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CH3OH as working fluid
Energy Conversion and Management 166 (2018) 433–444
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Numerical investigation of the thermal performance of compressor-assisted double-effect absorption refrigeration using [mmim]DMP/CH3OH as working fluid
T
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Wei Chen , Qiang Sun, Yang Bai, Bin Zhang College of Electromechanical Engineering, Qingdao University of Science & Technology, Qingdao 266061, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Double effect absorption refrigeration Compressor assisted Ionic liquid Coefficient of performance Exergy efficiency
The thermal performance of compressor-assisted double-effect absorption refrigeration (CDAR) was numerically investigated and comprehensively analyzed with 1, 3-dimethylimidazolylium dimethylphosphate/methanol ([mmim]DMP/CH3OH) as working fluid. The CDAR system was modeled and simulated based on the proposed mathematical model of the compression process by considering the mass and energy conservation of each component. The effects of compression ratio and heat source temperature on the system’s operating state, including solution temperature, refrigeration concentration, mass flow, and heat load of each component, were calculated and discussed. Variations in the coefficient of performance and exergy efficiency in four cases were simulated and compared. Results suggested that placing the assisting compressor between the evaporator and absorber was a good option, and placing the assisting compressor between two generators was also acceptable. The exergy losses of each component were calculated and compared. The largest exergy loss occurred in the lowtemperature generator and accounted for approximately one-third of the total exergy input. The main reason for the exergy loss in the diffusion absorption refrigeration system was heat transfer with a temperature difference.
1. Introduction Absorption refrigeration has been widely applied in low-grade heat sources [1], such as solar energy [2], geothermal energy [3], biomass energy [4], and industrial waste heat [5]. The working fluid of absorption refrigeration is composed of an absorbent and a refrigerant [6]. The main role of the absorbent is to reduce the saturated vapor pressure of the working fluid solution [7] to ensure absorption in the absorber of absorption refrigeration. Therefore, the absorbent is the key component of the working fluid. Ionic liquids (ILs) are organic ionic compounds with melting points lower than room temperature [8]. ILs are miscible with most refrigerants, such as Freon, alkane, and alcohol [9]. The vapor pressure of a solution containing an IL and a refrigerant is largely reduced because the vapor pressure of ILs is negligible. Additionally, ILs possess excellent properties of high thermal stability, low combustibility, and non-corrosiveness [10]. Therefore, ILs are potential absorbents in absorption refrigeration. The concept of using ILs as absorbents in absorption refrigeration was proposed by Yokozeki in 2006 [11]. Research on IL absorption refrigeration has become popular in recent decades. Shiflett et al. [12]
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Corresponding author at: Songling Road 99, Qingdao, China. E-mail address: [email protected] (W. Chen).
https://doi.org/10.1016/j.enconman.2018.04.060 Received 8 February 2018; Received in revised form 8 April 2018; Accepted 15 April 2018 Available online 03 May 2018 0196-8904/ © 2018 Elsevier Ltd. All rights reserved.
investigated the thermal performance of absorption refrigeration using IL/Freon as working fluid. An optimal coefficient of performance (COP) of 0.539 for the DMF/R22 system was reported. Liang et al. [13] numerically investigated the cycle characteristic of IL absorption refrigeration using alcohols as a refrigerant. Su et al. [14] simulated the theoretical cycle of absorption refrigeration by adopting [hmim]Cl/ H2O and [Emim]AC/H2O as working fluids. They found that the thermal performance of the [Emim]AC/H2O system is better than that of [hmim]Cl/H2O. Ángel et al. [15] investigated the possibility and potential of absorption refrigeration with IL/CO2 as working fluid and indicated that the best absorbent for supercritical CO2 is [bmpyrr] [Tf2N]. Shiflett et al. [16] investigated the thermal performance of the IL/NH3 absorption system and discovered that absorption refrigeration using [DMEA][AC]/CO2 achieves an optimal COP. They also confirmed that IL absorption refrigeration possesses an excellent industrial application potential. The COP and generation temperature of multi-effect absorption refrigeration are significantly higher than those of a single-effect system. The most widely used working fluid in multi-effect absorption refrigeration is LiBr/H2O [17]. The LiBr concentration in the solution from the generator increases with the generation temperature, and this
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Nomenclature
Subscript
A, B, b AU cp COP f h Lb p qm Q p s Sg v w W
1,2…16 0 ΑΒ, Α act C CD CM EV ex HG HX in, out IL LG LX v
parameters for EOS of CH3OH total heat conductance (kJ/K) specific heat capacity (kJ/(kg·K)) coefficient of performance function Specific enthalpy (kJ/kg) latent heat (kJ/kg) pressure (kPa) mass flow (kg/s) heat flow (kW) pressure (kPa) specific entropy (kJ/(kg·K)) entropy production (kJ/K) specific volume (m3/kg) specific power (kW/kg) power (kW)
status point environmental absorber actual process critical parameter condenser compressor evaporator exergy high temperature generator high temperature exchanger parameter of inlet and outlet ionic liquid low temperature generator low temperature exchanger vapor
Greek symbols
Superscript
γ η φ ω
0 E is S
compression ratio efficiency activity coefficient mass fraction
reference point excessive parameter isentropic process saturation
and analyzed, and the exergy losses of each component were calculated and discussed.
increment significantly increases the risk of crystallization in the solution heat exchanger [18]. In addition, the corrosion of LiBr/H2O solution is extremely strong at high temperatures [19]. The application of multi-effect LiBr/H2O absorption refrigeration is thus largely restricted. Multi-effect absorption refrigeration using IL as working fluid can completely prevent the problems of corrosion and crystallization in the LiBr/H2O system because of the low melting temperature and noncorrosiveness of ILs. ILs as working fluid are more suitable for multieffect absorption refrigeration than LiBr/H2O. However, the deflation range of IL absorption systems is smaller than that of LiBr/H2O systems [13,14]. A small deflation range results in a high circulation ratio and causes COP deterioration [12,15]. The most reasonable approach to improve the deflation range is introducing an assisting compressor into the absorption cycle [20]. Boer et al. [21] numerically studied double-effect absorption refrigeration with a compressor placed between the evaporator and absorber and with TEGDME/CH3OH and TEGDME/TFE as working fluids. Kim et al. [22] conducted simulations for a basic triple-effect cycle and four proposed compressor-assisted cycles with LiBr/H2O as working fluid. Dereje et al. [23] investigated the thermal performance of a combined absorption power and refrigeration cycle with an integrated compressor. Wang et al. [24] numerically investigated the thermal performances of the absorption compression hybrid refrigeration system recovering condensation heat for generation. Shu et al. [25] simulated the thermal performance of a proposed compressor-assisted triple-effect LiBr/H2O absorption cooling cycle coupled with a Rankine cycle driven by hightemperature waste heat. They reported that the integrated compressor improves the thermal performance of multi-effect absorption refrigeration. In this study, a mathematical model of the compression process was established based on the equation of state (EOS), the enthalpy equation, and the entropy equation of superheated methanol vapor. Steady modeling and simulation of compressor-assisted double-effect absorption refrigeration (CDAR) system with [mmim]DMP/CH3OH as working fluid were conducted in consideration of the mass and energy conservation of each component of the proposed system. The influences of compression ratio and heat source temperature on the operating states and thermal performance of the CDAR system were simulated
2. Thermodynamic properties of working fluid The vapor liquid equilibrium (VLE) of the [mmim]DMP/CH3OH solution is crucial for the simulation of the thermal performance of the CDAR system. The vapor phase of [mmim]DMP/CH3OH is pure CH3OH vapor because the vapor pressure of [mmim]DMP is negligible. The vapor pressure of the [mmim]DMP/CH3OH solution can be calculated as follows:
p = x2 φ2 p2S
(1)
where x2 is the mole fraction of CH3OH in the solution, φ2 is the activity coefficient of CH3OH, and p2S is the saturation pressure of pure CH3OH. φ2 can be calculated using the universal quasichemical functional group activity coefficient (UNIFAC) model [26]. p2S can be calculated using the Antoine equation [27]. The specific enthalpy and entropy of the [mmim]DMP/CH3OH solution are the most essential properties to the simulation of the thermal performance of the CDAR system. The specific enthalpy of the binary solution can be calculated as
h = ω1
∫T
T 0
cp,IL dT + ω2
∫T
T 0
cp,R dT + h 0E +
∫T
T
0
cp dT
(2)
The specific entropy of the binary solution can be calculated as [26]
s = ω1
∫T
T 0
(cp,1/ T ) dT + ω2
∫T
T 0
(cp,2/ T ) dT + h0E/ T0 +
∫T
T
0
(cp/ T ) dT (3)
where T0 is ambient temperature, which is 298.15 K, and T0 is the reference temperature for the calculation of specific enthalpy and entropy. The value of T0 is 273.15 K. h 0E is the excess enthalpy of the solution at T0. ω1 and ω2 are the mass fractions of [mmim]DMP and CH3OH in the binary solution, respectively. cp,1 and cp,2 are the specific heat capacities of [mmim]DMP and CH3OH, respectively. cp stands for the specific capacity of the [mmim]DMP/CH3OH solution. The expression of h 0E and the specific capacities can be found in our previous work [28]. 434
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condensation and generation processes in LG. Arrows (12, 14) and (13, 14) denote the condensation process in the condenser, and arrow (14, 1) represents the evaporation process in the evaporator.
The specific enthalpy and entropy of the superheated vapor of CH3OH at T and p can be derived as
h=
s=
∫T ∫T
TS 0
TS 0
cp,1 dT + Lb +
∫T
T S
cp,v dT
(cp,1/ T ) dT + Lb / T S +
∫T
T S
(4)
(cp,v / T ) dT
4. Modeling and simulation 4.1. Mathematic model of compression process
(5)
S
where T is the saturation temperature that corresponds to vapor pressure p and cp,v is the specific heat capacity of the CH3OH vapor at constant pressure. Lb is the latent heat of CH3OH. Latent heat can be predicted by the Chen equation [29].
