Question

Water is the working fluid in an ideal Rankine cycle with reheat. Superheated vapor enters the turbine at 12 MPa, 480 °C and the pressure at the exit of the second stage turbine is 8 kPa. Steam expands through the first stage turbine to 1 MPa and then is reheated to 440 °C. Saturated liquid water leaves the condenser. After the pump, pressure goes back to 12 MPa. Find: 

(1) Sketch the process on a T-s diagram and justify the location of each point. (10')

(2) Find specific enthalpy at each point from \(\mathrm{h}_{1}\) to \(\mathrm{h}_{6}\) in \(\mathrm{kJ} / \mathrm{kg}\). (18')

(3) The net work per unit of steam flow \(\frac{W_{c y c l e}}{m}\) in \(\mathrm{kJ} / \mathrm{kg}\). (2')

(4) Total heat addition per unit of steam flow in the boiler \(\frac{Q_{i n}}{m}\), in \(\mathrm{kJ} / \mathrm{kg}\). (2')

(5) Heat loss per unit of steam flow in the condenser \(\frac{\dot{Q}_{\text {out }}}{\mathrm{m}}\), in \(\mathrm{kJ} / \mathrm{kg}\). (2')

(6) Thermal efficiency \eta. (2')

(7) Knowing that liquid in a steam turbine causes corrosion, based on the phase of water at the end of each turbine, is it a good design and why? (4')

Answer 1

To find the net worl output of the system and the thermal efficiency, we must start by finding the enthalpy at all the 4 points of the T-s diagram. This can be done by using the saturated and superheated steam table.

Answer to Que7). As it can be interpreted from the solution that the phase of water at end of turbine is 96.25 for the first stage and 91.65 percent. In general, if the quality of steam at end of turbine is more than 90 percent, there is no significant erosion to the turbine blades. But in long term, there might be some erosion because of this wetness. To reduce the erosion,the state of steam must be atleast dry saturated at the end of each turbine.