Análisis termoeconómico de un ciclo compacto de CO2 con eyector

Equation Chapter 1 Section 1 Trabajo Fin de Grado Grado en Ingeniería de las Tecnologías Industriales Mención en Energía Autor: Andrés Morillo Navarro Tutor y publicador: José Manuel Salmerón Lissén Tutor: Bernardo Peris Pérez Dpto. Ingeniería Energética Escuela Técnica Superior de Ingeniería Universidad de Sevilla Sevilla, 2020 Análisis termoeconómico de un ciclo compacto de CO2 con eyector Trabajo Fin de Grado Ingeniería de las Tecnologías Industriales Autor: Andrés Morillo Navarro Autor: Andrés Morillo Navarro Tutor y publicador: José Manuel Salmerón Lissén Profesor titular Tutor: Bernardo Peris Pérez Profesor ayudante doctor Dpto. de Ingeniería Energética Escuela Técnica Superior de Ingeniería Universidad de Sevilla Sevilla, 2020 Análisis termoeconómico de un ciclo compacto de CO2 con eyector Thermoeconomic analysis of CO2 ejector refrigeration cycle Trabajo Fin de Grado: Análisis termoeconómico de un ciclo compacto de CO2 con eyector Thermoeconomic analysis of CO2 ejector refrigeration cycle Autor: Andrés Morillo Navarro Tutor y publicador José Manuel Salmerón Lissén Tutor: Bernardo Peris Pérez El tribunal nombrado para juzgar el Proyecto arriba indicado, compuesto por los siguientes miembros: Presidente: Vocales: Secretario: Acuerdan otorgarle la calificación de: Sevilla, 2020 El Secretario del Tribunal Agradecimientos A José Manuel por brindarme la oportunidad de hacer este trabajo, a mi profesor y tutor Bernardo por todo lo aprendido y la experiencia vivida, y a mi familia y amigos por el apoyo continuo e incodicional. Dedicado a mi madre María y mi padre Juan Luis que me han permitido llegar hasta aquí. Andrés Morillo Navarro Sevilla, Resumen Actualmente, la industria de refrigeración está adoptando una estrategia proactiva de sustitución de gases fluorados por alternativas más sostenibles con bajo potencial de efecto invernadero. El R744 es un refrigerante natural que ha sido ampliamente propuesto para aplicaciones de refrigeración comercial. Su uso en sistemas de cascada o tipo “booster” permite producir simultáneamente frío para aplicación de enfriamiento y congelación. Sin embargo, cuando únicamente se requiere una etapa de evaporación a baja temperatura, el uso del R744 en ciclos de tipo transcríticos es escasa. Los principales motivos son debidos al bajo rendimiento del ciclo (COP, por las siglas en inglés) en climas cálidos, así como las limitaciones técnicas encontradas en los compresores comerciales para alcanzar las relaciones de compresión extremas requeridas por el ciclo. A la luz de estos inconvenientes, y dada la creciente necesidad de equipos para aplicaciones de baja temperatura que utilicen fluidos sostenibles y que puedan operar en climas cálidos, este trabajo propone el uso del R744 en el Ciclo de Refrigeración con Expansión por Eyector (EERC, por las siglas en inglés). Para evaluar la viabilidad de la propuesta, este estudio lleva a cabo una evaluación termoeconómica. Para ello, se ha desarrollado un modelo completo del sistema, incluyendo un eyector bifásico, un compresor comercial de doble etapa, y se han simulado condiciones de evaporación desde -10 ºC hasta -38.5ºC, la cual se reveló como la temperatura más baja alcanzable con este sistema para evitar el punto triple dentro del eyector. La optimización se realizó utilizando el Valor Presente Neto como función objetivo. De este modo, los resultados mostraron que, en comparación con el ciclo transcrítico utilizado como sistema de referencia, el EERC permite utilizar compresores comerciales más pequeños dentro de unos límites operativos más amplios. Además, se alcanzaron mejoras del COP superiores al 22% a la vez que se reducían los costes de inversión y energéticos. Así, se puede concluir que el EERC utilizando R744 es viable para aplicaciones de producción de frio a baja temperatura en climas cálidos. List of Figures Fig. 2-1. RC: (a) architecture with double-stage compressor, intercooler, and internal heat exchanger; (b) P-h diagram of transcritical cycle with CO2. 