# Exploration of a simple helium closed cycle gas turbine

Simple gas turbine, compression ratio 2.7, turbine inlet temperature 900°C

# Introduction

The objective of this exploration is to guide you in your first steps of using Thermoptim, by making you discover the main screens and functionalities associated with a simple vlosed cycle gas turbine model.

You will discover the layout of the screens of the points and the processes, the way in which they can be reconfigured and calculated, the concepts of useful and purchased energies making it possible to draw up the global energy balances.

You will visualize the cycles in the (h, ln(P)) thermodynamic diagram and you will carry out sensitivity studies of the cycle to the outside temperature, the turbine inlet temperature and the compression ratio.

In its simplest and most widespread form, a closed cycle gas turbine is composed of four elements:

- a compressor, centrifugal or axial, which has the role of compressing the working fluid;
- a heater in which the fluid is heated to a high temperature;
- a generally axial turbine in which the gas leaving the heater is expanded.
- a cooler in which the gas leaving the turbine is cooled.

In this form, the gas turbine constitutes a continuous flow engine. Note that the compression work represents approximately 60% of the expansion work.

The name gas turbine comes from the state of the working fluid, which always remains gaseous.

In this example, the heater is a nuclear reactor.

## Settings retained

In this example, a flow rate of 140 kg/s of helium enters at point 1 into a compressor with a polytropic efficiency of 0.9, at a pressure of 24.7 bar and a temperature of 30°C.

It is compressed to 70 bar and then directed to the reactor core, from which it exits at point 3, at 900°C and 66.5 bar.

This flow is expanded to 26 bar in a turbine (3-4) used among other things to drive the compressor, and then cooled to point 1 at 30°C, which closes the cycle.

## Technological aspects

The compressor and the expansion turbine are generally multi-stage. The axial rotors consist of a stack of discs, either mounted on a central hub, or assembled in a drum around their periphery. The materials used range from aluminum or titanium alloys for the first stages to steel alloys and refractory alloys for the last stages, which can withstand temperatures reaching 500°C.

The nuclear reactor heater is made of graphite-coated low-enriched uranium pebbles. In this cycle, helium plays both the role of heat transfer fluid in the nuclear reactor and of working fluid.

# Loading the model

The model is loaded by opening the diagram file and an appropriately configured project file.

Start by loading the model, then perform the other proposed activities.

## Loading the model

Click on the following link: Open a file in Thermoptim

You can also open the diagram file (HeHTR24.dia) using the "File/Open" menu from the diagram editor menu, and the project file (HeHTR24.prj) using the "Project files/Load a project " menu from the simulator.

## Discovery of Thermoptim

The diagram editor allows you to describe graphically and qualitatively the system studied. It includes a palette presenting the different representable components and a work panel where these components are placed and interconnected by vector links.

The simulator allows you to quantify and then calculate the model described in the diagram editor. It includes the lists of the different points, processes, nodes and exchangers of the model.

Display these two windows and study their content.

## Main components of the model

How many main components does the cycle use?

Open the diagram editor and count the components of the model.

Please note: to answer this question, do not count the inputs and outputs of fluids among the components

3 4 5

## Mechanical energy

Which component (s) involve mechanical energy?

the compressor and the heater the turbine and the cooler the compressor and the turbine the turbine

## Energies involved

Enter the values in the text fields below. Your answer is evaluated against the correct value, with an interval corresponding to a precision which depends on the question.

### Remember that the energies received by a system are counted positively, and those it supplies to the outside are counted negatively. In Thermoptim screens, they are therefore positive or negative, depending on the case.

### However, in these exercises, enter only the absolute values of the capacities involved (in MW)

Value of compression power?

Value of the power of the turbine?

Value of net mechanical power?

Value of the thermal power supplied to the machine?

Value of the efficiency?

# Model settings

In this section, we will make the link between the model statement and the configuration of the main points and processes

## Settings retained

The state of point 1 at the compressor inlet is known: temperature of 30° C and pressure of 24.7 bar.

Open point 1 and examine its settings.

Its pressure is equal to 24.7 bar, and its temperature 30°C.

The compressor was set as follows: adiabatic, polytropic reference, polytropic efficiency equal to 0.9, and open system. Its compression ratio is calculated as the ratio of the pressure of the downstream point (2) to that of the upstream point (1). It is equal to 2.83.

Open the "compressor" process, and examine its settings.

It connects point 1 and point 2, and its configuration is "adiabatic", "polytropic reference", with a polytropic efficiency equal to 0.9.

The pressure of 70 bar is tet at point 2.

Open point 2. Its setting is "unconstrained", which means that the pressure and its temperature are independent.

When the "compressor" process is calculated, the temperature of point 2 is determined.

If you change the pressure of point 2, for example by entering 80 bar, the new end of compression temperature is calculated. It differs from the previous one.

The heater is modeled by an "exchange" process which allows the temperature of the compressed helium to be brought to 900°C. Its setting does not pose any particular problem except for the choice of the outlet point pressure.

