Direct integration method API520, 2008

[rbel038]

Hi,

I want to follow Annex B eqn (B.2) and use a direct integration of the isentropic nozzle formula to work out the max flow through a bursting disc orifice.

I understand that the terms come from an isentropic flash at each 'pressure step' through the burst disc but what i dont get is how you know the condition at the throat (v_t , specific volume) somewhere inbetween upstream condition and vena contracta?.

some clarification on this and any advice would be appreciated. If i wanted to also model the process insethalpically the same equation applies? Ie: the properites for each step come from isenthalpic flash instead of isentropic.

Many thanks

 

[TD2K]

You don't need to know the P and T at the throat. You simply do a series of isentropic flashes in small pressure steps ( I just do it from starting pressure to atmospheric) and then calculate the integral which is turn gives you a mass flux rate. The highest mass flux rate along with a Kd gives you the required area.

 

[apetri]

I would recommend this thread,

http://eng-tips.com/viewthread.cfm?qid=329093

it includes an Excel page which does the work,
as commented by TD2K the procedure described in API solves a series of isentropic or isenthalpic flash operations,
Prode has also a different method to solve the HEM model plus HNE , NHNE etc.

 

[rbel038]

Thanks for the replys, the API formula finds the maximum mass flux by dividing the integral by 'vt' the specific volume at the throat condition. My first problem was that i thought this was being integrated too... until i opened my eyes and read the formula correctly. I havent gone back to the problem yet but im still unsure following API's formula how you are supposed to find 'vt'

I am building a calc that uses several models to produce an envelope for discharge reaction force. So its still worthwhile understanding the API formula for me.

 

[apetri]

in the suggested thread you'll find the equation

Hin+Vin^2=Hout+Vout^2

with Hin, Vin, Hout, Vout fluid enthalpy and speed
which is the basis of the method,
I utilize the same procedure as that included in the Excel page (which does use Prode Properties for isentropic flash, enthalpy and volume)
the method takes in account the contribute of Vout (Vin is normally not included being very low compared to Vout)

 

[Latexman]

I don't fully understand why a direct integration of the isentropic nozzle formula would be used to model a pipe with a rupture disk in it. I think the isothermal or adiabatic pipe flow model (with an appropriate, certified K_RD) would be a better choice. Anyone else think this?

Good luck,
Latexman

 

[apetri]

Latexman, it was the original request,
API 520 annex B includes discussion of direct integration procedure which one can solve as shown.
There are several alternatives, for example one could estimate critical mass flow in a specified section (Prode has a rigorous method to calculate speed of sound in gas, liquid and two-phase fluids with HEM methodology) then introduce some correction.