Help with airflow calculation within a pipe 3

[Kalle1202]

Hello everyone!

Iam looking for someone who can support me with a airflow calculation within a pipe for us.
Attached is a sketch with more details. The airflow can be between 5 and 10scfm per 1ft pipe length.
We have two pipes each with a length of 4m or 13.16ft. The air leaves the pipes at 1cm holes that are drilled into both sides of the pipe. Additionally the first 1m of the pipes are supposed to supply 6.2% of the total airflow, between 1 and 2m 19%, between 2 and 3m 31% and the last meter from 3 to 4m is supposed to supply 43%. Last the air is supplied from a collection chamber to the pipes. Two questions are to answer: 1) How many holes do we need and what is their distance to ensure an even airflow with the noted percentages. Also which pipe diameter should be chosen? 2) How big must the collection chamber be to provide enough pressure to both pipes.

I would be very thankful for every tip. I hope I can help the community in the future with environmental engineering related questions.

 

[miningman]

I will look forward to the responses here but my immediate thought is nowhere near enough information here for a meaningfull response.. What is the pressure of the supplied air??? What is the depth of submergence??? Why are you not approaching the vendor for guidance??? etc etc etc

 

[Kalle1202]

Hey miningman thanks for your message. Maybe we can work towards the solution step by step.
So the buoyancy force in the air collection box equals the pressure in the perforated air pipes. I was thinking of using a collection box with H = 1m and 25cm in diameter. The buoyancy force should be about 12.5^2 * pi() = app. 500kg per 0.5m2 equals about 10.000N/m2 or 0.1bar. So the air pressure in the pipes would be about 0.1bar.

Then lets take a 10cm pipe diameter with 1cm hole size. Average airflow volume is 7.5SCFM or about 12nm3/hr per 1ft of pipe or 158nm3/hr per 4m pipe. If I wanted to have an even airflow throughout the whole pipe how many holes would I need and what distance should the holes have to each other?

 

[katmar]

The basic design philosophy for this type of problem is to make the pipe diameter large enough to ensure that the pressure drop along the pipe is negligible. This ensures that each orifice "sees" the same differential pressure and a uniform flow rate per orifice can be calculated and used for every orifice. If this is not done, then the flow calculation for every orifice is different and it enormously complicates the problem.

You have not shown how deep the sparger is in the water. For the sake of an example I will assume it is 5 m below the surface, and I will assume that we want 50 kPa pressure drop across the orifices. This means that the air pressure will be 100 kPag in the pipe.

Air at 100 kPag and 20C has a density of about 2.4 kg/m3 and a viscosity of 0.018 cP. The flow rate of 158 Nm3/h is equal to about 0.056 kg/s. Assuming this flow for the entire 4 m length and requiring a maximum pressure drop of 5% of the pressure drop through the orifice (i.e. 2.5 kPa) means that the pipe ID must be at least 35 mm.

For these flow rates and pressures the proposed orifice size of 10 mm is far too big. Under these conditions a 2 mm hole will give a flow of 0.00090 kg/s. The first zone at 6.2% of the 0.056 kg/s total requires a flow of 0.0035 kg/s and 3.85 holes. Zones 2, 3 and 4 require 11.8, 19.3 and 26.8 holes respectively. Obviously these would be rounded up to 4, 12, 20 and 27.

I have had to assume a few numbers here to be able to perform the calculation, but they illustrate the method and you can fill in the correct numbers to get the right answer.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[Kalle1202]

Hey Katmar,

thanks a lot for your help. I tried to put together your information and what I found here

http://www.cheresources.com/invisio...forated-pipe-distributor-sizing-calculations/

into an excel spreadsheet. (Please see attached)

I come here and there to similar results but the end result doesn't seem right. We have 3.5m water depth at the top of the perforated pipes. From the buoyancy force I calculate that the pressure in the pipes should be about 112kPa. I assume you calculated that divided by two to get the pressure loss of the orifices = 56kPa.

