Supersonic Velocity in Flare Line

[Ninja1980]

If we consider a PSV as a converging diverging nozzle with sonic velocity in the throat and the outlet pressure being lower than the throat pressure, is it possible to experience supersonic velocities in the outlet line? I.e. in the same way as a Laval Nozzle.

This question has been bugging me for some time.

Thanks

 

[Latexman]

It is common practice to model a safety valve as a flow nozzle, which is a converging nozzle, not a converging-diverging nozzle. Take a look at this FAQ: faq1203-1293

Good luck,
Latexman

 

[hacksaw]

sonic conditions can indeed occur in the vent line. real possibility in hp pipeline psv's and hp steam psv's

 

[hfgnick]

My understanding is this. Sonic velocity can develop and will develop in the throat of the nozzle if the downstream pressure in the pipe is less than the critical sonic pressure of about 0.5 times the pressure upstream of the relief valve. A relief valve is not a converging-diverging nozzle but only a converging. The pressure in the pipe immediately downstream of the relief valve is dependent on and due to the friction loss in the pipe from the relief valve at pipe inlet to the pipe exit for the give flow. If below critical pressure then sonic velocity and flow will develop in the throat, if above then sonic velocity and critical pressure will not develop in the throat. If sonic flow and critical pressure develops then the flow will try to increase past the relief valve in the pipe since it is entering a larger area pipe and expanding. However since the pipe is an imperfect diverging nozzle there will be tremendous loss of energy due to internal fluid friction that will reduce the flow to sonic and pressure to the pressure at the inlet of the pipe. In addition flow cannot reach sonic in a pipe but only at the exit of the pipe based on the subsonic and supersonic frictional equations, ie, if flow is below sonic then friction pressure drop causes velocity to increase, if above sonic then friction pressure drop causes velocity to decrease. Therefore only place sonic velocity can exist in a pipe is at the exit (or connection to a larger pipe).

 

[hfgnick]

I meant to say in the response that the loss of energy due to internal fluid friction would reduce to flow to subsonic at the inlet of the pipe (not sonic).

 

[hacksaw]

I stand corrected, sonic at the discharge inless there are diameter changes or restrictions in the discharge pipe

 

[Ninja1980]

Latexman - As most PSVs have an outlet larger than the inlet pipework, they could be thought of as a very crude converging-diverging nozzle.

As hfgnick pointed out:

"However since the pipe is an imperfect diverging nozzle there will be tremendous loss of energy due to internal fluid friction that will reduce the flow to sonic"

I tend to agree with this statement, thanks for your input.

 

[Latexman]

Ninja1980 - not really, it's much closer to a 3 dimensional sudden expansion. The nozzle diameter of a PSV is even less than the inlet connection. At full disk lift, the flow comes to the end of the nozzle, turns 90 degrees and flows radially out because the disk is overhead. Then, the flow from 360 degrees around the nozzle/disk area gathers on it's way to the discharge. This is a very turbulent, chaotic flow pattern. This is not even close to the gently diverging boundary of a Laval nozzle that creates streamline flow that does not separate from the boundary and create turbulence and vortices.

Good luck,
Latexman

 

[sailoday28]

Should any portion of the nozzle orifice have a diverging area downstream of the minimum area, there will be a supersonic flow if choking had occured. With supersonic flow, depending on how the downstream area changes, it is highly likely that a shock will occur, Pressure downstream of the shock can be higher than the critical pressure at the nozzle throat.