Compilation of lecture notes on ‘Improved Rankine Cycles’ in thermodynamics for engineering students.
Lecture Note # 1.
Carnot and Rankine Cycle:
Carnot cycle is the most efficient thermodynamic cycle for all the heat engines utilising the heat energy and producing mechanical energy. We have also observed that there are limitations for the use of this cycle in practice.
The ideal practical cycles for IC Engines are Otto cycle (for Petrol and gas engines) and Diesel cycle (for Diesel or oil engines). Similarly the ideal practical cycle for steam—is the Rankine Cycle.
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Figure 22.1 shows saturated cycle for both Carnot and Rankine cycle. Carnot cycle is 1’–2–3–4′ and Rankine cycle 1–2–3–4.
Comparing these two cycles we observe that all the processes except water heating 1–1′ are reversible processes. Rankine cycle efficiency is less than Carnot efficiency because of only one irreversible process 1–1′. If we could eliminate this irreversibility, we can get the Rankine cycle efficiency same as that of Carnot efficiency.
To eliminate this irreversible process, we have to heat water from 1–1′ by some internal sources only. This type of the heating of water within the cycle is called Regenerative heating of water.
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Lecture Note #
2. Regenerative Feed Heating Cycle:
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Regenerative feed water heating can be achieved with the help of steam extracted or bled from the turbine, in the device called feed water heaters.
This irreversibility can be eliminated by the process of regeneration i.e., by internal and reversible heat exchange between the steam expanding in the turbine and water in the economizer. Figure 22.2 shows a flow diagram and a T-s diagram of the process for a saturated Rankine cycle.
The feed water after the condenser is carefully passed over the turbine, where it receives heat from the expanding steam reversibly at all times (i.e., with zero temperature difference). The water is progressively heated until it enters the steam generator at point B. The economizer and the irreversibilities introduced along with it are thus eliminated. The cycle would receive and reject heat at constant temperature and would have same efficiency as that of Carnot cycle, working between same temperature limits.
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This heating of feed water is called ideal regenerative feed water heating. It is however not employed as it has some serious limitations.
They are as follows:
Limitations of Ideal Regeneration:
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1. Water is flowing outside the turbine in tubes while the steam is expanding over turbine blades placed inside. In this situation, no adequate surface is available for effective heat transfer.
2. The mass flow rates of water and steam are very large. Hence effectiveness of heat exchange is very low.
3. The final dryness of steam leaving the turbine is very low and amount of moisture content is unacceptable for proper turbine operation and efficiency.
Lecture Note # 3. Practical-Regenerative Feed Water Heating
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In practical method of feed water heating, economizer is not eliminated totally but its size is reduced. The steam expands adiabatically through the turbine as usual. The feed water at 4 (Refer Fig. 22.2) is heated in steps and not continuously, by the steam bled from the turbine at selected stages. Heating of liquid takes place in heat exchangers, called feed water heaters.
Feed water heating was introduced in early 1920’s and since then has become an important and essential component of large thermal power plants, which use between five to eight such feed water heaters.
Feed water heating is done in steps and not continuously. The feed water therefore enters the boiler below point B. Also, feed water heaters themselves are heat exchangers (They are practically very much like condensers) and have their own irreversibilities and losses. Thus we cannot attain an ideal situation of Fig. 22.2 and Rankine cycle cannot attain Carnot efficiency. A well designed Rankine cycle is however a closest practical cycle to Carnot and hence is widely accepted for most power plants.
Lecture Note # 4. Reheat Cycle
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Raising the turbine inlet pressure i.e., boiler outlet pressure or boiler working pressure as well as raising the temperature of superheat improves the thermal efficiency of the Rankine cycle. Higher working pressures and temperatures increase mean temperature Tm of heat addition; and takes Tm closer to gas line ab reducing the irreversibilities. Refer Fig. 22.7 (b).
Increasing the inlet pressure from P1 to P2 however results in the lowering of the final dryness fraction from 4 to 4′ and all the stages after point d on the expansion line get progressively wet steam. The moisture present in the steam, in the form of suspended water particles hit the high speed turbine blades with large relative velocities and erodes them.
