Numerical Evaluation of Thermal Performances of Diffusion

Energy Conversion and Management 152 (2017) 201–213

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Energy Conversion and Management

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Numerical evaluation of thermal performances of diﬀusion–absorption MARK refrigeration using 1,3-dimethylimidazolylium dimethylphosphate/ methanol/helium as working ﬂuid ⁎ Bin Zhang, Wei Chen , Qiang Sun, Zhanli Miao

College of Electromechanical Engineering, Qingdao University of Science & Technology, Qingdao 266061, China

ARTICLE INFO ABSTRACT

Keywords: The thermal performances of diffusion–absorption refrigeration using 1,3-dimethylimidazolylium dimethyl- Diffusion–absorption refrigeration phosphate/methanol/helium as working fluid were numerically analyzed. The operating characteristics of Ionic liquid bubble pump, boiler, and evaporator were investigated. The variations in the coefficient of performance and ffi Coe cient of performance exergy efficiencies with different heat inputs of the bubble pump and boiler were simulated and discussed. The Exergy efficiency thermal performances were compared with those of the butane/nonane/helium and lithium bromide/water/ helium systems. The trend of variation in coefficient of performance is accordance to that of the experimental results for butane/nonane/helium system. The optimal coefficient of performance of the proposed system was lower than that of the lithium bromide/water/helium system. But the proposed system possessed the advantages of non-crystallization and non-corrosion, and it could operate at a higher boiler temperature. The exergy losses of each component were calculated and compared with one another. The largest four exergy losses occurred in the condenser, absorber, boiler, and bubble pump, which accounted for approximately two thirds of the total exergy input. The main reason for the exergy loss of the diffusion absorption refrigeration system was the heat transfer with temperature difference.

1. Introduction non-corrosion, non-crystallization, high thermal stability, and negli- gible vapor pressure [7]. A series of studies has proven that the ILs with Absorption refrigeration provides cooling driven by medium- and imidazolyl cations are excellent alternatives for the traditional absor- low-grade heat sources [1]. This process has been applied in the energy, bents in traditional absorption system [8]. Dong et al. [9] inspected the pharmaceuticals, food, chemical industry, and biological engineering latent application of IL/H2O in absorption refrigeration. Liang et al. disciplines. The absorption refrigeration using traditional working fluid [10] investigated the possibility and potential of using alcohols in ionic of lithium bromide (LiBr)/water (H2O) [2] is the most mature absorp- liquid absorption refrigeration. Yokozeki et al. [11] studied the thermal tion system with the application history of several decades. However, performance of absorption refrigeration using ILs as absorbent and the LiBr/H2O solution is corrosive at high temperature, and is prone to Freon as refrigerant. Ángel et al. [12] simulated the theoretical cycle of crystallize at low temperature [3]. The absorption refrigeration using absorption refrigeration using 1-butyl-3-methylimidazolium hexa- traditional working fluid of ammonia (NH3)/water (H2O) [4] is another fluorophosphate ([bmim]PF6)/carbon dioxide (CO2) as working fluid. widely used absorption system. For the H2O/NH3 systems, the using of Shiflett et al. investigated the thermal performances of IL absorption the rectifier is unavoidable, which will result in the deterioration of refrigeration using NH3 [13] as refrigerant. It is indicated that ab- thermal performances [5]. In a word, the development and application sorption refrigeration using 1,3-dimethylimidazolylium dimethylpho- of traditional absorption refrigeration are limited by the inherent de- sphate ([mmim]DMP)/methanol (CH3OH) as working fluid possesses fects of the binary solutions of NH3/H2O and LiBr/H2O. excellent theoretical cycle characteristics [14]. Absorption refrigeration using ionic liquids (ILs) as absorbent has Absorption refrigeration systems are two level pressurized systems become a research hotspot in recent years [6]. IL is a type of organic with pressure difference between the condenser and the evaporator. salt existing as liquid form at room temperature. This organic salt is The pressure difference makes the solution pump become an indis- favorable solvent with distinctive physical and chemical properties of pensable device for the absorption system. The solution pump is a

⁎ Corresponding author at: Songling Road 99, Qingdao, China. E-mail address: [email protected] (W. Chen). http://dx.doi.org/10.1016/j.enconman.2017.09.048 Received 21 May 2017; Received in revised form 15 September 2017; Accepted 16 September 2017 0196-8904/ © 2017 Published by Elsevier Ltd. B. Zhang et al. Energy Conversion and Management 152 (2017) 201–213

Nomenclature Greek symbols

AU total heat conductance (kJ/K) α void fraction

cp specific heat capacity (kJ/(kg·K)) ϕ volume flow ratio g gravity (m2/s) η efficiency

G1, G2 intermediate function for DAR model ϕlo friction factor h specific enthalpy (kJ/kg), height (m) ηex exergy efficiency k local resistance coefficient ρ density (kg/m3) L length (m) σ surface tense (N/m)

Lb latent heat (kJ/kg) τ slip ratio H lift height of bubble pump (m) ω mass fraction p pressure (kPa)

qm mass flow (kg/s) Subscript 3 qV volume flow (m /s) Q heat flow (kW) 1,2…16 status point s specific entropy (kJ/(kg·K)) 298.15 at 298.15 K

Sgen entropy production (kJ/K) A absorber T temperature (K) B boiler C condenser List of abbreviations E evaporator GHX gas heat exchanger COP coeﬃcient of performance IL ionic liquid

C4H10,C9H20 butane, nonane L liquid CH3OH methanol p ﬁxed pressure DAR diﬀusion absorption refrigeration R refrigerant

H2, He hydrogen, helium SHX solution heat exchanger IG inert gas SC sub-cooler IL ionic liquid V vapor

LiBr/H2O lithium bromide/water [mmim]DMP 1,3-dimethylimidazolylium dimethylphosphate/me- Superscript thanol VLE vapor-liquid equilibrium E excessive parameter S saturation mechanical device with moving parts and is driven by electric power In this study, a mathematical model of bubble pump is established [15]. The consumption of electric power obviously increases the op- considering the vapor–liquid equilibrium (VLE) of the [mmim]DMP/ erational costs of the absorption system. Platen and Munters invented CH3OH system and the conservations of mass, momentum, and energy. the diffusion–absorption refrigeration (DAR) in the1920s to overcome The transport characteristics of bubble pump are studied. The steady the aforementioned shortcomings [16]. The DAR system operates at a modeling and simulation of the DAR system using [mmim]DMP/ uniform pressure [17]. In addition to the absorbent and the refrigerant, CH3OH/He as working fluid are conducted based on the model of an auxiliary inert gas (IG), usually helium (He) or hydrogen (H2) [18], bubble pump. The thermal performances of the DAR system and the is injected to the DAR system to keep the pressure balance of the con- exergy losses of each component are investigated and discussed. denser and evaporator. The solution pump in absorption refrigeration is taken place by the bubble pump [19], which is driven by heat sources. The most significant advantage of the DAR over the absorption re- 2. Thermodynamic properties frigeration is its zero electric power consumption [20]. Therefore, the

