processes

Article Modeling of Novel Thermodynamic Cycles to Produce Power and Cooling Simultaneously

Wilfrido Rivera 1,*, Karen Sánchez-Sánchez 1, J. Alejandro Hernández-Magallanes 2, J. Camilo Jiménez-García 3 and Alejandro Pacheco 1

1 Instituto de Energías Renovables, Universidad Nacional Autónoma de México, Temixco 62580, Morelos, Mexico; [email protected] (K.S.-S.); [email protected] (A.P.) 2 Facultad de Ciencias Químicas, Universidad Autónoma de Nuevo León, Av. Universidad s/n, Ciudad Universitaria, San Nicolás de los Garza, Nuevo León 66455, Mexico; [email protected] 3 Area de Ingeniería en Recursos Energéticos, Departamento de Ingeniería de Procesos e Hidráulica, Universidad Autónoma Metropolitana, Campus Iztapalapa, Av. San Rafael Atlixco 186 Col. Vicentina, Iztapalapa CDMX 14387, C.P. 09340, Mexico; [email protected] * Correspondence: [email protected]; Tel.: +52-5556229740



Received: 7 February 2020; Accepted: 5 March 2020; Published: 9 March 2020


Abstract: Thermodynamic cycles to produce power and cooling simultaneously have been proposed for many years. The Goswami cycle is probably the most known cycle for this purpose; however, its use is still very limited. In the present study, two novel thermodynamic cycles based on the Goswami cycle are presented. The proposed cycles use an additional component to condense a fraction of the working fluid produced in the generator. Three cycles are modeled based on the first and second laws of thermodynamics: Two new cycles and the original Goswami cycle. The results showed that in comparison with the original Goswami cycle, the two proposed models are capable of increasing the cooling effect, but the cycle with flow extraction after the rectifier presented higher irreversibilities decreasing its exergy efficiency. However, the proposed cycle with flow extraction into the turbine was the most efficient, achieving the highest values of the energy utilization factor and the exergy efficiency. It was found that for an intermediate split ratio value of 0.5, the power produced in the turbine with the flow extraction decreased 23% but the cooling power was 6 times higher than that obtained with the Goswami Cycle.

Keywords: absorption cooling cycles; Goswami cycle; simultaneous power and cooling; ammonia-water

1. Introduction It has been demonstrated that the consumption of conventional energy sources such as oil, natural gas, and coal, contributes to serious environmental problems, like global warming. In this situation, actions like the use of clean energy sources, the reduction of energy consumption, the efficiency improvement of energy systems, or the minimization and reuse of waste heat energy in industrial processes, become significantly relevant. In the last decades, a lot of research and technological development efforts have been carried out to analyze and propose different ways of producing electricity with minimal economic and environmental impact. This research effort has led to increasingly efficient technologies capable of taking advantage of different types of clean energy or industrial waste heat. A strategy usually considered to increase the efficiency of the cycles for the production of electricity is the implementation of cogeneration systems to make possible the simultaneous production of several types of useful energy, typically electricity and heat, or electricity and cooling effect. Some of the most relevant papers related to producing power and cooling simultaneously are presented in the following.

Processes 2020, 8, 320; doi:10.3390/pr8030320 www.mdpi.com/journal/processes Processes 2020, 8, 320 2 of 25

Kalina [1,2] developed a combined cycle for power generation able to recover waste heat. One of the main differences with the existing vapor cycles was the use of ammonia-water. The efficiencies obtained by the original Kalina cycle and its first versions were between 1.35 and 1.9 times higher than those achieved by the Rankine cycle. El-Sayed and Tribus [3,4] extended the available data for the ammonia-water mixtures and presented a comparison of the Rankine cycle and a modified version of the Kalina cycle. Marston [5] developed several computational models to optimize the simplified Kalina cycle and compared his results with those presented by El-Sayed and Tribus [4]. Park and Sonntag [6] developed a preliminary study of the Kalina cycle in connection with a combined power system. The comparison revealed the superiority of the Kalina cycle over the Rankine cycle, having advantages from the point of view of the first and second laws of thermodynamics. Rogdakis and Antonopoulos [7] suggested a new power cycle working with the ammonia-water mixture and its comparison with the Rankine cycle. The new cycle offered good performance, obtaining first law efficiency values up to 20% higher than those of the Rankine cycle. Nag and Gupta [8] simulated and analyzed the effect of several thermal parameters on the performance of the Kalina cycle. The authors found that the concentration mixture at the inlet of the turbine, as well as the separator temperature, have a significant effect on the system performance. Another case of cycles’ comparison is reported by Dejfors et al. [9], who contrasted the performance for a couple of configurations of the Rankine and Kalina cycles when they were used for direct-fired cogeneration applications. In one of the configurations considered, the reheater was not used, and the Rankine cycle offered a power generation between 4% and 11% higher than the offered by the Kalina cycle. In the second case, when the reheater was included, the authors found that the Kalina cycle reached the highest power generation. Goswami [10] proposed a modification of the Kalina cycle, improving the efficiency by the simultaneous production of power and cooling effect. This cycle was understood as a combination of the Rankine cycle using ammonia as the working fluid, and an absorption cooling system operated with the ammonia-water mixture. The authors concluded that the cost of the technology associated with using a solar source to supply the heat to drive the combined cycle was not competitive with that of the fossil-fuel-based technologies. Goswami [10] and Xu et al. [11] proposed a new cycle that was capable of producing power as the primary goal and cooling effect. The novelty of this work was that, instead of carrying out the conventional condensation process, as it was usually performed in the Kalina cycle, an absorption-condensation process was used. From the simulations performed, the authors concluded that this cycle could achieve high thermal efficiencies when it utilized a heat source of approximately 400 K. In addition, the authors proposed some options to get a more competitive cost for this type of plant. Lu and Goswami [12] also analyzed the cycle for power and cooling, but this time focusing on the optimization of the cooling effect instead of the power output, as it had been accomplished by Xu et al. [11]. The authors characterized the thermal behavior for the cycle at different refrigeration temperatures and found that, theoretically, temperatures as low as 205 K could be achieved with this cycle. Hasan et al. [13] performed the optimization of the cycle from the perspective of the second law of thermodynamics. The authors found that the maximum irreversibility took place in the absorber, followed by the rectifier and the solution heat exchanger. In a later study, Hasan et al. [14] investigated the exergy destruction in every component of the cycle. The authors found that the exergy efficiency did not necessarily increase with an increment in the heat source temperature, but that this temperature had an important effect on the fraction of power and cooling produced. Tamm and Goswami [15] experimentally demonstrated the feasibility of the Goswami cycle and compared the experimental results with those obtained from the simulation. Their results showed that the generation and absorption processes approached the expected trends. In addition, it was identified that the thermal efficiency of the cycle was reduced by 20.6%, due to the irreversibilities considered; for the same reason, 11.8% less work output and 37.7% less refrigeration capacity was obtained, respectively. Vijayaraghavan and Goswami [16] investigated the use of several organic working fluids with this cycle and compared their performance with the observed by the conventional mixtures. It was found that the thermodynamic efficiencies of the novel mixtures were lower than those obtained with ammonia-water. Processes 2020, 8, 320 3 of 25

