Output power-calculations on tesla turbine

[Knight Rider]

Homework Statement

Hi!

I'm currently working on my school project, for which I've constructed a tesla turbine, and to complete it I'll have to make some calculations on the efficiency.

As I don't want a efficiency result that depends on a generator I've decided to mount a flywheel, with measurements and weight determined, on the turbine shaft.

The plan is to calculate the flywheel's moment of inertia and then multiply it with the angular acceleration, which should equal with the torque if I'm not wrong. Then I'll calculate the output power with help of the torque and RPM.

However I'm not sure if I'm totally right... I've done some hypotethical calculations on the issue presuming that:

- the weight of the flywheel is 5 kg, that is has a diameter of 10 cm and has the shape of a solid cylinder.

- we run the turbine with a fluid pressure of 1 BAR.

- that we register the shaft's current RPM every 0,5 second with the help of a tachometer with the following result: 1050 RPM, 1100 RPM, 1150 RPM

Homework Equations

Moment of inertia of the flywheel: I = 0,5 x m x r
Angular velocity of the flywheel: 2pi x (RPM/60)
Angular acceleration of the flywheel: deltasomethingvalue/time = rad/s^2
Torque of the turbine: moment of inertia x angular acceleration = torque
Average power output of the turbine between 1050 RPM and 1100 RPM with a fluid pressure of 1 BAR: P = t x rpm x 2 x pi

The Attempt at a Solution

Moment of inertia of the flywheel:

I = 0,5 x m x r
I = moment of inertia measured in kg m^2
0,5 = constant
m = total mass of the flywheel measured in kg
r = radius of the solid cylinder measured in meters
That gives:
I = 0,5 x 5 x 0,05 = 0,125 kg m^2

Angular velocity of the flywheel:

2pi x (RPM/60)
That gives:
1: (6,28 * (1050 / 60) = 109,9 radians/sec
2: (6,28 * (1100 / 60) = 115,1 radians/sec
3: (6,28 * (1150 / 60) = 120,4 radians/sec

Angular acceleration of the flywheel:

deltasomethingvalue/time = rad/s^2
(115,1 - 109,9) / 0,5 sec = 10,4 rad/s^2

Torque of the turbine:

moment of inertia x angular acceleration = torque
That gives us a average torque between 1050 RPM - 1100 RPM as following:
0,125 x 10,4 rad/s^2 = 1,3 Nm

Average power output of the turbine between 1050 RPM and 1100 RPM with a fluid pressure of 1 BAR:
P = t x rpm x 2 x pi = 1,3 x 1075 x 2 x 3,14

= 146,2 watt

I'm I right? I'm worried over the fact that I don't consider the width/height of the flywheel in my calculations for example. Note that english is not my native language and neither have I worked on above formulas before.

 

[Knight Rider]

BOMP! BOMP! BOMP!

I really need help with this...

 

[kland1]

BOMP! BOMP! BOMP!

I really need help with this...

Hello Knight Rider,

I really appreciate the amount of thought you have put into the mathematics of your efficiency question.

However in an effort to be efficient in calculating efficiency have you considered going back to that generator idea? Think of it this way;

1) With a generator you can tie a electrical load onto the generator and directly calculate the energy you are creating.

2) With the generator approach it is super simple to calculate your energy losses in the generator, wire and load. Especially if you get a nice fancy electronic load for the energy produced part.

3) Then you can take you "energy in" calculations based on the 1 bar input and get the result by subtracting the two.

Take a look at this Tesla Turbine driven 125KW generator set with a base load of three 1500watt incandescent loads. http://www.seabirdadventure.com/tesla-turbine/tesla-turbines-are-very-different There are two pictures not running and running.

In this case the energy in is 105hp, soon to be 165hp by changing the inlet fuel pressure from 150psi to 3000psi on the H2O2 catalyzing engine. This little engine you can see as the small silver canister between the fuel inlet pressure gauge and the Tesla Turbine inlet to the disk pack. The Tesla Turbine then turns at approximately 7254rpm's which goes through a 4.03 : 1 transmission which reduces the generator input rpm to 1800.

By taking the inlet power of 105hp subtracting out the bearing and transmission losses, converting the torque through the transmission on to the generator, knowing the generator has an efficiency of 97.8% and then calculating in the loads and the amperage draw up to the point where the system starts lagging - this will give me total power out which at this point is approximately 37KW.

I can get the total efficiency of the system by converting wattage to HP and then dividing the two for the result. In this case about 47.7% efficiency at this point. also here is an article of Tesla Efficiency http://www.seabirdadventure.com/tes...chives/three-keys-to-tesla-turbine-efficiency

Hope this helps, Kris