Thermodynamics turbocharger question

In summary, the discussion focused on finding the turbocharger rpm, efficiency, and temperature of the air leaving the turbo for a 10 L truck engine with 100% volumetric efficiency. The approach involved using the ideal gas law and volumetric equation to determine mass flow rate, then referencing a compressor map to find the corrected air flow and pressure ratio. The ideal and actual exiting temperatures of the air were calculated using equations for isentropic conditions and efficiency, but information on the turbine efficiency and temperatures was still needed. It was suggested to use the adiabatic flame temperature and 1st law of thermodynamics to calculate the work requirement for the compressor and determine the outlet temperature needed for the turbine, which could then be used to find
  • #1
thorx440
11
0

Homework Statement


A 10 L truck engine has a volumetric efficiency of 100%. It has a turbocharger which increased the mass flow of air and its pressure by a factor of 2 when the engine is running at 4300 rpm. Find the turbocharger rpm, efficiency, and the temperature of the air leaving the turbo.

Inlet conditions are 1 atm and 80 degrees F. The AFR is 98% and therefore the volume occupied by fuel is negligible. Also, the turbocharger can be assumed to be adiabatic

(Also given compressor map not shown here)

The attempt at a solution
So I first used the ideal gas law to find the density of air at the given conditions. Using this density, I then used the volumetric equation to find the mass flow rate through the turbo, and doubled that value since it is increased by a factor of two. Now by looking at the compressor map, I have the corrected air flow, as well as the pressure ratio, which allowed me to find the rpm as well as the compressor efficiency. This is where I got stuck. Assuming an isentropic turbo, I was able to find the ideal exiting temperature of the air using the T2 = T1(P2/P1)^(k-1/k) equation. Using that value, I then plugged it back into the efficiency equation and found the actual exiting temperature of the air. Now I have the inlet and outlet temps of the air in the compressor, as well as the turbo rpm speed, but know nothing about the turbine efficiency or temperatures. Is there a relationship between the turbine and compressor that I am missing? Or is there another way to find the temperature of the turbine?

I am assuming that I need to find the outlet temperature of the turbine, and then go about finding the efficiency of the turbine. With the efficiency of the compressor and the turbine, I can then find the efficiency of the whole turbocharger. I am just not seeing how to find any information on just the turbine.

Any help?
 
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  • #2
Can't you calculate the turbine inlet temperature assuming the exhaust from the engine is adiabatic using the adiabatic flame temperature knowing the AFR? Using AFR, you can get the molar ratio and balance the equation and solve for the T adiabatic using a reference temperature and the enthalpies of the reactants can be looked up and use the Cp(T_ad-T_ref) relation for enthalpy of each product. 1st law of thermo in effect. Steady, so the dt term is gone. Left with mass flow rate * enthalpy terms. Instead of mass, you can do molar relation instead.

Knowing that, you know the work requirement of the compressor and you can calculate what the outlet temp needs to be for the turbine to get your work out. Then calculate efficiency.
 

Related to Thermodynamics turbocharger question

What is a thermodynamics turbocharger?

A thermodynamics turbocharger is a device that uses exhaust gases from an engine to compress air and increase its density before it enters the engine. This results in improved engine efficiency and increased power output.

How does a thermodynamics turbocharger work?

A thermodynamics turbocharger works by using a turbine and a compressor connected by a shaft. The turbine is powered by the exhaust gases, causing the compressor to spin and compress the air before it enters the engine. This compressed air allows for more fuel to be burned, resulting in increased power output.

What are the benefits of using a thermodynamics turbocharger?

The main benefits of using a thermodynamics turbocharger include increased engine power, improved fuel efficiency, and reduced emissions. It also allows for smaller and lighter engines to produce the same amount of power as larger engines without a turbocharger.

What are the common materials used in a thermodynamics turbocharger?

The most common materials used in a thermodynamics turbocharger include steel, aluminum, and titanium. These materials are chosen for their strength, durability, and heat resistance properties necessary for the high temperatures and pressures within the turbocharger.

What are the potential drawbacks of using a thermodynamics turbocharger?

One potential drawback of using a thermodynamics turbocharger is turbo lag, which refers to the delay in power delivery due to the time it takes for the turbine to spin up. Another drawback is the increased strain on the engine, which may lead to decreased longevity. Additionally, some turbochargers may produce excess heat, which can be damaging to the engine if not properly managed.

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