Theoretical Evaluation of the Maximum Work of Free-Piston Engine Generators

• Published in: Journal of non-equilibrium thermodynamics Vol. 42; no. 1; pp. 31 - 58
• Main Author: Kojima, Shinji
• Format: Journal Article
• Language: English
• Published: Berlin De Gruyter 01.01.2017; Walter de Gruyter GmbH
• Subjects: Adiabatic flow; adjoint equations; Brayton cycle; Calculus; Calculus of variations; Compressing; Compression ratio; Computing time; Control theory; Cycle ratio; Efficiency; Electric currents; engine; free piston; Friction; Generators; Heat engines; Investigations; Joule heat; Mathematical analysis; Optimization; Otto cycle; Pressure ratio; thermal efficiency; Thermodynamic efficiency; Variables
• ISSN: 0340-0204; 1437-4358
• DOI: 10.1515/jnet-2015-0089

Utilizing the adjoint equations that originate from the calculus of variations, we have calculated the maximum thermal efficiency that is theoretically attainable by free-piston engine generators considering the work loss due to friction and Joule heat. Based on the adjoint equations with seven dimensionless parameters, the trajectory of the piston, the histories of the electric current, the work done, and the two kinds of losses have been derived in analytic forms. Using these we have conducted parametric studies for the optimized Otto and Brayton cycles. The smallness of the pressure ratio of the Brayton cycle makes the net work done even when the duration of heat addition is optimized to give the maximum amount of heat addition. For the Otto cycle, the net work done is positive, and both types of losses relative to the gross work done become smaller with the larger compression ratio. Another remarkable feature of the optimized Brayton cycle is that the piston trajectory of the heat addition/disposal process is expressed by the same equation as that of an adiabatic process. The maximum thermal efficiency of any combination of isochoric and isobaric heat addition/disposal processes, such as the Sabathe cycle, may be deduced by applying the methods described here.