A question about turbocharger
 

Im doing a research recently, need to get the turbine spinning speed at different working conditions. Yet, lacking of equipments, does anybody know how to get the spinning speed by Mathematics method?
Thanks a lot!:)

For a free-flowing application you would do a volumetric calculation based on the volume of the exhaust turbine and the volume of exhaust gas (combined with a few other factors like pressure drop). For a real-world application, you would then have to subtract the resistance from the compressor and friction...

-BC

if i get the pressure and the temperature of the exhaust gas, and the parameter after it passing through the turbine, is it enough? Is there any formulas I can use?

For a lot of data and calculations as it applies to vehicle turbochargers, look on a torrent search engine for "Maximum Boost" by Corky Bell.

It seems a complicated question. I decide to check the information in the labrary first. Thank you for your help.

Definitely not a simple calculation, and I'm not sure you'll find a simple formula. You definitely need a lot more information than just temperature and pressure, you have to know the geometry of the vanes and have a complete 3D model of the entire turbine system (as well as some information about the exhaust system to which it is attached).

Why are you looking to determine turbine speeds? Maybe there is another way to skin the cat...

-Bob C.

ask the manufacturer. They usually have volumes of info they can look up.

You should be able to find flow maps for most turbochargers online.
Here's an example:
https://www.turbofast.com.au/img/t3-s60.JPG

Now I realize that it is not a simple question. Maybe I should deal with it based on a computer software. But the direct way to solve the problem is to measure the turbocharger rotational speed by equipment, right?

Again, not so easy - since many turbos spin at 30,000 to 60,000 RPM (and I've heard of some at 100k+ RPM), attaching equipment will most likely create additional drag (affecting your reading), and/or create a balance issue with the spinning turbine (which would cause it to self-destruct in short order). Besides, a tach to read 60,000 RPM is pretty highly specialized.

Are you trying to design a turbocharger?

-BC

If you look at the flow chart I posted above, the (mostly) horizontal curves with the big numbers next to them are RPM values. The map starts at 56,400 RPM. A super-60 T3 (60 referring to the .60 A/R value) is a middle of the road to slightly large turbo for automotive applications. Larger turbos may spin slower, smaller ones may spin faster.
The ovals are regions of efficiency if I recall correctly. The closer to the middle oval, the more efficient the compressor will be operating.
Pressure ratio refers to how much boost the compressor is producing. 1.00 = atmospheric pressure x 1 = no boost. 2.00 = atmospheric pressure x 2 = ~14.7 psi. The chart maxes out at about 2.8, or 26 psi of boost.
Air flow in lbs/min along the bottom will depend on your engine's displacement and volumetric efficiency (how efficient it is at moving air) as well as how much boost you're running.

I'm not quite sure the compressor info will help him much, since that's the intake side.

Use an optical tach. No weight addition and you can just read off the compressor shaft.

That link isn't exactly what you are looking for but it's close.

Yeah, but unless you've got some horrific blow-by issues or a boost leak, the air flow being fed to the engine should be directly related to the exhaust flow coming out. A properly sized turbine and compressor pair should be able to drive each other, again assuming there are no mechanical or design issues with the engine.
The question the flow map really addresses is how well paired would the turbo be with a given engine... How much boost will it take to shove a given flow rate of air through said engine and how efficient will the turbo be under those conditions. Once you've figured out where you will be on the map, reading off the shaft RPM is easy.

i think garrett has full explanations and guides on selecting a turbo and all the math involved on their web site. very well written out as i remember

I thought of capturing the turbine sound with a microphone and a small circuit to detect the main frequency.

That should work or magnitize a single blade on the intake fin and use a hall or inductive pickup to measure the rpm that way. Heat is one of the problems however for the sensors. Depending upon the diameter and weight of the impeller the speed can be pretty high.

Correct, I also suggest studying the Ferrari F-40 engine.

They utilized turbos that offer varying amounts of boost throughout the RPM cycle. We looked at their design for the layout of some 4.7L Dodge Dakota turbo setups.