Solar energy-assisted CCHP cycles for dairy applications in rural sector with effect assessment of reheating on novel CO₂ working fluid

Abstract

This study investigates two configurations of novel solar energy-assisted combined cooling, heating and power (CCHP) systems suitable for the dairy industry. The system uses carbon dioxide (CO₂) as the working fluid. The cooling and heating outputs were used for the simultaneous chilling and pasteurization of milk. The electrical power produced in the turbine is used to run the compressor and cater to the miscellaneous electrical demands of the dairy farm, thereby achieving grid independence. A detailed thermodynamic analysis was performed on the two configurations (with and without reheating) to identify the impact of various independent parameters on system performance. In addition, an irreversibility analysis was performed on the components in both configurations to obtain an idea of the losses occurring in the system. It is observed that the addition of the reheater provides a better specific net power output by approximately 4% over a variation of 6000 kPa in the cycle maximum pressure.

Keywords:

• CCHP
• carbon dioxide
• rural
• reheat
• dairy
• trigeneration
• solar

REVIEWING EDITOR:

• Pham D. T., University of Birmingham, UK

SUBJECTS:

• Power & Energy
• Technology
• Clean Tech

1. Introduction

The simultaneous creation of cooling, heating and electrical power from a single source of energy (preferably renewable energy) is known as combined cooling, heating and power (CCHP), or trigeneration. Over the years, several CCHP methods that utilize a range of fuels have been developed for various applications (Cho et al., 2014; Al Moussawi et al., 2016). CCHP systems are particularly appealing in applications like dairy, building, cement plant, paper mill and pharmaceuticals that require uninterrupted cooling, heating and electrical power (grid-free) outputs. CCHP systems are used in rural dairy facilities that demand all three outputs simultaneously without any grid dependence. The dairy industries are characterized by a high demand for electricity, and energy for heating and cooling, necessary for obtaining a finished quality product. Pasteurization and chilling are two crucial components of milk processing in dairy facilities. Pasteurization is used to render milk for human consumption. Pasteurization is the process of heating milk to either 63 °C for 30 min or 72 °C for 15 s in a controlled atmosphere. This step is followed by rapid cooling of the milk to low temperatures, which inhibits the growth of dangerous microorganisms in milk (Milk Facts, 2015). Milk collection is scattered across nations such as India, while processing is carried out centrally. Increasing the energy efficiency of milk processing is important in countries such as India, where cattle herds are widely dispersed in different parts. Further, the current stress status of national electrical networks in view of increased electricity demand would be prudent to go for renewable energy sources for rural-based sectors, such as dairy facilities. Solar energy and biomass are the major renewable energy sources in rural areas. Given that solar energy is a fluctuating source in nature, any shortfall can be compensated for by biomass.

This study examines a unique CCHP system aided by solar energy that is ideal for a dairy farm with CO₂ as the process fluid. Carbon dioxide (CO₂) as working fluid offers high power density when used in power plants. It is non-toxic, non-flammable and inexpensive, abundantly available in nature and is environment-friendly. CO₂ has a low critical temperature (t_cric) of 31.1 °C (304.25 K) and critical pressure (P_cric) of 7.38 MPa. Hence, it is easy to realize it in supercritical state and thereby achieve higher cycle efficiency. However, working with supercritical CO₂ (s-CO₂) poses certain technical challenges, such as high pressure safety and lack of sufficient experience with s-CO₂ cycles. In addition, s-CO₂ can also be used as heat transfer fluid (HTF) in solar thermal systems, thereby providing the opportunity of direct integration of the solar subsystem with the transcritical cycle. Recently, CO₂ has been studied as a process fluid for both power and refrigeration cycles (Dostal et al., 2004). COP for CO₂-based cycles was less than that for conventional refrigerant-based subcritical cycles. This was ascribed to the large temperature glide over which heat rejection occurred in the CO₂ cycles. However, studies have shown that they are highly beneficial when both the cooling and heating outputs are utilized effectively. According to previous research, the use of CO₂ in Brayton cycles can result in very compact power systems. In view of this, it is believed that the proposed CCHP system, which works on a combination of a transcritical refrigeration cycle and Brayton power cycle, will be used in rural-based dairy operations. The impact of modifying the suggested cycle on the overall performance of the system was evaluated in this study. Some current studies in the field of CCHP systems are discussed below.

Studies on CO₂-based systems with different configurations and for various applications are available in the literature (Chen & Lundqvist, 2006; Wang et al., 2009). The early studies were limited to thermodynamic aspect (Palmero-Marrero & Oliveira, 2011; Al-Sulaiman et al., 2011) and performance study under different operating conditions (Xu et al., 2010; Huicochea et al., 2011). Wang et al. (2012) demonstrated the steady-state thermodynamic performance of a CCHP system with transcritical CO₂ powered by solar energy. The general design was a hybrid of Brayton and Ejector refrigeration cycles. The same authors presented details of the solar aspect of the system in (Wang et al., 2009). Jradi and Riffat (2014) reviewed CCHP systems. Support mechanisms, prime movers, cooling technologies, system configurations, fuels and renewable energy supplies have all undergone advancements. It was discovered that the operating strategy has a significant impact on the performance of the CCHP systems.

The role of climate conditions on CCHP systems has also been analysed by the authors using different configurations (Boyaghchi & Heidarnejad, 2015; Zhai et al., 2009). Tora and El-Halwagi (2011) created a systematic process for the integrated design of a CCHP system with a steam turbine in the power loop and an absorption refrigeration cycle for the cooling and heating loops that incorporates solar energy as a renewable energy source with minimal greenhouse gas (GHG) emissions.

