Pipe Air Blowing - Exit Velocity of Air

[Marwan1303]

TL;DR

how can we calculate the velocity at which the air escapes the pipeline after the rupture disc blows?

Suppose an isolated pipeline of known dimensions is being filled with air from the atmosphere (via a compressor) to a gauge pressure P1=2barg. A rupture disc at one end of the pipeline blows at this pressure, and the air inside the pressurized pipeline is released to the atmosphere. The rupture disc is the same size as the pipeline (same diameter). Given the P1=2barg, P2=atmospheric pressure, the temperature of the air T=40C, pipe diameter D=12in, and pipe length L=2700m, how can we calculate the velocity at which the air escapes the pipeline after the rupture disc blows?

 

[Baluncore]

Welcome to PF.

Consider a short length at the opened end, there is a mass of air with unbalanced forces due to the rupture of the disk. You can use F = m·a to compute acceleration from pressure.

The sound of the disk rupture initially travels back down the pipe as an internal pressure reduction wave, at the speed of sound. There would be some compressive heating of the external atmosphere as the wavefront spreads. I expect that would result in a local shockwave for a short distance, followed by the air from inside the tube that would be cooled as it expanded.

After half the air has escaped the tube pressure would fall below atmospheric pressure, then flow back in again and repeat. You have a resonant organ pipe.

 

[Marwan1303]

What if, instead of a rupture disc, a quick release valve was used to release the pressure from the pipeline to the atmosphere. You can consider valve-opening to be instantaneous. Can we use Poiseulle's law or Bernoulli's principle to determine the exit velocity of the air

 

[Baluncore]

You can consider valve-opening to be instantaneous.

The initial flow velocity will be zero. The rupture will be heard at the speed of sound, then the air in the tube will begin to accelerate towards a maximum, then decelerate to a halt, flow back, and repeat.

Exactly when do you want to know the velocity, because velocity is changing continuously.

 

[Delta2]

Exactly when do you want to know the velocity, because velocity is changing continuously

Mind me if i answer for the OP but i would want to know the maximum value of velocity of the air at the exit of pipe.

 

[Baluncore]

Mind me if i answer for the OP but i would want to know the maximum value of velocity of the air at the exit of pipe.

How would you solve it ?
Inside the tube is 2 bar gauge = 3 bar abs. Outside is 1 bar abs.
Ignoring temperature changes, the pressure difference driving the acceleration will be positive until when 2/3 of the air mass has left the tube. I expect that will be the instant of maximum velocity.

 

[Delta2]

How would you solve it ?
Inside the tube is 2 bar gauge = 3 bar abs. Outside is 1 bar abs.
Ignoring temperature changes, the pressure difference driving the acceleration will be positive until when 2/3 of the air mass has left the tube. I expect that will be the instant of maximum velocity.

I am not sure how I would solve it. Fluid dynamics is not my forte. One thought is to use Bernoulli principle but then you say that the velocity of air is oscillating, which makes Bernoulli not suitable(I think).

 

[Baluncore]

Fluid dynamics is not my forte.

Come on in. The water is fine.

It does appear to be a transmission line problem with a flow limitation and loss due to the pipe wall and viscosity. Maybe the only tractable solution is FEM, a numerical simulation.
It would be necessary to model position, pressure, temperature, density, mass and velocity for each parcel of air in the line. I wonder how one could define a parcel, each metre or litre of tube, or maybe each kg of air ?

 

[Marwan1303]

The initial flow velocity will be zero. The rupture will be heard at the speed of sound, then the air in the tube will begin to accelerate towards a maximum, then decelerate to a halt, flow back, and repeat.

Exactly when do you want to know the velocity, because velocity is changing continuously.

The scenario in question simulates a typical pipeline cleaning methodology that uses air blowing to compress a pipeline to a specific pressure until the rupture disc blows. The result is quick decompression of the line and the flushing out of debris or dirt that is resting in the pipeline. My concern to determine whether a minimum air velocity in the pipeline is achieved as air exits it. For the lines in question, that minimum velocity ranges from 30-60m/s. How can I confidently determine that this minimum velocity is achieved?

 

[Baluncore]

The line will not be emptied of all material. Up to 1/3 of the air mass will remain in the pipeline, along with about 1/3 of the debris. So although you would be dislodging some material from the wall, you would need to then flush the debris from the line. Would I be correct in thinking that the line is a water pipeline and that after blowing it is flushed with water?

