Calculating WORK done by a turbine (CO2 powered turbo)

[obanion]

Which of these equations which I have been given correctly describe the amount of work done by a turbine?
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W=work
PR=pressure ratio of turbine inlet to outlet
delta(v)=change in volume

W=PR*delta(V)

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POWER = { mdot * k * R * T1 * [1 - (P2/P1)^((k-1)/k)] } / { 1 - k }

POWER = shaft horsepower required, in kJ/sec.
mdot = mass flow rate of air (in kg/sec)
k = ratio of specific heats for air (around 1.395 for air in the temperature ranges we're talking about)
R = the universal gas constant for air (0.287 kJ/kg-K)
T1 = the air inlet temperature to the compressor (in degrees K)
P2/P1 = the pressure ratio for the turbo outlet to inlet (in absolute, not gauge, pressures)

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The results are FAR different. The first suggests that using a very small turbine wheel and housing, using a small total flow rate (about 10% of what's going through the compressor), will effectively drive a large compressor, so long as there is lots of pressure at the turbine inlet. Say 100psi or more. Now, obviously this isn't a good idea for a typical turbo, connected through the exhaust stream. But if you were blowing CO2 gas through there, no problem.

The other equation suggests the opposite, that it would take a insane amount of CO2 to drive the process, so much that usage isn't practical.

Basically I'm trying to determine if you have a super small turbine (rated for 6lb/min at 3:1 PR), and a large compressor (rated for 70lb/min), could the turbine produce sufficient power by passing 5-10lb/min of CO2, at 100-200psi of backpressure?

 

[GregLocock]

The first equation is obviously wrong. It is dimensionally incorrect for a start.

I am surprised your thermodynamics course did not cover this, it is first or second year stuff.

Cheers

Greg Locock

 

[Andy330hp]

Perhaps he was trying to express the equation W = (integral) p*dV for equation 1?

 

[obanion]

I don't really need to be able to calculate the EXACT numbers at this point. I just need to know what extream the truth lies at for plotting the amount of CO2 needed. If it will take >20lb/min of CO2 flow, it simply isn't practical. If I can pull this off with <10lb/min of CO2, then it's worth gathering the parts together to conduct some experiments.

 

[SBBlue]

Okay, a couple of questions here. . . . .

I think you have thoughts of driving a supercharger with your CO2 driven turbine. Is that right?

If so -- what is the efficiency of the turbine and supercharger? How much boost do you want the supercharger to provide? How much air flow is the supercharger expected to handle?

Next question -- you say you are going to use a turbine with a 3:1 pressure ratio. If you are using 100-200 psi to drive the turbine and you have a 3:1 pressure ratio, then the pressure of the gas coming out of the turbine will be 33-66 psi, which is well above atmospheric pressure.

I would think that you would wind up with two problems; 1) With that much of a pressure gradient, the turbine will overspeed, and 2) if it doesn't overspeed, the efficiency will go way down -- this may or may not be important, but you won't get the same efficiency as you would with an actual 3:1 pressure ratio.

Finally -- your second set of equations is the correct approach.