Studies on the thermodynamic characteristics of sequential Carnot cycles and its application in heat pump systems

Abstract

Since the fossil fuels, which meet most of the energy requirements in the world, are not environmental friendly and its present stocks are finite, various renewable energy sources have been introduced as a promising option to fill increasing demand of worldwide energy. Although some typical renewable energy sources, such as solar photovoltaic energy, wind energy, and hydrogen energy of fuel cells, are directly converted into electricity, a lot of renewable sources, such as solar thermal energy, industrial waste heat, geothermal energy, and ocean thermal energy, still exist in the form of heat. These thermal energy sources categorized as low grade heat source because they have low temperature and relatively small heat capacity, requires some thermodynamic cycles to generate useful power. Generally, Carnot cycle, has been used in the evaluation of the thermal system as a standard. However, considering that the characteristics of renewable heat sources are different from those of conventional sources, it may not be the best choice to use just a single Carnot cycle for analyzing renewable thermal energy system as it deals with the heat source of infinite heat capacity. Therefore, the sequential Carnot cycle has been suggested, where a number of individual Carnot cycles are arranged in parallel. In contrast to the original Carnot cycle, the sequential cycle considers the temperature change in heat sources which occurs at the heat transfer process between the cycle and heat sources. Moreover, in case of a sequential Carnot cycle, the heat transfer rate between the cycle and heat sources is calculated by taking account of temperature difference between them. In this study, the thermodynamic characteristics of sequential Carnot cycles, such as the efficiency and power output of the system in various conditions, are investigated. Using basic model for the sequential system, which is advanced from the initial one suggested earlier, the performance of sequential Carnot cycles is calculated in an analytical way. For the analysis, only fundamental relations of thermodynamics and heat transfer are utilized, instead of complex numerical techniques. The effect of major variables, which are the number of individual Carnot cycles in the system, the inventory of heat exchangers used and the final temperature of heat sources, on the system performance is researched and some optimization processes are also conducted based on those results. During the analysis, some symbolic expressions are obtained, which can be utilized effectively in actual situations. Also, to bridge the gap between the practical thermal system and the sequential Carnot cycle, more detailed sequential system models are proposed. Different from the previous one, this model adopts the heat sink with finite heat capacity and has some internal irreversibilities in contrast with Carnot cycles. How these features influences the system performance is discovered by analytical equations which are derived from the process similar to that used in the basic model. By the way, throughout the theoretical research, the interesting phenomenon is obeserved, which is that the efficiency of the sequential system increases along with the number of individual Carnot cycles in the system. Paying attention to the possibility that this result can also be applied to actual thermodynamic systems, the numerical simulation using thermodynamic properties of real working fluids is carried out targeting organic Rankine cycles (ORC) and heat pumps. As a result, it is found that the concept of sequential cycles has advantages in actual cases. Finally, the experimental setup for a sequential heat pump, which has two refrigeration cycles in one system, is prepared to validate the result of numerical calculation. The experiment is conducted with not only a sequential heat pump, but also a simple conventional heat pump, which have the same heat capacity. After comparing coefficients of performance (COP) of both systems, it can be found that the sequential heat pump has higher efficiency than the simple heat pump. It can be expected that the result of this research, such as simple expressions from sequential Carnot cycles, is widely used in various situations related with renewable thermal energy sources or a lot of researches about sequential thermal cycles will be initiated by this study.