25 Fig. 2-2. EERC: (a) architecture with double-stage compressor, intercooler, internal heat exchanger, and ejector-expander; (b) P-h diagram of transcritical cycle with CO2. 26 Fig. 2-3. Not scaled phase diagram for CO2. 26 Fig. 3-1. Schematic of ejector, pressure, and velocity profile. 28 Fig. 3-2. Operating limits of commercial CO2 compressors: (a) gas cooler pressure vs. evaporating temperature; (b) pressure ratio vs. evaporating temperature. 30 Fig. 3-3. Black-box model of the double-stage compressor with intercooler. 31 Fig. 3-4. Operating envelope of the double-stage compressor with intercooler: white dots are used for correlations development and blue crosses are used for the model validation. 31 Fig. 3-5. Black-box model validation: (a) specific electric power absorbed by the double-stage compressor; (b) intercooler specific capacity; (c) compressor discharge temperature at the upper stage. 33 Fig. 3-6. Flowchart of the thermoeconomic optimization procedure. 37 Fig. 4-1. EERC modified envelope: (a) DORIN; (b) GEA; (c) FRASCOLD. 40 Fig. 4-2. EERC and RC thermodynamic performance: (a) COP; (b) electric power absorbed by the compressor; (c) gas cooler capacity. 42 Fig. 4-3. Ejector parameters analysis: (a) entrainment ratio; (b) Elbel’s efficiency. 43 Fig. 4-4. Normalized investment cost optimizing the NPV. 44 Fig. 4-5. NPV of the EERC and RC cycle for different refrigeration capacities. 44 Nomenclature Acronyms A Area (m2) C Cost (€) ce Cost of electricity (€/kWh) COP Coefficient of Performance EERC Ejector-Expansion Refrigeration Cycle GWP Global Warming Potential h Enthalpy (kJ·kg-1) HFC Hydrofluorocarbon HP High Pressure stage i Interest rate (%) IC Intercooler IHX Internal Heat Exchanger LMTD Logarithmic Mean Temperature Difference LP Low Pressure stage M Mach number m󰇗 Mass flow rate (kg·s-1) n Years of operation NPV Net Present Value (€) OH Operation Hours in a year P Pressure (bar) q Specific thermal power (kJ·kg-1) Q Thermal power (kW) RC Reference cycle s Entropy (kJ·kg-1·K-1) T Temperature (K) u Velocity (m·s-1) U Overall heat transfer coefficient (kW·m-2·K-1) V󰇗 Volumetric flow rate (m3·s-1) w Specific electric power absorbed (kJ·kg-1) W Electric power absorbed (kW) Greek symbols β Thermal expansion coefficient (K-1) 𝜀 Effectiveness ϵ Void fraction η Efficiency (%) ρ Density (kg·m-3) ϕ Efficiency due to frictional loss ω Entrainment ratio Subscripts as After shock wave c Compressor d Diffuser of the ejector e Evaporator gc Gas cooler i Inlet l liquid phase m Mixed flow o Outlet p Primary fluid p1 Primary nozzle exit s Secondary fluid t Throat of the nozzle v vapor phase y Flow at the location of choking 1 INTRODUCTION Global warming has become one of the main social challenges in recent years. To face this problem, governments and organizations are encouraging companies to reduce greenhouse emissions through more restrictive environmental regulations. In this way, the Kigali amendment on substances that deplete the ozone layer, which came into force in 2019 by the ratification of 65 countries, aimed to reduce the HFC production and consumption to avoid a temperature increase of 0.4 ºC at the end of the century [1]. Among energy consumer sectors, the refrigeration industry highlights, whose demand is expected to be raised to 72% during the present century [2]. Furthermore, the refrigeration industry consumes tons of fluorinated refrigerants with high values of Global Warming Potential (GWP), which are intended to be gradually replaced by more sustainable alternatives. In Europe, the F-Gas Regulation is responsible for a progressive phase-out of fluorinated fluids with high GWP in refrigeration