Mixed refrigerant composition shift due to throttle valves opening in auto cascade refrigeration system☆

Xiongwen Xu ,Jinping Liu *,Le Cao

1 School of Electric Power,South China University of Technology,Guangzhou 510640,China

2 Guangdong Province Key Laboratory of Efficient and Clean Energy Utilization,Guangzhou 510640,China

3 State Key Laboratory of Subtropical Building Science,South China University of Technology,Guangzhou 510640,China

Keywords:Auto cascade Refrigeration Composition shift Throttle

ABSTRACT Auto cascade refrigeration(ACR)cycle with phase separators is widely used in the cryogenic system.The composition of mixed refrigerant has a great effect on the performance of the system.Based on the assumption of in finite volume of phase separator,ACR system with one phase separator is simulated in this paper.The variation of refrigerant composition under different valves opening is obtained.A related experimental system is set up to verify the variation.The result shows that when the valve opening connected to the evaporator increases or the valve opening under the phase separator decreases,the low-boiling component concentration of the working mixture passing through the compressor and condenser increases,while the high-boiling component concentration decreases.Furthermore,the variations of condensation pressure and evaporation pressure under different valves opening are also observed.This paper is helpful to deepen the understanding of ACR system.

1.Introduction

Auto cascade refrigeration(ACR)system employing non-azeotropic mixed-refrigerant is widely used in many industrial fields with cooling temperature ranging from?200°C to?40°C,such as natural gas liquefaction,cooling infrared sensors,cryosurgery,cryo-preservation,and water vapor cryo-trapping.Nowadays,the idea is extent to many refrigeration cycles,such as Alexeev and Quack[1]refrigerator,Missimer[2]refrigerator and many naturalgas liquefaction cycles[3-7].

In the ACR system,liquid fraction enriched with high-boiling components separated at a relatively high temperature level,is throttled to precool the separated vapor fraction that contains more low-boiling components.Then,the separated vapor is condensed and throttled to obtain a lower temperature level.

In all refrigerators employing non-azeotropic mixture,the working refrigerant composition is decisive.Lots of literatures reported the composition shift because of the different dissolubilities to the lubricant oil[8,9],liquid hold up[10-16]and leakage[17-19].Nevertheless,few people focused on the composition shift due to the throttle openings in ACR system with phase separators.Moreover,some even neglected it and adopted the composition of charged refrigerant as working refrigerant to analysis ACR system[20].

However,the system mechanism would somewhat be confused if the composition shift caused by the throttles opening is neglected.For example,in the simplified flow sheet illustrated in Fig.1,when the throttle valve opening under the phase separator(Valve G in Fig.1)increases,the flow resistance of the system decreases.As a result,the condensation pressure goes down and the evaporation pressure goes up.The decreased condensation pressure decreases the liquid fraction ratio of the mixed refrigerant stream entering the phase separator.In order to keep the balance between the liquid in flow and out flow of the phase separator,the refrigerant flow rate passing through the throttle valve under the phase separator should decrease.That is,the increase of the throttle valve opening under phase separator decreases the flow rate passing through it,which violates our common sense.

Fig.1.Flow Sheet of ACR cycle with one phase separator.A—compressor;B—condenser(after cooler);C—phase separator;D—evaporative condenser(regenerative heatexchanger);E,G—throttle valves;F—evaporator;1-10 are node numbers in ACR cycle.

The operation principle of ACR cycle with phase separators is extremely complicated,of which the throttles are intensively interacted.Guangming Chen et al.reported experimental research on the throttle opening in ACR system[21],but the experiment result was irregular because the effect of throttle devices opening on circulated mixed refrigerant composition was not considered.

Thus,the effect of the throttle valves opening on the working refrigerant composition is essential to understand the mechanism of ACR system equipped phase separators.Thus,a mathematical model to simulate the working process under different throttle devices opening is set up in this paper.Then,experiments are done to verify the phenomenon of the working mixed refrigerant composition variation in ACR system.

2.Mathematical Component Model

2.1.Heat exchanger

Heat transfer with mixed-refrigerant gas-liquid flow is a complex process that no mathematical model can precisely descript up to now.Fortunately,it is not the focus of this paper and moreover,some assumptions of refrigerant hold-up in this paper make it meaningless to seek a precise model for the heat exchanger simulation.Therefore,the simplest model, fixed minimum temperature approach model is applied to heat transfer simulation,namely,

Assuming the flow rate of the second heat transfer fluid is large enough,the minimum temperature approach occurs at the outlet of the refrigerant side in the condenser and evaporator.Hence,the fixed temperature of the second heat transfer fluid will fix the temperature of the refrigerant at the outlet of the heat exchangers as well.

