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Supersonic vs Subsonic

05/31/2012 12:33 PM

I'm having trouble trying to model what's going on in a gas system.

The system: a 10" piping with natural gas is flowing (intermittently) into a blowdown silencer (9 ft in diameter). Immediately before the blowdown silencer is a restriction orifice. The gas upstream is at 1200 psig and we expect a 600 psi pressure drop across the restriction orifice. The blowdown silencer is open to atmosphere so the back pressure is 15 psia.

What I need: I have to calculate the force exerted on the back wall of the blowdown silencer in order to design the foundations, anchor bolts, etc.

I know the force would be the same as the thrust force, but what I'm having trouble with (since I have to use old knowledge that hasn't been accessed in many years) is finding the velocity and density of the gas when it hits the wall.

I'd appreciate some good suggestions on how to model this...would the system go sonic at the orifice and then supersonic after followed by some shock waves to bring it down to subsonic? Or should I set a normal shock wave at the exit plane to make it easier to calculate. Or is there any reason to believe it would go supersonic?

Any other good ideas would help too. Just trying to gather some knowledge from a large group.

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Guru

Join Date: Jul 2005
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#1

Re: Supersonic vs Subsonic

05/31/2012 3:18 PM

Somebody appears to have put some thought into it, as the orifice ΔP is given as 600 psi, ~ upstream pressure x (1 - rc) where rc = critical pressure ratio, ~ 0.5. Whereas upstream minus downstream pressure ~ 1200 psi.

Velocity in the orifice is sonic ~ 330 m/s (actual velocity, at 600 psi). You need the orifice dia to work out mass flow etc. It won't go supersonic anywhere. To achieve that you'd need a converging section down to the throat, followed by diverging.

But why do you think there are any net forces on the silencer foundations? Isn't the 10" pipe flanged to the silencer? If so any force on the silencer due to gas hitting it just causes stress in the steel.

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#2

Re: Supersonic vs Subsonic

05/31/2012 3:30 PM

I'm working with the process group to get that mass flow rate. I think the orifice diameter will be 0.25 times the pipe diameter.

"To achieve that you'd need a converging section down to the throat, followed by diverging."

What you describe here is what's confusing me. I understand that with just pipe, we can only get up to sonic velocity. The choked area of the restriction orifice ensures that. However, there are sudden expansions in area immediately after the orifice plate (going from 2.5" diameter to 10" diameter) and then immediately exiting the nozzle into the blowdown silencer (10" diameter to 9' diameter). This isn't the same as a diverging nozzle?

To answer your last questions, these calculations are to help the civil design of this new silencer. The gas will exert a force on the back side of the silencer which will in turn create shear stress and bending or axial stresses in the anchor bolts. I'm trying to see how much stress it will exert. I have no experience with this before so it might be significant or it might be negligible.

Thanks for the input!

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#3

Re: Supersonic vs Subsonic

05/31/2012 4:26 PM

Not my field but the front face of the silencer has the same area as the back face less the area of the 10" pipe, only a slight difference. The velocity in the silencer is low so the kinetic energy of the gas is low.

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#4

Re: Supersonic vs Subsonic

05/31/2012 4:30 PM

The velocity of the gas coming out of the pipe will be very high. I'm hoping sonic or less because then it's easy to calculate.

I think for a first run, I'll calculate it using sonic velocities at the cross sectional area of the pipe. Hopefully this gives reasonable numbers.

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#5

Re: Supersonic vs Subsonic

05/31/2012 5:01 PM

With an orifice there is sonic velocity in the throat if the downstream pressure is < ~ 0.5 x upstream pressure, then the velocity dissipates downstream of the orifice. If there is a converging section down to the throat, followed by a properly designed diverging section, can go supersonic in the diverging section. The mass flow does not increase, but as the gas flows through the diverging section, although the area is increasing (which you would expect to cause a fall in velocity) the gas density falls even faster, so the velocity increases. That's why jet engines for supersonic flight have a diverging exhaust duct. To answer your question, immediately exiting the nozzle (or orifice) into a larger pipe isn't the same as a diverging nozzle, and won't give supersonic flow.

I'm not sure whether an orifice immediately followed by a diverging section (in other words a sharp entry straight into a diverging cone) would go supersonic, but you're not trying to do that.

I still think the forces will be internal in the steel, trying to stretch the pipe away from the silencer, as pipe pushes backwards in reaction to the gas flowing out, and the silencer pushes the other way as the gas flow impinges on it.

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#6

Re: Supersonic vs Subsonic

05/31/2012 5:08 PM

Thanks for the input. You're probably right...it's a worst case scenario assuming it the way I am. The pipe will absorb some of the reaction forces thus making my stresses on the foundation smaller. When I get process input I'll run the calculations and see what comes out.

Thanks again...I don't remember ever covering an immediate change in area in my gas dynamics course. It was always a converging or diverging cone where we typically ignored the length it took to make the area change.

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#7

Re: Supersonic vs Subsonic

06/01/2012 1:10 AM

As soon as the gas leaves the orifice, it will go to atmospheric, so it will be moving away from the orifice essentially vertically as much as horizontally. Calculate the velocity of the volume of gas in the 10 inch pipe and you are there.

The silencer is larger diameter but the baffles that it uses for the muffling action will see essentially the 10" pipe velocity.

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#8

Re: Supersonic vs Subsonic

06/01/2012 3:56 AM

Consider the implications of the orifice being absent due to some unforeseen reason. If the equipment needs to be designed for 1200psig instead of 600psig in this case, make it so.

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#9

Re: Supersonic vs Subsonic

06/01/2012 6:37 AM

Not sure how the orifice could go AWOL, but when it is in place, 600 psi is not the actual downstream pressure, which the silencer must be designed for. It's the effective downstream pressure at sonic orifice flow, used to calculate orifice ΔP and hence flowrate.

OP has said the silencer is open to atmosphere, downstream pressure 15 psia. It might be a bit higher due to headloss in the silencer.

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#10

Re: Supersonic vs Subsonic

08/28/2012 9:38 PM

Sorry Cingold for the late reply. I marked the thread as "of interest" but could not contribute at the time.

Reading through all comments I have some thoughts I want to share:

1. if you only rest the pipe on the foundation but don't lock it in there will be less stress on the foundation bolts and most stress goes onto the pipe. Basically you have to design the system as such that the Pipe can be closed off and pipe does not break.

2. When I say don't lock it that means let the pipe be able to move inside a bracket or so. Reason is that you might get bending forces in the pipe which would try to escape the "grip" similar to a garden hose that rattles loose from your hand. This will put some stress on your bolts. Be aware of some upwards lift that might occur.

Sorry I think the last one is the hardest to calculate, but probably also the least prominent force.

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