- Email: [email protected]
A study on the new separate heat pipe refrigerator and heat pump
Applied Thermal Engineering 24 (2004) 2737–2745 www.elsevier.com/locate/apthermeng
A study on the new separate heat pipe refrigerator and heat pump Z. Ling
*
Shanghai University of Engineering Science, NO. 350, Xian-Xia Road, Shanghai 200336, People’s Republic of China Received 22 July 2003; accepted 12 April 2004 Available online 25 June 2004
Abstract A new separate heat pipe refrigerator and heat pump is suggested based on the general three temperature thermal jet refrigerator and heat pump cycle. Sub-cooled hot water or other appropriate liquid heated by low grade heat sources forms the hot end and another heat pipe containing evaporator and condenser ends, adiabatic section of two-phase ejector and throttling tube is as the cold end of the separate heat pipe system. Performance relations for the thermal jet refrigerator and heat pump of such system is analyzed and a method of thermodynamic performance analysis is recommended. Primary prediction shows the feasibility of such heat pipe system for cold and warm water supply. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Heat pipe refrigerator; Separate heat pipe; Thermal Jet refrigerator; Thermal heat pump
1. Introduction Heat pipe and two-phase thermosyphon technology has been fully developed and widely applied in different fields especially in the thermal, chemical and aerospace engineering. The research achievements in recent years also showed that the heat pipe and two-phase thermosyphon concept could perspectively be developed to realize new energetic heat pipes such as heat pipe engine [1], heat pipe turbine [2] as well as heat pipe pumps [3,4]. In the field of air-conditioning and refrigeration, with the requirement of utilizing low grade or low enthalpy solar thermal, geothermal and industrial waste energy sources, appropriate thermal
*
Tel./fax: +86-21-62912993. E-mail address: [email protected] (Z. Ling).
1359-4311/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2004.04.002
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refrigerator and heat pump [5] system are the aim of many researchers for achieving a more high level of the coefficient of performance, compactness and cost effectiveness. Besides the present equipments based on the mechanic compression or absorption principle, the thermal jet refrigerator operating with classical and pure refrigerants as well as non-azeotropic mixtures has got impressive research improvements in recent years. The sub-cooled hot water was suggested by the author to be the driving working medium for the jet refrigerator [6] in view of its potential in COP performance and the direct utilization in the solar cooling, district cooling and building airconditioning energy saving together with the improvement on environmental protection. The suggested system employs the two-phase flashing nozzle flow to convert the sub-cooled hot water directly to compressible vapor–liquid dispersed jet flow in the two-phase ejector so as to avoid partially or wholly the input heat of vaporization as in the conventional vapor jet refrigeration system [7,8]. It should be noted that a vapor jet refrigerating system using water as the working medium was developed and published in 2001 by Nguyen et al. [9] and the refrigerating heat pipe concept with vapor jet compression was issued by Smirnov and Kosoy [10]. In this paper, a concept of combining the heat pipe and two-phase thermosyphon principle with the sub-cooled hot water thermal jet refrigeration system is suggested and thus a new separate heat pipe jet refrigerator or heat pump configuration is performed and analyzed. The constructional design study has been done for the first stage experimental work. A method of thermodynamic analysis is introduced for the performance prediction and design of such system.
2. About the thermal refrigerator and heat pump Ideal refrigerator and heat pump cycles all belong to the reversed Carnot cycle. Generally, the thermal refrigerator is a device for giving the useful cool from the waste heat and the thermal heat pump is used for giving useful heat from waste heat sources. When we analyze the process of the reversed Carnot cycle in a region of two phase states shown on the P –h diagram in Fig. 1, for the compression type heat pump with the input work W , the coefficient of performance is: COPHP ¼ QC =W ¼ ðh2 h3 Þ=ðh2 h1 Þ. As h2 ¼ h1 þ W and h3 ¼ h4 ¼ h1 QE , so COPHP ¼ 1 þ QE =W ¼ 1 þ COPRF . Therefore, in this case the COP of the refrigerator is always less than
P
3
QC
4
2
1 QE
h
Fig. 1. P –h diagram of the reversed Carnot cycle in two-phase states.