To improve the thermal efficiency of the cycle over and above that of superheat cycle as well as to improve the final dryness of steam, reheating of steam is used.
Figure 22.10 (a) and (b) shows a schematic flow diagram and T-s diagram of Rankine cycle that uses superheat and re-superheat or reheat.
Reheating is re-superheating of steam at point 2 after it expands in high pressure section of turbine. The steam after expansion is sent to the steam generator where it is reheated (re-superheated) to the original temperature with the help of hot flue gases. The reheated steam now expands in the low pressure section of the turbine to the condenser pressure.
There are following advantages of reheat cycle is:
1. In reheat cycle, heat is added twice; from 6 to 1 and from 2 to 3. This increases the value of Tm — the temperature of heat addition and keeps the evaporator, superheat reheat portion from 7 to 3 closer to the flue gas line ae. This results in higher cycle efficiency.
2. It improves the final dryness of steam (from 4′ to 4) and reduces turbine blade erosion.
3. It increases cycle work by increasing the cycle area. This increases the turbine power.
Modern fossil fuel power plants employ superheat and at least one stage of reheat. Some employ two. More than two reheats however, result in cycle complications and increased capital costs that are not justified by improvements in efficiency.
Effect of Reheat Pressure Ratio on Cycle Efficiency:
The pressure p2 at which the steam is reheated affects the cycle efficiency. Figure 22.11 shows the relation between increase in the efficiency Δη percent and the ratio of reheat pressure to initial pressure.
At p2/p1 = 1 there is no reheat and Δη = 0. As p2 is lowered the efficiency improves and reaches the maximum at p2 equal to about 20 percent of p1. Lowering p2 further decreases the efficiency and at p2/p1 less than say 0.025 the efficiency decreases and Δη becomes negative. The optimum pressure ratio is between 0.2 and 0.25.
The superheat reheat plant is often designated by p1/T1/T3 in bar and degrees centigrade. The above case for example is 170/500/500 while a double reheat may be designated as 150/490/500/510 etc.
Lecture Note # 5. Typical Layout of a Steam Power Plant:
Figure 22.12 shows a typical layout of a steam power plant. It shows steam and water circuits of the plant which includes re-heaters and feed water heaters. Note the positions of four closed feed water heaters and one open feed water heater (deaerator). Note also that there are two hp, two ip and one Ip feed water heater.
Lecture Note # 6. Combined Cycle Power Plants:
In combined cycle power plants both gas and steam turbines supply electrical power to the grid. The idea of combined cycle has grown out of the need to improve the simple Brayton-cycle efficiency by utilising the waste heat in the turbine exhaust gases. This can be done by regeneration also.
The regeneration however has some serious drawbacks as given below:
i. Regeneration does not increase output. In fact regeneration reduces turbine pressure ratio and hence the net plant output by a few percent.
ii. Because of large heat transfer surfaces and large gas and air piping; regeneration makes the plant costly.
iii. With regeneration the optimum pressure ratio for maximum efficiency reduces sharply (from 20 – 30 to 7 – 10). This reduces the power output.
Thus raising the efficiency of a gas turbine plant by regeneration is costly. A means was sought whereby both efficiency and power are increased. A solution was found in using the large quantity of energy in the turbine exhaust, to generate steam for a steam turbine plant. This is a natural solution. Gas turbine is a high temperature machine (1100°C – 1625°C) while steam turbine is a low temperature machine (550 – 650°C). The joint operation with gas turbine at “hot end” and a steam turbine at “cold end” is called a combined-cycle power plant.
Advantages of Combined Cycle Power Plant:
i. High overall plant efficiency—over 50% can be attained.
ii. High total power-combined power of GT and ST is available.
iii. Quick starting of plant-GT can be started quickly.
iv. Low water requirement-GT needs no cooling. Only water required is for the condenser circulation. Sometimes condensers also are air cooled, [e.g. Uran combined-cycle plant]. Then water requirement is very low. Considering huge quantities of water required for condensers, this is a distinct advantage.
v. Phased installation—GT plant which takes less time to be installed, is installed first and stars producing power, while ST plant is being constructed.
vi. Low pollution level—In the CC plant operation, formation of NOx and CO2 is much lower than that in coal fired plant.
vii. Can be used for both peak load and base load operations.
