Thermodynamics Fundamentals
3.2 Steam Power Cycle: Energy and Exergy Considerations
64 3 Thermodynamics Fundamentals
3.2 Steam Power Cycle: Energy and Exergy Considerations 65 ηB=m˙S(h3−h2)
˙
mF·LHV (3.29)
The efficiency of the steam generator is, however, determined mostly indirectly – by the losses of the steam generator. The steam generator losses with respect to the fuel power are (Doleˇzal 1990)
– loss through unburned combustibles (κU), – loss through sensible heat of the slag (κS), – flue gas loss (κFG) and
– loss through radiation and convection of the steam generator (κRC).
Accordingly, the steam generator efficiency is
ηB =1−κU−κS−κFG−κRC (3.30) For the thermal efficiency of the real cycle, which represents the ratio of the inner power output of the turbine Pi(the power of the turbine without mechanical losses) to the steam energy supplied, this becomes
ηth= Pi
˙
mS,j•Δhj
(3.31) where ˙ms,j are the individual mass flows of water/steam andΔhj stands for the respective increases of enthalpy attained in the steam generator. For the simple steam process shown in Fig. 3.5, analogous to Eq. (3.20), this is
ηth= Pi
˙
mS(h3−h2) (3.32)
The efficiency of the cycleηth, in contrast to the efficiency of the loss-free process ηth,0, is decreased by friction losses during expansion in the turbine. These losses are taken into account by the isentropic turbine efficiencyηi,T:
ηi,T= ηth
ηth,0 = h3−h4
h3−h4,id (3.24)
With the inner power of the turbine Piand the mechanical output of the turbine shaft Pm, the relevant equation for the mechanical efficiencyηmis
ηm= Pm
Pi
(3.33)
66 3 Thermodynamics Fundamentals for the generator efficiency
ηGen = PGen
Pm
(3.34) and for the auxiliary power efficiency
ηaux= Pne
PGen
(3.35) If the feed pump is driven electrically, and also if driven by a steam turbine, the driving power of the feed pump is commonly added to the auxiliary power. In the case of a turbine-driven feed water pump, the power of the feed pump turbine is taken into account in calculating the thermal efficiency of the real cycle and added to the power output of the main turbine in Eq. (3.31).
Often, the turbine or turbine generator efficiencyηTis used, which represents the ratio of the gross electrical output and, if necessary, the mechanical power output (in the case of feed pumps with a steam turbine drive) to the steam energy input:
ηT= P∗Gen
˙
ms,j·Δhj =ηth·ηm·ηGen (3.36) with
PGen∗ =PGen+Paux,m (3.37)
If the feed pump is driven by a steam turbine, the power output of the turbine gener- ator P∗Genincreases, surpassing the gross output PGenby the amount of the mechan- ical output of the turbine drive Paux,m. Where the feed pump is driven electrically, the power output P∗Gen equals the generator output PGen. The turbine generator efficiency, in contrast to the thermal efficiency of the cycle, also takes into account the losses occurring in the turbine and the generator.
Therefore the auxiliary power efficiency becomes ηaux= Pne
P∗Gen = P∗Gen−Paux,el−Paux,m
P∗Gen (3.38)
Besides an energy efficiency, it is also possible to develop an expression for the total and single exergy efficiencies:
ζne=ζB·ζth·ζGen·ζaux·ζm·ζP (3.39) Given that the fuel energy and exergy differ only very slightly, the total energy and exergy efficiencies are almost equal. Significant differences, however, arise for the single efficiencies, in particular in the process of energy conversion in the steam
3.2 Steam Power Cycle: Energy and Exergy Considerations 67 generator and in the energy conversion process of the real cycle. The mechanical efficiency and the generator efficiency have the same values if the friction heat is not utilised (Herbrik 1993).
3.2.1 Steam Generator Energy and Exergy Efficiencies
Analogous to the energy efficiency ηB of the steam generator, and in accordance with Eq. (3.29), the exergy efficiencyζBof the boiler can be defined as
ζB=m˙S(e3−e2)
˙ mF·eF
(3.40) where ˙mSis the steam mass flow, ˙mFis the fuel mass flow and eF stands for the fuel’s, e2for the water’s and e3for the superheated steam’s exergy.
From Eq. (3.29), it follows by transformation that
˙ mS
˙ mF
=ηB
LHV h3−h2
(3.41) For the input of exergy, the ambient temperature Tais incorporated:
e3−e2=h3−h2−Ta(s3−s2) (3.42) If Eqs. (3.41) and (3.42) are inserted into Eq. (3.40), then the following expres- sion is derived:
ζB=LHV eF ηB
1−Ta
s3−s2 h3−h2
(3.43) or
ζB=LHV eF ηB
e3−e2
h3−h2 (3.44)
for the boiler exergy efficiency.
The boiler exergy efficiency indicates which part of the supplied fuel exergy eF
is maintained as exergy of the steam. This efficiency, in contrast toηB, assesses the energy conversion in the steam generator.
The exergy efficiency thus essentially depends on two factors. The first factor,ηB
LHV/ eF, represents the losses through flue gas and radiation. The second factor can be calculated from the feed water inlet and exiting live steam state quantities. This factor implicitly includes the considerable exergy losses through the irreversibilities of combustion and heat transfer.
