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Discharge of Pressure Vessel into Pipe with Regulator

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Old   October 31, 2015, 19:57
Default Discharge of Pressure Vessel into Pipe with Regulator
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Filip Gajowniczek
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Hello forum,

I am attempting to model a transient system in which a charged pressure vessel (gas cylinder) discharges into a pipe system. The gas leaves the gas cylinder and enters a pressure regulator; the gas exits the pressure regulator into a long pipe in which heat transfer and friction effects are significant.

I am attempting to split the model into two parts. First the discharge of the vessel into the pressure regulator, and later into the pipe downstream of the regulator.

From my review of literature, I have found that the isentropic nozzle relations are applicable to the discharge of most pressure vessels. However, I wanted to study the transient effects of the flow and therefore do not want to assume a constant mass flow rate out of the cylinder. Instead I would like to use discrete time steps and assume the mass flow rate is constant during these time steps.

I have been able to locate solutions to volume averaged parameters of the gas in the pressure vessel which are derived from the balance of energy of both the pressure vessel walls and the gas itself. I was planning on using these solutions (which require some numerical integration) in order to determine the temperature, pressure, and density of the gas at the outlet of the pressure vessel.

However, I am getting confused by how to handle the pressure at the outlet. Normally, this pressure is constant (and usually atmospheric); however, i would expect the pressure at the outlet of the container to decrease as the pressure within the gas cylinder itself decreases.

My current idea is to assume that the pressure at the outlet of the regulator is constant and known. I would treat the throttling process occuring in the regulator as isenthalpic. Using the conservation of total enthalpy I could "guess" the pressure upstream of the regulator, and use this pressure in the calculation of the mass flow rate leaving the vessel according to the isentropic nozzle relations. I would repeat this iteratively until the guessed pressure produced a mass flow rate (from which a gas velocity entering the pressure regulator could be calculated) would produce an accurate solution to the conservation of enthalpy in the regulator.

Can somebody tell me the validity of the approach I have described, or even some good literature to read on this topic. Any help would be greatly appreciated.

Cheers,
Filip Gajowniczek
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