Suction pressure pin and suction temperature Tin are the given parameters for the assisting compressor. Specific enthalpy hin and specific entropy sin can be calculated with Eqs. (2) and (3). For the isentropic compression process, the equations of momentum and energy conservation can be written as
3. System description
is f1 = pout −γpin = 0
Fig. 1 shows a schematic of the CDAR system. The CDAR system consists of a high-temperature generator (HG), a low-temperature generator (LG), a high-temperature solution heat exchanger (HX), a low-temperature solution heat exchanger (LX), a condenser (CD), an absorber (AB), an evaporator (EV), two assisting compressors (CM1, CM2), two solution pumps (SP1, SP2), and several valves. The CDAR system contains two solution loops. In one loop, [mmim]DMP/CH3OH with a low IL concentration (weak solution) from the absorber is lifted to HG by SP1. In HG, the weak solution is heated by the heat source. The refrigerant CH3OH is desorbed from the solution, and the IL concentration of the [mmim]DMP/CH3OH solution increases. The solution with a high IL concentration is called a strong solution. The strong solution flows back to the absorber due to the pressure difference between HG and the absorber. HX is placed between HG and the absorber. When the weak and strong solutions pass through HX, the weak solution is preheated by the strong solution, and the strong solution is precooled by the weak solution. The heat exchange in HX can reduce the heat loads of HG and the absorber. In the other loop, the weak solution from the absorber is lifted to LG by SP2. The CH3OH vapor from HG is compressed by CM1 and flows into LG. In LG, the CH3OH vapor condenses, and condensation heat is released. The refrigerant CH3OH evaporates from the weak solution because of the condensation heat. The weak solution is concentrated and becomes a strong solution. The strong solution flows back to the absorber due to the pressure difference between LG and the absorber. LX placed between LG and the absorber. The role of LX is similar to that of HX. The CH3OH liquid and the CH3OH vapor from LG flow to the condenser. CH3OH is in a saturated liquid state as it flows out of the condenser. The latent heat of CH3OH is eliminated by the cooling water. Then, the CH3OH saturated liquid passes through the throttle valve (V1) and flows to the evaporator. In the evaporator, the CH3OH saturated liquid evaporates and becomes CH3OH vapor. The vapor from the evaporator is compressed by CM2 and flows to the absorber. In the absorber, the compressed vapor is absorbed by the strong solution from HG and LG. Then, the solution is diluted and becomes weak. Fig. 2 presents the thermodynamic cycle of the CDAR system in a P–T diagram of the [mmim]DMP/CH3OH binary system. The black curves, marked by x2 and percentage, show the relationship of CH3OH pressure and temperature with different CH3OH mole fractions, which are drawn according to the VLE of the [mmim]DMP/CH3OH solution. The solution loop for HG is denoted by the red curves, and the solution loop for LG is denoted by the green curves. The thermal processes of the refrigeration are marked as the blue curves. The black points in Fig. 2 represent the operating status of the CDAR system. The numbers of the operating status in Fig. 2 are in accordance with those in Fig. 1. Arrow (1, 2) represents the compression process in CM2. Arrows (2, 3), (9, 3), and (6, 3) represent the absorption process in the absorber. Arrows (3, 4) and (5, 6) represent the heat exchange process in HX. Arrows (3, 7) and (8, 9) denote the heat exchange process in LX. Arrow (9, 10) represents the generation process in HG. Arrow (10, 11) indicates the compression process in CM1. Arrows (11, 12) and (7, 13) represent the
f2 =
(6)
is is hout −h in−wCM is pout
=0
(7)
is the outlet pressure of isentropic compression, hout is specific enthalpy of isentropic compression, wCM
is is the where outlet of the is the specific compression power of isentropic compression, and γ is the compression ratio of the assisting compressor. For the superheated CH3OH vapor, EOS can be derived as is is is / TC ) RTout A1 + A2 Tout + A3 exp(−kTout − is is 2 vout−b (vout−b)
is f3 = pout −
−
is is B1 + B2 Tout / TC ) + B3exp(−kTout is 3 (vout−b)
(8)
is Tout
is the outlet temperature of isentropic compression. The where adjustable parameters for EOS are presented in Table 1 [30]. For the superheated CH3OH vapor, the enthalpy and entropy equations can be expressed as is f4 = hout −
f5 =
∫T
TS 0
∫T
TS 0
cp,1 dT + Lb +
∫T
(cp,1/ T ) dT + Lb / T S +
is
Tout S
cp,v dT
is Tout S T
∫
(cp,v / T ) dT −sin
(9) (10)
Eqs. (6)–(10) form a nonlinear equation group with five variables
Fig. 1. Schematic of the CDAR system. 435
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phase, and the superheat degree of the refrigeration flow out of the evaporator is set to 2 K. (6) The isentropic compression efficiencies of the two assisting compressors, CM1 and CM2, are set to 0.5. (7) The thermal losses of the entire CDAR system are ignored, and the powers of the two solution pumps, SP1 and SP2, are omitted. On the basis of these assumptions, a steady model of the CDAR system was built in consideration of the mass and energy conservation of each system component. For HG, the solution mass conservation, IL mass conservation, and energy conservation can be obtained with
Table 1 The adjustable parameters for the EOS [30].
R b A1 A2 A3
Value 82.0561 10.1920 −1.41994 × 107 1.17640 × 104 −5.15589 × 1010
Parameters B1 B2 B3 k TC
Value
(15)
qm,4 h4 + QHG = qm,5 h5 + qm,10 h10
(16)
(T16−T5)−(T17−T5) ln[(T16−T5)/(T17−T5)]
(17)
The entropy production for HG can be calculated as 9
Sg,HG = qm,5 s5 + qm,10 s10−qm,4 s4−QHG/ T5
1.26559 × 10 −7.62529 × 105 5.45122 × 1012 −11 513.15
p = γpin
(18)
For LG, the solution mass conservation, IL mass conservation, and energy conservation are obtained as
qm,7 = qm,8 + qm,13
(19)
qm,7 ω7 = qm,8 ω8
(20)
qm,8 h8 + qm,13 h13−qm,7 h 7 = qm,12 h12−qm,11 h11 = QLG
(21)
where QLG is the heat flow of LG and can be written as
QLG = (AU )LG (T12−T18)
(11)
(22)
The entropy production for LG can be calculated as
The specific compression power, wact, can be calculated as
Sg,LG = qm,8 s8 + qm,12 s12 + qm,13 s13−qm,11 s11−qm,7 s7 (12)
(23)
For the absorber, the solution mass conservation, IL mass conservation, and energy conservation are given by
where ηCM is the thermal efficiency of the assisting compressor, which is set to 0.5. The specific enthalpy of the actual compression outlet, hout, can be calculated as
hout = h in + wact
qm,4 ω4 = qm,5 ω5
QHG = (AU )HG
and five equations. The nonlinear equation group can be solved using is is , vout , the Jacobi iterative method [31]. Then, the five variables, p pout is is is Tout , hout , and wCM, can be obtained. For the actual compression process, outlet pressure pout can be calculated with
wact = w is/ ηCM
(14)
where ω is the mass fraction of IL, qm is the mass flow, and QHG is the heat flow of HG. The last item can be written as
Fig. 2. Thermodynamic cycle of the CDAR system in the P-T diagram.
Parameters
qm,4 = qm,5 + qm,10
(13)
The outlet temperature of the actual compression process, Tout, can be calculated with Eq. (4). The outlet specific volume of the actual compression process, vout, can be calculated based on the EOS of CH3OH. Finally, the outlet specific entropy of the actual compression process, sout, can be calculated with Eq. (5).
qm,3 = qm,1 + qm,6 + qm,9
(24)
qm,3 ω3 = qm,6 ω6 + qm,9 ω9
(25)
qm,1 h1 + qm,6 h6−qm,9 h9 = qm,3 h3 + QAB
(26)
where QAB is the heat flow of the absorber and can be written as
QAB = (AU )AB
(T3−T18)−(T3−T19) ln[(T3−T18)/(T3−T19)]
(27)
The entropy production for the absorber can be calculated as
4.2. Modeling of the CDAR system
Sg,AB = qm,3 s3−qm,1 s1−qm,6 s6−qm,9 s9−QAB/ T3
The following assumptions were made to establish a steady model of the CDAR system.
qm,12 = qm,14
(29)
qm,12 h12 = qm,14 h14 + QCD
(30)
(28)
For the condenser, mass and energy conservation are obtained by
(1) The CDAR system is simulated under the steady-state condition. (2) The lumped parameter method is used for the modeling of the CDAR system. Thus, the concentration and temperature distributions of the solution in the absorber, HG, and LG are uniform. (3) For solution and refrigerant flows, the vapor pressure drops along the tube are omitted. (4) The mass transfer pressure difference of generation, absorption, evaporation, and condensation is ignored. (5) The refrigeration flow out of the condenser is in a saturated liquid
where QCD is the heat flow of the condenser and can be written as
QCD = (AU )CD
(T14−T19)−(T14−T20) ln[(T14−T19)/(T14−T20)]
(31)
The entropy production for the absorber can be calculated as
Sg,CD = qm,14 s14−qm,13 s13−QCD/ T13
(32)
For the evaporator, mass and energy conservation are obtained by 436
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qm,1 = qm,15
(33)
qm,1 h1 = qm,15 h15 + QEV
(34)
derivatives of the temperature of all components were calculated with small elemental changes in ΔT. Similarly, given the assumed values of T6 and THG (T5), parameters Τ4, T17, ωHG (ω5), qm,10, and QHG were calculated by Eqs. (14)–(17) and Eqs. (37) and (39). Then, the energy conservations of HG and HX were verified. Based on the verification results, the assumed values of T6 and THG were adjusted using the Newton–Raphson method until the calculation results converged. Given the assumed values of T9 and TLG (T8), parameters Τ7, Τ11, T12, T13, ωLG (ω8), qm,13, and QLG were calculated by Eqs. (19)–(22) and Eqs. (38) and (40). Then, the energy conservations of LG and LX were verified. Based on the verification results, the assumed values of T9 and TLG were adjusted using the Newton–Raphson method until the calculation results converged. Given the assumed values of TCD (T14) and TEV (T1), parameters Τ15, Τ19, T20, T21, QCD, and QEV were calculated by Eqs. (29)–(35). Then, the energy conservations of CD and EV were verified. Based on the verification results, the assumed values of TCD and TEV were adjusted using the Newton–Raphson method until the calculation results converged.
