Question

Consider a steam power plant that operates on an ideal reheat–regenerative Rankine cycle with one open feedwater heater, one closed feedwater heater, and one reheater. Steam enters the turbine at 10MPa and 550c and is con- densed in the condenser at a pressure of 10 kPa. Some steam is extracted from the turbine at 4 MPa for the closed feedwater heater, and the remain- ing steam is reheated at the same pressure to 550c The extracted steam is completely condensed in the heater and is pumped to 10 MPa before it mixes with the feedwater at the same pressure. Steam for the open feed- water heater is extracted from the low-pressure turbine at a pressure of 0.5 MPa. Determine the fractions of steam extracted from the turbine as well as the thermal efficiency of the cycle.

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Answer 1

The complete cycle and the pressure p, Temperature T, and enthalpy h extracted from steam charts are represented on a T-S diagram shown below.

Let the mass fractions extracted at 4MPa be x, and that at 0.5MPa be y.

The steam extracted at 4MPa is used to heat the water from 3'-4. The steam cools from 5-3

The steam extracted at 0.5MPa is used to heat the water from 2'-3. the steam cools from 7-2.

Assuming no heat losses in the feed water heaters, we get two equations with mass fractions as unknowns.

-----------------------------------------------(1)

, assuming h2'~h2 (pump work is assumed to be negligible)

-------------------------------------------(2)

,assuming h1'~h1 (pump work is assumed to be negligible)

In the cycle, turbine output happens along 4-5 and 6-8, and external heater input happens between 3'-4. For simplification, we shall ignore pump work and heat losses to atmosphere.

Thermal Efficiency of the cycle is given by

Substituting values, we got earlier,