Martin and Goswami [17] proposed a new parameter called effective coefficient of performance (COP) to evaluate the effectiveness of the cooling production in the combined power and cooling cycle. It was found that when the authors used this parameter to optimize the rectifier, the effective COP achieved values of 5; however, when the optimized parameter was the work output, the maximum value for this parameter was just 1.1. An approximation to real operating conditions of the Goswami cycle was proposed and analyzed by Vidal et al. [18], who carried out a simulation utilizing the exergy method to assess the cycle performance. The authors performed the simulation considering reversible and irreversible processes to show the effect of the irreversibilities in each component. The exergy efficiency for the cycle in the irreversible cases was 53% and 51% when the input heat was supplied at temperatures of 125 ◦C and 150 ◦C, respectively. Zhang and Lior [19] developed a new combined cycle for power and cooling production, combining an ammonia-water Rankine cycle, and an ammonia refrigeration cycle. Both cycles were interconnected by absorption, separation, and heat transfer processes. For a maximum cycle temperature of 450 ◦C, the energy and exergy efficiencies obtained were 27.7% and 55.7%, respectively. A novel semi-closed combined cycle for the generation of power and cooling was introduced by Boza et al. [20]. The authors used a semi-closed gas turbine called a high-pressure regenerative turbine engine (HPRTE) and an absorption cooling system. The waste heat from the exhaust gas of the HPRTE was utilized to power the absorption cooling system. The authors analyzed the cycle performance for two cases: Work output of 10 kW and 40 kW. A more detailed parametric analysis for the Goswami cycle was performed by Demirkaya et al. [21], who modeled the cycle. The authors demonstrated that when the ammonia vapor was superheated after the rectification process, the cycle efficiencies increased, but the cooling capacities decreased. The dynamic modeling of a novel cooling, heat, power, and water microturbine combined cycle was carried out by Ryu et al. [22]. The proposed cycle was able to offer some benefits, including increased efficiency, high part-power efficiency, low lapse rate, compactness, low emissions, lower air and exhaust flow, and condensation of cold water. Padilla et al. [23] proposed a combined Rankine–Goswami cycle and analyzed its thermodynamic performance. The authors reported that the maximum first and second law effective efficiencies were 36.7% and 24.7%, respectively. Mendoza et al. [24] proposed the use of low-capacity absorption cooling systems to produce power and refrigeration with a scrolled expander and working fluids like ammonia-water, ammonia-lithium nitrate, and ammonia-sodium thiocyanate. The proposed system achieved different capacities of power and cooling. After this investigation, the same group of work extended the analysis of the combined cycles for taking advantage of the mid-temperature heat sources. Ayou et al. [25] analyzed several combined cycles for the simultaneous or alternative production of power and refrigeration. The authors concluded that an interesting application for the combined cycles was the efficient use of solar thermal installations throughout the year to produce variable amounts of electricity and cooling according to specific building demand, thus reducing the consumption of primary energy significantly. Muye et al. [26] investigated the annual performance of an absorption power and cooling system using solar energy, utilizing the ammonia-water mixture and a biomass auxiliary system. It was concluded that an increase in the heat source temperature benefited the power production but not the cooling power; also, it was demonstrated that an increase in the cooling water temperature resulted in a detriment of both cycle outputs: Power and cooling. Barkhordarian et al. [27] proposed a novel power and cooling cycle operated with the ammonia-water mixture for two cooling temperature levels by using two evaporators. It was found that the cycle achieved an exergy efficiency of 38.97% and a thermal efficiency of 19% for the studied case. An innovative cascading cycle involving an organic Rankine cycle and an adsorption refrigeration cycle was proposed by Jiang et al. [28]. The working fluids utilized in both cycles were refrigerant 245fa and silica-gel/LiCl. The system achieved maximum values for power and cooling of 232 kW and 4.94 kW, respectively, for a driving temperature of 95 ◦C, a cooling water temperature of about 25 ◦C, and a chilled water temperature of 10 ◦C. The exergy efficiencies for the cascading system were better than those of the pumpless ORC and the absorption chiller when the hot water temperature was 95 ◦C. Shankar and Srinivas [29] and Shankar et al. [30] analyzed a solar cooling Processes 2020, 8, 320 4 of 25 cogeneration plant that consists of a Kalina cycle with extra components such as a dephlegmator, a separator, a superheater, a subcooler, and an extra throttling valve. In the simulation, the energy is supplied by a solar collector and a fuel furnace. The authors compare the performance of the proposed system with an absorption cooling plant and a power plant operating individually under the same operating conditions, and the authors concluded that the proposed system is more efficient than the conventional systems. The highest energy utilization factor reported by the authors was 0.39. As can be seen from the bibliographic review, there have been several studies related to the Goswami cycle. Most of this research has been focused mainly on three topics: The maximization of the first and second law efficiencies, the search of the optimum operative conditions for incrementing either the power or the cooling capacities, and the analysis of the effect that several important parameters have on the system performance. However, none of the articles presented in the literature reviewed are based on the Goswamy cycle adding only a condenser and an expansion valve to significantly increase the cooling effect by taking advantage of the latent heat of vaporization. Neither was any study found that analyzed the operation of the system based on flow extractions in the turbine at an intermediate pressure, or after the regenerator to increase the cooling effect. Therefore, in the present study, two novel cycles capable of producing power and cooling simultaneously are presented. The proposed cycles are analyzed and compared to each other and with the Goswami cycle reported in the literature.

2. System Description

2.1. Goswami Cycle (Model I) . An amount of heat QG is supplied to the generator to desorb part of the working fluid from the absorbent, but since the ammonia-water mixture is a zeotropic fluid, a small amount of water is evaporated together with the ammonia (7). A rectifier is used to condensate the evaporated water, . which returns to the generator (8), producing almost pure ammonia vapor (9). An amount of heat QR is supplied in the reheater to increase the temperature of the ammonia in the vapor phase. The ammonia . leaving the reheater passes to the turbine (10), producing an amount of power WT. The ammonia leaving the turbine at lower pressure and temperature (11) passes to the cooler, producing the cooling . effect Q . The working fluid then passes to the absorber (12), where it is absorbed by the solution with E . low ammonia concentration coming from the generator, delivering an amount of heat QA. The solution leaving the absorber (1) is pumped to the economizer (2), where it is heated (3) by the solution leaving the generator (4), which reduces its temperature (5) and then passes through the expansion valve (6) before entering the absorber, starting the cycle again. The indicated numbers correspond to the streamlines in Figure1. Processes 2020, 8, 320 5 of 25 Processes 2020, 8, x FOR PEER REVIEW 5 of 24

Figure 1. Goswami cycle. Figure 1. Goswami cycle. 2.2. Goswami Cycle with a Condenser and a Flow Division after the Rectifier (Model II) 2.2. Goswami Cycle with a Condenser and a Flow Division after the Rectifier (Model II) This cycle operates in a very similar manner to the Goswami cycle previously described in SectionThis cycle2.1, but operates a condenser in a very has similar been added manner to condensateto the Goswami part of cycle the ammoniapreviously produced described in in the Sectiongenerator, 2.1, but as cana condenser be seen in has Figure been2 .added At the to exit condensate of the rectifier part of (9), the the ammonia working produced fluid is split in the into generator,two streams, as can one be streamseen in goesFigure to 2. the At condenser the exit of (14)the rectifier where it(9), is condensedthe working (15) fluid and is split then into expanded two streams,through one the stream expansion goes valve to the reducing condenser its pressure (14) where and it temperature is condensed (16), (15) while and the then remaining expanded fluid throughcontinues the toexpansion the reheater valve (13), reducing and then its to pressure the turbine and (10) temperature to produce (16), power while as inthe the remaining Goswami fluid Cycle. continuesThe ammonia to the leavingreheater the (13), turbine and then (11), andto the the turbine condenser (10) entersto produce the evaporator power as (17),in the producing Goswami the Cycle.cooling The e ffammoniaect. The ammonialeaving the in the turbine vapor (11), phase, an leavingd the condenser the evaporator, enters goes the toevaporator the absorber (17), (12), producingwhere it isthe absorbed cooling byeffect. the solutionThe ammonia leaving in thethe generator.vapor phase, The leaving rest of thethe cycleevaporator, operates goes in ato similar the absorberway to the(12), Goswami where it cycle is absorbed described by previously. the solution It isleaving important the togenerator. mention thatThe inrest the of present the cycle cycle, operatesthe heat in exchanger a similar way where to thethe coolingGoswami eff ectcycle takes described place is previously. named an evaporator,It is important instead to mention of cooler that as in in thethe Goswamipresent cycle, cycle. the This heat change exchanger in the where nomenclature the cooling occurs effect since, takes in place the proposed is named cycle,an evaporator, the cooling insteadeffect isof mainlycooler producedas in the byGoswami the latent cycle. heat This of the change ammonia, in the which nomenclature changes from occurs the liquidsince, phasein the to proposedthe vapor cycle, phase, the while cooling in the effect Goswami is mainly cycle prod the coolinguced by eff theect islatent mainly heat produced of the ammonia, by the sensible which heat changesgained from by the the vapor liquid of phase the working to the vapor fluid. phase, while in the Goswami cycle the cooling effect is mainly produced by the sensible heat gained by the vapor of the working fluid. ProcessesProcesses 20202020, 8, 8x, FOR 320 PEER REVIEW 6 of6 of24 25

Figure 2. Goswami cycle with a condenser and a flow division after the rectifier. Figure 2. Goswami cycle with a condenser and a flow division after the rectifier. 2.3. Goswami Cycle with a Condenser and a Flow Division into the Turbine (Model III) 2.3. GoswamiThis cycle Cycle is with similar a Condenser to the modified and a Flow Goswami Division cycle, into the described Turbine (Model in Section III) 2.2, but in the present cycle,This a cycle fraction is similar of the to ammonia the modified in the Goswami vapor phasecycle, enteringdescribed the in Section turbine 2.2, (10) but is in extracted the present at an cycle,intermediate a fraction pressure of the (13)ammonia to be condensed in the vapor in the phas condensere entering as can the be turbine seen in Figure(10) is3 .extracted The ammonia at an in intermediatethe liquid phase pressure leaving (13) theto be condenser condensed (14) in passes the condenser through as the can expansion be seen in valve, Figure reducing 3. The ammonia its pressure inand the temperatureliquid phase (15). leaving The restthe ofcondenser the ammonia, (14) passes which isthrough not extracted, the expansion is completely valve, expanded reducing in its the pressureturbine and producing temperature power. (15). The ammoniaThe rest leavingof the a themmonia, turbine which (11) is is mixed not extracted, with the ammonia is completely leaving expandedthe condenser in the beforeturbine entering producing the evaporator power. The (16). ammo Thenia total leaving amount the of turbine ammonia (11) enters is mixed the evaporatorwith the ammoniaproducing leaving the cooling the condenser effect. The before rest entering of the cycle the operatesevaporator in a(16). similar The way total to amount that described of ammonia by the enterstwo previousthe evaporator cycles. producing the cooling effect. The rest of the cycle operates in a similar way to that described by the two previous cycles. ProcessesProcesses 20202020, 8, 8x, FOR 320 PEER REVIEW 7 of7 of24 25

