Conduction 1. A thermodynamic analysis of a proposed Brayton cycle gas turbine yie 5 MW of net power production. The compressor, at an average temper of T = 400°C, is driven by the turbine at an average temperature of Th 1000°C by way of an L = 1m-long, d= 70mm - diameter shaft of therm conductivity k = 40 W/m K. Compressor Combustion chamber Turbine d

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Conduction
1. A thermodynamic analysis of a proposed Brayton cycle gas turbine yields P=
5 MW of net power production. The compressor, at an average temperature
of T. = 400°C, is driven by the turbine at an average temperature of T₁ =
1000°C by way of an L = 1m-long, d= 70mm - diameter shaft of thermal
conductivity k = 40 W/m K.
Compressor
min
T
Combustion
chamber
Shaft
L
Turbine
Th
out
(a) Compare the steady-state conduction rate through the shaft connecting the hot
turbine to the warm compressor to the net power predicted by the thermodynamics-
based analysis.
(b) A research team proposes to scale down the gas turbine of part (a), keeping all
dimensions in the same proportions. The team assumes that the same hot and cold
temperatures exist as in part (a) and that the net power output of the gas turbine is
proportional to the overall volume of the device. Plot the ratio of the conduction through
the shaft to the net power output of the turbine over the range 0.005 m s Ls 1 m. Is a
scaled-down device with L = 0.005 m feasible?
Transcribed Image Text:Conduction 1. A thermodynamic analysis of a proposed Brayton cycle gas turbine yields P= 5 MW of net power production. The compressor, at an average temperature of T. = 400°C, is driven by the turbine at an average temperature of T₁ = 1000°C by way of an L = 1m-long, d= 70mm - diameter shaft of thermal conductivity k = 40 W/m K. Compressor min T Combustion chamber Shaft L Turbine Th out (a) Compare the steady-state conduction rate through the shaft connecting the hot turbine to the warm compressor to the net power predicted by the thermodynamics- based analysis. (b) A research team proposes to scale down the gas turbine of part (a), keeping all dimensions in the same proportions. The team assumes that the same hot and cold temperatures exist as in part (a) and that the net power output of the gas turbine is proportional to the overall volume of the device. Plot the ratio of the conduction through the shaft to the net power output of the turbine over the range 0.005 m s Ls 1 m. Is a scaled-down device with L = 0.005 m feasible?
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