where QEV is the heat flow of the absorber and can be written as
(T21−T1)−(T22−T1) ln[(T21−T1)/(T22−T1)]
QEV = (AU )EV
(35)
The entropy production for the absorber can be calculated as
Sg,EV = qm,1 s1−qm,15 s15−QEV / T1
(36)
For HX and LX, the energy conservations can be obtained by
qm,4 h4−qm,3 h3 = qm,5 h5−qm,6 h6 = QHX
(37)
qm,7 h7−qm,3 h3 = qm,8 h8−qm,9 h9 = QLX
(38)
where QHX and QLX are the heat flows of HX and LX, respectively, and can be written as
QHX = (AU )HX QLX = (AU )LX
(T5−T4 )−(T6−T3) ln[(T5−T4 )/(T6−T3)]
(T8−T7)−(T9−T3) ln[(T8−T7)/(T9−T3)]
(39) 5. Results and discussion (40)
Fig. 4 presents the effects of the compression ratio of CM1, γG, on the operating conditions of each component, namely, (a) THG, TLG; (b) TEV, TCD, TAB; and (c) ωHG, ωLG, ωAB. In the calculation, the compression ratio of CM2, γA, was fixed to 1. Fig. 4(a) shows that with the increase in γG, THG decreased linearly, but TLG increased linearly. With the increase of γG, the suction effect of CM1 improved. The enhanced suction effect largely reduced the vapor pressure of HG. This reduction led to increases in the difference in the mass transfer pressure between the solution and the vapor phase in HG. The increased difference in mass transfer pressure caused the increase of the mass flow of the vaporized refrigerant. The increased refrigerant vapor took an increased amount of heat away from HG to LG, which finally led to a decrease in THG and an increase in TLG. Fig. 4(b) shows that with the increase in γG, TCD and TAB increased, but TEV decreased. The increased γG caused the increased TLG. As the pressure drops along the tube were omitted, the vapor pressure of the condenser was equal to that of the LG. With the increase of TLG, the vapor pressure of the LG and the condenser increased. This result shows that saturation temperature absolutely increases with increasing saturation pressure. Therefore, the condensation temperature, TCD, increased. The increment in γG caused an increase in the mass flow of the refrigerant to the evaporator. The cooling capacity of the evaporator was improved, which led to an increase in the temperature difference between the refrigerant and the chilled water. Given that the inlet temperature of the chilled water was fixed, the evaporation temperature, TEV, decreased. The increase in γG caused an increase in the mass flow of the refrigerant vapor to the absorber, which meant that the increased latent heat was carried into the absorber. Therefore, the heat load of the absorber increased, which finally led to an increase in TAB. Fig. 4(c) indicates that the CH3OH mass fractions of ωHG, ωLG, and ωAB decreased with the increase in γG. The suction effect of CM1 was
The entropy productions for HX and LX can be calculated as
Sg,HX = qm,4 s4 + qm,6 s6−qm,5 s5−qm,3 s3
(41)
Sg,LX = qm,7 s7 + qm,9 s9−qm,8 s8−qm,3 s3
(42)
The COP of the CDAR system is defined as
COP =
QEV QHG + WCM1 + WCM 2
(43)
The exergy efficiency of the CDAR system is defined as
ηex =
QEV [(T0/ T1)−1] QHG [1−(T0/ T5)] + WCM1 + WCM 2
(44)
CDAR is a self-balancing system with an electronic control device. The working conditions of the CDAR system are directly determined by the heat flows and the total thermal conductance of each component. To determine the total thermal conductance of each component, we proposed a basic design of the operating conditions, which are shown in Table 2. The average temperature differences and heat flows of the components were easily calculated based on the basic design of operating conditions. The total thermal conductance of each component was obtained and fixed for the simulation, as presented in Table 3. 4.3. Calculation algorithm of the simulation The detailed calculation algorithm of the CDAR system is shown in Fig. 3. Seven parameters (THG, TLG, TAB, TCD, TEV, T6, and T9) were determined by iterative methods because the CDAR system is self-balancing. The assumed input values of the parameters were set for the iteration according to the basic design of the working conditions. Then, the values of these parameters were adjusted until the iterative results converged. The CDAR system was simulated using MATLAB/Simulink. The thermodynamic parameters of the working fluid and the total thermal conductance of each component were initially inputted. For the simulation, the compression ratio of CM1 (γG) and the compression ratio of CM2 (γA) were initialized. The operating mass flows, qm,16, qm,18, qm,21, qm,4, and qm,7, were set to 0.15, 0.5, 0.3, 0.056, and 0.056 kg/s, respectively. The operating temperatures of T18 and T21 were set to 293.15 and 290.15 K, respectively. Given the assumed values of TEV (T3), parameters T2, T19, ωAB (ω3), and QAB were calculated based on Eqs. (24), (25), and (27). Then, the energy conservation of the absorber was verified. On the basis of the verification results, the assumed values of TEV were adjusted using the dichotomy method until the calculation results converged. The first
Table 2 The operating conditions of the basic design.
437
Point
T (K)
p (kPa)
ω
Point
T (K)
p (kPa)
ω
1 2 3 4 5 6 7 8 9 10 11
281.36 291.35 305.67 370.84 414.26 332.60 339.11 354.40 315.43 414.26 426.21
6.646 7.975 7.975 222.8 222.8 15.22 43.16 43.16 8.932 222.0 266.4
1.000 1.000 0.289 0.289 0.211 0.211 0.289 0.236 0.236 1.000 1.000
12 13 14 15 16 17 18 19 20 21 22
364.37 354.40 317.15 281.36 480.00 414.33 293.15 301.13 303.37 290.15 282.20
266.4 43.16 43.16 6.646 – – – – – – –
1.000 1.000 1.000 1.000 – – – – – – –
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vapor phases in HG. Therefore, the increased γG led to an increase in qm,HG. Fig. 4(a) shows that increased γG led to an increase in TLG and TCD, and the increase rate of TLG was higher than that of TCD. With the obvious increase in TLG, the increase in the vapor pressure of LG was slight, which was conducive to the generation process. Therefore, the increased γG led to an increase in qm,LG. Fig. 5(b) indicates that with the increase in γG, the heat load of HG, QHG, and the heat load of LG, QLG, showed a linear increase. The increase in γG caused a decrease in THG, which resulted in an increase in the average temperature difference between the heat source and the solution in HG. Therefore, the increased γG led to an increase in QHG. The increase in γG caused an increase in qm,HG, which meant that more latent heat taken by the refrigerant vapor was inputted to LG. Therefore, the increased γG led to an increase in QLG. Fig. 6 presents the effects of the compression ratio of CM2, γA, on the operating conditions of each component, namely, (a) THG, TLG; (b) TEV, TCD, TAB; and (c) ωHG, ωLG, ωAB. In the calculation, the compression ratio of CM1, γG, was set to 1. Fig. 6(a) indicates that with the increase in γG, THG decreased linearly, but TLG increased linearly. With the increase of γA, the compression effect of CM2 improved. The enhanced compression effect largely increased the vapor pressure of the absorber. This condition led to increases in the difference in the mass transfer pressure between the solution and the vapor phase in the absorber. The increased difference in the mass transfer pressure caused the increase in the mass flow of the vaporized refrigerant. The heat capacity of the solution out of the absorber increased because the heat capacity of CH3OH was significantly higher than that of [mmim]DMP. In the same heat source condition, the increase in the solution heat capacity resulted in a decrease in THG. The decreased THG caused the increase in the difference in the heat transfer temperature between the heat source and the solution. With the fixed total thermal conductance, the increased difference in the heat transfer temperature led to the increase of the heat flow of HG and the mass flow of the vaporized refrigerant in HG. The increased refrigerant vapor took an increased amount of heat away from HG to LG, which led to an increase in TLG. Fig. 6(b) shows
Table 3 The calculation of the total thermal conductance of each component. Component (j)
Expression of ΔTj
ΔTj (K)
Qj (kW)
(AU)j/(W/K)
HG
(T16 − T5) − (T17 − T5) ln[(T16 − T5) / (T17 − T5)]
9.59
9.848
1026.5
LG CD
T12−T8
9.97 14.87
5.658 4.724
567.5 317.6
(T14 − T19) − (T14 − T20) ln[(T14 − T19) / (T14 − T20)] (T3 − T18) − (T3 − T19) ln[(T3 − T18) / (T3 − T19)]
7.87
16.72
2125.3
EV
(T21 − T1) − (T22 − T1) ln[(T21 − T1) / (T22 − T1)]
4.82
11.06
2297.0
HX
(T5 − T4 ) − (T6 − T3) ln[(T5 − T4 ) / (T6 − T3)] (T8 − T 7) − (T9 − T3) ln[(T8 − T 7) / (T9 − T3)]
34.52
8.443
244.6
12.32
4.733
384.2
AB
LX
enhanced with the increase in γG, thereby causing an obvious pressure decrease in HG. In the context of VLE theory, the obvious pressure decrease of HG resulted in a decrease in ωHG. The pressure decrease of HG also led to increases in the difference in the mass transfer pressure between the solution and the vapor phase in HG. The increased difference in mass transfer pressure caused the increase of the mass flow of the evaporated refrigerant. The increased refrigerant vapor took an increased amount of heat away to LG, which increased the heat load of LG and finally led to an increase in the evaporation capacity of LG. The increased evaporation capacity of LG led to a decrease in ωHG. The increase in γG caused an increase in TAB. In the context of VLE theory, the increased TAB resulted in a decrease in ωAB. Fig. 5 shows the effects of γG on the operating conditions of each component, namely, (a) qm,HG, qm,LG; (b) QHG, QLG. Fig. 5(a) indicates that with an increase in γG, the mass flow of refrigerant flow out of HG, qm,HG, and the mass flow of refrigerant flow out of the LG, qm,LG, showed a linear increase. The increase in γG caused a decrease in THG. This condition was conducive to the heat transfer between the heat source and the solution. In addition, γG caused the suction effect of CM1. This condition was conducive to the mass transfer between the liquid and
Fig. 3. Calculation algorithm of the CDAR system. 438
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Fig. 5. Effects of compression ratio of CM1, γG, on the operating conditions of each component: (a) qm,HG, qm,LG; (b) QHG, QLG.
to an increase in ωAB. The increased γA resulted in a decrease in THG. In the context of VLE theory, the increased THG resulted in an increase in ωHG. The increased γA resulted in a decrease in TCD, which meant that the vapor pressure of LG increased. In the context of VLE theory, the increased vapor pressure of LG caused the increase in ωLG. Fig. 7 presents the effects of the compression ratio of CM2, γA, on the operating conditions of each component, namely, (a) qm,HG, qm,LG; (b) QHG, QLG. Fig. 7(a) indicates that with the increase in γA, the mass flow of refrigerant flow out of HG, qm,HG, and the mass flow of refrigerant flow out of LG, qm,LG, showed a linear increase. The increase in γA led to an increase in ωHG, ωLG, and ωAB. The compression effect of CM2 was enhanced with the increase in γA, which caused an obvious pressure increase in the absorber. In VLE theory, the increased pressure in the absorber can significantly enhance the mass transfer of the absorption process and cause the rapid increase of ωAB. For variations of ωHG and ωLG, the increased γA caused the temperature changes of THG and TLG. These changes then led to the increases of ωHG and ωLG. The result implies that the influence of γA on ωAB is more direct than that on ωHG and ωLG. And the increase rate of ωAB was higher than the increase rates of ωHG and ωLG. Therefore, the deflation ranges of the solution in HG and LG increased. Naturally, the increased γA led to an increase in qm,HG and qm,LG. Fig. 7(b) shows that with an increase in γA, the heat load of HG, QHG, and the heat load of LG, QLG, showed a linear increase. The increased γA caused an increase in qm,HG. The increase of the mass flow of generation required much heat. Meanwhile, the increase in γA caused a decrease in THG, which resulted in an increase in the average temperature difference between the heat source and the solution in HG. Therefore, the increased γG led to an increase in QHG. The increased γG also led to an increase in qm,HG, which meant that more latent heat taken away by the refrigerant vapor was inputted to LG. Therefore, the
Fig. 4. Effects of the compression ratio of CM1, γG, on the operating conditions of each component: (a) THG, TLG; (b) TEV, TCD, TAB; (c) ωHG, ωLG, ωAB.
that with the increase in γA, TCD and TAB increased, but TEV decreased. The increase in γA caused a decrease in the vapor pressure of the absorber, and more refrigerant vapor was absorbed in the absorber. The heat load of QAB increased, resulting in the increase of the average temperature difference between the cooling water and the absorber. With the fixed inlet temperature of the cooling water, the increased temperature difference caused the increase in TAB. The increased γA led to an increase in TLG, which caused an increase of the vapor pressure of LG and the condenser. The increase in the vapor pressure in the condenser led to an increase in TCD. The increase in γA caused the enhancement of the suction effect of CM2. The enhanced suction effect reduced the vapor pressure of the evaporator, which caused a decrease in TEV. Fig. 6(c) indicates that the CH3OH mass fractions of ωHG, ωLG, and ωAB increased with γA. According to the previous analysis, the increased γA led to increases in the difference in the mass transfer pressure between the solution and the vapor phase in the absorber. The increased difference in mass transfer pressure caused the increase of the mass flow of the vaporized refrigerant. Therefore, the increased γA led 439
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Fig. 7. Effects of compression ratio of CM2, γA, on the operating conditions of each component: (a) qm,HG, qm,LG; (b) QHG, QLG.
