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Keywords = transcritical cycle

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41 pages, 2244 KB  
Review
Cutting-Edge Research: Artificial Intelligence Applications and Control Optimization in Advanced CO2 Cycles
by Jiaqi Dong, Yufu Zheng, Jianguang Zhao, Jun Luo and Yijian He
Energies 2025, 18(19), 5114; https://doi.org/10.3390/en18195114 - 25 Sep 2025
Viewed by 373
Abstract
In recent years, advanced CO2 cycles, including supercritical CO2 power cycles, transcritical CO2 power cycles and refrigeration cycles, have demonstrated significant potential for application across a broad spectrum of energy conversion processes, owing to their high efficiency and compact components [...] Read more.
In recent years, advanced CO2 cycles, including supercritical CO2 power cycles, transcritical CO2 power cycles and refrigeration cycles, have demonstrated significant potential for application across a broad spectrum of energy conversion processes, owing to their high efficiency and compact components that are environmentally benign and non-polluting. This study presents a comprehensive review of the dynamic performance and control strategies of these advanced CO2 cycles. It details the selection of system configurations and various control strategies, detailing the principles behind different control strategies, their applicable scopes, and their respective advantages. Furthermore, this study conducts a comparison between the joint control strategy and single control strategies for CO2 cycles, demonstrating the superiority of the joint control strategy in CO2 cycles. It then delves into the potential of novel control technologies for CO2 cycles, using model-based control technology powered by artificial intelligence as a case study. This study also offers an extensive overview of control theory, methodology, scope of application, and the pros and cons of various control strategies, with examples including extreme value-seeking control, model predictive control (MPC) based on an artificial neural network model, and MPC based on particle swarm optimization. Finally, it explores the application of AI-controlled CO2 cycles in new energy vehicles, solar power generation, aerospace, and other fields. It also provides an outlook on the development direction of CO2 cycle control strategies in light of the evolving trends in the energy sector and advancements in AI methodologies. Full article
(This article belongs to the Special Issue Challenges and Research Trends of Energy Management)
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22 pages, 2131 KB  
Review
Research Progress on CO2 Transcritical Cycle Technology for Building Heating and Cooling Applications
by Weixiu Shi, Haiyu Chang, Junwei Zhou, Bai Mu, Shuang Quan and Lisheng Pan
Buildings 2025, 15(16), 2952; https://doi.org/10.3390/buildings15162952 - 20 Aug 2025
Viewed by 1018
Abstract
This review focuses on the advancements of CO2 transcritical cycle technology in building indoor environmental regulation, particularly in combined heating and cooling applications. The paper highlights the energy efficiency and environmental benefits of CO2 as a natural refrigerant, which has zero [...] Read more.
This review focuses on the advancements of CO2 transcritical cycle technology in building indoor environmental regulation, particularly in combined heating and cooling applications. The paper highlights the energy efficiency and environmental benefits of CO2 as a natural refrigerant, which has zero ozone depletion potential (ODP) and very low global warming potential (GWP). It provides a comprehensive overview of recent optimization strategies, including distributed compression, the integration of ejectors and expanders, and the design improvements of key components such as gas coolers, compressors, and throttling valves. Through optimization strategies such as dual-system cycles, this technology can achieve a COP improvement of 15.3–46.96% in heating scenarios; meanwhile, with the help of distributed compression technology, its cooling capacity can be enhanced by up to 26.5%. The review also examines various operating conditions such as discharge pressure and subcooling, which significantly affect system performance. The paper concludes by identifying the current challenges in the application of CO2 systems, such as high initial costs and system stability under extreme conditions, and suggests future research directions to overcome these limitations and improve the practical application of CO2 transcritical cycles in the building industry. Overall, it is concluded that the development of expander-compressors holds great potential for achieving better performance and represents a promising direction for future advancements in this field. Full article
(This article belongs to the Special Issue Development of Indoor Environment Comfort)
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20 pages, 3672 KB  
Article
Comparative Analysis of Transcritical CO2 Heat Pump Systems With and Without Ejector: Performance, Exergy, and Economic Perspective
by Xiang Qin, Shihao Lei, Heyu Liu, Yinghao Zeng, Yajun Liu, Caiyan Pang and Jiaheng Chen
Energies 2025, 18(12), 3223; https://doi.org/10.3390/en18123223 - 19 Jun 2025
Viewed by 1046
Abstract
To promote renewable energy utilization and enhance the environmental friendliness of refrigerants, this study presents a novel experimental investigation on a transcritical CO2 double-evaporator heat pump water heater integrating both air and water sources, designed for high-temperature hot water production. A key [...] Read more.
