Unit - 3
Vapour Power Cycles
The Carnot cycle is the most efficient cycle operating between two specified temperature limits. Thus, it is natural to look at the Carnot cycle first as a prospective ideal cycle for vapor power plants.
However, the Carnot cycle is not a suitable model for power cycles.
Thus, cycle is completed.
Net work done = Heat supplied – heat rejected
= T1 (s2 - s3) - T2 (s2 - s3)
= (T1 – T2) (s2 - s3)
Carnot Efficiency η = Work done / Heat supplied = (T1 – T2) (s2 - s3) / T1 (s2 - s3)
= (T1 – T2) / T1
Limitations or Impracticalities of Carnot Cycle:
Though Carnot cycle is simple (thermodynamically) and has the highest thermal efficiency for given values of T1 and T2, still it is impossible to produce in actuality because:
Some of these problems could be eliminated by executing the Carnot cycle in a different way, as shown in Fig.
Ideal Rankine Cycle
The above diagrams illustrate the various processes of a simple Rankine Cycle applied to a simple steam powered power plant.
Let us the various processes.
Analysis of Rankine Cycle
Assume 1 kg of steam in the cycle and applying SFEE to various processes, we get,
for Process 1-2
Pump work = h2 - h1 = ʃ-V dp
for Process 2-3
Heat supplied in boiler (qi) = h3 - h2
For Process 3-4
Work done in turbine = WT= h3 - h4
For Process 4-1
Heat rejected in condenser (qr) = h4 – h1
Efficiency of Rankine Cycle (η)
Efficiency of Rankine Cycle η = (Shaft work) / (Heat supplied)
= WT – WP / qi
= {(h3 - h4) - (h2 - h1)} / h3 - h2
Methods of improving efficiency of 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. The cycle that results is the Rankine cycle, which is the ideal cycle for vapor power plants. The ideal Rankine cycle does not involve any internal irreversibilities
1-2 isentropic compression in pump
2-3 constant pressure heat addition in a boiler
3-4 isentropic expansion in turbine
4-1 constant pressure heat rejection in condenser
(qin – qout) + (win –wout) =he-hi (KJ/Kg)
Pump (q=0)
wpump.in=h2-h1
Wpump.in=v(P2-P1)
H1=hf@ p1 & v = v1= vf@ pi
Boiler (w=0) qin =h3-h2
Turbine (q=0) Wturb. Out =h3-h4
Condenser (w=0) qout = h4-h1
Wnetb= qin – qout = Wturbo.out-Wpump.in
Earlier we have explained that increasing the steam pressure at inlet to turbine and decreasing the steam pressure at exhaust will increase the thermal efficiency of Vapour Power cycle. In this system the moisture problem will be encountered at the final stage of the turbine. To overcome this problem the ideal reheat and Regenerative cycle procedures will be used. In practice reheat and regeneration both are used for improve the overall efficiency of the vapour power cycles. The reheat Rankine cycle is shown in Figure 10.7. In this cycle extra low-pressure turbine is added. In reheat Rankine cycle; the steam which is collected from the HP 90 Vapour Power Cycles turbine is reheated with the help of fine gases in the boiler furnace. Then the reheated steam is sent to the LP turbine and the regular power cycle. The two turbines are used here because reheating is done at higher pressures only. The reheating can be done two or more stages, which will be determined by economical consideration.
Advantages of Reheat Cycles
• Reheated steam eliminated the erosion and corrosion to the blades of the turbine,
• Turbine output will be increased,
• ηth will be increased,
• Final dryness fraction is improved,
• Nozzle and blade efficiencies are increased, and
• Specific steam consumption is decreased.
Efficiency Calculation of Reheat Cycle the total heat added per kg of steam
Q = (h1 – h5) + (h3 – h2) – wP kJ/kg
Work done = W = (h1 – h2) + (h3 – h4) – wP kJ/kg
where, wP = Pump work = h6 – h5
Efficiency of reheat cycle 
How can we take advantage of the increased efficiencies at higher boiler pressures without facing the problem of excessive moisture at the final stages of the turbine?
1. Superheat the steam to very high temperatures. It is limited metallurgically.
2. Expand the steam in the turbine in two stages, and reheat it in between (reheat)
.
In steam power plants, steam is extracted from the turbine at various points. This steam, which could have produced more work by expanding further in the turbine, is used to heat the feedwater instead. The device where the feedwater is heated by regeneration is called a regenerator, or a feedwater heater (FWH).
A feedwater heater is basically a heat exchanger where heat is transferred from the steam to the feedwater either by mixing the two fluid streams (open feedwater heaters) or without mixing them (closed feedwater heaters).
Open Feed Water
An open (or direct-contact) feedwater heater is basically a mixing chamber, where the steam extracted from the turbine mixes with the feedwater exiting the pump. Ideally, the mixture leaves the heater as a saturated liquid at the heater pressure.
Closed Feedwater Heater
Another type of feedwater heater frequently used in steam power plants is the closed feedwater heater, in which heat is transferred from the extracted steam to the feedwater without any mixing taking place. The two streams now can be at different pressures, since they do not mix
The closed feedwater heaters are more complex because of the internal tubing network, and thus they are more expensive. Heat transfer in closed feedwater heaters is less effective since the two streams are not allowed to be in direct contact. However, closed feedwater heaters do not require a separate pump for each heater since the extracted steam and the feedwater can be at different pressures. Open feedwater heaters are simple and inexpensive and have good heat transfer characteristics. For each heater, however, a pump is required to handle the feedwater.