applications. According to this regulation, refrigeration systems that use working fluids with a GWP higher than 150 will be forbidden in 2020. Moreover, to accelerate this process towards the use of more friendly fluids, the European Parliament established by the Regulation No 517/2014 [3] quotas to HFCs that penalized high GWP refrigerants, aiming to reduce the F-Gases commercialization to 21% by 2030 [4]. In response to this requirement, natural refrigerants emerge as a solution with null or marginal GWP. Accordingly, refrigeration companies are now involved in a proactive strategy to fulfill the future demand with more sustainable systems. The most currently investigated natural refrigerants are ammonia (R717), hydrocarbons, and CO2 (R744). Ammonia is currently being used in food retail applications. However, despite the suitable performance reachable using R717, its adoption is not widespread due to its toxicity [5]. Hydrocarbons, such as propane or isobutane, also achieve great performance ratios. These fluids are used in domestic and commercial systems that require minimum refrigerant charges, due to its flammability and explosion hazard [6]. CO2 is a non-flammable, nontoxic fluid with a GWP of 1. Its production is considered simple and cheap, besides recoverable [7]. The main drawback of R744 is associated with its high discharge pressure, which exceeds the critical point in warm climates. Nonetheless, the main technical constraints related to the pressure are already overcome [8]. Indeed, many companies are promoting the R744 use for a combined cooling and freezing production. Cascade cycles can operate with CO2 in the low-temperature circuit, and ammonia, or HFCs in the high-temperature circuit, solving problems of high-pressure operations and achieving great values of COP. Different alternatives can be found in the literature to be used as high-temperature refrigerant for cascade systems with R744, natural fluids like propane [9], fluorinated fluids such as R513A as a replacement of R134a, or pure and azeotropic mixtures of hydrofluorocarbons [10]. Furthermore, R744 can also be used in booster systems for a combined cooling and freezing production. This system operates in the subcritical cycle in cold climates and transcritical cycle in warm climates, exhibiting satisfactory performance ratios. Numerous improvements are proposed in the literature to enhance the COP of the booster cycle with R744 [11]. P. Gullo et al. [12] compared the booster transcritical CO2 system with parallel compressors to the direct expansion system using R404A, concluding that the use of parallel compressors improved the COP by 30% in booster systems. This investigation stated that ejector expanders may be installed in different parts of the cycle, reducing the pressure ratio in the compressor and achieving COP improvements up to 27%, depending on the boundary conditions [13]. Recently, Zolcer et al. [14] demonstrated that the combination of ejectors and parallel compression in transcritical systems exhibited suitable efficiencies, with savings ranging between 8 and 10% compared to the basic transcritical system operating in warm climates. The ejector was considered a breakthrough for CO2 refrigeration systems, which enabled to decrease the compression ratio, and allowed to reduce the compressor discharge temperature. Accordingly, Elbel et al. [15] used the ejector to lift the suction pressure of the compressor, obtaining reductions in the compressor consumption compared to the Introduction 22 basic cycle. Santini et al. [16] experimentally compared the CO2 cycle to the ejector transcritical system, demonstrating reductions in the discharge temperature up to 35 K. Jin et al. [17] studied a CO2 transcritical system for cooling and dehumidification, authors realized that a two-phase ejector implementation provided a COP improvement