2-2-2 Ideal Rankine cycle

Power Plant Vapor Power Cycles

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2-2-2 Ideal Rankine cycle:

Many of the impracticalities associated with the Carnot cycle can be

eliminated by superheating the steam in the boiler and condensing it

completely in the condenser. As shown in figure 2.3 the cycle called

Rankine cycle, which is the ideal cycle for vapour power plants.

Figure 2.3: Schematic Layout of ideal Rankine cycle.


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The T-S diagram of ideal Rankine cycle is shown in figure 2.4.

Figure 2.4: T-S diagram of ideal Rankine cycle

The ideal Rankine cycle consists of the following four processes:

1-2 Isentropic compression in a pump

2-3 Constant pressure heat addition in a boiler

3-4 Isentropic expansion in a turbine

4-1 Constant pressure heat rejection in a condenser


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2-2-2-1Energy Analysis of the Ideal Rankine Cycle

All four components associated with the Rankine cycle (the pump, boiler,

turbine, and condenser) are steady-flow devices, and thus all four processes

that make up the Rankine cycle can be analyzed as steady-flow processes.

The boiler and the condenser do not involve any work. The pump and the

turbine are assumed to be isentropic.

1-2 Pump Work process:

Wpump= Wp = (h2 h1) kJ/kg

= vf (P2 P1) kJ/kg

Where: vf for P2 from steam table and P1 and P2 are in kPa

PWmpowerPump.

in kW 2-3 Heat Supplied in Boiler: Qsupply process

23sup hhQ ply kJ/kg

23

.

sup hhmQ ply kW

3-4 Turbine work

43 hhWT kJ/kg

43

.

urbine hhmpowerT in kW

Where : .

m is the mass flow rate of steam in kg/sec


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h1 and h2 can be taken from steam table for P1 and P2 respectively.

P2 = high pressure (or) boiler pressure (or) inlet to turbine pressure

P1 = low pressure (or) condenser pressure

Also, we can use Mollier diagram to find h1 and h2.

4-1 Constant pressure condensation

14 hhQrejected kJ/kg

14

.

kWin hhmQrejected

h1 = hf at low pressure P1

Net Work

Wnet = WT - Wp

Thermal Efficiency: It is ratio of network to the heat supplied.

supplyQ

Woror net

thermalrankinecycle

23

1243

supply hh

hhhh

Q

WW PT

hr-kW

kg

3600

netWSSC


12

ratioWork T

net

W

W

The back work ratio : 43

12

hh

hh

W

Wbwr

T

P

EXAMPLE 2

Steam is the working fluid in an ideal Rankine cycle. Saturated vapor enters

the turbine at 8.0 MPa and saturated liquid exits the condenser at a pressure

of 0.008 MPa. The net power output of the cycle is 100 MW.

Determine for the cycle:

(a) the thermal efficiency, (b) the back work ratio, (c) the mass flow rate of

the steam, in kg/h, (d ) the mass flow rate of the condenser cooling water, in

kg/h, if cooling water enters the condenser at 15º C and exits at 35º C.

SOLUTION


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State 1 pump : P1 = 0.008 MPa, h1 = hf@P1 = 173.88 kJ/kg

saturated liquid v1=vf@P1 = 1.0084×10-3 m3/kg

State 2 boiler : p2 = 8.0 MPa

s2 = s1

Wpump=v1(P2 - P1)= 1.0084×10-3 (8 - 0.008)

= 8.06 kJ/kg

h2=h1 + Wpump

= 173.88 + 8.06 = 181.94 kJ/kg

State 3: p3 = 8.0 MPa h3 = 2758.0 kJ/kg

saturated vapor s3 = 5.7432 kJ/kg . K

State 4: p4 = 0.008 MPa

s3 = s4 s4= s3 = 5.7432 kJ/kg . K

6361.7

5926.07432.544

fg

f

s

ssx

6745.04x

h4= hf + x4 hfg= 173.88 + 0.6745*2403.1

h4=1794.8 kJ/kg

(a) The thermal efficiency is:

23

1243

supply hh

hhhh

Q

Wnetthermal


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23

1243

hh

hhhhthermal

94.1810.2758

88.17394.1818.17940.2758thermal

%1.37371.0thermal

(b) The back work ratio is

43

12

hh

hh

W

Wbwr

T

P

8.17940.2758

88.17394.181

T

P

W

Wbwr

%84.01037.8 3bwr

(c) The mass flow rate of the steam can be obtained from the expression for

the net power given in part (a)

)()( 1243

..

hhhh

Wm cycle

)06.8()2.963(

360010)100(.

3.

m

hkgm /1077.3 5.

(d) winwoutwws TTCmhhm.

14

.

15352.488.1738.17941077.3.

5wm

hkgmw /102.7 6.


