Investigation of polytropic corrections for the piston-in-cylinder primary standard used in dynamic calibrations of pressure sensors

The increasing demands for more accurate dynamic measurements of pressure in different industrial and scientific applications require the use of sensors with suitable dynamic characteristics. This paper discusses a development of a piston-in-cylinder primary standard for dynamic calibration of pressure sensors. The time-varying pressure generated by a piston-in-cylinder pressure generator can be traceable to measurements of the static pressure and length at the highest and the lowest pulsation frequencies, where the process can be considered as adiabatic and isothermal, respectively. The main limitation of such a dynamic pressure calibrator to provide SI-traceable dynamic calibrations in the transition frequency range of polytropic pulsations is the fact that the value of the polytropic index depends on the degree to which the heat transfers to the surroundings during the generation of the time-varying pressure. In order to investigate the polytropic index, which defines the ratio of the amplitude of the generated relative pressure change to the amplitude of the relative volume change of the gas in the piston-in-cylinder calibrator, the analytical solution in the frequency domain is presented. The analytical solution was derived on the basis of the lumped physical-mathematical model for the gas in the cylinder chamber of the piston-in-cylinder dynamic pressure calibrator. The experimentally obtained polytropic index for the built piston-in-cylinder calibrator confirms the results obtained from the analytical solution. The paper ends with an estimation of the measurement uncertainty related to the polytropic corrections and the time-varying pressure amplitude generated by the developed piston-in-cylinder calibrator.