Investigation of Energy Dissipation in an Ejector Refrigeration Cycle

Transcription

1 Ivestigatio of Eergy Dissipatio i a Ejector Refrigeratio Cycle Christia Tischedorf 1 Deise Jaotte 2 Ricardo Fiorezao 1 Wilhelm Tegethoff 2 1 Techical Uiversity Brauschweig, Departmet of Thermodyamics 2 TLK Thermo GmbH Has-Sommer-Straße 5, Brauschweig Germay c.tischedorf@tu-bs.de Abstract The preseted work focuses o the differeces i eergy dissipatio i each cycle compoet compared to the eergy dissipatio of the whole ejector refrigeratio cycle. With help of this aalysis, improvemet of eergetic efficiecy by usig a ejector ca be set i relatio to the potetial improvemet i efficiecy of other compoets such as heat exchagers. Iformatio about etropy productio associated with eergy dissipatio allows for a objective estimatio of the optimizatio potetial of each compoet withi a ejector refrigeratio cycle. I additio, the improvemet due to the specific process cotrol of the ejector cycle compared to the covetioal heat pump cycle ca be aalyzed. The eergetic beefit gaied usig a ejector depeds o the refrigerat used. The refrigerats R134a ad R744 (CO 2 ) were compared i regard to the etropy productio of the heat pump system. I order to simulate a ejector refrigerat cycle ad to evaluate the eergy dissipatio by meas of etropy productio, existig models for cycle compoets were modified. Applyig the secod law of thermodyamics, local distributio of etropy productio as well as the overall etropy produced i each compoet was determied. The aalysis showed that etropy productio is caused by two types of effects. Oe part results from real effects such as pressure drop ad heat trasfer, the other part is due to the modelig assumptios made. Thus, the ivestigatio of eergy dissipatio leads to a deeper uderstadig of the model. The simulated amout of etropy produced is summarized i a record, so that the results ca be read easily by other programs, e.g. programs that visualize eergy ad etropy flows. I the preseted ivestigatio the etropy flow ad dissipatio effects were aalyzed by meas of diagrams, such as Sakey diagrams. The complete heat pump system has bee simulated usig the Modelica library TIL (TLK-IfT-Library) i order to determie the eergy dissipatio i each cycle compoet. With the modified TIL models, other process cotrols ca also be ivestigated. This approach offers the opportuity to aalyze the eergy dissipatio i detail, ad differs i that sese from the commoly used techique of itegrated eergy balaces ad COP determiatios. Keywords: etropy aalysis; refrigeratio; compressio cycle; simulatio; CO2; R134a 1 Itroductio The pressure differece betwee the high ad low pressures i CO 2 refrigerat systems is high compared to other refrigerats, e.g. R134a. Previous ivestigatios by other authors have show that i a covetioal refrigeratio cycle, the pressure differeces cause sigificat throttlig losses. Usig a expasio valve results i a isethalpic throttlig process, which meas that the kietic eergy is completely dissipated ad the evaporatio ethalpy is reduced compared to a isetropic process. Usig a ejector is oe way to recover part of the lost kietic eergy ad to icrease refrigeratio capacity. As a result, the eergetic efficiecy (COP) of the refrigerat system will be improved. I additio to the improvemet caused by a ejector, the COP ca be raised by optimizatio of other cycle compoets. The key issues are the comparative cost effectiveess of the modificatios, as well as the questio of which compoets have the most optimizatio potetial. Therefore, a aalytical techique eablig oe to recogize optimizatio potetial is eeded i order to assess the alterative solutios. The required techique was developed durig the project preseted i this work. Oe approach to ivestigate the potetial is to ap- The Modelica Associatio, DOI: /ecp