DAR system can be used in areas without electricity. The VLE of [mmim]DMP/CH3OH is the most essential property of In the prototype system proposed by Platen and Munters, the the DAR system. This property determines whether the [mmim]DMP/ working fluid is NH3/H2O/H2 with H2 as IG. Kouremenos et al. [21] CH3OH/He mixture can be used as working fluid for the DAR system. studied the thermal performance of the DAR system using He as IG. The The VLE of [mmim]DMP/CH3OH can be predicted using the universal simulation results of Zohar et al. [22] indicated that the coefficient of quasichemical functional group activity coefficient (UNIFAC) model performance (COP) of the DAR system using He as IG was 40% higher [24]. than that of the system using H2 as IG. Zohar et al. [23] also studied the The specific enthalpies and entropies of the [mmim]DMP/CH3OH effects of condensate subcooling on the thermal performance of the solution and the gas mixture of CH3OH/He are indispensable properties DAR system. The subcooling was found to be not conducive to the to the calculation of the thermodynamic performances of the DAR system. For DAR systems using NH3/H2O/IG as working fluids, the system. The specific enthalpy of the [mmim]DMP/CH3OH solution can vapor phase from the generator contains both NH3 and H2O, which be calculated by makes the rectifier an indispensable device for the DAR system. Chen T T T et al. [16] found that the heat loss in the rectifier of the DAR system was E hω=+++1 ∫∫ cdTωp,IL 2 cdThp,R 298.15 ∫ cdTp (1) the greatest factor leading to the decrease in the thermal performance. 273.15 273.15 298.15 In view of the excellent thermal performances of the IL absorption The specific entropy of the [mmim]DMP/CH OH solution can be system, ILs can also be used as the absorbent in the DAR system, which 3 calculated by [14] makes the DAR system avoid using the rectifier. Therefore, the DAR using IL as absorbent should possess good cycle characteristics.

202 B. Zhang et al. Energy Conversion and Management 152 (2017) 201–213

T T E [mmim]DMP/CH3OH solution. The points in Fig. 2 show the para- sω=++1 ∫∫( cp,IL / TdTω ) 2 ( cTdThp,R / )298.15 /298.15 273.15 273.15 meters of the critical status. The marked numbers in Fig. 2 are in ac- T cordance with those in Fig. 1. The arrow (9, 10) stands for the process + ∫ (/)cTdTp (2) 298.15 of solution lift in the bubble pump. The arrows (10, 1) and (10, 2) stand E ω where h298.15 is the excessive enthalpy of the solution at 298.15 K. 1 for the solution concentration process and the gasification process in and ω2 are the mass fractions of the [mmim]DMP and CH3OH of the the boiler, respectively. The arrows (2, 4) and (7, 4) represent the solution, respectively. cp,IL and cp,R are the specific heat capacities of evaporation and diffusion processes in the evaporator. The arrows (12, [mmim]DMP and CH3OH. cp is the specific capacity of the [mmim] 14) and (16, 9) represent the heat exchange process in the SHX. The DMP/CH3OH solution. The expressions of the specific heat capacities arrows (4, 5) and (6, 7) represent the heat exchange process in the GHX. are listed in Appendix A. The arrows (5, 6) and (15, 16) stand for the absorption processes of the

The speciﬁc enthalpy of the gas mixture of He and CH3OH is cal- vapor and liquid phases, respectively. culated by 4. Modeling and simulation TS T T hw=+2 () cdTLpR,b++ cdTwpv , 3( cdTp,He ) ∫∫∫273.15 TS 273.15 (3) The thermal bubble pump is an essential component of the DAR

The specific entropy of the gas mixture of He and CH3OH is calcu- system and is used to circulate solution in the system. Therefore, the lated by mass transport model of the bubble pump is described separately. The DAR system can be stably modeled on the basis of the mass transport TS T S s=+ w2 ( ( cpR,b /) T dT L / T+ ( cpv, /) T dT) model of the bubble pump by considering the mass, momentum, and ∫∫273.15 TS T energy conservations of each system component. + wcTdT3 ((/))p,He ∫273.15 (4) 4.1. Mass transport model of bubble pump S where T is the saturation temperature. w2 and w3 are the mass fractions of the [mmim]DMP and He of the vapor phase, respectively. cp,v is the In the bubble pump, the refrigerant is desorbed from the solution fi speci c heat capacity of CH3OH vapor at constant pressure. Lb is the and forms bubbles in the solution with the input of heat to the bubble latent heat of CH3OH. The latent heat can be predicted by the Chen pump. The bubbles in the solution will decrease the density of the fi equation [25], which is also listed in Appendix A. cp,He is the speci c working fluid in the narrow tube. The two-phase working fluid flows up heat capacity of He. The properties of He are close to those of the ideal the narrow tube because of the density difference between the fluids in gas under the temperature and pressure conditions of the DAR system. the reservoir and in the narrow tube. The mass transport model of the fi Therefore, the speci c heat capacity of He can be set to a constant of bubble pump is developed on the basis of the momentum conservation 5.1391 kJ/(kg·K). of the two-phase working fluid, which is listed in Appendix B.

3. System description 4.2. Stable modeling of diﬀusion absorption refrigeration

Fig. 1 presents the schematic of a DAR system. The DAR system To establish the stable model of the DAR system, several assump- consists of a reservoir, a bubble pump, a boiler, a condenser, an eva- tions are presented as follows: porator, an absorber, a solution heat exchanger (SHX), a gas heat exchanger (GHX), and a sub-cooler. In the DAR system, CH3OH is the (1) Simulation of the DAR system is conducted on the steady-state refrigerant, and [mmim]DMP is the absorbent. The [mmim]DMP/ conditions.