ranging between 12 and 60% in comparison to the standard cycle. Other improvements proposed for the CO2 systems have been proven with suitable results, such as the study of Zolcer et al. [18], who used an adiabatic gas cooler to save between 8 and 12% of power consumption in warm climates. When a single-stage evaporation at low temperature is required, different alternatives to R744 are generally adopted. For instance, low-temperature refrigeration is common in the food industry, exposing products to temperatures below -30 ºC for a longer preservation [19]. This application is typical in cold storage cabinets and rooms [20], freezing tunnels [21], and shipboard cold stores [22]. Typical refrigerants used in these applications are natural refrigerants such as ammonia, with the above-mentioned issue of toxicity [23], or HFC working fluids like R404A or R449A, that have high values of GWP. In other words, the R744 use for low-temperature refrigeration is associated with cascade and booster architectures, as Table 1-1 lists. The main reason why the transcritical CO2 cycle is not commonly adopted is due to the low Coefficient of Performance (COP) achieved, especially in warm climates, besides the technical limitations of commercial compressors to reach extreme pressure ratios, which are imposed by low evaporating temperatures and high discharge pressures. Table 1-1. Low-temperature refrigeration applications using CO2. Cycle typology Te (ºC) Working fluid Load (kW) COP Tgc (ºC) Ref. Cascade system -50 R717/R744 207 1.15 35 [24] Cascade system -56 R717/R744 267 1.13 40 [25] Booster -34 R744 65 1.319 46 [26] Parallel Booster -32 R744 25,5 1 40 [27] Booster with ejector -35 R744 30 1.5 35 [28] Parallel Booster with ejector -32 R513a/R744 41 1.5 40 [29] Taking this into consideration, this stduy proposes the architecture of the Ejector-Expansion Refrigeration Cycle (EERC) to overcome these drawbacks for low-temperature refrigeration using R744 as working fluid in warm climates. The EERC adoption has demonstrated advantages in the literature using different refrigerants, such as the reduction of power consumption, lower discharge temperatures, and better values of COP compared to the basic cycle. For instance, Deng et al. [30] studied the EERC system for air conditioning applications, reporting a COP improvement of 22% with respect to the conventional vapor compression cycle. Yari et al. [31] tested an EERC demonstrating the compression ratio reductions, lower values of discharge temperature, and improvements in the COP up to 21%. The basic EERC is also able to be improved when increasing the subcooling degree. In this way, Bai et al. [32] analyzed the transcritical two-stage CO2 cycle with a split-cycle for subcooling, reaching performance improvements up to 7.7%. Recently, Liu et al. [33] studied the EERC using a thermoelectric subcooling that improved the COP by 39.34%. To assess the thermodynamic and economic feasibility of the proposal, a thermoeconomic optimization of the CO2 EERC is conducted for low-temperature refrigeration in warm climates. The model of the system is developed considering a two-phase flow ejector, a double-stage compressor with intercooler, and an internal heat exchanger for superheating-subcooling. As a novelty, this investigation examines the maximum operating limits of the EERC considering thermodynamic bounds, such as the triple point of the R744 inside the ejector, and the technical restrictions of the 23 Análisis termoeconómico de un ciclo compacto de CO2 con eyector operating envelope of commercial compressors. Thereby, the influence of the proposal over the COP, total investment cost, and Net Present Value (NPV) will be revealed. The rest of the document is organized as follows. Section 2 describes the proposed transcritical CO2 EERC for low-temperature refrigeration. Section 3 describes