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BRAYTON CYCLE THE IDEAL CYCLE FOR GAS-TURBINE ENGINES

We were discussing Otto cycle, an ideal cycle for internal combustion spark ignition reciprocating engines or simply petrol engines and also Diesel cycle, the ideal cycle for the operation of internal combustion compression ignition reciprocating engines in our previous posts.

Today we will see here another very important topic i.e. Brayton cycle: The ideal cycle for gas turbine engine with the help of this post.

Brayton cycle: The ideal cycle for gas turbine engine

In our previous post, we were discussing working principle of open cycle gas turbine. We have also already discussed that closed cycle gas turbine engines are usually used in nuclear power stations and also used as standby power unit for the hydro electric power stations.

Compressor, Turbine, heat exchanger for heating the working fluid termed as heating chamber and heat exchanger for cooling the working fluid termed as cooling chamber are the main components of closed cycle gas turbine engine.

Open cycle gas turbine engine could be modelled as closed cycle gas turbine engine. Combustion process will be replaced here by constant pressure heat addition from an external source in heating chamber and discharge process will be replaced by constant pressure heat rejection in cooling chamber.

Let us see the arrangements of various components of Brayton cycle or Joule cycle

Air will enter in to the compressor, where pressure and temperature of air will be increased. Now air at high pressure and high temperature will enter to the heating chamber as shown in above figure.
Working fluid i.e. high pressure and high temperature air will be heated from an external source in heating chamber. High temperature nuclear rods are used here for heating the working fluid i.e. air. Hence working fluid i.e. air will have high pressure and high temperature at the discharge of the heating chamber.

High pressure and high temperature air will enter in to the turbine, where high pressure and high temperature air will be expanded through the turbine. Pressure and temperature of the air, both will be dropped here.

There will be drop in temperature of air but still temperature of air will be high, while pressure of air will be reduced up to the pressure at which air will enter in to the cooling chamber.

Air will be cooled in to the cooling chamber at constant pressure up to its original temperature with the help of continuous circulating cold water and hence heat will be rejected here at constant pressure. Again cold air coming from cooling chamber will enter to compressor for repeating the cycle.

As we can observe here that exhaust air is not rejected to atmosphere but also exhaust air re-circulated to the cooling chamber and therefore this cycle will be termed as closed cycle gas turbine engine.

Work energy will be generated from the turbine during the expansion of high pressure and high temperature air and some part of this generated work will be used to drive the compressor and hence compressor and turbine are assembled with common shaft as shown in above figure.

Let us see the processes involved in Brayton cycle or Joule cycle

Process 1-2: Isentropic compression process, air entering in to the compressor will be compressed here at high pressure and high temperature. Pressure will be increased from P1 to P2 and volume will be decreased here from V1 to V2. Temperature will be increased from T1 to T2 and entropy will remain constant as this process will be isentropic process.

Process 2-3: Constant pressure heat addition in to the heating chamber. Air will be heated from an external source in heating chamber. Temperature of working fluid i.e. air will be increased here from T2 to T3 and entropy will also increased from S2 to S3.
Process 3-4: Isentropic expansion process, high pressure and high temperature air will be expanded through the turbine. Pressure of working fluid i.e. air will be reduced here from P3 to P4 and volume will be increased here from V3 to V4. Temperature will also be reduced from T3 to T4 and entropy will remain constant as this process will be isentropic process.

Process 4-1: This process indicates the constant pressure heat rejection process, where Air will be cooled in to the cooling chamber at constant pressure up to its original temperature with the help of continuous circulating cold water. Working fluid i.e. air will be cooled here from T4 to T1 and entropy will also reduced from S4 to S1.

Let us see here the thermal efficiency of the Brayton cycle or Joule cycle

As we can see here from PV and TS Diagram, all four processes of Brayton or joule cycle are executed in steady flow devices and therefore we will analyze these processes as steady flow processes.

We will see here the various energy calculations for unit mass
Input heat energy, qin = h3-h2= CP (T3-T2)
Output heat energy, qout =h4-h1= CP (T4-T1)

Thermal efficiency of the ideal Brayton cycle will be determined as follow
As we can see that process 1-2 and 3-4 are isentropic processes and we have also observed here that P2=P3 and P4=P1
Let us substitute above equations into the relationship of thermal efficiency of ideal Brayton cycle and we will have following equation.
Where rP is the pressure ratio and k is the specific heat ratio. We can say from above equation of thermal efficiency of Braytron cycle that thermal efficiency of Braytron cycle will be dependent over the pressure ratio and specific heat ratio of the working fluid.

Do you have any suggestions? Please write in comment box.
We will see another topic in our next post in the category of thermal engineering.

Reference:

Engineering thermodynamics by P. K. Nag
Engineering thermodynamics by Prof S. K. Som
Image courtesy: Google

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