evaporator, and absorber increased. The increased refrigerant mass flows led to the increase in the heat loads in all three components, resulting in the increase in the difference in the heat transfer temperatures among the three components. In the same cooling water and chilled water condition, the increased heat transfer temperature differences resulted in an increase in TCD and TAB and a decrease in TEV. Fig. 8(c) indicates that with the increase in Tsource, the CH3OH mass fractions of ωHG, ωLG, and ωAB increased. The increased Tsource caused ΤHG, ΤLG, and ΤAB to increase. Under the condition of fixed vapor pressure, when the solution temperature increases, the concentration of volatile components should decrease. Therefore, the increased temperatures led to a decrease in the CH3OH mass fractions of the solution in all three components. Fig. 9 presents the effects of heat source temperature, Tsource, on the operating conditions of each component, namely, (a) qm,HG, qm,LG; (b) QHG, QLG. Fig. 9(a) shows that with the increase in Tsource, the mass flows of qm,HG and qm,LG showed a linear increase. The increase in Tsource increased the difference in the heat transfer temperature between the heat source and the solution in HG. Therefore, the increased Tsource directly led to an increase in THG. In the context of VLE theory, the increased Tsource resulted in the increase of qm,HG. Furthermore, the increase of the refrigerant from HG increased the latent heat for the LG, thereby increasing qm,LG. Fig. 9(b) indicates that with the increase in Tsource, the heat loads of QHG and QLG showed a linear increase. The increase in Tsource caused an increase in the average temperature difference between the heat source and the solution in HG. Therefore, the increased Tsource resulted in an increase in the heat load of QHG, and the increased QHG caused an increase in qm,HG. More latent heat was inputted to LG, and the heat load of QLG increased. Finally, the increased QLG caused an increase in qm,LG. In addition, the increase rates of qm,HG and qm,LG decreased with the increase in Tsource because the increased Tsource led to an obvious increment in TCD, which was not conducive to
Fig. 6. Effects of compression ratio of CM2, γA, on the operating conditions of each component: (a) THG, TLG; (b) TEV, TCD, TAB; (c) ωHG, ωLG, ωAB.
increased γA caused an increase in QLG. Fig. 8 shows the effects of heat source temperature, Tsource, on the operating conditions of each component, namely, (a) THG, TLG; (b) TEV, TCD, TAB; (c) ωHG, ωLG, ωAB. In the calculation, the compression ratio of γG and γA was fixed to 1. Fig. 8(a) shows that with the increase in Tsource, solution temperatures THG and TLG showed an increase. The increase in Tsource increased the difference in the heat transfer temperature between the heat source and the solution in HG. Under the condition of fixing the total heat conductance of HG, the increased difference in heat transfer temperature resulted in the increase of the heat flow to the solution. Therefore, the increased Tsource directly led to an increase in THG. The mass flow of the refrigerant vapor from HG increased with THG, which caused an increase in the condensation heat released in LG. The increased condensation heat resulted in an increase in TLG. Fig. 8(b) shows that with the increase in Tsource, TCD and TAB increased, but TEV decreased. The increase of in Tsource caused the increase in THG and TLG, which was conducive to the generation processes in HG and LG. Therefore, the refrigerant mass flows in the condenser, 440
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Fig. 9. Effects of heat source temperature, Tsource, on the operating conditions of each component: (a) qm,HG, qm,LG; (b) QHG, QLG.
When γA was high, COP decreased with the increase in γG. Considering the upper limit of the deflation range, the influence of γG on the deflation ranges of HG and LG was significant with low γA but negligible with high γA. In addition, because the pressure of CM1 was much higher than that of CM2, the input power of CM1 was larger than that of CM2. Therefore, COP increased slowly at low γA and decreased at high γA. Fig. 10(b) indicates that ηex increased with the increase in γA but decreased with the increase in γG. Increased γA led to an increase in QEV and a decrease in TEV, which resulted in an increase in the exergy produced in the evaporator. In addition, the power of CM2 was small. Therefore, the increased γA resulted in an increase in ηex. Increased γG can also increase the exergy produced in the evaporator. However, the power of CM1 was large, which obviously increased the exergy input of the CDAR system. Therefore, the increased γG resulted in a decrease in ηex. Fig. 11 shows the effects of Τsource on COP and ηex in four cases of compressor ratios (Case I: γG = 1, γA = 1; Case II: γG = 1.2, γA = 1.2; Case III: γG = 1.44, γA = 1; Case IV: γG = 1, γA = 1.44). Fig. 11(a) shows the variation of COP on Τsource in four cases. With the increase in Τsource, COP increased when Τsource was low but declined when Τsource was high. Such outcome can be attributed to the fact that the increased Τsource caused the increases of QEV and QHG. When Τsource was low, the increase rate of QEV was more rapid than that of QHG. Therefore, with the increase in Τsource, COP increased when Τsource was low. With the increase of Τsource, TCD and TAB increased, thereby slowing down the increase rate of QEV. With the increase of Τsource, QHG still increased rapidly. When Τsource was high, the increase rate of QHG was more rapid than that of QEV, thereby leading to the decrease of COP. In the four cases, the optimum values of 1.032, 1.106, 1.058, and 1.151 were observed at Τsource = 452 °C, 417 °C, 428 °C, and 403 °C, respectively. The
Fig. 8. Effects of heat source temperature, Tsource, on the operating conditions of each component: (a) THG, TLG; (b) TEV, TCD, TAB; (c) ωHG, ωLG, ωAB.
the generation process in HG and LG. Fig. 10 shows the effects of γA and γG on the thermal properties of the CDAR system, namely, (a) COP and (b) ηex. Fig. 10(a) indicates that with the increase in γA, COP increased, but the increase rate of COP showed a declining trend. The increase in γA led to an increase in the vapor pressure of the absorber, which was conducive to the absorption process. The refrigerant concentration of the solution from the absorber increased, which was conducive to the generation processes in HG and LG. Therefore, the increased γA caused an increase in the deflation ranges of HG and LG, which led to an increase in the mass flow of the refrigerant in the evaporator. The increased mass flow of the refrigerant resulted in an increase in cooling capacity, which finally led to an increase in COP. Fig. 6(b) indicates that with the increase in γA, TCD and TAB increased, but TEV decreased. The variation trends of TCD, TAB, and TEV negatively affected COP. Therefore, the increment rate of COP declined. When γA was low, COP increased with the increase in γG. 441
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Fig. 10. Effects of γA and γG on the thermal properties of the CDAR system: (a) COP and (b) ηex. Fig. 11. Effects of Τsource on COP and ηex in four cases of compressor ratios.
use of the assisting compressor decreased the optimal Τsource and increased the optimal COP of the absorption system. Fig. 11(b) shows the variation of ηex on Τsource in the four cases. For Cases I and III, with the increase in Τsource, ηex increased when Τsource was low but declined when Τsource was high. The optimum values of 0.1668 and 1.8610 were observed at Τsource = 389 °C and 361 °C, respectively. The trend can be attributed to the fact that increases in Τsource led to the increases of the output exergy in QEV and the input exergy in QHG. When Τsource was low, the growth rate of exergy in QEV was faster than that in QHG, and ηex increased. With the increase of Τsource, the input exergy in QHG increased rapidly. When Τsource was high, the growth rate of exergy in QHG was faster than that in QEV, and ηex decreased. For Cases II and IV, no peak appeared for ηex in the proposed temperature range. This result suggests that the lower limit of Τsource was largely reduced by the assisting compressor. For COP and ηex, Case IV was the best case, followed by Case II. When Τsource was low, Case III was better than Case I. When Τsource was high, Case III was worse than Case I. Therefore, the assisting compressor placed between the evaporator and absorber was the better choice. The assisting compressor placed between HG and LG improved the cooling capacity of the CDAR system and reduced the evaporation temperature. When Τsource was high, the COP and ηex of Case III were only slightly lower than those of absorption refrigeration without an assisting compressor. Therefore, the assisting compressor placed between HG and LG was also an acceptable choice. Fig. 12 presents the exergy flow schematic of the CDAR system in the basic operating conditions. The CDAR system comprises three inputs to CM1, CM2, and HG. The exergy inputs to CM1, CM2, and HG are 0.301, 0.233, and 4.159 kW, which account for 6.4%, 5.0%, and 88.6% of the total exergy input, respectively. In HG, the temperature
decreased from T16 to T5, and the vaporization of the refrigerant caused an exergy loss of 0.424 kW, which accounts for 9.1% of the total exergy input. In LG, the phase changes (condensation and vaporization) of the refrigerant and the heat transfer with a temperature difference resulted in an exergy loss of 1.407 kW, which accounts for 29.9% of the total exergy input. In the condenser, the phase change of condensation led to an exergy loss of 0.238 kW, which accounts for 6.0% of the total exergy input. In the evaporator, the phase change of the evaporation caused an exergy loss of 0.738 kW, which accounts for 15.7% of the total exergy input. In the absorber, the liquefaction of the refrigeration and the heat transfer with a temperature difference led to an exergy loss of 0.556 kW, which accounts for 11.8% of the total exergy input. In HX and LX, the heat transfer with a temperature difference caused exergy losses of 0.581 and 0.292 kW, which account for 12.4% and 6.3% of the total exergy input, respectively. In CM1 and CM2, the changes in energy form (from work to heat) caused exergy losses of 0.214 and 0.198 kW, which account for 4.6% and 4.2% of the total exergy input, respectively. The largest exergy loss occurred in LG, which accounts for approximately one-third of the total exergy input. This result suggests that the most significant reason for the exergy loss in the CDAR system was heat transfer with a temperature difference. Therefore, an effective measure to improve the exergy efficiency of the CDAR system is to appropriately increase the heat transfer area of the components.
6. Conclusion In this study, the operating characteristics and thermal performance 442
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Fig. 12. Exergy flow schematic of the CDAR system.
of a CDAR system using [mmim]DMP/CH3OH as working fluid were numerically studied. Thermal performance was compared under different compression ratios. The major conclusions are as follows:
[4]
(1) With the increase in γG, parameters TLG, TCD, TAB, qm,HG, qm,LG, QHG, and QEV increased, but THG, TEV, ω HG, ω LG, and ω AB decreased. With the increase in γA, parameters TLG, TCD, TAB, ω HG, ω LG, ω AB, qm,HG, qm,LG, QHG, and QEV increased, but THG and TEV decreased. With the increase in Tsource, parameters TLG, TLG, TCD, TAB, qm,HG, qm,LG, QHG, and QEV increased, but TEV, ω HG, ω LG, and ω AB decreased. (2) COP and ηex increased with an increase in γG. When γA was low, COP increased with the increase in γG. When γA was high, COP decreased with the increase in γG. ηex decreased with the increase in γA. (3) With the increase in Tsource, COP declined after the initial rise; ηex declined after the initial rise for Cases III and IV, but showed a trend of decline for Case I and Case II. (4) Placing the assisting compressor between the evaporator and absorber was the best choice, but placing the assisting compressor between two generators was also acceptable. (5) The largest exergy loss occurred in LG, and heat transfer with a temperature difference was the main reason for the exergy losses.
[5] [6]
[7]
[8]
[9]
[10] [11]
[12] [13] [14] [15]
Acknowledgements
[16]
This research is supported by the National Natural Science Foundation of China (Grant No. 51506104), the Source Innovation Application Foundation Research Project of Qingdao (Grant No. 17-1-135-jch), and the Promotive Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province (Grant No. BS2014NJ021).
