5: The Brayton Cycle

5: The Brayton Cycle  

The operation of ramjet and gas turbine ("jet") engines can be expressed, in its most basic form, as a "Brayton Cycle" or "Gas Turbine Cycle" . There are four steps involved:  

Step

Thermodynamic Process

1. Compress the working fluid (air)

 

Adiabatic Compression

2. Add heat to the fluid

 

Constant Pressure Heat Addition

3. Extract work from the fluid by allowing it to expand

 

Adiabatic Expansion

 

4. Cool the fluid

Constant Pressure Heat Extraction

 

 

Note: Step 4 occurs in the atmosphere after the engine has passed. We don't worry about it because we don't need to re-use the same air, or pay to cool it.
Examples      
Brayton Cycle Analysis  

Net work output = work done by the system in Step (3) minus the work put into the system in Step (1).  

Net heat input=heat put in during Sep (2), assuming that we don't pay to cool the air, and cannot recover the heat that is lost in the exhaust gases.  

Ideal Cycle Efficiency=(Net work output) / (Net heat input)  

Net work output per unit mass flow rate =  

Net heat input = Efficiency  

Dividing throughout by specific heat ,     Now, the process from (A) to (B) is isentropic, as is (C) to (D). Also, pressure is constant from B to C, and from D to A.

Thus, and    

Thus,  

These are extremely useful results. Note: 1. As the engine "overall pressure ratio" increases, efficiency increases towards 1. This means that to get high efficiency, we must use a high pressure ratio.   2. efficiency = (heat added - heat wasted) / (heat added)   Thus, to increase efficiency, a). Increase Tc, the highest temperature in the engine b). Bring TD down as close to TA as possible: expand through the nozzle, and extract the maximum work possible. c). Reduce TB: take out heat from the compressor using heat transfer to the fuel (this is considered in supersonic-combustion engines which use cryogenic fuel).   3. If TD <TA, you get efficiency > 1: a perpetual motion machine. Thus, we see that in reality, the exhaust temperature cannot be lower than the ambient temperature.      

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