Work Limits in Imperfect Sequential Systems with Heat and Fluid Flow

Abstract

This paper analyses physical limits of multistage production or consumption of mechanical energy (work) in sequential heat-mechanical operations characterized by finite rates. The benchmark system, where these limits are evaluated, is a cascade of imperfect stages through which a resource fluid flows with 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 work 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 thermal resistances. Dynamic limits on work are obtained which 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 exergy is found 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 heatpump mode of the system.