Advanced Polytropic Efficiency and H-S Diagram Application

Abstract

Abstract The polytropic efficiency is the best quality measure for compressing or expanding engines for compressible fluids. Compressor- and gas-turbine 1D cycle performance simulation methods use it preferably. In steam expanding engine simulation the isentropic efficiency definition is dominating. However, the polytropic efficiency is well applicable for steam expansion based on recent papers of the author [1], [2]. Most applications of polytropic efficiency assume adiabatic change of state. In current turbomachinery, external heat exchange in the blading is often negligible due to short residence time and established external insulations. However, in (historic) reciprocating engines as well as in some current concepts external heat exchange plays an important role forcing to understand this effect as well. This paper aims at understanding the effects of external heat exchange on the polytropic efficiency calculated with a recursive numeric integration algorithm for any finite pressure ratio in expansion. I select as a teaching appliance a historically well-documented reciprocating Uni-(directional)-flow steam engine involving steam condition with condensation (assuming equilibrium). The older reciprocating steam engines (with alternating flow direction in the cylinders) have both internal heat exchange and external heat losses during expansion. “Our” uniflow engine was a considerable historic improvement step including internal heat exchange in a documented manner. This allows demonstrating the features and the interpretation of the polytropic efficiency based on the use of the current IAPWS steam data.