A thorough examination of the transcritical CO₂ heat pump was presented by Sarkar et al. (2004), Yefeng et al. (2014) and Kasaeian et al. (2020) presented an overview of various solar-based polygeneration systems consisting of devices, such as gas turbines, ORC, absorption heat pumps, electrolysers and distillation units. These technologies are sustainable and viable options for meeting future energy needs. Vutukuru et al. (2019) investigated an ejector-based solar-aided CCHP system for daily use. The impact of different operational parameters on the COP, specific net power production (F1) and specific milk flow rate (F2) were demonstrated. When comparing the ejector and work recovery expander configurations, the work recovery expander configuration exhibited a higher COP. Ravindra and Ramgopal (2018, 2019) investigated the energy efficiency of innovative solar CCHP designs for dairy applications. In Ravindra and Ramgopal (2019), an expansion turbine and a throttle valve in the refrigeration loop were compared. It was discovered that using an expansion turbine instead of a throttle valve enhanced the performance under all conditions. The expansion turbine was replaced by an ejector (Ravindra and Ramgopal, 2019). Under similar milk-handling capacity conditions, an ejector-based system resulted in a lower requirement of compressor power and a much higher net electrical power production than a throttle valve-based system. Zarei et al. (2022), analysed a polygeneration arrangement that combines photovoltaic thermal (PVT) and flat plate collector (FPC). A detailed thermodynamic and economic analysis was conducted for a newly designed cooling, heating and power (CCHP) system powered by solar energy for domestic applications. Saini et al. (2020a, 2020b) proposed novel solar-driven CCHP systems and studied the effect of operating parameters on energy-exergy performances. The systems consisted of evacuated tube collector, ORC and ejector cycle. Mohsenipour et al. (2020) presented thermodynamic and economic analyses of a solar-based CCHP system designed for a greenhouse for lettuce and tomato cultivation. It is observed that for tomato cultivation more fuel is saved and for lettuce cultivation, more water is stored by using the CCHP system. Alirahmi et al. (2020) proposed a novel integrated system based on geothermal and solar energies. Energy, exergy and exergo-economic analyses were carried out on the system. Engineering equation solver (EES) and MATLAB software were used for the analysis. Dabwan and Pei (2020) presented thermodynamic, economic and environmental analyses of a novel integrated solar gas turbine CCHP system for production of power, heat and cooling. It is observed that proper locations to utilize the solar hybrid power plants are the places with high levels of solar irradiance and low ambient temperature.

Mohammadi and Powell (2020) proposed and analysed novel integrated cogeneration and trigeneration configurations based on CO₂ vapour compression systems. The systems were analysed for a 1000 kW capacity and evaporator temperatures of −35 °C to −45 °C. Dabwan et al. (2020) presented the thermodynamic, economic and environmental analyses of a trigeneration system (TGS) integrated with linear Fresnel reflector (LFR). The study revealed that the integration of LFR technology with a conventional TGS in high insolation regions has more economic feasibility compared to equivalent TGS integrated with CO₂ capturing technology, while achieving the same emissions reduction result. Wu et al. (2020) proposed a biomass gasification CCHP system with solar energy. Solar energy and biomass are efficiently utilised in a cascaded manner. Thermodynamic performances under design and off-design conditions along with economic performances are evaluated. Kasaeian et al. (2020) presented an overview on various solar-based polygeneration systems consisting of devices like gas turbine, ORC, absorption heat pump, electrolyser and distillation unit. These technologies are sustainable and viable options for future energy needs. Li et al. (2020) presented a comprehensive evaluation of low-grade solar TGS using PVT collectors. They identified the limiting factors for optimum system design. Tsimpoukis et al. (2021) presented a detailed energy and economic analysis of a novel supercritical CO₂-based solar-biomass TGS for operation in the climate of Athens. The TGS utilized solar energy in parabolic trough collectors and biomass energy as the supplementary source, in order to increase the temperature of high-pressure CO₂ and produce power in the turbine which is coupled to a generator. Bellos and Tzivanidis (2021) performed a dynamic investigation on solar-fed TGS. The configuration is investigated on dynamic basis by using TRNSYS software. Cao, Dhahad, Sharma, ABo-Khalil, et al. (2022) and Cao, Dhahad, Sharma, Anqi, et al. (2022) performed detailed thermodynamic and economic studies on novel CCHP configurations. According to Cao, Dhahad, Sharma, ABo-Khalil, et al. (2022) and Cao, Dhahad, Sharma, Anqi, et al. (2022), a comparative study is made with two different working fluids, i.e. CO₂ and Nitrous oxide. According to Cao, Dhahad, Sharma, ABo-Khalil, et al. (2022) and Cao, Dhahad, Sharma, Anqi, et al. (2022), a 3E analysis (energy, exergy and economic) of a polygeneration setup is performed. Khalid and Kumar (2022) developed and assessed a solar-based TGS using hydrogen for vehicular application in self-sustained community. The TGS fulfilled the electricity, cooling and hydrogen requirements for the community. Akram et al. (2023) presented a parametric analysis based on energy and exergy studies for a solar-assisted TGS where solar power tower assembly is employed. García-Domínguez et al. (2023) analysed a solar driven ORC-absorption-based CCHP system with a novel exergy approach. As the solar field outlet temperature increases, both the energy and exergy efficiency of the CCHP system increase. In the analysed range, the net power produced in the ORC can be doubled. Alshuraiaan (2023) investigated the operation of the solar TGS, which uses collectors with Nano fluids based on water. Comparative analysis showed that the addition of nanoparticles leads to a decrease in the heat capacity of the circulating liquid. Parvez et al. (2023), made an assessment of solar-assisted CCHP system using energy, exergy and CO₂ mitigation approach. The effect of very influencing parameters like direct normal irradiance (DNI), extraction pressure, turbine back pressure, turbine inlet pressure and pump inlet temperature were ascertained on energy and exergy efficiencies for the TGS. Almatrafi et al. (2023) presented a new tower solar collector-based TGS. the system performance is analysed using varying parameters of solar irradiation, hot oil temperature, process heat pressure and ambient temperature to investigate the influence on electrical power, cooling capacity, refrigeration exergy, energy utilization factor (EUF) and system exergy efficiency. Increasing direct normal irradiation (DNI) from 500 to 1000 W/m² reduces the system EUF and exergy efficiency from 53.62% to 43.12% and from 49.02% to 25.65%, respectively.

