A universal expression for optimum specific work of reciprocating heat engines having endoreversible carnot efficiencies

Abstract

Irreversible heat transfer (finite time) analysis is used to obtain the optimum thermodynamic specific work potential at maximum power for various practical reciprocating cycles having endoreversible Carnot efficiencies. The theory of finite-time thermodynamics for reciprocating endoreversible cycles with heat transfer irreversibilities gives rise to an optimum efficiency at maximum power output, of η=1−(TL/TH)0·5 for Carnot-like cycles in contrast to the upper limit for Carnot-like cycles of η=1−(TL/TH) obtained from infinite-time thermodynamics. It is shown here that, additionally, for this same general family of regenerative reciprocating cycles which includes the Stirling, the Ericsson and the reciprocating Carnot cycle, the finite-time optimum specific work output at maximum power, (wopt), is exactly half of that obtained for infinite-time reversible cycles (Carnot work, wrev) operating between the same temperature limits (i.e., wopt=½wrev). To accomplish this, the analysis makes use of time symmetry to minimize overall cycle time and to thus optimize net cycle power. Based on linear heat transfer laws, the expression for optimum specific work is shown to be independent of heat conductances. Moreover, this optimum specific work output is the same expression for all of the members of this family of cycles. This analysis makes use of the ideal gas model with constant specific heats, though the results are shown to be universal for the Carnot cycle for vapours and real gases. A sample calculation is given which shows that while operating under the same optimized conditions, the endoreversible Stirling engine will have the same thermal efficiency as the endoreversible Ericsson, but will have a higher optimum power output. The optimum power of the reciprocating endoreversible Carnot engine will be superior to both. Copyright © 1999 John Wiley & Sons, Ltd.