Why do you not use a water driven pig to clean the inside of the pipe?
https://en.wikipedia.org/wiki/Pigging

 

[russ_watters]

This is a pretty difficult/non-standard problem. Rather than a true flow, I imagine the entire mass of air expanding like a spring. The backwards propagation of the pressure wave is a complication though. Maybe a numerical model using a collection of tiny [lossy]springs?

 

[Baluncore]

Maybe a numerical model using a collection of tiny [lossy]springs?

The cooling of the expanding air will reduce the velocity. The boundary layer on the wall will reduce the flow rate. The degree of wall cleaning is a problem of boundary layer and interior ballistics. There is also the exterior ballistics problem, with the discharge of a massive scatter-gun, and a risk of local pollution, injury to property, people and wildlife.

Maybe an electrical model could help. A charged transmission line, open circuit at both ends, is suddenly discharged from one end to ground. The voltage on the distributed capacitance of the line is an analogue of pipeline pressure. The electrical current is an analogue of air flow. The inductance of the line represents the inertia of the air mass.

I know there are software systems for modeling water distribution pipelines.
Is there a software system for modeling stop-start gas flow in pipelines?

 

[gmax137]

Is there a software system for modeling stop-start gas flow in pipelines?

There is the GOTHIC computer code (now a Zachry Engineering product, developed originally by Batelle, EPRI, and NAI). It solves the conservation equations for mass, momentum and energy for multicomponent, multi-phase compressible flow in lumped parameter and/or multi-dimensional (1, 2, or full 3D) geometries.

This could certainly model the pipeline described above, we use it where I work for much more complicated systems. Maybe overkill but the user interface makes developing a model pretty straightforward. The OP's pipeline at 2700 meter is way larger than anything I have done with GOTHIC, I'm not sure if that would cause issues.

 

[Marwan1303]

So would that mean that a numeric simulation is the only way to determine the ballpark of the true velocity of air escaping the pipeline?

 

[Baluncore]

So would that mean that a numeric simulation is the only way to determine the ballpark of the true velocity of air escaping the pipeline?

Yes.
What does the pipeline carry when not full of air ?

 

[Marwan1303]

It is currently empty as it is undergoing commissioning activities. During operation, it will carry LPG.

 

[Baluncore]

Is the pipeline roughly horizontal and straight ?
What is the approximate altitude, above sea level ?

 

[Marwan1303]

Is the pipeline roughly horizontal and straight ?
What is the approximate altitude, above sea level ?

mostly horizontal with minor elevations and depressions. At around sea level

 

[Baluncore]

The scenario in question simulates a typical pipeline cleaning methodology that uses air blowing to compress a pipeline to a specific pressure until the rupture disc blows. The result is quick decompression of the line and the flushing out of debris or dirt that is resting in the pipeline. My concern to determine whether a minimum air velocity in the pipeline is achieved as air exits it. For the lines in question, that minimum velocity ranges from 30-60m/s. How can I confidently determine that this minimum velocity is achieved?

I assume that the required velocity to clear the pipe was specified at 1 bar absolute. From that, the dynamic air pressure exerted on an object in the pipe can be calculated. Pd = ½ · d · v² ;
Since the density of the internal air will change during the discharge, we need to know the dynamic air pressure reached, not the velocity reached. And we need to know the peak dynamic pressure reached for each point along the pipeline.
Does that seem reasonable ?

 

[Baluncore]

For the lines in question, that minimum velocity ranges from 30-60m/s. How can I confidently determine that this minimum velocity is achieved?

I thought it would be fun to try writing a 1D numerical model for the discharge. So I started setting it all up which has made getting some initial values easy.
Volume of the pipeline = 197.0 m³
Initial pressure difference = 200.0 kPa
Potential energy = 39.402 Megajoules
Initial air density = 3.337 kg/m³
Mass of air in the pipeline = 657.5 kg
Equating the initial PE to the final KE gives an average velocity of released air = 346.19 m/s
But the speed of sound in air at 40°C = 353.75 m/s
I do expect some of the air to form a shock wave.

There is no question that the air will exceed 30 to 60 m/s. The question is; will there be places in the pipeline that do not reach that velocity.