M, T, W, F =* 2:00 – 3:00
June 5, 2000
The following report, submitted to Roy Aircraft Engines Incorporated for an efficiency study, is an analysis of a turbojet engine completed by thermodynamically studying each main component that constitutes a turbojet engine. RAE Incorporated requested software that would calculate the theoretical maximum output velocity, using input data imputed by the user of the program. The calculations are made assuming idealized conditions. In the analysis, the turbojet was broken down into its fundamental parts, which consist of an inlet, compressor, burner, turbine, and nozzle.
Description of Turbojet Components
Third, the compressed air is combined with fuel and is ignited within the combustor. The process within the combustor is assumed to be isentropic. The resulting high temperature fluid is used to turn the fourth component of the turbojet, the turbine.
Next, the turbine is used to extract energy from the heated flow coming from the burner. This is done by this flow of gas passing through blades on a free spinning shaft. The turbine generates just enough energy to drive the compressor. When the flow passes through the turbine, the pressure and temperature are decreased.
The next step is optional within the program. Here an afterburner is used to reheat the exiting gas from the turbine. This is done by injecting additional fuel into the gas exiting from the turbine. Igniting this mixture produces a higher temperature at the nozzle, as a result the final velocity of the jet engine is increased.
Finally, the flow comes through the nozzle where no thermodynamic work is performed on the flow by the nozzle. The temperature remains constant through the nozzle while the pressure and velocity of the flow will change as dictated by the design of the nozzle. The nozzle is used to produce thrust and used to conduct the exhaust gases back to the free air.
For the analysis of the turbojet, several assumptions were made and are as follows:
1. Air behaves as a compressible, ideal gas.
2. Flow through the diffuser, nozzle, compressor and combustor is
3. The engine is insulated, there is no loss of heat to the surrounding air.
4. The engine is operating at steady state.
5. Work by the turbine is equal to the work required by the compressor.
6. Pressure through the compressor / burner is constant.
7. Kinetic and potential energy are zero except at the intake of the inlet and the exit of the nozzle.
Using the Program
The program is a MATLAB script so the first thing that must be done to run it is to start MATLAB. On a *nix system, the best way to run the program is to start MATLAB in the directory with the thermo.m and the findvf.m files. After MATLB starts type thermo (or thermot3 to find Vf using T3 instead of Qin), at the MATLAB prompt. On Microsoft Windows systems, make sure the path containing the thermo.m, thermot3.m, findvf.m and findvft3.m files is in the MATLAB path and then type thermo at the MATLAB prompt.
Once the program is running, the user will have the option to find Vf for a system without an afterburner, a system with an afterburner or to quit. Once the user has made their selection they will be prompted for the essential values needed to calculate Vf. When this is done the value for Vf will be displayed and if the system with the afterburner is selected, then the value for Vf with and without the afterburner will be displayed. Entering the compression ratio is optional and if it is not entered, the program will find the maximum value for Vf and the compression ratio that will give the maximum value.
Final Velocity vs. Compression Ratio Graphs
Figure 1 – Without Afterburner
Figure 2 – With Afterburner
Conclusion / Discussion
During the development of the software, we were able to see general relationships between the different variables the user imputes and the output velocity of the jet engine. We were able to see that the compression ratio has a large affect on the final velocity. As seen from Figure 1 & 2, the relation between the final velocity and compression ratio is not linear. Our program determined the most efficient compression ratio, while not using an afterburner, was 11.8 while the other variable data remained constant.
We were also able to see a linear relationship between the diffuser/nozzle ratio and the final velocity. However, we did not find a ratio that would maximize the output velocity of the jet engine.
We were able to see a non-linear relation between the heat input from the combustor and the final velocity. Due to a small sample size, we were unable to see the addition of more heat input reducing the final velocity. However, we know there must be a maximum value for heat input to maximize the velocity, or one would be able to continue adding any heat input one would want to have incredibly high output velocities. Finally, we were able to see a great increase to the final velocity due to the use of an afterburner. This can be seen from figure 1 & 2.