CH3OH with a low IL concentration (weak solution) from the reservoir (2) The vapor pressure drops in tubes and the diffusion process are is lifted to the boiler by the bubble pump. The bubble pump is driven by the heat. In the boiler, the weak solution is heated again by the heat source to produce high-pressure CH3OH vapor. Meanwhile, the IL concentration of the solution rises, because the refrigerant CH3OH is desorbed from the solution. The solution with a high IL concentration is called strong solution. Because of the diffusion effect, the CH3OH mo- lecular in the vapor phase transports from the boiler to the condenser, where the CH3OH vapor is condensed into saturated liquid. The saturated CH3OH liquid flows to the evaporator. The strong solution passes through the SHX and the sub-cooler because of gravity before finally flowing into the absorber. From Fig. 1, it can be found that a gas loop is constituted by the evaporator, absorber, GHX, and reservoir. In the absorber, the strong solution absorbs the vapor CH3OH molecules, which leads to a decrease in the CH3OH partial pressure in the IG. The decrease in the CH3OH partial pressure results in a decrease in the density of the vapor phase in the absorber because the density of CH3OH is higher than that of He in the same pressure. Therefore, the IG in the absorber rises to the evaporator. The liquid CH3OH from the condenser begins evaporating in a very low temperature because the CH3OH partial pressure of the IG is very low. After the absorption, the strong solution from the boiler be- comes a weak solution and flows back to the reservoir. Fig. 2 presents the thermodynamic cycle of the DAR system in the P-

T diagram of [mmim]DMP/CH3OH. The black curves, marked by x2, show the relationship of CH3OH partial pressure and temperature in Fig. 1. Schematic of a DAR system. diﬀerent CH3OH mass fractions, which is drawn based on the VLE of the

203 B. Zhang et al. Energy Conversion and Management 152 (2017) 201–213

pump are veriﬁed. Based on the veriﬁcation results, the assumed values

of T10 and qm,9 are adjusted using the dichotomy method until the calculation results are convergent. Similarly, given the assumed values

of T11 and qm,11, the parameters of ω11, T12, qm,13, and T15 can be calculated on the basis of the vapor–liquid equilibrium of the boiler and the energy conservation of the SHX. Then, the mass and energy conservation of the boiler are veriﬁed. On the basis of the veriﬁcation re-

sults, the assumed values of T11 and qm,11 are adjusted using the Newton–Raphson method until the calculation results are convergent.

The ﬁrst derivatives of T11 and qm,11 are calculated with the small elemental changes of ΔT11 and Δqm,11. The calculation principles of T7 and T5 are the same as those of T10, qm,9, T11, and qm,11. In addition, T7 and T5 are adjusted using the dichotomy method. To equalize T8 and T16, an algebraic constraint module is created in Simulink, and an ODE45 (Dormand–Prince) solver is used. The entire simulation is con-

vergent once T8 is equal to T16.

Fig. 2. Thermodynamic cycle of the DAR system in P-T diagram. 5. Results and discussion

neglected, which means that the partial pressure of the boiler is The simulation results for DAR system using [mmim]DMP/CH3OH/ fl – ff equal to that of the condenser. He as working uid are presented in Figs. 4 12. The e ects of heat (3) The refrigerant flowing out of the evaporator is in the saturated input on the characteristics of the bubble pump, the boiler, the eva- vapor phase. porator and the thermal performances of the DAR system are described (4) The mass flow of the gas loop is determined by the refrigerant and discussed. In addition, the exergy analysis for the DAR system is evaporation rate in the evaporator and the refrigerant concentra- also conducted. tions of points 4 and 7 [26]. ff (5) The absorption efficiency for the absorber, ηab, is set to 0.75 [26]. 5.1. E ects of heat input on the characteristics of the bubble pump (6) The heat losses in high-temperature components and the cold loss in the evaporator are neglected. Fig. 4 presents the mass transport performance of the bubble pump with submergence ratios (h/H) of 0.25, 0.30, 0.35, and 0.40. An in- Given the above assumptions, the DAR system can be stably mod- crease in the volumetric flow of the liquid phase, results in an increase eled on the basis of the mass, momentum, and energy conservations of in the volumetric flow of the vapor phase, and the increase rate shows a each system component. The detailed modeling of the proposed system rising trend. On fixed qV,10V, the qV,10L decreases with a decrease in the is presented in Appendix C. submergence ratio. The DAR system is a self-balancing system that does not use any The mass transport model of the bubble pump indicates that the electronic control device. The operating conditions of the DAR system increase in the qV,10L leads to an increase in the slip ratio, the ratio of are directly determined by the heat inputs (Qp, QB) and the total qV,10V and qV,10L, which results in an increase in qV,10V. The value of thermal conductance of each component. A basic design of the oper- qV,10L is gradually approaching the constant with continuously rising ating conditions is proposed by referencing to the literature [27] to qV,10V. The mass transport capability of the bubble pump is hence make the setting of the total thermal conductance of each component, limited. as shown in Table 1. The heat flow and the temperature difference of When the submergence ratio drops, the void fraction of the lift tube each component can be easily calculated based on the design of oper- should increase to maintain the pressure difference, which drives the ating condition. The total thermal conductance of each component is flows of the bubble pump. The increase in the void fraction will lead to determined and fixed for the simulation, which is shown in Table 2. a decrease in qV,10L. Therefore, the high submergence ratio is conducive to the mass transport of the bubble pump.

Fig. 5 shows the variation trends of qV,10L and qV,10V in function of 4.3. Calculation algorithm of the simulation Qp and QB obtained from the simulations, namely, (a) Qp, (b) QB. Fig. 5(a) depicts that qV,10L and qV,10V rise with an increase in Qp. And Fig. 3 presents the detailed calculation algorithm of the DAR system. the growth rate of qV,10L decreases, but the growth rate of qV,10V in- Several parameters, including T7, T5, T8, T10, T11, qm,9, and qm,11 are creases. Fig. 5(b) illustrates that qV,10L and qV,10V rise with an increase determined by iterative methods given that the DAR system is self- in QB. balancing. The assumed input values of the parameters above are used The increase in Qp causes an increase in the vapor production in the for calculation. Then, the assumed values of these parameters are ad- bubble pump and in the temperature of [mmim]DMP/CH3OH solution. justed until the calculation results are convergent. The entire simulation Therefore, qV,10V rises. The increase in the [mmim]DMP/CH3OH of the DAR system is conducted with MATLAB/Simulink. The structural parameters and the meteorological parameters of the DAR system and Table 1 ﬂ the thermodynamic parameters of the working uids are initially in- Proposed operating conditions of the basic design. putted. The operation conditions of Qp, QB, Psys, T0, and Tcool are the Variable Value/K Variable Value/K initialized. For the simulation, the values of Psys, T0, and Tcool are set to 100 kPa, 303.15 K, and 286.15 K, respectively. T1 377.2 T9 348.3 The assumed values of T , T , T , q , and q are set in ac- 8 10 11 m,9 m,11 T2 315.3 T11 377.2 cordance with the proposed operating conditions of the basic design. T3 280.7 T13 377.2 T 302.8 T 338.5 Given the assumed values of T10 and qm,9, the parameters of T9, qm,10L, 5 14 T6 315.4 T15 315.7 ω10, uv, and uL can be calculated on the basis of the energy conservation T 291.8 T 311.8 of the SHX and the mass transport model of the bubble pump. Then, the 7 16 T8 315.5 Tcool 286.15 vapor–liquid equilibrium and the energy conservation of the bubble

