. The downstream line of the glass tube consists of copper tube 1, copper tube 2, and plastic tube 3. Copper tube 1 is 4 mm (0.16 in.) in inner diameter and 6 mm (0.24 in.) in outer diameter. Copper tube 2 is 10 mm (0.40 in.) in inner diameter and 12 mm (0.47 in.) in outer diameter. Plastic tube 3 is 25 mm (0.98 in.) in inner diameter and 32.4 mm (1.28 in.) in outer diameter. Between tube 1 and tube 2 is the first sudden enlargement of the cross section, and between tube 2 and tube 3 is the second sudden enlargement of the cross section.

The total C[O.sub.2] mass flow rate is obtained by time-averaged change in the mass of the C[O.sub.2] cylinder directly measured by the electronic balance. The mass flow rate of the stream through the coil tube is measured by a mass flowmeter. The pressures and temperatures upstream and downstream of the glass tube are measured with piezoelectric pressure sensors and K-type thermocouples, respectively. All data are collected by a data logger. The measured uncertainties are estimated to be 0.61% in the mass flow rate, 0.21% in pressure, and 0.8 K in temperature. The upstream vapor quality of the glass tube is determined by the isenthalpic mixing process of the two streams, and the thermodynamic properties are computed according to Span and Wagner (1996). The uncertainty in upstream vapor quality is estimated to be 3.5%.

[FIGURE 4 OMITTED]

Experimental Conditions and Results

A prescribed upstream vapor quality and upstream pressure of the glass tube were set by controlling the two regulating valves and the temperature of thermostats, and the formation of solid C[O.sub.2] was observed. Experimental conditions are given in Table 1. The upstream pressure of the glass tube was 5.7-6.3 MPa (827-914 lbf x [in..sup.-2]), while the upstream vapor qualities are 0.00, 0.64, 0.84, 0.96, and 0.98.

Channel 1. When the saturated liquid C[O.sub.2] was released, i.e., when the upstream vapor quality was 0.00, solid C[O.sub.2] did not form in the glass tube but was observed to deposit in the downstream plastic tube 3. The downstream pressure showed large oscillations around 0.6 MPa (87 lbf x [in..sup.-2]), which is higher than the C[O.sub.2] triple-point pressure. The maximum value of the downstream pressure was 0.94 MPa (136 lbf x [in..sup.-2]). So solid C[O.sub.2] actually formed in copper tube 2 downstream of the pressure sensor and located in plastic tube 3, sometimes completely blocking plastic tube 3, as shown in Figure 5.

When the upstream vapor quality of the glass tube was 0.64 and 0.84, solid C[O.sub.2] was only observed in plastic tube 3. No obvious blockage was observed, and the downstream pressure was around 0.4 MPa (58 lbf x [in..sup.-2]) with oscillations, which is lower than the C[O.sub.2] triple-point pressure. The maximum values of the downstream pressure were 0.48 MPa (70 lbf x [in..sup.-2]) and 0.53 MPa (77 lbf x [in..sup.-2]). It seemed that solid C[O.sub.2] formed between the glass tube and pressure sensor, and it blocked plastic tube 3 partially.

When C[O.sub.2] with upstream vapor qualities of 0.96 and 0.98 was released, solid C[O.sub.2] was observed being formed in the glass tube and deposited both at its enlargement and in plastic tube 3, as shown in Figure 6. The maximum value of the downstream pressure was 0.35 MPa (51 lbf x [in..sup.-2]), which is lower than the C[O.sub.2] triple-point pressure. Periodic complete blockage in the glass tube was observed. This is just what we had been afraid would occur--entire blocking in a geometric configuration that resembled very much the internal geometry of safety valves (A) and (C).

[FIGURE 5 OMITTED]

The reason for the blockage in the glass tube is that the high upstream vapor quality reduces the mass flow rate and the fluid velocity through the channel. Although it also reduces the solid content in the flow, the influence of the fluid velocity is more important. The pressure drop in the downstream pipe becomes much smaller than with a lower upstream vapor quality. The pressure is dropped down to the triple-point pressure in channel 1, and solid C[O.sub.2] was formed in the channel. Moreover, the solid C[O.sub.2] formed is easy to deposit in the channel because of the obstruction of the flow path and the change of flow direction. Such deposition of solid C[O.sub.2] will lead to the freezing of the safety valve.

