Modeling Compressible Air Flow In A Charging Or Discharging Vessel And Assessment Of Polytropic Exponent

In this work, the classic problem of charging and discharging of a pressurized tank is studied. This experiment allows students to gain a deeper understanding of polytropic processes and compressible flows. The experiment apparatus described in this study allows for direct measurement of the pressure and temperature within the tank, and utilizes a LabView based computerized data acquisition system. To assure accurate measurements of these parameters, a fast-response thermocouple and a high accuracy variable reluctance pressure transducer is employed. A model was developed to predict the pressure and temperature of the air in the tank during charging and discharging. The model incorporates compressible flow in both sonic and subsonic flow regimes, and models the air as undergoing a general polytropic process. The model was compared with experimental data to empirically determine the polytropic exponent. The values of polytropic exponent obtained through the phenomenological model were compared to those determined by a graphical technique to determine to polytropic exponent. Results show that the polytropic exponent varies with initial pressure and throat area, as well as with time. Thus a constant value for polytropic exponent generally yields an unsatisfactory prediction for temperature and pressure. It is found that a discharge coefficient must be included in the analysis to accurately match the data, due to frictional effects through the throat. Further, the experiment also indicates that heat transfer through the vessel walls plays a major role in the process.