<p>The polytropic process is a thermodynamic model process, in which the polytropic efficiency remains constant during the process.&nbsp;The polytropic process is a reversible and non-adiabatic process, in which losses associated with the turbomachinery is represented by increasing the entropy that flows in with heat across the surface boundary; and thus, the useful energy degrades.&nbsp;The polytropic path for a specific polytropic efficiency&nbsp;is a unique path, which can be mathematically modeled. In this paper a precise mathematical model for the polytopic process is developed for the first time. The mathematical model can be used to accurately explain the change of thermodynamic states along the polytropic path. Also, using the mathematical model for the polytropic path, derivatives of thermodynamic relationships can be effectively&nbsp;used to interpret difficulty of the compression or expansion applications based on thermodynamic conditions measured at the inlet and discharge nozzles of a compressor or an expander.&nbsp;Using real gas thermodynamic relationships for the polytropic process, the polytropic path can be accurately approximated using sequential cubic polynomials. The use of polynomial approximants can significantly improve the calculation time to accurately approximate the polytropic path and calculate polytropic efficiency and polytropic work associated with a specific compression or expansion application.&nbsp;</p>

Mathematical Modeling of the Polytropic Process Using the Sequential Cubic Polynomial Approximation

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2021/volume/84898

Turbo Expo 2021

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