Channel 2. Under all the measured conditions, only a small amount of solid C[O.sub.2] was located at the outlet of the capillary, which did not have a great influence on the flow, as shown in Figure 7. Because of the high velocity of the C[O.sub.2] vapor in the glass tube and no obstruction in the flow direction, no heavy blockage occurred in the glass tube. The downstream pressure of the glass tube has an oscillation similar to that for channel 1, which means no blockage will occur in relief valve (B).

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

Channel 3. Solid C[O.sub.2] was not observed in the glass tube but was observed to be formed in downstream plastic tube 3 and to block it. The downstream pressure of the glass tube was as high as about 1.2-2.0 MPa (174-290 lbf x [in..sup.-2]). The downstream pressure increased very quickly, and the mass flow rate decreased rapidly. The decreased mass flow rate means decreased fluid velocity, more deposition of solid C[O.sub.2], and severer blockage in plastic tube 3. After a few minutes, the downstream tube, which went up to the ceiling and out of the room, was almost completely blocked by solid C[O.sub.2], as shown in Figure 8. As the downstream pressure is so high that it exceeds the reliable operating pressure of plastic tube 3, the experiments were stopped before there was a rupture of plastic tube 3. The experiments showed that a complete blockage of the entire downstream line will take place if a severe deposition of solid C[O.sub.2] occurs in the safety valve house.

ANALYSIS OF FLOW PROCESS IN THE SAFETY VALVE AND ITS DOWNSTREAM LINE

Model

The experiments with channel 1 have shown the blockage characteristics of different types of safety valves and the influence of upstream vapor quality. But more factors affect the formation of solid C[O.sub.2]. They are the upstream pressure, the geometry of the safety valve and its downstream line, and the opening of the safety valve. The influence of these parameters is difficult to study experimentally. One reason is that the upstream pressure is limited by the ambient temperature because of the limitation of the experimental setup. Another reason is the much increased number of tube samples required in order to identify the influence of geometry because of the difficulty in controlling the opening in the glass tube under such high pressures. Thus, theoretical study is necessary.

Since the C[O.sub.2] pressure along the release path is the key parameter in deciding the formation and blockage of solid C[O.sub.2] and a detailed flow field is unnecessary, a simplified model to calculate the pressure along the release path is developed here, and the effect of various parameters on the pressure will be discussed.

The calculation model is divided into six subprocedures: (1) critical flow through the gap between the disc and seat, (2) injection expansion flow from the gap into the valve house, (3) vapor-liquid two-phase pipe flow in inlet, outlet, and downstream pipe, (4) vapor-solid two-phase flow in outlet and downstream pipe, (5) sudden expansion pipe flow, and (6) sudden contraction flow.

[FIGURE 8 OMITTED]

The critical mass flow through the gap is calculated with the homogeneous equilibrium model as follows:

[dot.m] = [A.sub.0][square root of (2([h.sub.0, in] - [h.sub.t])]/[v.sub.t] (4)

with the inlet stagnation specific enthalpy

[h.sub.0, in] = [x.sub.0, in][h.sub.g, 0, in] + (1 - [x.sub.0, in])[h.sub.l, p, in] (5)

the specific enthalpy of the fluid at the gap outlet (throat cross section)

[h.sub.t] = [x.sub.t][h.sub.g, t] + (1 + [x.sub.t])[h.sub.l, t] (6)

and the pressure at the gap outlet (throat cross section)

[p.sub.t] = [p.sub.0, in](2/[[kappa] + 1])[.sup.[kappa]/([kappa] - 1)] (7)

where [dot.m] denotes mass flow rate, A is the cross-sectional area, h is specific enthalpy, v is specific volume, x is vapor quality, and [kappa] is adiabatic exponent of C[O.sub.2]. The subscript 0,in denotes the inlet stagnation state, l is liquid, g is gas, and t is throat.

The flow quality at the gap outlet [x.sub.t] is computed according to the assumption of isentropic state change as follows:

[x.sub.t] = [[x.sub.0, in]([s.sub.g, 0, in] - [s.sub.l, 0, in]) + [s.sub.l, 0, in] - [s.sub.l, t]]/[[s.sub.g, t] - [s.sub.l, t]] (8)

where s denotes specific entropy.

