Project

ME 325 Project (Spring 2026)

The deadline is May 2nd, when you would need to upload (on Blackboard) a 5 minute video

presentation, power point slides, and supplemental information/calculations/figures by 11:00pm.

You do not need to add a written report, but your slides might need details of your method and

supporting figures.

Project background and description

One technology being evaluated is the supercritical Brayton cycle operating on CO2. This is a

closed cycle for which every state is supercritical. The reason you want supercritical fluid is

because it is very dense, and thus the power requirement for compression is lower. The

turbomachinery (turbines and compressors) might be 10 times smaller than the turbines in a

Rankine cycle! Many different supercritical fluids will do, but CO2 is considered promising

because its critical point is 73.8 bar and 31.1°C. Thus, you can make the lowest temperature of the

cycle essentially room temperature, and many existing heat exchangers can handle the waste heat

near room temperature. Admittedly the pressures are very high, but this can be managed. For a

couple of reasons which you might look up1, one of the most promising configurations is the

recompression closed Brayton cycle, which employs two compressors and two stages of

regeneration. In terms of the block diagram, it is shown below in Fig. 1. The main flow is split at

state 8 and merged at state 3. We would like to evaluate the pressure ratio and split that can

lead to the highest efficiency of the cycle and compare this to other power cycles. We will make

modest assumptions for the near state-of-the-art components that might be achievable soon. You

are asked to prepare a short, high-impact presentation for the plant designer to use to decide the

design of the plant.

Figure 1: Schematic diagram of the recompression closed Brayton cycle considered in this

project.

1 https://www.energy.gov/sites/prod/files/2016/06/f32/QTR2015-4R-Supercritical-Carbon-Dioxide- Brayton%20Cycle.pdf

You can assume the following:

1) There are no leaks, heat loss, or pressure drop throughout cycle. Thus P1, P8, P7, P6 are

all equal. Similarly, P2, P3, P4, and P5 are all equal.

2) The isentropic efficiencies of the compressors are 88% max.

3) The isentropic efficiency of the turbine is 90% max.

4) The maximum temperature that the turbines can see is 650°C. This will represent your

maximum T5. Note this is not achieved with a direct combustor in this case but imagine

an external combustor that efficiently adds heat (between states 4 and 5)

5) The regenerators have a maximum effectiveness of 90%.

6) The cycle is running on CO2 and must always be above the critical pressure and

temperature of CO2. P1 and T1 should be just above the CP of CO2.

7) You cannot assume that the cycle is a cold air standard. This is a very poor

assumption for near critical CO2. Don’t use any air standard assumption. You should use

thermodynamic software like Coolprop in order to figure out the properties of the fluid at

different states.

Hints:

1) The parameters p2/p1 and y are unknown, so you must use iterations in order to find the

possible combinations that could make a practical cycle, and then further iterate to optimize

your solution. In iteration, you would normally guess parameters for a solution and then

check the solution. More advanced iteration can help you rigorously choose your next

parameter set, but this is beyond the scope of this class.

2) While this type of solution might seem overwhelming, you can make some engineering

decisions to limit the range of parameters, and avoid searching in a large parameter space. As

an example, p2/p1 cannot be so high that the temperature before the heat exchanger is higher

than 650°C. You will find that these types of considerations will help you link possible

parameters.

3) You will find it easier to generate a spreadsheet or a computer script which calculates the

states of the Brayton cycle. This calculation is easily automated for different choices of

compressor ratios, etc. using CoolProp.

4) It is possible to automate the determination of states in real fluids. Tools like CoolProp can do

this.

5) Even when you calculate all the states and evaluate the efficiency of the cycle, using First Law

analysis, there are considerations that can invalidate the cycle (i.e. a parameter choice that will

prove wrong since it violates the second law, impractical temperatures and pressures, flow rates,

etc.). For example, an answer that involves a negative flow rate in the regenerator, or negative

entropy change in the absence of cooling, would clearly violate thermodynamic principles, and

thus would not be acceptable.

Deliverables

1) A recorded video presentation of no more than 5 minutes highlighting your analysis with

powerpoint slides. Audio is as important as the visual content. Note that Powerpoint allows you to

narrate your slides, so you would not need a camera for this. Technical content and clarity are more

important than style, visual effects, etc. However, your presentation is aimed at a technical

audience, i.e. delivering an impactful presentation to help an engineering manager choose a design.

Your presentation should include the following:

a) Extremely brief description of how you set up the problem. (More details in extra slides)

b) Show the operating envelope. This is the process parameters p2/p1 and y that could work.

Briefly describe what limits that envelope.

c) Recommendation of the best process choices for overall efficiency

d) Comparison of this solution against a Rankine or normal gas turbine cycle operating with

similar parameters.

e) Sensitivity of your solution to the extrema of your assumptions. For example, does your

solution greatly change if you cannot get a turbine to operate at 650°C? What if your

isentropic efficiencies or regenerator effectiveness are little lower?

2) Your powerpoint slide deck.

3) An example calculation of a cycle or the code you used to calculate the cycle.

Rubric: Impactful presentation (30%), Optimal solution and method (30%), Example

calculations/supplemental (40%).

Mathematical and thermodynamic background

1) You can use the first law analysis of open systems to write down the equations for the cycle efficiency. It will be a set of simple equations with many unknown parameters. (i.e. the enthalpies of many states, etc.)

2) You will notice immediately that you have many more unknown variables than known or given parameters. You will need to formulate a system of equations to solve the problem. For a well constrained/defined system, you will end up with the same number of equations and unknown variables. Some of these equations you can write explicitly (like using the first law of thermodynamics in an open system for the regenerators). Other properties are linked by fluid-specific equations, which may be tabulated (like an equation of state that links the pressure, density, and temperature of a fluid) or the enthalpy or entropy of a fluid. In the present case, fluid properties are interrelated by the given tables or via the software CoolProp (see #4 below). Of course, in the present case, you will not have equations to work with, rather you would need to look at the tables or use CoolProp to find a property of a known state of a given fluid.

3) Eventually, you need to know two additional parameters not specified in order to close the system (i.e. have a number of unknowns equal to the number of equations). These two parameters in this project are given to be P2/P1 and y. This is a selection that was made for you, so that the problem be more tractable. After this point, you will need to guess values of these parameters (P2/P1 and y) in order to solve the cycle. Different choices for these parameters will lead to different solutions (i.e. value of efficiency) for the cycle. In principle, some choice of these parameters would lead to higher values for efficiency, but finding the best choice is not trivial (it involves an iterative process, which is frequently used in engineering). But remember, in all cases, all your parameters would have to satisfy the equations that apply for the problem and have physical meaning. Furthermore, the best solution cannot violate the second law of thermodynamics or other practical considerations.

4) For the purposes of this project, you can perform iterations to observe trends rather than exhaustively finding the optimal parameters. Using CoolProp can help you determine the properties in an automated fashion. In engineering, one is better served by keeping all but one parameter fixed and changing this one parameter to designate how the main outcome variable (cycle efficiency in our case) is affected. For example, does a higher value of y when P2/P1 are fixed, increase or decrease the efficiency of the cycle? This method would guide you towards improving efficiency as you modify the assumed value of each of the guessed parameters P2/P1 and y.