# 1. Why are the back work ratios relatively high in gas turbine engines? 2. What 4 processes make up the simple ideal Brayton cycle?

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1 1. Why are the back work ratios relatively high in gas turbine engines? 2. What 4 processes make up the simple ideal Brayton cycle? 3. For fixed maximum and minimum temperatures, what are the effect of the pressure ratio on (a) the thermal efficiency and (b) the net work output of a simple ideal Brayton cycle? 4. What is the back work ratio? What are typical back work ratios for gas-turbine engines? 5. How do the inefficiencies of the turbine and the compressor affect (a) the back work ratio and (b) the thermal efficiency of a gas-turbine engine? 6. A simple ideal Brayton cycle with air as the working fluid has a pressure ratio of 10. The air enters the compressor at 520 R and the turbine at 2000 R. Accounting for the variation of specific heats with temperature, determine (a) the air temperature at the compressor exit, (b) the back work ratio, and (c) the thermal efficiency. 7. A simple Brayton cycle using air as the working fluid has a pressure ratio of 8. The minimum and maximum temperatures in the cycle are 310 and 1160 K. Assuming an isentropic efficiency of 75 percent for the compressor and 82 percent for the turbine, determine (a) the air temperature at the turbine exit, (b) the net work output, and (c) the thermal efficiency. 8. Repeat Problem 7 using constant specific heats at room temperature. 9. Air is used as the working fluid in a simple ideal Brayton cycle that has a pressure ratio of 12, a compressor inlet temperature of 300 K, and a turbine inlet temperature of 1000 K. Determine the required mass flow rate of air for a net power output of 70 MW, assuming both the compressor and the turbine have an isentropic efficiency of (a) 100 percent and (b) 85 percent. Assume constant specific heats at room temperature. 10. A stationary gas-turbine power plant operates on a simple ideal Brayton cycle with air as the working fluid. The air enters the compressor at 95 kpa and 290 K and the turbine at 760 kpa and 1100 K. Heat is transferred to air at a rate of 35,000

2 kj/s. Determine the power delivered by this plant (a) assuming constant specific heats at room temperature and (b) accounting for the variation of specific heats with temperature. 11. Air enters the compressor of a gas-turbine engine at 300 K and 100 kpa, where it is compressed to 700 kpa and 580 K. Heat is transferred to air in the amount of 950 kj/kg before it enters the turbine. For a turbine efficiency of 86 percent, determine (a) the fraction of the turbine work output used to drive the compressor and (b) the thermal efficiency. Assume variable specific heats for air. 12. Repeat Problem 11 using constant specific heats at room temperature. 13. A gas-turbine power plant operates on a simple Brayton cycle with air as the working fluid. The air enters the turbine at 120 psia and 2000 R and leaves at 15 psia and 1200 R. Heat is rejected to the surroundings at a rate of 6400 Btu/s, and air flows through the cycle at a rate of 40 lbm/s. Assuming the turbine to be isentropic and the compressor to have an isentropic efficiency of 80 percent, determine the net power output of the plant. Account for the variation of specific heats with temperature. 14. For what compressor efficiency will the gas-turbine power plant in Problem 9 80E produce zero net work? 15. A gas-turbine power plant operates on the simple Brayton cycle with air as the working fluid and delivers 32 MW of power. The minimum and maximum temperatures in the cycle are 310 and 900 K, and the pressure of air at the compressor exit is 8 times the value at the compressor inlet. Assuming an isentropic efficiency of 80 percent for the compressor and 86 percent for the turbine, determine the mass flow rate of air through the cycle. Account for the variation of specific heats with temperature. 16. Repeat Problem 15 using constant specific heats at room temperature. 17. The single-stage compression process of an ideal Brayton cycle without regeneration is replaced by a multistage compression process with intercooling between the same pressure limits. As a result of this modification, a. Does the compressor work increase, decrease, or remain the same?