204 B. Zhang et al. Energy Conversion and Management 152 (2017) 201–213

Table 2 Determination of the total thermal conductance of each component.

Component (j) Expression of ΔTj Qj/W ΔTj/K (AU)j/(W/K)

Condenser (TT1 −−−0)( TT20) 436.3 34.25 12.74 ln[(TT1 −−0)/( TT20)] Evaporator TTcool− 3 83.8 5.45 15.38 Absorber (TTTTT15+++ 16 5 6)/4 − 0 77.9 8.28 9.41 GHX (TT6 −−−5)( T7 T4) 84.7 11.74 7.21 ln[(TT6 −−5)/( T7 T4)] SHX (TT11 −−9)( TT14 − 8) 271.7 25.84 10.51 ln[(TTTT11 −−9)/( 14 8)] Sub-cooler (TT14−− 0)( TT15 −0) 169.6 18.97 8.94 ln[(TTTT14−− 0)/( 15 0)] solution temperature leads to decreased viscosity in the liquid phase.

The increase in qV,10V and the decrease in viscosity finally result in increased qV,10L. The increase in the volume flows of the liquid and vapor phases causes an increase in the slip ratio. The increase in the slip ratio is Fig. 4. Mass transport performance of the bubble pump. conducive to the vapor transport but is not conducive to the liquid transport. Therefore, the growth rates of qV,10L and qV,10V show dif- of QB with Qp of 0.1, 0.2, 0.3, 0.4, and 0.5 kW, namely, (a) qm,10, (b) ferent trends. T10, (c) x2,10. Fig. 6(a) indicates that the total mass flow entering the The growth of QB causes an increase in T11, which leads to an in- boiler, qm,10, rises with increases in QB and Qp. Fig. 6(b) implies that the crease in the inlet temperature of the bubble pump (T9). The growth of temperature of the solution and vapor entering the boiler, T10, increase T9 is conducive to the vapor production in the bubble pump and finally with an increase in QB. Fig. 6(c) presents that the refrigerant mole leads to increases in qV,10L and qV,10V. fraction of the solution out of the bubble pump, x2,10, decreases with an increase in QB and a decrease in Qp. ff 5.2. E ects of heat input on the characteristics of the boiler The increases in QB and Qp cause increases in the vapor and liquid mass flows of the bubble pump. The vapor and liquid flowing out of the Fig. 6 shows the variation trends of qm,10, T10, and x2,10 in function

Fig. 3. Calculation algorithm of the DAR system.

205 B. Zhang et al. Energy Conversion and Management 152 (2017) 201–213

Fig. 5. Variations of qV,10L and qV,10V in function of Qp and QB: (a) Qp, (b) QB. bubble pump will enter the boiler. Therefore, the total mass ﬂow entering the boiler, qm,10, rises, which is consistent with the characteristics of the bubble pump.

The increasing QB leads to the temperature increase of the solution out of the boiler, which results in the temperature increase of the solution entering the bubble pump, T9. The increasing T9 results in an increase in T10. T10 drops with an increase in Qp. The increase in Qp causes an increase in qm,10, which means the [mmim]DMP/CH3OH solution needed to be heated increases. The heat ﬂow of QB remains unchanged. Therefore, the temperature of heated ﬂow, T10, will decrease.

The increasing QB and decreasing Qp lead to an increase in T10. The vapor pressure of p10,V is equal to the system pressure, which is ﬁxed for the simulation. On condition of ﬁxed vapor pressure, the increasing temperature results in a decrease in the mole fraction of refrigerant in the solution.

Fig. 7 shows the variation trends of qm,11, T11, and x2,11 in function of QB on with Qp of 0.1, 0.2, 0.3, 0.4, and 0.5 kW, namely, (a) qm,11, (b) Fig. 6. Variation trends of qm,10, T10, and x2,10 in function of QB with Qp of 0.1, 0.2, 0.3, T11, (c) x2,11. Fig. 7(a) depicts that the solution mass flow out of the 0.4, and 0.5 kW: (a) qm,10, (b) T10, (c) x2,10. boiler, qm,11, rises with increases in QB and Qp. Fig. 7(b) presents that the [mmim]DMP/CH3OH solution temperature in the boiler, T11, rises flow of QB remains unchanged. Therefore, the temperature of heated with an increase in QB, and decreases with an increase in Qp. Fig. 7(c) flow will decrease, which is easily understood intuitively. indicates that the CH3OH mole fraction of the solution in the boiler, The increase in QB leads to an increase in the vaporized refrigerant x2,11, decreases with an increase in QB. from the solution, which results in a decrease in x2,11. x2,11 increases The increases in QB and Qp cause increases in the solution mass flow with an increase in Qp. The increase in Qp causes a decrease in qm,10L, entering the bubble pump, qm,10L. Relative to qm,10L, the mass flow of whereas the heat flow of QB remains unchanged. Hence, the vaporized vaporized refrigerant, qm12, is small, which is about ten percent of refrigerant from the solution is essentially unchanged, but the mass qm,10L. And its influence on qm,11 can be neglected. Therefore, the in- flow of the solution increases. The concentration decrease of the solu- creasing QB and Qp leads to an increase in qm,11. tion in the bubble pump drops, which results in an increase in x2,11. The increase in Qp causes an increase in qm,10L, which means the [mmim]DMP/CH3OH solution needed to be heated increases. The heat

206 B. Zhang et al. Energy Conversion and Management 152 (2017) 201–213

The increase in QB causes an increase in the boiler temperature, and the increase in Qp causes an increase in the mass flow into the boiler, which are both conducive to the vapor production in the boiler. The vapor mass flow from the boiler is equal to the liquid mass flow into the

evaporator, qm,3. Therefore, the increase in the heat ﬂows of the bubble pump and boiler causes the rise of qm,3. The increases in QB and Qp cause the growth of qm,3, which results in an increase in the cooling capacity of the system. The increase in the cooling capacity leads to an increase in the temperature diﬀerence

between Tcool and T3. Therefore, the evaporating temperature, T3, decreases with ﬁxed Tcool. The increases in QB and Qp lead to an increase in qm,3. The mass conservation and the ﬁxed concentration of He in the vapor phase

imply that the increase in qm,3 finally leads to an increase in qm,7. The increases in QB and Qp cause an increase in the heat flow of the absorber, QA, which will lead to an increase in T6. The increase in T6 finally causes an increase in T7 with fixed total heat conductance of the GHX.

