تجزیه و تحلیل عملکرد مقایسه ای از موتورهای غیر قابل برگشت حرارتی کارنو تحت حداکثر چگالی توان و شرایط قدرت حداکثر

This paper reports the finite time thermodynamic optimization based on the maximum power density criterion for an irreversible Carnot heat engine model which includes three types of irreversibilities: finite rate heat transfer, heat leakage and internal irreversibility. The obtained results are compared with those results obtained by using the maximum power criterion. The design parameters under the optimal conditions have been derived analytically and the effects of the irreversibilities on the general and optimal performances are investigated. The results showed that the design parameters at maximum power density lead to smaller and more efficient heat engines. It is also seen that the irreversibilities have a greater influence on the performances at maximum power density conditions with respect to the ones at maximum power conditions. Also in this study, the optimal conductance allocation parameter is investigated at both maximum power density and maximum power conditions by assuming a constrained total thermal conductance in the case when there is no heat leakage. The relation between the conductance allocation parameter and the thermal efficiencies at maximum power density and maximum power is also investigated. The obtained results generalize the result of previous studies on this subject and provide guidance to optimal design in terms of power, thermal efficiency and engine sizes for real heat engines.

Power optimization studies of heat engines using finite time thermodynamics analysis were started by Chambadal [1] and Novikov [2] in 1957 and 1958 and were continued by Curzon and Ahlborn [3] in 1975. They extended the reversible Carnot cycle to the endoreversible cycle by taking the irreversibility of finite-time heat transfer into account. By introducing finite time processes, a new field: ‘finite time thermodynamics’ was born, and thus, more realistic limits have been adapted for real heat engine performances. During the last decade, many optimization studies for heat engines based on endoreversible and irreversible models have been performed by considering finite time and finite size constraints under various heat transfer modes, mainly linear and non-linear ones. The reader who is interested in these optimization works could refer to a literature survey written by Bejan [4]. Usually, in these studies, the power output, thermal efficiency, entropy generation and the ecological benefit were chosen for optimization criteria. However, the performance analyses based on the above optimization criteria do not take the effect of engine sizes related to the investment cost into account. In order to include the effects of engine size in the performance analysis, Sahin et al. [5] introduced a new optimization criterion called the maximum power density (MPD) analysis. Using the MPD criterion, they investigated optimal performance conditions for reversible [5] and irreversible [6] non-regenerative Joule–Brayton heat engines. In their study, they maximized the power density (the ratio of power to the maximum specific volume in the cycle) and found design parameters at MPD conditions, which lead to smaller and more efficient Joule–Brayton engines than those engines working at maximum power (MP) conditions. Erbay et al. [7], Erbay and Yavuz [8], Chen et al. [9] and Medina et al. [10] applied the MPD technique to the Ericsson, Stirling, Atkinson and regenerative Joule–Brayton engines, respectively. In their analyses, they discussed the advantages of the MPD performance conditions in comparison to the MP conditions in terms of thermal efficiency and engine sizes. Sahin et al. [11] applied the MPD technique to the endoreversible Carnot heat engine which can be considered as a theoretical comparison standard for all real heat engines in finite time thermodynamics and thus generalized the endoreversible MPD analyses results. They also demonstrated that the thermal efficiency at MPD conditions varies between and for 0≤x≤1 where τ is the ratio of heat sink to heat source temperature and x is the conductance allocation parameter. In this paper, the MPD performance analysis performed by Sahin et al. [11] for the endoreversible Carnot heat engine model is extended to an irreversible Carnot heat engine model by considering internal irreversibility and heat leakage effects. In this context, the optimal performance and design parameters under MPD conditions are investigated. The obtained results are comparatively discussed with respect to the results obtained by using the MP performance criterion.

A comparative performance analysis based on MPD and MP criteria has been performed for irreversible Carnot heat engines which include the major irreversibilities existing in real heat engines. The analysis showed that the thermal efficiency at MPD conditions is greater than the one at MP conditions, for an irreversible heat engine. However, the thermal efficiency advantage of the MPD conditions with respect to MP conditions decreases as the internal irreversibility and heat leakage increase. This result indicates that the reducing effect of the internal irreversibility and heat leakage on the thermal efficiency at MPD conditions is greater in comparison to the one at MP conditions. Thus, it is more important to take precautions to reduce internal irreversibility and heat leakage in the design of a heat engine working at MPD conditions with respect to the one working at MP conditions. It is found that the optimal conductance allocation parameter at MPD conditions () is approximately constant around 0.4, and it is not much affected by τ and RΔS ( Fig. 8(a) and (b)) but the optimal conductance-allocation parameter at MP conditions changes with RΔS (see Eq. (32)). When we compare the optimal conductance-allocation parameters at MPD and MP conditions, we observe that for RΔS>0.45. When there is no heat leakage, the thermal efficiency at MP conditions is independent of the conductance-allocation parameter (see Eq. (31)) but the thermal efficiency at MPD conditions depends on the conductance-allocation parameter ( Eq. (29)). Eq. (29) indicates that the thermal efficiency at MPD conditions varies between and for 0≤x≤1. Furthermore, it is shown that engine sizes designed at MPD conditions would be smaller but require higher maximum pressure than those operating at MP conditions. The results presented in this analysis generalize the results of the previous studies on this subject and may provide guidelines for determination of the optimal design and operating conditions of real heat engines.