Figure 3. Goswami cycle with a condenser and a flow division into the turbine. Figure 3. Goswami cycle with a condenser and a flow division into the turbine. 3. Mathematical Model 3. MathematicalThe mathematical Model model is based on energy, total mass, and individual species mass balances for eachThe component mathematical of the model system. is based on energy, total mass, and individual species mass balances for each component of the system. 3.1. Assumptions 3.1. AssumptionsThe following assumptions were considered in the development of the mathematical models for theThe three following cycles: assumptions were considered in the development of the mathematical models fori. the Thermodynamicthree cycles: equilibrium conditions are considered in each cycle. i. ii. ThermodynamicThe cycles operate equilibrium in steady-state conditions conditions. are considered in each cycle. ii. iii. TheHeat cycles losses operate from in the steady-state components conditions. are considered negligible. iii.iv. HeatThe losses refrigerant from the is considered components in are saturation considered conditions negligible. at the exit of the condenser. iv.v. TheThe refrigerant solution isis consideredconsidered inin saturationsaturation conditionsconditions atat thethe exitexit ofof thethe absorbercondenser. and generator. v.vi. ThePressure solution losses is considered due to frictionin saturation are neglected conditions in at each the exit component, of the absorber with the and exception generator. of the vi. Pressureexpansion losses valves due and to friction the turbine. are neglected in each component, with the exception of the vii.expansionThe throttling valves process and the in turbine. the valves is isenthalpic. vii. The throttling process in the valves is isenthalpic. 3.2. Main Equations 3.2. Main Equations Besides the thermal loads in the heat exchangers, the power produced by the turbine and the workBesides consumed the thermal by the loads pump, in thethe otherheat exchangers, three important the power parameters produced were by utilized the turbine to evaluate and the the workperformance consumed of by the the system, pump, being the theseother thethree following: important parameters were utilized to evaluate the performanceThe energy of the utilization system, being factor these (EUF) the is following: defined as the useful energy produced either in the form of heatThe or energy work divided utilization by the factor energy (EUF) supplied is defined to the as systemthe useful [31], energy which produced can be written either as: in the form of heat or work divided by the energy supplied to the system [31], which can be written as: Processes 2020, 8, 320 8 of 25

. . QE + Wnet EUF = . . (1) QG + QR . . . where Q , Q , Q , represent the heat loads in the evaporator, generator, and reheater, respectively, . E G R while Wnet represents the net power produced by the cycle calculated as the power produced by the . . turbine WT minus the power consumed by the pump WP. Although the EUF is a useful parameter, which indicates the total amount of useful energy produced by a system, this parameter has the problem of adding different types of energy, such as heat and work. For this reason, it is important to use another expression that does not have the mentioned problem, as it is the case of the exergy efficiency, which is defined as the useful exergy produced divided by the exergy consumed by the system, which can be written as: .   . T0 TE Wnet + − Q TE E ηEX = .   .   (2) T0 T0 QG 1 + QR 1 − TG − TR where T0 represents the environment temperature, and the rest of the variables have the conventional meaning. The third parameter, related to the exergy efficiency, is the irreversibility, which indicates the exergy lost by the system, and it is calculated as the useful exergy delivered by the system minus the exergy supplied to it.

. " . ! . !# " . . !# T0 T0 T0 TE I = QG 1 + QR 1 Wnet + QE − (3) − TG − TR − TE

The main equations used for the simulation of the Goswami cycle (Model I), the Goswami cycle modified with a flow division and using a condenser (Model II) and the Goswami cycle modified with a flow extraction in the turbine and using a condenser are presented in Tables1–3, respectively.

Table 1. Main equations for the Goswami cycle.

Goswami Cycle (Model I) Generator (G) Absorber (A) ...... m3 + m8 = m4 + m7 m6 + m12 = m1 ...... m3X3 + m8X8 = m4X4 + m7X7 m6X6 + m12X12 = m1X1 ...... m3h3 + m8h8 + QG = m4h4 + m7h7 m6h6 + m12h12 = m1h1 + QA Rectifier (Re) Economizer (EC) ...... m7 = m8 + m9 m2h2 + m4h4 = m3h3 + m5h5 . . . m X = m X + m X η = (h h )/(h h ) 7 7 8 8 9 9 EC 3 − 2 4 − 2 . . . . m7h7 = m8h8 + m9h9 + QRe Pump (P) . . Reheater (R) W = m (h h )/η P 1 2 − 1 P . . .  . .   . .  m9h9 + QR = m10h10 EUF = Wnet + QC / QG + QR .   . T0 TE Turbine (T) Wnet+ − QE . TE  . .  ηEX = .   .   = η T0 T0 WT T m10h10 m11h11 QG 1 +QR 1 − − TG − TR Cooler or Evaporator (C) . h .   .  i h . .  i T0 T0 T0 TE . I = QG 1 + QR 1 Wnet + QE − . . − TG − TR − TE m11h11 + QE = m12h12 Processes 2020, 8, 320 9 of 25

Table 2. Main equations for the Goswami cycle with flow division.

Goswami Cycle with a Condenser and a Flow Division after the Rectifier (Model II) Generator (G) Absorber (A) ...... m3 + m8 = m4 + m7 m6 + m12 = m1 ...... m3X3 + m8X8 = m4X4 + m7X7 m6X6 + m12X12 = m1X1 ...... m3h3 + m8h8 + QG = m4h4 + m7h7 m6h6 + m12h12 = m1h1 + QA Rectifier (Re) Economizer (EC) ...... m7 = m8 + m9 m2h2 + m4h4 = m3h3 + m5h5 . . . m X = m X + m X η = (h h )/(h h ) 7 7 8 8 9 9 EC 3 − 2 4 − 2 . . . . m7h7 = m8h8 + m9h9 + QRe Pump (P) . . Reheater (R) W = m (h h )/η P 1 2 − 1 P . . . m13h13 + QR = m10h10 Condenser (C)

Turbine (T) . . . .  . .  m h = m h + Q W = η m h m h 14 14 15 15 C T T 10 10 − 11 11  . .   . .  Evaporator (E) EUF = Wnet + QE / QG + QR . . . .   . T0 TE m h + Q = m h Wnet+ − QE 17 17 E 12 12 TE . ηEX = .   .   m T0 T0 14 QG 1 +QR 1 SR = . TG TR m9 − − . h .   .  i h . .  i T0 T0 T0 TE I = QG 1 + QR 1 Wnet + QE − − TG − TR − TE

Table 3. Main equations for the Goswami cycle with flow extraction in the turbine.

Goswami Cycle with a Condenser and a Flow Division into the Turbine (Model III) Generator (G) Absorber (A) ...... m3 + m8 = m4 + m7 m6 + m12 = m1 ...... m3X3 + m8X8 = m4X4 + m7X7 m6X6 + m12X12 = m1X1 ...... m3h3 + m8h8 + QG = m4h4 + m7h7 m6h6 + m12h12 = m1h1 + QA Rectifier (Re) Economizer (EC) ...... m7 = m8 + m9 m2h2 + m4h4 = m3h3 + m5h5 . . . m X = m X + m X η = (h h )/(h h ) 7 7 8 8 9 9 EC 3 − 2 4 − 2 . . . . m7h7 = m8h8 + m9h9 + QRe Pump (P) . . Reheater (R) W = m (h h )/η P 1 2 − 1 P . . . m9h9 + QR = m10h10 Condenser (C) . . . = + Turbine (T) m13h13 m14h14 QC PR = PH/PInt . . .  . .   . .  m10 = m11 + m13 EUF = Wnet + QE / QG + QRe

.  . . .  .   . T0 TE WT = ηT m10h10 m11h11 m13h13 Wnet+ − QE − − TE η = .   .   EX T0 T0 Evaporator (E) QG 1 +QR 1 − TG − TR . . . m17h17 + QE = m12h12 . h .   .  i h . .  i . = T0 + T0 + T0 TE m13 I QG 1 T QR 1 T WT QE T− SR = . − G − R − E m10

3.3. Input Data The input data for the modeling of the three cycles are listed in Table4. As can be seen, the range of the generation temperature was set at 90 to 150 ◦C, simulating the waste heat supplied by an industrial process. The rest of the parameters have conventional values. Processes 2020, 8, 320 10 of 25

Table 4. Input data.

