Exercise 5 Turbomachines

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ENERGY CONVERSION A 2019-20 1 Exercises Turbomachines Exercise 1 Consider a closed-loop gas cycle expander operating alternatively with helium (molar mass 4 kg/kmol) or argon (40) and operating with the following conditions:  inlet total pressure: 5 bar(a)  inlet total temperature: 800 °C  outlet pressure: 1 bar  mass flow rate: 20 kg/s Please: i. determine the number of stages; ii. sketch possible velocity triangles for the first and the last stage; iii. sketch the blade profile in the blade-to-blade as well as meridian planes; iv. determine the optimal rotational speed. Exercise 2 Consider an adiabatic axial-flow turbine expanding a monoatomic perfect gas (molecular mass equal to 150 kg/kmol) from the following initial conditions:  total pressure: 100 bar  total temperature: 800 °C down to the expander outlet pressure of 10 bar. The working fluid mass flow is 100 kg/s. Considering a single-stage machine: i. determine accurately the velocity triangles of a single-stage machine; ii. determine the rotational speed corresponding to an aspect ratio h/D of 0.25. Moreover, considering a three-stage machine: iii. sketch the velocity triangles of repeated stages assuming a three-stage machine; iv. explain why the three-stage machine allows for higher efficiencies. Exercise 3 Consider a single-shaft steam turbine rotating at 3000 rpm and characterized by:  high pressure mass flow rate = 100 kg/s  low pressure mass flow rate = 70 kg/s  steam conditions at turbine inlet flange: 40 bar, 550 °C  condensation pressure = 0.05 bar (33 °C) Please: i. determine the velocity triangles and mean diameter of first last stages, ii. compute the blade height at rotor outlet; iii. comment the expected efficiencies for the two stages. Exercise 4 Consider a single-shaft steam turbine…