A Brayton cycle with regeneration using air as the working fluid has a pressure ratio of 7. The minimum and maximum temperatures in the cycle are 310 and 1150 K. Take an isentropic efficiency of 75 percent for the compressor and 82 percent for the turbine and an effectiveness of 65 percent for the regenerator. Determine the total exergy destruction associated with the cycle, assuming a source temperature of 1500 K and a sink temperature of 290 K. Also, determine the exergy of the exhaust gases at the exit of the regenerator. Use variable specific heats for air.
The exergy destruction associated with each process of the Brayton cycle and the exergy of the exhaust gases at the exit of the regenerator.
Answer to Problem 148P
The exergy destruction associated with process 1-2 of the given Brayton cycle is
The exergy destruction associated with process 3-4 of the given Brayton cycle is
The exergy destruction associated with regeneration process of the given Brayton cycle is
The exergy destruction associated with process 5-3 of the given Brayton cycle is
The exergy destruction associated with process 6-1 of the given Brayton cycle is
The exergy of the exhaust gases at the exit of the regenerator is
Explanation of Solution
Show the regenerative Brayton cycle with air as the working fluid, on
Consider, the pressure is
Write the pressure and relative pressure relation for the process 1-2.
Write the pressure and relative pressure relation for the process 3-4.
Write the expression of efficiency of the compressor
Write the expression of efficiency of the turbine
Write the expression of net work output by the gas turbine
Here, work done by the turbine is
Write the expression of effectiveness of the regenerator
Write the expression of heat input to the regenerative Brayton cycle
Write the expression of heat rejected by the regenerative Brayton cycle
Write the expression of thermal efficiency of the given turbine
Write the energy balance equation on the heat exchanger.
Write the expression of exergy destruction associated with the process 1-2 of the given Brayton cycle
Here, the temperature of the surroundings is
Write the expression of exergy destruction associated with the process 3-4 of the given Brayton cycle
Here, entropy of air at state 3 as a function of temperature is
Write the expression of exergy destruction associated with the regeneration process of the given Brayton cycle
Here, entropy of air at state 5 as a function of temperature alone is
Write the expression of exergy destruction associated with the process 5-3 of the given Brayton cycle
Here, the temperature of the heat source is
Write the expression of exergy destruction associated with the process 6-1 of the given Brayton cycle
Here, the temperature of the sink is
Write the expression of stream exergy at the exit of the regenerator (state 6)
Here, the specific enthalpy of the surroundings is
Write the expression of change entropy for the exit of the regenerator
Here, entropy of air at the surroundings as a function of temperature alone is
Conclusion:
Refer Table A-17, “Ideal gas properties of air”, obtain the properties of air at a temperature of
Substitute 7 for
Refer Table A-17, “Ideal gas properties of air”, obtain the properties of air at a relative pressure of 10.88
Refer Table A-17, “Ideal gas properties of air”, obtain the properties of air at a temperature of
Substitute
Refer Table A-17, “Ideal gas properties of air”, obtain the property of enthalpy
Rearrange Equation (III), and substitute
Refer Table A-17, “Ideal gas properties of air”, obtain the property of entropy
Rearrange Equation (IV), and substitute
Refer Table A-17, “Ideal gas properties of air”, obtain the property of entropy
Substitute
Substitute 0.65 for
Refer Table A-17, “Ideal gas properties of air”, obtain the property of entropy
Substitute
Substitute
Refer Table A-17, “Ideal gas properties of air”, obtain the properties of air at a enthalpy of
Substitute
Substitute
Substitute 290 K for
Thus, the exergy destruction associated with process 1-2 of the given Brayton cycle is
Substitute 290 K for
Thus, the exergy destruction associated with process 3-4 of the given Brayton cycle is
Substitute 290 K for
Thus, the exergy destruction associated with regeneration process of the given Brayton cycle is
Substitute 290 K for
Thus, the exergy destruction associated with process 5-3 of the given Brayton cycle is
Substitute 290 K for
Thus, the exergy destruction associated with process 6-1 of the given Brayton cycle is
Refer Table A-17, “Ideal gas properties of air”, obtain the properties of air at a temperature of
At the exit of the regenerator, pressure remains constant,
Substitute
Substitute
Thus, the exergy of the exhaust gases at the exit of the regenerator is
Want to see more full solutions like this?
