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Modeling Compressible Air Flow in a Charging or Discharging Vessel and Assessment of Polytropic Exponent

Abstract

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.

Introduction

The analysis of a pressurized air tank being charged or discharged is one of the most common applications of compressible flow presented in undergraduate fluid mechanics courses. The scenario usually involves an initially pressurized vessel which is suddenly open to a lower outside pressure (such as atmosphere) through a small opening. The goal of this experiment is to predict either the time required to discharge the tank, or the pressure inside the tank, after a specified time. The exercise is useful to students because it is a rather straightforward application of conservation of mass, and introduces the concepts of choked and subsonic flows. Further, the solution integrates aspects of thermodynamics and heat transfer, making for an excellent capstone experiment in thermal sciences.

The most comprehensive solution to the problem is presented by Bober et al.1 They applied conservation of energy to a discharging tank of air to predict the temperature and pressure inside the tank as a function of time. They analyzed both choked-flow and subsonic regimes, and incorporated the heat transfer through the walls of the tank. The authors modeled the flow through the exit nozzle as isentropic, and the heat transfer as natural convection at the inside and outside wall surfaces. They approximated the heat transfer through the wall as quasi- steady-state. In spite of these simplifications, excellent agreement was found between the model and experimental data. However, the solution itself is complicated, involving the application of

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Thorncroft, G., & Patton, J. S., & Gordon, R. (2007, June), Modeling Compressible Air Flow In A Charging Or Discharging Vessel And Assessment Of Polytropic Exponent Paper presented at 2007 Annual Conference & Exposition, Honolulu, Hawaii. 10.18260/1-2--2911