Polytropic Process and Real Gas Behavior in Performance Evaluation of Centrifugal Compressors

The conventional polytropic process model, 𝑝𝑣𝑛̅ = 𝑐̅, often found in thermodynamic textbooks, is inadequate for accurately describing real gases and may lead to contradiction with the second law of thermodynamics. This paper presents an improved approach to evaluation of the polytropic performance of centrifugal compressors using real gas thermodynamic relationships. The solution technique is based upon a constant efficiency, temperature-entropy path represented by Taher-Evans cubic polynomials. Additionally, the Taher-Evans cubic polynomial method is employed to explain the inaccuracies associated with assuming a constant polytropic exponent in the 𝑝𝑣𝑛̅ = 𝑐̅ model, highlighting how this incorrect assumption may violate the second law of thermodynamics.