the thermodynamic and economic model developed to conduct the analysis. Section 4 shows the optimization and discusses the results of the study. And finally, Section 5 summarizes the main conclusions of the document. Introduction 24 2 SYSTEM DESCRIPTION This study proposes the use of R744 for low-temperature refrigeration in warm climates employing the EERC architecture. This cycle configuration allows reducing the pressure ratio in the compressor, which represents the main drawback to overcome in this study. Notice that, according to the previous review, the evaporating temperature of low-temperature refrigeration is around -30 ºC (14.3 bar), and the use of R744 in warm climates requires to operate in transcritical conditions, reaching discharge pressures above 73.8 bar. Besides the extreme pressure ratio that may support the compressor, which is analyzed in the forthcoming section, the high value of discharge temperature is also a constraint that requires technical solutions. Different possibilities to reduce the compressor discharge temperatures can be found in the literature [34]. The most common solution is the introduction of an intercooler between the two compression stages since it is a simple, cost-effective, and reliable method. In this way, Chen et al. [35] conducted an experimental investigation that demonstrated a 23% reduction in the discharge temperature by using the intercooler in the CO2 refrigeration system. Manjili et al. [36] tested an intercooler between the two compression stages of the EERC that decreased the exergy destruction rate of the compressors by 60.89%. Furthermore, the adoption of an intercooler in a double-stage compressor can also improve the COP of the transcritical CO2 refrigeration cycle, such as Wang et al. [37] demonstrated. Accordingly, the compression process considered in the study also includes a double-stage compressor with intercooler (IC). The architecture of the basic system is shown in Fig. 2-1.a, which is considered as Reference Cycle (RC) for comparisons. The Internal Heat Exchanger (IHX) is used to avoid liquid droplets in the suction port of the compressor, ensuring a superheating degree. At the same time, the IHX provides a subcooling at the outlet of the gas cooler, which increases the vaporization enthalpy, as can be appreciated in Fig. 2-1.b. This figure also depicts the reduction of the discharge temperature using the double-stage compressor with intercooler. (a) (b) Fig. 2-1. RC: (a) architecture with double-stage compressor, intercooler, and internal heat exchanger; (b) P-h diagram of transcritical cycle with CO2. The RC can be further improved by adopting the ejector-expander. EERC architecture is shown in Fig. 2-2.a, which illustrates that the suction from the evaporator is now conducted by the secondary nozzle of the ejector, the fluid from the gas cooler is used as the primary flow to drive the ejector, 2 3GAS COOLER IHX IC LP HP DOUBLE STAGE COMPRESSOR WITH INTERCOOLER EVAPORATOR 3’ 4 1’ 1 Triple line Critical point P3’ 4 3 1’ 2 1 h System modeling 32 The outputs of the model are set as second-order correlations to achieve suitable values of R2. The correlation for each output (k) is shown in Eq. (22), whose coefficients and respective R2 are collected in Table 3-1. Moreover, Fig. 3-5 represents the accuracy of the model by validating its prediction using operating conditions different from the ones used to set the correlations. 