From the above studies, it can be understood that worldwide there is an upsurge in research on CCHP systems assisted with renewable energy sources. However, studies on direct integration of solar subsystem into the CCHP system with a single working fluid are limited. This study investigates a CCHP system for the dairy industry that combines a Brayton power cycle with a transcritical CO₂ refrigeration cycle. The cycle is powered by concentrating solar collectors using CO₂ as HTF (Vutukuru et al., 2019) and directly integrated into the system, and the fundamental cycle is identical to that examined by Vutukuru et al. (2019), however, the ejector is replaced by a throttle valve expander. In addition, studies on the effects of reheating in CO₂ systems for dairy applications are limited. This article presents a study of the impact of reheating in CO₂-based CCHP systems for dairy applications in rural areas. Two cycle configurations were considered for the study: (1) a solar-assisted CCHP cycle with a throttle valve, and (2) a solar-assisted CCHP cycle with a throttle valve and reheater. The performances of these configurations are compared, and the impacts of major operating factors on the cycle performance are investigated to determine the bounds within which the proposed CCHP system can function efficiently.

2. Cycle configurations

The schematic and T-s diagrams of various solar-assisted CCHP systems are shown in Figures 1 and 2, respectively. Compression, isobaric heat supply, expansion, isobaric heat rejection, throttling and isobaric/isothermal heat addition were the six processes involved in both setups. After absorbing heat from the milk in the evaporator, CO₂ vapour is compressed to supercritical pressure by a compressor. Subsequently, the supercritical CO₂ is heated isobarically, first in the recovery heat exchanger (RHX) and then in a gas heater. A solar subsystem consisting of a parabolic solar collector (PTC) and an auxiliary heater (if the collector is unable to produce an appropriate quantity of heat) heats the CO₂ in the gas heater. For power generation, heated high-pressure CO₂ was expanded in the turbine. It is then cooled by a RHX, process heat exchanger (PHX) and ambient heat rejection device, which rejects low-temperature waste heat. Finally, it passes through a throttling valve before entering the evaporator, which chills milk. Milk enters the milk heat exchanger at 4°C and is heated first in the milk heat exchanger, then to 73 °C in the PHX, and finally chilled to the needed 4 °C in the evaporator. Hot-pasteurized milk from PHX transfers heat with cold incoming milk in the milk heat exchanger. The system operating parameters are chosen such that there is a net generation of electrical power that can meet some or all of the dairy plant’s auxiliary electrical demands.

Figure 1. (a) Schematic and (b) T-s diagram of C1 configuration.

Figure 2. (a) Schematic and (b) T-s diagram of C2 configuration.

The overall system performance can be improved by modifying the fundamental cycle outlined above. Multi-stage expansion with reheating is the second configuration in this study. The waste heat coming from the turbine is at a considerable high temperature and pressure which can generate additional electrical power through a reheat arrangement. The presence of additional electrical power can result in a better COP. However, the additional components will result in higher exergy losses for the system. These aspects are analysed thermodynamically in this paper. Table 1 lists the symbols used to indicate the studied cycle configurations.

Table 1. List of configurations analysed and their symbols used in plots.

Configuration	Symbol
Solar-assisted CCHP cycle with Throttle valve	C1
Solar-assisted CCHP cycle with Reheater & Throttle valve	C2

3. Thermodynamic analysis

While writing the mass balance and energy balance equations for various system components, the following simplification assumptions were made:

1. The system is assumed to operate under steady-state conditions.

2. The frictional pressure drops and heat losses across all components were minimal.

3. Turbines are considered to have fixed isentropic efficiency

4. The refrigerant should exit the evaporator as saturated vapour.

5. The refrigerant compressed in the compressor is believed to be adiabatic but irreversible.

6. The temperature of the refrigerant after the reheater (C2 configuration) is identical to the temperature at the input of the high-pressure turbine.

7. The ambient temperature is assumed to be the exit temperature of the fluid at the ambient heat rejection unit.

8. Changes in the kinetic and potential energy across refrigerant and milk are minimal across all components.

9. It is also expected that raw milk enters the dairy plant at 4 °C and exits the dairy plant at 4 °C after pasteurization and cooling. Consequently, milk has no net energy gain or loss.

10. Results are based on a constant refrigerant flow rate of 1 kg/s.

11. The results reported here assume that the heat exchange in the evaporator (from milk to CO₂) for milk chilling is identical to the heat exchange in the PHX (from CO₂ to milk) for milk pasteurization. Furthermore, to make the cycle self-sufficient (i.e. without requiring external electrical power), the restriction of having a constant positive net-work output is enforced.