2.2.Compressor

The mass flow rate through compressor(mc)is dependent on the density of the refrigerant at the compressor inlet(ρsuc),the displacement rate of the compressor(Vcomp)and its volumetric efficiency(ηv).Assuming the expanding process of the gas in clearance volume as isentropic process,the mathematical model of compressor can be descripted through Eqs.(2)and(3)[22].

where c represents the clearance volume ratio of compressing cavity in compressor,pdand psrepresent the discharge pressure and suction pressure of compressor respectively,and k is the isotropic expansion coefficient of refrigerant,which could be gotten as follows:

where cpand cvare the specific heat at constant pressure and constant volume,respectively.

2.3.Throttle valves

Using Wile's empirical formula,the mass flow rate through throttle valve(mva)can be calculated as

where CDis the flow factor,Avais the minimum flow area in valve,ρinrepresents the density of inlet fluid and voutis the specific volume of outlet fluid.

2.4.Simulation

In a given ACR system,the mixed-refrigerant distribution is inhomogeneous and hard-modeled.Thus,it is difficult to obtain the working refrigerant composition.To elucidate the relationship between the composition in circulation and the charged composition,Lakshmi-Narasimhan and Venkatarathnam conducted numerous experiments and summarized the results to conclude the linear relation ship between these variables[23].However,this result was only applicable to the particular system they tested.

To realize the system simulation,at least one refrigerant stream composition needs to get from the charged composition.Therefore,the following condition that an enough large scale of phase separator is employed in the system and enough refrigerant is charged is assumed.It can guarantee that most refrigerant is stored in the phase separator when the system is running so that the liquid refrigerant composition in the phase separator is approximate to the charged refrigerant composition.

As the system is running,the liquid and gas refrigerant in the phase separator can be considered as saturated state,respectively.When the refrigerant temperature at the outlet of the condenser(T3)is fixed,the pressure in the phase separator(condensation pressure,pc)can be determined as follows:

where Rland Rgrepresent the refrigerant composition of liquid and gas in the phase separator,respectively,Psatliqand RVsatliq,which are related to the physical property of the refrigerant,are the mathematical functions to get the bubble point pressure and bubble composition of a given refrigerant by the temperature,respectively.Eqs.(7)and(8)mean that the pressure and the gas composition in the phase separator are certain and irrespective of the valves opening because of the fixed temperature(T4=T3)and fixed refrigerant composition of the liquid in the phase separator.Thus,the composition of the refrigerant stream to the evaporator is invariable under 100%separation effectiveness of the phase separator.

In the whole simulation process,three conditions must be guaranteed.First,the refrigerant sucked by compressor is wholly gasified.Secondly,the refrigerant before the valve to evaporator is wholly liquefied.Thirdly,the system can make refrigeration effect,i.e.,the temperature of node 7 is less than node 8.For simplification,heat loss in the whole system and pressure drop in the heat exchangers and joint pipes are neglected.

Sequential modular method is applied in this paper to simulate ACR system.The mathematical models representing individual units are coded separately as subroutines in the simulators.The mathematical models are integrated so that the output stream data including pressure,temperature,enthalpy,etc.can be calculated with given input stream data.

Heat-exchangers in which cold stream is derived from the hot stream are known as regenerative heat exchangers.The stream in regenerative heat exchangers or closed-cycle is called recycle stream that needs to be torn in simulation.There are two recycle streams in the ACR cycle as shown in Fig.1,one due to heat recycling in the evaporative-condenser and the other due to recycling of mass(Stream 1).Streams 6 and 1 in Fig.1 are chosen to be torn.

The simulation process is listed in Table 1.The thermodynamic properties of mixtures are calculated by commercial software Refprop9(National Institute of Standards and Technology).

Table 1 Simulation procedure

The working conditions are set according to experiment descripted here inafter and the minimum temperature approach of heat exchangers is set as 3 K.

3.Experiment

As mentioned above,ACR system with phase separators is mainly applied in the cryogenic field.Kruse pointed out that when the evaporation temperature was higher than?48°C,ACR system would lose advantages to the general refrigeration system[24].However,a cryogenic experimental system requires good insulation measures and it will take a long time to reach the stable state,which will inevitably increase the experimental expenses.Considering the aim of this study is to investigate the effect of throttle valves opening on the composition shift rather than cryogenic temperature,the propane/isobutane mixture as refrigerant working at normal temperature level is used in our experimental rig and the working temperature ranges from 0 to 100°C.

3.1.Description of experimental rig

The experimental system mainly consists of a set of ACR cycle system,a hot water loop and a cold water loop as shown in Fig.2.

The ACR system consists of a compressor,a condenser,two expansion valves,an evaporator,a regenerative heat exchanger(evaporative condenser),and a phase separator.The detailed information of main components in experimental setup is listed in Table 2.

Water is used as the secondary heat transfer fluid in the condenser and evaporator.The water temperature is controlled and kept stable by the PID intelligent temperature controller and control valve,and the water temperature fluctuation can be kept below 1.5 K.

