Stabilizing a bubble in a water tunnel

[Ninet]

Hello,

I am trying to find the required flow rate for stabilization of a bubble (to control the sinking and rising of bubble) in the water tunnel. I found the velocity of sinking bubble in the water (when the flow rate is zero) but I am not sure how to use that to find flow rate of my system to control the sinking and rising of bubble. I would greatly appreciate any help. Thank you.

Here is how I calculated velocity of sinking bubble:

FBD--> W (weight) = D (drag) + B (Buoyancy)

W= γAir * V , V= volume
B= γwater* V
Drag=(1/2)* ρ*U^2* (π/4)*(D^2)*Cd , where ρ= density of Water, U= velocity, D= bubble's diameter and Cd= drag coefficient
Cd (Drag Coefficient)= 24/ Re
Re= ρ*U*D*(1/μ)

U (Velocity) = (SG bubble]-1)*(γwater)*D^2*(1/18)*(1/[μwater)

 

[mfb]

Maybe I am missing something, but can't you just multiply the flow velocity by the cross-section of the tunnel (and the density of water for mass flow)?

 

[Ninet]

Sorry, I think I didn't explain the problem very well. I am trying to determine the the flow velocity in a way that can stabilize a sinking bubble in a tunnel. (Tunnel is tapered and the size is fixed)

 

[mfb]

To make it stable, I guess you'll need some active control, or a position-dependent flow velocity (=a position-dependent width of your tunnel or some other way to change the current flow).
Otherwise, even tiny deviations from the "right" flow will get your bubble to the bottom or the top after a while.

 

[Ninet]

well, first I want to calculate the maximum flow velocity in my system to figure out required pump. I am not sure how to calculate the flow velocity based on the shape of the tunnel and the sinking rate of bubble.

 

[mfb]

If you know how fast your bubble sinks without flow, then your flow velocity upwards at the position of the bubble has just to be this velocity. It is not constant over the cross-section, but that's probably an issue that can be sorted out later.

It would help to get more context. Do you have a sketch of the setup?

 

[Ninet]

Thank you mfb for your help. I think my calculation for velocity of sinking bubble without flow should be correct. But then as you said when there is a flow the flow velocity changes in different cross section of tunnel. I draw a basic sketch of tunnel and the rectangle in the sketch is the desired range to keep the bubble stable. Also, how can I calculate drag on a bubble when there is a flow?

 

[mfb]

If the object is sinking without flow, the current position is instable - upwards flow increases with height.

Also, how can I calculate drag on a bubble when there is a flow?

All you need is the velocity relative to the fluid. As the bubble velocity is supposed to be zero, this is just the velocity of the fluid.