3 b. Does the back work ratio increase, decrease, or remain the same? 18. The single-stage expansion process of an ideal Brayton cycle without regeneration is replaced by a multistage expansion process with reheating between the same pressure limits. As a result of this modification, a. Does the turbine work increase, decrease, or remain the same? b. Does the back work ratio increase, decrease, or remain the same? 19. A simple ideal Brayton cycle without regeneration is modified to incorporate multistage compression with inter-cooling and multistage expansion with reheating, without changing the pressure or temperature limits of the cycle. As a result of these two modifications, a. Does the net work output increase, decrease, or remain the same? b. Does the back work ratio increase, decrease, or remain the same? d. Does the heat rejected increase, decrease, or remain the same? 20. A simple ideal Brayton cycle is modified to incorporate multistage compression with intercooling, multistage expansion with reheating, and regeneration without changing the pressure limits of the cycle. As a result of these modifications, a. Does the net work output increase, decrease, or remain the same? b. Does the back work ratio increase, decrease, or remain the same? d. Does the heat rejected increase, decrease, or remain the same? 21. For a specified pressure ratio, why does multistage compression with intercooling decrease the compressor work, and multistage expansion with reheating increase the turbine work? 22. In an ideal gas-turbine cycle with intercooling, reheating, and regeneration, as the number of compression and expansion stages is increased, the cycle thermal efficiency approaches (a) 100 percent, (b) the Otto cycle efficiency, or (c) the Carnot cycle efficiency. 23. Consider an ideal gas-turbine cycle with two stages of compression and two stages of expansion. The pressure ratio across each stage of the compressor and

4 turbine is 3. The air enters each stage of the compressor at 300 K and each stage of the turbine at 1200 K. Determine the back work ratio and the thermal efficiency of the cycle, assuming (a) no regenerator is used and (b) a regenerator with 75 percent effectiveness is used. Use variable specific heats. 24. Repeat Problem 23, assuming an efficiency of 80 percent for each compressor stage and an efficiency of 85 percent for each turbine stage. 25. Consider a regenerative gas-turbine power plant with two stages of compression and two stages of expansion. The overall pressure ratio of the cycle is 9. The air enters each stage of the compressor at 300 K and each stage of the turbine at 1200 K. Accounting for the variation of specific heats with temperature, determine the minimum mass flow rate of air needed to develop a net power output of 110 MW. 26. Repeat Problem 25 using argon as the working fluid. 27. A gas turbine has an overall pressure ratio of 5 and a maximum cycle temperature of 550 C. The turbine drives the compressor and an electric generator, the mechanical efficiency of the drive being 97%. The ambient temperature is 20 C and the air enters the compressor at a rate of 15kg/s; the isentropic efficiencies of the compressor and turbine are 80% and 83%. Neglecting changes in kinetic energy, the mass flow rate of fuel and all pressure losses, calculate: i. Power output ii. Cycle efficiency iii. Work ratio Cp and γ may be taken as 1.005kJ/kgK and 1.4 for air and 1.15kJ/kgK and for combustion and expansion processes. 28. In a marine gas turbine unit HP stage turbine drives the compressor and a LP stage turbine drives the propeller through suitable gearing. The overall pressure ratio is 4/1., the mass flow rate is 60kg/s, the maximum temperature is 650 C and the air intake condition are 1.01 bar and 25 C. The isentropic efficiencies of the compressor, HP turbine and LP turbine are 0.8, 0.83 and 0.85 respectively and the mechanical efficiency of both shafts is 98%. Neglecting kinetic energy, changes and the pressure loss in combustion, calculate; i. Pressure between turbine stages

5 ii. Cycle efficiency iii. Shaft power Cp and γ may be taken as 1.005kJ/kgK and 1.4 for air and 1.15kJ/kgK and for combustion and expansion processes. 29. For the unit of problem 28, calculate the cycle efficiency obtainable when a heat exchanger is fitted. Assume a thermal ratio of In a gas turbine, generating set 2 stages of compression are used with an intercooler between stages. The HP turbines the HP compressor and the LP turbines drives the LP compressor and the generator. The exhaust from a LP turbine passes through a HE, which transfers heat to the air leaving the HP compressor. There is a reheat combustion chamber between turbine stages, which raises the gas temperature to 600 C, which is also the gas temperature at the entry to the HP turbine. The overall pressure ratio is 10/1, each compressor having the same pressure ratio and the air temperature at the entry to the unit is 20 C. The HE thermal ratio may be taken as 0.7 and the intercooling is complete between compressor stages and 0.85 for both turbine stages and that 2% of the work of each turbine is used in overcoming friction. Neglecting all losses in pressure, and assuming that velocity changes are negligibly small, calculate; i. Power output in kilowatts for a mass flow of 115 kg/s ii. Overall cycle efficiency of the plant 31. A motorcar gas turbine unit has 2 centrifugal compressor in series giving an overall pressure ratio of 6/1. The air leaving the HP compressor passes through a HE before entering the combustion chamber. The expansion is in 2 stages, the first stage driving the compressors and the second stage driving the car through gearing. The stage leaving the LP turbine passes through the HE before exhausting to atmosphere. The HP turbine inlet temperature is 800 C and the inlet temperature to the unit is 15 C. The isentropic efficiency of the compression is 0.8 and that of each turbine is 0.85; the mechanical efficiency of each shaft is 98%. The HE thermal ration may be assumed neglecting pressure losses and changes in kinetic energy, calculate; i. Overall cycle efficiency ii. Power developed when the air mass flow is 0.7kg/s iii. Specific fuel consumption when the caloric value of the fuel used is 42600kJ/kg and the combustion efficiency is 97%.