2 ply the secod law of thermodyamics to determie the produced etropy i each refrigeratio cycle compoet, so that a basic aalysis of the compoet efficiecies is possible. This approach was itroduced i [Frake04]. I the preseted work, the ivestigatio was carried out usig the Modelica library TIL to simulate the refrigeratio cycles. TIL is a compoet library for steady-state ad trasiet simulatio of fluid systems such as heat pump, air coditioig, refrigeratio or coolig systems, developed by TLK-Thermo GmbH ad TU Brauschweig, Istitute for Thermodyamics [for a detailed descriptio see [Richter08]]. The advatage of TIL is that it has a very shallow iheritace structure, which makes the models easy to uderstad ad exted. The results of the etropy aalysis were visualized by bar ad Sakey charts usig the ewly developed software EergyViewer by TLK- Thermo GmbH, i order to simplify the iterpretatio of the effects. 2 Simulated Refrigeratio Cycle Figure 1: Object diagram of the simulated cycle I the preseted work, a ejector heat pump used for heatig water for domestic use ad floor heatig usig R744 or R134a as refrigerat was simulated. The pricipal fuctioality of a commo ejector refrigerat cycle is described i the followig literature [Elbel06]. For this ivestigatio, the commo ejector refrigeratio cycle was modified. A object diagram of the modified ejector refrigeratio cycle is show i figure 1. The cycle cosists of the followig compoets: gas cooler (R744)/ codeser (R134a), medium pressure evaporator (MP), low pressure evaporator (LP), valve, separator, compressor ad ejector. I additio, a temperature cotroller ad a super-heatig cotroller were added i the cycle. As well, a high pressure cotroller was added to the ejector compoet model. The heat pumps were simulated at the followig coditios. heatig capacity for both operatio modes: 5000 W temperature floor heatig water: 30 C to 35 C temperature domestic hot water: 10 C to 60 C overall heat trasfer capability gas cooler/codeser: 1400 W/K overall heat trasfer capability evaporator LP/MP: 500 W/K heat exchager pressure drop R744 refrigerat: 1 bar heat exchager pressure drop R134a refrigerat: 0,2 bar water mass flow rate evaporator equal for all simulatios water temperature of heat source 10 C high pressure set to optimize the coditios i the gas cooler/codeser (low mea drivig temperature differece) The water that serves as a heat source first flows through the evaporator MP ad afterward through the evaporator LP. The temperature cotroller cotrols the speed of the compressor, such that the desired output temperature is achieved by a costat water mass flow rate through the gas cooler or codeser. The cotroller itegrated i the ejector cotrols the high pressure level by settig the mass flow rate through the drivig ozzle. The cotroller determies a high pressure level, which ca be adjusted such that optimal coditios are foud i the gas cooler or codeser. The super-heatig cotroller is used to create optimal coditios i the evaporator LP. 3 Effects Causig Etropy Productio i the Cycle Compoets A importat distictio must be made betwee etropy productio caused by umerical errors based o The Modelica Associatio,

3 modelig assumptios ad the etropy produced due to real physical effects. The umerical errors deped o the mathematical model as well as o the degree of discretizatio whe usig a discretized model. The real physical effects deped o the quality ad the costructio of the refrigeratio cycle compoets ad ca be iflueced by the specific process cotrol. I additio to this, the produced etropy is depedet o the refrigerat used. I the preseted work the followig etropy producig effects geerated i the cycle compoets were ivestigated: Heat Exchager pressure drop, heat trasfer ad umerical errors (modelig) Valve pressure drop (isethalpic expasio) Compressor efficiecy based model Ejector special efficiecy based model Separator mixig effects 3.1 Heat Exchager Figure 2: Illustratio of cell structure of a tube The heat exchagers used for the ivestigatio cosist of tubes coected via heat ports. The umber of tubes ad the directio i which the medium flows through them ca vary. The maer of coectio specifies the kid of heat exchager. For this paper, couterflow heat exchagers cosistig of oe liquid ad oe refrigerat tube were used. The medium used i the liquid tube was water. The tubes are divided ito cells, ad each tube is comprised of two types of cells: wall cells ad fluid cells (see figure 2). The fluid cells ca be either liquid or refrigerat cells, depedig o the type of medium flowig through them. The coectio of fluid ad wall cells via heat ports allows the exchage of heat betwee the cells. The temperature of the coected heat ports of two cells are set equal. The heat trasfer iside the cell betwee the medium ad the heat port is determied by the heat trasfer relatio ad the heat trasfer coefficiet. I the cell model, equatios to determie