11.1 The Carnot cycle
A working medium which changes its state of
aggregation throughout a cycle permits a practical realization of the Carnot
cycle.
It will be recalled that the Carnot cycle comprises
two adiabats and two isotherms. A practical
realization of adiabatic processes involves no great difficulties. The
deviation of real adiabatic processes of expansion and compression from an isentrop because of the irreversibility of flow processes
leads, of course, to a decrease in the thermal efficiency of a cycle. However,
this decrease is insignificant.
In practice, isothermal addition and rejection of
heat in gas thermopower plants involves
insurmountable difficulties. As it was shown in Sec. 7.9 and in Chapter 10, to
realize actual processes as close to isothermal processes as possible,
multistage air compression is undertaken with intermediate cooling of the
compressed air (in compressors) and gradual addition of heat (in gas-turbine
plants).
Vapour power cycles are quite different.
When a substance is in flow, the isobaric process
of heat addition and rejection can be most simply realized. The process of
isobaric heat addition and rejection at a constant temperature was already
considered above.
Fig. 11.1
This process involves a change of phase of a pure
substance, from a liquid state into a gaseous state. In fact, inside the
two-phase region of a pure substance isobars coincide with isotherms,
consequently, the isobaric process of heat addition to wet steam (i.e. vapourization),
just as the isobaric process of heat rejection from wet steam (i.e.
condensation), which are easily realized in practice, are also isothermal
processes. It follows that if wet vapour (steam) is used as a working medium,
the resulting cycle, composed of two adiabats and two isobars (which are also
isotherms), will be the Carnot cycle.
A schematic diagram of a thermopower plant in which
a Carnot cycle is realized with wet steam as a working medium is shown in Fig.
11.1. Wet steam with a small dryness fraction x flows into steam boiler 1.
By the fuel burned in the boiler furnace (coal, fuel oil, natural gas,
etc.) heat is added to the wet steam and its dryness fraction rises to a value
close to one. In the boiler heat is added to the steam at a constant pressure p1
and a constant temperature T1
Steam flows from the boiler into steam turbine 2.
Upon expansion in the turbine the steam flow acquires a considerable
kinetic energy which converts on the turbine blades into the kinetic energy of
rotation of the turbine wheel; the kinetic energy is then converted into
electric power with the aid of electric generator 3 rotated by the steam
turbine.
At the turbine's exit the wet steam is at a
pressure p2 and a temperature T2 corresponding
to this pressure. Steam then flows into condenser 4, a heat-exchanger in
which cooling water removes heat from the steam; steam condenses in the
condenser, and, consequently, its dryness fraction diminishes.
The process of heat rejection from the steam in the
condenser proceeds at a constant pressure.
From the condenser wet steam enters compressor 5
where it is compressed adiabatically to pressure p1. Wet steam then flows again into the
boiler and the cycle closes.
Therefore, on the section of the cycle covering the
compressor's exit to the turbine's entry the pressure of the working medium is p1,
and on the section from the turbine exit to the compressor's entry the
pressure of the working fluid is p2. Of course, due to the
inevitable hydraulic losses suffered as the steam flows through pipelines, the
pressure drops somewhat along the flow, but this
pressure drop can be ignored in the first approximation.
Fig. 11.2
The cycle described is shown on p-v and T-s
diagrams in Fig. 11.2. In the boiler heat q1 is added to
the steam along isobar-isotherm 4-1, steam expands in the turbine along
adiabat 1-2, heat q2 is rejected in the condenser
along isobar-isotherm 2-3, and steam is compressed in the compressor
along adiabat 3-4. In the course of adiabatic expansion from the state
close to the right boundary curve into the state close to the left boundary
curve, the wetness of the steam increases. Heat should be rejected in the
condenser until the wet steam reaches the state determined by the following
condition: when compressed adiabatically from state 3 with a pressure p2
to state 4 with a pressure p1, the final state of
the working fluid should not lie outside the saturation region.
The thermal efficiency of a reversible Carnot cycle
realized with wet steam, just as of the Carnot cycle realized with any other
working medium, is determined from Eq. (3.32):
An actual cycle involving wet steam and composed of
two isobar-isotherms and two adiabats is represented on the T-s diagram
shown in Fig. 11.3, taking into account the irreversible friction losses
suffered when the steam expands in the turbine and is compressed in the
compressor. The difference (s2 — s1) represents the
increase in enthalpy of steam as a result of adiabatic expansion, due to
friction, and (s4 — s3) is the increase in the enthalpy
of steam upon compression in the compressor.
It follows that the Carnot cycle can be realized
with wet steam. Inasmuch as the critical temperature of water is low(374.15
°C), the difference between the lower (about 25 °C) and higher (not exceeding
350 °C) cycle temperatures is also small, since in approaching the critical
point the length of the isobar-isothermal section 4-1 reduces
considerably and, consequently, the non-isentropic sections 1-2 and 3-4,
reducing the thermal efficiency of the cycle, become more important; the
area ratio of the cycle diminishes (Fig. 11.3).
Fig. 11.3
However,
even within that comparatively narrow interval of limiting temperatures, the
efficiency of a reversible Carnot vapour cycle is of considerable magnitude.
Nevertheless, taking into account the operating
conditions for the equipment of a thermal power plant, it is inexpedient to
realize this cycle in practice. When operating with wet steam, a mixture of dry
steam and suspended droplets of water, the bladings of the turbine and
compressor operate under very difficult conditions, the flow of the working
medium is imperfect from the viewpoint of gas-dynamics and the internal
relative efficiency of these machines,
As a result, the internal absolute efficiency of
the cycle is relatively low.
It is also important that the compressor used to
compress wet steam at low pressures and great specific volumes is a rather
cumbersome device, requiring an excessively high-power drive.
For these reasons the Carnot cycle for wet steam
has not found practical application.