Steam system PSV sonic flow

[wilfully12]

All

I have a situation at the moment. I have a steam system with a seemingly undersized tailpipe - the flow will go critical / sonic. The relief is to atmosphere as it is steam.

The question is, where will the flow go sonic? My understanding is that on the initial release of the PSV into an empty tailpipe the flow will be sonic. As the back pressure builds up the "sonic" point will move downstream in the pipeline. I would expect the sonic point to be at the release point (i.e. atmosphere). I am very confused at the moment by the dynamics of the system.

The PSV goes into a short (1m) 6" line, an elbow, then expands into a 5m 8" line. Is it possible the flow could be sonic at two points, i.e. the 6" line and at atmosphere?

Cheers

 

[wilfully12]

Also the concept of a "pressure discontinuity" is exercising me, but I gather in a sonic system there will likely be one at the tip (along with a lot of noise!)

 

[zdas04]

The flow will be sonic at the point that the pressure doownstream of a restriction is at or below the critical pressure:

P(crit)=P(upstream)*(2/(k+1))^(k/(k-1))

You have to solve this sort of problem iteratively. First, assume that the dP down your tail pipe is insignificant. Get a flow rate through the PSV at sonic velocity. Then calculate the friction drop at that velocity in your tail pipe (I do that by solving the AGA equation for Upstream pressure and putting in sonic rate and atmospheric downstream). If the upstream pressure is greater than P(crit), then you are not getting sonic flow through the PSV and you are not getting the flow through the PSV you've designed for.

Here's where it gets interesting. If the upstream pressure in the pipe is less than P(crit) then the pressure at the downstream side of the PSV is equal to P(crit). Now the dP down the pipe results in a pressure at the exit pipe that has its own P(crit)--if that is lower than atmospheric pressure, the exhaust can be a second sonic stream. In fact, you could have a third sonic stream at the change in pipe diameter.

The key to this calculation is that as long as the downstream pressure is less than or equal to P(crit) then the sonic stream at the exit is exactly at P(crit). That pressure drops rapidly as you move away from the exit as the high-velocity stream does work pushing static gases out of the way.

David