Computer Models Using Spreadsheets To Study Heat Engine Thermodynamics

Marine Power Systems is the second term of a two term course in thermodynamics at the U.S. Naval Academy. This is an applied thermodynamics course and is taught by the Marine Engineering faculty. One of the primary objectives of this thermodynamics course is to teach the thermodynamics of heat engines. Marine Power Systems takes the study of Heat Engine Cycles beyond the first step, introduction of how to work the Heat Engine Cycles. The Midshipmen at the Naval Academy write computer models of the heat engine cycles to study the thermodynamics of heat engines. The best example of the thermodynamic cycle modeled is the Brayton Cycle. The Marine Engineering students use a spread sheet program on their personal computers to model the Air Standard Brayton Cycle and run experiments by varying the independent variables. INTRODUCTION Traditionally, engineering students learn most or all of the thermodynamic cycles that are in common use to model heat engines. They may learn to work around the Air Standard Cycle for Otto, Diesel and Brayton by assuming air behaves as an ideal gas with constant specific heats. They may also treat the working fluid as a real gas and use Gas Tables or in the case of the Rankine Cycle, Steam Tables. However, it is possible they may never exercise the models to run experiments because that requires working the cycles repeatedly. Learning to work all of the thermodynamic cycles fills up much of the course and working any of the cycles repeatedly is both laborious and very time consuming. In order to learn what causes the cycle efficiency to increase and what does not, it is necessary to use the thermodynamic model to run experiments. The best way to study the thermodynamic cycles is to use the computer to solve the equations and find the net work and efficiency of the Air Standard Cycle. Assuming the working fluid is air and that it behaves as an ideal gas, allows the prediction of temperature in an isentropic process such as compression or expansion. Using constant specific heats it is possible to calculate the work and the cycle efficiency. Once the model is written, it is very easy to solve the cycle repeatedly using the computer while varying any independent variable of interest. Most of the work is in plotting the results of the experiments. The students learn the results of varying the parameters and at the same time develop a variety of computer skills. The Marine Engineering Majors study applied thermodynamics in a second term course titled Marine Power Systems. They learn to work the ideal Otto, Diesel, Brayton and Rankine Cycles, even though they learned them to some degree during the first term of thermodynamics. In P ge 354.1 Marine Power Systems, the Midshipmen learn both the ideal cycle and the actual cycle for Brayton and Rankine. They make the ideal gas assumption, the Air Standard Cycle, for Otto, Diesel and Brayton. In addition, they treat air as a real gas in the compressor of the gas turbine and use the products of combustion for the working fluid in the combustor and turbines of the gas turbine engine and the Brayton Cycle that models it. They use steam for the Rankine Cycle and use the Steam Tables and Mollier Diagram to solve the ideal cycle, actual cycle and the Rankine Cycle with Regeneration. SCOPE OF ASSIGNMENT Only the gas power cycles with the ideal gas assumption are used for the student modeling efforts. In house computer models are used to study the Brayton Cycle with air as a real gas as well as the Rankine Cycle. Then students write their own models to study the variables affecting the gas power cycles in greater depth. The Marine Engineers are assigned five different computer projects with the later assignments build on the earlier models unless the assignment entails switching to a new gas power cycle. The current and most common assignment is for five levels of the Brayton Cycle. The students start by writing a computer model of the Air Standard Brayton Cycle and vary the pressure ratio from a minimum to a maximum value encountered in gas turbines. They use a spread sheet because it is easier and fairly similar to programming in Basic only without the Read and Write statements. They are able to complete more assignments and plots of results. COMPUTER MODELS OF CYCLES Marine Power Systems is organized such that the Marine Engineering students do a computer project consisting of five assignments. One of the five computer assignments is included below in its complete form as an example, in Table 1. As can be seen in Table 1, the problem is defined for the students within a realistic range of existing gas turbine operating parameters. In fact, this problem is set up at the design conditions of the navy’s most common main propulsion system, the LM2500 Marine Gas Turbine. This fulfills one of the objectives of the project, that the project will help the Marine Engineers learn about existing marine propulsion systems. In