Z. Ling / Applied Thermal Engineering 24 (2004) 2737–2745
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Fig. 2. The reversed Carnot cycle of thermal refrigerator and heat pump.
that of the heat pump by 1 for the ideal cycle at the same evaporator and same condenser temperature in the two-phase states of the working medium. For the thermal refrigerator and heat pump, there are three temperature levels, the heat source temperature TB , the condenser temperature TC and the evaporator temperature TE . The reversed Carnot cycle is expressed on the T –S diagram in Fig. 2. Since the Carnot cycle is completely reversible and receives and rejects heat reversibly and isothermally, so: COPTRF ¼ QE =QB and COPTHP ¼ QC =QB ¼ ðQB þ QE Þ=QB . Therefore the relation between thermal refrigerator and thermal heat pump in wholly reversible condition follows also COPTRF ¼ COPTHP 1. For the real process it will be different from 1. By the thermal jet pump system it is possible to regulate the temperature level of TC and TE by the ejector process with certain means, so it is feasible to realize the jet refrigerator and heat pump in the same system. This forms one of the characteristics of the thermal jet system. 3. The separate heat pipe thermal jet refrigerator and heat pump Fig. 3 is the general thermal jet pump refrigerator system using the sub-cooled hot water as the driving medium without considering the preheat and regeneration. As evaluated in [6], the COPRF for sub-cooled hot water of 0.4 MPa and 85 °C could be greater than that for the steam of 143 °C at the same pressure level. For such thermal jet refrigerator system, the evaporator and condenser are to be operated in low vacuum pressure. It is correspondingly 0.001227 and 0.004241 MPa for an evaporation and condensation temperature of 10 and 30 °C, respectively. Obviously, the design and the efficiency of the two-phase nozzle with flashing critical flow is the key problem to be solved for such system. Since the heat pipe is a successful heat transfer device and could be worked with the condensation and the evaporation process in vacuum with water as the medium, it is rational to constitute the flashing thermal jet refrigerator or heat pump system into a separate heat pipe as shown in Fig. 4. This is really a double or superseded heat pipe. The hot end is the heater of the driving hot water by low enthalpy energy sources as described in the above. For solar heater it could be a solar collector put on the roof top. If the height is enough, it will constitute with the lower heat pipe as a closed thermosyphon loop without the installation of a pump, but for general utilizing cases the pump is used for pressurizing and regulating of the working regime.
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Fig. 3. Thermal jet refrigerator or heat pump system.
QB Heat source PB TB
B Hot end
A Cold end heat pipe
Evaporator water loop
PE TE
Evaporator section
water level QE Cool water
Ejector
(1-µ)M
Two phase nozzle
Mixing chamber Connection tabe
Diffuser To vacuum pump
PC TC
water level Condenser section
QC Warm water Condenser water loop
Pump
Fig. 4. Schema of the separate heat pipe jet refrigerator and heat pump.
Z. Ling / Applied Thermal Engineering 24 (2004) 2737–2745
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The secondary or main heat pipe has the evaporation section in the upper end and the condensation section in the lower end with the adiabatic section in the middle. The adiabatic section includes a two-phase ejector and thin throttle tube which connects the evaporation chamber with the condensation chamber and the difference in pressure or vacuum is balanced by the gravity of the water column and the resistance in working. The hot sub-cooled water is connected to the twophase nozzle through internal tube imbedded in the evaporator end. The water in the evaporator chamber is evaporated at the suction pressure PE created by the high two-phase jet from the nozzle exit. By the evaporation, the water in the heat exchange tube loop is cooled down to TE þ DT for the refrigeration or cooling usage. The two streams in the ejector are mixed in the mixing chamber and diffused to the pressure PC in the diffuser and directly flow into the condensation chamber. The cooling tube loop keeps the condenser in a temperature of TC and the two-phase wet steam is condensed in the condenser by heat transfer to the water in the cooling tube loop and raise the water temperature to TC DT for the required warm water usage. The condensed water flows out by two parts: one part through the connection throttle tube and the other part through the pump P in the loop and returned to the hot end or heater [8]. For example: at TE ¼ 5 °C and TC ¼ 30 °C, the corresponding pressure difference is 307.4 mm water column height and even in case of TE ¼ 5 °C and TC ¼ 35 °C, the column height is 484.4 mm, so it is rather feasible, compact and enough for the ejector and connection tube to be installed in the adiabatic section.
4. Method of thermodynamic performance analysis with loss and dryness consideration 4.1. Thermodynamic analysis On Fig. 5 is shown the thermodynamic process of the suggested separate heat pipe thermal jet refrigerator and heat pump. PB , PE , and PC are respectively the pressure (as stagnation in general)
Fig. 5. h–S diagram of the flashing thermal jet refrigerator system.