Based on the above assumptions, steady-state and steady flow energy equations were written for each component. Because the compressor is assumed to be adiabatic but irreversible, its performance is designated by isentropic efficiency and is calculated using the empirical correlation developed by Robinson and Groll (1998) for supercritical CO₂: (1) $${\eta }_c=0.815+0.022\left(\frac{P_{\mathit{\text{high}}}}{P_{\mathit{\text{low}}}}\right)-0.0041{\left(\frac{P_{\mathit{\text{high}}}}{P_{\mathit{\text{low}}}}\right)}^2+0.0001{\left(\frac{P_{\mathit{\text{high}}}}{P_{\mathit{\text{low}}}}\right)}^3$$(1)

The performance of the RHX is designated in terms of the heat exchanger effectiveness, and considering the large variation in the specific heat of CO₂, the effectiveness of the RHX is defined as (2) $${\epsilon }_{\mathit{\text{rhx}}}=\frac{Q_{\mathit{\text{rhx}},\mathit{\text{act}}}}{Q_{\mathit{\text{rhx}},\mathrm{\text{max}}}}$$(2) where the maximum possible heat transfer rate in the RHX is given by: (3) $$Q_{\mathit{\text{rh}},\mathrm{\text{max}}}=\mathrm{\text{min}}\left(Q_{\mathit{\text{rhx}}\mathrm{\text{max}},c},Q_{\mathit{\text{rhx}}\mathrm{\text{max}},h}\right)$$(3) where Q_rhxmax,c and Q_rhxmax,h are the maximum possible heat transfer rates in the RHX with the cold fluid reaching the minimum possible temperature and the hot fluid reaching the maximum possible temperature, respectively.

For the multi-stage expansion cycle (Figure 2), the reheater pressure is taken as the geometric mean of the turbine inlet pressure and gas cooler pressure (Sarkar and Bhattacharyya, 2009).

The overall COP of the CCHP system is defined as: (4) $$\mathrm{\text{COP}}=\frac{W_{\mathrm{\text{net}}}+Q_{\mathrm{\text{gc}}1}+Q_{\mathrm{\text{evap}}}}{Q_{\mathrm{\text{solar}}}}$$(4) where the net power output W_net from the system is given by: (5) $$W_{\mathrm{\text{net}}}=W_{\mathrm{\text{turbine}}}-W_{\text{compressor}}$$(5) where Q_gc1 is the heat transferred during milk pasteurization from CO₂ in the PHX. Q_evap is the refrigeration effect produced in the evaporator and Q_solar is the solar heat input.

3.1. Performance parameters relevant for dairy farm

As the system is applied to a dairy plant, a few additional performance parameters are defined.

The specific net power output (F1) is defined as the ratio of the net electrical power output to the solar heat input (Vutukuru et al., 2019). This performance parameter is related to the net electrical power obtained after the compressor input power is taken, and provides an insight into the electrical energy part of the CCHP system to meet the power demand of the dairy plant. (6) $$\mathrm{F}1\text{=}\frac{W_{\text{net}}}{Q_{\text{solar}}}$$(6)

The specific milk flow rate (F2) is the ratio of the rate of milk processed to the solar heat input (Vutukuru et al., 2019). The performance parameter was obtained solely from the effects related to milk processing. (7) $$\mathrm{F}2\text{=}{\mathrm{m}}_{\text{mw}}=\frac{m_{\text{milk}}}{Q_{\text{solar}}}$$(7)

3.2. Exergy loss analysis

In reality, a system contains several irreversible processes. Exergy loss is a key factor in determining the thermodynamic performance of a system. The exergy loss was computed by balancing the exergy of each component in the system. The ratio of the partial exergy loss to the total exergy loss was used to compute the proportion of exergy loss for each component.

For both CCHP configurations (i.e. with and without reheating), the exergy loss computation equations for all components are as follows:

Exergy loss in compressor (8) $$I_{\mathrm{\text{comp}}}=T_0\left(S_{\mathrm{\text{comp}},\mathrm{\text{out}}}-S_{\mathrm{\text{comp}},\mathrm{\text{in}}}\right)$$(8)

Exergy loss in RHX (9). $$I_{\mathit{\text{rhx}}}=T_0\left[\left(S_{\mathrm{\text{hot}},\mathrm{\text{out}}}+S_{\mathrm{\text{cold}},\mathrm{\text{out}}}\right)-\left(S_{\mathrm{\text{hot}},\mathrm{\text{in}}}+S_{\mathrm{\text{cold}},\mathrm{\text{in}}}\right)\right]$$(9).

Exergy loss in Turbine (10) $$I_{\mathrm{\text{turb}}}=T_0\left(S_{\mathrm{\text{turb}},\mathrm{\text{out}}}-S_{\mathrm{\text{turb}},\mathrm{\text{in}}}\right)$$(10)

Exergy loss in (PHX (11) $$I_{\mathrm{\text{gc}}1}=\left[Q_{\mathrm{\text{gc}}1}\left(\frac{T_0}{T_{\mathrm{\text{gc}}1}}\right)\right]-\left[T_0\left(S_{\mathrm{\text{gc}}1,\mathrm{\text{in}}}-S_{\mathrm{\text{gc}}1,\mathrm{\text{out}}}\right)\right]$$(11)

Exergy loss in Ambient heat rejection unit (12) $$I_{\mathrm{\text{gc}}2}=\left(h_{\mathrm{\text{gc}}2,\mathrm{\text{in}}}-h_{\mathrm{\text{gc}}2,\mathrm{\text{out}}}\right)-\left(T_0\left(S_{\mathrm{\text{gc}}2,\mathrm{\text{in}}}-S_{\mathrm{\text{gc}}2,\mathrm{\text{out}}}\right)\right)$$(12)

Exergy loss in the throttle valve (13) $$I_{\mathrm{\text{tv}}}=T_0\left(S_{\mathrm{\text{gc}}2,\mathrm{\text{out}}}-S_{\mathrm{\text{evap}},\mathrm{\text{in}}}\right)$$(13)

Exergy loss in Evaporator (14) $$I_{\mathrm{\text{evap}}}=\left[T_0\left(S_{\mathrm{\text{evap}},\mathrm{\text{out}}}-S_{\mathrm{\text{evap}},\mathrm{\text{in}}}\right)\right]-\left[Q_{\mathrm{\text{evap}}}\left(\frac{T_0}{T_{\mathrm{\text{evap}}}}\right)\right]$$(14)

The exergy loss of the PTC, which also acts as a reheater for C2 configuration is estimated as follows: The overall exergy loss in the PTC is the sum of the exergetic optical and thermal losses.

The exergetic optical losses (I_loss,opt) are calculated as: (15) $$I_{\mathrm{\text{loss}},\mathrm{\text{opt}}}=\left(1-{\eta }_{\mathit{\text{opt}}}\right)E_s$$(15) where Es denotes the undiluted solar radiation exergy flow. It was determined using the Patela model, which considers the sun to be a radiation reservoir of temperature (T_sun), with an estimated value of 5770 K in the outer layers. (16) $$E_s=Q_s\left[1-\frac{4}{3}\left(\frac{T_{\mathit{\text{am}}}}{T_{\mathit{\text{sun}}}}\right)+\frac{1}{3}{\left(\frac{T_{\mathit{\text{am}}}}{T_{\mathit{\text{sun}}}}\right)}^4\right]$$(16) where Q_s is the solar energy available at the aperture of the collector. It is calculated as the product of the collector aperture (A_a) and the direct beam solar irradiation (G_b) (Vutukuru and Ramgopal, 2021). (17) $$Q_s=A_a.G_b$$(17)

The optical efficiency (η_opt) is the product of the concentrator reflectance (ρ), intercept factor (γ), cover transmittance (τ), absorber absorbance (α), and incident angle modifier (K). (18) $${\eta }_{\mathrm{\text{opt}}}=\rho .\gamma .\tau .\alpha .K\left(\theta \right)$$(18)

The exergetic thermal losses (I_loss,th) are calculated as: (19) $$I_{\mathrm{\text{loss}},\mathrm{\text{th}}}=Q_{\mathrm{\text{loss}}}\left(1-\frac{T_{\mathrm{a}m}}{T_r}\right)$$(19) where Q_loss is the thermal loss of the solar collector, expressed as the sum of radiation and convection losses. (20) $$Q_{\mathrm{\text{loss}}}=A_{\mathit{\text{co}}}.h_{\mathrm{\text{air}}}.\left(T_c-T_{\mathit{\text{am}}}\right)+A_{\mathit{\text{co}}}.\sigma .{\epsilon }_c.\left({T_c}^4-{T_{\mathrm{\text{sky}}}}^4\right)$$(20) where A_co is the outer cover area, and h_air is the coefficient of heat transfer between the cover and ambient air.

The cover temperature (T_c) was assumed to be close to the ambient temperature (T_am) because of the existence of an evacuated-tube collector. (21) $$T_c=T_{\mathrm{a}m}+\Delta T$$(21)

The receiver temperature (T_r) is assumed close to the fluid temperature. (22) $$T_r=\frac{T_{\mathrm{\text{in}}}+T_{\mathrm{\text{out}}}}{2}$$(22)

The sky temperature (T_sky) is estimated by using the following equation (23) $$T_{\mathrm{\text{sky}}}=0.0553{T_{\mathrm{\text{am}}}}^{1.5}$$(23)

The total exergetic loss in the parabolic trough collector is expressed as: (24) $${\mathrm{I}}_{\text{loss}}={\mathrm{I}}_{\text{loss},\text{opt}}+{\mathrm{I}}_{\text{loss},\text{th}}$$(24)

For C1 configuration, the total exergy loss is (25) $${\mathrm{I}}_{\text{total}}={\mathrm{I}}_{\text{comp}}+{\mathrm{I}}_{\text{rhx}}+{\mathrm{I}}_{\text{turb}1}+{\mathrm{I}}_{\text{gc}1}+{\mathrm{I}}_{\text{gc}2}+{\mathrm{I}}_{\text{tv}}+{\mathrm{I}}_{\text{evap}}+{\mathrm{I}}_{\text{loss}1}$$(25)

For C₂ configuration, the total exergy loss is (26) $${\mathrm{I}}_{\text{total}}={\mathrm{I}}_{\text{comp}}+{\mathrm{I}}_{\text{rhx}}+{\mathrm{I}}_{\text{turb}1}+{\mathrm{I}}_{\text{turb}2}+{\mathrm{I}}_{\text{gc}1}+{\mathrm{I}}_{\text{gc}2}+{\mathrm{I}}_{\text{tv}}+{\mathrm{I}}_{\text{evap}}+{\mathrm{I}}_{\text{loss}1}+{\mathrm{I}}_{\text{loss}2}$$(26)

T_evap and T_gc are the external fluid thermodynamic average temperatures in the evaporator and the PHX, respectively. The thermodynamic average temperature of the external fluid in the evaporator is determined as (27) $$T_{\mathrm{\text{evap}}}=\frac{T_{\mathrm{\text{ext}},\mathrm{\text{in}}}-T_{\mathrm{\text{ext}},\mathrm{\text{out}}}}{\mathrm{\text{ln}}\hspace{0.17em}\left(\frac{T_{\mathrm{\text{ext}},\mathrm{\text{in}}}}{T_{\mathrm{\text{ext}},\mathrm{\text{out}}}}\right)}$$(27) where T_ext,in and T_ext,out denote the external fluid inlet and outlet temperatures, respectively. The external fluid thermodynamic average temperature in the PHX, T_gc, was estimated in the same way as that for the evaporator.

