Compressible flow through a pipe into a vessel under a vacuum

[tmengineer]

Hello,

I am designing a vent system (atmospheric air flowing though a pipe + vent into the tank) to relieve the under-pressure caused from quickly cooling a tank at 85 deg C to 10 deg C (due to a CIP process).

I have calculated using crude thermodynamics that the maximum volumetric flow rate required to relieve the tank is 4.7 m^3/s. (The assumptions used in this calculation will slightly overestimate the flow rate, but not by a significant amount)

I then used the methodology in Perry's Chemical Engineer's handbook 8th Ed p6-23 "Adiabatic Frictionless nozzle flow" to calculate the that the flow through the nozzle as 3.218m^3/s given the T, P and k of my gas for an 8" nozzle (corresponding to a Mach number of 0.197)

I then used the methodology in Perry's p6-24 "Adiabatic flow with friction in a duct of constant cross section" to calculate the volumetric flow through an 8" pipe, 10m long with 1 elbow. In this calculation the volumetric flow rate calculated is 1.430m^3/s. The volumetric flow rate that corresponds to mach number = 1 in the pipe is 8.618 m^3/s.

I'm having trouble putting these three pieces of information together.

Does this mean that the volumetric flow through the pipe that was calculated is the maximum value and so will restrict the flow into the vessel (as v(pipe) < v(nozzle) < v(required)? The tanks are already using this system and they are working fine, this is simply a back calculation to justify why they're in use.

Any feedback would be greatly appreciated!

 

[hacksaw]

The 8.618 m^3/s is a limiting flow condition that occurs when sonic flow conditions are reached at the discharge into your tank, if there is enough pressure drop to support it. Perry's will inform you of the critical pressure drop required.

3.218m^3/s flow is associated with fluid velocities 62.7 m/s with line losses quickly rising with flow

 

[LittleInch]

If you are worried about your tank collapsing, the primary piece of information you need to use is the max negative differential pressure the tank can stand (often not many millibars). Then you work out whether your pipe / nozzle can supply it. An 8" nozzle and pipe will almost certainly not be able to handle this sort of volume.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[Latexman]

Just curius, why do you think you need to use compressible flow? Or, why isn't an incompressible flow model good enough? It comes down to what LittleInch talked about, which establishes what the max. [&Delta;]P is for this problem.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[LittleInch]

See this post.

http://www.eng-tips.com/viewthread.cfm?qid=359136

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[tmengineer]

Thank you for the replies!

Oh sorry, I should have said: I've used Finglow (Engineering software that uses the ASME VIII equations) to calculate that the maximum under-pressure that the tank can withstand is 0.011MPa. From my crude thermodynamics the maximum under-pressure that the vessel is subjected to is 0.00283 MPa. Does this mean that the tank will always be able to sustain the pressure? If there was no vacuum relief then would there be some long term mechanical damage to the tank being subjected to this?

I think there will be two failure modes for the flow into the tank.

1) Where the flow into the tank reaches Mach 1 and causes shockwaves as it expands through the nozzle

2) Where the flow into the tank is too slow such that it does not relieve the under pressure fast enough and then then tank implodes.

I am happy with failure mode number (1) and understand that part ok I think. What I can't determine is under what conditions with failure mode (2) occur. At the minute the pipe is 10m long with one elbow but I'd like to use this same methodology on a tank with a 25m pipe and 3 elbows - eventually the pipe will become so restricting that failure mode (2) comes into effect.

@Latexman: the calculations that I have been doing are from compressible flow scenarios and methodologies because air is flowing into the tank. Would the use of an incompressible flow model be appropriate?

 

[hacksaw]

you have to start with the tank design data and the actual process operating conditions it is subjected. You also have to decide what standards you are tasked to use

at bit puzzled by your concerns yet no mention of manditory vacuum relief required by the tank design

 

[LittleInch]

I get 1.97 sm3/sec for a free vent.

For a differential pressure of 0.1 bar, it sounds about right.

At small changes in pressure incompressible flow is a valid assumption.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[Latexman]

[&Delta;]P/P'₁ = 11,000 Pa/101,325 Pa = 0.11

Basically, the design flow must be far less than Mach 1 or the tank will implode. I recommend your design [&Delta;]P/P'₁ be conservatively < 0.11

In that case, incompressible methods will be fine.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[davefitz]

The technical search term to use is "Fanno Flow" for compressible flow of gases thru a constant area pipe, with mach 1 flow at the discharge. The sum (fL/d) for the pipe straight length, elbows, valves ,tees, etc needs to be accurately computed to ensure correct prediction of the acoustically choked flow.

"Whom the gods would destroy, they first make mad "

 

[Latexman]

Dave, as usual, you are correct, but if the OP uses that in this case, he could be setting the plant up to suck in the tank.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.