## Exploration of a steam power plant with reheat

You have so far studied the simple cycle of a steam power plant. You will now see how it can be improved, our aim being to minimize irreversibilities.

We have seen that real engine cycles deviate significantly from the Carnot cycle. The differences arise from, among other things, the following points:

- the cold source temperature is much higher than ambient temperature;

- the hot source temperature is much lower than the maximum flame temperature;

- the heat intake is done in part at variable temperature;

- the presence of irreversibilities in the components.

In practice, modifications to elementary cycles essentially concern:

- splitting compressions and expansions into several stages to approach isothermal transformations;

- increasing the operating temperature range;

- performing heat intakes or releases at temperatures as close as possible to the source temperatures.

The reference cycle we will use for steam power stations is a variant of the configuration presented in the guided exploration S-M3-V7: the low pressure is set at 0.023 bar, the high pressure at 165 bar, and the superheat temperature is 560°C, as shown in this diagram (project and diagram files: "steam_ref.prj" and "steam_ref.dia").

Let us calculate the Carnot efficiency for this cycle, with Tc = 15 + 273.15 = 283.15 K and Th = 1000 + 273.15 = 1273.15 K: η = 78%.

The actual efficiency is therefore close to 50% of the maximum theoretical efficiency.

As seen above, it is possible to improve such a cycle by staging compressions and expansions. Steam power plants with reheat apply expansion staging.

A first idea to improve the Hirn cycle is to approach the Carnot cycle by implementing reheat. In this case, we begin by partially expanding the fluid. It is then passed again through the boiler, where it is heated at the new pressure back to the maximum cycle temperature. This operation can optionally be repeated several times.

This results in efficiency gains of a few percent. Most importantly, as shown in the diagram, it increases the steam quality at the end of the expansion. This is valuable for extending the life of turbine blades, as liquid droplets are abrasive and can cause erosion.

The price to pay is higher complexity. However, since the expansion must be staged anyway in large turbines, this improvement has no major technological impact on the power plant design.

### Loading a cycle with reheat model

Click on the following link: Open a file in Thermoptim

You can also:

- download the file VapeurResurch7cci1.thopt;

- open it in Thermoptim by using the "Open Project…" line of the "Project" menu in the simulator screen;

- select the "diagram" tab.

Click this button

You can also open the diagram using the "Interactive Charts" line in the "Special" menu of the simulator screen. This opens an interface linking the simulator and the diagram. Double-click in the field at the top left of this interface to choose the desired diagram type (here "Vapors").

Once the diagram is open, choose "water" from the Substance menu, and select "(h, p)" from the "Diagram" menu.

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_RefEnThin.txt" then "cycle_ReheatEnThin.txt" from the list of available cycles.

You will get the plot of the cycles in the (h, ln(P)) diagram: the new cycle in black and the reference cycle in blue.

We can observe the clear increase in steam quality at the end of the expansion, as mentioned above.

The settings for the reheat cycle are very close to those of the reference cycle (a variant of the one presented in guided exploration S-M3-V7).

The main change concerns the modeling of the turbine. For simplicity, we considered in the reference model that it had a constant isentropic efficiency regardless of the high and low pressures. However, this hypothesis can be improved.

To correctly model the reheat, we will use a new concept: polytropic efficiency.

For a turbine, isentropic efficiency is defined as the ratio of the actual work provided by the turbine to the work it would have provided if the adiabatic expansion were ideal (reversible).

Knowing the isentropic efficiency ηs gives no indication of the path followed by the fluid during the irreversible expansion. To determine this path, additional assumptions are required.

One of the most common assumptions leads to the widely used notion of polytropic efficiency, which may cover slightly different definitions depending on the author.

The hypothesis we use here considers that irreversibilities are uniformly distributed throughout the expansion. This amounts to assuming that, during any infinitely small stage of the transformation, the isentropic efficiency keeps a constant value. By definition, this value is equal to the polytropic efficiency ηp, which thus appears to be an infinitesimal isentropic efficiency.

For multi-stage machines with a large number of stages constructed similarly (as is the case for steam turbines), this efficiency has a clear physical meaning: it is, in a way, the elementary efficiency of a single stage.

Knowing the polytropic efficiency of a stage, it is possible to determine the isentropic efficiency of the entire multi-stage machine. This global efficiency varies according to the number of stages, which is itself linked to the expansion ratio.

Modeling a multi-stage turbine using a polytropic approach is therefore more realistic than assuming a constant isentropic efficiency.

In Thermoptim, you can define compression or expansion by choosing one approach or the other, and switch between them without difficulty, as you will see.

Based on this, the high and low-pressure turbines in the reheat cycle model are defined using the polytropic reference, with a polytropic efficiency equal to 0.805.

Open the high-pressure turbine screen to see how Thermoptim calculates the equivalent isentropic efficiency.

To do this, select the options "isentropic reference" and "Calculate the efficiency, the outlet point being known", then click on "Calculate".

The value of the isentropic efficiency of the machine during expansion from 165 bar to 10 bar is thus determined: 0.8385. This allows you to switch between settings without difficulty.

For the continuation of this guided exploration, return to the initial configuration: polytropic reference, polytropic efficiency equal to 0.805, and calculation mode "Set the efficiency and calculate the process".

With these settings and an intermediate pressure of 10 bar, the result of the reheat cycle modeling is provided by Thermoptim: the efficiency increases from 38% for the reference cycle to 41.8%.

What is the value of the useful power?

What is the value of the heat input (thermal power supplied)?

Reheat has the effect of increasing the useful power.

For comparison, this synoptic view provides you with the performance values of the reference unit.

By how much does the useful power increase?

By what value does the heat input increase?

### Exercise: Optimize the intermediate pressure

Look for the intermediate pressure that leads to optimal performance.

Check whether the intermediate pressure of 10 bar has been chosen correctly by studying its influence on cycle performance (efficiency and power).

You have learned that "exchange" type processes offer an option called "isobaric", which automatically propagates the pressure from the upstream point to the downstream point. The "reheat" process has been set in this way.

To change the value of the intermediate pressure, open the screen for point 4, modify its pressure, and click "Calculate". Then recalculate several times in the simulator screen until the balance stabilizes.

This exploration has allowed you to see the benefit of staging the expansion followed by a reheat on the plant's performance.

It also demonstrated that it is better to model multi-stage turbomachines using a polytropic approach.