Guaranteeing turbulent flow in a gas pipe

[Jehannum]

In the gas industry engineers often have to purge gas pipes. For example, if repair work must be done on a gas line the fuel gas in the system must be removed before work can be done safely.

The Institute of Gas Engineers and Managers (IGEM) publication IGE/UP/1 stresses the need to achieve a minimum purge velocity when purging, to ensure that purge flow is turbulent. Laminar flow could leave undisturbed layers of fuel gas (of a different density to the purge gas) in pipes.

To help engineers achieve this IGEM provide a table that gives minimum purge velocity for a given pipe diameter. Some sample figures are below:

50 mm pipe, 0.6 m / s
...
200 mm pipe, 0.7 m / s
...
400 mm pipe, 1.0 m / s

My question is this: if Reynolds number for gas in a circular pipe is proportional to pipe diameter, why is a faster purge velocity needed for larger pipes? Wouldn't it be the opposite, i.e. a larger pipe diameter would mean you could have a slower purge velocity and still get the Reynolds number you need (say > 4000) to ensure turbulent flow?

 

[Chestermiller]

Maybe you need to have a certain shear stress at the wall. For turbulent flow, if f = 0.079/Re^0.25, how would the velocity vary with diameter so that the shear stress is constant?

 

[Jehannum]

After going around in circles in Wikipedia and other sources I think I'm beginning to get a glimmer of sense. I have found out:

(Fanning) friction factor is the ratio between shear stress and flow kinetic energy density​

So I surmise that:

Friction factor is proportional to shear stress divided by the square of flow velocity​

Rearranging this tells me that:

Shear stress is proportional to friction factor x the square of flow velocity​

In the purging standard (see original post), it says that friction factor can be taken as 0.0044 [1 + 43.5 d^-1] for natural gas, where d = pipe diameter (mm). In terms of proportionality:

Friction factor decreases with increasing pipe diameter​

So, to keep shear stress constant:

If pipe diameter increases, flow velocity must increase, which is what we see in the tables in the purging standard.​

Would this chain of reasoning be correct? To understand all this I have had to make drastic simplifications: i.e. reducing equations to "if one thing goes up, this other thing goes down", but this is sufficient for my conceptual understanding - and it answers my original question.

Can you tell me why it could be necessary that shear stress be constant?

 

[Chestermiller]

After going around in circles in Wikipedia and other sources I think I'm beginning to get a glimmer of sense. I have found out:

(Fanning) friction factor is the ratio between shear stress and flow kinetic energy density​

So I surmise that:

Friction factor is proportional to shear stress divided by the square of flow velocity​

Rearranging this tells me that:

Shear stress is proportional to friction factor x the square of flow velocity​

In the purging standard (see original post), it says that friction factor can be taken as 0.0044 [1 + 43.5 d^-1] for natural gas, where d = pipe diameter (mm). In terms of proportionality:

Friction factor decreases with increasing pipe diameter​

So, to keep shear stress constant:

If pipe diameter increases, flow velocity must increase, which is what we see in the tables in the purging standard.​

Would this chain of reasoning be correct? To understand all this I have had to make drastic simplifications: i.e. reducing equations to "if one thing goes up, this other thing goes down", but this is sufficient for my conceptual understanding - and it answers my original question.

Can you tell me why it could be necessary that shear stress be constant?

If there is some kind of deposit or buildup at the wall, it takes a higher shear stress to sweep it away.

 

[Chestermiller]

I tried to do a curve fit to the relationship you gave. It seemed to be fit well by $V=0.544e^{0.00148 D}$. This doesn't seem to relate to constant shear stress at the wall.

 

[Jehannum]

As well as minimum purge velocity they also give minimum purge flow rate (Q_p). This figure is actually given to more significant figures. Here is the full range they give in the table:

[diameter (mm), Q_p (m³ / h)]
[20, 0.7]
[25, 1.0]
[32, 1,7]
[40, 2.5]
[50, 4.5]
[80, 11]
[100, 20]
[125, 30]
[150, 38]
[200, 79]
[250, 141]
[300, 216]
[400, 473]
[450, 575]
[600, 1230]
[750, 2390]
[900, 3440]
[1200, 6960]

 

[Chestermiller]

From this data, I get $Q=0.0006492D^{2.2533}$. Plot the data, and see what you get.