FROM Evan Situ Jeremy Jaynes and Weston Gray TO John Haglund SUBJECT Thermodynamic Analysis of the Mercury 50 Gas Turbine Engine DATE 5 3 16 Introduction As requested in class on April 27 2016 we performed a thermodynamic analysis of the Solar Turbines Mercury 50 packaged gas turbine engine electric generator station The Mercury 50 is a electric generator station that is capable of providing up to 4 6 MW of electric power even in remote locations It being small scale meaning you can transport it by train or on a flatbed truck makes it convenient for getting it out to places that may not have a ton of electricity being produced near by such as oilfields pipelines etc while still providing a fair amount of power All you need to power the machine is a fuel source such as natural gas which these locations readily have Using our knowledge of the Brayton Cycle information provided from the manufacturer s detailed product specifications sheet and data from our analysis we performed tasks on the performance and operating parameters and calculated results were compared to the manufacturer s specifications These tasks included finding the thermal efficiency of the overall generator the heat rate of the engine the fuel input rate and the fuel cost of the electric power produced Thermodynamic Modeling The thermodynamic cycle used for the sophisticated gas turbine engine was the Brayton Cycle The working fluid involved was air which is modeled as an ideal gas throughout the whole cycle The cycle consisted of a compressor with 85 efficiency combustion chamber a turbine with 85 efficiency a regenerator with an 85 efficiency and exhaust and an electricity producing generator with an efficiency of 98 For this cycle there were six key processes The first process was a compression process from states one to two that can be initially modeled as an isentropic process for future purposes With the pressure ratio of the compressor and the two intensive properties of the air at the inlet of the system known we determined the relative pressure at state two by using equation 1 r Pressure P P 1 r2 r1 With the relative pressure under ideal conditions at state two known we easily determined more intensive properties such as the ideal specific enthalpy value for the second state Then we substituted the ideal specific enthalpy value for the second state the specific enthalpy value for the first state and the compressor efficiency into equation 2 which was the efficiency formula With only one unknown variable in the efficiency formula we evaluated the actual enthalpy of the second state We then used the actual enthalpy of the second state to find the rest of the properties of the second state With known values of specific enthalpy at states one and two to use the specific work input by the compressor was computed by using equation 3 W h h Ideal 2 Ideal 1 compressor W Actual h 2Actual h 1 w c h 2a h 1 2 3 Next heat regeneration occurred from states two to five The regenerator of a certain efficiency was modeled as a device that extracts thermal energy from the exhaust gases to preheat the air entering the combustion chamber Assuming the regenerator was well insulated and negligible of kinetic and potential energy the maximum heat transfer from the exhaust gases to the air was expressed in equation 4 and the extent to which a regenerator approaches an ideal regenerator was expressed in equation 5 q regen h 5 h 2 h 5 h 2 h 4 h 4 5 FROM Evan Situ Jeremy Jaynes and Weston Gray TO John Haglund SUBJECT Thermodynamic Analysis of the Mercury 50 Gas Turbine Engine DATE 5 3 16 We used these helpful equations after the firing temperature and the intensive properties at each state were determined The regenerator efficiency formula was manipulated for the purposes of finding the specific enthalpy value at state five After we solved for the specific enthalpy value at state five the amount of regenerated heat was evaluated Next the third process that occurred from states five to three was heat input and the sixth process that occurred from states six to one was heat rejection Heat input was calculated by using equation 6 and heat rejection was calculated by using equation 7 In addition the process from states four to six showed how much heat was regenerated throughout the Brayton Cycle q in h 3 h 5 q out h 6 h 1 6 7 Finally the last process occurred from states three to four was the generation of net specific work output by the turbine With the turbine efficiency and the specific enthalpy value at state three known we used equation 8 to calculate the actual specific enthalpy value at state four Then we used equation 9 to determine the net specific work output produced by the turbine T h 3 h 4a h 3 h 4s w T h 3 h 4a 8 9 With known values of w c and w T to work with the specific net work was computed by using equation 10 After the specific net work was computed equation 11 was used to finally find the electric work output in kilowatts w net w T w C 10 W elec mass flow rate of air w net 11 Solution Approach to an Implicit Problem The only implicit problem throughout this project was guessing and checking firing temperatures at the turbine inlet At each temperature we determined the specific enthalpy and the relative pressure values at state three Then we subtracted the specific enthalpy value at state three by the specific net work output by the turbine during as isentropic expansion process to obtain the specific enthalpy value at state four With the specific enthalpy value at state four known we determined the relative pressure value at state four by thorough perusal of the air property tables and interpolation Then we divided the relative pressure value at state four by the relative pressure value at state 3 to match the inverse of the known pressure ratio After eight guesses we obtained the right match of the inverses of the pressure ratios at the right firing temperature for the turbine inlet Although we found the correct firing temperature for the turbine inlet we still confirmed the accuracy of the firing temperature by using a different method to determine the specific enthalpy value at state four and the relative pressure value at state four First we determined the specific enthalpy value and the relative pressure value at state three by using air property tables and by interpolation Then we divided relative pressure value at state three by the known pressure ratio Second with the relative pressure value at state four