HW_4 Gas Turbine-brayton Cycle Homework and Conceptual Questions

March 18, 2018 | Author: jbecker | Category: Gas Compressor, Gas Turbine, Temperature, Thermodynamics, Physics & Mathematics


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ME 302 Homework #49-83C (7th ed) What four processes make up the simple Brayton cycle? 9-76C For a simple ideal Brayton cycle with fixed minimum and maximum temperatures, how does the pressure ratio effect the: a) the thermal efficiency b) the net work output 9-77C What is the back work ratio? What are typical back work ratio values for gas-turbine engines? 9-78C Why are the back work ratios relatively high in gas turbine engines? 9-79C For a gas turbine engine, how do the inefficiencies of the turbine and the compressor affect a) The back work ratio b) The thermal efficiency 9-83 (9-89 7th) A simple Brayton cycle using air as the working fluid has a pressure ratio of 10. The minimum and maximum temperatures in the cycle are 295 and 1240 K. Assuming an isentropic efficiency of 83 percent for the compressor and 87 percent for the turbine, determine (a) the air temperature at the turbine exit, (b) the net work output, and (c) the thermal efficiency. 9-86 (9-94 7th) Consider a simple Brayton cycle using air as the working fluid; has a pressure ratio of 12; has a maximum cycle temperature of 600°C; and operates the compressor inlet at 100 kPa and 15°C. Which will have the greatest impact on the backwork ratio: a compressor isentropic efficiency of 80 percent or a turbine isentropic efficiency of 80 percent? Use constant specific heats at room temperature. 9-87 (9-95 7th) 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. Answers: (a) 352 kg/s, (b) 1037 kg/s 9-88 (9-98 7th)An aircraft engine operates on a simple ideal Brayton cycle with a pressure ratio of 10. Heat is added to the cycle at a rate of 500 kW; air passes through the engine at a rate of 1 kg/s; and the air at the beginning of the compression is at 70 kPa and 0°C. Determine the power produced by this engine and its thermal efficiency. Use constant specific heats at room temperature. 9-93 (9-101 7th) A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 800 kPa. Air enters the compressor at 30°C and leaves at 330°C at a mass flow rate of 200 kg/s. The maximum cycle temperature is 1400 K. During operation of the cycle, the net power output is measured experimentally to be 60 MW. Assume constant properties for air at 300 K with c = 0.718 kJ/kg·K, cp = 1.005 kJ/kg·K, R = 0.287 kJ/kg·K, k = l.4. (a) Sketch the T-s diagram for the cycle. (b) Determine the isentropic efficiency of the turbine for these operating conditions. (c) Determine the cycle thermal efficiency. 9-94 (9-102 7th) A gas-turbine power plant operates on a modified Brayton cycle shown in the figure with an overall pressure ratio of 8. Air enters the compressor at 0°C and 100 kPa. The maximum cycle temperature is 1500 K. The compressor and the turbines are isentropic. The high pressure turbine develops just enough power to run the compressor. Assume constant properties for air at 300 K with c = 0.718 kJ/kg·K, cp = 1.005 kJ/kg·K, R = 0.287 kJ/kg·K, k = 1.4. (a) Sketch the T-s diagram for the cycle. Label the data states. (b) Determine the temperature and pressure at state 4, the exit of the high pressure turbine. (c) If the net power output is 200 MW, determine mass flow rate of the air into the compressor, in kg/s. Answers: (b) 1279 K, 457 kPa, (c) 442 kg/s Figure P9-94 Other relevant problems 9-81 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. 9-82 Repeat Problem 9-81 using constant specific heats at room temperature. 9-96 in 7th ed. 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. Example problems 9-90 used as example in notes (9-100 in 7th) 9-85 – an extension of 9-83 (9-89 and 9-91 in 7th) Reasoning for results for 9-86
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