To promote renewable energy utilization and enhance the environmental friendliness of refrigerants, this study presents a novel experimental investigation on a transcritical CO2 double-evaporator heat pump water heater integrating both air and water sources, designed for high-temperature hot water production. A key innovation of this work lies in the integration of an ejector into the dual-source system, aiming to improve system performance and energy efficiency. This study systematically compares the conventional circulation mode and the proposed ejector-assisted circulation mode in terms of system performance, exergy efficiency, and the economic payback period. Experimental results reveal that the ejector-assisted mode not only achieves a higher water outlet temperature and reduces compressor power consumption but also improves the system’s exergy efficiency by 6.6% under the condition of the maximum outlet water temperature. Although the addition of the ejector increases initial manufacturing and maintenance costs, the payback periods of the two modes remain nearly the same. These findings confirm the feasibility and advantage of incorporating an ejector into a transcritical CO2 compression/ejection heat pump system with integrated air and water sources, offering a promising solution for efficient and environmentally friendly high-temperature water heating applications. Full article
(This article belongs to the Special Issue Advances in Supercritical Carbon Dioxide Cycle)
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28 pages, 3486 KB  
Article
Thermo-Economic Potential of Carnot Batteries for the Waste Heat Recovery of Liquid-Cooled Data Centers with Different Combinations of Heat Pumps and Organic Rankine Cycles
by Xiaoyu Zhou, Xinxing Lin, Wen Su, Ruochen Ding and Yaran Liang
Energies 2025, 18(6), 1556; https://doi.org/10.3390/en18061556 - 20 Mar 2025
Cited by 2 | Viewed by 1419
Abstract
To fully recover abundant waste heat and reduce the operation cost in liquid-cooled data centers, a Carnot battery consisting of a heat pump (HP) and organic Rankine cycle (ORC) is proposed. Due to the existence of different cycle states for HPs and ORCs, [...] Read more.
To fully recover abundant waste heat and reduce the operation cost in liquid-cooled data centers, a Carnot battery consisting of a heat pump (HP) and organic Rankine cycle (ORC) is proposed. Due to the existence of different cycle states for HPs and ORCs, four different cycle combinations are considered. To evaluate and compare their performances, thermo-economic models are developed. Under the design conditions, the optimal working fluid combinations are first determined for each battery. On this basis, thermodynamic and economic performances of the four batteries are analyzed in detail. The results indicate that the system consisting of a subcritical HP/transcritical ORC achieves the highest round-trip efficiency at 76%. Notably, the round-trip efficiency of the system can exceed 100% at low ORC condensing temperatures. Additionally, the system cost is about 767–796 USD/kW∙h, depending on the cycle combinations. Furthermore, the effects of operating parameters on system performances are also investigated. Finally, with the objective of maximum round-trip efficiency, key parameters of four batteries are optimized. The results reveal that the system with a subcritical HP/subcritical ORC attains a maximum round-trip efficiency of 83% after optimization. These research results contribute to the development of green data centers and the reduction of power costs. Full article
(This article belongs to the Section J: Thermal Management)
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22 pages, 3843 KB  
Article
Performance Improvement of the LNG Regasification Process Based on Geothermal Energy Using a Thermoelectric Generator and Energy and Exergy Analyses
by Amin Mohammadi and Akbar Maleki
Sustainability 2024, 16(24), 10881; https://doi.org/10.3390/su162410881 - 12 Dec 2024
Viewed by 1244
Abstract
In this paper, a new approach is proposed to improve the performance of the LNG regasification process in a geothermal-transcritical CO2–LNG cycle by using thermoelectric generators. Energy and exergy analyses were applied to the proposed system and the plant’s performance is [...] Read more.
In this paper, a new approach is proposed to improve the performance of the LNG regasification process in a geothermal-transcritical CO2–LNG cycle by using thermoelectric generators. Energy and exergy analyses were applied to the proposed system and the plant’s performance is compared with the conventional CO2–LNG cycle. To achieve the optimal solution for the system, a multi-objective optimization technique based on a genetic algorithm is used. This study’s findings revealed that in the conventional CO2–LNG cycle, the highest exergy destruction occurs in the preheater. However, integrating a thermoelectric generator allows a portion of this destroyed exergy to be converted into power. The proposed system demonstrated 2% less exergy destruction compared to the conventional system. Moreover, the TEG contributes additional power, increasing the net output power of the system by 24%. This improvement ultimately enhances the overall exergy efficiency of the system. The analysis also concluded that, although a lower LNG mass flow rate reduces the system’s net power output, it improves the exergy efficiency. Overall, the proposed system exhibits an 8.37% higher exergy efficiency and a 24.22% greater net output power compared to the conventional CO2–LNG cycle. Full article
(This article belongs to the Section Energy Sustainability)
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49 pages, 9536 KB  
Review
The Great Versatility of Supercritical Fluids in Industrial Processes: A Focus on Chemical, Agri-Food and Energy Applications
by Manita Kamjam, Somkiat Ngamprasertsith, Ruengwit Sawangkeaw, Manop Charoenchaitrakool, Romain Privat, Jean-Noël Jaubert and Michel Molière
Processes 2024, 12(11), 2402; https://doi.org/10.3390/pr12112402 - 31 Oct 2024
Cited by 6 | Viewed by 5270
Abstract
Long a thermodynamic curiosity, supercritical fluids (SCFs) have gradually gained ground in today’s life, generating an increasing number of new, efficient processes in diverse industrial sectors and fueling active R&D programs. Indeed, the versatility of SCFs allows them to serve a wide variety [...] Read more.
Long a thermodynamic curiosity, supercritical fluids (SCFs) have gradually gained ground in today’s life, generating an increasing number of new, efficient processes in diverse industrial sectors and fueling active R&D programs. Indeed, the versatility of SCFs allows them to serve a wide variety of applications. The list includes not only food processing, biofuel production, extraction of biomolecules marketable as medicines, cosmetics and nutraceuticals, but also emerging technologies for the production of electrical power, based on supercritical or transcritical thermodynamic cycles. This jointly authored article will provide a review of important applications covered by our laboratories in the agri-food, chemical and energy sectors. We will then try to detect recent trends and outline future prospects. Full article
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27 pages, 4733 KB  
Article
Simultaneous Optimization of Exergy and Economy and Environment (3E) for a Multistage Nested LNG Power Generation System
by Zhenzhen Chen, Xinglin Yang, Junhu Zou, Qiang Lei and Bin Yan
J. Mar. Sci. Eng. 2024, 12(10), 1850; https://doi.org/10.3390/jmse12101850 - 16 Oct 2024
Cited by 1 | Viewed by 1149
Abstract
The study introduces an innovative three-stage nested power generation system that enables the cascading utilization of LNG cold energy. It makes the most of wasted energy by using ship jacket cooling water (JCW) and exhaust gas (EG) as heat sources, a trans-critical carbon [...] Read more.
The study introduces an innovative three-stage nested power generation system that enables the cascading utilization of LNG cold energy. It makes the most of wasted energy by using ship jacket cooling water (JCW) and exhaust gas (EG) as heat sources, a trans-critical carbon dioxide cycle as internal circulation, and utilizing the pressure exergy of LNG. We choose two azeotrope mixing fluids that match the requirements and create four cases for the outer and middle cycle working fluids in the three-stage nested system. To discover the ideal system performance from the perspectives of exergy (E), economy (E), and environment (E), four cases were subjected to multi-objective optimization using the multi-objective particle swarm optimization technique (MOPSO). Finally, the optimal solution was found by applying the TOPSIS decision-making method. Through comparative analysis, the optimal system is selected among the four optimization results. R170 (22.66%) and R1150 (77.34%) are used as the outer circulating working medium, while R170 (90.86%) and R1270 (9.14%) are utilized as the inter-cycle working fluid. The net output work is 575.75 kW, the optimal exergy efficiency is 46.09%, the optimal electricity production cost is $0.04009 per kWh, the carbon dioxide emissions can be reduced by 36,910 tons, and the payback period is 2.548 years. After optimization, a more energy-efficient and environmentally friendly power generation system is obtained. Full article
(This article belongs to the Section Ocean Engineering)
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21 pages, 5049 KB  
Article
A Novel Fuel-Based CO2 Transcritical Cycle for Combined Cooling and Power Generation on Hypersonic Aircrafts
by Yijian He, Lisong Wang, Jiaqi Dong and Qifei Chen
Energies 2024, 17(19), 4853; https://doi.org/10.3390/en17194853 - 27 Sep 2024
Cited by 1 | Viewed by 1063
Abstract
This study focuses on the great challenges for combined cooling and power supply on hypersonic aircrafts. To address the issues of low thermal efficiency and high fuel consumption of heat sink by the existing CO2 supercritical Brayton cycle, a novel fuel-based CO [...] Read more.