the heat flow are implemeted. A similar modelig of heat trasfer ad fluid flow is preseted i [Patakar80]. The umber of wall ad fluid cells i each tube determies the degree of discretizatio (fiite volume approach). A itroductio to the fiite volume approach ca be foud i [Bauma06]. I order to model the etropy productio withi the heat exchagers, a hierarchical approach was followed. First the etropy productio due to the aforemetioed effects was determied for each cell of the heat exchager. The secod law of thermodyamics for a trasiet system yields: d(sm) dt = With d(sm) dt ṁ i s i + Ṡ Q + Ṡ Q prod + Ṡ p prod + ṠM prod (1) beig the chage of etropy of the cell. The terms ṁis i ad Ṡ Q specify the etropy coveyed by mass ad heat flows. Ṡ Q prod, Ṡ p prod, ṠM prod represet the etropy productio rate due to heat trasfer, pressure drop ad modelig respectively. Heat trasfer ad pressure drop are real effects that cause etropy productio, which ca be determied by formulas preseted later. The last productio term, however, is due to the modelig of the cell as a volume with costat medium properties such as ethalpy or temperature. For a fluid cell this ca be illustrated by the image of a agitator stirrig the medium iside the cell so that it is perfectly mixed. Because of the modelig assumptios, the ethalpy of the medium iside the cell matches the ethalpy at the outlet port of the cell. Likewise, the temperature of the medium iside the cell matches the temperature at the outlet port of the cell. If there is a temperature chage, this mixig of the cell cotet produces etropy. This etropy productio Ṡ M prod is umerical error ad differs from ṠMi,T prod the etropy productio due to mixig of two streams of ideal gas ṁ a ad ṁ b with temperature T a ad T b respectively which is preseted i [Cerbe07] as follows: prod = ṁ ac ma t Mi t a l T Mi + ṁ b c mb t Mi t T b l T Mi (2) a T b Ṡ Mi,T with T Mi beig the mixig temperature ad c m the mea specific heat capacity of stream a or b. Hece Ṡ M prod has to be determied via the secod law. Trasformig equatio 1 ad settig dm dt = ṁi yields: The Modelica Associatio,

4 This formula ca be liearized Ṡ M prod = m ds dt ṁ i (s i s) Ṡ Q Ṡ Q prod Ṡ p prod (3) The idex i labels the variables of stream i flowig i or out of the cell. The variables of the medium iside the cell do ot have idex labels. Each fluid cell has oly oe ilet ṁ i ad oe outlet stream ṁ out. The modelig assumptio yields s = s out so that the equatio ca be simplified further. Ṡ M prod = m ds dt ṁ i(s i s) Ṡ Q Ṡ Q prod Ṡ p prod (4) Without heat trasfer ad pressure drop, there ca still be etropy produced by cotiuously mixig the fluid iside the cell. I the case that the specific etropy at ilet ad iside the cell are ot equal, the last term i the equatio does ot reduce to zero. This occurs if the temperatures are ot equal because the specific etropy depeds o pressure ad temperature. Ṡ M prod = m ds dt ṁ i(s i s) (5) Each fluid cell emits a heat flow Q at the heat port with the temperature T hp. This flow coveys etropy that ca be determied by the followig equatio. Ṡ Q = Q T hp (6) Before beig emitted, the heat flow is trasferred from the medium iside the cell (temperature T ) to the heat port (temperature T hp ). The temperature gradiet betwee T hp ad T is determied by the heat trasfer relatio ad the heat trasfer coefficiet. I the cell model, the equatios for the heat trasfer pheomea are implemeted. This heat trasfer causes etropy productio, which ca be determied accordig to [Beja88] as follows. Ṡ Q prod = Q T Q (7) T hp Pressure drop betwee the ilet ad outlet port also leads to etropy productio. It ca be determied as preseted i [Beja88]. i Ṡ p prod = ṁ v T d p (8) h=cost out Ṡ p prod = ṁ v p (9) T p represets the pressure drop. Equatio 1 has to be adapted for the determiatio of the etropy productio iside a wall cell. Sice there is o medium flowig through the wall cell, there are o terms for etropy trasportatio via mass flow, ad o pressure drop occurs. The etropy productio due to the modelig of the wall cell ca be determied accordig to the followig equatio: Ṡ M prod = m ds dt Ṡ Q Ṡ Q prod (10) Heat ca be emitted at each of the heat ports i with the overall etropy coveyed because of heat flow beig Ṡ Q = ṠQ,i. Each of the summads Ṡ Q,i ca be determied accordig to equatio 6. The heat trasfer from the medium iside the cell to