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of the driving sub-cooled hot fluid, the suction fluid from the evaporator section and at the exit of the diffuser. The fluid at A expands in the two-phase nozzle to PS at point 1 through A ! B0 ! 1. 00 The evaporated steam at E is driven through the suction chamber, expands a little to PS in the bell mouth section where it mixes with the high speed two-phase jet and experiences the momentum exchange and heat transfer in the mixing chamber. The real or irreversible final state at the exit is in point 4. Point C is the state at the exit of diffuser and the pressure is increased to PC . C ! C0 is the process of condensation. One part of the condensate flows out of the heat pipe and pumped to point P and heated again by process P ! B0 . The other part under the pressure difference flows through the thin pipe (as throttled) to the evaporator section at point E where it is evaporated to 00 E and to be sucked back again. For an ideal and loss free mixing process the driving liquid at state B0 mixed with the driven 00 00 00 liquid at state E to the state M on the intersection of lines B0 E and C0 C with a flow rate ratio which is called the entrainment ratio of the ejector expressed by lid ¼ ME =MB ¼ ðh0B hM Þ=ðhM h00E Þ ¼ ðSB0 SM Þ=ðSM SE00 Þ
ð1Þ
From the thermodynamic relation hM h0C ¼ ðSM SC0 ÞTC
ð2Þ
Combining (1) and (2), we can write hM ¼ ½ðh00E h0B ÞðTC SC0 h0C Þ TC ðSB0 h00E SE00 h0B Þ =½TC ðSE00 SB0 Þ ðh00E h0B Þ
ð3Þ
If we define the vapor content (or dryness) of two-phase flow mixture as X, for the ideal process of mixing XM ¼ ðhM h0C Þ=ðh00C h0C Þ ¼ ðSM SC0 Þ=ðSC00 SC0 Þ
ð4Þ
The real turbulent mixing process is very complex. Due to the wall friction, momentum exchange and heat transfer etc. there are the loss and entropy increase and the final real state at the exit of diffuser is at C. The vapor content at C is XC . Thus we can define the perfectness of the jet compression process in the extent of vapor phase change and define the dryness coefficient as fX ¼ XC =XM
ð5Þ
XC ¼ ðhC h0C Þ=ðh00C h0C Þ ¼ ðSC SC0 Þ=ðSC00 SC0 Þ
ð6Þ
hC ¼ h0C þ XM fX ðh00C h0C Þ
ð7Þ
and so From the energy balance relation of the ejector ðMB þ ME ÞhC ¼ ðMB h0B Þ þ ðME h00E Þ ¼ ðMB þ MC Þh0C þ XC ðMB þ ME ÞrC
ð8Þ
Here rC denotes the heat of vaporization at TC rC ¼ h00C h0C
ð9Þ
From the energy balance in the condenser section ðMB þ ME ÞðhC h0C Þ ¼ MB ðh0B h0C Þ þ ME ðh00E h0C Þ
ð10Þ
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so l ¼ ½ð2h0B h0C Þ ðhC þ XC rC Þ =½ðhC þ XC rC Þ ð2h00E h0C Þ
ð11Þ
4.2. Performance estimation From the three given temperatures, pressure PA and assumed fX , after getting the entrainment ratio or mass flow rate ratio l, one can predict the performance with the given requirement of cooling or warm capacity QE or QC and design the size relations of different parts of the separate heat pipe including the ejector. The mass flow rate of the suction flow or that circulating inside the secondary heat pipe is determined from the required cooling capacity QE ME ¼ QE =ðh00E hE Þ
ð12Þ
and the mass flow rate of the driving liquid is MB ¼ ME =l
ð13Þ
the possible warm capacity is QC ¼ ðMB þ ME ÞðhC h0C Þ
ð14Þ
The coefficient of performance of the refrigerator is then COPTRF ¼ QE =QB ¼ lðh00E h0E Þ=ðh0B h0C Þ
ð15Þ
in which we neglect for simplicity the work of the pump which is roughly ðPP PC Þ=c. The coefficient of performance of the heat pump is COPTHP ¼ ð1 þ lÞðhC h0C Þ=ðh0B h0C Þ
ð16Þ
Finally the difference between the two coefficient of performance is DCOP ¼ COPTHP COPTRF ¼ ½ð1 þ lÞðhC h0C Þ lðh00E hC Þ =ðh0B h0C Þ
ð17Þ
The above relation are used in the computer performance simulation. The influence of dryness coefficient on the COP of heat pipe thermal jet refrigerator and heat pump are shown in Fig. 6. It
Fig. 6. Example of performance prediction.
