# Exploration of a steam plant in the entropy diagram

# Introduction

he objective of this guided exploration is to introduce you to the cycle of a steam power plant in the thermodynamic entropy (T, s) diagram.

It complements exploration S-M3-V7, where the cycle was presented, with explanations on its settings and its representation in the (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 m6.1 in Chapter 6 model list.
- or directly open the diagram file (steam_light.dia) using the "File/Open" menu in the diagram editor menu, and the project file (steam_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 water (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 "Vapors").

Once the diagram is open, choose "water" from the 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 "cycle_lightEnThin.txt" from the list of available cycles. Then click on the "Connected points" line in the Cycle menu.

## Cycle analysis

Points 1 and 2 representing liquid compression are almost superimposed, and the heating in the liquid state almost coincides with the saturated liquid line.

The vaporization is done according to a horizontal line segment.

Isobaric superheating corresponds to the maximum peak of the cycle, and irreversible expansion results in an increase in entropy, point 4 being located in the liquid-vapor equilibrium zone (steam quality equal to 0.835).

Condensation takes place along the horizontal line segment (4 - 1).

## Identification of some characteristic points in the diagram

Enter a point in liquid zone

What is the point in two-phase zone?

What is the point with the highest temperature?

# Comparison with the Carnot cycle

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

η = (T1 - T2)/T1 = 1 - T2/T1

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 (15°C) 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 "steamTColdSource.txt" from the list of available cycles.

What is the temperature difference (water - cold source)?

Note that water condenses at a temperature higher than that of the cold source

## Second step: the value of the temperature of the hot source (600° C) 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 "steamTHotSource.txt" from the list of available cycles.

What is the temperature difference (end of superheating - hot source)?

Please note that the hot source temperature must be higher than that of superheating.

## 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 "steamCarnot.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.

Let us call DeltaThot the difference between the high temperature of the Carnot cycle and the average value of that of water between points 3a and 3

Call DeltaTcold the difference between the low temperature of the Carnot cycle and that of the condenser

## Temperature differences between the steam power plant and external sources

Indicate which of these statements is true.

In practice, due to finite heat exchanger dimensions, the working fluid cannot be at the same temperature as external sources, which constitutes a first difference with the Carnot cycle.

DeltaThot is almost 10 times higher than DeltaTcold DeltaThot is almost 30 times higher than DeltaTcold DeltaThot is close to DeltaTcold DeltaThot is almost 10 times lower than DeltaTcold DeltaThot is almost 30 times lower than DeltaTcold

## Taking into account expansion 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, as a first approximation, be assumed to be adiabatic, and even isentropic, the irreversibilities taking place in the pump being low. However, we deviate significantly from the Carnot cycle because the temperature at the end of compression remains very close to that of the cold source, instead of that of the hot source

What is the average Delta T between the hot source and the economizer?

# Conclusion

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