Intermediate Thermodynamics Project

posted in: Research Paper | 0

Upload a short video presentation on Blackboard by 10pm. You should also upload supplemental materials, including powerpoint slides at the same time.

Project background and description The availability of inexpensive natural gas has resulted in a shift of the energy source for power generation. For many reasons, natural gas is burned in the combustors of gas turbines. The Brayton cycle is the standard power cycle of gas turbines, and includes a compressor, a combustion chamber, and a turbine. Even with regeneration, which preheats the compressed air going into the combustor using the turbine exhaust gases, the exhaust temperature of the gases leaving the Brayton cycle is generally high, and offers a large source of heat.

A combined cycle can be formed by using that excess heat to run another process. The part of the cycle with the direct consumption of fuel is called the topping part of the combined cycle. The part of the cycle running on the reject heat is called the bottoming part of the combined cycle. In this example, the exhaust temperature is in an intermediate range: high enough that it makes sense to use the otherwise waste heat to heat up a working fluid in a bottoming Rankine cycle for additional conversion of that heat to work, but low enough that a working fluid other than water might be more suitable for the Rankine cycle to run more efficiently. This project involves the engineering analysis of an exotic combined cycle for electric power generation that also requires selection of the working fluid for the bottoming Rankine cycle.

Figure 1 shows a combined cycle formed by a gas turbine (top) and an organic Rankine bottoming cycle (bottom). Steady-state operating conditions are marked on the figure. The plant designer would like to evaluate three different working fluids — propane, R134a, and water for the Rankine cycle.

For each working fluid, specify workable ranges for p8 (turbine inlet pressure) and T8 (turbine inlet temperature); also determine the turbine exit pressure p9. You must investigate the influence of p8, T8, p9 and compressor pressure ratio (p2 / p1) on the net combined- cycle electricity production and on the combined-cycle thermal efficiency. Owing to internal irreversibilities, the generator electricity output is 95% of the input shaft power for both units. The regenerator preheats air entering the combustor. In the evaporator, hot exhaust gas from the regenerator vaporizes the Rankine cycle working fluid.

Identify the bottoming working fluid and operating conditions that result in the greatest net combined-cycle electricity production. Repeat the process for greatest combined-cycle thermal efficiency. Apply engineering modeling compatible with that used in the text and in the class for Rankine cycles and cold-air-standard analysis of gas turbines. You are asked to prepare a short, high-impact presentation for the plant designer to use for deciding the design of the plant.

Figure 1: Schematic diagram of the combined cycle considered in this project.

Hints:

1) As there are four unknown parameters, p8, T8, p9 , and p2/p1, you will have to use iterations in order to find the possible combinations that could make a practically viable combined cycle, and then further iterate in order 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 in order to limit the range of parameters, and avoid searching in a large parameter space. As an example, p9 controls the pressure of the condenser and thus the temperature of the condenser in the Rankine cycle. You can use the saturated temperature of the working fluids to eliminate some pressures for p9 quite easily. Also, the

3

condenser cannot operate at cryogenic temperatures if it is going to reject heat in a terrestrial application! Similarly, if the post combustion temperature in the Brayton part of the cycle is limited to 1200K, you would know that a pressure ratio resulting in a higher temperature than 1200K will not make sense! You will find that these types of considerations will help you link possible parameters.

3) You will probably find it easier to generate a spreadsheet or a computer script which calculates the states of the Brayton cycle. Since you may assume a cold-air standard cycle, this calculation is easily automated for different choices of compressor ratios, etc.

4) It is possible to automate the determination of states in real fluids. Tools like CoolProp can do this. However, this is not necessary to solve the problem, which can be solved with the steam-tables in the back of your textbook.

5) Even when you calculate all the states and evaluate efficiency and power of the combined cycle, using First Law analysis, there are many considerations that can invalidate the cycle (i.e. a parameter choice that will prove wrong since it violates the second law, really impractical temperatures and pressures, flow rates, etc.). For example, an answer that involves negative flow rate in the feedwater, or negative entropy change in the absence of cooling, would clearly violate thermodynamic principles, and thus would not be acceptable.