Then I dont understand how you get to 2.4kg/m3 for the air density. In the excel spreadsheet is a graph that shows a air density of about 1.3kg/m3 at 112kPa. At that density I get a very similar flow rate of about 0.057kg/s. Lets choose a 10cm pipe diameter so we can neglect pressure drop by pipe friction.

I am afraid that a 2mm hole would clog therefore the hole size should be at least 10mm. However I dont know the flow rate at a 10mm opening under these conditions but I assume its about 0.0009kg/s * (78.54mm2/3.14mm2) = 0.0225kg/s.
At a total airflow of 0.057kg/s I get only 3 holes

So to get to bigger holes could we increase the air pressure by increasing the height of the air collecting box to 2m instead of 1m? Also the blower has a maximum capacity of 400SCFM and I wouldnt mind to operate it at 75% of capacity = 300SCFM or 241nm3/h. Then the air density should be about 2.9kg/m3 (according to your value) and the air flow at 242nm3/hr is about 0.105kg/s. Still not enough for 10mm holes but closer. Finally I could eliminate one of the two perforated pipes so that we have only 1 pipe with L = 4m instead of 2 just in case that helps.

 

[LittleInch]

Kalle, You don't seem to quite get the basics here or understand the excellent response from Katmar

First off be sure to be consistent as to whether you're using absolute pressure or guage pressure relative to atmosphere.

At 3.5m deep the pressure of the water is about 35kpa(g). "Buoyancy" has nothing to do with it.

Given that your well / "air collection chamber" dimension Y is now 2m, the pressure of the air in the tubes will be approx. 55 kPa(g)or 155 kPa(a) as this will be the water pressure being exerted on the air. As air is very low density compared to water, the pressure difference in 2m is negligible unlike water.
Katmar has assumed 100kPa(g)for the air supply and 5m deep.

Your 1.3 kg/m3 is at a pressure of 113kPa (a) or about 10 kpA(g) That's why you have a discrepancy in density.

Why would a 2mm hole clog up? Can't you filter the air going in?

In any case Katmar has assume 50kPa across your orifice. In your design you have 20kPa so to get the same flow the orifice would need to be bigger - say 3 or maybe 4mm, but not 10.

The flow and density of your blower is not relevant so long as it is enough to maintain the water level in the air collection chamber at around 2m below your tubes. Any more air volume will simply leakout around the bottom and bubble up to the surface.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[Kalle1202]

Hey LittleInch thanks for your great response. The air is filtered but the water might contain particles that settle in the air holes. Therefore a 10mm hole would be better. Can I not reduce the number of holes to increase their diameter? Do you know what the airflow per orifice would be at 20kpa?

 

[LittleInch]

I rather suspect you really need to have some sort of decent velocity going through the hole in order to prevent water going backwards into the pipe between "bubbles".

Now what that is I don't know but would suspect you're into 2-3 m/sec so you get a stream of air and not a succession of large bubbles.

Also most orifice calcs are for a single fluid, not what you're doing.

Some testing and trials I think are also needed as I also suspect the exact shape of the hole will be crucial - a hole drilled into a pipe? or a flat surface? or a more jet like nozzle.

Try searching for air water sparger design and gems like this turn up

https://mottcorp.com/sites/default/files/sparger_design_guide.pdf

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[katmar]

The only way to get larger holes would be to lower the pressure in the sparger and decrease the pressure drop through the orifice. But when the pressure in the pipe gets low it is harder to keep it constant along the length. I agree that 2 mm holes are on the small side, but your flow rates are very low. You will break a lot of drill bits along the way!

I have installed spargers using this design method, but with 4 to 6 mm holes, in reactors, yeast fermenters, vaporizers and in-line water heaters (injecting steam). All very successfully. If you have a little bit of margin with your supply pressure you can generally regulate the flow to exactly what you need.

The spargers in the link given by LittleInch use sintered metal particles, giving thousands of very small holes. They do work well, but it might be tricky getting different flow rates along the length of the sparger.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"