oe heat port or vice versa causes etropy productio. Each productio term Ṡ Q prod,i ca be determied i accordace with equatio 7 ad has to be summed i order to determie the overall etropy productio due to heat trasfer, Ṡ Q prod = ṠQ prod,i. The etropy productio resultig from modelig assumptios Ṡ M prod (see equatio 10) represets oly small umerical errors. There is o mixig iside the wall cell ad the term Ṡ M prod ca be eglected. I order to calculate the etropy productio due to each effect for the whole tube, the results of the etropy productio i the cells are summed. The results of the refrigerat ad the liquid tube are the summarized to determie the etropy produced withi the whole heat exchager. 3.2 Valve I the valve model (cotrol valve) the refrigerat is throttled adiabatically. It is assumed that the kietic eergy of the flowig refrigerat is completely dissipated. Sice the valve has bee modeled as a compoet without volume, the secod law for the valve has be applied i the steady state form. ṁ i s i + Ṡ T prod = 0 (11) As the mass flow rate ṁ i ad the specific etropy s i at the ilet ad outlet ports are kow, this equatio is used to determie the overall produced etropy. The Modelica Associatio,

5 Proceedigs 7th Modelica Coferece, Como, Italy, Sep , 2009 S Tprod = m i si (12) 3.3 Compressor The compressor model is based o a efficiecy model with isetropic, volumetric ad effective isetropic efficiecy. Furthermore, a heat flow from the housig surface to the surroudigs is cosidered, but is set to zero i the simulatio. The mai etropy productio i the compressor is caused by the followig loss mechaisms, which result from the compressio process of a reciprocatig type compressor. These are: frictio losses due to mechaical compoets such as pistos ad pisto rigs ad swash plate, throttlig losses that take place i the valves, flow chaels ad chambers, the heat trasfer betwee the differet compressor compoets, e. g. the suctio ad discharge chamber, the leakage losses ad losses caused by the cotrol valve. Sice the compressor is modeled as a volumeless compoet, the secod law for the compressor has to be applied i steady state form: m i si + S Q + S Tprod = 0 (13) Figure 3: Exploded view of a ejector the exchage of mometum is ot ideal ad etropy will be produced, the ejector ca partly recover the kietic eergy. However, the etropy produced has ot bee determied i detail for this work. A simplified approach has bee used istead, ad the etropy productio rate for steady state has bee determied as the differece betwee ilet ad outlet etropy flow rates accordig to the secod law i steady state. S Tprod = m i si (14) 3.5 Separator The separator model is similar to the refrigerat cell model apart from the fact that o heat trasfer or press Q specifies the etropy flow that is discharged with sure loss is cosidered, ad that the refrigerat is ot the heat flow. mixed, but separated ito liquid ad gaseous phase. The etropy productio rate is determied by the fol3.4 Ejector lowig equatio. Whe a medium is throttled i a covetioal valve, frictio losses occur ad the kietic eergy of the medium is completely dissipated. I a ejector, however, the kietic eergy of a primary flow at high pressure ca be partly used to compress a secodary flow ad thus to dimiish the compressio work doe i the compressor. Figure 3 illustrates the fuctioality of a ejector. The drivig flow exits the drivig ozzle with a high velocity ad carries with it a flow from the suctio ozzle. Sice the cross sectio of the suctio ozzle becomes progressively arrower, the suctio flow is accelerated ad the pressure drops. Both the suctio ad drivig flows exchage mometum, are mixed i the mixig tube ad flow through a diffuser before leavig the ejector. The pressure iside the diffuser icreases with decreasig velocity. The ejector is modeled usig a aalogous model cosistig of several separate compoets. Because The Modelica Associatio, 2009 S Tprod = m ds m i si dt (15) As there are o effects producig etropy S Tprod is equal to zero. 3.6 Implemetatio of Etropy Productio i TIL I the Modelica library TIL, the specific etropy s is implemeted as a fuctio of p ad h. I order to reduce the idex of the differetial algebraic equatio system, the terms i the etropy equatio have to be expressed by meas of state variables used for the descriptio of the system. This implies that the term ds dt (derivative of the specific etropy with respect to time) had to be rewritte i terms of p ad h. To trasform the equatio Bridgema tables, which ca 308