For our study, the LS2 collector was used as a reference, and the module dimensions and optical properties were assumed accordingly, as shown in Table 2.

Table 2. Model dimensions and optical parameters.

Parameter	Values
Aperture area (Aa)	39 m^2
Solar beam radiation (Gb)	900 W/m^2
Optical efficiency (ηopt)	0.754
Outer cover diameter (Dco)	0.115 m
Cover emittance (εc)	0.9
Convection coefficient between cover and ambient (hair)	10 W/m^2K
Concentration ratio (C)	22.74

Table 3. Parameters considered for the study.

Parameters	Values/ranges
Turbine isentropic efficiency	0.85
Recovery heat exchanger effectiveness	0.4
Ambient temperature	35 °C/33–38 °C
Milk Heat exchanger effectiveness	0.85
Turbine inlet temperature	500 °C/500–600 °C
Evaporator temperature	2 °C
Cycle maximum pressure (Phigh)	20 MPa/19–25 MPa
Gas cooler pressure (Pmed)	9 MPa/8–10 MPa

Based on the above equations, cycle calculations for various configurations were estimated using the EES for the following input data.

4. Model validation

As the CCHP system configurations proposed are new, the whole system cannot be validated with existing data from literature. Hence the subsystems are validated using previous literature. For the power cycle and specific net power output (ratio of net electrical power output per rate of solar heat input), the results are validated with previous study by Vutukuru et al. (2019) and the results are shown in Table 4 for same input parameters. As shown, the deviations which occur due to the assumptions taken are very small, which are fairly acceptable.

Table 4. System validation of this study with previous work.

Parameters	Previous study	This study	% Deviation
COP	0.795	0.8	0.63
Specific net power output (F1) (kW/kW)	0.72	0.75	4.1

5. Results and discussion

A commercially available software EES, which provides an in-built mathematical and thermodynamic property functions is used for solving the thermodynamic model described above. Calculations are done for a CO₂ mass flow rate of 1 kg/s. As the inlet temperature of the raw milk and the exit temperature of the processed milk are both taken as 4 °C, the evaporator temperature is chosen as 2 °C with a terminal temperature difference of 2 K for heat transfer (Vutukuru et al., 2019). For simplicity, the exit temperature of ambient heat rejection unit is assumed to be equal to the ambient temperature. Results are obtained for higher ambient temperatures (above critical temperature of CO₂) so that the system always operates in transcritical mode. Higher ambient temperatures are also more relevant for tropical countries such as India. A fixed value of 0.85 is taken for the isentropic efficiency of the turbine (Vutukuru et al., 2019). A default value of 0.4 is used for the effectiveness of RHX (Vutukuru et al., 2019), however, its effect on performance of the system is studied by varying it over a practically useful range. The default values of other operating parameters considered for the system and the ranges over which they are varied is shown in Table 3. Wherever applicable, the basis for choosing input values are provided by citing relevant references from which these values are taken.

5.1. Effect of ambient temperature

Figure 3 shows the impact of the ambient temperature on the COP and specific milk flow rate (F2) for both configurations (C1 and C2 shown in Figures 1 and 2). For this study, the other parameters are kept constant as the values stated in Table 3. A rise in ambient temperature results in a reduction in the COP and F2. Higher ambient temperature decreased the liquid fraction in the evaporator, thereby reducing the cooling output. This reduces the milk-handling capacity, which results in a reduction in F2. Similar trends were observed for both configurations with C1, resulting in a better output compared to C2. From the point of view of dairy industry, the lower ambient temperature condition will result in higher specific milk flow rate. Further, the ambient temperatures considered are very close to the critical temperature of CO₂ (T_cric = 31.1 °C) which can result in significant changes in thermo physical properties of CO₂. The trends clearly show the need for optimizing the gas cooler pressure based on the requirements of power output and milk flow rate. The TGS s offer an interesting possibility of suitably setting the gas cooler pressure based on what is more important, milk flow rate or net power output. Over the specified range of ambient temperature, COP reduces by about 23%. This can be attributed to the significant changes in thermophysical properties of CO₂ near the critical temperature region. Similarly, specific milk flow rate also shows a reduction of about 20%.

Figure 3. COP and F2 variation with ambient temperature.

5.2. Effect of solar heater exit temperature

The influence of the exit temperature of the solar heater on the COP and specific net power output (F1) is shown in Figure 4. For this study, the other parameters are kept constant as the values stated in Table 3. The highest temperature in the cycle corresponds to the solar heater exit temperature which is also the inlet temperature for the turbine. The reheater exit temperature is assumed the same as the maximum cycle temperature in C2 setup. An increase in the turbine power production increases the net electrical power output. However, a considerable rise in the solar heat input diminishes the COP of the cycle. The cooling and heating outputs remained unchanged when the exit temperature of the solar heater increases. The higher temperatures in solar heater are possible with gaseous HTF s where CO₂ is being actively considered as HTF. Over the specified range of temperature, COP shows a 15% reduction for both the configurations.

Figure 4. COP and F1 variation with Solar heater exit temperature.

A trade-off was observed between COP and F1. F1 rises with increasing temperature. The F1 for the C2 configuration was higher than that for the C1 configuration. The specific power output shows significant rise as turbine inlet temperature and pressure increase. Thus whenever the required power output is high, the system has to be operated at higher turbine inlet temperature at the cost of reduced COP.

5.3. Effect of gas cooler pressure

The effects of the gas cooler pressure on the COP, F1 and F2 are shown in Figure 5. Figure 5(a) depicts the COP levels that result in positive net electrical power production. It should be noted that the operating regime of the gas cooler pressure is greater in C2 configuration for the default values of the parameters given in Table 3. For both setups, the rise in the COP is large in the lower pressure ranges. Higher gas cooler pressure will result in lower power production across the turbine. However, the heating output significantly contributes to the rise in COP. The COP for both the configurations result in about 60% increase over the specified range of gas cooler pressure.

