A stationary gas turbine engine is used for generating electricity during times
ID: 1853203 • Letter: A
Question
A stationary gas turbine engine is used for generating electricity during times of peak demand. Dry air at Tamb = 20oC and Patm = 1 atm enters the compressor. The pressure of the air is increased to Pc,out = 6 atm in the compressor. The isentropic efficiency of the compressor is ?c=0.76. The air leaving the compressor is mixed with methane that enters at Tfuel=15oC and Pfuel = Pc,out and the mixture is combusted. The methane flow rate is adjusted so that the combustion reaction uses 300% excess air. The combustion products are expanded in a turbine with an isentropic efficiency of ?t=0.83. A generator mounted on the same shaft as the turbine and compressor produces Wgen=500kW of electrical power with a generator efficiency of ?gen =0.92. Pressure and thermal losses in the piping can be neglected in this analysis. a) Determine the temperature of the air entering the combustor at state 2 (at the exit of the compressor). b) Determine the temperature of the combustion products leaving the combustor and entering the turbine at state 3. c) Determine the volumetric flow rate of the air entering the compressor. d) Determine the efficiency of the gas turbine engine relative to the lower heating value of the methane. (LHVmethane = 50,032 kJ/kg)Explanation / Answer
a.Expansion is an isentropic process. if we are providing pressure gauges we can measure the pressure at state point 3 and 4. (T3/T4)= (P3/p4)^(1.4/.4) where T4 is the temperate at the end of expansion.
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b.The net thrust of a turbojet is given by:[6][7]
where:
is the rate of flow of air through the engine
is the rate of flow of fuel entering the engine
is the speed of the jet (the exhaust plume) and is assumed to be less than sonic velocity
is the true airspeed of the aircraft
represents the nozzle gross thrust
represents the ram drag of the intake
If the speed of the jet is equal to sonic velocity the nozzle is said to be choked. If the nozzle is choked the pressure at the nozzle exit plane is greater than atmospheric pressure, and extra terms must be added to the above equation to account for the pressure thrust.[8]
The rate of flow of fuel entering the engine is very small compared with the rate of flow of air.[6] If the contribution of fuel to the nozzle gross thrust is ignored, the net thrust is:
The speed of the jet must exceed the true airspeed of the aircraft if there is to be a net forward thrust on the airframe. The speed can be calculated thermodynamically based on adiabatic expansion.[9]
A simple turbojet engine will produce thrust of approximately: 2.5 pounds force per horsepower (15 mN/W).
c.It is important to determine the actual flow rate of your compressor so that you purchase the correct Nitrox Controller system. Purchasing a system that does not deliver enough oxygen will not meet the Dive Shop operator's needs, while purchasing a system that is oversized is unnecessarily expensive. While all air compressors have a rating, most of them deliver less air flow than this rating. The actual flow rate of your compressor might surprise you.
You can determine the average flowrate of your air compressor by timing how long it takes your compressor to fill a known volume of air to a pre-determined pressure.
1. Depending on the size of your charging system, you should hook up multiple empty (0 psi) air tanks. Filling up more tanks will yield a more accurate evaluation of your air compressor's flow rate. If you can, use your compressor to fill at least 4 air tanks. Standard aluminum 80 cylinders in fact contain 77.4 cubic feet of air at 3000 psi. (Catalina Cylinders)
2. Start with the air tanks completely empty and the valve on the air tanks closed. Hook the air tanks up to your charging station. Isolate your air banks, and charge your header up to 3000 psi using your air compressor. The air in your system from the compressor all the way to the valves on the air tanks themselves should be at 3000 psi.
3. Now start your timer and open the valves on the air tanks that you are filling. When the pressure in the tanks and in the air header reaches 3000 psi, you have effectively charged the volume in the air tanks. (i.e. 4 air tanks x 77.4 cubic feet per tank = 309.6 cubic feet) Now divide this volume by the amount of time it took, and you have your actual compressor flowrate. ( i.e. 309.6 cubic feet / 22.0 minutes = 14.1 cfm flowrate )
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