This study focuses on the great challenges for combined cooling and power supply on hypersonic aircrafts. To address the issues of low thermal efficiency and high fuel consumption of heat sink by the existing CO2 supercritical Brayton cycle, a novel fuel-based CO2 transcritical cooling and power (FCTCP) system is constructed. A steady-state simulation model is built to investigate the impacts of combustion chamber wall temperatures and fuel mass flow rates on the FCTCP system. Thermal efficiency of the CO2 transcritical cycle reaches 25.2~32.8% under various combustion chamber wall outlet temperatures and endothermic pressures. Compared with the supercritical Brayton cycle, the thermal efficiency of novel system increases by 54.5~80.9%. It is found from deep insights into the thermodynamic results that the average heat transfer temperature difference between CO2 and fuel is effectively reduced from 153.4 K to 16 K by split cooling of the fuel in the FCTCP system, which greatly enhances the matching of CO2–fuel heat exchange temperatures and reduces the heat exchange loss of the system. Thermodynamic results also show that, in comparison to the supercritical Brayton cycle, the cooling capacity and power generation per unit mass flow rate of working fluid in the FCTCP system increased by 75.4~80.8% and 12.9~51.6%, respectively. The FCTCP system exhibits a substantial performance improvement, significantly enhancing the key characteristic index of the combined cooling and power supply system. This study presents a novel approach to solving the challenges of cooling and power supply in hypersonic aircrafts under limited fuel heat sink conditions, laying the groundwork for further exploration of thermal management technologies of hypersonic aircrafts. Full article
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20 pages, 16364 KB  
Article
Performance and Economic Analysis of Two Types of High-Temperature Heat Pump Based on New Refrigerants
by Dahan Sun, Jiang Qin and Zhongyan Liu
Appl. Sci. 2024, 14(17), 7735; https://doi.org/10.3390/app14177735 - 2 Sep 2024
Viewed by 2018
Abstract
This paper proposes, for the first time, the research concept of comparing energy and economy between transcritical cycle high-temperature heat pumps and subcritical cycle high-temperature heat pumps with new refrigerants. Experiments and simulations are conducted to compare the system performance and economy of [...] Read more.
This paper proposes, for the first time, the research concept of comparing energy and economy between transcritical cycle high-temperature heat pumps and subcritical cycle high-temperature heat pumps with new refrigerants. Experiments and simulations are conducted to compare the system performance and economy of two heat pumps, and the effects of different factors on the performance of two heat pumps are analyzed. The results show that R744/R1234yf (90/10) and R515-1 are the preferred refrigerants for transcritical cycle heat pumps and subcritical cycle heat pumps, respectively. The COP of the R744/R1234yf (90/10) transcritical heat pump is generally higher than that of the R515B-1 subcritical heat pump, and compared to the R515B-1 subcritical heat pump, the cost recovery period of the R744/R1234yf (90/10) transcritical heat pump is about 9–15 years. Therefore, it is recommended that users who use heat pumps for a long time choose transcritical cycle heat pumps. Meanwhile, with the change of evaporation temperature, the system COP of the R515B-1 subcritical heat pump and R744/R1234yf (90/10) transcritical heat pump increases by 61.11% and 65.91%, respectively. In addition, the optimal charge amount for the R515B-1 subcritical heat pump is 81.8% of that of the R744/R1234yf (90/10) transcritical heat pump. Full article
(This article belongs to the Special Issue Energy Efficiency in Buildings and Its Sustainable Development)
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26 pages, 2685 KB  
Article
Energy and Exergy Analysis of Transcritical CO2 Cycles for Heat Pump Applications
by Marco Gambini, Michele Manno and Michela Vellini
Sustainability 2024, 16(17), 7511; https://doi.org/10.3390/su16177511 - 30 Aug 2024
Cited by 1 | Viewed by 2115
Abstract
Heat pumps are recognized as a key tool in the energy transition toward a carbon-neutral society, enabling the electrification of the heating sector at least for low- and medium-temperature heat demands. In recent years, natural refrigerants have been reconsidered due to their low [...] Read more.
