An insulated steam turbine is to produce 100 MW of power. Superheated steam enters the turbine at 12 MPa and 600°C, and saturated water exits the turbine at a pressure of 80 kPa. There are two design constraints to be considered:

Question

(1) The turbine blade design requires that the quality of the steam to be no less than 0.90 to maintain blade durability.
(2) The maximum mass flow rate of steam that the system can utilize is 100 kg/s.
Plot the mass flow rate of steam necessary to produce 100 MW of power for exit qualities ranging from 0.9 to 1.0, and then determine the range of exit qualities that satisfy both design constraints. Determine the necessary mass flow rate of the steam.

Given: P1 = 12.0 MPa; T1 = 600°C; W?=100 MW=100,000 kW; P2 = 80 kPa; Steam
State 1 is the inlet, state 2 is the outlet.
Assume: Q? = 0 (insulated) Also, for a turbine, assume steady-state, steady-flow, single-inlet, single-outlet flow, with ?KE = ?PE = 0

Answer 1

With these assumptions, the First Law for open systems reduces to W?=m?(h1?h2)
So m?=W?h1?h2
For steam, the following properties can be found:
h1 = 3609.02 kJ/kg
Exit state enthalpy values depend on the quality
Considering the two constraints, the range of exit qualities that meets both criteria is
0.9 ? x2 ? 0.975
The minimum mass flow rate of the steam is 85.4 kg/s, and the maximum is 100 kg/s.