Deliverables:

1) You are asked to record a video presentation of no more than 5 minutes highlighting your analysis with powerpoint slides. Audio is as important as the visual content. Technical content and clarity are more important than style, visual effects, etc., but please prepare these for a technical audience. Your presentation should include the following:

  1. a) Brief conceptual description of how different working fluids impact the performance of the combined cycle.
  2. b) Brief description of how you set up the problem. c) Description of the process parameters that could work. d) Description of what considerations eliminated other choices. e) Recommendation of the best choices for efficiency, power generation

2) You are also asked to supplement your analysis with graphs and sample calculations (no need to show all iterative cycles, just one) to be submitted along with your powerpoint slide deck.

Also see: Lab 8: Chemical Processes

Additional hints on solving the project problem

Mathematical background

1) You can use the first law analysis of open systems in order to write down the equations for net power generation in the combined cycle and efficiency. It will be a set of simple equations with many unknown parameters. (i.e. the enthalpies of many states, e.g. 8-11, the mass flow rates, 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 to link power, mass flow rates, and enthalpy differences). 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).

3) Eventually, you will find that you need to know four additional parameters in order to close the system (i.e. have a number of unknowns equal to the number of equations). These four parameters in this project are given to be P2/P1 , T8 , P8 , and P9. 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 four parameters (P2/P1, T8 , P8 , and P9) in order to solve the cycle. Different choices for these parameters will lead to different solutions for the cycle. In principle, some choice of these parameters would lead to maximum values for power and efficiency, but finding that choice is not trivial (it involves an iterative process, that is frequently used in engineering). But remember, in all cases, all your parameters would have to satisfy the equations that apply for the problem.

4) For the purposes of this project, you might just try a few iterations to observe trends (even if you have to solve the calculations by hand, i.e. determine enthalpies and other properties from the applicable tables) rather than exhaustively finding the optimal parameters, using CoolProp that can determine the properties in an automated fashion. In engineering, one is better served by keeping all parameters fixed and changing another parameter, to designate how the main outcome variable is affected. For example, does a higher value of T8 when P2/P1 , P8 and P9 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 four parameters.

Practical example of the solution procedure:

Identify the properties necessary for efficiency and power, as above. The system of equations between the given properties, guessed properties, and efficiency and power will have to be solved one time, after which time you can just plug in different values for the guesses. Here are the details for one iteration for R-134a. (I pulled the numbers from CoolProp, your values for enthalpy will be different if you use the tables from the back of your textbook, but the differences in enthalpies should be very close)

1) Guess the four parameters identified from the start: a) P2/P1 = 10, b) T8 = 450 K, c) P8 = 20 bar, d) P9 = 12 bar.

2) From the given/guessed properties and constant pressure processes, you can solve for the pressures everywhere P2, P3, P4, etc.

3) Calculate isentropic state 2s, i.e. T2s

4) Calculate state 2 accounting for isentropic efficiency of compressor. (in this case, T2 = 629K)

5) Calculate isentropic state 5s

6) Calculate state 5 accounting for the isentropic efficiency of the turbine (in this case, T5 = 708K)

7) Calculate state 3 using regenerator equation. (I got T3 = 692 K)

8) Calculate state 6 using the energy balance on the regenerator.

9) Identify mass flow rate of the air in the gas turbine part of the cycle by comparing net power and the information from the turbine and compressor. (I got 0.65 kg/s)

10) Specific enthalpy and entropy of the R-134a state going into the turbine of the Rankine cycle can be obtained from your guess. You need to make sure it is a vapor state…

11) Calculate the isentropic state 9 using your guessed P9 and the fact that s8 = s9s

12) Use the isentropic efficiency of the turbine to calculate the real state 9 (I got T9 = 432 K)

13) Identify the density of the saturated liquid leaving the condenser. You can use this along with the pressure difference to calculate the isentropic power of the pump.

14) Use the isentropic efficiency of the pump to calculate the real power of the pump.

15) Use the energy balance on the heat exchanger in order to calculate the mass flow throughout the Rankine cycle. (I got 0.39 kg/s)

16) The above steps should result in values for all the parameters you need in order to calculate total thermal efficiency and total power. (I got 102.1 kW, and an efficiency of 31%)

17) Evaluate the feasibility of the result. Does the system violate the second law of thermodynamics anywhere? Are the values of temperature and pressure at different states appropriate?

18) Change parameters (sensibly) and repeat the above steps to determine whether you could find another set of the four parameters that produce a higher efficiency and/or maximum net power.

Last Updated on December 4, 2020 by Essay Pro