Heat pumps are recognized as a key tool in the energy transition toward a carbon-neutral society, enabling the electrification of the heating sector at least for low- and medium-temperature heat demands. In recent years, natural refrigerants have been reconsidered due to their low environmental impact: among them, CO2 is a safe option without an impact on the ozone layer and low global warming potential compared to synthetic fluids. However, as a consequence of its thermophysical properties, its thermodynamic cycle is transcritical and is particularly suitable for specific end-user temperature profiles. This paper analyzes in a systematic and thorough way the most significant modifications to the reference cycle that have been proposed in the literature to improve the performance, finding how the optimal configurations change with a change in the rated operating conditions (inlet temperature and temperature glide of the heat demand, and ambient temperature). Exergy analysis explains why there is an optimal gas cooler pressure and why its trend with the average temperature is split into two distinct regions, clearly recognizable in all cycle layouts. The maximum coefficient of performance (COP) of the reference cycle varies in the 1.52–3.74 range, with a second-law efficiency of 6.4–36.1%, for an optimal gas cooler pressure of up to 15.45 MPa, depending on the ambient temperature and end-user temperature profile. The most effective modification is the cycle with an ejector and internal heat exchanger, which raises the COP to 1.84–4.40 (second-law efficiency 8.7–45.56%). The presented results provide an extensive guide to understanding the behavior of a transcritical CO2 cycle and predict its performance in heat pump applications. Full article
(This article belongs to the Special Issue Energy Storage, Conversion and Sustainable Management)
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28 pages, 6325 KB  
Article
Optimizing Low-Temperature Three-Circuit Evaporative Cooling System for an Electric Motor by Using Refrigerants
by Dmytro Konovalov, Ignat Tolstorebrov, Yuhiro Iwamoto, Halina Kobalava, Jacob Joseph Lamb and Trygve Magne Eikevik
Energies 2024, 17(16), 3942; https://doi.org/10.3390/en17163942 - 9 Aug 2024
Cited by 2 | Viewed by 2193
Abstract
This article presents modeling results and a comprehensive analysis of evaporative cooling systems designed for electric motors using the refrigerants R744 (trans-critical), R134a, R600a, and R290. This study aims to determine the most suitable refrigerant for use in a cooling system, optimize the [...] Read more.
This article presents modeling results and a comprehensive analysis of evaporative cooling systems designed for electric motors using the refrigerants R744 (trans-critical), R134a, R600a, and R290. This study aims to determine the most suitable refrigerant for use in a cooling system, optimize the system design, and calculate the maximum achievable motor power while adhering to specified temperature constraints. The modeling was validated by an experimental setup, which had the cooling system’s configuration featuring three circuits for motor housing, stator, and rotor cooling, respectively. The modeling of an evaporative system was used to present the cooling efficiency under varying loads and external temperature conditions. Mathematical modeling encompasses complex algorithms to simulate heat transfer phenomena, accounting for fluid dynamics and refrigeration cycle dynamics. The analyses revealed trends in winding temperature, rotor temperature, air temperature inside the motor, heat transfer coefficient, coefficient of performance (COP), and motor power across different operating conditions while using different cooling refrigerants. The maximal heat transfer coefficients were calculated for all the refrigerants for winding temperatures in the range from 32 to 82 °C, while air temperature and rotor temperatures were between 42 and 105 °C and 76 and 185 °C, respectively. Lowering the evaporation temperature of the coolant to −35 °C resulted in a significant decrease in the winding temperature to 15 °C, air temperature to 38 °C, and maximum rotor temperature to 118 °C at a motor power of 90 kW. Refrigerant R744 emerged as a promising option, offering high heat transfer coefficients and achieving high motor power within temperature limits. At the same time, the COP was lower when compared with other working fluids because of the high ambient temperature on the gas cooler side. Full article
(This article belongs to the Section E: Electric Vehicles)
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14 pages, 3342 KB  
Article
Exploring the Potential of Silicon Tetrachloride as an Additive in CO2-Based Binary Mixtures in Transcritical Organic Rankine Cycle—A Comparative Study with Traditional Hydrocarbons
by Mashhour A. Alazwari and Muhammad Ehtisham Siddiqui
Processes 2024, 12(7), 1507; https://doi.org/10.3390/pr12071507 - 17 Jul 2024
Viewed by 1282
Abstract
Carbon dioxide (CO2) has been recognized as one of the potential working fluids to operate power generation cycles, either in supercritical or transcritical configuration. However, a small concentration of some of the additives to CO2 have shown promising improvements in [...] Read more.