A gas chromatography instrument with a thermal conductivity detector(TCD)is used to analyze the mixture composition.It employs an elaborated capillary column to separate the components in the mixture.The signal generated by the detector is sent to the computer where the chromatogram of the sample can be obtained.The normalizing peak area method is used to determine the mixture compositions.The injection control valve controls the injecting amount of the sample.Composition measurement uncertainty is about0.5%.Table 3 shows the main measurement apparatus.

3.2.Test condition and test method

As mentioned above,the ACR experimental rig employs propane/isobutene mixture as refrigerant.In our experiments,the mass fraction of propane is about 0.5,namely,molar fraction of propane is about 56.86%,and the charged mass of refrigerant is 4 kg.

The temperatures of the water as the secondary heat transfer fluid supplied for condenser and evaporator are set to 55 °C and 25 °C,respectively.To prevent the water freeze,the lowest temperature of water circulated in the cold water loop must be higher than 0°C.Thus,the throttle valves opening in the experimental system cannot be too small.Of course,they also cannot be too large,or else the system cannot make refrigeration effect.In order to cover the operating ranges over different valves opening,the opening ratio of Valve G varied from 7.25%to 20.75%in the experiment(7.25%,10.75%,14.25%,17.5%,20.75%)and that of Valve E ranged from 10.75%to 30%(10.75%,14.25%,24%,30%)with 20 cross-over experiments.Each experiment measures the pressure,temperature and refrigerant composition of the gas at the compressor inlet and in the phase separator as shown in Fig.2.

4.Results and Discussion

4.1.Simulation results and discussion

Table 4 lists the detailed simulation parameters.The simulation results of the composition shift of the working refrigerant in the compressor and condenser under different valves opening are indicated in Fig.3.It shows that the working propane concentration goes up with the increased opening of the valve connected to evaporator(Valve E in Fig.1)or the decreased opening of the valve under the phase separator(Valve G in Fig.1),exactly the reverse of the variation of the working isobutene concentration.Because of the restriction of the three conditions mentioned above,the feasible region of each opening of the valve under phase separator is different.When the opening of the valve under phase separator is small,the refrigerant before the valve to evaporator cannot be easily condensed,and thus,the maximum opening of the valve to the evaporator is small.When the opening of the valve under phase separator is large,the refrigerant sucked by the compressor cannot be easily gasified.Thus,the minimum opening of the valve to the evaporator increases with increasing opening of the valve under phase separator.On the other hand,the refrigeration effect decreases when the valve opening under the phase separator increases.Therefore,the maximum opening of the valve to the evaporator may decrease as illustrated by the rightmost two curves on Fig.3.

Fig.2.Experimental system of ACR cycle with one phase separator.1-10 are node numbers in ACR cycle.

Table 2 Main components of experimental setup

Table 3 Measurement apparatus applied in the experimental setup

In the phase separator,low-boiling component concentration in the gas is higher than that in the liquid.The opening increase of valve connected to evaporator will increase the flow rate of the stream passing through the evaporator,and decrease the flow rate of the stream passing through the valve under the phase separator.The former contains more low-boiling component,and the latter contains more high-boiling component.Therefore,the blend of the two streams,i.e.,the whole stream passing through the compressor and condenser will contain more low-boiling component.The composition variation with respect to the opening of valve under phase separator can be explained by the same way.

The theoretical analysis above is based on an ideal system.Actually,it is impossible to keep the composition of liquid in phase separator invariable when the working condition changes.In all actual system,the condensation pressure will decrease when the valves opening increases.Nevertheless,the analysis above is sufficient to disclose the mechanism of the working refrigerant composition shift caused by the throttle valves opening in ACR system.

In fact,the refrigerant held in the high-pressure space of the system determines the condensation pressure.When the throttle valves opening increase,more refrigerant will hold in the low-pressure space of the closed system and less in the high-pressure space.As a result,evaporation pressure increases and condensation pressure decreases.The variation ratio of condensation pressure is related to the refrigerant amount held in the high-pressure space.More refrigerant amount held in the high-pressure space decreases its relative variation caused by the throttle valves opening and ultimately decreases the effect on the condensation pressure.Therefore,the larger volume of the phase separator and condenser means that more mixed refrigerant could be charged and held in the high-pressure space in ACR system,leading to slower condensation pressure variation caused by the throttle valves opening.If the volume of the phase separator and the mixed-refrigerant charge amount were in finite,the condensation pressure would be constant no matter how the valves opening change.

