YANBU INDUSTRIAL COLLEGE
Thermo-Fluid Systems
MET401
Department of Mechanical Engineering Technology
1 1 kg
Turbine
2 3 3
m1
4 5 1
m i
m2 i 1
m3
Boiler Condenser
1-m1
1 m1 m2
16 1 kg 15 6
13 12 10 9 7
14 11 8 pump
Feedwater heaters
Module II- Analysis of Steam Cycles
2006
© Dr Rahim K. Jassim
PhD, MEMgt, BSc(hons) , P.E., MASME, MIPENZ, Reg. Eng
(Module II)
Analysis of Steam Cycles
2.1- Analysis of Carnot Cycle
Having defined the reversible process and considered some factors that make processes
irreversible. Let us pose the question. If the efficiency of all heat engine is less than 100%,
what is the maximum (most) efficiency cycle we can have.
The important point to be made here is that the Carnot cycle, regardless of what the working
substance may be, always has the same four basic processes. These processes are,
1-2 Reversible isothermal process in which heat is transferred to or from the high temperature
reservoir.
2-3 Reversible adiabatic process in which the temperature of the working fluid decreases from
the high temperature to the low temperature.
3-4 Reversible isothermal process in which heat is transferred to or from the low temperature
reservoir.
4-1 Reversible adiabatic process in which the temperature of the working fluid increases from
the low temperature to the high temperature.
High temp.
reservoir
QH
1
Boiler
2 Turbine
Pump (Condenser) (Pump)
(Turbine)
W
Condenser
4 (Evaporator)
3
QL
Low temp.
reservoir
Figure (2.1 a)
T
QH
Figure (2.1b) 1 2
TH
TC
4 3
QL
S1=S4 S2=S3
The efficiency of the Carnot engine is S
(2.1)
Where TH and TL are the absolute temperatures (K).
Carnot cycle is regarded as totally reversible cycle (see Figures 2.1a and b), and the efficiency
of Carnot cycle is the highest efficiency of a cyclic device can have, also is used as a reference
point to evaluate the real cycle performance.
2.2- Rankine Cycle
Rankine cycle is shown in more details in Figure (2.2)
Figure (2.2) A simple steam power plant
Figures (2.3) Rankine cycle on P-v, T-s and h-s coordinates (a,b,c)
Rankine Cycle efficiency
(2.2)
The enthalpy at point (4) can be calculated as follows,
(2.3)
(2.4)
v3 = vf at P3
2.3- Analysis of Rankine cycle
a- Cycle efficiency
The performance of the power plant is expressed in terms of the thermal or cycle efficiency
which defined as the ratio of the net work output to the heat input this, thus
(2.5)
b- Net positive Heat Rate (NPHR)
An alternative and widely used performance parameter for the power plant is called “Net Positive
Heat Rate” or Plant Net Heat Rate (PNHR) which is the rate of heat supplied per unit rate of net
work output. The and are both expressed in the same units, the heat rate is simply the
reciprocal of . In the SI units however, the heat rate was usually expressed as so many kJ of
heat input per kWh of net work out in these units
Net Positive Heat Rate = (2.6)
c- Boiler efficiency
(2.7)
where
: fuel mass flow rate (kg/s)
HHV: fuel Higher Heating Value (kJ/kg), which can be defined as the heat liberated in kJ by
complete combustion of 1 kg of fuel (see module III-section 3.1.2.2).
d- Overall efficiency
(2.8)
2.4-The effect of irreversibility
a- Frictional pressure drop in the steam pipe and across the governing throttle value
between boiler and turbine.
T b- Frictional effects in flow through
PB the turbine and pump.
3
Pt
3
PA
2
2 (a)
1 4 44 TA
Pump Losses Turbine and
piping Losses
PB
s2s
2
s4 s4 Pt
h S
3 PA
3
(b)
4
4
4
x
T
Io
s3 s4 s
Figure (1.4)
2.5-Lost work due to irreversibility
If the condenser temperature TA is taken to be the same as the temperature To of the
environment, this is a special case of a more general and important theorem in the study of the
availability (exergy).
Lost Work = Increase in = (2.9)
2.6-Alternative expressions for Rankine cycle efficiency in Terms of available energy
(exergy)
In practice, the exhaust steam entering the condenser is always wet. The steam is then
condensed at constant temperature in the ideal condenser. In these circumstances an
alternative expression for the exact Rankine cycle efficiency may be written down from a study
of availability (exergy). If , for purpose of analysis, the environment temperature T o is taken as
being the same the condenser temperature TA, then the turbine, condenser and feed pump of
the ideal Rankine cycle together constitute an ideal non-cycle open-circuit steady flow work-
producing device exchanging heat reversibly with the environment at temperature TA. In this
device, all internal processes are reversible and the heat exchange with the environment is
reversible since there is zero temperature difference between the fluid and the environment in
the heat exchange process.
