Evaluation of Polytropic Calculation Methods for Turbomachinery Performance

Performance calculations for centrifugal compressors have been based on polytropic analysis for many years. The basic polytropic equation, in which head is found from gas pressure, temperature, and compressibility factor at the end points of compression, is applied by virtually all engineers involved with turbomachinery design, selection, or operation. The problems and errors associated with this simple calculation method when applied to nonideal gases have long been recognized. Schultz [1] proposed a correction factor to the head equation to compensate for the errors. This “polytropic head factor” correction is required by the ASME Power Test Code 10 [2] for the evaluation of compressor performance. Recently, the accuracy of even the corrected head equation has been questioned for the compression of gases to high pressures and an alternative calculation method has been proposed by Mallen and Saville [3]. Although differences were found between their method and the Schultz method of up to three percent, they did not show which method was more accurate. This paper evaluates the accuracy of these previous calculation methods and shows that both have errors for some compression calculations. In addition, a new polytropic calculation method is described and is shown to be substantially more accurate than the methods of both [1] and [3], thus allowing more precise evaluations of compressor performance.