Energy Vol. II. No.6. PP. 573-577. 1986 Printed in Gnat Britain. 0360-5442/86 93.COt.00 Q 1986 Pergamon Press Ltd. EXERGY ANALYSIS OF COMPRESSION AND EXPANSION PROCESSES zyxwvutsrqponmlkjihgfedcbaZY SERGIO S. STECCO and GIAMPAOLO MANFRIDA Department of Energetics, University of Florence via S. Marta 3, 50139 Firenze, Italy zyxwvutsrqponmlkjih (Received 4 March 1985) Abstract-The thermodynamics of compression and expansion processes in turbomachinery are examined. Rational efficiencies are defined and their relation to isentropic and polytropic efficiencies are discussed. Multistage turbines with extractions are optimized. This approach yields expressions that are independent of the concept of thermodynamic irreversibility. h k L 2 s T W X enthalpy NOMENCLATURE ratio of constant pressure and constant volume specific heats exergy loss polytropic exponent mass flow specific entropy temperature work steady-flow exergy: X = (h - h,,) - TO(s - s,,) Greek /3 pressure ratio c exponent: t = (k - l)/k nP polytropic efficiency qs isentropic efficiency qx rational efficiency Subscripts compressor referred to j-th stage real turbine reference state of the environment initial thermodynamic state final isentropic thermodynamic state final real thermodynamic state INTRODUCTION It has been stated that energy-related processes require a second-law analysis, if the quality as well as the energy involved are to be evaluated.le3 Some authors have expressed doubts about the significance of extending this type of analysis to compression or expansion tur- bomachines4 thus restricting the benefits of the second-law approach to cycles and thermal or chemical processes. We demonstrate the utility of the second-law approach in the optimization of turbo- machinery. DEFINITIONS OF EFFICIENCY FOR TURBOMACHINERY Compression processes (p > 1) For perfect gases, the isentropic and polytropic efficiencies are vsc = (p’ - I)/[@‘“_‘I’” - I], (1) (2) ‘Iw = mt/(m - 1). For compression, we have 4x < vpc. 573 (3)