W el W net ηm ηel
Turbine Wt
1 Q o
Q
Condenser
Figure (1.5) A To T A
4
Feed
pump Wp
The alternative Rankine efficiency expression is given by
(2.10)
where
(2.11)
(2.12)
2.7-Rational Efficiency (exergetic efficiency)(ψ)
The rational efficiency can be expressed in the following forms
(2.13)
where is the ratio of fuel chemical exergy (o) to Net Calorific Value (NCV). Table (2.1) shows
a typical values of for some industrial fuels and other combustible substances.
Fuel
Different types of coal 1.06-1.1
Wood 1.15-1.3
Different fuel oils and petrol 1.04-1.08
Natural gas 1.04
Hydrogen 0.985
Carbon Monoxide 0.973
Table (2.1)
(2.14)
2.8- Specific Fuel and Steam Consumption
a. specific fuel consumption = (2.15)
where
and mechanical efficiency , electrical efficiency
b. specific steam consumption = (2.16)
2.9- The Reheat Rankine Cycle
In the last section we noted that the efficiency of the Rankine cycle could be increased by
increasing the pressure during the addition of heat. However, the increase in pressure also
increases the moisture content of the steam in the low pressure end of the turbine. The reheat
cycle has been developed to take advantage of the increased efficiency with higher pressures,
and yet avoid excessive moisture in the low pressure stages of the turbine. This cycle is shown
schematically and on a T-s diagram in Figure 1.7. The unique feature of this cycle is that the
steam is expanded to some intermediate pressure in the turbine and is then reheated in the
boiler, after which it expands in the turbine to the exhaust pressure. Thus, the total heat input
and total turbine work output for a reheat cycle become,
(2.17)
(2.18)
It is evident from the T-s diagram that there is very little gain in efficiency from reheating the
steam, because the average temperature at which heat is supplied is not greatly changed. The
chief advantage is in decreasing to a safe value the moisture content in the low pressure stages of
the turbine. If metals could be found that would enable us to superheat the steam to 5, the simple
Rankine cycle would be more efficient than the reheat cycle, and there would be no need for the
reheat cycle.
(a)
(b)
Figure (2.7 a)
Figure (2.7 b)
Figure (2.7 c)
T PB Pr
3
5
Q R
4
Q B
PA
2
2
6
TA = T o
1
Q A
I P
Turbine Losses
s2s S6
2
S
Figure (2.8)
h3 h4
η HPt
h
3 h3 h4
T 5
h5 h6
HP Turbine
ηLPt
LP Turbine
expansion
expansion
h5 h6
4
4
x
6 Sat. vap. line
6 To
I To S
I HP I LP
s
Figure (2.9)
Figure (2.9) show the expansion is not isentropic; in this case the cycle thermal efficiency can be
expressed
(2.19)
1.10- The Regenerative Rankine Cycle
Another important variation from the Rankine cycle is the regenerative cycle which uses
feedwater heaters as shown in Figure (2.10). In this cycle the coming water from the condenser
before entering the boiler is heated by steam extracted or bled from the turbine at different
stages and pushed to feedwater heater/s. In doing so, the thermal efficiency of the cycle will be
improved significantly, reduces the steam flow to the condenser (needing smaller condenser)
and reduces the temperature difference between the condenser (reduces the operating cost).
Figure (2.10) Regenerative cycle with two direct contact feedwater heaters
Feedwater heaters are two types; open (contact) heaters and closed heaters. In an open type
heater, the extracted steam is allowed to mix with feedwater and both leave the heater at a
common temperature (Figure 2.10 a). In a closed heater, the fluids are kept separate and are
not allowed to mix together (Figure 2.11).
1 1 kg
7ac
Turbine
2 3 3
m1
4 5 1
m
i 1
i
m2
m3
Boiler Condenser
1-m1
1 m1 m2
16 1 kg 15 6
13 12 10 9 7
14 11 8
(a)
Feedwater heaters
n
1
m
i 1
i
m1 m2 m3
n: number
of
Drain feedwater
cooler heaters
1 kg 1 kg
n
m
i 1
i
Steam trap
3
(b)
m1 m2 m3
1
i 1
mi
2
1 kg 1 kg
m1+m2+m3
(c) m1
m1+ m2
Steam trap
Figure (2.11)
T
1
2
16 14
13 11 3
10 8 4
7
6 5
T
1
7 2
6
5
3
4
8
s
Cycle efficiency
Refer to Figure (2.10 (a))
Pumps work
= (2.20)
Total turbine work
(2.21)
Total heat input
(2.22)
(2.23)
Steam extracted
(1) the energy balance for heater 1 gives
(2.24)
(2.25)
(2) the energy balance for heater 1 gives
(2.26)
(2.27)
(see Figure 2.11 (a))
= (2.28)
(2.29)
(2.30)
(2.31)