the initial computer assignment, the student must use a spread sheet, the one they are issued or any other they may have, to solve the equations necessary to work the Air Standard Brayton Cycle. They must calculate the temperature of the air after compression and the work of compression. The spread sheet must calculate the temperature of the air after expansion and the work of expansion. They must find the net work of the cycle and combine it with the heat supplied to find the cycle thermal efficiency and then with the mass flow rate of the working fluid to find the power produced by the gas turbine engine. This touches several objectives. The students learn how to work the Brayton Cycle and they learn how to use a spread sheet and a computer to solve problems and write a simple mathematical model. The students learn to copy the one line model to work the cycle over a range of values for the independent variable. They run an experiment using the model to determine the effect of varying the pressure ratio on the cycle efficiency and on the cycle net work, the work of compression, the work of the turbine and on the power produced by the gas turbine for the mass P ge 354.2 flow rate at the design conditions. Table 1. Example of a Computer Project Using a Spread Sheet. Marine Power Systems COMPUTER ASSIGNMENT #1 EN361, 1998 K.L. Tuttle OBJECTIVES: To determine the effect of varying pressure ratio in the Air Standard Brayton Cycle on the following dependent variables: { Compressor Work { Turbine Work { Cycle Net Work { Power Produced by the Cycle Net Work { Cycle Thermal Efficiency GIVEN: Air Standard Brayton Cycle { Constant Specific Heats { Air as the working fluid { Input parameters: a) Atmospheric Pressure: 14.7 psia b) Inlet Air Temperature: 100 °F c) Turbine Inlet Temperature: 2138 °F d) Air, mass flow rate: 140 lb /sec m REQUIREMENTS: Use a personal computer and a spreadsheet to write a computer program that will perform a thermodynamic analysis of the Ideal Brayton Cycle. For the information supplied in the section above and a pressure ratio of 2, assume that air is an ideal gas and calculate the temperature at each state point. Find the compressor work, the turbine work, the net work produced by the cycle, the power developed by an engine following the cycle, and the cycle thermal efficiency. Modify your spreadsheet, computer program to repeat the above calculations holding all input parameters constant with the exception of the pressure ratio. Vary the pressure ratio from 2 to 30 in increments of one unit. Use the graphics capability of your spreadsheet to produce properly scaled and labeled plots of the following results keeping Pressure Ratio as the independent variable: { Compressor Work, Turbine Work and Net Work, show on one graph. { Horsepower { Cycle Thermal Efficiency Discuss your results as they appear on your plots and as tabulated and draw your conclusions as they relate to each stated objective. As a minimum, the discussion shall include the objectives demonstrated by the curves, such as: { the effect that increasing the pressure ratio has on cycle efficiency, power and net work as well as compressor work and turbine work, P ge 354.3 { any other pertinent observations you may have made based on your plots and table of data. Table 1. Example of a Computer Project Using a Spread Sheet. (cont.) FOR YOUR REPORT : Create a typed cover sheet with your name, course, section, due date and date submitted; turn the cover sheet into an executive summary. An Executive Summary should describe the project and stand alone by stating the following: Title, Objective, Conclusions and Recommendations. Make up an appropriate title(please include CP1), state the conclusions as given or list in separate statements starting each with “To determine the effect of varying .... on...” Place the material in the following order: { Executive Summary, one page. { The required plots { The tabulated data, spreadsheet. { The typed discussion of results • State what each graph is a plot of • State what each graph shows in terms of what effect the independent variable has on the dependent variable. • Mention any significant observations or results The final part of the computer work is to plot the results of the experiments. The results are most meaningful if the students are able to see the cycle net work superimposed on the plots of compressor work and turbine work. Since the scale is common to all three lines, the relative values of the numbers is obvious as is the rate of change in each of the plots. The fact that the cycle net work peaks at some intermediate value is also prominently displayed. The students learn computer plotting skills for data presentation for reports or publications and for effective presentations. They also learn to talk to their figures and to discuss their results. One of the most important aspects of the assignment is the Executive Summary. The Executive Summary consists of the title of the project, the objectives of the experiment