In this cycle, the pressure drops in the heater and the cooler were considered to be not negligible, and they were assumed to be equal to 5% of the inlet pressure.

Evolution (3–4) is an irreversible adiabatic expansion from 66.5 bar to 26 bar, with polytropic efficiency η = 0.9.

This evolution is modeled by the "turbine" process.

The upstream state of the fluid is that of point 3, the pressure and temperature of which are known.

For the downstream point, only the pressure is known.

Open the "turbine" process, and examine its setting.

It connects point 3 and point 4, and its setting is "adiabatic", "polytropic reference", with a polytropic efficiency equal to 0.9.

It is in point 4 that the outlet pressure of 26 bar is set.

If you change the value of the polytropic efficiency, the new outlet temperature is calculated.

# Cycle plot in the (h, ln (P)) diagram

## First step: loading the helium (h, ln (P)) diagram

We will now study the cycle in the (h, ln (P)) diagram, which allows you to read directly read on the abscissa axis the enthalpies put into play.

Click this button

You can also open the diagram using the "Interactive Charts" 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, select "(h, p)" in the "Graph" menu, and click on the line "Load a gas from the data base" in the Gas editor menu, and choose "He" from the protected compound gases.

If you do not have access to the (h, P) diagram of the gas turbine, open the Help/Global settings menu in the Thermoptim simulator screen, check the "(h, P) diagram for gas" option at the bottom on the left, then close the window by clicking on "OK".

Restart Thermoptim. The (h, P) charts should be displayable.

If the window is displayed correctly, but without showing the lines of iso-values the diagram, it is undoubtedly that the interval for displaying the values is not the right one, due to the previous settings.

It is possible to modify the calculation and display values by playing on the parameters in the diagram menus:

- Open the Diagram/X-axis menu line, then enter a minimum of 0 and a maximum of 5500 to define the values of the enthalpies to be displayed
- Open the Diagram/Y-axis menu line, then enter a minimum of 10 and a maximum of 80 to define the values of the pressures to be displayed
- If the lines of iso-values are not the right ones, open the menu line Diagram/parameters, then enter the following values to define the iso-values to be displayed:
  - Temperatures between 0°C and 1000°C
  - Pressures between 10 and 80 bar

## 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_He.txt" from the list of available cycles. Then click on the "Connected points" line in the Cycle menu.

## Cycle analysis

Point 1 is close to the abscissa axis, at the level of isobar P = 24.7 bar. The non-reversible adiabatic compression leads to point 2, on the isobar P = 70 bar.

The change in enthalpy between points 1 and 2 is proportional to the power consumed by the compressor.

The heating in the nuclear reactor leads to point 3, at the intersection of the isobar P = 66.5 bar and the isotherm T = 900°C.

The change in enthalpy between points 2 and 3 is proportional to the power supplied to the heater.

Given that there are pressure drops, the evolution is not horizontal.

Evolution (3–4) is a non-reversible adiabatic expansion from 66.5 bar to 26 bar. The change in enthalpy between points 3 and 4 is proportional to the power generated by the turbine.

The cooling of helium leads to point 1.

Given that there are pressure drops, the evolution is not horizontal.

# Variation in performance when helium temperature changes

The previous model assumed that the inlet compressor temperature was 30°C.

Let us now examine the operation of the plant when the outside temperature is 35°C.

Enter this value in point 1, then recalculate it.

Then recalculate several times in the simulator screen until the balance stabilizes.

Once the settings have been made, in order for the modifications to appear in the diagram editor, hide the values, then re-display them, by selecting the menu line "Special/Show values" twice, or by typing twice the F3 key.

## Reduction in useful power

The increase in helium temperature has the effect of reducing the useful power

For comparison, here are the performance values of the cycle with helium temperature of 30°C (first part of the exploration)

by how much does the useful power decrease?

by how much decreases the purchased power?

## First law balance

what is the value of the compression power?

## Power produced by the turbine

what is the value of the power produced by the turbine?

## Efficiency value

what is the value of the efficiency?

# Determination of polytropic efficiency when the state of the exit point is known

The initial model (T1 = 30°C) assumed that the polytropic efficiency of the compressor was known.

Let us now examine the configuration of the model when we know not its value but that of the state of the exit point (225°C, 70 bar).

Go back from the initial setting and enter these values in the screens of points 1 and 2, then recalculate them.

In the screen of the "compressor" process, select the option "Calculate the efficiency, the outlet point being known" at the bottom right, then recalculate the process.

What is the new value of the polytropic compression efficiency? (enter its value between 0 and 1)

It is thus possible to set compression or expansion knowing either its polytropic efficiency or the state of its outlet point.

# Conclusion

This exploration introduced you to Thermoptim and using this software package to make settings for a simple model.

You can perform others to analyze the sensitivity of the model to various parameters, such as the polytropic efficiency of the turbine.

We recommend that you read the Thermoptim documentation, and in particular the first two volumes of its reference manual.

Other guided explorations will allow you to study variants of this cycle to improve performance.