5.4. Eﬀects of heat input on thermal performances of proposed system

Fig. 9 presents the variation trends of f in the function of QB with Qp values of 0.1, 0.2, 0.3, 0.4, and 0.5 kW. f decreases with the increase in

QB, and the decrease rate of f shows a declining trend. f increases with the increase in Qp. The increase in QB leads to an increase in the amount of vaporized refrigerant from the solution, subsequently causing the deflated range of the DAR system to increase. The increase of the deflated range finally causes f to decrease. Generally, f is inversely pro- portional to the deflated range. Therefore, the decrease rate of f with

the increase in QB shows a declining trend. Fig. 7(c) shows that the increase in Qp leads to increases in x2,11, indicating that the decrease in the solution concentration in the bubble pump drops and results in the decrease of the deﬂated range of the DAR system. Finally, the decrease of the deﬂated range causes the increase in f. Fig. 10 presents the variation trends of thermal performances of the

DAR system in function of Qp, namely, (a) TC and QC, (b) TE and QE, and (c) COP and ηex. Fig. 10(a) shows that TC and QC rise with an increase in Qp. Fig. 10(b) demonstrates that with increasing Qp, the cooling capacity of QE enhances, but the evaporating temperature TE drops. Fig. 10(c) depicts that with an increase in Qp, the COP and ηex of the DAR system grow when Qp is low but decline when Qp is high. The increasing Qp causes an increase in qm,1, which leads to the growth of the heat load of the condenser, QC. On condition of fixed total heat conductance of the condenser, the increasing QC causes an increase in the difference between TC and T0. Therefore, the increasing Qp results in an increase in TC. The increasing Qp causes an increase in qm,3. The increasing qm,3 results in an increase in the cooling capacity of the evaporator, QE.On condition of fixed total heat conductance of the evaporator, the in-

creasing QE leads to an increase in the temperature difference between Tcool and TE. Therefore, the evaporator temperature, TE, drops with fixed Tcool. Fig. 7. Variation trends of q , T , and x in function of Q with Q of 0.1, 0.2, 0.3, When QB is low, the increasing Qp causes a rapid increase in QE. m,11 11 2,11 B p η 0.4, and 0.5 kW: (a) qm,11, (b) T11, (c) x2,11. Therefore, COP and ex show an increasing trend. When Qp is high, the increase rate of QE slows down, but the heat input of the DAR system still rises linearly. Therefore, COP and η show a decreasing trend. The 5.3. Effects of heat input on the characteristics of the evaporator ex optimal values of COP and ηex are 0.147 and 0.055, respectively. The optimal values appear at Q of 0.35 kW. Fig. 8 shows the variation trends of q , T , q , and T in function p m,3 3 m,7 7 In Fig. 10(c), the dotted line with open mark presents the experi- of Q with different Q of 0.1, 0.2, 0.3, and 0.4 kW, namely, (a) q , (b) B p m,3 mental data of the DAR system using butane/nonane/helium (C H / T , (c) q , (d) T . Fig. 8(a) presents that q rises with increases in Q 4 10 3 m,7 7 m,3 B C H /He) as working fluid [28]. The operation conditions, the struc- and Q . Fig. 8(b) implies that the evaporating temperature, T , drops 9 20 p 3 tural parameters, and the heat input (Q ) of the DAR system in the with increases in Q and Q . Fig. 8(c) illustrates that the mass flow of B B p literature are different from those of the proposed system. Therefore, gas loop entering the evaporator, q , rises with increases in Q and Q . m,7 B p the direct comparison of the values of COP is meaningless. Experi- Fig. 8(d) shows that the temperature of gas loop entering the eva- mental data are referenced for the qualitative comparison of the var- porator, T7, rises with increases in QB and Qp. iation trend of COP in the function of Qp. The experimental COP of the

207 B. Zhang et al. Energy Conversion and Management 152 (2017) 201–213

Fig. 8. Variations of qm,3, T3, qm,7, and T7 in function of QB with Qp of 0.1, 0.2, 0.3, and 0.4 kW: (a) qm,3, (b) T3, (c) qm,7, (d) T7.

growth of QC and the decrease of difference between TC and T0. Therefore, TC rises with fixed T0. The increasing QB leads to an increase in qm,1, which results in an increase in QE. On condition of fixed Tcool, the increase in QE results in a decrease in TE. With increasing QB, the increase rate of QE and the decrease rate of TE slow down. The increasing QB causes an increase in TC, which leads to a decrease in the cooling capacity per unit mass of the refrigerant. Therefore, the variation trends of QB and TC become flat with increasing QB. When QB is low, the increasing QB causes a rapid increase in QE. Therefore, COP and ηex show an increasing trend. When QB is high, the increase rate of QE slows down, but the heat input of the DAR system still rises linearly. COP and ηex consequently show a decreasing trend. The optimal values of COP and ηex are 0.141 and 0.052, and the optimal values appear at Qp of 0.35 and 0.30 kW, respectively. The variation in COP on QB for LiBr/H2O/He system is also calculated and shown in Fig. 11(c) using the dotted line with open mark with

the same model of this work. The COP of [mmim]DMP/CH3OH/He is lower than that of the LiBr/H2O/He system when QB < 0.3 kW. By Fig. 9. Variation of f in function of QB with Qp of 0.1, 0.2, 0.3, 0.4, and 0.5 kW. contrast, the COP of the [mmim]DMP/CH3OH/He system is higher than that of the LiBr/H2O/He system when QB > 0.3 kW. The optimal COP C4H10/C9H20/He system also shows the trend of initial rise and sub- of the [mmim]DMP/CH3OH/He system is lower than that of the LiBr/ sequent decrease. This trend is consistent with the trend observed in H2O/He system. Nevertheless, the [mmim]DMP/CH3OH/He system this work. The same variation trend of COP in the function of Q has p possesses the advantages of non-crystallization and non-corrosion and also been reported in the literature [26]. can operate at a high boiler temperature. Fig. 11 presents the variation trends of thermal performances of the