Variable Operation Range Increment

PH (kPa) 2000–4000 500 T ( C) 10–10 5 E ◦ − TA = TC (◦C) 20–40 5 TG (◦C) 90–150 10 ∆T(◦C) 10–50 20 SR (-) 0–1 0.1 ηP (-) 0.80 ηEC (-) 0.70 ηT (-) 0.85 xR 0.995 mr (kg/s) 1

3.4. AlgorithmProcesses 2020, 8, x FOR PEER REVIEW 10 of 24 The algorithm followed for the simulation of the Model III is shown in Figure4. The algorithms for Model3.4. IAlgorithm and II are similar but eliminating all related with the intermediate pressure. The input parameters were:The algorithm The temperatures followed for the ofsimulation generation of the (TModelG = TIII7 is), shown evaporation, in Figure (T4. TheE = algorithmsT12) and absorption for Model I and II are similar but eliminating all related with the intermediate pressure. The input (TA = T1), the temperature difference in the reheater (∆T), the high pressure (PH), the Split Ratio (SR), parameters were: The temperatures of generation (TG = T7), evaporation, (TE = T12) and absorption (TA the mass of the refrigerant (mr), the economizer effectiveness (ηEC), the pump efficiency (ηP), and = T1), the temperature difference in the reheater (ΔT), the high pressure (PH), the Split Ratio (SR), the the turbine efficiency (η ). The system was modeled operating with the ammonia-water mixture. mass of the refrigerantT (mr), the economizer effectiveness (η), the pump efficiency (η), and the The physicalturbine properties efficiency (η were). The takensystem fromwas modeled Ibrahim operating and Klein with the [32 ammonia-water]. Appendix mixture.A shows The all the data obtainedphysical from theproperties modeling were taken for the from nominal Ibrahim and case. Klein [32]. Appendix A shows all the data obtained from the modeling for the nominal case.

FigureFigure 4. Algorithm 4. Algorithm flowflow chart chart for for the themodeling modeling of the three of the cycles. three cycles.

4. Results Since the behavior of the Goswami cycle operating with the ammonia-water mixture has been previously reported by other authors [10,12]. This section is structured in the following way. Section Processes 2020, 8, 320 11 of 25

4. Results Since the behavior of the Goswami cycle operating with the ammonia-water mixture has been previously reported by other authors [10,12]. This section is structured in the following way. Section 4.1 shows the results of the first cycle proposed (Model II). Section 4.2 shows the behavior of the second system proposed (Model III), and Section 4.3 shows the performance comparison for the two proposed cycles regardingProcesses 2020, the 8, x FOR Goswami PEER REVIEW cycle. 11 of 24 4.1 shows the results of the first cycle proposed (Model II). Section 4.2 shows the behavior of the 4.1. Goswami Cycle with a Condenser and a Flow Division after the Rectifier (Model II) second system proposed (Model III), and Section 4.3 shows the performance comparison for the two Figuresproposed5–8 cyclesillustrate regarding the results the Goswami of the modelingcycle. of the Goswami cycle modified including a flow division at the exit of the generator and the use of a condenser for a case base, which considers a 4.1. Goswami Cycle with a Condenser and a Flow Division after the Rectifier (Model II). PH = 3000 kPa, a TG = 130 ◦C, a TC = 30 ◦C and an increment of temperature in the reheater ∆T = 10 ◦C. FigureFigures5 illustrates 5–8 illustrate the power the results produced of the bymodelin the turbineg of the andGoswami the coolingcycle modified e ffect including produced a in the flow division at the exit of the generator and the use of a condenser for a case base, which considers a evaporator as a function of the split ratio (SR) of the working fluid extracted after the rectifier. A value PH = 3000 kPa, a TG = 130 °C, a TC = 30 °C and an increment of temperature in the reheater ΔT = 10 °C. of SR = 0 means that all the ammonia in the vapor phase passes to the turbine, while a value of SR = 1, Figure 5 illustrates the power produced by the turbine and the cooling effect produced. in the means thatevaporator all the as working a function fluid of the goes split to ratio the condenser.(SR) of the working As can fluid be seen extracted from theafter figure, the rectifier.WT decreases A . . value of SR = 0 means that all the ammonia in the vapor phase passes to the turbine, while a value of while Q increases with the increment of SR. For an SR = 0, the maximum WT produced by the system E . SR = 1, means that all the working fluid goes to the condenser. As can be seen from the figure, W is 250 kW with a QE about 100 kW; however, for an intermediate value of SR, which can be for instance decreases. while Q increases with the increment of SR. For an SR = 0,. the maximum W produced 0.5, although W decreases to a value of 115 kW (at a T = 10 C), Q increases significantly up to a by the systemT is 250 kW with a Q about 100 kW; however,E − for ◦an intermediateE value of SR, which value ofcan about be for 600 instance kW, which 0.5, although is 600% W higher decreases than to thea value cooling of 115 e ffkWect (at produced a TE = −10 at °C), SR Q= 0.increases This fact can be an advantagesignificantly for up industriesto a value of thatabout require 600 kW, a which significant is 600%cooling higher than eff ect.the cooling On the effect other produced hand, itat can be . SR = 0. This fact can be an advantage for industries that require a significant cooling effect. On the observed that the evaporator temperature affects WT at low SR values, but the effect is also negligible other hand, it can be observed that the evaporator temperature. affects W at low SR values, but the at higher SR values. In addition, it can be seen that QE does not have a significant change with the effect is also negligible at higher SR values. In addition, it can be seen that Q does not have a variationsignificant of the evaporator change with temperature.the variation of the evaporator temperature.

. . Figure 5. WT and QE as a function of SR for Model II for different evaporator temperatures. Figure 5. W and Q as a function of SR for Model II for different evaporator temperatures. The variation of the EUF as a function of SR for different evaporator temperatures is illustrated in The variation of the EUF as a function of SR for different evaporator temperatures is illustrated Figure6in. TheFigure EUF 6. The values EUF increased values increased with anwith increment an increment of SR. of SR. The The minimum minimum values values ofof thethe EUF were obtainedwere at obtained SR = 0, varyingat SR = 0, varying between between 0.10 and 0.10 0.17.and 0.17. The The maximum maximum valuesvalues were were achieved achieved at SR at = SR = 1, varying1, between varying between 0.32 and 0.32 0.79, and which 0.79, which were betweenwere between 3 and 3 and 6 times 6 times higher higher than than the the minimum minimum values. . values. This significant increase was due to the considerable increment of Q showed in Figure 6, This significant increase was due to the considerable increment of QE showed in Figure6, according to Equationaccording (1). In addition,to Equation it (1). can In be addi seention, that it can the be evaporator seen that the temperature evaporator temperature considerably considerably affects the EUF affects the EUF for higher values of SR, since when SR = 1, the maximum EUF was 0.32 at a TE = −10 for higher values of SR, since when SR = 1, the maximum EUF was 0.32 at a TE = 10 ◦C, while at °C, while at TE = 10 °C the EUF was 0.79. − TE = 10 ◦C the EUF was 0.79. Processes 2020, 8, 320 12 of 25 Processes 2020, 8, x FOR PEER REVIEW 12 of 24 Processes 2020, 8, x FOR PEER REVIEW 12 of 24

Figure 6. Energy utilization factor (EUF) as a function of split ratio (SR) for Model II for different Figure 6. Energy utilization factor (EUF) as a function of split ratio (SR) for Model II for different Figure 6. Energy utilization factor (EUF) as a function of split ratio (SR) for Model II for different evaporatorevaporator temperatures. temperatures. evaporator temperatures.

As mentionedAs mentioned in Sectionin Section 3.2 3.2,, although although thethe EUF is is a a useful useful parameter, parameter, which which indicates indicates the total the total As mentioned in Section 3.2, although the EUF is a useful parameter, which indicates the total amountamount of useful of useful energy energy produced produced by by a a system, system, thisthis parameter parameter has has the the problem problem of adding of adding different different amount of useful energy produced by a system, this parameter has the problem of adding different typestypes of energy. of energy. For this For reason, this reason, Figure Figure7 illustrates 7 illustra thetes exergy the exergy e fficiency efficiency as a function as a function of the evaporatorof the types of energy. For this reason, Figure 7 illustrates the exergy efficiency as a function of the temperatureevaporator for temperature three different for three values different of SR. values At SR of= SR.0 theAt SRη = values0 the η are values the highest are the sincehighest all the evaporator temperature for three different values of SR. At SREX = 0 the η values are the highest since all the ammonia in the vapor phase is supplied to the turbine to produce power, which is ammoniasince inall the the vapor ammonia phase in isthe supplied vapor phase to the is turbine supplied to to produce the turbine power, to produce which is power, high-quality which energy,is high-quality energy, while at SR = 1 the η values are the lowest since all the ammonia is used as whilehigh-quality at SR = 1 the energy,ηEX values while areat SR the = lowest1 the η since values all theare ammoniathe lowest issince used all as the heat, ammonia which is is used low-quality as heat, which is low-quality energy. In addition, it can be observed that the η values increase and energy.heat, In which addition, is low-quality it can be observedenergy. In thataddition, the η itEX canvalues be observed increase that and the then η remain values increase almost constantand then remain almost constant and even decrease with the increment of the evaporator temperature. and eventhen decreaseremain almost with constant the increment and even of thedecrease evaporator with the temperature. increment of Thisthe evaporator behavior occurredtemperature. because . This behavior occurred because Q increases with the increment of TE; however, at higher TE values, This behavior occurred because Q increases with the increment of TE; however, at higher TE values, Q increases with the increment of TE; however, at higher TE values, the term of temperatures that E the term. of temperatures that multiplies Q in Equation (2) considerably decreases, thus decreasing the term of temperatures that multiplies Q in Equation (2) considerably decreases, thus decreasing multipliesη. QE in Equation (2) considerably decreases, thus decreasing ηEX. η.