𝑘=𝑎0+𝑎1·𝑃𝑠𝑢𝑐 +𝑎2·𝑃𝑔𝑐 +𝑎3·𝑇𝐼𝐶 +𝑎4·𝑃𝑠𝑢𝑐 2+𝑎5·𝑃𝑔𝑐 2+𝑎6·𝑇𝐼𝐶 2+𝑎7·𝑃𝑠𝑢𝑐 ·𝑃𝑔𝑐 +𝑎8·𝑃𝑠𝑢𝑐 ·𝑇𝐼𝐶 +𝑎9·𝑃𝑔𝑐 ·𝑇𝐼𝐶 (22) Table 3-1. List of coefficients used in the second order correlation of Eq. (22). k 𝐰𝐜 (kJ/kg) 𝒒𝐈𝐂 (kJ/kg) 𝐓𝐝𝐢𝐬𝐜𝐡 (ºC) 𝒂𝟎 138.94 42.21 -46.65 𝒂𝟏 -16.58 20.89e-1 -11.41 𝒂𝟐 39.79e-1 -85.90e-3 52.4e-1 𝒂𝟑 37.89e-1 -15.09e-1 87.03e-1 𝒂𝟒 23.30e-2 -68.88e-3 21.42e-2 𝒂𝟓 -11.14e-3 -40.87e-5 -75.92e-4 𝒂𝟔 20.14e-2 -24.49e-3 39.91e-2 𝒂𝟕 14.80e-3 48.04e-4 10.54e-3 𝒂𝟖 -21.62e-3 17.40e-3 -55.01e-3 𝒂𝟗 -14.79e-2 22.66e-3 -31.77e-2 𝑹𝟐 99.46e-2 89.38e-2 99.89e-2 (a) 50 100 150 200 250 300 50 100 150 200 250 300 wcexperimental (kJ/kg) wcblack-box model (kJ/kg) 33 Análisis termoeconómico de un ciclo compacto de CO2 con eyector (b) (c) Fig. 3-5. Black-box model validation: (a) specific electric power absorbed by the double-stage compressor; (b) intercooler specific capacity; (c) compressor discharge temperature at the upper stage. 3.3 Thermoeconomic analysis methodology The thermodynamic model is developed considering energy balances in each component of the cycle. The main equations used for the evaporator, gas cooler, internal heat exchanger, compressor, and intercooler are collected in Table 3-2. 20 30 40 50 60 70 80 20 30 40 50 60 70 80 qIC experimental (kJ/kg) qIC black-box model (kJ/kg) 20 50 80 110 140 170 20 50 80 110 140 170 Tdisch experimental (ºC) Tdisch black-box model (ºC) System modeling 34 Table 3-2. Energy balance equations of the components of the cycles. Component Cycle Energy balance equation Eq. Evaporator EERC 𝑄𝑒=𝑚󰇗𝑠·(ℎ6−ℎ5) (23) RC 𝑄𝑒=𝑚󰇗𝑇·(ℎ1−ℎ4) (24) Gas cooler EERC 𝑄𝑔𝑐 =𝑚󰇗𝑝·(ℎ2−ℎ3) (25) RC 𝑄𝑔𝑐 =𝑚󰇗𝑇·(ℎ2−ℎ3) (26) Internal heat exchanger EERC/RC 𝜀𝐼𝐻𝑋 =𝑇1′−𝑇1 𝑇3−𝑇1 (27) ℎ1′ −ℎ1=ℎ3−ℎ3′ (28) Compressor EERC 𝑊𝑐=𝑚󰇗𝑝·𝑤𝑐 (29) RC 𝑊𝑐=𝑚󰇗𝑇·𝑤𝑐 (30) Intercooler EERC 𝑄𝐼𝐶 =𝑚󰇗𝑝·𝑞𝐼𝐶 (31) RC 𝑄𝐼𝐶 =𝑚󰇗𝑇·𝑞𝐼𝐶 (32) Considering that both cycles, EERC and RC, are compared within the same boundary conditions, the size of each component can be calculated to assess the respective total investment cost. Thus, according to the operating limits, the IHX effectiveness defined by Eq. (27) could be optimized using as restriction the maximum discharge temperature of the compressor. The heat transfer area can be obtained from the thermal load and the LMTD method by Eq. (33) and (34). The overall heat transfer coefficients are assumed from the commercial software and those values reported in the literature, as Table 3-3 shows. 𝑄=𝑈·𝐴·𝐿𝑀𝑇𝐷 (33) 𝐿𝑀𝑇𝐷=(𝑇ℎ𝑖 −𝑇𝑐𝑜)−(𝑇ℎ𝑜 −𝑇𝑐𝑖) 𝑙𝑛 (𝑇ℎ𝑖 −𝑇𝑐𝑜 𝑇ℎ𝑜 −𝑇𝑐𝑖)·𝐹 (34) Table 3-3. Overall heat transfer coefficient considered. Heat exchanger Type 𝑼(𝑾 𝒎𝟐·𝑲) Ref Evaporator Crossflow heat exchanger 50 [48] Gas cooler Crossflow heat exchanger 40 Intercooler Crossflow heat exchanger 40 Internal heat exchanger Brazed plate heat exchanger 180 [49] 35 Análisis termoeconómico de un ciclo compacto de CO2 con eyector Thermodynamic performance and investment costs are analyzed simultaneously to reach the optimum design by a thermoeconomic analysis. To establish the total investment cost of the system, individual costs of the components are needed. The cost correlations used for the main components of the cycles are collected in Table 3-4. With regard to the compressor Eq. (35) is used, which has been developed from the budget of the commercial compressor. In particular, the displacement volume has been considered as the parameter that most influences the cost of the compressor. The ejector cost correlation has been obtained from the literature as Eq. (36), which directly depends on its operating conditions. The correlations used to obtain the costs of the heat exchangers use the heat transfer area as the main parameter, which were obtained using commercial costs and equations reported in literature, from Eq. (37) to Eq. (40). Other investment costs, related to fitting and piping, control devices, or refrigerant cost, are considered by Eq. (41). Table 3-4. Investment cost correlation of the components. Component Cost correlation Eq. Ref. Compressor 𝐶𝑐𝑜𝑚𝑝 =4727.31+1122.02·𝑉󰇗𝑑𝑖𝑠 (35) [47] Ejector 𝐶𝑒𝑗𝑒𝑐𝑡𝑜𝑟 =15962·𝑚󰇗 (𝑇3 0.0001·𝑃3)0.05·(𝑃7 10)−0.75 (36) [50] Evaporator 𝐶𝑒=2465.96+96.39·𝐴 (37) [48] Internal heat exchanger 𝐶𝐼𝐻𝑋 =190+310·𝐴 (38) [51] Intercooler 𝐶𝐼𝐶 =1397·𝐴0.89 (39) [49] Gas cooler 𝐶𝑔𝑐 =1397·𝐴0.89 (40) [49] Miscellaneous 𝐶𝑜𝑡ℎ𝑒𝑟 =1.3∑𝐶𝑥 (41) [51] To