Now,the issue mentioned in the first part of this paper can be explained.When the opening of the valve under the phase separator increases,the flow rate passing through it increases.It increases the concentration of high boiling components in the refrigerant stream passing through the compressor and condenser.Although the condensation pressure decreases,the liquid fraction of the flowentering the phase separator still increases.Consequently,the in flow and out flow of the liquid and gas refrigerant in the phase separator can keep balance,respectively.The t-x diagram in Fig.4 shows the state variation of the refrigerant in the phase separator.Once the opening of the valve under the phase separator increases,the state of the mixed refrigerant will slip from Point 3 to 3′in Fig.4 and the liquid fraction of Point 3′is greater than Point 3.

Table 4 Simulation parameters

Fig.3.Composition variation of the refrigerant passing through compressor with respect to the valves opening in simulation.R comp,prop is propane molar concentration of the working refrigerant passing through the compressor;OPE is opening of the valve to the evaporator.

Fig.4.Variation of t-x state of refrigerant in the phase separator when the opening of the valve under phase separator increases.

4.2.Experimental results and discussion

Based on the experiments,the variation of refrigerant composition working with different throttle valves opening is obtained as shown in Figs.5 and 6.Comparing Fig.5 to Fig.3,the variation trend of refrigerant composition passing through compressor in experiments conforms to the simulation result,but the propane concentration in experiments is less than the simulation result.The main reason is that the phase separator is not large enough,and some refrigerants enriched with propane are held in the evaporative-condenser and evaporator.As a result,the propane concentration of the liquid in the phase separator is lower than the charged refrigerant.

Fig.5.Composition variation of the refrigerant passing through the compressor with respect to the valves opening in experiments.R comp,prop is the propane molar concentration of the working refrigerant passing through the compressor;OPE is the opening of the valve to the evaporator.

Fig.6.Composition variation of the gas refrigerant in the phase separator with respect to the valves opening in experiments.R comp,prop is the propane molar concentration of the working refrigerant passing through the compressor;OPE is the opening of the valve to the evaporator.

Since it is impossible to employ an in finitely large scale of phase separator and to charge in finite amount refrigerant,the refrigerant composition in the phase separator varies under different valves opening,so as the condensation pressure as shown in Figs.6 and 7.Increasing the opening of either valve,the condensation pressure goes down,while the evaporation pressure goes up,most surprisingly,the propane concentration of the gas refrigerant in the phase separator,namely,the refrigerant passing through the evaporator always decreases.Actually,at a fixed temperature,when the condensation pressure decreases,propane fractions in both saturated gas and liquid decrease,as shown in Fig.4.It means that the propane concentrations of both gas or liquid refrigerant in the phase separator go down.

Fig.7.Pressures variation with respect to the valves opening in experiments.OPE is the opening of the valve to the evaporator.

5.Conclusions

This paper theoretically and experimentally investigated the effect of throttle valves opening on the working refrigerant composition of auto-cascade refrigeration system.Some conclusions are summarized as follows.

In ACR system with one phase separator,with increasing opening of the valve connected to the evaporator or decreasing opening of the valve under the phase separator,the concentration of low boiling components of the stream passing through compressor increases,while that of high boiling components decreases.

With increasing openings of the throttle valves,condensation pressure decreases,while evaporation pressure increases,and simultaneously,the concentration of volatile components of the stream passing through evaporator decreases.The variation of condensation pressure is related to the refrigerant amount stored in the high-pressure space of the running system,i.e.,the phase separator,the condenser and part of regenerative heat exchanger.More refrigerant stored in the high pressure space,slower variation of condensation pressure will be.

Nomenclature

Avaminimum flow area in valve,m2

CDflow factor

c clearance volume ratio of compressing cavity in compressor

cpspecific heat at constant pressure,kJ·kg?1·K?1

cvspecific heat at constant volume respectively,kJ·kg?1·K?1

G mass flow,kg·s?1

k isotropic expansion coefficient of refrigerant

mcmass flow rate through compressor,kg·s?1

mvamass flow rate through throttle valve,kg·s?1

OP opening of throttle valves

pccondensation pressure,MPa

pddischarge pressure of compressor,MPa

pssuction pressure of compressor,MPa

Psatliqmathematical function to get the bubble point pressure of a given refrigerant by temperature

R refrigerant molar composition

Rgrefrigerant composition of the gas in the phase separator

Rlrefrigerant composition of the liquid in the phase separator

RVsatliqmathematical function to get the bubble composition of a given refrigerant by temperature

T temperature,°C

Δtminminimum temperature approach,K

ΔtRHEminimum temperature approach of the regenerative heat exchanger(evaporative condenser),K

Vcompthe displacement rate of the compressor,m3·s?1

voutspecific volume of the working fluid at valve outlet,m3·kg?1

x components mass fraction of mixed refrigerant

ε1,ε2tiny value

ηvvolumetric efficiency of the compressor

ρindensity of fluid at valve inlet,kg·m?3

ρsucdensity of the refrigerant at the compressor suction,kg·m?3

Subscripts

comp compressor