[17]
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[19] [20]
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Numerical investigation of the thermal performance of compressor-assisted double-effect absorption refrigeration using [mmim]DMP/CH3OH as working fluid
T
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Wei Chen , Qiang Sun, Yang Bai, Bin Zhang College of Electromechanical Engineering, Qingdao University of Science & Technology, Qingdao 266061, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Double effect absorption refrigeration Compressor assisted Ionic liquid Coefficient of performance Exergy efficiency
The thermal performance of compressor-assisted double-effect absorption refrigeration (CDAR) was numerically investigated and comprehensively analyzed with 1, 3-dimethylimidazolylium dimethylphosphate/methanol ([mmim]DMP/CH3OH) as working fluid. The CDAR system was modeled and simulated based on the proposed mathematical model of the compression process by considering the mass and energy conservation of each component. The effects of compression ratio and heat source temperature on the system’s operating state, including solution temperature, refrigeration concentration, mass flow, and heat load of each component, were calculated and discussed. Variations in the coefficient of performance and exergy efficiency in four cases were simulated and compared. Results suggested that placing the assisting compressor between the evaporator and absorber was a good option, and placing the assisting compressor between two generators was also acceptable. The exergy losses of each component were calculated and compared. The largest exergy loss occurred in the lowtemperature generator and accounted for approximately one-third of the total exergy input. The main reason for the exergy loss in the diffusion absorption refrigeration system was heat transfer with a temperature difference.
1. Introduction Absorption refrigeration has been widely applied in low-grade heat sources [1], such as solar energy [2], geothermal energy [3], biomass energy [4], and industrial waste heat [5]. The working fluid of absorption refrigeration is composed of an absorbent and a refrigerant [6]. The main role of the absorbent is to reduce the saturated vapor pressure of the working fluid solution [7] to ensure absorption in the absorber of absorption refrigeration. Therefore, the absorbent is the key component of the working fluid. Ionic liquids (ILs) are organic ionic compounds with melting points lower than room temperature [8]. ILs are miscible with most refrigerants, such as Freon, alkane, and alcohol [9]. The vapor pressure of a solution containing an IL and a refrigerant is largely reduced because the vapor pressure of ILs is negligible. Additionally, ILs possess excellent properties of high thermal stability, low combustibility, and non-corrosiveness [10]. Therefore, ILs are potential absorbents in absorption refrigeration. The concept of using ILs as absorbents in absorption refrigeration was proposed by Yokozeki in 2006 [11]. Research on IL absorption refrigeration has become popular in recent decades. Shiflett et al. [12]
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Corresponding author at: Songling Road 99, Qingdao, China. E-mail address: [email protected] (W. Chen).
https://doi.org/10.1016/j.enconman.2018.04.060 Received 8 February 2018; Received in revised form 8 April 2018; Accepted 15 April 2018 Available online 03 May 2018 0196-8904/ © 2018 Elsevier Ltd. All rights reserved.
investigated the thermal performance of absorption refrigeration using IL/Freon as working fluid. An optimal coefficient of performance (COP) of 0.539 for the DMF/R22 system was reported. Liang et al. [13] numerically investigated the cycle characteristic of IL absorption refrigeration using alcohols as a refrigerant. Su et al. [14] simulated the theoretical cycle of absorption refrigeration by adopting [hmim]Cl/ H2O and [Emim]AC/H2O as working fluids. They found that the thermal performance of the [Emim]AC/H2O system is better than that of [hmim]Cl/H2O. Ángel et al. [15] investigated the possibility and potential of absorption refrigeration with IL/CO2 as working fluid and indicated that the best absorbent for supercritical CO2 is [bmpyrr] [Tf2N]. Shiflett et al. [16] investigated the thermal performance of the IL/NH3 absorption system and discovered that absorption refrigeration using [DMEA][AC]/CO2 achieves an optimal COP. They also confirmed that IL absorption refrigeration possesses an excellent industrial application potential. The COP and generation temperature of multi-effect absorption refrigeration are significantly higher than those of a single-effect system. The most widely used working fluid in multi-effect absorption refrigeration is LiBr/H2O [17]. The LiBr concentration in the solution from the generator increases with the generation temperature, and this
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Nomenclature
Subscript
A, B, b AU cp COP f h Lb p qm Q p s Sg v w W
1,2…16 0 ΑΒ, Α act C CD CM EV ex HG HX in, out IL LG LX v
parameters for EOS of CH3OH total heat conductance (kJ/K) specific heat capacity (kJ/(kg·K)) coefficient of performance function Specific enthalpy (kJ/kg) latent heat (kJ/kg) pressure (kPa) mass flow (kg/s) heat flow (kW) pressure (kPa) specific entropy (kJ/(kg·K)) entropy production (kJ/K) specific volume (m3/kg) specific power (kW/kg) power (kW)
status point environmental absorber actual process critical parameter condenser compressor evaporator exergy high temperature generator high temperature exchanger parameter of inlet and outlet ionic liquid low temperature generator low temperature exchanger vapor
Greek symbols
Superscript
γ η φ ω
0 E is S
compression ratio efficiency activity coefficient mass fraction
reference point excessive parameter isentropic process saturation
and analyzed, and the exergy losses of each component were calculated and discussed.
increment significantly increases the risk of crystallization in the solution heat exchanger [18]. In addition, the corrosion of LiBr/H2O solution is extremely strong at high temperatures [19]. The application of multi-effect LiBr/H2O absorption refrigeration is thus largely restricted. Multi-effect absorption refrigeration using IL as working fluid can completely prevent the problems of corrosion and crystallization in the LiBr/H2O system because of the low melting temperature and noncorrosiveness of ILs. ILs as working fluid are more suitable for multieffect absorption refrigeration than LiBr/H2O. However, the deflation range of IL absorption systems is smaller than that of LiBr/H2O systems [13,14]. A small deflation range results in a high circulation ratio and causes COP deterioration [12,15]. The most reasonable approach to improve the deflation range is introducing an assisting compressor into the absorption cycle [20]. Boer et al. [21] numerically studied double-effect absorption refrigeration with a compressor placed between the evaporator and absorber and with TEGDME/CH3OH and TEGDME/TFE as working fluids. Kim et al. [22] conducted simulations for a basic triple-effect cycle and four proposed compressor-assisted cycles with LiBr/H2O as working fluid. Dereje et al. [23] investigated the thermal performance of a combined absorption power and refrigeration cycle with an integrated compressor. Wang et al. [24] numerically investigated the thermal performances of the absorption compression hybrid refrigeration system recovering condensation heat for generation. Shu et al. [25] simulated the thermal performance of a proposed compressor-assisted triple-effect LiBr/H2O absorption cooling cycle coupled with a Rankine cycle driven by hightemperature waste heat. They reported that the integrated compressor improves the thermal performance of multi-effect absorption refrigeration. In this study, a mathematical model of the compression process was established based on the equation of state (EOS), the enthalpy equation, and the entropy equation of superheated methanol vapor. Steady modeling and simulation of compressor-assisted double-effect absorption refrigeration (CDAR) system with [mmim]DMP/CH3OH as working fluid were conducted in consideration of the mass and energy conservation of each component of the proposed system. The influences of compression ratio and heat source temperature on the operating states and thermal performance of the CDAR system were simulated
2. Thermodynamic properties of working fluid The vapor liquid equilibrium (VLE) of the [mmim]DMP/CH3OH solution is crucial for the simulation of the thermal performance of the CDAR system. The vapor phase of [mmim]DMP/CH3OH is pure CH3OH vapor because the vapor pressure of [mmim]DMP is negligible. The vapor pressure of the [mmim]DMP/CH3OH solution can be calculated as follows:
p = x2 φ2 p2S
(1)
where x2 is the mole fraction of CH3OH in the solution, φ2 is the activity coefficient of CH3OH, and p2S is the saturation pressure of pure CH3OH. φ2 can be calculated using the universal quasichemical functional group activity coefficient (UNIFAC) model [26]. p2S can be calculated using the Antoine equation [27]. The specific enthalpy and entropy of the [mmim]DMP/CH3OH solution are the most essential properties to the simulation of the thermal performance of the CDAR system. The specific enthalpy of the binary solution can be calculated as
h = ω1
∫T
T 0
cp,IL dT + ω2
∫T
T 0
cp,R dT + h 0E +
∫T
T
0
cp dT
(2)
The specific entropy of the binary solution can be calculated as [26]
s = ω1
∫T
T 0
(cp,1/ T ) dT + ω2
∫T
T 0
(cp,2/ T ) dT + h0E/ T0 +
∫T
T
0
(cp/ T ) dT (3)
where T0 is ambient temperature, which is 298.15 K, and T0 is the reference temperature for the calculation of specific enthalpy and entropy. The value of T0 is 273.15 K. h 0E is the excess enthalpy of the solution at T0. ω1 and ω2 are the mass fractions of [mmim]DMP and CH3OH in the binary solution, respectively. cp,1 and cp,2 are the specific heat capacities of [mmim]DMP and CH3OH, respectively. cp stands for the specific capacity of the [mmim]DMP/CH3OH solution. The expression of h 0E and the specific capacities can be found in our previous work [28]. 434
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condensation and generation processes in LG. Arrows (12, 14) and (13, 14) denote the condensation process in the condenser, and arrow (14, 1) represents the evaporation process in the evaporator.
The specific enthalpy and entropy of the superheated vapor of CH3OH at T and p can be derived as
h=
s=
∫T ∫T
TS 0
TS 0
cp,1 dT + Lb +
∫T
T S
cp,v dT
(cp,1/ T ) dT + Lb / T S +
∫T
T S
(4)
(cp,v / T ) dT
4. Modeling and simulation 4.1. Mathematic model of compression process
(5)
S
where T is the saturation temperature that corresponds to vapor pressure p and cp,v is the specific heat capacity of the CH3OH vapor at constant pressure. Lb is the latent heat of CH3OH. Latent heat can be predicted by the Chen equation [29].