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could be seen that the COPTRF of refrigerator utilizing sub-cooled hot water of 85 °C (about 0.4 MPa in pressure) with TC ¼ 30 °C and TE ¼ 10 °C is rather acceptable in the real fX range of above 0.9. The value of COPHP )COPRF is slightly greater than 1 in the real process and is increased with the increase of fX . It could be smaller than 1 in very low fX which is out of the range of the real design. 4.3. Relation between the dryness coefficient and efficiency of the ejector process For the thermal fluid dynamic calculation, design and test of the ejector, usually the efficiency is based on the energy and friction loss of the flow process in different parts of the ejector. Basically the energy efficiency of ejector could be written as gEJ ¼ gN gS gM gD
ð18Þ
It represents the combined result of sub-efficiency in the nozzle, suction chamber, mixing chamber and diffuser. Expressed in a product causes difficulties in defining, and measuring in the experiment. As the loss is related directly with the total enthalpy decrease or the entropy increase, from the thermodynamic point of view, one can also express the loss in the ejector as follows with reference to Fig. 5 DhEJ ¼ DhN þ DhS þ DhM þ DhD ¼ TS ðDSN þ DSS þ DSM Þ þ TC DSD
ð19Þ
From the flow loss and mixing irreversibility, we can write DhN þ DhS ¼ TS ðDSN þ DSS Þ ¼ ðhM h0M Þ
ð20Þ
DhM þ DhD ¼ TS DSM þ TC DSD ¼ ðh0M hC Þ
ð21Þ
DhEJ ¼ hM hC
ð22Þ
so Therefore the energy efficiency of ejector can be expressed as gEJ ¼ 1
TS ðDSN þ DSS þ DSM Þ þ TC DSD DhEJ ¼1 hM h5 hM h5
ð23Þ
in which hM h5 represents the isentropic enthalpy drop of the input working medium when mixed irreversibly, the above definition seems easier to be predicted, measured and determined from the experiment. h5 is on the constant Ps line which can be calculated from the flow in the inlet of the mixing chamber. Roughly one can also take Ps ¼ PE for primary prediction. As S5 ¼ SM , and from Eq. (4), SM ¼ XM ðSC00 SC0 Þ þ SC0
ð24Þ
Besides, h5 ¼ rE ðSS SS0 Þ=ðSS00 SS0 Þ þ h0S
ð25Þ
h5 ¼ rS ½XC ðSC00 SC0 Þ=fX þ ðSC0 SS0 Þ =ðSS00 SS0 Þ þ h0S
ð26Þ
So,
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and gEJ ¼ 1 DhEJ =fhM rS ½XC ðSC00 SC0 Þ=fX þ ðSC0 SS0 Þ =ðSS00 SS0 Þ þ h0S g
ð27Þ
Eq. (27) is the relation between dryness coefficient and enthalpy efficiency. So in the analysis and calculation fX could be estimated from the test results of ejector or from existed ejector loss model and data together with the thermodynamic parameters used.
5. Conclusion 1. A new separate heat pipe thermal jet refrigerator and heat pump is suggested and configurated. With the sub-cooled hot water as the first choice of the driving liquid, the new type of heat pipe refrigerator is feasible, compact and could be efficient in utilizing the low grade energy sources such as industrial waste heat, solar thermal etc. Development of efficient two-phase ejector is important in realizing practical device. 2. A method of thermodynamic performance analysis and calculation of the coefficient of performance with given three temperatures for such device is introduced. The analytical relation between refrigerator and heat pump for the same system is developed. For the same system and device, therefore, the working regime could be changed by regulation of the pressure level of PC and PE . 3. Primary performance calculation and configuration design performed show the feasibility of such device and further experimentation and development is underway working on.