Figure 7. ηEX as a function of TE for Model II at three different values of SR. Processes 2020, 8, x FOR PEER REVIEW 13 of 24

Figure 7. η as a function of TE for Model II at three different values of SR.

Figure 8 illustrates the system’s irreversibilities as a function of the evaporator temperature for three different values of SR. The results plotted in this figure are related to the variation of the η Processes 2020, 8, 320 13 of 25 values reported in Figure 7 since as it can be observed, the irreversibilities decrease with the increment of TE, which is the opposite to the variation of η. This behavior was expected since a decreaseFigure in8 theillustrates irreversibilities the system’s led irreversibilitiesto an increase as of a functionη . In addition, of the evaporator it can be temperature seen that forthe irreversibilitiesthree different valuesare theof lowest SR. The at SR results = 0 since plotted in this in thiscase, figure all the are ammonia related toproduced the variation was used of the in ηtheEX turbinevalues reported to produce in Figure power.7 since as it can be observed, the irreversibilities decrease with the increment of TEFrom, which the is theanalysis opposite of tothis the cycle, variation it can of ηbeEX .co Thisncluded behavior that was the expectedsystem has since the a decrease capability in theof producingirreversibilities higher led amounts to an increase of cooling of η EXpower,. In addition, which ca itn canbe useful be seen for that certain the irreversibilitiestype of industries are that the requirelowest at a SRgreat= 0 amount since in of this cooling case, all and the not ammonia too much produced electric was power; used however, in the turbine from tothe produce exergy power. point of view, the system is less efficient as the SR values increase.

Figure 8. IrreversibilityIrreversibility as as a a function function of of T E forfor Model Model II II at at three three different different values of SR.

4.2. GoswamiFrom the Cycle analysis with ofa Condenser this cycle, and it can a Flow be concluded Division into that the the Turbine system (Model has the III). capability of producing higher amounts of cooling power, which can be useful for certain type of industries that require a greatFigures amount 9–12 of cooling illustrate and the not modeling too much results electric of the power; Goswami however, cycle, from including the exergy a condenser point of and view, a flowthe system division is lessinto ethefficient turbine, as the for SR the values same increase.base case set in Section 4.1 for Model II. Figure 9 illustrates the power produced by the turbine and the cooling effect as a function of SR of4.2. the Goswami ammonia Cycle extracted with a Condenser from the andturbine a Flow at an Division intermediate into the Turbinepressure. (Model In the III) present cycle, a value of SR = 0 means that all the ammonia is expanded throughout the entire turbine, while SR = 1 means Figures9–12 illustrate the modeling results of the Goswami cycle, including a condenser and a that all the ammonia is extracted at an intermediate pressure to go to the condenser. As can be seen flow division into the turbine, for the same base case set in Section 4.1 for Model II. in Figure 5, W decreases while Q increases with the increment of SR. It was proven that for an SR Figure9 illustrates the power produced by the turbine and the cooling e ffect as a function of SR of = 0, the W values were exactly the same as those reported in Figure 5 since all the ammonia was the ammonia extracted from the turbine at an intermediate pressure. In the present cycle, a value of expanded through the turbine. However, at SR = 1, the W was not zero, as in Figure 5, since in the SR = 0 means that all the ammonia is expanded throughout the entire turbine, while SR = 1 means present cycle, all the ammonia was expanded in the turbine at an intermediate pressure. For an that all the ammonia is extracted at an intermediate pressure to go to the condenser. As can be seen in intermediate. value of SR = 0.5,. the W decreased to a value of 170 kW (at a TE = −10 °C), but Q Figure5, WT decreases while Q increases with the increment of SR. It was proven that for an SR = 0, significantly. increased to a valueE of about 600 kW, which was 6 times higher than the cooling effect the WT values were exactly the same as those reported in Figure5 since all the ammonia was expanded produced at SR = 0. As was shown in Figure. 5, in Figure 9 it can be observed that the evaporator through the turbine. However, at SR = 1, the W was not zero, as in Figure5, since in the present cycle, temperature affects W at low SR values, but itsT effect was also negligible at high SR values. all the ammonia was expanded in the turbine at an intermediate pressure. For an intermediate value . . of SR = 0.5, the W decreased to a value of 170 kW (at a T = 10 C), but Q significantly increased to T E − ◦ E a value of about 600 kW, which was 6 times higher than the cooling effect produced at SR = 0. As was . shown in Figure5, in Figure9 it can be observed that the evaporator temperature a ffects WT at low SR values, but its effect was also negligible at high SR values. Processes 2020, 8, 320 14 of 25 Processes 2020, 8, x FOR PEER REVIEW 14 of 24 Processes 2020, 8, x FOR PEER REVIEW 14 of 24

. . Figure 9. WW T andand QQE as as a a function function of of SR SR for for Model Model III III for for di differentfferent evaporator evaporator temperatures. temperatures. Figure 9. W and Q as a function of SR for Model III for different evaporator temperatures. FigureFigure 10 10 illustrates illustrates the the EUF EUF as aas function a function of SR of at SR di ffaterent different evaporator evaporator temperatures. temperatures. In a similar In a Figure 10 illustrates the EUF as a function of SR at different evaporator temperatures. In a way,similar as inway, Figure as in6, theFigure EUF 6, values the EUF significantly values sign increasedificantly withincreased the increment with the ofincrement SR. The minimumof SR. The similar way, as in Figure 6, the EUF values significantly increased with the increment of SR. The valuesminimum of the values EUF wereof the obtained EUF were at SR obtained= 0, varying at SR between = 0, varying 0.10 and between 0.17, while 0.10 the and maximum 0.17, while values the minimum values of the EUF were obtained at SR = 0, varying between 0.10 and 0.17, while the achievedmaximum at values SR = 1 wereachieved in a rangeat SR between= 1 were 0.35in a andrange 0.84, between being between0.35 and 3 0.84, and 6being times between higher than 3 and the 6 maximum values achieved at SR = 1 were in a range between 0.35 and 0.84, being between 3 and 6 minimumtimes higher values. than In the addition, minimum these va valueslues. In were addition, considerably these highervalues thanwere those considerably achieved higher by Shankar than times higher than the minimum values. In addition, these values were considerably higher than andthose Srinivas achieved [30 ],by who Shankar reported and aSrinivas maximum [30], energy who reported utilization a maximum factor of 0.39 energy for their utilization proposed factor cycle. of those achieved by Shankar and Srinivas [30], who reported a maximum energy utilization factor of. As0.39 was for mentioned their proposed previously, cycle. As this was significant mentioned increase previously, was due this to significant the considerable increase increment was due ofto QtheE 0.39 for their proposed cycle. As was mentioned previously, this significant increase was due to the illustratedconsiderable in Figure increment9. In addition,of Q illustrated it can be seenin Figure that evaporation 9. In addition, temperature it can be considerably seen that evaporation a ffects the considerable increment of Q illustrated in Figure 9. In addition, it can be seen that evaporation EUFtemperature at higher considerably values of SR. affects the EUF at higher values of SR. temperature considerably affects the EUF at higher values of SR.

Figure 10. EUF a function of SR for Model III for different evaporator temperatures. FigureFigure 10. 10. EUFEUF a a function function of of SR SR for for Model Model III III fo forr different different evaporator evaporator temperatures. temperatures.