Suction pressure pin and suction temperature Tin are the given parameters for the assisting compressor. Specific enthalpy hin and specific entropy sin can be calculated with Eqs. (2) and (3). For the isentropic compression process, the equations of momentum and energy conservation can be written as
3. System description
is f1 = pout −γpin = 0
Fig. 1 shows a schematic of the CDAR system. The CDAR system consists of a high-temperature generator (HG), a low-temperature generator (LG), a high-temperature solution heat exchanger (HX), a low-temperature solution heat exchanger (LX), a condenser (CD), an absorber (AB), an evaporator (EV), two assisting compressors (CM1, CM2), two solution pumps (SP1, SP2), and several valves. The CDAR system contains two solution loops. In one loop, [mmim]DMP/CH3OH with a low IL concentration (weak solution) from the absorber is lifted to HG by SP1. In HG, the weak solution is heated by the heat source. The refrigerant CH3OH is desorbed from the solution, and the IL concentration of the [mmim]DMP/CH3OH solution increases. The solution with a high IL concentration is called a strong solution. The strong solution flows back to the absorber due to the pressure difference between HG and the absorber. HX is placed between HG and the absorber. When the weak and strong solutions pass through HX, the weak solution is preheated by the strong solution, and the strong solution is precooled by the weak solution. The heat exchange in HX can reduce the heat loads of HG and the absorber. In the other loop, the weak solution from the absorber is lifted to LG by SP2. The CH3OH vapor from HG is compressed by CM1 and flows into LG. In LG, the CH3OH vapor condenses, and condensation heat is released. The refrigerant CH3OH evaporates from the weak solution because of the condensation heat. The weak solution is concentrated and becomes a strong solution. The strong solution flows back to the absorber due to the pressure difference between LG and the absorber. LX placed between LG and the absorber. The role of LX is similar to that of HX. The CH3OH liquid and the CH3OH vapor from LG flow to the condenser. CH3OH is in a saturated liquid state as it flows out of the condenser. The latent heat of CH3OH is eliminated by the cooling water. Then, the CH3OH saturated liquid passes through the throttle valve (V1) and flows to the evaporator. In the evaporator, the CH3OH saturated liquid evaporates and becomes CH3OH vapor. The vapor from the evaporator is compressed by CM2 and flows to the absorber. In the absorber, the compressed vapor is absorbed by the strong solution from HG and LG. Then, the solution is diluted and becomes weak. Fig. 2 presents the thermodynamic cycle of the CDAR system in a P–T diagram of the [mmim]DMP/CH3OH binary system. The black curves, marked by x2 and percentage, show the relationship of CH3OH pressure and temperature with different CH3OH mole fractions, which are drawn according to the VLE of the [mmim]DMP/CH3OH solution. The solution loop for HG is denoted by the red curves, and the solution loop for LG is denoted by the green curves. The thermal processes of the refrigeration are marked as the blue curves. The black points in Fig. 2 represent the operating status of the CDAR system. The numbers of the operating status in Fig. 2 are in accordance with those in Fig. 1. Arrow (1, 2) represents the compression process in CM2. Arrows (2, 3), (9, 3), and (6, 3) represent the absorption process in the absorber. Arrows (3, 4) and (5, 6) represent the heat exchange process in HX. Arrows (3, 7) and (8, 9) denote the heat exchange process in LX. Arrow (9, 10) represents the generation process in HG. Arrow (10, 11) indicates the compression process in CM1. Arrows (11, 12) and (7, 13) represent the
f2 =
(6)
is is hout −h in−wCM is pout
=0
(7)
is the outlet pressure of isentropic compression, hout is specific enthalpy of isentropic compression, wCM
is is the where outlet of the is the specific compression power of isentropic compression, and γ is the compression ratio of the assisting compressor. For the superheated CH3OH vapor, EOS can be derived as is is is / TC ) RTout A1 + A2 Tout + A3 exp(−kTout − is is 2 vout−b (vout−b)
is f3 = pout −
−
is is B1 + B2 Tout / TC ) + B3exp(−kTout is 3 (vout−b)
(8)
is Tout
is the outlet temperature of isentropic compression. The where adjustable parameters for EOS are presented in Table 1 [30]. For the superheated CH3OH vapor, the enthalpy and entropy equations can be expressed as is f4 = hout −
f5 =
∫T
TS 0
∫T
TS 0
cp,1 dT + Lb +
∫T
(cp,1/ T ) dT + Lb / T S +
is
Tout S
cp,v dT
is Tout S T
∫
(cp,v / T ) dT −sin
(9) (10)
Eqs. (6)–(10) form a nonlinear equation group with five variables
Fig. 1. Schematic of the CDAR system. 435
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phase, and the superheat degree of the refrigeration flow out of the evaporator is set to 2 K. (6) The isentropic compression efficiencies of the two assisting compressors, CM1 and CM2, are set to 0.5. (7) The thermal losses of the entire CDAR system are ignored, and the powers of the two solution pumps, SP1 and SP2, are omitted. On the basis of these assumptions, a steady model of the CDAR system was built in consideration of the mass and energy conservation of each system component. For HG, the solution mass conservation, IL mass conservation, and energy conservation can be obtained with
Table 1 The adjustable parameters for the EOS [30].
R b A1 A2 A3
Value 82.0561 10.1920 −1.41994 × 107 1.17640 × 104 −5.15589 × 1010
Parameters B1 B2 B3 k TC
Value
(15)
qm,4 h4 + QHG = qm,5 h5 + qm,10 h10
(16)
(T16−T5)−(T17−T5) ln[(T16−T5)/(T17−T5)]
(17)
The entropy production for HG can be calculated as 9
Sg,HG = qm,5 s5 + qm,10 s10−qm,4 s4−QHG/ T5
1.26559 × 10 −7.62529 × 105 5.45122 × 1012 −11 513.15
p = γpin
(18)
For LG, the solution mass conservation, IL mass conservation, and energy conservation are obtained as
qm,7 = qm,8 + qm,13
(19)
qm,7 ω7 = qm,8 ω8
(20)
qm,8 h8 + qm,13 h13−qm,7 h 7 = qm,12 h12−qm,11 h11 = QLG
(21)
where QLG is the heat flow of LG and can be written as
QLG = (AU )LG (T12−T18)
(11)
(22)
The entropy production for LG can be calculated as
The specific compression power, wact, can be calculated as
Sg,LG = qm,8 s8 + qm,12 s12 + qm,13 s13−qm,11 s11−qm,7 s7 (12)
(23)
For the absorber, the solution mass conservation, IL mass conservation, and energy conservation are given by
where ηCM is the thermal efficiency of the assisting compressor, which is set to 0.5. The specific enthalpy of the actual compression outlet, hout, can be calculated as
hout = h in + wact
qm,4 ω4 = qm,5 ω5
QHG = (AU )HG
and five equations. The nonlinear equation group can be solved using is is , vout , the Jacobi iterative method [31]. Then, the five variables, p pout is is is Tout , hout , and wCM, can be obtained. For the actual compression process, outlet pressure pout can be calculated with
wact = w is/ ηCM
(14)
where ω is the mass fraction of IL, qm is the mass flow, and QHG is the heat flow of HG. The last item can be written as
Fig. 2. Thermodynamic cycle of the CDAR system in the P-T diagram.
Parameters
qm,4 = qm,5 + qm,10
(13)
The outlet temperature of the actual compression process, Tout, can be calculated with Eq. (4). The outlet specific volume of the actual compression process, vout, can be calculated based on the EOS of CH3OH. Finally, the outlet specific entropy of the actual compression process, sout, can be calculated with Eq. (5).
qm,3 = qm,1 + qm,6 + qm,9
(24)
qm,3 ω3 = qm,6 ω6 + qm,9 ω9
(25)
qm,1 h1 + qm,6 h6−qm,9 h9 = qm,3 h3 + QAB
(26)
where QAB is the heat flow of the absorber and can be written as
QAB = (AU )AB
(T3−T18)−(T3−T19) ln[(T3−T18)/(T3−T19)]
(27)
The entropy production for the absorber can be calculated as
4.2. Modeling of the CDAR system
Sg,AB = qm,3 s3−qm,1 s1−qm,6 s6−qm,9 s9−QAB/ T3
The following assumptions were made to establish a steady model of the CDAR system.
qm,12 = qm,14
(29)
qm,12 h12 = qm,14 h14 + QCD
(30)
(28)
For the condenser, mass and energy conservation are obtained by
(1) The CDAR system is simulated under the steady-state condition. (2) The lumped parameter method is used for the modeling of the CDAR system. Thus, the concentration and temperature distributions of the solution in the absorber, HG, and LG are uniform. (3) For solution and refrigerant flows, the vapor pressure drops along the tube are omitted. (4) The mass transfer pressure difference of generation, absorption, evaporation, and condensation is ignored. (5) The refrigeration flow out of the condenser is in a saturated liquid
where QCD is the heat flow of the condenser and can be written as
QCD = (AU )CD
(T14−T19)−(T14−T20) ln[(T14−T19)/(T14−T20)]
(31)
The entropy production for the absorber can be calculated as
Sg,CD = qm,14 s14−qm,13 s13−QCD/ T13
(32)
For the evaporator, mass and energy conservation are obtained by 436
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qm,1 = qm,15
(33)
qm,1 h1 = qm,15 h15 + QEV
(34)
derivatives of the temperature of all components were calculated with small elemental changes in ΔT. Similarly, given the assumed values of T6 and THG (T5), parameters Τ4, T17, ωHG (ω5), qm,10, and QHG were calculated by Eqs. (14)–(17) and Eqs. (37) and (39). Then, the energy conservations of HG and HX were verified. Based on the verification results, the assumed values of T6 and THG were adjusted using the Newton–Raphson method until the calculation results converged. Given the assumed values of T9 and TLG (T8), parameters Τ7, Τ11, T12, T13, ωLG (ω8), qm,13, and QLG were calculated by Eqs. (19)–(22) and Eqs. (38) and (40). Then, the energy conservations of LG and LX were verified. Based on the verification results, the assumed values of T9 and TLG were adjusted using the Newton–Raphson method until the calculation results converged. Given the assumed values of TCD (T14) and TEV (T1), parameters Τ15, Τ19, T20, T21, QCD, and QEV were calculated by Eqs. (29)–(35). Then, the energy conservations of CD and EV were verified. Based on the verification results, the assumed values of TCD and TEV were adjusted using the Newton–Raphson method until the calculation results converged.