References [1] Y. Kobayashi, Heat pipe Engine and Its Thermo-dynamic Cycle, in: Proceedings 5th IHPC, 1984.5. [2] P. Johnson, A. Akbarzadeh, et al., Heat Pipe Turbine Becoming a Reality, in: Proceedings of 5th IHPS, 1996, pp. 338–343. [3] I. Shekriladze et al., Solar powered Water Pump on the basis of Pulsating Heat Pipe, in: Proceedings 9th IHPC, 1995.5. [4] K.GI, S. Maezawa, Development of Thermal Powered Membrane Pump by Application of Heat Pipe, in: Proceedings 10th IHPC, 1997.9. [5] Ch. Mostofizadeh, Thermische Warmepumpe, Elektrowarme im Technischen Ausbau, 35, 1977, A1, pp.35–36. [6] Z. Ling, M. Groll, Thermo-fluid Dynamic Study of Hot Water Jet Pump Refrigeration System, in: Proceedings 4th IHPS, 1994.5. [7] Z. Ling et al., Investigation on Subcooled Flashing Nozzle Flow with Vaporization Enhancement, in: Proceeding of 4th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics, 1997.6, Band 3, pp.1693–1700. [8] Z. Ling Patent No. 99113880.5, China. [9] V.M. Nguyen, S.B. Riffat, P.S. Doherty, Development of a Solar-powered Passive Ejector Cooling System, Applied Thermal Engineering 21 (2001) 157–168. [10] H.F. Smirnov, B.V. Kosoy, Refrigerating Heat Pipes, Applied Thermal Engineering 21 (2001) 631–641.
A study on the new separate heat pipe refrigerator and heat pump Z. Ling
*
Shanghai University of Engineering Science, NO. 350, Xian-Xia Road, Shanghai 200336, People’s Republic of China Received 22 July 2003; accepted 12 April 2004 Available online 25 June 2004
Abstract A new separate heat pipe refrigerator and heat pump is suggested based on the general three temperature thermal jet refrigerator and heat pump cycle. Sub-cooled hot water or other appropriate liquid heated by low grade heat sources forms the hot end and another heat pipe containing evaporator and condenser ends, adiabatic section of two-phase ejector and throttling tube is as the cold end of the separate heat pipe system. Performance relations for the thermal jet refrigerator and heat pump of such system is analyzed and a method of thermodynamic performance analysis is recommended. Primary prediction shows the feasibility of such heat pipe system for cold and warm water supply. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Heat pipe refrigerator; Separate heat pipe; Thermal Jet refrigerator; Thermal heat pump
1. Introduction Heat pipe and two-phase thermosyphon technology has been fully developed and widely applied in different fields especially in the thermal, chemical and aerospace engineering. The research achievements in recent years also showed that the heat pipe and two-phase thermosyphon concept could perspectively be developed to realize new energetic heat pipes such as heat pipe engine [1], heat pipe turbine [2] as well as heat pipe pumps [3,4]. In the field of air-conditioning and refrigeration, with the requirement of utilizing low grade or low enthalpy solar thermal, geothermal and industrial waste energy sources, appropriate thermal
*
Tel./fax: +86-21-62912993. E-mail address: [email protected] (Z. Ling).
1359-4311/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2004.04.002
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refrigerator and heat pump [5] system are the aim of many researchers for achieving a more high level of the coefficient of performance, compactness and cost effectiveness. Besides the present equipments based on the mechanic compression or absorption principle, the thermal jet refrigerator operating with classical and pure refrigerants as well as non-azeotropic mixtures has got impressive research improvements in recent years. The sub-cooled hot water was suggested by the author to be the driving working medium for the jet refrigerator [6] in view of its potential in COP performance and the direct utilization in the solar cooling, district cooling and building airconditioning energy saving together with the improvement on environmental protection. The suggested system employs the two-phase flashing nozzle flow to convert the sub-cooled hot water directly to compressible vapor–liquid dispersed jet flow in the two-phase ejector so as to avoid partially or wholly the input heat of vaporization as in the conventional vapor jet refrigeration system [7,8]. It should be noted that a vapor jet refrigerating system using water as the working medium was developed and published in 2001 by Nguyen et al. [9] and the refrigerating heat pipe concept with vapor jet compression was issued by Smirnov and Kosoy [10]. In this paper, a concept of combining the heat pipe and two-phase thermosyphon principle with the sub-cooled hot water thermal jet refrigeration system is suggested and thus a new separate heat pipe jet refrigerator or heat pump configuration is performed and analyzed. The constructional design study has been done for the first stage experimental work. A method of thermodynamic analysis is introduced for the performance prediction and design of such system.
2. About the thermal refrigerator and heat pump Ideal refrigerator and heat pump cycles all belong to the reversed Carnot cycle. Generally, the thermal refrigerator is a device for giving the useful cool from the waste heat and the thermal heat pump is used for giving useful heat from waste heat sources. When we analyze the process of the reversed Carnot cycle in a region of two phase states shown on the P –h diagram in Fig. 1, for the compression type heat pump with the input work W , the coefficient of performance is: COPHP ¼ QC =W ¼ ðh2 h3 Þ=ðh2 h1 Þ. As h2 ¼ h1 þ W and h3 ¼ h4 ¼ h1 QE , so COPHP ¼ 1 þ QE =W ¼ 1 þ COPRF . Therefore, in this case the COP of the refrigerator is always less than
P
3
QC
4
2
1 QE
h
Fig. 1. P –h diagram of the reversed Carnot cycle in two-phase states.