Figure 11 illustrates the η as a function of the evaporator temperature at three different Figure 11 illustrates the η as a function of the evaporator temperature at three different values of SR for Model III. As can be observed, the η rapidly increases with an increment in the values of SR for Model III. As can be observed, the η rapidly increases with an increment in the Processes 2020, 8, 320 15 of 25

ProcessesFigure 2020, 118, x illustratesFOR PEER REVIEW the ηEX as a function of the evaporator temperature at three different values15 of 24 of SR for Model III. As can be observed, the ηEX rapidly increases with an increment in the evaporator temperaturesevaporator temperatures and then remains and then almost remains constant almost for constant the three for dithefferent three SR different values. SR This values. behavior This occurredbehavior becauseoccurred the because exergy the required exergy inrequired the generator in the togenerator produce to a coolingproduce e ffa ectcooling at low effect evaporator at low temperaturesevaporator temperatures is very high, is whichvery high, reduces whichηEX reduces. However, η. asHowever, the evaporator as the evaporator temperature temperature increases, theincreases, exergy the required exergy in required the generator in the decreases generator following decreases an following asymptotic an asymptotic behavior. On behavior. the other On hand, the itother can hand, be seen it thatcan thebe seenηEX valuesthat the are η slightly values higher are slightly at higher higher SR values. at higher This SR behavior values. This is opposite behavior to thatis opposite illustrated to that in Figureillustrated7. This in Figure e ffect 7. takes This place effect since, takes inplace the since, present in cycle,the present the energy cycle, andthe energy exergy areand moreexergy effi areciently more used, efficiently since theused, cooling since powerthe cool produceding power is produced similar to is that similar obtained to that with obtained Model II,with but Model the power II, but produced the power with produced Model with III is Model considerably III is considerably higher. The higher. highest The value highest of the value exergy of ethefficiency exergy is efficiency 50%, which is is50%, considerably which is considerably higher than the higher value than reported the value by Padilla reported et al. by [23 Padilla], which et was al. 24%,[23], butwhich lower was than 24%, that but reported lower bythan Zhang that andreported Lior [ 19by], whichZhang wasand 55.7%. Lior [19], However, which the was proposed 55.7%. cycleHowever, has the the advantage proposed of cycle requiring has fewerthe advantage components of thanrequiring the cycle fewer proposed components by Zhang than and the Lior cycle [19] sinceproposed their by system Zhang consists, and Lior in [19] fact, since of two their cycles system (the consists, power cyclein fact, and of thetwo cooling cycles (the cycle) power operating cycle inand parallel. the cooling cycle) operating in parallel.

Figure 11. ηEX as a function of TE for Model III at three different values of SR. Figure 11. η as a function of TE for Model III at three different values of SR. The variation of the irreversibilities (I) as a function of the evaporator temperature for three differentThe valuesvariation of SR of for the Model irreversibilities III is illustrated (I) as in a Figure function 12. Itof can the be evaporator observed thattemperature the I values for present three different values of SR for Model III is illustrated in Figure 12. It can be observed that the I values an opposite behavior than that observed for the ηEX in Figure 11, since a decrease in irreversibilities η leadspresent to anan exergyopposite effi ciencybehavior increase. than that For thisobserved system, for the the I values in are Figure almost 11, the since same independentlya decrease in ofirreversibilities the SR value. leads to an exergy efficiency increase. For this system, the I values are almost the same independently of the SR value. Processes 2020, 8, 320 16 of 25 Processes 2020, 8, x FOR PEER REVIEW 16 of 24 Processes 2020, 8, x FOR PEER REVIEW 16 of 24

Figure 12. Irreversibilities as a function of T for Model III at three different values of SR. Figure 12. Irreversibilities as a function of TEE for Model III at three different values of SR. Figure 12. Irreversibilities as a function of TE for Model III at three different values of SR. Figure 13 shows the exergy efficiency as a function of turbine efficiency for Model III at three FigureFigure 13 13 shows shows the the exergy exergy efficiency efficiency as as a a functi functionon of of turbine turbine efficiency efficiency for for Model Model III III at at three three different values of SR. It can be seen that η increases with the increment of η . This behavior was differentdifferent values values of of SR. SR. It It can can be be seen seen that that ηηEX increases increases with with the the increment increment of of ηη.T .This This behavior behavior was was expected, since by increasing η , the turbine produces more work, thus increasing the exergy efficiency expected,expected, sincesince byby increasingincreasingT ηη, , thethe turbineturbine producesproduces moremore work,work, thusthus increasingincreasing thethe exergyexergy η η of theefficiency entire system.of the entire In addition, system. itIn can addition, be observed it can thatbe observed at low values that at of lowT, thevaluesEX ofare η more, thedependent η are efficiency of the entire system. In addition, it can be observed that at low values of η, the η are onmore the SR dependent values than on the at highSR valuesηT. This than happens, at high η since. This low happens, values since of the low SR values imply of that the mostSR imply of the more dependent on the SR values than at high η. This happens, since low values of the SR imply workingthatthat most most fluid of of the isthe expanding working working fluid fluid in the is is expanding turbineexpanding and in in verythe the turbine turbine little is and and being very very used little little for is is being thebeing cooling used used for for eff ectthe the andcooling cooling asthe η effectis low, and thus as the η isis low, low thus too. the However, η is low at hightoo. However, SR values, at ahigh larger SR partvalues, of thea larger working part of fluid the is Teffect and as the ηEX is low, thus the η is low too. However, at high SR values, a larger part of the beingworkingworking used fluidfluid to produce isis beingbeing the usedused cooling toto produceproduce effect, the thusthe coolingcooling the effi effect,effect,ciency thusthus of the thethe turbine efficiencyefficiency has ofof a the lowerthe turbineturbine effect hashas on aa the effilowerlowerciency effect effect of the on on entirethe the efficiency efficiency system. of of the the entire entire system. system.

FigureFigure 13. 13.η ηEXas as a a function function ofof ηηTfor for Model Model IIIIII atat threethree didifferentfferent values of of SR. SR. Figure 13. η as a function of η for Model III at three different values of SR. Processes 2020, 8, 320 17 of 25 Processes 2020, 8, x FOR PEER REVIEW 17 of 24

Figure 14 illustrates the behavior of ηEX as a function of the pressure ratio (PR) at three different Figure 14 illustrates the behavior of η as a function of the pressure ratio (PR) at three different values of SR for Model III. As can be observed, the ηEX rapidly increases with an increment of SR values of SR for Model III. As can be observed, the η rapidly increases with an increment of SR achieving a maximum value and then decreases. This happens because the increment of PR causes an achieving a maximum value and then decreases. This happens because the increment of PR causes increase of the work produced by the turbine, and, therefore, ηEX, (see Equation (2)). However, if PR an increase of the work produced by the turbine, and, therefore, η, (see Equation (2)). However, if continues rising, the pressure difference between PH and PL becomes very high, increasing the pump’s PR continues rising, the pressure difference between PH and PL becomes very high, increasing the work, which causes the net power to diminish and, therefore ηEX. pump’s work, which causes the net power to diminish and, therefore η.

Figure 14. η as a function of pressure ratio (PR) for Model III at three different values of SR. Figure 14. ηEX as a function of pressure ratio (PR) for Model III at three different values of SR. 4.3. Comparison of the Performance for the Three Different Thermodynamic Cycles 4.3. Comparison of the Performance for the Three Different Thermodynamic Cycles. Figures 15–18 compare the performance of the Goswami cycle (Model I), and the two novel Figures 15–18 compare the performance of the Goswami cycle (Model I), and the two novel proposed cycles at the same operating conditions. proposed cycles at the same. operating. conditions. Figure 15 compares WT and QE as a function of SR at the conditions of the base case established Figure 15 compares W and Q as a function of SR at the conditions of the base case in Section 4.1. Since in the traditional Goswami cycle, the ammonia mass flow rate is not split at the established in Section 4.1. Since in the traditional Goswami cycle,. the ammonia. mass flow rate is not exit of the rectifier, or into the turbine, thus SR = 0. Therefore WT and QE appear as a single point in split at the exit of the rectifier, or into the turbine,. thus SR = 0. Therefore. W and Q appear as a Figure 13. As illustrated in Figures5 and9, W decreased, and Q significantly increased with an single point in Figure 13. As illustrated in FiguresT 5 and 9, W Edecreased, and Q significantly increment of SR. It is important to notice that although there is a power decrease in the two proposed increased with an increment. of SR. It is important to notice that although there is a power decrease in models, the decrease of WT is less significantW with Model III than with Model II. For an SR value = 0 the two proposed models, the decrease. of is less significant with Model III than with Model II. Forthe Goswamian SR value cycle = 0 has the the Goswami highest cycleWT = has212 the kW, highest but just W 110 = kW 212 of kW, cooling but just power. 110 ForkW an of SRcooling= 0.5, . . power.WT for ModelFor an IISR is = 106 0.5, kW, W while for Model for Model II is 106 III is kW, 161 while kW and for a ModelQ = 618 III kWis 161 for kW both and cycles. a QIn = terms618 kW of . E . W forpercentages, both cycles.WT Indecreased terms of 50%percentages, for Model II and decreased 23% for 50% Model forIII, Model and bothII and increased 23% for theModelQ inIII, about and . E both increased the Q in about 6 times compared to the Goswami cycle. For SR = 1, W = 0 for 6 times compared to the Goswami cycle. For SR = 1, WT = 0 for Model II since all the working fluid . Model II since all the working fluid produced is used for cooling purposes, while for Model III W = produced is used for cooling purposes, while for Model III WT = 100 kW, which was around 50% of the 100 kW, which was around 50% of the power produced by the turbine, compared. with the Goswami power produced by the turbine, compared with the Goswami cycle, but Q was about 10 times higher cycle, but Q was about 10 times higher than that produced with Ethe Goswami cycle. This than that produced with the Goswami cycle. This considerable increase shows the high capability of considerable increase shows the high capability of Model III to produce a cooling effect and still Model III to produce a cooling effect and still produce a reasonable amount of electrical power. produce a reasonable amount of electrical power. Processes 2020, 8, 320 18 of 25 Processes 2020, 8, x FOR PEER REVIEW 18 of 24

Processes 2020, 8, x FOR PEER REVIEW 18 of 24

. . W Q FigureFigure 15. 15.Comparison Comparison of ofW T andand QE as as a function of of SR SR for for the the three three models. models.

