12 replies to this topic

[jerald04]

Dear all,

I am currently evaluating some existing steam PRVs which are vented to the atmosphere via an open pipe. One puzzling fact I noticed after I did some calculations to the tail pipe is that these outlet pipings of steam PRVs (which are vented to the atmosphere) will achieve Mach No. more than 1 (i.e. supersonic) when I use the PRV's RATED capacity and the existing open pipe diameter.

My question is: Is it theoretically possible for the PRV's outlet piping to reach more than mach no 1 during relieving?

Or

will the outlet pipe get choked at mach no.1, hence restricting the actual relieving capacity of the PRV?

The open pipe connected to the PRV outlet is about 7 meters long.


Meanwhile, I tried searching around books to find out more on compressible flow behaviour, and I found one interesting explanation from C&R Chem. Eng. Vol. 1, Chapter 4, Section 4.5:

"Unlike the orifice or nozzle, the pipeline maintains the area of flow constant and equal
to its cross-sectional area. There is no possibility therefore of the gas expanding laterally.
Supersonic flow conditions can be reached in pipeline installations in a manner similar
to that encountered in flow through a nozzle, but not within the pipe itself unless the
gas enters the pipe at a supersonic velocity."


From the above paragraph, I am interpreting that it is possible for PRV discharge outlet to achieve supersonic flow condition (Mach > 1) because sonic flow conditions are created through the PRV's orifice. Whereas if a compressible fluid started off as a sub-sonic flow in a pipe, it will never be able to reach supersonic flow conditions no matter how much dP is provided along the pipe, as it will get choked at sonic condition (M = 1).

Greatly appreciate replies and comments to my question/ interpretation.

[fallah]

Supersonic velocity can be atained in the diverging part of a properly designed converging/diverging nozzle.

In my opinion, supersonic flow can not be achieved in the PSV discharge outlet (due to constant cross section), and if PSV back pressure would be such that sonic flow could be achieved, then without tail pipe the sonic flow is atained just at PSV outlet. With the mentioned condition (possibility of having sonic flow at PSV nozzle outlet) if there is tail pipe the mass rate of flow decreases such that the sonic velocity obtained at end of tail pipe.

[latexman]

PRVs are modelled as a converging nozzle only. Without a diverging section between the converging nozzle (PRV) and the outlet pipe, it will be impossible to attain supersonic flow. It is common to have sonic flow at the nozzle exit and/or the tailpipe exit.

[JoeWong]

I guess no one PRV can attain supersonic flow and i don't see reason behind having supersonic flow in PRV...

It is impossible to attain supersonic flow in discharge pipe . Sonic flow is possible in discharge piping. Mass flow may increase with increase backpressure in the PRV tail pipe.

When sonic flow occur in discharge piping, you shall ensure the maximum flow (with correspondent backpressure) is lower than relief flow.

If the maximum flow is lower than rated flow (based on certain backpressure), calculation of PRV capacity and maximum flow in the discharge (under sonic flow) shall be checked thoroughly to avoid flow limitation...Also check with PRV vendor the potential of chattering...

Noise and vibration at sonic flow (especially present of intensified dynamic strain in pipe expose to sonic flow) shall take extra care...

Hope this post helps...
Is PSV tail pipe & lateral at CHOKED (Mach no = 1) Accpetable ?

[fallah]

Mass flow may increase with increase backpressure in the PRV tail pipe.

In my opinion with fixed upstream pressure,mass flow decreases with increase backpressure in the PRV tail pipe.

When sonic flow occur in discharge piping, you shall ensure the maximum flow (with correspondent backpressure) is lower than relief flow.

Maximum flow is attained when sonic flow occurs in discharge piping.With fixed backpressure relief flow would be equal to/lower than maximum flow.
May you clarify if you think i am not on right track?

[JoeWong]

Mass flow may increase with increase backpressure in the PRV tail pipe.

In my opinion with fixed upstream pressure,mass flow decreases with increase backpressure in the PRV tail pipe.

When sonic flow occur in discharge piping, you shall ensure the maximum flow (with correspondent backpressure) is lower than relief flow.

Maximum flow is attained when sonic flow occurs in discharge piping.With fixed backpressure relief flow would be equal to/lower than maximum flow.
May you clarify if you think i am not on right track?

PRV outlet backpressure will increase with flow. Once the tail pipe attacin sonic flow with particular backpressure and mass flow, higher mass flow will be attained with higher backpressure. This backpressure shall always be checked to ensure it does not affect the PRV relief capability.

[fallah]

[/quote]
Once the tail pipe attacin sonic flow with particular backpressure and mass flow, higher mass flow will be attained with higher backpressure.
[/quote]

Attached you will find part of useful explanation (sent by your website) nearly about the subject of our discussion,and may clarify the issue.

Attached Files

•  R_O_Phenomenons.pdf   35.5KB   97 downloads

[JoeWong]

Once the tail pipe attacin sonic flow with particular backpressure and mass flow, higher mass flow will be attained with higher backpressure.

