Calculating the energy required to spool a turbocharger

[devon1996]

I am interested in figuring out a general formula for how much energy it takes to spin up a turbocharger if we know the diameter of the wheel,mass, target rpm, and time to go from stationary to full speed. The goal is to get a general idea of what engine speed is required to get a turbo to spool on any engine configuration. Once I have the formula I want to compare known dyno graphs to see how the energy to overcome inertia compares to engine output when the turbo spools

 

[jack action]

This is so wrong on so many levels.

I am interested in figuring out a general formula for how much energy it takes to spin up a turbocharger

Simple, $E = \frac{1}{2}I\omega^2$ (source)

and time to go from stationary to full speed

It has no influence on the amount of energy needed to reach a certain rpm.

The goal is to get a general idea of what engine speed is required to get a turbo to spool on any engine configuration.

Knowing how much energy it takes to spin up a turbocharger won't help you for that.

to see how the energy to overcome inertia compares to engine output when the turbo spools

You will not find out any relationship between the two.

The engine output will depend mostly on the turbocharger mass flow rate, which in turn will depend on the turbocharger rpm. So it doesn't mean that if the energy doesn't go to the engine output, that it goes to spin the turbocharger. It is just that there is not the same amount of air that goes into the engine at different turbine rpm.

 

[devon1996]

This was my line of thought. On a gasoline engine every horsepower you make you put one horsepower worth of heat into the exhaust and one into the cooling system. So if it took say 50 hp to bring the turbine up to speed plus 10 hp to compress the air at that speed you'd need say 60 hp worth of exhaust flow to make whatever boost. And so then you could go to a dyno graph and see if it spooled at say 80 hp or whatever.