The injection process from the gap into the valve house is calculated by assuming homogeneous isentropic expansion because the sudden expansion from the small gap between the disc and seat into the larger volume of the valve house happens very rapidly, and the fluid has no chance to exchange heat and mass with the surrounding fluid. According to this assumption, we get the vapor quality in the valve house,

[x.sub.v] = [[x.sub.0, in]([s.sub.g, 0, in] - [s.sub.l, 0, in]) + [s.sub.l, 0, in] - [s.sub.l, v]]/[[s.sub.g, v] - [s.sub.l, v]] (9)

and the specific enthalpy of the fluid in the valve house,

[h.sub.v] = [x.sub.v][h.sub.g, v] + (1 + [x.sub.v])[h.sub.l, v], (10)

where the subscript v denotes the valve house.

The inlet/outlet pipe of the safety valve is assumed to be a straight smooth tube, and the pressure drop of vapor-liquid two-phase flow is represented by the Martinelli-Nelson correlation (Guo 2002):

[DELTA]p = 12.82[X.sub.tt.sup.-1.47](1 - [x.sub.avg])[.sup.1.8](2f[G.sup.2]/[[rho].sub.l])(L/D) (11)

with

G = [4[dog.m]]/[[pi][D.sup.2]] (12)

f = 0.046/[Re.sub.l.sup.0.2] (13)

[X.sub.tt] = ([1 - [x.sub.in]]/[x.sub.in])[.sup.0.9]([[rho].sub.g]/[[rho].sub.l])[.sup.0.5]([[mu].sub.g]/[[mu].sub.l])[.sup.0.1] (14)

[x.sub.avg] = 0.05([sigma]/[g([[rho].sub.l] - [[rho].sub.g])])[.sup.0.5] (15)

[Re.sub.l] = [4[dot.m](1 - [x.sub.in])]/[[pi]D[[mu].sub.l]] (16)

[sigma] = 2.67 - 0.172([T.sub.in] - 273.15 - 10) (17)

where L is the pipe length, D is the pipe diameter, G is the mass flux, f is the Fanning friction factor, Re is the Reynolds number, [X.sub.tt] is the Martinelli number, [x.sub.avg] is the average vapor quality, [sigma] is the surface tension, g is the gravitational acceleration, and [mu] is the dynamic viscosity; the subscript in denotes inlet.

The vapor quality at the outlet is obtained by assuming a constant enthalpy during flow.

[x.sub.out] = [[h.sub.in] - [h.sub.l, out]]/[[h.sub.g, out] - [h.sub.l, out]] (18)

where the subscript out denotes outlet.

The vapor-solid flow in the outlet and downstream pipe is calculated according to the empirical correlation (Lian 1989) by modifying the viscosity with the solid-phase composition.

[DELTA]p = ([xi][G.sup.2]/2[rho])(L/D) (19)

with the Darcy friction factor

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

G = [4[dot.m]]/[[pi][D.sup.2]] (21)

[rho] = [[rho].sub.g][[1 - [phi]]/[1 - [x.sub.in]]] (22)

where

Re = [4[dot.m]]/[[pi]D[mu]] (23)

the volume fraction of the solid phase [phi]

[phi] = [[[rho].sub.g](1 - [x.sub.in])]/[[[rho].sub.g](1 - [x.sub.in]) + [x.sub.in][[rho].sub.s]] (24)

and the viscosity of the mixture

[mu] = [[mu].sub.g](1 + 2.5[phi]) (25)

The vapor quality at the outlet is obtained by assuming an isenthalpic flow.

[x.sub.out] = [[h.sub.in] - [h.sub.s, out]]/[[h.sub.g, out] - [h.sub.s, out]] (26)

The pressure drop for the sudden expansion and contraction is obtained by the general experimental correlations (VDI 1997). The pressure drop for the sudden expansion is

[DELTA][p.sub.exp] = [epsilon](1 - [epsilon])[G.sup.2]/[rho], (27)

while the pressure drop for the sudden contraction is

[DELTA][p.sub.con] = [[epsilon].sub.vc.sup.2](1 - [[epsilon].sup.2] + [[zeta].sub.irr])[G.sub.vc.sup.2]/[rho], (28)

where the ratio of the cross-sectional area is

[epsilon] = ([D.sub.small]/[D.sub.large])[.sup.2], (29)

the contraction coefficient is

[[epsilon].sub.vc] = 1/[0.639[square root of (1 - [epsilon])] + 1], (30)

the area of the contraction cross section is

[A.sub.vc] = [[epsilon].sub.vc][pi][D.sub.small.sup.2]/4, (31)

the mass flux is, correspondingly,

[G.sub.vc] = [dot.m]/[A.sub.vc], (32)

and the irreversible resistance coefficient is

[[zeta].sub.irr] = ([1/[[epsilon].sub.vc]] - 1)[.sup.2]. (33)