6 32. In a gas turbine generating station the overall compression ratio is 12/1, performed in 3 stages the pressure ratios of 2.5/1, 2.4/1 and 2/1 respectively. The air inlet temperature to the plant is 25 C and intercooling between stages reduces the temperature to 40 C. The HP turbine drives the HP and intermediatepressure compressor stages; the LP turbine drives the LP compressor and the generator. The gasses leaving LP turbine are passed through a HE, which heats the air leaving the HP compressor. The temperature at the inlet to the HP turbine is 650 C. The gases leave the HE at a temperature of 200 C. The isentropic efficiency of each compressor stage is 0.83 and the isentropic efficiency of the HP and LP turbine are 0.85 and 0.88 respectively. Take the mechanical efficiency of each shaft as 98%. The air mass flow is 140kg/s. neglecting pressure losses and changes in kinetic energy and taking the specific heat of water as 4.19 kj/kgk, calculate, i. Power output in kilowatts ii. Cycle efficiency iii. Flow of cooling water required for the intercoolers when the rise in the water temperature must not exceed 30K; iv. The HE thermal ratio 33. In a gas turbine plant, air enters a compressor at atmospheric condition of 15 C, bar and is compressed through a pressure ratio of 10. The air leaving the compressor passes through a HE before entering the combustion chamber. The hot gases leave the combustion chamber at 800 C and expand through an HP turbine, which drives the compressor. On leaving the HP turbine the gases pass through a reheat combustion chamber, which raises the temperature of the gases to 800 C before they expand through the power turbine, and then to the HE where they flow in counter-flow to the air leaving the compressor. Using the data below, neglecting the mass flow rate of fuel and changes of velocity throughout, calculate: i. Air flow rate required for a net power output of 10MW ii. Work ratio of the cycle iii. Temperature of the air entering the first combustion chamber iv. Overall cycle efficiency Isentropic efficiency of compressor, 80%; isentropic efficiencies of HP and power turbine, 87 and 85%; mechanical efficiency of HP turbine-compressor drive, 92%; mechanical efficiency of power turbine drive, 94%; thermal ratio of HE, 0.75; pressure drop on air side of HE, bar; pressure drop in first combustion chamber, 01 bar; pressure drop in reheat combustion chamber,0.08 bar; pressure drop on gas side of HE, 0.1 bar.

7 34. An open cycle gas turbine plant is used to generate power in an oil refinery. The gas turbine unit drives a generator, which supplies electric motors of 2400 kw; the overall mechanical and electrical efficiency is 92%. Some of the exhaust gas from the turbine at 530 C is supplied to a furnace in the refinery at a rate of 2 kg/s; the reminder of the exhaust gas is passed in counter flow through a HE where it heats the air leaving the compressor, and then passes to exhaust at 400 C. The compressor has a pressure ratio of 8 and the air entry is at 1.013bar and 20 C. The pressure loss in the air of the heat exchanger is 0.16bar, the pressure loss in the combustion chamber is 0.12 bar, and the pressure loss in the gas side of HE is 0.05bar. The isentropic efficiencies of the compressor and turbine are 0.85 and 0.92 respectively. Neglecting heat losses in the HE, and the mass flow rate of fuel, calculate: i. Mass flow rate of air entering the compressor; ii. Temperature of the air entering the combustion chamber; iii. Overall cycle efficiency 35. A closed cycle gas turbine plant using helium as the working fluid is proposed for an experimental nuclear reactor. The helium is compressed in 2 stages with an intercooler between stages. Before passing through a heater where it is heated externally by the reactor coolant, the helium is pre-heated in a HE where it is in counter flow with the helium leaving the turbine. The helium leaving the turbine is cooled in the HE before passing through a cooler where it is cooled by cooling water to the required inlet temperature to the compressor, and the cycle is complete. Using the data below, calculate the overall cycle efficiency. Pressure and temperature at the entry to the first compressor, 18 bar and 30 C; pressure ratio for each compressor, 2; temperature of helium leaving the intercooler, 30 C; temperature of helium, entering the turbine, 800 C; isentropic efficiency of each compressor, 0.83; isentropic efficiency of the turbin, 0.86; effectiveness of the HE, 0.8; pressure loss as a percentage of the inlet pressure to each component: intercooler and external cooler, 1%; each side of HE, 2%; external heater, 3%. Take γ for helium as 1.666

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