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Gas turbine analysis

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gas turbine analysis

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Gas turbine analysis

1. 1. The measured temperature profile provided to you is not the actual temperature profile of the gas. There is heat transfer from the viscous dissipation of gas onto the thermocouple bead, leading to a higher temperature reading than the actual static temperature. Normally this is not an issue, however, because we are measuring high speed flow, the viscous dissipation is not negligible. There are three equations that can be used to describe this phenomenon: 푇! = 푇! + 푉! 2푐! 푇! = 푇! + 푟 푉! 2푐! 푇! 푇! = 푃! 푃! !!! ! The first equation is the relationship between the total and static temperature. The total temperature is the temperature of the gas if it were to be isentropically brought to rest, in other words, the kinetic energy would be completely converted into thermal energy. The second equation describes how the static temperature relates to the temperature that was measured with the thermocouple. The variable “r” is called the recovery factor, and for this experiment you can set the value of this term to 0.7. The last equation describes the ratio of total and stagnation temperatures and pressures, where k is the ratio of specific heats. The equation below was found by eliminating the total temperature and the velocity from the three equations above. The static temperature can then be solved for and used to calculate the velocity and temperature. The profile data provided on moodle gives the difference between the total and static pressures, and you should have the value of the ambient pressure reading from the day of the experiment. 푇! = 푇! 푟 푃! 푃! !!! ! − 1 + 1 The equations below could be useful in calculating the required results for your presentation. The analysis of the turbine and compressor are straight forward, however the analysis of the combustor and nozzle are a little more involved. The combustor is not a perfect combustor, and will have an efficiency of less than one. 푄!"#\$ = 휂!"#\$푚!퐿퐻푉 푄!"#\$ = 푚!"#ℎ!"# − 푚!"ℎ!" To analyze the nozzle and evaluate the total mass flow rate through the engine, the temperature and velocity profile at the exit of the nozzle need to be evaluated.
2. 2. 휂!! = 푚!"! 푉! 2 푚!퐿퐻푉 Thermal efficiency 푚 = 휌푉푑퐴 = 휌푉푟푑푟푑휃 Mass flow rate 푡ℎ푟푢푠푡 = 푚푉 = 휌푉!푑퐴 = 휌푉!푟푑푟푑휃 Thrust of the engine 푚 푉! 2 = 휌 푉! 2 푑퐴 = 휌 푉! 2 푟푑푟푑휃 The kinetic energy flux As you go through the analysis, ask yourself if your data makes sense. What values are you expecting, and what are some ways to estimate the values to check your calculations? This will help you spot any gross errors.