Pressure at discharge elbow exit of PSV

[Nivrah]

Hi all,
I have got a question pertaining to the equation used in ASME B31.1 Non-mandatory Appendix 2 where it calculates the pressure at discharge elbow exit (P1).
1.Does anyone know where this formula comes from?
2.The ASME code also tells that an alternative method should be used for verification. What other methods are available?
3. If I was working with air as fluid, what equation can I use to calculate the pressure at discharge elbow exit?

thanks a lot

 

[Bill3752]

Nivrah, not 100% sure what you are looking for. I presume you are referring to ASME VIII, Div 1. I believe this is referenced in B31.3.

If what you are looking for is the pressure at the outlet of the RV, then you would need to calculate the back pressure from the RV (or in your case the elbow) to the exit of the relief valve piping. This would be the sum of the builtup dP due to frictional losses, plus the normal back pressure if any (i.e. 0 if to atmosphere).

The frictional loss is function of rate through the piping, diameter, and head loss due to P&F.

I don't know if this helps.

 

[Nivrah]

Bill3752,
the formula in ASME B31.1 appendix 2 calculates the pressure at the elbow exit.See attacched doc.I want to know where this formula comes from. By the way, this formula is valid for steam only.
hence, for my 3rd question, as referred from my first post, I would like to know whether there is an alternative formula if air was the working fluid.
thanks,

 

[mariog123]

I'm afraid I cannot answer to your question; I have no reference on the B31.1 fluid mechanics model- which is specific to steam.
I just suspect V1 is the critical speed- and p1 is a result of that model.

To understand why I think so, I propose you to consider a simplified model as steady state adiabatic flow evolution of a perfect gas,
FROM resting state (p0, density0, T0, enthalpy0, speed=0, sonic speed=a0, enthalpy0)
--->
TO choked state (p*, density*=rho*, T*, speed=critical speed=a*)

Here a* is the critical speed in choked section (where the flow speed equals the "sound" speed at Mach=1) and a0 is the sonic speed for resting fluid.
By similitude with the "well known" expression a0= sqrt(kRT0), we can fix the expression of "critical" speed as a*= sqrt(kRT*).
For perfect gas, there is a simple correlation between T* and T0 based on energy conservation of one dimensional adiabatic evolution:
T*/T0=a*^2/a0^2=2/(k+1)
Again, this is a specif form based on "perfect gas" approach.

If we are able to know/ calculate the mass flow-rate W (lets say by theory combined with experiments, as it is the case for PSVs), we may consider the continuity equation of the steady state flow as
W=rho* A*a* where A* is choked area.
so
rho*=W/( A*a*)
If we are interested to evaluate p*, we can consider the gas state equation
p*= rho* R T*= WRT*/( A*a*)
We can manipulate by math the p* expression as
p*= WkRT*/( kA*a*)= W [a*^2] /(kA*a*)= W a* /(kA*)

Obviously, there is other model more appropriate for steam (as it is that one followed by B31.1) that consider in other way the conservation of energy (based on h0- stagnation enthalpy) for a* evaluation. And for sure, when evaluate p*, their model should be more elaborate than the "perfect gas steady state" approach...

My best regards.

 

[mariog123]

BTW, the same "p" expression can be recovered from a serious work-
Pressure Safety Valve Thrust Forces for Compressible Gas or Vapor Flow, Robert D’Alessandro- Proceedings of the International Symposium on Runaway Reactions and Pressure Relief Design, October 31 to November 2, 2005, Cincinnati, Ohio.

The only "contribution" I had it was to simplify the way leading to that expression, since Mr.D’Alessandro made there a quite sophisticated fluid mechanics model..

regards

 

[Nivrah]

@ mariog 123,
I appreciate your model, in fact:"I just suspect V1 is the critical speed- and p1 is a result of that model."; i guess ASME B31.1 takes it that a worst case scenario would indeed be sonic velocity and its associated pressure at the elbow exit.Hence, a conservative approach has been undertaken by ASME.

Thanks again

 

[psafety]

I hard-pipe discharges in air service and put a half coupling & drain line just after the RV discharge if discharging outdoors. I can't remember seeing a drip pan ell on anything but steam. This is more for the condensing steam as it warms the vent in a relief scenario + rain.

 

[Duwe6]

Believe it or not, your best raincap for anything but steam [needs a drip pan] is a coffee can. That way when the operator hears a PRV blow, he gets immediate visual verification by looking for which pipe is missing the can.

A little 'hillbilly', but a fairly elegant solution.