# Exploration of a gas turbine in the entropy diagram

# Introduction

The objective of this exploration is to introduce you to the cycle of a gas turbine in the (T, s) entropy thermodynamic diagram.

It complements guided exploration (S-M3-V8) where the cycle was presented, with explanations on its settings and its representation in the diagram (h, ln (P)) diagram.

# Loading the model

We will now study the ejector refrigeration cycle.

## Load the model

Click on the following link: Open a file in ThermoptimOpen a file in Thermoptim

You can also:

- either open the "Project files/Example catalog" (CtrlE) and select model m6.2 in Chapter 6 model list.
- or directly open the diagram file (GT_light.dia) using the "File/Open" menu in the diagram editor menu, and the project file (GT_light.prj) using the "Project files/Load a project" menu in the simulator.

# Cycle plot in the (T,s) entropy diagram

## First step: loading the air (T,s) entropy diagram

Click this button

You can also open the diagram using the "Interactive Diagrams" line in the "Special" menu of the simulator screen, which opens an interface that links the simulator and the diagram. Double-click in the field at the top left of this interface to choose the type of diagram desired (here "Ideal gases")..

Once the diagram is open, choose "air" from the protected compound gases substance menu, and select "(T,s)" from the "Diagram" menu.

## Second step: loading a pre-recorded cycle corresponding to the loaded project, the layout of which has been previously refined in order to be more precise

Click this button

You can also open this cycle as follows: in the diagram window, choose "Load a cycle" from the Cycle menu, and select "GT_light_25Thin.txt" from the list of available cycles. Then click on the "Connected points" line in the Cycle menu.

## Cycle analysis

The "air inlet" point is located near the abscissa axis, at the intersection with the horizontal isotherm T = 25° C and the isobar P = 1 bar. The non-reversible adiabatic compression leads to point 2, on the isobar P = 16 bar.

The heating in the combustion chamber leads to point 3 at the intersection of the isobar P = 16 bar and the isotherm T = 1150°C.

Evolution (3–4) is a non-reversible adiabatic expansion from 16 bar to 1 bar. The entropy of point 4 is therefore greater than that of point 3.

## Apparent plot anomaly

Apparently, the cycle layout presents an anomaly: at the end of the isobaric evolution (2–3) corresponding to the combustion chamber, there is a sudden discontinuity.

This comes from the fact that the cycle involves several fluids: air, fuel and combustion gases. Strictly speaking, it cannot be accurately represented on a single diagram.

In this case, points 3 and 4 have the composition of the combustion gases, and their representation on the air diagram places them on incorrect isobars. If we load the diagram of the combustion gases, they are on the correct isobars, but this is no longer the case for points 1 and 2.

# Comparison with the Carnot cycle

η = (T1 - T2)/T1 = 1 - T2/T1

The Carnot cycle is the one that leads to the best efficiency.

It is given by this formula, T1 and T2 being the temperatures of the hot and cold sources (T1 > T2), expressed in K and not in°C.

We will now examine the temperature differences between the working fluid and the hot and cold sources.

## First step: the value of the temperature of the cold source is displayed on the diagram

Click this button

You can also open this cycle as follows:

- in the diagram window, choose "Load a cycle" from the Cycle menu
- and select "gasTColdsource.txt" from the list of available cycles.

## Second step: the value of the temperature of the hot source is displayed on the diagram

Click this button

You can also open this cycle as follows:

- in the diagram window, choose "Load a cycle" from the Cycle menu
- and select "gasTHotsource.txt" from the list of available cycles.

## Third step: loading of the Carnot cycle relating to external sources. Attention, point D has no physical reality.

Click this button

You can also open this cycle as follows:

- in the diagram window, choose "Load a cycle" from the Cycle menu
- and select "gazCarnot.txt" from the list of available cycles.

## Calculation of Carnot efficiency

To calculate Carnot efficiency, determine the values in Kelvin ​​of the hot and cold source temperatures, and apply the formula above.

Enter the temperature value of point A in Kelvin

Enter the temperature value of point B in Kelvin

Calculate Carnot's efficiency and enter it

## Fourth step: comparison of the project cycle and the Carnot cycle

You will now be able to compare the project cycle and the Carnot cycle.

## Isobaric combustion

The pressurized air burns at constant pressure with a fuel (light distillate, natural gas).

Given the shape of the isobars in an entropy diagram (resembling exponentials), the difference is important for this evolution compared to the Carnot cycle which stipulates that the thermal machine exchanges heat at constant temperature with the hot source.

## Taking into account expanstion irreversibilities

Expansion can be assumed to be adiabatic, but not isentropic. This results in irreversibilities and therefore a difference with the Carnot cycle.

What is the increase in entropy due to expansion?

What would the power of the turbine be if it was isentropic?

## Taking into account compression irreversibilities

Compression can be assumed to be adiabatic, but not isentropic. This results in irreversibilities and therefore a difference with the Carnot cycle.

What would be the compression power if it were isentropic?

What is the increase in entropy due to compression?

## Release of combustion gases into the atmosphere

In a simple gas turbine, the combustion gases leave the turbine at a temperature close to 500° C, and are released into the atmosphere, which constitutes a major source of irreversibility and a notable difference with the Carnot cycle.

# Conclusion

This exploration allowed you to familiarize yourself with the representation of the cycle of a gas turbine in the entropy diagram and to compare it with the Carnot cycle.