unsteady mass flow calculation
unsteady mass flow calculation
(OP)
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
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





RE: unsteady mass flow calculation
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 ??
RE: unsteady mass flow calculation
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...
RE: unsteady mass flow calculation
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 !?