Case Study – Discharge of a Pressure Vessel
The challenge
An engineering company manufactures pressure vessels that contain gas at high
pressure. The company would like to be able to calculate the time taken for a
pressure vessel to discharge its contents once the end valve is opened.
Pressure vessel
The solution
The time taken for a pressure vessel to discharge its contents can be calculated
very accurately with some simple mathematical modelling, without the need for a
complex simulation involving computational fluid dynamics (CFD).
Atkinson Science created a Windows application which calculates the fall in gas
pressure in a pressure vessel against time until the gas pressure is equal to the
external pressure (usually the atmospheric pressure). The application is based on
simple thermodynamic theory involving isentropic flow of a perfect gas. It can be
applied to any gas by specifiying two known thermodynamic properties of the gas.
The rate of discharge depends on whether there is heat transfer through the vessel
wall to the gas during the discharge. If the discharge is very rapid then there
will be little time for heat transfer to occur and the temperature in the pressure
vessel will fall. In this case the user can specify no heat transfer in the
Windows application. If the discharge is very slow then the temperature in the
pressure vessel will remain close to the external temperature because of heat
transfer through the vessel wall. In this case the user can specify constant gas
temperature in the Windows application.
In most cases the pressure in the vessel will be so high that the flow through the
valve will reach sonic speed when the valve is opened and the flow will choke
(the rate of flow will be independent of the external pressure). When the gas
pressure has dropped sufficiently the flow will unchoke. The Windows application
calculates the fall in pressure from when the value is opened to when the gas
pressure equals the external pressure, taking into account the change from choked
flow to unchoked flow.
In the figure below the Windows application has been set up to calculate the time
taken for a pressure vessel of 0.05 cubic metres containing compressed air at
10 bar to discharge fully to the atmosphere through a valve of diameter 5 mm. The
discharge is so rapid that heat transfer to the vessel can be ignored. One can
see that the discharge is complete after 27 seconds.
Windows application
The benefits
The engineering company now has software that is inexpensive and easy to use that
enables it to calculate the time taken for its range of pressure vessels to
discharge fully when the end valve is opened. The software can be applied to
any gas, given two known thermodynamic properties of the gas.
Try our free-to-use
web version of the Pressure Vessel Windows application.