The upstream thermodynamic properties, the downstream backpressure, and the geometric parameters of the safety valve and its downstream line are given, and the pressure along the release path is computed in the procedure. The calculation steps are: (1) calculate the inlet pipe and the critical flow between the gap and the disc, (2) assume a pressure in the valve house with which the injection process from the gap outlet into the valve house is calculated, (3) calculate the length of the downstream line with the procedure of the outlet pipe of safety valve and the downstream line, and (4) compare the real length of the downstream line with the calculated value. If the difference is less than 0.1%, then the computation is finished; otherwise, adjust the assumed value of the pressure in the valve house and go to step (2).

Results of Modeling

The calculation results for the experimental geometry parameters are obtained to examine the present modeling procedures. The results showed that the present empirical correlations (the dashed line in Figure 9) greatly underestimate the pressure drop, which is about 50% of the measured value. So a multiple factor of 2 was decided to be added to frictional factor of the present correlations, Equation 20; the predicted pressure is the real line shown in Figure 9.

Calculations for more common conditions of the safety valve have been made. The values for the reference geometry parameters are those given in Table 2, unless any other specified values are stated. D denotes diameter, L is the length of the tube, Z is the total lift, and z is the lift during release; subscripts 0, i, o, v, d denote bore, inlet, outlet, valve house, and downstream tube, respectively.

The calculated results are shown in Figures 10-12. The pressure [p.sub.v] in the valve house for various upstream vapor qualities is shown in Figure 10a in the case of upstream pressure [p.sub.in] = 4 MPa (580 lbf x [in..sup.-2]), diameter ratio of the outlet pipe to the bore [D.sub.o]/[D.sub.0] = 1.1, and the values of the other geometric parameters given in Table 2. The upstream thermodynamic parameters correspond to the saturated fluid in the evaporator of the C[O.sub.2] transcritical refrigeration system. Figure 10a indicates that the pressure [p.sub.v] increases with the increase of valve opening. The influence of the upstream vapor quality [x.sub.in] on the pressure [p.sub.v] is negligible for smaller openings but it increases with the opening.

[FIGURE 9 OMITTED]

The pressure [p.sub.v] for various diameter ratios of inlet/outlet pipe to the bored [D.sub.o]/[D.sub.0], [D.sub.i]/[D.sub.0] is shown in Figure 10b for the case of upstream pressure [p.sub.in] = 4 MPa (580 lbf x [in..sup.-2]), upstream vapor quality [x.sub.in] = 0.0, and the values of other geometry parameters given in Table 2. Figure 10b implies that the diameter ratio of the inlet/outlet tube to the bore [D.sub.o]/[D.sub.0], [D.sub.i]/[D.sub.0] has significant influence on the pressure [p.sub.v]. The pressure [p.sub.v] increases if the diameter ratio reduces. The C[O.sub.2] pressure drops down to the triple-point pressure in the safety valve house if the opening is less than 70% or the diameter ratio [D.sub.o]/[D.sub.0], [D.sub.i]/[D.sub.0] is larger than 1.4. Otherwise, solid C[O.sub.2] may form in the outlet tube of the safety valve or in the downstream line.

The pressure [p.sub.v] for various ratios of the total lift to the bore diameter Z/[D.sub.0] is shown in Figure 11 for the case of upstream pressure [p.sub.in] = 3 MPa (435 lbf x [in..sup.-2]), upstream vapor quality [x.sub.in] = 1.0, and the values of other geometry parameters given in Table 2. The upstream thermodynamic parameters correspond to the saturated vapor in the condenser of the C[O.sub.2] subcritical refrigeration system (for example, the low-temperature side of the C[O.sub.2] cascade refrigeration system). Figure 11 shows that, under all conditions, the pressure [p.sub.v] is lower than the triple-point pressure of C[O.sub.2]. That means solid C[O.sub.2] may be formed in the safety valve. The pressure [p.sub.v] increases if the ratio of the total lift to the bore diameter Z/[D.sub.0] increases. The influence in the case of smaller openings is relatively slighter than in the case of larger openings.