Z. Ling / Applied Thermal Engineering 24 (2004) 2737–2745
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Fig. 2. The reversed Carnot cycle of thermal refrigerator and heat pump.
that of the heat pump by 1 for the ideal cycle at the same evaporator and same condenser temperature in the two-phase states of the working medium. For the thermal refrigerator and heat pump, there are three temperature levels, the heat source temperature TB , the condenser temperature TC and the evaporator temperature TE . The reversed Carnot cycle is expressed on the T –S diagram in Fig. 2. Since the Carnot cycle is completely reversible and receives and rejects heat reversibly and isothermally, so: COPTRF ¼ QE =QB and COPTHP ¼ QC =QB ¼ ðQB þ QE Þ=QB . Therefore the relation between thermal refrigerator and thermal heat pump in wholly reversible condition follows also COPTRF ¼ COPTHP 1. For the real process it will be different from 1. By the thermal jet pump system it is possible to regulate the temperature level of TC and TE by the ejector process with certain means, so it is feasible to realize the jet refrigerator and heat pump in the same system. This forms one of the characteristics of the thermal jet system. 3. The separate heat pipe thermal jet refrigerator and heat pump Fig. 3 is the general thermal jet pump refrigerator system using the sub-cooled hot water as the driving medium without considering the preheat and regeneration. As evaluated in [6], the COPRF for sub-cooled hot water of 0.4 MPa and 85 °C could be greater than that for the steam of 143 °C at the same pressure level. For such thermal jet refrigerator system, the evaporator and condenser are to be operated in low vacuum pressure. It is correspondingly 0.001227 and 0.004241 MPa for an evaporation and condensation temperature of 10 and 30 °C, respectively. Obviously, the design and the efficiency of the two-phase nozzle with flashing critical flow is the key problem to be solved for such system. Since the heat pipe is a successful heat transfer device and could be worked with the condensation and the evaporation process in vacuum with water as the medium, it is rational to constitute the flashing thermal jet refrigerator or heat pump system into a separate heat pipe as shown in Fig. 4. This is really a double or superseded heat pipe. The hot end is the heater of the driving hot water by low enthalpy energy sources as described in the above. For solar heater it could be a solar collector put on the roof top. If the height is enough, it will constitute with the lower heat pipe as a closed thermosyphon loop without the installation of a pump, but for general utilizing cases the pump is used for pressurizing and regulating of the working regime.
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Fig. 3. Thermal jet refrigerator or heat pump system.
QB Heat source PB TB
B Hot end
A Cold end heat pipe
Evaporator water loop
PE TE
Evaporator section
water level QE Cool water
Ejector
(1-µ)M
Two phase nozzle
Mixing chamber Connection tabe
Diffuser To vacuum pump
PC TC
water level Condenser section
QC Warm water Condenser water loop
Pump
Fig. 4. Schema of the separate heat pipe jet refrigerator and heat pump.
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The secondary or main heat pipe has the evaporation section in the upper end and the condensation section in the lower end with the adiabatic section in the middle. The adiabatic section includes a two-phase ejector and thin throttle tube which connects the evaporation chamber with the condensation chamber and the difference in pressure or vacuum is balanced by the gravity of the water column and the resistance in working. The hot sub-cooled water is connected to the twophase nozzle through internal tube imbedded in the evaporator end. The water in the evaporator chamber is evaporated at the suction pressure PE created by the high two-phase jet from the nozzle exit. By the evaporation, the water in the heat exchange tube loop is cooled down to TE þ DT for the refrigeration or cooling usage. The two streams in the ejector are mixed in the mixing chamber and diffused to the pressure PC in the diffuser and directly flow into the condensation chamber. The cooling tube loop keeps the condenser in a temperature of TC and the two-phase wet steam is condensed in the condenser by heat transfer to the water in the cooling tube loop and raise the water temperature to TC DT for the required warm water usage. The condensed water flows out by two parts: one part through the connection throttle tube and the other part through the pump P in the loop and returned to the hot end or heater [8]. For example: at TE ¼ 5 °C and TC ¼ 30 °C, the corresponding pressure difference is 307.4 mm water column height and even in case of TE ¼ 5 °C and TC ¼ 35 °C, the column height is 484.4 mm, so it is rather feasible, compact and enough for the ejector and connection tube to be installed in the adiabatic section.