where QEV is the heat flow of the absorber and can be written as
(T21−T1)−(T22−T1) ln[(T21−T1)/(T22−T1)]
QEV = (AU )EV
(35)
The entropy production for the absorber can be calculated as
Sg,EV = qm,1 s1−qm,15 s15−QEV / T1
(36)
For HX and LX, the energy conservations can be obtained by
qm,4 h4−qm,3 h3 = qm,5 h5−qm,6 h6 = QHX
(37)
qm,7 h7−qm,3 h3 = qm,8 h8−qm,9 h9 = QLX
(38)
where QHX and QLX are the heat flows of HX and LX, respectively, and can be written as
QHX = (AU )HX QLX = (AU )LX
(T5−T4 )−(T6−T3) ln[(T5−T4 )/(T6−T3)]
(T8−T7)−(T9−T3) ln[(T8−T7)/(T9−T3)]
(39) 5. Results and discussion (40)
Fig. 4 presents the effects of the compression ratio of CM1, γG, on the operating conditions of each component, namely, (a) THG, TLG; (b) TEV, TCD, TAB; and (c) ωHG, ωLG, ωAB. In the calculation, the compression ratio of CM2, γA, was fixed to 1. Fig. 4(a) shows that with the increase in γG, THG decreased linearly, but TLG increased linearly. With the increase of γG, the suction effect of CM1 improved. The enhanced suction effect largely reduced the vapor pressure of HG. This reduction led to increases in the difference in the mass transfer pressure between the solution and the vapor phase in HG. The increased difference in mass transfer pressure caused the increase of the mass flow of the vaporized refrigerant. The increased refrigerant vapor took an increased amount of heat away from HG to LG, which finally led to a decrease in THG and an increase in TLG. Fig. 4(b) shows that with the increase in γG, TCD and TAB increased, but TEV decreased. The increased γG caused the increased TLG. As the pressure drops along the tube were omitted, the vapor pressure of the condenser was equal to that of the LG. With the increase of TLG, the vapor pressure of the LG and the condenser increased. This result shows that saturation temperature absolutely increases with increasing saturation pressure. Therefore, the condensation temperature, TCD, increased. The increment in γG caused an increase in the mass flow of the refrigerant to the evaporator. The cooling capacity of the evaporator was improved, which led to an increase in the temperature difference between the refrigerant and the chilled water. Given that the inlet temperature of the chilled water was fixed, the evaporation temperature, TEV, decreased. The increase in γG caused an increase in the mass flow of the refrigerant vapor to the absorber, which meant that the increased latent heat was carried into the absorber. Therefore, the heat load of the absorber increased, which finally led to an increase in TAB. Fig. 4(c) indicates that the CH3OH mass fractions of ωHG, ωLG, and ωAB decreased with the increase in γG. The suction effect of CM1 was
The entropy productions for HX and LX can be calculated as
Sg,HX = qm,4 s4 + qm,6 s6−qm,5 s5−qm,3 s3
(41)
Sg,LX = qm,7 s7 + qm,9 s9−qm,8 s8−qm,3 s3
(42)
The COP of the CDAR system is defined as
COP =
QEV QHG + WCM1 + WCM 2
(43)
The exergy efficiency of the CDAR system is defined as
ηex =
QEV [(T0/ T1)−1] QHG [1−(T0/ T5)] + WCM1 + WCM 2
(44)
CDAR is a self-balancing system with an electronic control device. The working conditions of the CDAR system are directly determined by the heat flows and the total thermal conductance of each component. To determine the total thermal conductance of each component, we proposed a basic design of the operating conditions, which are shown in Table 2. The average temperature differences and heat flows of the components were easily calculated based on the basic design of operating conditions. The total thermal conductance of each component was obtained and fixed for the simulation, as presented in Table 3. 4.3. Calculation algorithm of the simulation The detailed calculation algorithm of the CDAR system is shown in Fig. 3. Seven parameters (THG, TLG, TAB, TCD, TEV, T6, and T9) were determined by iterative methods because the CDAR system is self-balancing. The assumed input values of the parameters were set for the iteration according to the basic design of the working conditions. Then, the values of these parameters were adjusted until the iterative results converged. The CDAR system was simulated using MATLAB/Simulink. The thermodynamic parameters of the working fluid and the total thermal conductance of each component were initially inputted. For the simulation, the compression ratio of CM1 (γG) and the compression ratio of CM2 (γA) were initialized. The operating mass flows, qm,16, qm,18, qm,21, qm,4, and qm,7, were set to 0.15, 0.5, 0.3, 0.056, and 0.056 kg/s, respectively. The operating temperatures of T18 and T21 were set to 293.15 and 290.15 K, respectively. Given the assumed values of TEV (T3), parameters T2, T19, ωAB (ω3), and QAB were calculated based on Eqs. (24), (25), and (27). Then, the energy conservation of the absorber was verified. On the basis of the verification results, the assumed values of TEV were adjusted using the dichotomy method until the calculation results converged. The first
Table 2 The operating conditions of the basic design.
437
Point
T (K)
p (kPa)
ω
Point
T (K)
p (kPa)
ω
1 2 3 4 5 6 7 8 9 10 11
281.36 291.35 305.67 370.84 414.26 332.60 339.11 354.40 315.43 414.26 426.21
6.646 7.975 7.975 222.8 222.8 15.22 43.16 43.16 8.932 222.0 266.4
1.000 1.000 0.289 0.289 0.211 0.211 0.289 0.236 0.236 1.000 1.000
12 13 14 15 16 17 18 19 20 21 22
364.37 354.40 317.15 281.36 480.00 414.33 293.15 301.13 303.37 290.15 282.20
266.4 43.16 43.16 6.646 – – – – – – –
1.000 1.000 1.000 1.000 – – – – – – –
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vapor phases in HG. Therefore, the increased γG led to an increase in qm,HG. Fig. 4(a) shows that increased γG led to an increase in TLG and TCD, and the increase rate of TLG was higher than that of TCD. With the obvious increase in TLG, the increase in the vapor pressure of LG was slight, which was conducive to the generation process. Therefore, the increased γG led to an increase in qm,LG. Fig. 5(b) indicates that with the increase in γG, the heat load of HG, QHG, and the heat load of LG, QLG, showed a linear increase. The increase in γG caused a decrease in THG, which resulted in an increase in the average temperature difference between the heat source and the solution in HG. Therefore, the increased γG led to an increase in QHG. The increase in γG caused an increase in qm,HG, which meant that more latent heat taken by the refrigerant vapor was inputted to LG. Therefore, the increased γG led to an increase in QLG. Fig. 6 presents the effects of the compression ratio of CM2, γA, on the operating conditions of each component, namely, (a) THG, TLG; (b) TEV, TCD, TAB; and (c) ωHG, ωLG, ωAB. In the calculation, the compression ratio of CM1, γG, was set to 1. Fig. 6(a) indicates that with the increase in γG, THG decreased linearly, but TLG increased linearly. With the increase of γA, the compression effect of CM2 improved. The enhanced compression effect largely increased the vapor pressure of the absorber. This condition led to increases in the difference in the mass transfer pressure between the solution and the vapor phase in the absorber. The increased difference in the mass transfer pressure caused the increase in the mass flow of the vaporized refrigerant. The heat capacity of the solution out of the absorber increased because the heat capacity of CH3OH was significantly higher than that of [mmim]DMP. In the same heat source condition, the increase in the solution heat capacity resulted in a decrease in THG. The decreased THG caused the increase in the difference in the heat transfer temperature between the heat source and the solution. With the fixed total thermal conductance, the increased difference in the heat transfer temperature led to the increase of the heat flow of HG and the mass flow of the vaporized refrigerant in HG. The increased refrigerant vapor took an increased amount of heat away from HG to LG, which led to an increase in TLG. Fig. 6(b) shows
Table 3 The calculation of the total thermal conductance of each component. Component (j)
Expression of ΔTj
ΔTj (K)
Qj (kW)
(AU)j/(W/K)
HG
(T16 − T5) − (T17 − T5) ln[(T16 − T5) / (T17 − T5)]
9.59
9.848
1026.5
LG CD
T12−T8
9.97 14.87
5.658 4.724
567.5 317.6
(T14 − T19) − (T14 − T20) ln[(T14 − T19) / (T14 − T20)] (T3 − T18) − (T3 − T19) ln[(T3 − T18) / (T3 − T19)]
7.87
16.72
2125.3
EV
(T21 − T1) − (T22 − T1) ln[(T21 − T1) / (T22 − T1)]
4.82
11.06
2297.0
HX
(T5 − T4 ) − (T6 − T3) ln[(T5 − T4 ) / (T6 − T3)] (T8 − T 7) − (T9 − T3) ln[(T8 − T 7) / (T9 − T3)]
34.52
8.443
244.6
12.32
4.733
384.2
AB
LX
enhanced with the increase in γG, thereby causing an obvious pressure decrease in HG. In the context of VLE theory, the obvious pressure decrease of HG resulted in a decrease in ωHG. The pressure decrease of HG also led to increases in the difference in the mass transfer pressure between the solution and the vapor phase in HG. The increased difference in mass transfer pressure caused the increase of the mass flow of the evaporated refrigerant. The increased refrigerant vapor took an increased amount of heat away to LG, which increased the heat load of LG and finally led to an increase in the evaporation capacity of LG. The increased evaporation capacity of LG led to a decrease in ωHG. The increase in γG caused an increase in TAB. In the context of VLE theory, the increased TAB resulted in a decrease in ωAB. Fig. 5 shows the effects of γG on the operating conditions of each component, namely, (a) qm,HG, qm,LG; (b) QHG, QLG. Fig. 5(a) indicates that with an increase in γG, the mass flow of refrigerant flow out of HG, qm,HG, and the mass flow of refrigerant flow out of the LG, qm,LG, showed a linear increase. The increase in γG caused a decrease in THG. This condition was conducive to the heat transfer between the heat source and the solution. In addition, γG caused the suction effect of CM1. This condition was conducive to the mass transfer between the liquid and
Fig. 3. Calculation algorithm of the CDAR system. 438
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Fig. 5. Effects of compression ratio of CM1, γG, on the operating conditions of each component: (a) qm,HG, qm,LG; (b) QHG, QLG.
to an increase in ωAB. The increased γA resulted in a decrease in THG. In the context of VLE theory, the increased THG resulted in an increase in ωHG. The increased γA resulted in a decrease in TCD, which meant that the vapor pressure of LG increased. In the context of VLE theory, the increased vapor pressure of LG caused the increase in ωLG. Fig. 7 presents the effects of the compression ratio of CM2, γA, on the operating conditions of each component, namely, (a) qm,HG, qm,LG; (b) QHG, QLG. Fig. 7(a) indicates that with the increase in γA, the mass flow of refrigerant flow out of HG, qm,HG, and the mass flow of refrigerant flow out of LG, qm,LG, showed a linear increase. The increase in γA led to an increase in ωHG, ωLG, and ωAB. The compression effect of CM2 was enhanced with the increase in γA, which caused an obvious pressure increase in the absorber. In VLE theory, the increased pressure in the absorber can significantly enhance the mass transfer of the absorption process and cause the rapid increase of ωAB. For variations of ωHG and ωLG, the increased γA caused the temperature changes of THG and TLG. These changes then led to the increases of ωHG and ωLG. The result implies that the influence of γA on ωAB is more direct than that on ωHG and ωLG. And the increase rate of ωAB was higher than the increase rates of ωHG and ωLG. Therefore, the deflation ranges of the solution in HG and LG increased. Naturally, the increased γA led to an increase in qm,HG and qm,LG. Fig. 7(b) shows that with an increase in γA, the heat load of HG, QHG, and the heat load of LG, QLG, showed a linear increase. The increased γA caused an increase in qm,HG. The increase of the mass flow of generation required much heat. Meanwhile, the increase in γA caused a decrease in THG, which resulted in an increase in the average temperature difference between the heat source and the solution in HG. Therefore, the increased γG led to an increase in QHG. The increased γG also led to an increase in qm,HG, which meant that more latent heat taken away by the refrigerant vapor was inputted to LG. Therefore, the
Fig. 4. Effects of the compression ratio of CM1, γG, on the operating conditions of each component: (a) THG, TLG; (b) TEV, TCD, TAB; (c) ωHG, ωLG, ωAB.
that with the increase in γA, TCD and TAB increased, but TEV decreased. The increase in γA caused a decrease in the vapor pressure of the absorber, and more refrigerant vapor was absorbed in the absorber. The heat load of QAB increased, resulting in the increase of the average temperature difference between the cooling water and the absorber. With the fixed inlet temperature of the cooling water, the increased temperature difference caused the increase in TAB. The increased γA led to an increase in TLG, which caused an increase of the vapor pressure of LG and the condenser. The increase in the vapor pressure in the condenser led to an increase in TCD. The increase in γA caused the enhancement of the suction effect of CM2. The enhanced suction effect reduced the vapor pressure of the evaporator, which caused a decrease in TEV. Fig. 6(c) indicates that the CH3OH mass fractions of ωHG, ωLG, and ωAB increased with γA. According to the previous analysis, the increased γA led to increases in the difference in the mass transfer pressure between the solution and the vapor phase in the absorber. The increased difference in mass transfer pressure caused the increase of the mass flow of the vaporized refrigerant. Therefore, the increased γA led 439
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Fig. 7. Effects of compression ratio of CM2, γA, on the operating conditions of each component: (a) qm,HG, qm,LG; (b) QHG, QLG.