The pressure [p.sub.v] at various upstream pressures [p.sub.in] is shown in Figure 12 for the case of upstream temperature [T.sub.in] = 318 K, the ratio of the total lift to the bore diameter Z/[D.sub.0] = 0.2, and the values of other geometric parameters given in Table 2. The upstream thermodynamic parameters correspond to the outlet of the gas cooler of the C[O.sub.2] transcritical refrigeration system. Figure 12 explains that the pressure [p.sub.v] first decreases and then increases with the upstream pressure [p.sub.in], varying from 8 MPa (1160 lbf x [in..sup.-2]) to 13 MPa (1885 lbf x [in..sup.-2]). The pressure [p.sub.v] is lower than the triple-point pressure of C[O.sub.2] if the upstream pressure [p.sub.in] varies from 8 MPa (1160 lbf x [in..sup.-2]) to 12 MPa (1740 lbf x [in..sup.-2]). The pressure [p.sub.v] becomes larger than the triple-point pressure of C[O.sub.2] if upstream pressure [p.sub.in] is larger than 12 MPa (1740 lbf x [in..sup.-2]) and the opening is larger at the same time.

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

[FIGURE 12 OMITTED]

CONCLUSIONS AND DISCUSSION

The geometric and thermodynamic conditions for the formation and blockage of solid C[O.sub.2] in the safety valve and its downstream line are experimentally and analytically studied in this paper.

The experiments with glass tubes at ambient temperatures 293-298 K can be summarized as follows: no blockage was observed in the relief valve (B) and the blockage characteristics for the safety relief valve (C) and full-lift safety valve (A) depend on the upstream vapor quality of the safety valve. When releasing mainly liquid C[O.sub.2], solid C[O.sub.2] does not form in the safety valve itself, but a complete blockage is likely to occur in the downstream pipes. During release of a two-phase mixture with vapor quality between 0.6 and 0.8, solid C[O.sub.2] does not form in the safety valves, but partial blockage occurs in the downstream pipes. During release of a two-phase mixture with vapor quality higher than 0.9, solid C[O.sub.2] forms in the safety valve, and complete blockage can be observed.

A calculation procedure based on an empirical correlation of pressure drop was used to evaluate the geometric parameters of the safety valve on the formation of solid C[O.sub.2]. The theoretical calculations showed that (1) for the safety valves installed at the evaporator/gas cooler of the C[O.sub.2] transcritical refrigeration system and at the condenser of the C[O.sub.2] subcritical refrigeration system, solid C[O.sub.2] may mostly be formed in the safety valve house for the range of the geometric parameters [D.sub.o]/[D.sub.0], [D.sub.i]/[D.sub.0] = 1.1-2.0, Z/[D.sub.0] = 0.1-0.4, [D.sub.d]/[D.sub.0] = 4, and [L.sub.d]/[D.sub.0] = 1000; and (2) solid C[O.sub.2] may be formed in the downstream line, if the valve opening is larger than 70% and at the same time [D.sub.i]/[D.sub.0] < 1.4 or [p.sub.in] > 12 MPa (1740 lbf x [in..sup.-2]). In this calculation an isentropic expansion in the safety valve is assumed. The error caused by this assumption includes the overestimation of solid C[O.sub.2] content, which further leads to overestimation of the pressure drop of the downstream line. But the influence is limited because the influence of the solid content on the pressure drop is achieved by changing the viscosity of the vapor-solid mixture.

This study illustrates that the key parameter to determine the formation and blockage of the C[O.sub.2] safety valve is the C[O.sub.2] pressure along the release path. In order to avoid freezing and blockage in the safety valve, a simple structure of the disc of the safety valve, like the relief valve (B) and a high-pressure drop in the downstream line are preferred. The downstream pipe should be able to tolerate high pressure. Measures should be taken to prevent a blockage in the downstream line, for example, heating the part of the downstream pipe in which vapor-solid C[O.sub.2] flows or bypassing hot gas into the downstream line.

NOMENCLATURE

A = cross-sectional area, [m.sup.2] ([in..sup.2])

a = speed of sound, m [s.sup.-1] (in. [s.sup.-1])

C = percentage of the total lift

D = diameter, mm (in.)

f = Fanning friction factor

G = mass flux, kg [m.sup.-2] [s.sup.-1] (pound [in..sup.2] [s.sup.-1])

h = specific enthalpy, J x [kg.sup.-1] (lbf x in. poun[d.sup.-1])

K = reduction coefficient of the cross section

L = length, mm (in.)

p = pressure, MPa (lbf x [in..sup.-2])

Re = Reynolds number

s = specific entropy, J x [kg.sup.-1] x [K.sup.-1] (lbf x in. poun[d.sup.-1] x [K.sup.-1])

T = temperature, K

v = specific volume, [m.sup.3] x [kg.sup.-1] ([in..sup.3] x poun[d.sup.-1])

x = vapor quality

[X.sub.tt] = Martinelli number

Z = total lift of the safety valve, mm (in.)

z = lift of the safety valve, mm (in.)