4. Method of thermodynamic performance analysis with loss and dryness consideration 4.1. Thermodynamic analysis On Fig. 5 is shown the thermodynamic process of the suggested separate heat pipe thermal jet refrigerator and heat pump. PB , PE , and PC are respectively the pressure (as stagnation in general)
Fig. 5. h–S diagram of the flashing thermal jet refrigerator system.
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of the driving sub-cooled hot fluid, the suction fluid from the evaporator section and at the exit of the diffuser. The fluid at A expands in the two-phase nozzle to PS at point 1 through A ! B0 ! 1. 00 The evaporated steam at E is driven through the suction chamber, expands a little to PS in the bell mouth section where it mixes with the high speed two-phase jet and experiences the momentum exchange and heat transfer in the mixing chamber. The real or irreversible final state at the exit is in point 4. Point C is the state at the exit of diffuser and the pressure is increased to PC . C ! C0 is the process of condensation. One part of the condensate flows out of the heat pipe and pumped to point P and heated again by process P ! B0 . The other part under the pressure difference flows through the thin pipe (as throttled) to the evaporator section at point E where it is evaporated to 00 E and to be sucked back again. For an ideal and loss free mixing process the driving liquid at state B0 mixed with the driven 00 00 00 liquid at state E to the state M on the intersection of lines B0 E and C0 C with a flow rate ratio which is called the entrainment ratio of the ejector expressed by lid ¼ ME =MB ¼ ðh0B hM Þ=ðhM h00E Þ ¼ ðSB0 SM Þ=ðSM SE00 Þ
ð1Þ
From the thermodynamic relation hM h0C ¼ ðSM SC0 ÞTC
ð2Þ
Combining (1) and (2), we can write hM ¼ ½ðh00E h0B ÞðTC SC0 h0C Þ TC ðSB0 h00E SE00 h0B Þ =½TC ðSE00 SB0 Þ ðh00E h0B Þ
ð3Þ
If we define the vapor content (or dryness) of two-phase flow mixture as X, for the ideal process of mixing XM ¼ ðhM h0C Þ=ðh00C h0C Þ ¼ ðSM SC0 Þ=ðSC00 SC0 Þ
ð4Þ
The real turbulent mixing process is very complex. Due to the wall friction, momentum exchange and heat transfer etc. there are the loss and entropy increase and the final real state at the exit of diffuser is at C. The vapor content at C is XC . Thus we can define the perfectness of the jet compression process in the extent of vapor phase change and define the dryness coefficient as fX ¼ XC =XM
ð5Þ
XC ¼ ðhC h0C Þ=ðh00C h0C Þ ¼ ðSC SC0 Þ=ðSC00 SC0 Þ
ð6Þ
hC ¼ h0C þ XM fX ðh00C h0C Þ
ð7Þ
and so From the energy balance relation of the ejector ðMB þ ME ÞhC ¼ ðMB h0B Þ þ ðME h00E Þ ¼ ðMB þ MC Þh0C þ XC ðMB þ ME ÞrC
ð8Þ
Here rC denotes the heat of vaporization at TC rC ¼ h00C h0C
ð9Þ
From the energy balance in the condenser section ðMB þ ME ÞðhC h0C Þ ¼ MB ðh0B h0C Þ þ ME ðh00E h0C Þ
ð10Þ
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so l ¼ ½ð2h0B h0C Þ ðhC þ XC rC Þ =½ðhC þ XC rC Þ ð2h00E h0C Þ
ð11Þ
4.2. Performance estimation From the three given temperatures, pressure PA and assumed fX , after getting the entrainment ratio or mass flow rate ratio l, one can predict the performance with the given requirement of cooling or warm capacity QE or QC and design the size relations of different parts of the separate heat pipe including the ejector. The mass flow rate of the suction flow or that circulating inside the secondary heat pipe is determined from the required cooling capacity QE ME ¼ QE =ðh00E hE Þ
ð12Þ
and the mass flow rate of the driving liquid is MB ¼ ME =l
ð13Þ
the possible warm capacity is QC ¼ ðMB þ ME ÞðhC h0C Þ
ð14Þ
The coefficient of performance of the refrigerator is then COPTRF ¼ QE =QB ¼ lðh00E h0E Þ=ðh0B h0C Þ
ð15Þ
in which we neglect for simplicity the work of the pump which is roughly ðPP PC Þ=c. The coefficient of performance of the heat pump is COPTHP ¼ ð1 þ lÞðhC h0C Þ=ðh0B h0C Þ
ð16Þ
Finally the difference between the two coefficient of performance is DCOP ¼ COPTHP COPTRF ¼ ½ð1 þ lÞðhC h0C Þ lðh00E hC Þ =ðh0B h0C Þ
ð17Þ
The above relation are used in the computer performance simulation. The influence of dryness coefficient on the COP of heat pipe thermal jet refrigerator and heat pump are shown in Fig. 6. It
Fig. 6. Example of performance prediction.