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2-2-3 Real Vapour Power Cycles:

Fig. 2.5 : Temperature entropy diagram showing the effects of turbine and

pump irreversibilities.

TURBINE: The principal internal irreversibility experienced by the

working fluid is associated with expansion through the turbine. The work

developed in this process per unit of mass flowing is less than that for the

corresponding isentropic expansion 3 4s.The isentropic turbine efficiency

is:

PUMP: The work input to the pump required to overcome irreversibilities

also reduces the net power output of the plant. As illustrated by Process 1 2

of Fig. 2.5, the work input per unit of mass flowing is greater than that for

the corresponding isentropic process 1 2s. The isentropic pump efficiency

is:


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EXAMPLE 3

A steam power plant operates on the cycle shown in Figure. If the isentropic

efficiency of the turbine is 87 percent and the isentropic efficiency of the

pump is 85 percent, determine (a) the thermal efficiency of the cycle and (b)

the net power output of the plant for a mass flow rate of 15 kg/s.

SOLUTION:


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2-3 How Can Increase the Efficiency of the Rankine Cycle?

1. Lowering the Condenser Pressure (Lowers Tlow,avg)

The effect of lowering the condenser pressure on the Rankine cycle

efficiency is illustrated on a T-s diagram in Fig. 2-6. The colored area on this

diagram represents the increase in net work output as a result of lowering the

condenser pressure. The heat input requirements also increase (represented

by the area under curve 2'-2), but this increase is very small. Thus the overall

effect of lowering the condenser pressure is an increase in the thermal

efficiency of the cycle.

Figure 2.6 The effect of lowering the condenser pressure on the ideal

Rankine cycle.

To take advantage of the increased efficiencies at low pressures, the

condensers of steam power plants usually operate well below the

atmospheric pressure. This does not present a major problem since the vapor

power cycles operate in a closed loop.


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2. Superheating the Steam to High Temperatures (Increases Thigh,avg)

The average temperature at which heat is transferred to steam can be

increased without increasing the boiler pressure by superheating the steam to

high temperatures. The colored area on this diagram represents the increase

in the net work. The total area under the process curve 3-3' represents the

increase in the heat input. Thus both the net work and heat input increase as

a result of superheating the steam to a higher temperature. The overall effect

is an increase in thermal efficiency, however, since the average temperature

at which heat is added increases.

Superheating the steam to higher temperatures has another very desirable

effect: It decreases the moisture content of the steam at the turbine exit, as

can be seen from the T-s diagram (the quality at state 4' is higher than that at

state 4).

Figure 2.7: The effect of superheating the steam to higher temperatures on

the ideal Rankine cycle.


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3. Increasing the Boiler Pressure (Increases Thigh,avg)

Another way of increasing the average temperature during the heat-addition

process is to increase the operating pressure of the boiler, which

automatically raises the temperature at which boiling takes place. Notice that

for a fixed turbine inlet temperature, the cycle shifts to the left and the

moisture content of steam at the turbine exit increases.

Figure 2.8: The effect of increasing the boiler pressure on the ideal Rankine

cycle.


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EXAMPLE 4

Consider a steam power plant operating on the ideal Rankine cycle. Steam

enters the turbine at 3 MPa and 350°C and is condensed in the condenser at

a pressure of 10 kPa. Determine (a) the thermal efficiency of this power

plant, (b) the thermal efficiency if steam is superheated to 600°C instead of

350°C, and (c) the thermal efficiency if the boiler pressure is raised to 15

MPa while the turbine inlet temperature is maintained at 600°C.

SOLUTION: Solution (a)


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Solution (b)

(b) States 1 and 2 remain the same in this case, and the enthalpies at state 3

(3 MPa and 600°C) and state 4 (10 kPa and s4 = s3) are determined to be

Solution (c)

(c) State 1 remains the same in this case, but the other states change. The

enthalpies at state 2 (15 MPa and s2 = s1), state 3 (15 MPa and 600°C), and

state 4 (10 kPa and s4 = s3) are determined in a similar manner to be


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2-4 Reheat

There are some methods to improve cycle performance. The thermal

efficiency of the cycle can be improved by following methods:

(i) By reheating of steam

(ii) By regenerative feed heating

(iii) By water extraction

(iv) By using binary vapour

Reheating System

The T-s diagram of the ideal reheat Rankine cycle and the schematic of the

power plant operating on this cycle are shown in Fig. 2.9.

In the first stage (the high pressure turbine), steam is expanded

isentropically to an intermediate pressure and sent back to the boiler where it

is reheated at constant pressure, usually to the inlet temperature of the first

turbine stage. Steam then expands isentropically in the second stage (low-

pressure turbine) to the condenser pressure. Thus the total heat input and the

total turbine work output for a reheat cycle become:

2-2-2 Ideal Rankine cycle

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