Recently scientists and engineers have turned their attention again to carbon dioxide as a working fluid to increase the efficiency of the Brayton cycle. But why has this become such a focus all of a sudden?

The first reason is the economical benefit. The higher the efficiency of the cycle is, the less fuel must be burned to obtain the same power generation. Additionally, the smaller the amount of fuel burned, the fewer emission. Therefore, the increase in efficiency also positively affects the environmental situation. Also, by lowering the temperature of the discharged gases, it is possible to install additional equipment to clean exhaust gases further reducing pollution.

So how does all of this come together? Figure 1 demonstrates a Supercritical CO2 power cycle with heating by flue gases modeled in AxCYCLE™. This installation is designed to utilize waste heat after some kind of technological process. The thermal potential of the exhaust gases is quite high (temperature 800° C). Therefore, at the exit from the technological installation, a Supercritical CO2 cycle was added to generate electrical energy. It should be noted: if the thermal potential of waste gases is much lower, HRSG can be used. More information on HRSG here: https://blog.softinway.com/en/introduction-to-heat-recovery-steam-generated-hrsg-technology/

Any cycle of a power turbine installation should consist of at least 4 elements : 2 elements for changing the pressure of the working fluid (turbine and compressor) and 2 elements for changing the temperature of the body (heater and cooler). The cycle demonstrated in Figure 1 has an additional regenerator, which makes it possible to use a part of the heat of the stream after the turbine (which should be removed in the cooler) to heat the stream after the compressor. Thus, part of the heat is returned to the cycle. This increases the efficiency of the cycle, but it requires the introduction of an additional heat exchanger.

The heat exchangers used in the sCO2 cycle are of three basic types: heaters, recuperators, and coolers. Typical closed Brayton cycles using sCO2 as the working fluid require a high degree of heat recuperation.

Having examined this scheme and examined the process in detail, we can draw the following conclusions about the advantages of this cycle which is demonstrated in Figure 2:

- If the fluid at the inlet to the compressor is in a supercritical state and close to the critical point, then the pressure ratio is so small that we can use a compressor almost like a pump
- The installation comes out quite compact due to the high working pressure.
- Vastly reduced water consumption due to dry cooling (suitable for arid environments).

But in addition to the obvious advantages of this installation, there are also negative aspects:

- Even though the installation itself is compact, heat exchangers occupy a large portion of the size due to a large amount of heat transfer.
- Heat exchangers in a cycle without phase transition have a low heat transfer coefficient in comparison to cycles with phase transition as with a heat exchanger in a Carnot cycle. This results in a large metal consumption of heat exchangers and their high cost.

Thus, when designing the optimal supercritical CO2 cycle, two factors must be taken into account that affect the efficiency of the installation oppositely:

- An increase in the heat transferred in the regenerator leads to an increase in the efficiency of the cycle. Consequently, during operation, installation costs will be lower with the same power output.
- On the other hand, the more the regenerator transfers heat, the higher its dimensions and cost are. This leads to an additional capital investment in the installation.

Therefore, the designer must find a balance between these two factors to achieve the highest economic efficiency of the installation. For this balance, it is necessary to combine the calculation of the cycle with a preliminary design of heat exchangers in a single iterative process.

AxSTREAM NET™ is excellent for the design of heat exchangers of this cycle. It has many features for building hydraulic networks, including heat exchangers including:

- A wide range of built-in models for calculating heat transfer coefficients and hydraulic resistances, including CO2-specific ones. If you need to use your empirical data or use other formulas for calculation in AxSTREAM NET™, you can write this in the form of scripts in C # or Python, or use tabular data.
- A built-in model for calculating radiant heat transfer.
- It is possible to change the properties of materials depending on temperature.
- It is possible to conduct off-design calculations of heat exchangers in conjunction with the entire pipeline network, including in a transient setting.
- It is possible to automatically combine AxSTREAM NET™ calculations with the calculations of the cycle and other elements of the system (for example, turbines and compressors) through AxSTREAM ION™. This allows you to automate the process of optimizing the system and its components at different stages of design.

Let’s take a look at the design of heat exchangers in AxSTREAM NET™ using the example of a heater.

To start, let’s look at the design of the heater, demonstrated in Figure 3.

We can see that the design consists of an array of staggered microtubules, inside of which CO2 moves. These tubes are located inside a rectangular channel through which combustion products move. The heating gas and CO2 flows have a common countercurrent flow, although each tube is perpendicular to the gas flow.

A significant advantage of AxSTREAM NET™ is the ability to create schemes with different levels of details.

For example, at the initial stages of design, you just need to estimate the design of the future heat exchanger. At this stage, it is possible to create a simplified diagram of the heat exchanger. A simplified diagram of the heater is shown in Figure 4.

When constructing such a simplified scheme, the calculation of the heat exchanger will be based on the average flow parameters. But for this option, it is possible to make a slight modification in the design of the heat exchanger and its optimization. The total length of the snake-water pipes is modeled; the heat transfer coefficient is determined (the average for the entire length of the heat exchanger), radiation heat transfer can also be considered. It is easy to change the pipe lengths, their number across and along with the flow, pipe pitch, etc.

When the preliminary design of the heat exchanger is selected, it is possible to carry out its accurate calculation. An example of such a Heater simulation is shown in Figure 5. In the detailed method, the heat exchanger is “broken down into elements”, this way we can get accurate data, which takes place at a particular length of the apparatus. Here we can observe in detail all the characteristics of interest. For example, we can check the temperature of the pipe walls. In Figure 5, the change in this temperature is indicated by a colored outline.

When designing sCO2 cycles, we should take into account the fact that the dimensions of the heat exchangers will be significant. Therefore, it is important to optimize the parameters of the cycle and the design of its elements for maximizing the efficiency of the cycle at economically feasible sizes of the heat exchangers.

The use of the AxSTREAM NET™ tool is convenient for designing heat exchangers as it allows designers to create heat exchanger circuits with various levels of detail. Moreover, the calculation accuracy is very high: in comparison with CFD calculations, the difference is less than 5%!

Read more about AxSTREAM NET here: http://www.softinway.com/en/software-applications/cooling-flows-secondary-systems