evaporator, and absorber increased. The increased refrigerant mass flows led to the increase in the heat loads in all three components, resulting in the increase in the difference in the heat transfer temperatures among the three components. In the same cooling water and chilled water condition, the increased heat transfer temperature differences resulted in an increase in TCD and TAB and a decrease in TEV. Fig. 8(c) indicates that with the increase in Tsource, the CH3OH mass fractions of ωHG, ωLG, and ωAB increased. The increased Tsource caused ΤHG, ΤLG, and ΤAB to increase. Under the condition of fixed vapor pressure, when the solution temperature increases, the concentration of volatile components should decrease. Therefore, the increased temperatures led to a decrease in the CH3OH mass fractions of the solution in all three components. Fig. 9 presents the effects of heat source temperature, Tsource, on the operating conditions of each component, namely, (a) qm,HG, qm,LG; (b) QHG, QLG. Fig. 9(a) shows that with the increase in Tsource, the mass flows of qm,HG and qm,LG showed a linear increase. The increase in Tsource increased the difference in the heat transfer temperature between the heat source and the solution in HG. Therefore, the increased Tsource directly led to an increase in THG. In the context of VLE theory, the increased Tsource resulted in the increase of qm,HG. Furthermore, the increase of the refrigerant from HG increased the latent heat for the LG, thereby increasing qm,LG. Fig. 9(b) indicates that with the increase in Tsource, the heat loads of QHG and QLG showed a linear increase. The increase in Tsource caused an increase in the average temperature difference between the heat source and the solution in HG. Therefore, the increased Tsource resulted in an increase in the heat load of QHG, and the increased QHG caused an increase in qm,HG. More latent heat was inputted to LG, and the heat load of QLG increased. Finally, the increased QLG caused an increase in qm,LG. In addition, the increase rates of qm,HG and qm,LG decreased with the increase in Tsource because the increased Tsource led to an obvious increment in TCD, which was not conducive to
Fig. 6. Effects of compression ratio of CM2, γA, on the operating conditions of each component: (a) THG, TLG; (b) TEV, TCD, TAB; (c) ωHG, ωLG, ωAB.
increased γA caused an increase in QLG. Fig. 8 shows the effects of heat source temperature, Tsource, on the operating conditions of each component, namely, (a) THG, TLG; (b) TEV, TCD, TAB; (c) ωHG, ωLG, ωAB. In the calculation, the compression ratio of γG and γA was fixed to 1. Fig. 8(a) shows that with the increase in Tsource, solution temperatures THG and TLG showed an increase. The increase in Tsource increased the difference in the heat transfer temperature between the heat source and the solution in HG. Under the condition of fixing the total heat conductance of HG, the increased difference in heat transfer temperature resulted in the increase of the heat flow to the solution. Therefore, the increased Tsource directly led to an increase in THG. The mass flow of the refrigerant vapor from HG increased with THG, which caused an increase in the condensation heat released in LG. The increased condensation heat resulted in an increase in TLG. Fig. 8(b) shows that with the increase in Tsource, TCD and TAB increased, but TEV decreased. The increase of in Tsource caused the increase in THG and TLG, which was conducive to the generation processes in HG and LG. Therefore, the refrigerant mass flows in the condenser, 440
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Fig. 9. Effects of heat source temperature, Tsource, on the operating conditions of each component: (a) qm,HG, qm,LG; (b) QHG, QLG.
When γA was high, COP decreased with the increase in γG. Considering the upper limit of the deflation range, the influence of γG on the deflation ranges of HG and LG was significant with low γA but negligible with high γA. In addition, because the pressure of CM1 was much higher than that of CM2, the input power of CM1 was larger than that of CM2. Therefore, COP increased slowly at low γA and decreased at high γA. Fig. 10(b) indicates that ηex increased with the increase in γA but decreased with the increase in γG. Increased γA led to an increase in QEV and a decrease in TEV, which resulted in an increase in the exergy produced in the evaporator. In addition, the power of CM2 was small. Therefore, the increased γA resulted in an increase in ηex. Increased γG can also increase the exergy produced in the evaporator. However, the power of CM1 was large, which obviously increased the exergy input of the CDAR system. Therefore, the increased γG resulted in a decrease in ηex. Fig. 11 shows the effects of Τsource on COP and ηex in four cases of compressor ratios (Case I: γG = 1, γA = 1; Case II: γG = 1.2, γA = 1.2; Case III: γG = 1.44, γA = 1; Case IV: γG = 1, γA = 1.44). Fig. 11(a) shows the variation of COP on Τsource in four cases. With the increase in Τsource, COP increased when Τsource was low but declined when Τsource was high. Such outcome can be attributed to the fact that the increased Τsource caused the increases of QEV and QHG. When Τsource was low, the increase rate of QEV was more rapid than that of QHG. Therefore, with the increase in Τsource, COP increased when Τsource was low. With the increase of Τsource, TCD and TAB increased, thereby slowing down the increase rate of QEV. With the increase of Τsource, QHG still increased rapidly. When Τsource was high, the increase rate of QHG was more rapid than that of QEV, thereby leading to the decrease of COP. In the four cases, the optimum values of 1.032, 1.106, 1.058, and 1.151 were observed at Τsource = 452 °C, 417 °C, 428 °C, and 403 °C, respectively. The
Fig. 8. Effects of heat source temperature, Tsource, on the operating conditions of each component: (a) THG, TLG; (b) TEV, TCD, TAB; (c) ωHG, ωLG, ωAB.
the generation process in HG and LG. Fig. 10 shows the effects of γA and γG on the thermal properties of the CDAR system, namely, (a) COP and (b) ηex. Fig. 10(a) indicates that with the increase in γA, COP increased, but the increase rate of COP showed a declining trend. The increase in γA led to an increase in the vapor pressure of the absorber, which was conducive to the absorption process. The refrigerant concentration of the solution from the absorber increased, which was conducive to the generation processes in HG and LG. Therefore, the increased γA caused an increase in the deflation ranges of HG and LG, which led to an increase in the mass flow of the refrigerant in the evaporator. The increased mass flow of the refrigerant resulted in an increase in cooling capacity, which finally led to an increase in COP. Fig. 6(b) indicates that with the increase in γA, TCD and TAB increased, but TEV decreased. The variation trends of TCD, TAB, and TEV negatively affected COP. Therefore, the increment rate of COP declined. When γA was low, COP increased with the increase in γG. 441
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Fig. 10. Effects of γA and γG on the thermal properties of the CDAR system: (a) COP and (b) ηex. Fig. 11. Effects of Τsource on COP and ηex in four cases of compressor ratios.
use of the assisting compressor decreased the optimal Τsource and increased the optimal COP of the absorption system. Fig. 11(b) shows the variation of ηex on Τsource in the four cases. For Cases I and III, with the increase in Τsource, ηex increased when Τsource was low but declined when Τsource was high. The optimum values of 0.1668 and 1.8610 were observed at Τsource = 389 °C and 361 °C, respectively. The trend can be attributed to the fact that increases in Τsource led to the increases of the output exergy in QEV and the input exergy in QHG. When Τsource was low, the growth rate of exergy in QEV was faster than that in QHG, and ηex increased. With the increase of Τsource, the input exergy in QHG increased rapidly. When Τsource was high, the growth rate of exergy in QHG was faster than that in QEV, and ηex decreased. For Cases II and IV, no peak appeared for ηex in the proposed temperature range. This result suggests that the lower limit of Τsource was largely reduced by the assisting compressor. For COP and ηex, Case IV was the best case, followed by Case II. When Τsource was low, Case III was better than Case I. When Τsource was high, Case III was worse than Case I. Therefore, the assisting compressor placed between the evaporator and absorber was the better choice. The assisting compressor placed between HG and LG improved the cooling capacity of the CDAR system and reduced the evaporation temperature. When Τsource was high, the COP and ηex of Case III were only slightly lower than those of absorption refrigeration without an assisting compressor. Therefore, the assisting compressor placed between HG and LG was also an acceptable choice. Fig. 12 presents the exergy flow schematic of the CDAR system in the basic operating conditions. The CDAR system comprises three inputs to CM1, CM2, and HG. The exergy inputs to CM1, CM2, and HG are 0.301, 0.233, and 4.159 kW, which account for 6.4%, 5.0%, and 88.6% of the total exergy input, respectively. In HG, the temperature
decreased from T16 to T5, and the vaporization of the refrigerant caused an exergy loss of 0.424 kW, which accounts for 9.1% of the total exergy input. In LG, the phase changes (condensation and vaporization) of the refrigerant and the heat transfer with a temperature difference resulted in an exergy loss of 1.407 kW, which accounts for 29.9% of the total exergy input. In the condenser, the phase change of condensation led to an exergy loss of 0.238 kW, which accounts for 6.0% of the total exergy input. In the evaporator, the phase change of the evaporation caused an exergy loss of 0.738 kW, which accounts for 15.7% of the total exergy input. In the absorber, the liquefaction of the refrigeration and the heat transfer with a temperature difference led to an exergy loss of 0.556 kW, which accounts for 11.8% of the total exergy input. In HX and LX, the heat transfer with a temperature difference caused exergy losses of 0.581 and 0.292 kW, which account for 12.4% and 6.3% of the total exergy input, respectively. In CM1 and CM2, the changes in energy form (from work to heat) caused exergy losses of 0.214 and 0.198 kW, which account for 4.6% and 4.2% of the total exergy input, respectively. The largest exergy loss occurred in LG, which accounts for approximately one-third of the total exergy input. This result suggests that the most significant reason for the exergy loss in the CDAR system was heat transfer with a temperature difference. Therefore, an effective measure to improve the exergy efficiency of the CDAR system is to appropriately increase the heat transfer area of the components.
6. Conclusion In this study, the operating characteristics and thermal performance 442
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Fig. 12. Exergy flow schematic of the CDAR system.
of a CDAR system using [mmim]DMP/CH3OH as working fluid were numerically studied. Thermal performance was compared under different compression ratios. The major conclusions are as follows:
[4]
(1) With the increase in γG, parameters TLG, TCD, TAB, qm,HG, qm,LG, QHG, and QEV increased, but THG, TEV, ω HG, ω LG, and ω AB decreased. With the increase in γA, parameters TLG, TCD, TAB, ω HG, ω LG, ω AB, qm,HG, qm,LG, QHG, and QEV increased, but THG and TEV decreased. With the increase in Tsource, parameters TLG, TLG, TCD, TAB, qm,HG, qm,LG, QHG, and QEV increased, but TEV, ω HG, ω LG, and ω AB decreased. (2) COP and ηex increased with an increase in γG. When γA was low, COP increased with the increase in γG. When γA was high, COP decreased with the increase in γG. ηex decreased with the increase in γA. (3) With the increase in Tsource, COP declined after the initial rise; ηex declined after the initial rise for Cases III and IV, but showed a trend of decline for Case I and Case II. (4) Placing the assisting compressor between the evaporator and absorber was the best choice, but placing the assisting compressor between two generators was also acceptable. (5) The largest exergy loss occurred in LG, and heat transfer with a temperature difference was the main reason for the exergy losses.
[5] [6]
[7]
[8]
[9]
[10] [11]
[12] [13] [14] [15]
Acknowledgements
[16]
This research is supported by the National Natural Science Foundation of China (Grant No. 51506104), the Source Innovation Application Foundation Research Project of Qingdao (Grant No. 17-1-135-jch), and the Promotive Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province (Grant No. BS2014NJ021).
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