Centrifugal Compressor Polytropic Performance Evaluation: Taher-Evans Methods

Abstract The polytropic compression process is defined as a reversible and non-adiabatic process, in which the ratio of useful compression work to the change of enthalpy remains constant along the polytropic compression path. Unlike an isentropic process, the polytropic process accounts for unavoidable degradation of energy as governed by the second law of thermodynamics. Polytropic efficiency can be very accurately calculated by numerical integration along a defined path or by much less accurate, older polytropic exponent methods in a closed form solution. The Taher-Evans numerical integration methods for the calculation of polytropic performance of centrifugal compressors are based upon a constant efficiency, temperature-entropy polytropic path represented by a mathematical model employing cubic polynomials. In earlier papers published by the authors on Taher-Evans methods, the maximum relative deviation limit used for judging solution certainty of the calculation of the polytropic efficiency and polytropic work was chosen as ≤ 0.001% to show the high accuracy of Taher-Evans methods. The uncertainties associated with the realities of measured test data to determine a fluid’s thermodynamic and thermophysical properties using equations of state, however, may impose constraints on the overall accuracy for the calculation of the polytropic efficiency and the polytropic work in factory or field performance testing of centrifugal compressors in accordance with ASME PTC-10. In this paper, the use of Taher-Evans methods is explained for the factory and field test conditions that are required to achieve a relaxed maximum relative deviation limit ≤ 0.01% for reporting the calculation of the polytropic efficiency and polytropic work. For ASME PTC-10 type 1 and type 2 tests, this paper presents the selection criteria for the maximum number of sequential Taher-Evans cubic polynomial segments needed to achieve target relative deviations of either 0.001% or 0.01%. Example cases confirm that the Taher-Evans cubic polynomial methods yield highly accurate results while requiring fewer computing resources and reducing computing elapsed time compared with other endpoint or multi-step numerical methods. Also, a new relationship with a condensed expression is developed to precisely calculate the real gas polytropic volume exponent at each point along the polytropic path.