The back pressure turbine is used for supplying process steam to the facilities in private-use power producers. This type of steam turbine supplies not only electricity but also the process steam to the facilities. In other words, exhaust steam pressure is set to be the demanded pressure from the facility needs or outside needs. In the back pressure turbine, an effective heat drop will be small as shown in Fig. 2.13, therefore, the turbine output will be also small.
In the case where large amounts of steam are required by facilities for process steam, high thermal efficiency will be expected, which means the back pressure turbine will give advantage to private power utilities. And as the back pressure turbine consists of fewer turbine stages with simple structure and small exhaust parts, this results in lower equipment costs.
The back pressure turbine (or the extraction back pressure turbine) is adopted in many facilities such as oil refineries, petrochemical, paper-pulp, fiber, and food industries, where large amounts of steam are required.
Process steam demand and electricity demand change independently according to season. When there is an imbalance between process steam demand and electricity demand, the back pressure turbine cannot respond to this imbalance by itself, and this imbalance is adjusted by power supply increase or decrease from the network or by reduced pressure and temperature steam from the HP steam source.
Saved heat (E) by the back pressure turbine is shown in the following formula if the total heat of the steam is used effectively.
G: steam flow (kg/h),
: internal efficiency of back pressure turbine,
: internal efficiency of condensing turbine,
: adiabatic heat drops of back pressure turbine (kJ/kg),
: adiabatic heat drops of condensing turbine (kJ/kg),
: potential heat of steam in condenser (kJ/kg),
Pass Out Turbine
There are some cases where the power available from a back-pressure turbine is less than required by the plant (Fig. 1.32). This may be due to a low heating requirement, a high back pressure, or a combination of both. The problem may be overcome in a two-stage turbine, where the main incoming steam expands through the high-pressure stage and supplies the heating steam from the exhaust. The balance steam passes through the low-pressure stage of the turbine to satisfy the power requirement. For any further heating steam requirement at any other pressure and temperature, a number of stages may be incorporated in the turbine for optimum power and heating output.
A combined cycle gas turbine power plant is essentially an electrical power plant in which a gas turbine and a steam turbine are used in combination to achieve greater efficiency than would be possible independently. The gas turbine drives an electrical generator while the gas turbine exhaust is used to produce steam in a heat exchanger (called a Heat Recovery Steam Generator, HRSG) to supply a steam turbine whose output provides the means to generate more electricity. If the steam is used for heat (e.g., heating buildings) then the plant would be referred to as a cogeneration plant
Figure is simple representation of a CCGT system. It demonstrates the fact that a CCGT system is two heat engines in series. The upper engine is the gas turbine. The gas turbine exhaust is the input to the lower engine (a steam turbine). The steam turbine exhausts heat via a steam condenser to the atmosphere.
The combine cycle efficiency (ηCC) can be derived by the equation 1 Langston.
ηCC = ηB + ηR - (ηB * ηR) ... (1)
Equation (1) states that the sum of the individual efficiencies minus the product of the individual efficiencies equals the combine cycle efficiency. This simple equation gives significant insight to why combine cycle systems are successful
For example, suppose the gas turbines efficiency ηB is 40% (a reasonable value for a toady’s gas turbines) and that the steam turbine efficiency ηR is 30% (a reasonable value for Rankine Cycle steam turbine).
Utilizing equation (1) would lead to the following conclusion.
ηCC = 0.4 + 0.3 – (0.4 * 0.3)
ηCC = 0.58
ηCC = 58%
The combined cycle efficiency of 58% is much greater than either the gas turbine or the steam turbines efficiencies separately. The 58% value is slightly misleading in that system losses were ignored. Efficiency values in the 60% range have been recorded for CCGT systems in the past few years Chase.
In the vapour power cycles most commonly used working fluid is water. But at high temperatures to get the high efficiency of vapour power cycle, some other working fluids are used. At high temperatures a few working fluids are used, which are mercury, sodium, potassium and sodium-potassium mixtures. Among these, only mercury has been used in practice.
The working fluid should have the following characteristics:
• High Critical temperature and safe maximum pressure,
• Low triple point temperature,
• Condenser pressure which is not too low,
• High enthalpy of vaporization,
• Good heat transfer characteristics, and
• Inert, easy availability at low cost.
To increase the efficiency of Carnot cycle, with an increase in initial temperature or with the decrease in exit temperature of the fluid. At the normal pressure of 12 bar, the saturation temperature for water and mercury are 187o C, – 560o C, respectively. The highest temperature achieved in a power plant is about 550 – 600o C. Therefore, mercury is a better working fluid in the high temperature range, because its vaporization pressure is relatively low. Mercury vapour at high temperature with low pressure which avoid the difficulties connected with high pressure.
To get the high thermal efficiency of the power plant, by using two working fluids such as water and mercury, the binary vapour cycle has been developed. The power cycle, which is a combination of two cycles, one in the high temperature region and the other in the low temperature region, called the binary vapour cycle. In this cycle, the condenser of the high temperature cycle called the tapping cycle serves as the boiler of the low temperature cycle, termed the bottom cycle. Mercury water binary vapour cycle with
Cycle efficiency, 
References:
1. Engineering Thermodynamics by P. K. Nag, Publisher: TMH
2. Engineering Thermodynamics by P. Chattopadhyay, OXFORD
3. Fundamentals of Thermodynamics by Sonntag, Borgnakke, Van Wylen, John Wiley & Sons
4. Thermodynamics An Engineering Approach by Yunus A. Cingel and Michale A. Boles, TMH
5. Engineering Thermodynamics by M. Achyuthan, PHI
