Helium 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 (a) 100 percent and (b) 80 percent.
a)
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.
Answer to Problem 173RP
The thermal efficiency of helium for a net power output of 60 MW, assuming both the compressor and the turbine have an isentropic efficiency of
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
Explanation of Solution
Draw the
Consider, the pressure is
Consider
Write the expression to calculate the temperature and pressure relation ratio for the isentropic compression process 1-2s.
Here, the specific heat ratio is k.
Write the expression to calculate the temperature and pressure relation ratio for the isentropic expansion process 3-4s.
Write the expression for the effectiveness of the regenerator
Write the expression to calculate the net work output for the regenerative Brayton cycle
Here, the specific heat of helium at constant pressure is
Write the expression to calculate the heat input for the regenerative Brayton cycle
Write the expression to calculate the thermal efficiency of the given regenerative Brayton cycle
Write the expression to calculate the mass flow rate of helium flowing through the given regenerative Brayton cycle
Here, the net power output produced by the given regenerative Brayton cycleis
Conclusion:
From Table A-2, “Ideal-gas specific heats of various common gases”, obtain the following values for helium gas.
Substitute 300 K for
Substitute 1800 K for
Substitute 0.75 for
Substitute
Substitute
Equation (V).
Substitute
Thus, the thermal efficiency of helium for a net power output of 60 MW, assuming both the compressor and the turbine have an isentropic efficiency of
Substitute
Thus, 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
b)
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 80 percent.
Answer to Problem 173RP
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
The thermal efficiency of helium for a net power output of 60 MW, assuming both the compressor and the turbine have an isentropic efficiency of
Explanation of Solution
Consider
Write the expression to calculate the temperature and pressure relation for the isentropic compression process 1-2.
Write the expression to calculate the isentropic efficiency of the compressor
Write the expression to calculate the temperature and pressure relation for the isentropic expansion process 3-4.
Write the expression for the isentropic efficiency of the turbine
Write the expression for the effectiveness of the regenerator
Write the expression to calculate the net work output for the regenerative Brayton cycle
Here, the specific heat of helium at constant pressure is
Write the expression to calculate the heat input for the regenerative Brayton cycle
Write the expression to calculate the thermal efficiency of the given regenerative Brayton cycle
Write the expression to calculate the mass flow rate of helium flowing through the given regenerative Brayton cycle
Here, the net power output produced by the given regenerative Brayton cycle is
Conclusion:
Substitute 300 K for
Substitute 300 K for
Substitute 1800 K for
Substitute 1800 K for
Substitute 0.75 for
Substitute
Substitute
Substitute
Thus, 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
Substitute
Thus, the thermal efficiency of helium for a net power output of 60 MW, assuming both the compressor and the turbine have an isentropic efficiency of
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_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_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
- Consider a regenerative Brayton cycle operating with a pressure ratio of 8, where the air enters the compressor at 300 K and 100 kPa, while it enters the turbine at 1060 K. Assume that both the compressor and turbine are isentropic, that specific heats vary with temperature, and that the regenerator has an effectiveness of 74%. Round all intermediate calculations to three decimal places. 1. How much net work is produced in kJ/kg? Round your answer to two decimal places. 2. What is the thermal efficiency as a percentage (0% - 100%)? Round your answer to one decimal place. 3. What is the thermal efficiency as a percentage (0% - 100%) if there was no regenerator? Round your answer to one decimal place.arrow_forwardThe 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_forwardA spark-ignition engine has a compression ratio of 10, an isentropic compression efficiency of 85 percent, and an isentropic expansion efficiency of 90 percent. At the beginning of the compression, the air in the cylinder is at 13 psia and 60°F. The maximum gas temperature is found to be 2300°F by measurement. Determine the heat supplied per unit mass, the thermal efficiency, and the mean effective pressure of this engine when modeled with the Otto cycle. Use constant specific heats at room temperature. The properties of air at room temperature are R = 0.3704 psia·ft3/lbm·R, cp = 0.240 Btu/lbm·R, cv = 0.171 Btu/lbm·R, and k = 1.4. Question: The heat supplied per unit mass is ___________.Btu/lbm. The thermal efficiency is_________________%. The mean effective pressure is________________.psia.arrow_forward
- Explain why Brayton cycle is more preferred over Rankin cycle in power plant stations? And how would you enhance the performance of a Brayton cycle?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 net work output.arrow_forwardA Diesel cycle has a compression ratio of 22 and begins its compression at 85 kPa and 15°C. The maximum cycle temperature is 1200°C. Utilizing air-standard assumptions, determine the thermal efficiency of this cycle using variable specific heats.arrow_forward
- A simple Rankine cycle has a pump with an isentropic efficiency of 70%. The inlet and outlet pressures of the turbine are 6 MPa and 0.075 MPa, respectively, and steam enters the turbine at 550°C. Determine a) the isentropic efficiency of the turbine if the quality at the turbine outlet is to be ? = 1, b) the thermal efficiency of the cycle, c) the rate of heat input into the boiler if the net power output of the cycle is 10 MW.arrow_forwardIn an ideal Brayton cycle with regeneration, air is compressed from 80 kPa and 10°C to 400 kPa and 175°C, is heated to 450°C in the regenerator, and is then further heated to 1000°C before entering the turbine. Under cold-air-standard conditions, the effectiveness of the regenerator is (a) 33 percent (b) 44 percent (c) 62 percent (d) 77 percent (e) 89 percentarrow_forwardCompare the thermal efficiency of a two-stage gas turbine with regeneration, reheating, and intercooling to that of a three-stage gas turbine with the same equipment when the maximum cycle temperature is 800°C.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