DAR system in function of QB, namely, (a) TC and QC, (b) TE and QE, and (c) COP and ηex. Fig. 11(a) depicts that TC and QC rise with an increase 5.5. Exergy flow for diffusion absorption refrigeration in QB. Fig. 11(b) indicates that with increasing QB, QE grows, but TE drops. Fig. 11(c) shows that with an increase in QB, the COP and ηex of Fig. 12 presents the schematic of exergy flow for the DAR system on the DAR system rise when QB is low but drop when QB is high. the basic operating condition. The DAR system comprises two exergy The increasing QB leads to an increase in qm,1, which leads to the inputs to the bubble pump and the boiler. The exergy input to the

208 B. Zhang et al. Energy Conversion and Management 152 (2017) 201–213

Fig. 11. Variation trends of thermal performances of the DAR system in function of QB:

(a) TC and QC, (b) TE and QE, and (c) COP and ηex.

Fig. 10. Variation trends of thermal performances of the DAR system in function of Qp: (a) T and Q , (b) T and Q , and (c) COP and η . C C E E ex for the exergy loss in the SHX, GHX, and sub-cooler. The energy losses for the SHX, GHX, and sub-cooler are 14.7, 5.4, and 12.1 W, which bubble pump is 64.7 W, which accounts for 52.3% in the total exergy account for 11.9%, 4.4%, and 9.8% of the total exergy input, respec- input. In the bubble pump, the vaporization of refrigerant and the re- tively. In the absorber, the mass transfer with pressure difference and sistance of lift tube lead to an exergy loss of 19.0 W, which accounts for the heat transfer with temperature difference cause an exergy loss of 15.4% of the total exergy input. In the boiler, the temperature drop 21.3 W, which accounts for 17.2% of the total exergy input. The largest from T10L to T11 and the vaporization of refrigerant cause an exergy loss four exergy losses occur in the condenser, absorber, boiler, and bubble of 21.2 W, which accounts for 17.1% of the total exergy input. In the pump, which account for approximately two thirds of the total exergy condenser, the heat transfer with temperature difference between the input. The exergy losses of other four components are relatively condenser and the environment causes an exergy loss of 23.4 W, which smaller, which account for approximately one third of the total exergy accounts for 18.9% of the total exergy input. In the evaporator, the input. Overall, the most significant reason for the exergy loss of the mixing process and the heat transfer with temperature difference result DAR system is the heat transfer with difference. Therefore, appro- in an exergy loss of 6.5 W, which accounts for 5.4% of the total exergy priately increasing the heat transfer area of components to reduce the input. The heat transfer with temperature difference is the main reason heat transfer temperature difference is an effective measure to improve

209 B. Zhang et al. Energy Conversion and Management 152 (2017) 201–213

Fig. 12. Schematic of exergy ﬂow for the DAR system.

the thermal characteristic of the DAR system. (4) The optimal COP is lower than that of the LiBr/H2O/He system. However, the [mmim]DMP/CH3OH/He system possesses the ad- 6. Conclusion vantages of non-crystallization and non-corrosion and can operate with a high boiler temperature. In this study, the thermal performances and exergy conservation of (5) The largest four exergy losses occur in the condenser, absorber, the DAR system using [mmim]DMP/CH3OH/He as working ﬂuid are boiler, and bubble pump, and the main reason for the exergy loss is investigated. The thermal performances of the [mmim]DMP/CH3OH/ the heat transfer with temperature diﬀerence. He system are also compared with those of C4H10/C9H20/He and LiBr/ H2O/He systems. The major conclusions are listed as follows: Acknowledgements (1) The high submergence ratio is conducive to the mass transport of

the bubble pump. With an increase in qV,V, the qV,L increases, but This research is supported by the National Natural Science the increasing trend is not continuous. Fundation of China (Grant No.51506104 & No.51506103), the

(2) With increases in Qp and QB, the qm,2, qm,11,QC, and QE increase, Promotive Research Fund for Excellent Young and Middle-aged but the trends of COP and ηex ﬁrst increase and then decrease. Scientists of Shandong Province, China (Grant No. BS2014NJ021), and (3) The variation trend of COP on Qp is in accordance with the ex- the Basic Application Research of Innovation Program of Qingdao, perimental data for the C4H10/C9H20/He system. Shandong Province, China (Grant No. 17-1-1-35-jch).

Appendix A. Heat capacity and latent heat

The specific heat capacities of [mmim]DMP/CH3OH can be calculated by [14] 2 2 i i cAp/(kJ/(kg·K)) =+∑∑i ω(/)TKBi ω i==0 i 0 (A.1) where cp stands for the specific heat capacity, ω stands for the mass fraction of IL, and T stands for the temperature of solution. When ω = 0, the specific heat capacity of CH3OH (cp,R) is calculated. When ω = 1, the specific heat capacity of [mmim]DMP (cp,IL) is calculated. The regressive coefficients Ai, Bi, Ci are listed in Table A1. The latent heat can be calculated by the Chen equation [25] as follows

Table A1 Regressive coeﬃcients for speciﬁc heat capacities.

i 012

Ai −5.762 14.442 5.950

Bi 0.0273 0.0496 0.0251

210 B. Zhang et al. Energy Conversion and Management 152 (2017) 201–213

R 3.978Tb −+3.938 1.555ln Pb ()Tc Pc Lb = 1.07/TTbc− 1/ (A.2) where Pc is the critical pressure of methanol, Tc is the critical temperature, Tc = 512.58 K, Tb is the vaporization temperature and Pb is the saturation pressure at Tb.

Appendix B. Momentum conservation of the bubble pump

For the bubble pump, the momentum conservation equation of the working ﬂuid can be written by

ρLvgh−+−[(1)]ΔΔ αρ α ρ L gH =+ p 12 p (B.1) where ρL and ρv are the densities of the liquid and vapor phases in the lift tube, respectively. h and H are the heights of liquid level in the reservoir and bubble pump, respectively. α is the void fraction in the lift tube. Δp1is the pressure drop in the horizontal tube between the reservoir and the bubble pump. Δp2 is the pressure drop in the lift tube of the bubble pump. The void fraction of the lift tube can be calculated by [29]

α =+qqV,v/( V,V τq · V,L ) (B.2) where qV,V and qV,L are the volume ﬂows of the vapor and liquid phases in the lift tube, respectively.τ is the slip ratio. The slip ratio can be calculated by

⎛ ϕ ⎞ τG=+1 1 ⎜ −ϕG2⎟ ⎝1 + ϕG2 ⎠ (B.3) where ϕ is the volume ﬂow ratio and is given by

ϕqq= V,v/ V,l (B.4)

G1 and G2 are be calculated by −0.19 0.22 ⎛ qdm ⎞ ⎛ ρL ⎞ G1 = 1.578⎜⎟⎜⎟ ⎝ ηL ⎠ ⎝ ρV ⎠ (B.5)

2 −0.51 −0.08 ⎛ qdm ⎞⎛ qdm ⎞ ⎛ ρL ⎞ G2 = 0.0273⎜⎟⎜⎟⎜⎟ σρ η ρ ⎝ L ⎠⎝ L ⎠ ⎝ V ⎠ (B.6) where qm is the total mass flow of the bubble pump, d is the diameter of the lift tube, σ is the surface tension, and ηL is the viscosity of the liquid. The pressure drop in the horizontal tube between the reservoir and the bubble pump can be calculated by L ρu2 u2 Δpλ=++()kk12 1 d 2 2g (B.7) where L is the length of the horizontal tube; g is the gravity; ρ and u are the density and the velocity of the solution in the horizontal tube, respectively. k1 and k2 are the local resistance coefficients of the tube inlet and the right angle bend, which are set to 1.0 and 0.5, respectively. λ is the resistance coefficient along the tube, which can be calculated by λ = 64/Re (B.8) The pressure drop in the lift tube can be calculated by

2 qvH··l ΔpReϕ= 0.3164 −0.25 2 m 2 lo 2d (B.9) where v1 is the speciﬁc volume of the liquid phase in the lift tube. ϕlo is the friction factor of the pure liquid phase, which can be calculated by 20 1 ϕ 2 = ⎛1 ++⎞(1−α )1.75 lo ⎝ XX2 ⎠ (B.10)

0.5 0.9 −0.1 1 ⎛ ρL ⎞ α ⎛ μL ⎞ = ⎜⎟⎛ ⎞ ⎜⎟ X ⎝ ρV ⎠ ⎝1−α ⎠ ⎝ μV ⎠ (B.11) where μL and μV are the kinetic viscosities of the liquid and vapor phases in the lift tube, respectively.

Appendix C. Stable modeling of diﬀusion absorption refrigeration

For the bubble pump–boiler–condenser model, the mass conservation equations are given by qm,9=+=+qqqq m,10V m,10L m,11 m,13 (C.1) qm,9 ωqωqωIL,9 ==m,10V IL,9 m,11 IL,9 (C.2) qm,13==qq m,1 m,2 (C.3) The related energy conservation equations are given by

211 B. Zhang et al. Energy Conversion and Management 152 (2017) 201–213 qm,9 hQq9 +=p m,10V h10V + qm,10L h10L (C.4) qm,10V hqhQqhqh10V ++=+m,10L 10L B m,11 11 m,13 13 (C.5) qm,1hQ1 +=C qhm,2 2 (C.6) where Qp, QB, and QC are the heat ﬂows of the bubble pump, boiler, and condenser, respectively. Qp and QB are the input variables for the DAR system. QC can also be written as

()()TT10−−− TT 20 QCC= ()AU ln[(TT10−− )/( TT 20 )] (C.7)

where (AU)C is the total thermal conductance of the condenser, and T0 is the atmosphere temperature. The entropy production for the bubble pump, boiler, and condenser can be calculated by

Sqsg,p =+−−m,10V 10V qsqsQTm,10L 10L m,9 9p10/ (C.8)

SqsqsqsqsQTg,B =+−m,11 11 m,13 13 m,10V 10V −m,10L 10L − B/ 11 (C.9)

SqsqsQTg,C =−−m,2 2 m,1 1C10/ (C.10) For the evaporator–GHX–absorber model, the mass conservation equations can be written as qm,7+==qqq m,3 m,4 m,5 (C.11) qm,7 ωqωIL,7 = m,4 IL,4 (C.12) qm,15+=qq m,5 m,16 + q m,6 (C.13) The corresponding energy conservation equations can be written as qm,7 hqhQqh7 ++=m,3 3Em,4 4 (C.14)

()()TT65−−− TT 74 qm,4 ()hh54−= qm,7 ()() hh67 −= AU GHX ln[(TT65−− )/( TT 74 )] (C.15) qm,15hqhqhqhQ15 +=m,5 5 m,16 16 ++m,6 6 A (C.16) where (AU)GHX is the total thermal conductance of the GHX. QE and QA are the heat ﬂows of the evaporator and absorber, respectively, which can be calculated by

QEE3=−()(AU Tcool T ) (C.17)

QA =+++−()[(AUA T 15 T 16 T 5 T 6 )/4] T 0 (C.18) where Tcool is the temperature of the gas to be cooled that surrounds the evaporator. (AU)E and (AU)A are the total thermal conductance of the evaporator and absorber, respectively. The entropy production for the evaporator, GHX, and absorber can be calculated by

SqsqsqsQTg,E =−−−m,4 4 m,7 7 m,3 3E/ cool (C.19)

Sqsqsqsqsg,GHX =+−−m,7 7 m,5 5 m,6 6 m,4 4 (C.20)

SqsqsqsqsQTg,A =+m,6 6 m,16 16 −−−m,5 5 m,15 15 A/ 0 (C.21) The energy conservation equation and entropy production for the SHX can be given by

()()TT11−− 9 TT 14 − 8 qm,8 ()hh98−= qm,11 ( h11 − h 14 )() = AU SHX ln[(TT11−− 9 )/( TT 14 8 )] (C.22)

Sqsqsqsqsg,GHX =+m,9 9 m,14 14 −−m,11 11 m,8 8 (C.23) The energy conservation equation and entropy production for the sub-cooler can be given by

()()TT14−− 0 TT 15 − 0 QSC =−=qhhm,14 ()()14 15 AUSC ln[(TT14−− 0 )/( TT 15 0 )] (C.24)