The changes of state of the water are shown in Fig. 3.7. The water entering at temperature T2 first gets preheated, vaporised and superheated. The area below
68 3 Thermodynamics Fundamentals Fig. 3.7 Isobaric state
changes in the evaporator (Baehr and Kabelac 2006)
K
p
3
2 Tl
=Ta T2
Tm Tm
T3
T(p)
Ta
0 s2 s3 s
T
e3- e2
b3- b2
x=1
the isobar of the boiler pressure indicates the increase of the water’s enthalpy, expressed as
h3−h2=q23 (3.45)
This increase corresponds to the heat that the water absorbs in the steam gener- ator. The area between the isobar of the boiler pressure and the isotherm Taof the ambient temperature corresponds to the increase of the water’s exergy, e3−e2.
If the mean temperature of the heat addition Tm,in= h3−h2
s3−s2 (3.46)
is put into Eq. (3.43), the result is ζB=LHV
eF ηB
1− Ta
Tm,in
(3.47)
While the energy efficiency of a steam generator typically lies above 0.9, the corresponding value for the exergy efficiency ranges around 0.5.
3.2 Steam Power Cycle: Energy and Exergy Considerations 69 This low value is caused by
– exergy losses via flue gas and irradiation – about 6%, – the exergy loss of combustion – about 15% and – the exergy loss of the heat transfer – about 30%.
Losses through the sensible heat of the flue gas and through irradiation are taken into account in both the energy and exergy efficiency. Losses through the irreversibilities of combustion and heat transfer are only included in the exergy efficiency. Irreversible combustion and heat transfer convert about half of the fuel exergy input into anergy, while exergy cannot be made use of in the following energy conversion steps, having to be discharged as waste heat.
3.2.2 Energy and Exergy Cycle Efficiencies
Analogous to the energy efficiency of the Clausius–Rankine Cycle:
ηth= Pi
˙
mS(h3−h2) = w h3−h2
(3.48) it is possible to define an exergy efficiency:
ζth= Pi
˙
mS(e3−e2) = w e3−e2
(3.49) This efficiency specifies what part of the exergy taken up in the steam generator is converted into useful work. If the cycle is reversible, the thermal efficiency ζth
becomes 1; divergences from this ideal value represent thermodynamic losses. To break these down, the useful work is calculated as
w=h3−h4−(h2−h1)=e3−e4−(e2−e1)−Ta[(s3−s4)−(s2−s1)]
=e3−e2−(e4−e1)−eL34−eL12
(3.50) So the useful work obtained is the exergy taken up in the steam generator (e3−e2) minus the exergy losses – the exergy delivered in the condenser (e4−e1) and the exergy losses caused by irreversibilities in the feed pump (eL12) and in the turbine (eL34).
Hence, for the exergy cycle efficiency, the expression becomes ζth=1−e4−e1
e3−e2 −eL12+eL34
e3−e2 (3.51)
The losses of exergy are pictured in Fig. 3.8. The exergy loss of the feed pump, eL12, is small in contrast to the exergy loss of the steam turbine, eL34. The exergy loss of the steam turbine depends on the isentropic efficiency of the turbine.
70 3 Thermodynamics Fundamentals Fig. 3.8 Exergy losses of a
simple steam cycle (Baehr and Kabelac 2006)
ciritical point
p
3
4 p
2
1 Ta
0 s1s2 s3 s4 s
T
eL34 eL12
b3–b2 e4–e1 p1, T1
Given that in the condenser, the exergy e4−e1 is transferred to and then dis- charged to the environment with the cooling water, it has to be regarded as an exergy loss. A reduction of the exergy losses can be achieved by bringing the condensation temperature as close as possible to the ambient temperature by using a large heat transfer surface and a large cooling water mass flow.
In the condenser, the heat q41(which can be represented by the rectangular area below isobar 4 – 1 in the T−s diagram) is given off to the cooling water flow. It can be expressed as
q41 =b3−b2+eL =b3−b2+(e4−e1)+eL12+eL34 (3.52) Besides the exergy losses of the cycle, which arise through irreversibilities and convert exergy into anergy, the heat q41also comprises the anergy b3−b2taken up in the steam generator with the heat q23. From the condenser, therefore, the entire anergy load is discharged to the environment.
Typical exergy efficiencies of the cycle, which are around 0.9, are significantly above the typical energy efficiencies of about 0.45.
3.2.3 Energy and Exergy Efficiency of the Total Cycle
There is no influence on the overall efficiency by this differentiated – i.e. energetic or exergetic – approach. There are, however, clear differences when considering the steam generator efficiency and the thermal efficiency of the cycle. The exergy efficiency defines the place where the thermodynamic losses originate and hence better indicates the potential for efficiency increases (Baehr and Kabelac 2006).
References 71 The greatest exergy losses and thus the greatest potential for improving the efficiency are found in the steam generator section of the process. The losses in the turbine are significantly smaller.
References
Adrian, F., Quittek, C. and Wittchow, E. (1986). Fossil beheizte Dampfkraftwerke. Handbuchreihe Energie, Band 6, Herausgeber T. Bohn. Technischer Verlag Resch, Verlag T ¨UV Rheinland.
Baehr, H. D. and Kabelac, S. (2006). Thermodynamik: Grundlagen und technische Anwendungen.
Berlin, Heidelberg, Springer.
Doleˇzal, R. (1990). Dampferzeugung: Verbrennung, Feuerung, Dampferzeuger. Berlin, Heidelberg, New York, Springer.
Hahne, E. (2004). Technische Thermodynamik: Einf¨uhrung und Anwendung. M¨unchen [u.a.], Oldenbourg.
Herbrik, R. (1993). Energie- und W¨armetechnik. Stuttgart, Teubner.
Meyer, G. and Schiffner, E. (1989). Technische Thermodynamik. Leipzig, Fachbuch.
Strauß, K. (2006). Kraftwerkstechnik: zur Nutzung fossiler, nuklearer und regenerativer Energiequellen. Berlin [u.a.], Springer.