6 be foud i [Beja88] were used. This made the implemetatio more umerically effective by ot relyig o Dymola for the rearragemet of the equatio system. The discussed mathematical equatios to determie the etropy productio were implemeted i each model. The collectio of the results i the summary records simplifies the readout by other programs used to aalyze the results. 4 Visually Supported Aalysis of Simulatio Results The simulatio results were aalyzed with the help of 2d-plots which show the temperature relatios, ad Sakey diagrams which show the etropy flow beside the productio rates. Therefor the etropy flows at the ilet ad outlet port of each compoet were determied. The etropy productio caused by heat trasfer, pressure drop, umerical errors due to modelig ad the overall etropy productio were calculated accordig to the aforemetioed equatios ad illustrated by bar charts. The visualized etropy flows were ormalized for each medium such that the flow with the lowest specific etropy is equal to zero. With the help of the Sakey diagrams, the etropy shift withi the flows is visualized, ad for each medium the relatio of the etropy flows betwee the compoets becomes clear. Sakey diagrams are a powerful visualizatio method to aalyze all kid of flows. A detailed discussio of the applicatio of Sakey diagrams ca be foud i [Schmidt06]. Figure 4: Temperature profile of refrigerat, liquid ad wall cells iside the codeser (R134a domestic hot water) Figure 5: Temperature profile of refrigerat, liquid ad wall cells iside the gas cooler (R744 domestic hot water) 4.1 Etropy Productio i Heat Exchagers The diagrams i figures 4 ad 5 illustrate the temperature curves i the gas cooler (R744) ad the codeser (R134a) of a steady-state ejector refrigeratio cycle for domestic hot water. It ca be clearly see that the temperature glide i the gas cooler (R744) leads to a lower mea drivig temperature differece i the gas cooler tha i the codeser (R134a). I the evaporators, the refrigerat is evaporated at a early costat temperature ad exits the heat exchagers with low superheatig, which is cotrolled by the cotroller. This results i a lower mea drivig temperature differece ad lower etropy productio due to heat trasfer i the evaporators. See figure 7 ad 9 for etropy productio i the evaporators i relatio to etropy productio i the gas cooler / codeser. I figure 6 the profile of etropy productio due to differet effects is illustrated for the cells of the gas cooler. The cor- Figure 6: Profile of etropy productio iside the gascooler (R744 domestic hot water) respodig temperature profile is show i figure 5. Wherever high temperature differeces occur, the produced etropy due to heat trasfer ad mixig (modelig assumptio) is high. The etropy productio rate due to pressure drop is low i compariso to the productio rate due to heat trasfer ad mixig. The Modelica Associatio,

7 flow rate ad the refrigerat mass flow rate are greater. That shows that the R744 ejector refrigeratio cycle is better suited to heat water up to higher temperatures. 4.3 Compariso R744 ad R134a Ejector Cycle for Domestic Hot Water Figure 7: Etropy flow ad productio rate i a R744 heat pump cycle used to heat up hot domestic water. Etropy productio rate due to heat trasfer (Ṡ Q ), pressure drop (Ṡ p ), modelig (Ṡ M ) ad total etropy productio rate (Ṡ T ) for each compoet are represeted by bar charts. The etropy flow is ormalized to the lowest specific etropy of each medium. Etropy productio ad flows are represeted i differet scales. 4.2 Compariso R744 ejector cycle for domestic hot water ad floor heatig The figures 7 ad 8 show the Sakey diagrams of a steady state R744 ejector refrigeratio cycle for domestic hot water ad floor heatig operatio respectively. First, lookig at the gas cooler, it is show that the etropy productio caused by heat trasfer i the case of floor heatig operatio is higher tha i the case of domestic hot water operatio. This is due to the higher drivig temperature differece i the gas cooler i the floor heatig operatio. However, the etropy productio caused by mixig (modelig assumptio) i the case of floor heatig operatio is lower tha i the case of domestic hot water operatio, despite the greater refrigerat ad