Gravity Fed system (Conceptual Question)
 

Hello all,

I'm working on a team to design an Air Tanker plane (plane which drops retardant on fires). We're coming into the project half way through so the plane exist but it isn't performing as expected.

Its a gravity fed system with roughly 107" of head, during a drop, the flow rate of the first 1000 gallons of retardant is slow and then speeds up. So in the first 2 seconds the flow rate is slow and then it actually increases, then naturally as we loose head it decreases.

I'm thinking its because it takes time for gravity to act on the the water. However, using Bernoulli's equation thsi time for the fluid to accelerate is not represented... I'm wondering if i'm on the right track with my explanation, and if so, how would i mathematically represent the time for the fluid to accelerate? Any thoughts or opinions are appreciated!

well, your flow problem is governed by the equations of the fluid motion, therefore mass, momentum, energy and chemical species are the equations you should solve. In particular, the acceleration of the fluid can be determined from the momentum quantity.
Integral estimation could be done but I don't know enough about your problem ...

Wouldn't the initial two seconds be spent in achieving the expected velocity i.e. accelerating?

Also, how accessible is it for air to reach the space vacated by the falling fluid. Possibly the path of air is restricted initially causing the fluid not be released as expected. Remember the old trick where the water does not spill out of the tumbler when it's mouth is covered by a plate, even when held upside down.

See that's what I was thinking, it would take time to accelerate. But when i solve the problem using conservation of mass / Bernoulli i keep getting that the velocity of the fluid is :

V = sqrt(2*g*h) where h is height of the fluid in the container.

So the tiem for acceleration isn't represented...

I'm also suspicious of the venting, however before i tackle that i was hoping to get a working model to explain how the fluid accelerates..

well, first I am not sure from your problem that you can apply Bernouilli! Perhaps it would be suitable to be applied in the time-dependent form...

then, you have a chemical reaction, isn't it??

the retardant does complicate the situation, however we can't even get it to perform with water.

What i did was basically solve a bunch of steady state problems with a for loop in matlab to predict the flow rate per time.

I believe it meets all of the Bernoulli assumptions... lets say for the sake of discussion, that it does meet all assumptions, i just dont see where the time for fluid acceleration is taken into account...

well, you can use the unsteady form of the Bernouilli equation...
http://web.mit.edu/2.016/www/handout...ion_050921.pdf


Again, you should ensure that it can be applied....

Thank you for teh Ref. Document. It put me on the right track that's for sure. I finally have the acceleration represented.

Now I'm thinking it might be a venting issue, I'd like to use openfoam to simulate the problem. I've made a couple of attempts at it using teh interfoam solver...

It keeps on crashing midway through the analysis. One general question I have, do i need to actually mesh volumes of air to replace the water leaving the tank? Or can i just use some kind of boundary condition ?

I attached an image of the case I have been trying to run... The red represents water in the tank before the drop chute opens. (keep in mind the tank is very simplified)