Mathematical equation of a Jet Stream of Air

[Uridan]

Hi,

First of all, Happy new year to you all, I hope you enjoyed it as much as I did :), but its back to work for me now :(.
I am an electronics Student and doing a project about control systems to control a vertical jet stream of air coming out of a pipe.

My basic setup is a motor that blows out air from a pipe and a ping pong ball will eventually flout inside the low pressure of air stream coming out of the pipe, then a valve will be controlled to control the height of the ping pong ball.

I need help in understanding the physics and Maths behind the jet stream of air coming out of the pipe, since I need an equation that represents the jet stream of air. This will eventually be converted into laplace domain and used as the transfer function for my control system.

I have required some books about Thermodynamics and aerodynamics etc.. but can't come any close to a conclusion. I know about Bernoulli's equation and the pressure changes in the jet stream of air and why the ball eventually flouts inside it, but I have no clue in how I may find a mathematical equation that explains the behavior of this jet stream of air coming out the pipe.

Any help would be greatly appreciated :)

Thanks
Uridan

 

[Uridan]

Vertical jet stream of air

Hi,

Is there a way to find the transfer function of a vertical jet stream of air coming out of a pipe? The problem is that the stream of air is not inside a pre set volume, such as a wind tunnel. I don't thing that Bernoulli's equation is good since the pressure of the stream of air will change according to the pressure in the room.

Thanks
Uridan

 

[Uridan]

Control system for a jet stream of air

Hi fellow engineers,

I have a problem, how can I come out with a proper transfer function of a vertical jet stream of air coming out of a pipe to be able to use it in my design of a PID controller and Phase compensator ?

The thing is that I have no clue about Thermodynamics and such, I'm just electrical and electronics guy :).

Thanks
Uridan

 

[Uridan]

Equation for a vertical jet stream of air

Homework Statement

Got a small problem regards the Mathematical equation for a vertical jet stream of air. We all know that when air is coming out of a pipe it will create a pressure change, i.e the pressure will be lower at the center of the stream of air than the outside pressure (room pressure), I can't seem to find a way to be able to find the transfer function/mathematical relationship/topology of this jet stream of air.

Homework Equations

Bernolli's equation is : v^2/2 + P/p + g*h

Where P=Pressure , p= density

Which pressure is it referring to ? because the jet stream of air is being release in atmospheric pressure, (pressure found in the room).

p.s I am an electronics student and don't have any knowledge on Thermodynamics etc. I am using this for a PID controller and a phase compensator design.

Thanks
Uridan

 

[berkeman]

Hi fellow engineers,

I have a problem, how can I come out with a proper transfer function of a vertical jet stream of air coming out of a pipe to be able to use it in my design of a PID controller and Phase compensator ?

The thing is that I have no clue about Thermodynamics and such, I'm just electrical and electronics guy :).

Thanks
Uridan

Transfer function from what to what? What control variables do you have over the stream of air? What is its response to the control variables? Are you just able to control some pressure? Are you trying to suspend something in the air stream? What is the air stream used for?

 

[Uridan]

Hi Berkeman

My system is to control a valve which will allow an amount of volumetric air to pass through the pipe, so basically I am changing the pressure of air going out of the pipe.

I am to suspend a ping pong ball by the jet stream of air and control its height by controlling the valve.

To be able to do so I must find a transfer function for my model in s domain, thus the original equation must be in time domain, so I can obviously calculate my P or PI or PID controller needed to control the valve for such parameters.

Basically I am using Bernoulli's equation but some variables do not apply since I am not working inside a wind tunnel with a pre set volumetric change, and I've read that I must use some kind of Euler's equation but I got lost there and then lol.

Thanks
Uridan

 

[Danger]

I can't help you from a math standpoint, but something in your post bothers me. Doesn't the presence of the pipe (ie: ducted fan) automatically result in a pre-set volume?

 

[berkeman]

Hi Berkeman

My system is to control a valve which will allow an amount of volumetric air to pass through the pipe, so basically I am changing the pressure of air going out of the pipe.

I am to suspend a ping pong ball by the jet stream of air and control its height by controlling the valve.

To be able to do so I must find a transfer function for my model in s domain, thus the original equation must be in time domain, so I can obviously calculate my P or PI or PID controller needed to control the valve for such parameters.

Basically I am using Bernoulli's equation but some variables do not apply since I am not working inside a wind tunnel with a pre set volumetric change, and I've read that I must use some kind of Euler's equation but I got lost there and then lol.

Thanks
Uridan

Would it be permissible to use empirical data to set the PID loop up? Sounds like a pretty complicated simulation to figure it out computationally. I think I'll move this to the ME forum to get some better views. This is more of an ME question than an EE question.

 

[Cyrus]

Just make your controller ad-hoc. Tune the gains until the thing works. There is no reason as to why you need a transfer function in this situation.

 

[berkeman]

Ack. Multiple thread posts merged into one. Please don't multiple post, Uridan.

 

[minger]

I made a post about an axisymmetric plane jet, here:
https://www.physicsforums.com/showpost.php?p=2428184&postcount=6

From there you can get your jet velocity as a function of distance from the outlet. As far as the transfer function stuff, that's not my area; no idea.