Attached you will find part of useful explanation (sent by your website) nearly about the subject of our discussion,and may clarify the issue.

This article is related to RO (or PRV nozzle) with fixed upstream pressure, once downstream cross the critical pressure will lead to flow reduction.

I am referring to tail pipe with outlet pressure stay as ATM. The backpressure mean the tail pipe inlet pressure (PRV outlet) increase with mass flow.

[fallah]

This article is related to RO (or PRV nozzle) with fixed upstream pressure, once downstream cross the critical pressure will lead to flow reduction.

I am referring to tail pipe with outlet pressure stay as ATM. The backpressure mean the tail pipe inlet pressure (PRV outlet) increase with mass flow.

Seems you are discussing about variable upstream pressure and nonchocked flow condition....

If pressure in end of tail pipe (not surrounding) stay as ATM we are not faced with chocked flow,and obviously, with increasing DP around PSV (in nonchocked flow area) mass flow increases along with increasing in PSV back pressure (in PSV outlet) due to increasing in friction loss.

[JoeWong]

This article is related to RO (or PRV nozzle) with fixed upstream pressure, once downstream cross the critical pressure will lead to flow reduction.

I am referring to tail pipe with outlet pressure stay as ATM. The backpressure mean the tail pipe inlet pressure (PRV outlet) increase with mass flow.

Seems you are discussing about variable upstream pressure and nonchocked flow condition....

If pressure in end of tail pipe (not surrounding) stay as ATM we are not faced with chocked flow,and obviously, with increasing DP around PSV (in nonchocked flow area) mass flow increases along with increasing in PSV back pressure (in PSV outlet) due to increasing in friction loss.

Fallah,


I suggest you to model a PRV with tail pipe (make the tail pipe a bit long to see the effect) discharge to surrounding with pressure of 0f 101325 Pa (so called ATM) using FLARENET. Progressively increase mass flow until tail pipe see sonic flow. Then continue to increase the flow and check the pressure downstream of PRV. Then you will understand what i try to mean.

[fallah]

Fallah,

I suggest you to model a PRV with tail pipe (make the tail pipe a bit long to see the effect) discharge to surrounding with pressure of 0f 101325 Pa (so called ATM) using FLARENET. Progressively increase mass flow until tail pipe see sonic flow. Then continue to increase the flow and check the pressure downstream of PRV. Then you will understand what i try to mean.

No need to modelling the PRV.I think,I and you are going on the same track.
What you are saying is based on the concepts specify the nozzles behaviors in the cases of changing their inlet/outlet physical/operational parameters.

Suppose we have a PRV with P1 and P2 as inlet/outlet pressure,respectively,and in this condition its tail pipe see the sonic flow (then P2 would be the Critical Flow Nozzle Pressure) with the specified mass flowrate.

As you know,if we decide to increase the mass flowrate we can not do this with decreasing the downstream pressure (P2),and we have to increase upstream pressure from P1 to P'1.In this condition, Critical Flow Nozzle Pressure would be increased as well from P2 to P'2 according to maintain the critical value of the P1/P2 ratio.
Thus,we can see with increasing the flow by increasing the upstream pressure in sonic flow condition,higher pressure in downstream of PRV would be attained.

[jerald04]

Hi all,

Thank you for your kind inputs to this discussion.

My objectives of the discussion was to find out if it is possible to attain supersonic flow from a PRV outlet. This question came up because I achieve M > 1 while trying to evaluate some existing PRV outlet pipings.

After studying my calculations for a few days, I finally realised what went wrong with my calculations. I used the density of steam at 1kg/cm2A, which gave me a very large velocity value. In actual fact, the relieved steam (even at near the end of the open pipe) still have a slight pressure, which in reality can make a big impact to the velocity value. In other words, the density does vary significantly at different points of the open pipe no matter how short the tail pipe is (which is vented to the atmosphere).

My next question is, how should I go about to estimate the density of steam at various points of the open pipe?

A good idea would be to start off at the end of the tail pipe (just before it is vented to atmosphere). At this end point of the pipe (lets call it P2), there should still be a very slight pressure. Do I determine the pressure at P2 using exit loss?

Now, the tricky part is that to determine the pressure of steam at P2 by using exit loss, we need to have the flow velocity. However, I wouldnt be able to know the velocity without first knowing the density. This becomes a circular calcuation.

Any comments on this? Assume a value first?

[JoeWong]

You need to guess a pressure drop (just upstream exit point) which lead to a pressure, calculate temperature base on isenthalpic. Calculate pressure drop base on line pressure drop equation. If the calculated pressure not same as guessed pressure drop, readjust the guess pressure drop until both match. This only applicable to single section. You need to calculate until the location as you wish...It involve iterative calculations... best to use software i.e. FLARENET, HYSYS, etc to assist you.