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
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