تجزیه و تحلیل عملکرد یک موتور حرارتی بر اساس معیار بهینه سازی اقتصادی حرارتی جدید

A new kind of finite time thermoeconomic optimization analysis for an endoreversible heat engine has been performed. The objective function has been taken as the power output per unit total cost. The optimum performance parameters that maximize the objective function are investigated. In this perspective, some analytical equations for the optimum working fluid temperatures, optimum thermal efficiency, optimal distributions of heat exchanger areas and optimum specific power output were found in terms of economical and technical parameters. The effects of the design parameters on the optimal conditions have been discussed.

The thermal efficiency of a reversible Carnot cycle is an upper limit of efficiency for heat engines. According to classical thermodynamics, the Carnot efficiency is equation(1) where TL and TH are the temperatures of the cold and hot reservoirs, respectively. The thermal efficiency in Eq. (1) can only be achieved through the infinitely slow processes required by thermodynamic equilibrium. Therefore, it is not possible to obtain a certain amount of power output by using heat exchangers with finite heat transfer areas. If we require a certain amount of power output, the necessary heat exchanger areas would be infinite. Thus, the thermal efficiency given in Eq. (1) does not have great significance and is a poor guide for the performances of real heat engines. Chambadal [1], Novikov [2] and Curzon and Ahlborn [3] extended the reversible Carnot cycle to an endoreversible Carnot cycle by taking the irreversibility of finite time heat transfer into account and found that the efficiency at maximum power as, equation(2) Other than power maximization, Wu [4] and [5], Chen and Wu [6] and [7] and Chen et al. [8] have maximized specific power output (power output per unit total heat transfer area), and at the optimum conditions, they obtained the same result with maximum power conditions. Sahin et al. [9] performed power density (defined as the ratio of power to the maximum volume in the cycle) maximization analysis for the endoreversible heat engine cycle model and found the thermal efficiency at maximum power density conditions as, equation(3) where the conductance allocation parameter b=UHAH/(ULAL+UHAH). Angulo-Brown [10] proposed an ecological optimization criterion for performance analysis for the endoreversible heat engine and found that the thermal efficiency at maximum ecological objective function conditions is in good agreement with the arithmetic mean of the Carnot and the maximum power efficiencies, i.e. equation(4) De Vos [11] studied the thermoeconomics of the Novikov plant. He assumed that the investment cost is proportional to the size of the plant and the maximum heat input is an appropriate measure for that. He showed that the optimum performance depends on the relative costs of investment and fuel and also demonstrated that the optimum thermal efficiency lies between the maximum power and the Carnot efficiencies, i.e. equation(5) De Vos [11] found the optimum thermal efficiency as equation(6) where β is an economical parameter. In the Novikov plant, there is no finite rate heat transfer irreversibility in the cold side of the cycle, so the thermal conductance there tends to infinity. This means an infinite heat transfer area for a given overall heat transfer coefficient. For a more realistic thermoeconomic analysis, a model with finite rate heat transfer at both sides of the cycle has to be considered, i.e. the Curzon–Ahlborn model. Also, we think that it is more appropriate to take the size of the plant (which is assumed to be proportional to the investment cost) proportional to the total heat transfer area instead of the maximum heat input. Sahin and Kodal [12] and Kodal et al. [13] recently introduced a new optimization criterion called the finite time thermoeconomic optimization for refrigerators and heat pumps. More specifically, the cooling load for the refrigerator and the heating load for the heat pump per unit total cost were proposed as objective functions for the optimization. In this paper, this proposed optimization technique for refrigerators and heat pumps has been applied to the endoreversible heat engine, and the economical design conditions are obtained.

A new kind of thermoeconomic performance analysis using finite time thermodynamics has been conducted for an endoreversible heat engine. For a more general and realistic optimization, a new objective function which includes both investment and fuel consumption costs has been proposed. More specifically, the objective function has been taken as the power output per unit total cost. By optimizing this objective function, the optimum operating and design conditions were determined. In this perspective, equations of optimum working fluid temperatures, optimum thermal efficiency, optimal distributions of the heat exchanger areas and optimum specific power output were found in terms of economical and technical parameters. The effects of the relative fuel cost parameter, f on the optimum thermal efficiency and the optimum specific power output have also been discussed. In conclusion, the study performed for the endoreversible heat engine generalizes the results of previous studies and makes a link towards thermoeconomic design.