achieve the most cost-effective EERC an objective function that optimizes the efficiency of the system while reduces the investment and yearly power costs is required. In this case, the Net Present Value (NPV) has been considered the variable to be maximized. Some assumptions in the optimization process have been considered, which are collected in Table 3-5. Table 3-5. Economic and operating parameters considered. Economic parameters Value Units Interest rate (i) 5 % Operation years (n) 20 years Operation Hours in a year (OH) 4000 h Cost of electricity (ce) 0.1 €/kWh The thermoeconomic process of optimization is illustrated in Fig. 3-6. This flowchart shows thermodynamic and economic inputs to the process. The thermodynamic model starts assuming three iterative variables, which are the pressure of the gas cooler, the IHX effectiveness, and the initial ejector efficiency. The model of the EERC and the model of the two-phase flow ejector are independently solved. The System modeling 36 ejector efficiency calculated according to initial values is then upgraded in the cycle, starting an iterative process until the initial and final efficiencies of the ejector converge. Notice that the ejector efficiency sets the pressures of the cycle that, in turn, are used in the model of the ejector to solve critical velocities of the fluid and the final Elbel efficiency, requiring an iterative resolution. The IHX effectiveness is optimized using as restriction the maximum discharge temperature of the compressor according to the limits of the operating envelope. As a result, the performance of the system and size ratios of the components are obtained. These results along with the operating conditions of the refrigeration process, such as operating hours or the average cost of electricity, are used to estimate the total investment cost of the cycle and then, the NPV value. It should be noted that greater gas cooler pressures require a greater electric consumption in the compressor, which reduces the value of the COP. However, the efficiency of the ejector increases with such pressure, lifting the suction pressure of the compressor and reducing its pressure ratio. In other words, as the pressure in the gas cooler increases, the ejector efficiency also increases, but the theoretical cycle efficiency decreases. So, a thermoeconomic optimization using the NPV is required to achieve the most cost-effective solution. 37 Análisis termoeconómico de un ciclo compacto de CO2 con eyector Fig. 3-6. Flowchart of the thermoeconomic optimization procedure. = Thermodynamic inputs , , , , , Iterate variable , Solving thermodynamic cycle , , , , , Solving the ejector model , , , Thermoeconomic assessment ,, , , , , No Yes End Economic inputs , , , Set initial value Yes No Restriction Yes No System modeling 38 4 RESULTS AND DISCUSSION This document aims to analyze the possibilities of using the CO2 EERC for low-temperature refrigeration in warm climates. The extreme pressure ratio to be supported by the compressor in this application represent a technical challenge for commercial compressors. However, as it was previously mentioned, the combination of the EERC with a double-stage compressor could enable that possibility. Thus, the first analysis is conducted based on the operating envelope of the cycle. Fig. 4-1.a shows the original operating envelope of the commercial compressor with the reference cycle and the new limits achieved using the EERC. First, the minimum evaporating temperature reached is -38.5 ºC, which corresponds to a temperature inside the ejector close to the triple point. Thus, this temperature must be considered as the minimum possible using the EERC for lowtemperature refrigeration. Using the EERC, the actual suction pressure does not correspond to the evaporating pressure, but the pressure leaving the ejector. Therefore, the overall