water mass flow rates. The reaso for this is the lower temperature gradiets betwee the ilet ad outlet of the refrigerat as well as liquid tubes. With the heatig capacities equal i both the floor heatig ad domestic hot water operatio modes, i the floor heatig mode, the compressor ad the ejector produce more etropy, although the water mass The Sakey diagrams of a steady state R744 ad R134a ejector refrigeratio cycle for domestic hot water mode are illustrated i figure 7 ad 9. The results show that etropy productio caused by heat trasfer i the codeser (R134a) is sigificatly higher tha i the gas cooler (R744). This is due to the higher mea drivig temperature differece betwee the refrigerat ad the water i the codeser. The temperature curves i the codeser ad the gas cooler are illustrated i figure 4 ad 5. Because of the temperature glide i the gas cooler, the mea drivig temperature differece is lower. For the same reaso, the etropy productio resultig from mixig (modelig assumptio) is also higher i the codeser. I the R744 refrigeratio cycle, productio of etropy i the compressor ad ejector is higher, the reaso for this beig the differet refrigerat properties ad process cotrols. Because of this, the pressure differece betwee the high ad low pressure level i the R744 refrigeratio cycle is higher. A ejector heat pump usig R744 as refrigerat is suited to supply domestic hot water better tha a heat pump usig R134a, if particular attetio is directed to the etropy productio i the codeser or gas cooler. I additio, the eergy savig potetial with a ejector is higher i a R744 cycle tha i a R134a cycle. 5 Coclusios ad Outlook The preseted work shows how a aalysis of the dissipatio effects i thermodyamic systems ca be doe with the help of simulatio. For this purpose the equatios are preseted which are eeded to mathematically describe the observed etropy-producig pheomea. I particular, the etropy productio i the heat exchagers is examied. Etropy productio resultig from heat trasfer, pressure drop ad umerical error due to modelig are observed. Usig the example of a ejector heat pump, it is show how the resultig simulated etropy productio ca be visualized ad used i the dissipatio aalysis. The aalysis is carried out usig bar diagrams, Sakey diagrams ad 2d-plots. Heat pumps usig R134a ad R744 were compared for both domestic water heatig ad floor The Modelica Associatio,

8 to research whether the boudaries of the system ca be altered to produce a eve better aalysis or ot. I additio, it is plaed to carry out a more detailed aalysis of etropy productio withi the ejector model. Refereces [Bauma06] Bauma W., Buge U., Fredrich O., Schatz M., Thiele F. Fiite-Volume-Methode i der Numerische Thermofluiddyamik. Techische Uiversität Berli, Istitut für Strömugsmechaik ud techische Akustik: Vorlesugsmauskript, Berli, [Beja88] Beja A. Advaced Egieerig Thermodyamics. Joh Wiley & Sos, New York, Figure 8: Etropy flow ad productio rate i a R744 heat pump cycle used to heat water for floor heatig. [Beja02] Beja A. Fudametals of Exergy Aalysis, Etropy Geeratio Miimizatio, ad the Geeratio of Flow Architecture. I: Iteratioal Joural of Eergy Research vol.26 o.7 p , [Cerbe07] Cerbe G., Wilhelms, G. Techische Thermodyamik, Haser Verlag, Müche, [Elbel06] Elbel S., Hrjak P. Developmet of a Prototype Refrigerat Ejector used as Expasio Device i a Trascritical CO2 System,Presetatio VDA Alterative Refrigerat Witer Meetig Saalfelde, [Frake04] Frake U. Thermodyamische Prozessaalyse: Ursache ud Folge der Irreversibilität. Shaker, Aache, [Patakar80] Patakar S. Numerical Heat Trasfer ad Fluid Flow. Hemisphere Publ. Co, New York, Figure 9: Etropy flow ad productio rate i a R134a heat pump cycle used to heat domestic hot water. heatig. The ivestigatio shows that the heat pump with R744 is better suited for domestic hot water operatio. It is show that this aalysis method is suitable for ivestigatio of thermodyamic systems o the basis of etropy productio. I the future, it is plaed [Richter08] Richter C. Proposal of New Object- Orieted Equatio-Based Model Libraries for Thermodyamic systems. Brauschweig, Germay: PhD Thesis, Departmet of Mechaical Egieergig, Istitute of Thermodyamics, TU Brauschweig, [Schmidt06] Schmidt M. Der Eisatz vo Sakey- Diagramme im Stoffstrommaagemet. Beiträge der Hochschule Pforzheim, Nr. 124, Pforzheim, The Modelica Associatio,