On the Optimal Allocation of the Heat Exchangers of Irreversible Power Cycles

Abstract

Thermal engines are designed to produce mechanical power, while transferring heat from an available hot temperature source to a cold temperature reservoir (generally the environment). The thermal engine will operate in an irreversible power cycle, very often with an ideal gas as the working substance. Several power cycles have been devised from the fundamental one proposed by Carnot, such as the Brayton, Stirling, Diesel and Otto, among others. These ideal cycles have generated an equal number of thermal engines, fashioned after them. The real thermal engines incorporate a number of internal and external irreversibilities, which in turn decrease the heat conversion into mechanical power. A standard model is shown in Fig. 1 (Aragon-Gonzalez et al., 2003), for an irreversible Carnot engine. The temperatures of the hot and cold heat reservoirs are, respectively, TH and TL. But there are thermal resistances between the working fluid and the heat reservoirs; for that reason the temperatures of the working fluid are T1 and T2, for the hot and cold isothermal processes, respectively, with T1 < TH and TL < T2. There is also a heat loss Q leak from the hot reservoir to the cold reservoir and there are other internal irreversibilities (such as dissipative processes inside the working fluid). This Carnot-like model was chosen because of its simplicity to account for three main irreversibilities above, which usually are present in real heat engines. On the other hand, the effectiveness of heat exchangers (ratio of actual heat transfer rate to maximum possible heat transfer rate), influence over the power cycle thermal efficiency. For a given transfer rate requirement, and certain temperature difference, well-designed heat exchangers mean smaller transfer surfaces, lesser entropy production and smaller thermal resistances between the working fluid and the heat reservoirs. At the end all this accounts for larger power output from the thermal engine. Former work has been made to investigate the influence of finite-rate heat transfer, together with other major irreversibilities, on the performance of thermal engines. There are several parameters involved in the performance and optimization of an irreversible power cycle; for instance, the isentropic temperature ratio, the allocation ratio of the heat exchangers and the cost and effectiveness ratio of these exchangers (Lewins, 2000; Aragon-Gonzalez et al., 2008 and references there included). The allocation of the heat exchangers refers to the distribution of the total available area for heat transfer, between the hot and the cold sides of an irreversible power cycle. The irreversible Carnot cycle has been optimized with respect to the allocation ratio of the heat exchangers (Bejan, 1988; Aragon-Gonzalez et al., 2009).