Carbon dioxide (CO2) has been recognized as one of the potential working fluids to operate power generation cycles, either in supercritical or transcritical configuration. However, a small concentration of some of the additives to CO2 have shown promising improvements in the overall performance of the cycle. The current study is motivated by the newly proposed additive silicon tetrachloride (SiCl4), and so we perform a detailed investigation of SiCl4 along with a few well-known additives to CO2-based binary mixtures as a working fluid in transcritical organic Rankine cycle setup with internal heat regeneration. The additives selected for the study are pentane, cyclopentane, cyclohexane, and silicon tetrachloride (SiCl4). A comprehensive study on the energy and exergy performance of the cycle for warm regions is conducted at a turbine inlet temperature of 250 °C. The performance of the heat recovery unit is also assessed to highlight its importance in comparison to a simple configuration of the cycle. This study shows that the cycle operating with binary mixtures performs significantly better than with pure CO2, which is mainly due to its better heat recovery in the heat recovery unit. The results show that the optimal molar concentration of the additives is in between 20% and 25%. Besides having better thermal stability, SiCl4 shows an improvement in the cycle thermal efficiency by 6% points which is comparable to cyclopentane (7.3% points) and cyclohexane (7.8% points). The optimal cycle pressure ratio for SiCl4 is also relatively lower than for other additives. The energy efficiency of the cycle with pure CO2 is around 45% which is also increased to 58%, 63%, 64%, 60% with pentane, cyclopentane, cyclohexane, and SiCl4, respectively. These results suggest that additives like SiCl4 could make CO2-based cycles more viable for power generation in warm regions. Full article
(This article belongs to the Section Chemical Processes and Systems)
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19 pages, 964 KB  
Article
Bifurcation Analysis in a Coffee Berry-Borer-and-Ants Prey–Predator Model
by Carlos Andrés Trujillo-Salazar, Gerard Olivar-Tost and Deissy Milena Sotelo-Castelblanco
Mathematics 2024, 12(11), 1670; https://doi.org/10.3390/math12111670 - 27 May 2024
Cited by 2 | Viewed by 1264
Abstract
One of the most important agricultural activities worldwide, coffee cultivation, is severely affected by the Coffee Berry Borer (CBB), Hypothenemus hampei, considered the primary coffee pest. The CBB is a tiny beetle that diminishes the quantity and quality of coffee beans by [...] Read more.
One of the most important agricultural activities worldwide, coffee cultivation, is severely affected by the Coffee Berry Borer (CBB), Hypothenemus hampei, considered the primary coffee pest. The CBB is a tiny beetle that diminishes the quantity and quality of coffee beans by penetrating them to feed on the endosperm and deposit its eggs, continuing its life cycle. One strategy to combat CBBs is using biological control agents, such as certain species of ants. Here, a mathematical model (consisting of a system of nonlinear ordinary differential equations) is formulated to describe the prey–predator interaction between CBBs and an unspecified species of ants. From this mathematical perspective, the model allows us to determine conditions for the existence and stability of extinction, persistence or co-existence equilibria. Transitions among those equilibrium states are investigated through the maximum per capita consumption rate of the predator as a bifurcation parameter, allowing us to determine the existence of transcritical and saddle-node bifurcations. Phase portraits of the system are presented for different values of bifurcation parameter, to illustrate stability outcomes and the occurrence of bifurcations. It is concluded that an increase in bifurcation parameters significantly reduces the CBB population, suggesting that ant predation is an effective control strategy, at least theoretically. Full article
(This article belongs to the Special Issue Dynamics and Differential Equations in Mathematical Biology)
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25 pages, 4246 KB  
Article
Investigating the Dynamic Behavior of Integer and Noninteger Order System of Predation with Holling’s Response
by Kolade M. Owolabi, Sonal Jain and Edson Pindza
Mathematics 2024, 12(10), 1530; https://doi.org/10.3390/math12101530 - 14 May 2024
Cited by 4 | Viewed by 1629
Abstract
The paper’s primary objective is to examine the dynamic behavior of an integer and noninteger predator–prey system with a Holling type IV functional response in the Caputo sense. Our focus is on understanding how harvesting influences the stability, equilibria, bifurcations, and limit cycles [...] Read more.