Chapter 9 Solutions
Thermodynamics: An Engineering Approach
- 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 85 percent. Assume constant specific heats at room temperature.arrow_forwardAn air-standard Diesel cycle has a compression ratio of 16 and a cutoff ratio of 2. At the beginning of the compression process, air is at 95 kPa and 27°C. Determine the total exergy destruction associated with the cycle, assuming a source temperature of 2000 K and a sink temperature of 300 K. Also, determine the exergy at the end of the isentropic compression process. Account for the variation of specific heats with temperature.arrow_forwardHelium is used as the working fluid in a Brayton cycle with regeneration. The pressure ratio of the cycle is 8, the compressor inlet temperature is 300 K, and the turbine inlet temperature is 1800 K. The effectiveness of the regenerator is 75 percent. Determine the thermal efficiency and the required mass flow rate of helium for a net power output of 60 MW, assuming both the compressor and the turbine have an isentropic efficiency of 100 percent.arrow_forward
- 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. Does the compressor work increase, decrease, or remain the same?arrow_forwardHelium is used as the working fluid in a Brayton cycle with regeneration. The pressure ratio of the cycle is 8, the compressor inlet temperature is 300 K, and the turbine inlet temperature is 1800 K. The effectiveness of the regenerator is 75 percent. Determine the thermal efficiency and the required mass flow rate of helium for a net power output of 60 MW, assuming both the compressor and the turbine have an isentropic efficiency of 100 percent. Helium is an ideal gas with constant specific heats. The properties of helium are cp= 5.1926 kJ/kg.K and k = 1.667.arrow_forwardFor fixed maximum and minimum temperatures, what is the effect of the pressure ratio on the net work output of a simple ideal Brayton cycle?arrow_forward
- A gas-turbine power plant operating on an ideal Brayton cycle has a pressure ratio of 8. The gas temperature is 300 K at the compressor inlet and 1300 K at the turbine inlet. Utilizing the air-standard assumptions, determine (a) the gas temperature at the exits of the compressor and the turbine, (b) the back-work ratio, and (c) the thermal efficiency.arrow_forwardA gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 1600 kPa. The working fluid is air, which enters the compressor at 40°C at a rate of 850 m3 /min and leaves the turbine at 650°C. Assuming a compressor isentropic efficiency of 85 percent and a turbine isentropic efficiency of 88 percent, determine the net power output.arrow_forwardA Brayton cycle with regeneration using air as the working fluid has a pressure ratio of 7. The minimum and maximum temperatures in the cycle are 310 and 1150 K. Assuming an isentropic efficiency of 75 percent for the compressor and 82 percent for the turbine and an effectiveness of 65 percent for the regenerator, determine the air temperature at the turbine exit.arrow_forward
- A simple ideal Brayton cycle uses argon as the working fluid. At the beginning of the compression, P1 = 15 psia and T1 = 80°F; the maximum cycle temperature is 1200°F; and the pressure in the combustion chamber is 150 psia. The argon enters the compressor through a 3 ft2 opening with a velocity of 200 ft/s. Determine the rate at which entropy is generated by the cycle. The temperature of the source is the same as the maximum cycle temperature, and the temperature of the sink is the same as the minimum cycle temperature.arrow_forwardA gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 1200 kPa. The working fluid is air, which enters the compressor at 30°C at a rate of 150 m3/min and leaves the turbine at 500°C. Using constant specific heats for air and assuming a compressor isentropic efficiency of 82 percent and a turbine isentropic efficiency of 88 percent, determine (a) the net power output, (b) the work ratio, and (c) the thermal efficiency.arrow_forwardThe 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? (c) Does the thermal efficiency increase, decrease, or remain the same?arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY