why exhaust temp matters for turbos
Let's say a certain engine/turbo/exhaust combo has an exhaust total pressure of 45 psia before the turbo and ~15 psia after. That gives a pressure ratio of 3:1. Now assuming the turbine has an efficiency of 90% (polytropic), That gives a total temperature ratio 1.256.
Now this is the important part. We know the ratio of exhaust temp before and after the turbo, but that could mean 1500 (Rankine) before and 1194 after, or 1000 before and 796 after, or any other combination with the same ratio. The power output of the turbine is proportional to the change in total temperature, which is 306 for the first case but only 204 for the second case (the equation is massflow*specific heat*change in total temperature). Say the massflow is 50 lbm/min and the specific heat is .29 BTU/lbm *R. That means in the first case the turbine would be driving the impeller with 104 hp and in the second case 69 hp. You can see since the exhaust temp in the second case was 2/3 the first, the power to the impeller was also only 2/3. More power to the impeller of course means more boost & massflow.
My background is in jet engines, not turbos, so i realize some of my example numbers may not be realistic. Also, I know i can't just say the exhaust temp is higher in one case and everything else stays the same, but this is just a simple example to show a concept. Hopefully this will clear some things up for some people.
Cliffnotes: The power produced by the turbine is proportional to the change in total temperature across the turbine. And hotter exhaust means the change in temperature across the turbine is greater.
Can you support the above statement. Because it seems that the exit temperature could be high too, then the delta isn't necessarily greater. (maybe it was in the part about efficiency and temperature ratio and it just didn't sink in yet).

Is the efficiency based on a given temperature? How does the efficiency change when the "before" temp is significantly different that the rated temp?
Thats why Exhaust temps are vital to Turbo cars.
Or is it the pressure differential that dictates the wheel speed?
Or is it the temperature differential as P Mack was explaining?
And 2FAST4U, you just basically told me, "It's true, because, well, because it's true..."
I'm too hardheaded for that to work on me.
Or is it the pressure differential that dictates the wheel speed?
Or is it the temperature differential as P Mack was explaining?
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total pressure ratio= total temperature ratio^(gamma/(gamma-1)*polytropic efficiency)
gamma is the ratio of specific heat at constant pressure to specific heat at constant volume. For exhaust i'm using 1.3.
polytropic efficiency is ratio of actual turbine work to ideal turbine work for a differential pressure change. I'm assuming 90% for this.
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On my STS setup I will spool up MUCH faster when the engine and the turbo itself are hot and have been running for a bit. If I were to fire up the truck and immediately hit WOT the turbo will take forever to spool and in some cases won't even brake stall up to the desired psi durring a race.
I'm too hardheaded for that to work on me.

Turbine efficiency is normally given as a function of pressure ratio, mass flow, and turbine speed. I'd have to say the effect of temp would be negligable on efficiency.
So if a given turbo could produce 20psi in a front mount, if the temp dropped by a 1/3, it would now be capable of only 13-14psi. (I suppose it's more directly related to cfm than psi though. But I'm sure those are closely related too, if you can define enough variables...)
Yeah, somehow I missed any exposure to fluid dynamics, that I can recall... Therefore all the questions. I do vaguely remember that a theory can't be self-supporting though.
And to each new mind, even a well-proven concept is the same as a theory, until it is understood and incorporated. I got a t76 in place of my muffler on a stock motor and have full boost by 3700 rpms :-p .81 a/r
BTW, my friend also has a 67 turbo on is 370 9.0:1 motor, he hits full boost (9psi) by 2500! He could definately spool my 76 under 3k.
If the turbo hits full boost before 4k in 4th gear it means you need a bigger turbo
.Jose
.Jose

