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Circulation in Blowdown Flows

The blowdown of high pressure gas in a pressure vessel produces rapid adiabatic cooling of the gas remaining in the vessel. The gas near the wall is warmed by conduction from the wall, producing radial temperature and density gradients that affect the flow, the mass efflux rate and the thermodynamic states of both the outflowing and the contained gas. The resulting buoyancy-driven flow circulates gas through the vessel and reduces, but does not eliminate, these gradients. The purpose of this note is to estimate when blowdown cooling is rapid enough that the gas in the pressure vessel is neither isothermal nor isopycnic, though it remains isobaric. I define a dimensionless number, the buoyancy circulation number BC, that parametrizes these effects.