The paper’s primary objective is to examine the dynamic behavior of an integer and noninteger predator–prey system with a Holling type IV functional response in the Caputo sense. Our focus is on understanding how harvesting influences the stability, equilibria, bifurcations, and limit cycles within this system. We employ qualitative and quantitative analysis methods rooted in bifurcation theory, dynamical theory, and numerical simulation. We also delve into studying the boundedness of solutions and investigating the stability and existence of equilibrium points within the system. Leveraging Sotomayor’s theorem, we establish the presence of both the saddle-node and transcritical bifurcations. The analysis of the Hopf bifurcation is carried out using the normal form theorem. The model under consideration is extended to the fractional reaction–diffusion model which captures non-local and long-range effects more accurately than integer-order derivatives. This makes fractional reaction–diffusion systems suitable for modeling phenomena with anomalous diffusion or memory effects, improving the fidelity of simulations in turn. An adaptable numerical technique for solving this class of differential equations is also suggested. Through simulation results, we observe that one of the Lyapunov exponents has a negative value, indicating the potential for the emergence of a stable-limit cycle via bifurcation as well as chaotic and complex spatiotemporal distributions. We supplement our analytical investigations with numerical simulations to provide a comprehensive understanding of the system’s behavior. It was discovered that both the prey and predator populations will continue to coexist and be permanent, regardless of the choice of fractional parameter. Full article
(This article belongs to the Special Issue Numerical Solution of Differential Equations and Their Applications)
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23 pages, 6741 KB  
Article
Thermodynamic Analysis of an Increasing-Pressure Endothermic Power Cycle Integrated with Closed-Loop Geothermal Energy Extraction
by Hao Yu, Xinli Lu, Wei Zhang and Jiali Liu
Energies 2024, 17(7), 1756; https://doi.org/10.3390/en17071756 - 6 Apr 2024
Cited by 2 | Viewed by 1902
Abstract
The thermodynamic analysis of an increasing-pressure endothermic power cycle (IPEPC) integrated with closed-loop geothermal energy extraction (CLGEE) in a geothermal well at a depth from 2 km to 5 km has been carried out in this study. Using CLGEE can avoid some typical [...] Read more.
The thermodynamic analysis of an increasing-pressure endothermic power cycle (IPEPC) integrated with closed-loop geothermal energy extraction (CLGEE) in a geothermal well at a depth from 2 km to 5 km has been carried out in this study. Using CLGEE can avoid some typical problems associated with traditional EGS technology, such as water contamination and seismic-induced risk. Simultaneous optimization has been conducted for the structural parameters of the downhole heat exchanger (DHE), the CO2 mixture working fluid type, and the IPEPC operating parameters. The CO2-R32 mixture has been selected as the optimal working fluid for the IPEPC based on the highest net power output obtained. It has been found that, when the DHE length is 4 km, the thermosiphon effect is capable of compensating for 53.8% of the pump power consumption. As long as the DHE inlet pressure is higher than the critical pressure, a lower DHE inlet pressure results in more power production. The power generation performance of the IPEPC has been compared with that of the organic Rankine cycle (ORC), trans-critical carbon dioxide cycle (t-CO2), and single-flash (SF) systems. The comparison shows that the IPEPC has more net power output than other systems in the case that the DHE length is less than 3 km, along with a DHE outer diameter of 0.155 m. When the DHE outer diameter is increased to 0.22 m, the IPEPC has the highest net power output for the DHE length ranging from 2 km to 5 km. The application scopes obtained in this study for different power generation systems are of engineering-guiding significance for geothermal industries. Full article
(This article belongs to the Special Issue Development and Utilization in Geothermal Energy)
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