Question

a.Why the Carnot cycle is not a realistic model for steam power plant? Justify your answer. [3 marks]

b. A steam power plant operates on a simple ideal Rankine cycle between the pressure limits of 9 MPa and 15 kPa. The mass flow rate of the steam through the cycle is 35 kg/s. The moisture content of the steam at the turbine is not to exceed 10 %.

i. Generate the T - s (Temperature – specific entropy) diagram of the cycle. [4 marks]

ii. Determine the minimum turbine inlet temperature in °C. [6 marks]

iii. Calculate the thermal efficiency of the cycle. [4 marks]

iv. Does the performance of the given Rankine cycle improve if the steam leaves the turbine as saturated vapor? Explain your answer. [

Answer 1

a.)  

Carnot cycle is not a realistic model for steam power plant because of practical difficulties and the operation of equipment intended to carry out steps 2 to 3 (isentropic expansion) and 4 to 1 (isentropic compression).

The problem with isentropic expansion step (2 to 3) is that turbine takes in saturated steam to produce an exhaust with high liquid content, which causes severe erosion problems. Even more difficult is the design of a pump that takes in a mixture of liquid and vapor (point 4) and discharges a saturated liquid (point 1), which happens in isentropic compression step (4 to 1).

For these reasons, an alternative model cycle is taken as standard for power plants. It is called Rankine cycle.

b.)

(i)

T-S plot for Rankine cycle

Steps shown in the cycle are as follows:

1-2: Isobaric heating step, in boiler, in which superheated vapor is produced.

Note that in Carnot cycle step 1-2 produces saturated vapor.

2-3: Isentropic expansion of vapor, in turbine

3-4: Isobaric, isothermal condensation producing sarurated liquid.

Note that in Carnot cycle a mixture of liquid and vapor is produced in this step.

4-1: Isentropic pumping of liquid to boiler pressure.

(ii)

From the given data:

Turbine inlet pressure = 9 MPa

Steam quality is 100% at turbine inlet since steam is superheated.

From properties of steam at inlet condition:

T = 577 K or 304 C

Minimum turbine inlet temperature is 304 C.