How to determine the torque and rpm of a Stirling engine?

Question

I am actually working on making of a Stirling engine. I did some research work but most of the content on the internet is qualitative. So I am trying to build a small scale Stirling engine and trying to gather knowledge through trial and error way.

But since this is not my field of expertise so I thought to raise the question to the community first.

Suppose there is a Stirling engine whose Tcold is 0-degree Celsius and Thot is 200-degree Celsius. The piston is 35mm in diameter and the stroke is 24mm. The engine is made to run using air at a pressure of 2 bar.

Can anyone help me to determine the torque and rpm of this engine?

Answer 1

It will be determined by the system load and internal friction factors.

Here's some initial thoughts on how to determien this:

Your power, $P$, is equal to the product of the torque, $\tau$ and your angular velocity, $\omega$,

$$ P = \tau \omega. $$

Assuming a completely adiabatic system, $$ \dot Q = P, $$ where $\dot Q$ is your heat in.

Therefore, you'd be able to write,

$$ \tau = \frac{\dot Q}{\omega}. $$

Now, what you need to know from your system is, $\omega = f(\tau)$. how much torque is required to produce a certain angular velocity. Once you know this, the intersection of the two curves give you your operating point.