Figure 5. (a) COP and (b) F1 and F2 variation with gas cooler pressure.

As shown in Figure 5(b), there is a trade-off between F1 and F2. In both settings, F2 exhibits a linearly decreasing trend. The lower-pressure ranges showed a large rise in F1. This is due to the changes in the thermophysical characteristics of CO₂ near the critical zone. For a particular ambient temperature, increasing the gas cooler pressure results in reduction in power output from the turbine, thereby reducing W_net. As a result, F1 shows a decreasing trend. From a dairy perspective, a higher gas cooler pressure results in more milk processing capacity. Hence F2 shoes an increasing trend. Based on the requirement, gas cooler pressure has to be finalized for a particular milk handling capacity.

5.4. Effect of cycle maximum pressure

Figure 6 shows the influence of the maximum cycle pressure on the overall COP and F1. The COP varies slightly as the cycle maximum pressure improves. A higher cycle maximum pressure leads to a higher turbine power output and as a result, a better value of F1. This is due to an increase in the enthalpy difference across the turbine. Similarly, with a rise in cycle maximum pressure, the solar power input increases. In C2 configuration, the specific net power output is greater. It may be noted that operation at turbine pressures less than the given range yield turbine power output that is lower than the compressor power input, violating the constraint of net positive power output from the system. Operating at higher turbine inlet pressures are constrained by the material and safety considerations.

Figure 6. COP and F1 variation with cycle maximum pressure.

5.5. Effect of heat exchanger effectiveness

The effects of Milk HX and RHX on the milk flow rate and specific net power generation are shown in Figure 7. Effectiveness can be modified by keeping the other parameters constant. As shown in Figure 7(a), the effectiveness of the Milk HX has a substantial effect on the particular milk flow rate for both configurations (C1 and C2). Higher Milk HX effectiveness minimizes the temperature rise across the PHX for pasteurization, resulting in a larger mass flow rate of milk that can be processed for a given CO₂ flow rate. Because changes in Milk HX effectiveness have no influence on solar heat input, the milk flow rate rises dramatically for higher levels of Milk HX effectiveness.

Figure 7. (a) Effect of Milk HX effectiveness on F2. (b) Effect of recovery HX effectiveness on F1 and F2.

The effect of RHX efficacy on milk flow rate and F1 is shown in Figure 7(b). Higher RHX effectiveness lowers the amount of solar input required, thereby increasing the milk flow rate. A higher RHX efficacy results in greater heat transfer across the RHX, which results in a higher temperature at the collector intake. The solar heat input required for a fixed cycle maximum temperature decreases as the RHX efficiency rises. A reduced solar heat intake results in a higher value of F1. The rise in specific net power output and specific milk flow rate is predominant in C2 configuration. F1 shows an 85% rise over the range of cycle maximum pressure in C2 configuration which is primarily to the presence of second turbine. A higher RHX effectiveness leads to a higher COP for both configurations.

5.6. Effect of gas cooler pressure on total exergy loss

Figure 8 shows the impact of the gas cooler pressure (P_med) on the total exergy loss in both the setups. The exergy loss across PHX and ambient heat rejection units are the key contributors. The distinct pattern between 8000 and 8500 kPa is due to a large change in exergy loss throughout the evaporator, PHX and ambient heat rejection unit. This is due to the variation in the thermophysical properties of s-CO₂ near the critical region. The exergy loss across the compressor remains unchanged with variation in gas cooler pressure. For the present analysis, total exergy loss decreases by about 3% between 8000 and 8500 kPa for both the configurations and shows a marginal rise linearly. From a dairy point of view, the exergy loss across the evaporator and PHX where cooling and heating processes respectively are occurring need to be reduced for effective milk processing. This can be achieved by regular maintenance and cleaning schedules to prevent fouling of heat exchanger surfaces.

Figure 8. Effect of gas cooler exit pressure on total exergy loss for both the configurations.

5.7. Effect of cycle maximum pressure on total exergy loss

Figure 9 illustrates the influence of the maximum cycle pressure on the total exergy loss for both the systems. The overall exergy loss for both setups changes marginally with increasing cycle maximum pressures. The exergy loss throughout the PHX and ambient heat rejection unit contributes significantly, and a reduction in exergy loss is observed across the RHX. For the given set of operating parameters, the total exergy loss in C2 configuration was more than in C1 configuration. The exergy loss across the solar collector can be reduced by choosing suitable absorber tube material before construction. From the graph it is observed that total exergy loss for C1 configuration shows a reduction of around 3% over the entire range of cycle maximum pressure.

Figure 9. Effect of cycle maximum pressure on total exergy loss for both the configurations.

5.8. Effect of ambient temperature on total exergy loss

Figure 10 depicts the effect of ambient temperature on the total exergy loss for both designs. It should be noted that the ambient heat rejection unit exit temperature is assumed to be the ambient temperature. The total exergy loss for both setups changes marginally over the range of ambient temperatures considered. For C1 configuration, the total exergy loss shows a rise of 2.2% over the specified range. With increasing ambient temperature, the exergy loss in the ambient heat rejection unit increases. It is to be noted that the ambient temperatures considered are near the critical temperature region. The exergy loss across the PHX component decreases as the ambient temperature rises. The overall exergy loss for C2 configuration was greater than C1 configuration for a given ambient temperature.

Figure 10. Effect of ambient temperature on total exergy loss for both the configurations.