Figure 15. Comparison of W and Q as a function of SR for the three models. FigureFigure 16 compares 16 compares the the EUF EUF as as a a function function ofof SR for the the three three models. models. As Ascan canbe seen, be seen, the EUF the EUF values increased with the increment of SR. The minimum value of the EUF for the three models was values increasedFigure 16 with compares the increment the EUF as of a SR.function The minimumof SR for the value three of models. the EUF As forcan thebe seen, three the models EUF was 0.17, and it was obtained at SR = 0. The maximum EUF values for Models II and III were 0.66 and 0.17,values and it increased was obtained with the at increment SR = 0. The of SR. maximum The minimum EUF value values of forthe EUF Models for the II andthree III models were was 0.66 and 0.61, respectively, at SR = 1. As was previously mentioned, this significant increase was due to the 0.61,0.17, respectively, and it was at obtained SR = 1. at As SR was = 0. previouslyThe maximum mentioned, EUF values this for significantModels II and increase III were was 0.66 due and to the considerable increment of. Q . 0.61, respectively, at SR = 1. As was previously mentioned, this significant increase was due to the considerable increment of QE. considerable increment of Q .

Figure 16. Comparison of the EUF as a function of SR for the three models. FigureFigure 16. 16.Comparison Comparison of of thethe EUF as a a function function of of SR SR for for the the three three models. models. Figure 17 compares the η, for the three different cycles. As shown, the η slightly increased for Model III with the incrementη of SR, which means that the proposed cycle withη a flow extraction FigureFigure 17 compares 17 compares the theEX η, for, for the the three three di differentfferent cycles. cycles. As shown, the the ηEX slightlyslightly increased increased for in the turbine was better than the conventional Goswami cycle for any SR value. In addition, it can Modelfor III Model with III the with increment the increment of SR, of which SR, which means means that that the proposedthe proposed cycle cycle with with a flowa flow extraction extraction in the be seen that the η significantly decreased with the increment of SR for Model II. turbinein the was turbine better was than better the conventionalthan the conventional Goswami Gosw cycleami forcycle any for SR any value. SR value. In addition, In addition, it can it can be seen η that thebe seenηEX thatsignificantly the significantly decreased decreased with the incrementwith the increment of SR for of ModelSR for Model II. II. Figure 18 compares the I for the three different cycles. As it can be observed, the I increased for Model II from 251 kW at SR = 0, up to 344 kW at SR = 1. In addition, it is shown that the I decreased for Model III with the increment of SR. The I values for Models II and III were in concordance with the ηEX values reported in Figure 17, since an increment in the irreversibilities, led to a decrement in the ηEX and vice versa. Processes 2020, 8, x FOR PEER REVIEW 19 of 24

Processes 2020, 8, 320 19 of 25 Processes 2020, 8, x FOR PEER REVIEW 19 of 24

Figure 17. Comparison of the η as a function of SR for the three models.

Figure 18 compares the I for the three different cycles. As it can be observed, the I increased for Model II from 251 kW at SR = 0, up to 344 kW at SR = 1. In addition, it is shown that the I decreased for Model III with the increment of SR. The I values for Models II and III were in concordance with

the η values reported in Figure 17, since an increment in the irreversibilities, led to a decrement in Figure 17. Comparison of the ηEX as a function of SR for the three models. the η and viceFigure versa. 17. Comparison of the η as a function of SR for the three models.

Figure 18 compares the I for the three different cycles. As it can be observed, the I increased for Model II from 251 kW at SR = 0, up to 344 kW at SR = 1. In addition, it is shown that the I decreased for Model III with the increment of SR. The I values for Models II and III were in concordance with

the η values reported in Figure 17, since an increment in the irreversibilities, led to a decrement in the η and vice versa.

FigureFigure 18. 18.Comparison Comparison of of the the II asas aa functionfunction of of SR SR for for the the three three models. models.

5. Conclusions5. Conclusions TwoTwo novel novel thermodynamic thermodynamic cycles cycles based based onon thethe GoswamiGoswami cycle cycle were were proposed. proposed. These These cycles cycles havehave the capabilitythe capability of producingof producing a considerablya considerably highhigh amount of of cooling cooling power power compared compared to that to that producedproduced with with the Goswamithe Goswami cycle. cycle. The The three three cycles cycles were were analyzed analyzed based based on on the the first first and and second second laws Figure 18. Comparison of the I as a function of SR for the three models. of thermodynamics.laws of thermodynamics. For Model II, it was shown that the power produced by the turbine decreased, and the cooling 5.For Conclusions Model II, it was shown that the power produced by the turbine decreased, and the cooling powerpower increased increased considerably considerably with with the incrementthe increment of theof the split split ratio. ratio. The The increment increment of theof the cooling cooling power Two novel thermodynamic cycles based on the Goswami cycle were proposed. These cycles caused a significant increment in the energy utilization factor, but with an increment of the system have the capability of producing a considerably high amount of cooling power compared to that irreversibilities, which caused a decrease in the exergy efficiency. produced with the Goswami cycle. The three cycles were analyzed based on the first and second lawsOnthe of thermodynamics. other hand, from the analysis of Model III, it was also shown that the power produced by the turbineFor Model decreased II, it was while shown the that cooling the power power prod increaseduced by the as turbine the split decreased, ratio augmented; and the cooling however, the systempower increasedirreversibilities considerably decreased with significantlythe increment with of the the split increment ratio. The of theincrement split ratio, of the which cooling allowed an increase of the exergy efficiency. From the comparison among the three models, it was proven that the Goswami cycle produced the highest amount of electric power; however, the cooling power was considerably much lower than that produced with Model II and Model III. For a split ratio of 0.5, the power produced by the turbine Processes 2020, 8, 320 20 of 25 decreased 50% with Model II, and 23% with Model III, respectively, but the cooling power achieved with the novel cycles was 6 times higher than that produced with the Goswami cycle. For an SR value of 1, it was shown that the power produced by the turbine was zero with Model II, since all the working fluid produced was used for cooling purposes, while for Model III the power was around 100 kW, which was about 50% of the power produced by the turbine, compared with the Goswami cycle, . but QE was about 10 times higher than that produced with the conventional cycle.

Author Contributions: W.R. proposed the original idea and analyzed the results. K.S.-S. proposed the novel thermodynamic cycles, developed the mathematical models for the three cycles, and wrote the results section. J.A.H.-M. and J.C.J.-G. modeled the thermodynamic cycles and wrote part of the paper. A.P. carried out the bibliographic review. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

EBP Energy balance pump EBEc Energy balance economizer EUF Energy Utilization Factor (dimensionless) h Specific enthalpy (kJ/kg) I Irreversibility (kW) m Mass flow rate (kg/s) P Pressure (kPa) Q Heat power (kW) q Vapor fraction (dimensionless) RP Pressure ratio SR Split ratio (dimensionless) T Temperature (◦C) W Mechanical power (kW) X Ammonia concentration (% in weight) Greek letters η Efficiency (dimensionless) ∆T Temperature increment (◦C) Subscripts A Absorber C Condenser Cool Cooler E Evaporator Ec Economizer EX Exergy G Generator H High Int Intermediate L Low Net Net P Pump R Reheater r Refrigerant Re Rectifier T Turbine 0 Environment state Processes 2020, 8, 320 21 of 25

Appendix A

Table A1. Simulation data for the case base of Model III.

