unsteady mass flow calculation

[gio1]

Hello

I am having a hard time with the following problem:

Two vessels full of air at different pressures are connected through an orifice with a tap.

I need to size the orifice so that when the tap is open the pressures equalise after a given time t.

The flow is choked to start with and only after a while the mass flow rate starts to decrease. Any idea on how I could proceed?

Thanks

Gio1

 

[rb1957]

so you know the flow is initially chiked and later it stops being choked. you know the conditions required for choked flow, so when these are no longer achieved you know the flow is not choked. the mass flow rate dictates the change in pressure, and the time taken to achieve equilibrium. so what's the question ?

can you create a connection between the tanks that isn't choked ? (cause this is much simpler to solve) then change the geometry to achive the time you require ??

 

[gio1]

For the sake of simplicity I have assumed uncompressible flow when the choking disappears:

Mass_flow_rate=(Section_Area)x(density)xSQUARE_ROOT((2x(Pressure_drop)/(density))

This calcs is done iteratively with a spreadsheet: at each time step I calculate the mass flow rate, which I then subtract from the mass of gas in the higher pressure vessel and add to the other. This allows to calculate the updated pressures from which I calculate the mass flow rate and so forth.

The problem is that the mass flow rate seems to drop linearly with time and this doesn't look right to me: I would expect an exponential decay with a flattening as the pressures are close to equalising...

 

[rb1957]

agree with you, that doesn't seem intuitive ... but then often aero. problems aren't !

you've got the initial conditions, p1, p2, mdot. each time slice some mass flows from one to the other, redcuing p1, increasing p2 (depending on their respectives volumes), changing mdot ... seems reasonably straight-forward !?