Question

Problem 8.045 SI

Consider a regenerative vapor power cycle with two feedwater heaters, a closed one and an open one, and reheat. Steam enters the first turbine stage at 12 MPa, 560°C, and expands to 2 MPa. Some steam is extracted at 2 MPa and fed to the closed feedwater heater. The remainder is reheated at 2 MPa to 520°C and then expands through the second-stage turbine to 0.3 MPa, where an additional amount is extracted and fed into the open feedwater heater operating at 0.3 MPa.

The steam expanding through the third-stage turbine exits at the condenser pressure of 60 kPa. Feedwater leaves the closed heater at 210°C, 12 MPa, and condensate exiting as saturated liquid at 2 MPa is trapped into the open feedwater heater. Saturated liquid at 0.3 MPa leaves the open feedwater heater. Assume all pumps and turbine stages operate isentropically.


Determine for the cycle:

(a) the heat transfer to the working fluid passing through the steam generator, in kJ per kg of steam entering the firststage turbine.

(b) the percent thermal efficiency.

(c) the heat transfer from the working fluid passing through the condenser to the cooling water, in kJ per kg of steam entering the first-stage turbine.

Answer 1

a) Refer the diagram below for the cycle.

The input data and assiciated properties from steam tables are given below. We assume flow to turbine I as 1 kg/s

We calculate the cycle by components as follows:

For turbines

Since the expansions are isentropic, the outlet temperature and enthalpies are corresponding to inlet entrpies and outlet pressures.

Additionally for turbine-III, the outlet steam quality is calculated by inlet entropy and outlet pressure.

For Pumps

The putlet enthalpy is given by inlet entropy and outlet pressure (insetropic)

With the above, the calculated parameters are as below:

​

We now solve the mass flows by using heat balance equations

For closed FW heater

Or

Hence

Hence

For Open FWH

Or

Solving:

With the above the table becomes

The heat transfer to the working fluid is given by

Or

b) The total power output is given by the total turbine output(stages I,II and III) minus the pumping power

Hence

Or

Hence the cycle efficiency is

c) The heat transfer in the condenser is given by