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could be seen that the COPTRF of refrigerator utilizing sub-cooled hot water of 85 °C (about 0.4 MPa in pressure) with TC ¼ 30 °C and TE ¼ 10 °C is rather acceptable in the real fX range of above 0.9. The value of COPHP )COPRF is slightly greater than 1 in the real process and is increased with the increase of fX . It could be smaller than 1 in very low fX which is out of the range of the real design. 4.3. Relation between the dryness coefficient and efficiency of the ejector process For the thermal fluid dynamic calculation, design and test of the ejector, usually the efficiency is based on the energy and friction loss of the flow process in different parts of the ejector. Basically the energy efficiency of ejector could be written as gEJ ¼ gN gS gM gD
ð18Þ
It represents the combined result of sub-efficiency in the nozzle, suction chamber, mixing chamber and diffuser. Expressed in a product causes difficulties in defining, and measuring in the experiment. As the loss is related directly with the total enthalpy decrease or the entropy increase, from the thermodynamic point of view, one can also express the loss in the ejector as follows with reference to Fig. 5 DhEJ ¼ DhN þ DhS þ DhM þ DhD ¼ TS ðDSN þ DSS þ DSM Þ þ TC DSD
ð19Þ
From the flow loss and mixing irreversibility, we can write DhN þ DhS ¼ TS ðDSN þ DSS Þ ¼ ðhM h0M Þ
ð20Þ
DhM þ DhD ¼ TS DSM þ TC DSD ¼ ðh0M hC Þ
ð21Þ
DhEJ ¼ hM hC
ð22Þ
so Therefore the energy efficiency of ejector can be expressed as gEJ ¼ 1
TS ðDSN þ DSS þ DSM Þ þ TC DSD DhEJ ¼1 hM h5 hM h5
ð23Þ
in which hM h5 represents the isentropic enthalpy drop of the input working medium when mixed irreversibly, the above definition seems easier to be predicted, measured and determined from the experiment. h5 is on the constant Ps line which can be calculated from the flow in the inlet of the mixing chamber. Roughly one can also take Ps ¼ PE for primary prediction. As S5 ¼ SM , and from Eq. (4), SM ¼ XM ðSC00 SC0 Þ þ SC0
ð24Þ
Besides, h5 ¼ rE ðSS SS0 Þ=ðSS00 SS0 Þ þ h0S
ð25Þ
h5 ¼ rS ½XC ðSC00 SC0 Þ=fX þ ðSC0 SS0 Þ =ðSS00 SS0 Þ þ h0S
ð26Þ
So,
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and gEJ ¼ 1 DhEJ =fhM rS ½XC ðSC00 SC0 Þ=fX þ ðSC0 SS0 Þ =ðSS00 SS0 Þ þ h0S g
ð27Þ
Eq. (27) is the relation between dryness coefficient and enthalpy efficiency. So in the analysis and calculation fX could be estimated from the test results of ejector or from existed ejector loss model and data together with the thermodynamic parameters used.
5. Conclusion 1. A new separate heat pipe thermal jet refrigerator and heat pump is suggested and configurated. With the sub-cooled hot water as the first choice of the driving liquid, the new type of heat pipe refrigerator is feasible, compact and could be efficient in utilizing the low grade energy sources such as industrial waste heat, solar thermal etc. Development of efficient two-phase ejector is important in realizing practical device. 2. A method of thermodynamic performance analysis and calculation of the coefficient of performance with given three temperatures for such device is introduced. The analytical relation between refrigerator and heat pump for the same system is developed. For the same system and device, therefore, the working regime could be changed by regulation of the pressure level of PC and PE . 3. Primary performance calculation and configuration design performed show the feasibility of such device and further experimentation and development is underway working on.
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