Pressure Drop in Spargers for Pump Sizing 1

[Zarag]

I have a pressurized reactor, 2 bars (30 psi), in which I want to recirculate a fluid in order to mix it. A pump will draw the hot liquid from near the surface and inject it back into the tank near the bottom distrubuting it via a 'Y' shaped sparger tube with several 1 or 2 mm holes.

I want a flow rate of 16 gallons per min.

As far as I know the 2 bars won't make a difference to the pump performance once the seal is good. Using the Darcy-Weisbach eqn. I can calculate the P drop for the 10mm diam. inlet pipe but for the sparger hole geometry I am at a loss as to the pressure drop each causes. I found no tables for the calculation.

I should mention that I want to create turbulence so 2 phases mix so I calculate 50 X 1mm diam holes results in as fluid vel. of 25m/sec. This is gonna cause big head loss but how big?

Any suggestions? I am pretty new to the fluids area.


Thank you
Zarag

 

[stanier]

Being new to the fluid area I suspect that you wont have classic texts like Idelchek.

Suggest with the best will in the world the best way will be to build a model and test it. No amount of FEA is going to give you the answer. to build and test such a device could be done very quickly and be far more accurate.

The model could be made in PVC and connected to the water supply. Measure the flow by time weight analysis into a tank. Measure the pressure loss with and without the sparger.

You could build a small model and use dimensionless analysis for scale up if you are capable.

 

[Zarag]

Yes I am in a small Mexican town without the luxury of any texts.

Surely it can't be that complicated? Are there so many unknowns that k values for that type of fitting (the holes in the sparger) can´t be used with the hf=kV*V/2g added up as head losses for each hole.
The liquid is veg. oil.

I know the flow rate 1 litre/sec, and the dimension of the hole 1mm diam, so I get a velocity of 25.5m/s thru each of the 50 holes.


Getting FEA or modelling involved will not go down well.

 

[stanier]

The problem is that the further past the initial holes you get the head changes, flow patterns and eddies will impact on the approach velocity to each hole and thus any computation will be irrelevant.

You could take the hydraulic radius approach. Calculate the periphery of the total number of holes and the total cross section area and use the hydraulic radius to compute a head loss.

 

[MikeHalloran]

The pressure in the reactor is applied to both inlet and outlet of the pump, so it isn't important for what you're doing, except that it reduces the likelihood of cavitation in the pump.

You don't really have two phase flow, you have liquid at two temperatures. If the mixer works, the temperatures won't be very different.

Turbulence and high pressure drops are a pretty energy- costly way to effect mixing. It would probably be more effective to maximize the surface area of the 'hot' fluid that's exposed to the 'cold' fluid.

One way to do that is to arrange the spargers so that the stream leaving each discharge hole immediately encounters a flat plate, or, better, a flat- ended pin a little bigger than the hole, so that the cylindrical discharge flow is deflected radially into a circular sheet. I think the arrangement is called a 'pin nozzle'.



Mike Halloran
Pembroke Pines, FL, USA

 

[katmar]

I am a simple man, and my philosophy on solving difficult problems is to avoid them.

If you are trying to put 16 gpm through a 10 mm pipe you will have a velocity of 13 m/s. This is very high for liquids and you will get high pressure drops. In these circumstances FEA is probably necessary to get reliable results.

My approach would be to change the 10 mm pipe to a 40 mm pipe. The pressure drop through the pipe and Y-piece would then be negligible. Now you have a simple problem of designing 50 identical orifices - all with the same (for all practical purposes) pressure drop through them.

Life is complex enough without trying to make it worse.

 

[MikeHalloran]

Amen on the 40mm pipe. I can't think of a defensible reason for minimizing the diameter or volume of a manifold.



Mike Halloran
Pembroke Pines, FL, USA

 

[Zarag]

Thanks for the wisdom. I too try to be a simple man.

The 2 phases are methanol and the oil whose low miscibility means thay need turbulence to mix.

I'll go for the 40mm Y piece, I assume that means from the pump outlet onwards. That'll mean just a 0.8m/s vel. before the holes.

Should I make the draw down legth on suction side of the pump (drawing from above) the same diam. to reduce losses?

Zarag

 

[katmar]

Hi Zarag,

Yes, the suction side is even more important than the delivery side. Without having done any calculations, I would think that any additional mixing that you might get using a small diameter pipe would be small compared with the mixing in the pump and the sparger.

If you need more mixing than this, then install an in-line (static) mixer on the delivery side of the pump.

If the sparger holes are along the top of the pipe, it might be a good idea to put a few holes along the bottom (or vice versa) in case you get layering in the 40 mm pipe with the low velocity.