SqsqsQTg,SC =−−m,15 15 m,14 14 SC/ 0 (C.25) where (AU)SHX and (AU)SC are the total thermal conductance of the SHX and sub-cooler, respectively.The circulation ratio of the DAR system is defined as m 1−ω f ==10 11 m13 ωω911− (C.26) The COP of the DAR system is defined as Q COP = E QQBp+ (C.27) The exergy efficiency of the DAR system is defined as

212 B. Zhang et al. Energy Conversion and Management 152 (2017) 201–213

QTTE [(03 / )− 1] ηex = QTTQTTBp[1−+− (010 / )] [1 ( 011 / )] (C.28)

References [14] Chen W, Liang SQ. Thermodynamic analysis of absorption heat transformers using [mmim]DMP/H2O and [mmim]DMP/CH3OH as working fluids. Appl Therm Eng 2016;99:846–56. [1] Xu YJ, Jiang N, Pan F, Wang Q, Gao ZL, Chen GM. Comparative study on two low- [15] Sayadi Z, Thameur NB, Bourouis M, Bellagi A. Performance optimization of solar grade heat driven absorption-compression refrigeration cycles based on energy, driven small-cooled absorption–diffusion chiller working with light hydrocarbons. exergy, economic and environmental (4E) analyses. Energy Convers Manage Energy Convers Manage 2013;74:299–307. 2017;133:535–47. [16] Chen J, Kim KJ, Herold KE. Performance enhancement of a diffusion absorption [2] Tugcu A, Arslan O, Kose R, Yamankaradeniz N. Thermodynamics and economical refrigerator. Int J Refrig 1996;19:208–18. analysis of geothermal assisted absorption refrigeration system: Simav Case Study. J [17] Maiya MP. Studies on gas circuit of diffusion absorption refrigerator. In: 21st IIR Therm Sci Technol 2016;36:143–59. international congress of refrigeration, Washington DC, USA; 2003. [3] Kim S, Kohl PA. Analysis of [hmim][PF6] and [hmim][Tf2N] ionic liquids as ab- [18] Rattner AS, Garimella S. Low-source-temperature diffusion absorption refrigeration. sorbents for an absorption refrigeration system. Int J Refrig 2014;48:105–13. Part I: Modeling and cycle analysis. Int J Refrig 2016;65:278–311. [4] Leonzio G. Solar systems integrated with absorption heat pumps and thermal energy [19] Long Z, Luo Y, Li HS, Bu XB, Ma WB. Performance analysis of a diffusion absorption storages: state of art. Renew Sustain Energy Rev 2017;70:492–505. refrigeration cycle working with TFE–TEGDME mixture. Energy Build [5] Cai DH, Jiang JK, He GG, Li KQ, Niu LJ, Xiao RX. Experimental evaluation on 2013;58:86–92. thermal performance of an air-cooled absorption refrigeration cycle with [20] Rattner AS, Garimella S. Low-source-temperature diffusion absorption refrigeration. NH3–LiNO3 and NH3–NaSCN refrigerant solutions. Energy Convers Manage Part II: Experiments and model assessment. Int J Refrig 2016;65:312–29. 2016;120:32–43. [21] Kouremenos DA, Stegou-Sagia A. Use of helium instead of hydrogen in inert gas [6] Kim YJ, Gonzalez M. Exergy analysis of an ionic-liquid absorption refrigeration absorption refrigeration. Int J Refrig 1988;11:6–341. system utilizing waste-heat from datacenters. Int J Refrig 2014;48:26–37. [22] Zohar A, Jelinek M, Levy A, Borde I. Numerical investigation of a diffusion ab- [7] Farghaly A, Elsamadony M, Ookawara S, Tawfik A. Bioethanol production from sorption refrigeration cycle. Int J Refrig 2005;28(4):515–25. paperboard mill sludge using acid-catalyzed bio-derived choline acetate ionic liquid [23] Zohar A, Jelinek M, Levy A, Borde I. The influence of diffusion absorption re- pretreatment followed by fermentation process. Energy Convers Manage frigeration cycle configuration on the performance. Appl Therm Eng 2017;145:255–64. 2007;27(13):2213–9. [8] Ayou DS, Currás MR, Salavera D, García J, Bruno JC, Coronas A. Performance [24] Chen W, Liang SQ, Guo YX, Cheng KY, Gui XH, Tang DW. Thermodynamic per- analysis of absorption heat transformer cycles using ionic liquids based on imida- formances of [mmim]DMP/methanol absorption refrigeration. J Ther Sci zolium cation as absorbents with 2,2,2-trifluoroethanol as refrigerant. Energy 2012;21:557–63. Convers Manage 2014;84:512–23. [25] Chen NH. Generalized correlation for latent heat of vaporization. J Chem Eng Data [9] Dong L, Zheng DX, Nie N, Li Y. Performance prediction of absorption refrigeration 1962;10:207–10. cycle based on the measurements of vapor pressure and heat capacity of H2O+ [26] Taieb A, Mejbri K, Bellagi A. Detailed thermodynamic analysis of a diffusion ab- [DMIM]DMP system. Appl Energy 2012;98:326–32. sorption refrigeration cycle. Energy 2016;115:418–34.

[10] Liang SQ, Zhao J. Absorption refrigeration cycle utilizing a new working pair of [27] Saravanan R, Maiya MP. Experimental analysis of a bubble pump operated H2O/ ionic liquid type. J Eng Thermophys 2010;31:1627–30. LiBr vapour absorption cooler. App Therm Eng 2003;23:2383–97. [11] Yokozeki A. Theoretical performances of various refrigerant-absorbent pairs in a [28] Ezzine NB, Garma R, Bourouis M, Bellagi A. Experimental studies on bubble pump vapor-absorbent refrigeration cycle by the use of equation of state. Appl Energy operated diffusion absorption machine based on light hydrocarbons for solar 2005;80:383–99. cooling. Renew Energy 2010;35:464–70. [12] Ángel M, María DB. Thermodynamic analysis of absorption refrigeration cycles [29] Hewitt GF. Multiphase fluid flow and pressure drop. In: Heat exchanger design using ionic liquid + supercritical CO2 pairs. Supercrit Fluids 2010;55:852–9. handbook. Hemisphere publishing corporation, Washington; 1983. p. 2–13. [13] Yokozeki A, Shiflett MB. Vapor–liquid equilibria of ammonia + ionic liquid mix- tures. Appl Energy 2007;84:1258–73.

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