How much will flow through a pipe that is choked at the downstream end

[Shaheryar]

Hello all,

I am going to state my problem and my solution as well. I would appreciate comments, criticism from the members.
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I am working with a blowdown pipe open to atmosphere at the downstream end. The flow is 2-phase. I was originally trying to size the line based on 0.8 Mach at the tip and the resulting size was not very economical.

As a result of internal discussions I have the green light to revise the sizing for sonic flow at the end. Once the flow is sonic at the end, the tip of the pipe just before it discharges to atmosphere can have high pressure than atmospheric pressure since the choked condition at the tip will hold back pressure (whatever is left over from the starting pressure minus frictional loss).

I am using software (FALRENET) to calculate the end pressure. It tells me that the flow is choked and the Mach number is "one" and gives the pressure at the tip. For my peace of mind I would like to confirm that the required flow rate will actually flow across the choked point i.e. from the tip of the pipe to atmosphere.

To do this, my strategy is to consider this situation similar to the situation encountered across a PSV where the inlet is usually very high pressure and the outlet is low pressure and the flow is commonly choked across the PSV. API-520 provides an equation (even for 2-phase in Appendix D) for confirming the area required for choked flow scenarios. I think that by using the same equation and using the Pipe ID for the flow area I can confirm by a hand calculation that the required flow will actually go through the choking point.

Your feedback will be appreciated.

Thank you.

 

[BigInch]

Probably a reasonable check method.

You should be using a diffuser on the end to slow the velocity down and eliminate some of that noise you're going to make using sonic velocities to air.

Going the Big Inch!

http://virtualpipeline.spaces.msn.com

 

[sailoday28]

I am not familiar with your nomenclature. What is the relation between tip of the pipe and pipe exit? Is the tip the exit plane?
The following should also be answered:
Is there heat transfer (or the flow adiabatic)?

What is the fluid?

Are you assuming homogeneous flow?

How is friction factor determined?

Since you are at high Mach Numbers, how is sound speed calculated?


It would also be of interest to know the piping configuration and source conditions.

Regards

 

[davefitz]

If the flow was single phase steam, then the solution would be straightforward . For a constant area pipe with negligible heat transfer, then the equations to be used are the Fanno relationships. One version of the Fanno curves is an abbreviated set included in the ASME section VIII div 2 relief valve vent sizing appendix. For longer pipes ( larger fL/d) then the full Fanno equations should be iteratively solved.

Since you stated the flow is 2 phase, the situation is trickier. As I recall, the older ASME steam tables ( printed, McClintock + Sylvestri) had a chart in the back for choked 2 phase flow though pipes , mass flow vs h vs P. Correlating that to fL/d upstream of the exhaust would probably require iterative calculation.