operating envelope of the cycle can be expanded maintaining the pressure ratio and discharge pressure within the operating envelope of the compressor. Thus, maintaining evaporating temperatures above -38.5 ºC, discharge pressures up to 110 bar are allowed, which represent a 16.4% of improvement. Fig. 4-1.b represents the second compressor with its original envelope, that restrings the evaporating temperature to -40 ºC. Once again, this operating map is limited by the pressure ratio, as well as suction and discharge pressure and temperatures. Through the EERC the operating envelope can be extended, increasing the discharge pressure up to 29.5% for the evaporating temperature of -38.5 ºC. This improvement means that this compressor also could be used in warm climates, offering new possibilities of application. The most favorable compressor envelope for the use of the EERC is those whose minimum evaporating temperature is greater than -38.5 ºC. In those cases, the EERC enables reducing the evaporating temperature while allows higher dissipation temperatures. This scenario corresponds to the third compressor, which is illustrated in Fig. 4-1.c. Notice that, despite the evaporating temperature of the original compressor is limited to -30 ºC and the discharge pressure corresponds to subcritical conditions, the same compressor could be used in the EERC achieving evaporating temperatures of -38.5 ºC and operating in warm climates with transcritical conditions. a) 0 20 40 60 80 100 120 140 -60 -50 -40 -30 -20 -10 0 Pgc Te (ºC) DORIN (CD_2S) DORIN EERC Critical pressure Triple line Results and discussion 40 40 b) c) Fig. 4-1. EERC modified envelope: (a) DORIN; (b) GEA; (c) FRASCOLD. Once the capacity of the EERC to extend the operating limits of commercial compressors for lowtemperature refrigeration in warm climates is confirmed, a thermodynamic analysis of the system performance is conducted. Some assumptions are considered in the analysis, such as evaporating temperatures ranging from -10 ºC to -38.5 ºC, that were revealed the minimum values to avoid the triple point inside the ejector. Moreover, the outlet temperature of the gas cooler was set to 35 ºC, as average value of typical conditions in warm climates. Fig. 4-2.a shows a COP comparison between the EERC and the RC. To assess the influence on the performance, simulations with and without IHX have been conducted. As expected, the COP decreases as the evaporating temperature is reduced. However, a significant improvement can be achieved by the EERC, reaching a COP improvement of 34% without IHX compared to the RC. If the IHX is considered, the COP improvement concerning the RC is 22.7%, reaching a value of COP of 1.2 even in the most unfavorable conditions. Taking into account that these simulations keep constant the refrigeration capacity, it can be deduced that an electrical consumption reduction is obtained by using the EERC. This fact is appreciable in 0 20 40 60 80 100 120 140 160 -50 -40 -30 -20 -10 0 10 20 Pgc Te (ºC) GEA (Bock HG) GEA EERC Critical pressure 0 20 40 60 80 100 120 140 160 180 -50 -40 -30 -20 -10 0 10 20 30 Pgc Te (ºC) FRASCOLD (D) FRASCOLD EERC Critical pressure 41 Análisis termoeconómico de un ciclo compacto de CO2 con eyector Fig. 4-2.b, which represents the specific power absorbed by the compressor in function of the evaporating temperature. The decrease in power consumption is coherent to a pressure ratio reduction. Focusing on the lowest evaporating temperature, a power reduction of 34% is obtained adopting of the EERC, and 22.7% if the IHX is used. This significant improvement suggests that the cost of the compressor used in the EERC will be lower compared to the one used in the RC. Concerning the gas cooler capacity, Fig. 4-2.c illustrates a normalized comparison of thermal power. 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