P2 = P3 = P4 = P5 = P7 = P8 = P9 = P10 = 30 bar, P1 = P6 = P11 = P12 = P14 = 4.29 bar, P13 = P15 = 11.67 bar Property 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

T1 (◦C) 30 30 30 30 30 30 30 30 30 30 30 X1 0.534 0.534 0.534 0.534 0.534 0.534 0.534 0.534 0.534 0.534 0.534 h (kJ/kg) 103.7 103.7 103.7 103.7 103.7 103.7 103.7 103.7 103.7 103.7 103.7 1 − − − − − − − − − − − s1 (kJ/kg ◦C) 0.2908 0.2908 0.2908 0.2908 0.2908 0.2908 0.2908 0.2908 0.2908 0.2908 0.2908 m1 (kg/s) 5.096 5.096 5.096 5.096 5.096 5.096 5.096 5.096 5.096 5.096 5.096

T2 (◦C) 30.39 30.39 30.39 30.39 30.39 30.39 30.39 30.39 30.39 30.39 30.39 X2 0.534 0.534 0.534 0.534 0.534 0.534 0.534 0.534 0.534 0.534 0.534 h (kJ/kg) 99.69 99.69 99.69 99.69 99.69 99.69 99.69 99.69 99.69 99.69 99.69 2 − − − − − − − − − − − s2 (kJ/kg ◦C) 0.2934 0.2934 0.2934 0.2934 0.2934 0.2934 0.2934 0.2934 0.2934 0.2934 0.2934 m2 (kg/s) 5.096 5.096 5.096 5.096 5.096 5.096 5.096 5.096 5.096 5.096 5.096

T3 (◦C) 100.2 100.2 100.2 100.2 100.2 100.2 100.2 100.2 100.2 100.2 100.2 X3 0.534 0.534 0.534 0.534 0.534 0.534 0.534 0.534 0.534 0.534 0.534 h3 (kJ/kg) 225.1 225.1 225.1 225.1 225.1 225.1 225.1 225.1 225.1 225.1 225.1 s3 (kJ/kg ◦C) 1.255 1.255 1.255 1.255 1.255 1.255 1.255 1.255 1.255 1.255 1.255 m3 (kg/s) 5.096 5.096 5.096 5.096 5.096 5.096 5.096 5.096 5.096 5.096 5.096

T4 (◦C) 130 130 130 130 130 130 130 130 130 130 130 X4 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 h4 (kJ/kg) 364.3 364.3 364.3 364.3 364.3 364.3 364.3 364.3 364.3 364.3 364.3 s4 (kJ/kg ◦C) 1.617 1.617 1.617 1.617 1.617 1.617 1.617 1.617 1.617 1.617 1.617 m4 (kg/s) 4.096 4.096 4.096 4.096 4.096 4.096 4.096 4.096 4.096 4.096 4.096

T5 (◦C) 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 42.9 X5 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 h (kJ/kg) 39.79 39.79 39.79 39.79 39.79 39.79 39.79 39.79 39.79 39.79 39.79 5 − − − − − − − − − − − s5 (kJ/kg ◦C) 0.4908 0.4908 0.4908 0.4908 0.4908 0.4908 0.4908 0.4908 0.4908 0.4908 0.4908 m5 (kg/s) 4.096 4.096 4.096 4.096 4.096 4.096 4.096 4.096 4.096 4.096 4.096

T6 (◦C) 43.38 43.38 43.38 43.38 43.38 43.38 43.38 43.38 43.38 43.38 43.38 X6 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 0.4214 h (kJ/kg) 39.79 39.79 39.79 39.79 39.79 39.79 39.79 39.79 39.79 39.79 39.79 6 − − − − − − − − − − − s6 (kJ/kg ◦C) 0.5004 0.5004 0.5004 0.5004 0.5004 0.5004 0.5004 0.5004 0.5004 0.5004 0.5004 m6 (kg/s) 4.096 4.096 4.096 4.096 4.096 4.096 4.096 4.096 4.096 4.096 4.096 Processes 2020, 8, 320 22 of 25

Table A1. Cont.

P2 = P3 = P4 = P5 = P7 = P8 = P9 = P10 = 30 bar, P1 = P6 = P11 = P12 = P14 = 4.29 bar, P13 = P15 = 11.67 bar Property 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

T7 (◦C) 100.2 100.2 100.2 100.2 100.2 100.2 100.2 100.2 100.2 100.2 100.2 X7 0.9863 0.9863 0.9863 0.9863 0.9863 0.9863 0.9863 0.9863 0.9863 0.9863 0.9863 h7 (kJ/kg) 1425 1425 1425 1425 1425 1425 1425 1425 1425 1425 1425 s7 (kJ/kg ◦C) 4.292 4.292 4.292 4.292 4.292 4.292 4.292 4.292 4.292 4.292 4.292 m7 (kg/s) 1.029 1.029 1.029 1.029 1.029 1.029 1.029 1.029 1.029 1.029 1.029

T8 (◦C) 85.36 85.36 85.36 85.36 85.36 85.36 85.36 85.36 85.36 85.36 85.36 X8 0.6903 0.6903 0.6903 0.6903 0.6903 0.6903 0.6903 0.6903 0.6903 0.6903 0.6903 h8 (kJ/kg) 206.7 206.7 206.7 206.7 206.7 206.7 206.7 206.7 206.7 206.7 206.7 s8 (kJ/kg ◦C) 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 m8 (kg/s) 0.02945 0.02945 0.02945 0.02945 0.02945 0.02945 0.02945 0.02945 0.02945 0.02945 0.02945

T9 (◦C) 85.36 85.36 85.36 85.36 85.36 85.36 85.36 85.36 85.36 85.36 85.36 X9 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 h9 (kJ/kg) 1365 1365 1365 1365 1365 1365 1365 1365 1365 1365 1365 s9 (kJ/kg ◦C) 4.129 4.129 4.129 4.129 4.129 4.129 4.129 4.129 4.129 4.129 4.129 m9 (kg/s) 11111111111

T10 (◦C) 95.36 95.36 95.36 95.36 95.36 95.36 95.36 95.36 95.36 95.36 95.36 X10 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 h10 (kJ/kg) 1401 1401 1401 1401 1401 1401 1401 1401 1401 1401 1401 s10 (kJ/kg ◦C) 4.223 4.223 4.223 4.223 4.223 4.223 4.223 4.223 4.223 4.223 4.223 m10 (kg/s) 11111111111

T11 (◦C) 1.617 1.617 1.617 1.617 1.617 1.617 1.617 1.617 1.617 1.617 1.617 X11 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 h11 (kJ/kg) 1173 1173 1173 1173 1173 1173 1173 1173 1173 1173 1173 s11 (kJ/kg ◦C) 4.298 4.298 4.298 4.298 4.298 4.298 4.298 4.298 4.298 4.298 4.298 m11 (kg/s) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

T12 (◦C) 0 0 0 0 0 0 0 0 0 0 0 X12 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 h12 (kJ/kg) 1268 1268 1268 1268 1268 1268 1268 1268 1268 1268 1268 s12 (kJ/kg ◦C) 4.633 4.633 4.633 4.633 4.633 4.633 4.633 4.633 4.633 4.633 4.633 m12 (kg/s) 11111111111 Processes 2020, 8, 320 23 of 25

Table A1. Cont.

P2 = P3 = P4 = P5 = P7 = P8 = P9 = P10 = 30 bar, P1 = P6 = P11 = P12 = P14 = 4.29 bar, P13 = P15 = 11.67 bar Property 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

T13 (◦C) 38.59 38.59 38.59 38.59 38.59 38.59 38.59 38.59 38.59 38.59 38.59 X13 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 h13 (kJ/kg) 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 1291 s13 (kJ/kg ◦C) 4.285 4.285 4.285 4.285 4.285 4.285 4.285 4.285 4.285 4.285 4.285 m13 (kg/s) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

T14 (◦C) 30 30 30 30 30 30 30 30 30 30 30 X14 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 h14 (kJ/kg) 141.8 141.8 141.8 141.8 141.8 141.8 141.8 141.8 141.8 141.8 141.8 s14 (kJ/kg ◦C) 0.4995 0.4995 0.4995 0.4995 0.4995 0.4995 0.4995 0.4995 0.4995 0.4995 0.4995 m14 (kg/s) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

T15 (◦C) 0.1604 0.1604 0.1604 0.1604 0.1604 0.1604 0.1604 0.1604 0.1604 0.1604 0.1604 X15 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 h15 (kJ/kg) 141.8 141.8 141.8 141.8 141.8 141.8 141.8 141.8 141.8 141.8 141.8 s15 (kJ/kg ◦C) 0.5463 0.5463 0.5463 0.5463 0.5463 0.5463 0.5463 0.5463 0.5463 0.5463 0.5463 m15 (kg/s) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 . QG(kW) 1806 1806 1806 1806 1806 1806 1806 1806 1806 1806 1806 . Qrecal(kW) 35.85 35.85 35.85 35.85 35.85 35.85 35.85 35.85 35.85 35.85 35.85 . QA(kW) 1633 1633 1633 1633 1633 1633 1633 1633 1633 1633 1633 . QC(kW) 0 114.9 229.9 344.8 459.7 574.7 689.6 804.6 919.5 1034 1149 . Qrect(kW) 96.12 96.12 96.12 96.12 96.12 96.12 96.12 96.12 96.12 96.12 96.12 . QSHE(kW) 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655 1655 . WB(kW) 20.21 20.21 20.21 20.21 20.21 20.21 20.21 20.21 20.21 20.21 20.21 . WT(kW) 228 216.2 204.4 192.5 180.7 168.9 157 145.2 133.4 121.5 109.7 FUE 0.1646 0.2142 0.2638 0.3133 0.3629 0.4124 0.462 0.5115 0.5611 0.6106 0.6602

EfEX 0.4805 0.4793 0.4782 0.4771 0.476 0.4749 0.4738 0.4726 0.4715 0.4704 0.4693 I (kW) 236.1 236.6 237.1 237.6 238.1 238.6 239.1 239.6 240.1 240.6 241.1 Processes 2020, 8, 320 24 of 25

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