4 - Hamiltonian optimization of imperfect cascades

Abstract

This chapter analyzes limits on multistage production or consumption of mechanical energy (work) in sequential heat-mechanical operations characterized by finite rates. The benchmark system, for which these limits are evaluated, is a cascade of imperfect stages through which a resource fluid flows at a finite rate. Each stage consists of a fluid at flow, an imperfect work generator or consumer, and the environment. The problem investigated is that of limiting yield or consumption of power by the fluid that interacts sequentially with the environment in a finite time. A discrete, finite-rate model subsumes irreducible losses of work potential caused by irreversible properties of thermal resistances. Dynamical limits on work are obtained that bound one-stage or multistage energy convertors with production or consumption of power. These limits are expressed in terms of classical exergy and a residual minimum of entropy generation. A discrete generalization of classical thermal exergy is derived for systems with finite number of imperfect stages and finite holdup times. For this generalized exergy a hysteretic property is valid, meaning a difference between the maximum work delivered from engine mode and the minimum work added to the corresponding heat-pump mode of the system.