Optimal configurations for maximizing generalized output of two-finite-potential-reservoir endoreversible generalized engine cycles

Abstract

Universal optimization is a primary objective of the study of generalized thermodynamic optimization theory. Previously, research into dynamic optimization of cyclic processes such as heat engines, chemical engines, battery power circuits, and commercial engines was limited to the research objectives of the specific discipline involved; conclusions were unique to the scope of each application, making it impossible to reveal any commonality between the research objectives and conclusions of these different disciplines. Following a review of the existing literature on dynamic optimization of thermodynamic and chemical cycles, and research into the concept of generalized thermodynamic optimization theory, a physical model of an endoreversible generalized engine with two generalized finite potential reservoirs is established, and the corresponding dynamic optimization problem is formulated solving the generalized output maximization of a generalized engine cycle and its corresponding optimal cycle configuration with the constraint of generalized displacement conservation. Subsequently, universal optimization results are derived applying the Euler-Lagrange equation and average optimal control theory, and simplified optimization results are obtained based on the universal results when generalized flow rate and generalized speed satisfy three specific relationships. Application of the above findings to thermodynamic and isothermal chemical cycles, battery power circuits, and commercial engine cycles is discussed and the concept of generalized thermodynamic dynamic optimization for irreversible cycles is proposed. The work in this paper enriches and completes the generalized thermodynamic optimization theory.