5.9. Effect of solar heater exit temperature on total exergy loss

For both designs, the total exergy loss rises linearly as the outlet temperature of the solar heater increases. The PHX, RHX and ambient heat rejection unit exhibit significant changes in exergy loss. The exergy losses can be reduced by regular cleaning and maintenance to prevent fouling in heat exchanger which will improve efficiency. Over the entire range of the solar heater exit temperature, the total exergy loss in the C2 design was 16–19% more than that in the C1 configuration.

According to Figures 8–11, reheating (C2 configuration) merely increases the overall exergy loss; therefore, the inclusion of a turbine and PTC provides no additional benefit. However, from Figures 3–7, C2 outperforms C1 in terms of the COP and specific net power output (F1). Table 5 lists the individual exergy loss % for each component in both configurations with the default values mentioned in Table 3. The exergy loss percentage was computed by dividing the overall exergy loss by the ratio of the individual exergy loss throughout the component. The exergy loss for the turbine in C2 configuration is the sum of the values of both turbines. Similarly, the solar exergy loss is the total exergy loss in the PTC and the reheater (in our example, the PTC).

Figure 11. Effect of solar heater exit temperature on total exergy loss for both the configurations.

Table 5. Exergy loss comparative analysis for individual components in both configurations.

Configuration	Compressor	RHX	Solar collector	Turbine	PHX	Ambient heat rejection unit	Expansion valve	Evaporator
C1	7.59%	14.82%	5.59%	5.03%	27.6%	28.45%	8.87%	2.06%
C2	6.38%	15.81%	9.40%	4.01%	25.27%	29.87%	7.45%	1.73%

Significant exergy loss was detected across the PHX, ambient heat rejection unit, and RHX in both setups. This can be attributed to the working conditions of these components, where the operating pressure is close to the critical pressure, resulting in considerable changes in the thermophysical characteristics. From a dairy industry point of view, it is essential to identify the primary requirement i.e. more milk processing capacity or more electrical power for running the parasitic loads in dairy farm before finalising the suitable configuration.

6. Conclusions

In this article, a thermodynamic performance of a novel solar assisted TGS suitable for dairy plants is presented. A numerical model is used to predict the performance of the system. The proposed system may be viewed as a combination of a CO₂ based Brayton cycle with a transcritical CO₂ refrigeration cycle. The effects of the ambient temperature, solar heater exit temperature, gas cooler pressure, and cycle maximum pressure are analysed for both configurations (i.e. with and without reheating). In addition, the irreversibility rates associated with each component for both the configurations are calculated.

From the above study, the major conclusions drawn are:

1. The ambient temperature, gas cooler pressure and cycle maximum pressure have a significant effect on the overall performance of the CCHP system. The COP for both the configurations result in about 60% increase over the specified range of gas cooler pressure.

2. Higher Milk HX effectiveness significantly raises the specific milk flow rate (F2) for both the configurations. Under the specified input parameters varying milk HX effectiveness from 0.4 to 0.9 raises F2 between the range 0.002 kgs⁻¹kW⁻¹ to 0.015 kgs⁻¹kW⁻¹ for both the configurations

3. Significant exergy loss rates across the PHX, ambient heat rejection unit and RHX are observed in both the configurations. For a dairy industry, this can be reduced by proper maintenance and cleaning which will prevent fouling and improve performance and efficiency

4. Addition of reheater results in better specific net power output (F1). Change in solar heater exit temperature and cycle maximum pressure result in significant rise in F1 values for reheat configuration. This presents an interesting aspect for choosing the trigeneration configuration based on requirement.

The results presented here are based on very simple thermodynamic analysis with several simplifying assumptions. Hence even though the results presented may be correct qualitatively, for more accurate quantitative prediction a more detailed analysis of the system is needed. A detailed component-wise analysis is required to arrive at the practical feasibility of the system for dairy plants. Further, a detailed economic and life cycle analysis for commercialization of CCHP systems can be initiated for realising them in applications like dairy, building, etc., where heating, cooling and power are required.

Nomenclature
COP	=	Coefficient of performance act Actual
Cp	=	Specific heat capacity kJ/kg K am Ambient
F1	=	Specific net power output kW/kW c cold
F2	=	Specific milk flow rate kgs−1 kW−1 comp compressor
h	=	enthalpy, J kg−1 evap evaporator
HX	=	Heat exchanger gc gas cooler
I	=	Exergy loss h hot
m	=	mass flow rate, kg s−1 is isentropic
P	=	pressure, kPa max maximum
Q	=	heat transfer, kW min minimum
RHX	=	Recovery heat exchanger tot total
s	=	entropy, J kg−1 K−1 turb turbine
T	=	Temperature cric critical
u	=	velocity, ms−1
W	=	work transfer, kW
x	=	dryness fraction

Greek symbols
η	=	efficiency
ρ	=	density
ε	=	Effectiveness
Δ	=	Increment

Subscripts
act	=	Actual
am	=	Ambient
c	=	cold
comp	=	compressor
evap	=	evaporator
gc	=	gas cooler
h	=	hot
is	=	isentropic
max	=	maximum
min	=	minimum
tot	=	total
turb	=	turbine
cric	=	critical

Author contributions

VR: Writing original Draft, review, editing, methodology, formal analysis JG: Writing original Draft, review, editing, methodology, formal analysis MA: Writing original Draft, review, editing, methodology, Funding RC: Review, editing, methodology, formal analysis TS: Review, editing, methodology, formal analysis.

Disclosure statement

Authors confirm that there are no relevant financial or non-financial competing interests to report.

Data availability statement

The data that support the findings of this study are available from the corresponding author and first author, upon reasonable request.

Additional information

Funding

Open Access funding provided by the Qatar National Library. This work was supported by the Qatar National Library.