4 replies to this topic

[fallah]

Dears,

As you know,in the cases that back pressure of a PSV is well below critical flow pressure (Pcf) and discharge pipe terminated to atmosphere (or even into flare header with very large size) ther are two locations where pressure discontinuity (in the form of expanding jet/shock wave,...) might be occured:

-Between outlet plane of the nozzle of the PSV and inlet flange of discharge line

-Discharge pipe exit to atmosphere (or into large size flare header)

During relief, pressure difference between Pcf and superimposed back pressure included two above mentioned pressure discontinuities and pressure drop due to discharge pipe friction.

The question is: regardless of the pressure drop due to friction (could be calculated by specified relief load and pipe size,....) can we realize how much of total pressure discontinuity consumed in each of two above locations?

Any fast input highly appreciated.

Edited by fallah, 19 September 2009 - 06:37 AM.

[fallah]

Dears,

As you know,in the cases that back pressure of a PSV is well below critical flow pressure (Pcf) and discharge pipe terminated to atmosphere (or even into flare header with very large size) ther are two locations where pressure discontinuity (in the form of expanding jet/shock wave,...) might be occured:

-Between outlet plane of the nozzle of the PSV and inlet flange of discharge line

-Discharge pipe exit to atmosphere (or into large size flare header)

During relief, pressure difference between Pcf and superimposed back pressure included two above mentioned pressure discontinuities and pressure drop due to discharge pipe friction.

The question is: regardless of the pressure drop due to friction (could be calculated by specified relief load and pipe size,....) can we realize how much of total pressure discontinuity consumed in each of two above locations?

Any fast input highly appreciated.

Any input?

[jprocess]

Dears,

As you know,in the cases that back pressure of a PSV is well below critical flow pressure (Pcf) and discharge pipe terminated to atmosphere (or even into flare header with very large size) ther are two locations where pressure discontinuity (in the form of expanding jet/shock wave,...) might be occured:

-Between outlet plane of the nozzle of the PSV and inlet flange of discharge line

-Discharge pipe exit to atmosphere (or into large size flare header)

During relief, pressure difference between Pcf and superimposed back pressure included two above mentioned pressure discontinuities and pressure drop due to discharge pipe friction.

The question is: regardless of the pressure drop due to friction (could be calculated by specified relief load and pipe size,....) can we realize how much of total pressure discontinuity consumed in each of two above locations?

Any fast input highly appreciated.

For which applications do you need these info?

[latexman]

fallah,

Sorry for not giving any equations below, but I am not near my copy of Shapiro. I hope you can follow along with your favorite compressible flow book and find the equations you need.

Let us assume flow is indeed chocked at the outlet plane of the PSV nozzle and at the end of the tailpipe. Ironically, the starting point for this problem is at the end of the tailpipe, and one needs to work it backwards. I’ll explain.

If the PSV is on a relatively large vessel, you are in luck; the “stagnation temperature” is equal to the sizing temperature inside the vessel. Remember, the sizing pressure is equal to the set pressure plus the overpressure. The sizing temperature is the coincident temperature of the gas (or vapor) at the sizing pressure. If the vessel is small enough that the superficial gas velocity is significant, you’ll have to calculate the stagnation temperature (this is where your favorite compressible flow book comes in). Recall the stagnation temperature is the temperature which results when you slow the gas adiabatically to zero velocity. For a fixed stagnation temperature, which is what we have in adiabatic flow, all states with the same temperature have the same velocity.

With the stagnation temperature, you can now calculate the temperature at Mach 1 at the end of the tailpipe assuming adiabatic flow (see your book). Then all you need is to find the pressure at the end of the tailpipe which gives the gas the right density at Mach 1 velocity and temperature which equals the mass flow rate of the PSV (w = rho x V x A).

Now we know the discontinuity at the end of the tailpipe; it’s the pressure you just found minus the pressure of the surroundings outside the end of the tailpipe (either atmospheric pressure or the backpressure in the flare header).

Next, calculate the backpressure at the inlet flange of the tailpipe assuming adiabatic flow of the gas through the tailpipe (again, see your book). For the pressure at the outlet plane of the PSV nozzle you do the same thing you did to find pressure at the end of the tailpipe. We know it is at Mach 1 and you already have the temperature for that. So, find the pressure which gives the density at Mach 1 velocity and temperature which equals the mass flow rate of the PSV (w = rho x V x A). Now we know the discontinuity at the PSV nozzle.

[latexman]

fallah,

There is a similar, recent post at Eng-Tips. It is very specific with details, not a general question like yours, but it is essentially on the same subject. Here's a link:

http://www.eng-tips....d=254650&page=1