[dot.m] = mass-flow rate, kg x [s.sup.-1] (pound x [s.sup.-1])

Greek Symbols

[alpha] = coefficient of discharge

[epsilon] = ratio of cross-sectional area

[phi] = volume fraction

[kappa] = adiabatic exponent

[rho] = density, kg x [m.sup.-3] (pound x [m.sup.-3])

[sigma] = surface tension, Pa (lbf x [in..sup.-2])

[mu] = dynamic viscosity, Pa x s (lbf x s x [in..sup.-2])

[xi] = Darcy friction factor

Subscripts

0 = narrowest cross section

0,in = inlet stagnation state

d = downstream

avg = average

g = gas

gt = glass tube

i, in = inlet

l = liquid

o, out = outlet

sv = safety valve

t = throat

v = valve house

vc = contraction cross section

REFERENCES

Guo, L.J. 2002. Two-Phase and Multiphase Flow Dynamics (in Chinese). Xi'an, PR China: Xi'an Jiao Tong University Press.

Kim, M.J., J. Pettersen, and C.W. Bullard. 2004. Fundamental process and system design issues in C[O.sub.2] vapor compression systems. Progress in Energy and Combustion Science 30:119-74.

Krings, F. 1997. C[O.sub.2] safety valve (in German). PhD dissertation, Koln: Fachhochschule Koln, Fachbereich Anlagen- und Verfahrenstechnik. S, Matr. No. 107693.

Leser Gesamtkatalog 2002 (in German). Hamburg: Leser GmbH & Co. KG, Germany.

Lian, G.S. 1989. Fundamentals of Multiphase Flow (in Chinese). Hangzhou, PR China: Zhejiang University Press.

Lorentzen, G. 1993a. Revival of carbon dioxide as a refrigerant. H & V Engineer 66(721):9-14.

Lorentzen, G. 1993b. Revival of carbon dioxide as a refrigerant. H & V Engineer 66(722):10-12.

Span, R., and W. Wagner. 1996. A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 K at pressure up to 800 MPa. J. Phys. Chem. Ref. Data 25(6):1509-95.

VDI. 1997. VDI Waermeatlas (in German), chapter L. Verein Deutscher Ingenieure. Berlin: Verlag Berlin Heidelberg.

Dongping Huang

Guoliang Ding, PhD

Hans Quack, PhD

Received February 18, 2006; accepted June 6, 2006

Dongping Huang is a PhD candidate and Guoliang Ding is a professor at the Institute of Refrigeration and Cryogenics Engineering, Shanghai Jiao Tong University, Shanghai, PR China. Hans Quack is a professor of refrigeration and cryogenics engineering, Technische Universitaet Dresden, Dresden, Germany.
Table 1. Experimental Conditions

Upstream Pressure Upstream
 (lbf x Vapor Mass Flow Rate
(MPa) [in..sup.-2]) Quality (kg x [s.sup.-1]) ([lb.sup.-1])

5.7-6.3 827-914 0 0.020 0.044
5.7-6.3 827-914 0.64 0.018 0.040
5.7-6.3 827-914 0.84 0.016 0.035
5.7-6.3 827-914 0.96 0.014 0.031
5.7-6.3 827-914 0.98 0.011 0.024

Table 2. Reference Geometry Parameters

 [D.sub.i]/ [D.sub.o]/ [D.sub.v]/
[D.sub.0] Z/[D.sub.0] [D.sub.0] [D.sub.0] [D.sub.0]

6 mm (0.24 in.) 0.1 2 2 2

 [D.sub.d]/ [L.sub.i]/ [L.sub.o]/ [L.sub.d]/
[D.sub.0] [D.sub.0] [D.sub.0] [D.sub.0] [D.sub.0] z/Z

6 mm (0.24 in.) 4 2 2 1000 0-1
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Author:Huang, Dongping; Ding, Guoliang; Quack, Hans
Publication:HVAC & R Research
Geographic Code:4EUUK
Date:Jan 1, 2007
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