Lecture Note # 7. Combined Cycle Power Plant with Heat Recovery Boiler
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A gas turbine plant consists of air compressor (AC), combustion chamber (CC) and gas turbine (GT). The exhaust of the gas turbine goes to the heat recovery boiler (HRB) to produce superheated steam. The steam is used in a steam turbine plant which consists of steam turbine (ST), condenser (C), pumps (CP) and (BFP), feed water heater (FWH) and deareator (DA). The HRB consists of economizer (EC), boiler (B), drum (SD) and super-heater (SU). The gas goes to stack after HRB. Both steam and gas turbine drive electric generators (G).
The gas turbine is operated with a high air to fuel ratio (400 : 1) to ensure sufficient air in the gas turbine exhaust for further combustion. Plant output can be increased for short periods during load peaks by burning, additional full in supplementary fuel burners. HRB has no refractory lining nor water walls. Hence, its temperature is limited to 750°C.
In small plants steam turbine output is less than the gas turbine output by as much as 500 percent. In large plants, steam turbine output is greater than the gas turbine output by upto 8 : 1.
The supplementary firing equipment (SF) is interposed between the GT and HRB. The steam cycle is designed for high efficiency with reheat and full set of feed water heaters.
Lecture Note # 8. Combined Cycle Plant with Multi-Pressure Steam:
This plant allows the gas from MR to leave at a lower temperature and increases the efficiency of the plant.
Figure 22.17(a) shows a schematic flow diagram of the plant. The “dual-pressure cycle” has a HRB which has two steam circuits. The high pressure circuit supplies steam to the high pressure stages of the turbine and low pressure circuit supplies steam to the low pressure stages of the same turbine.
Figure 22.17(b) shows the temperature-enthalpy diagram of both gas and steam circuits in the HRB.
Exhaust gas leaving the gas turbine enters the Supplementary Firing (SF) at 4 and the HRB at 5, leaving it to the stack at 6. Condensate leaving the condenser at 8 enters the low pressure economizer at 10 via condensate pump, two feed water heaters, one DA and boiler feed pump. Process 10-11 is feed heating of low pressure circuit; followed by evaporation to 12 and superheat to 13. Superheated steam at 13 enters the steam turbine at low pressure stage.
Water from 11 is pumped by booster pump (BP) to 14 and goes to the high pressure economizer. Evaporation occurs from 15 to 16 and superheat to 17. High pressure superheated steam at 17 enters the steam turbine first stage.
In T-H diagram we see that low pressure steam boils at a lower temperature (12) below that of high pressure steam (15). Single high pressure circuit is shown by 10’—15—16—17 with gas leaving at 6′. Adding low pressure circuit allows the gas to leave at a lower temperature (6), thus extracting more energy from it and increasing overall cycle efficiency.
Lecture Note # 9. Irreversibilities in Rankine Cycle:
All ideal cycles whether gas cycles or vapour cycles are assumed to be made up of reversible processes only. In the actual cycles, however, irreversibilities are introduced because of factors like heat transfer through finite temperature difference, friction, mixing etc.
In Rankine cycle, we will discuss two kinds of irreversibilities:
i. External Irreversibilities:
Introduced as a result of temperature differences between combustion gases in the furnace and feed water or steam in the boiler tubes and the temperature differences between the condensing steam and condenser cooling water.
Figure 22.7 shows temperature vs heat exchanger path length diagrams for (b) parallel flow and (c) counter flow steam generators and effect of flow directions in the steam generators. L – 1 and e – B represent minimum approach point called pinch point; and is finite. For very small pinch point temperature difference, the overall temperature differences are low and hence reversibilities are lower but the size and cost of steam generators are high.
For very large pinch point temperature differences, size and cost of steam generators are low but overall temperature differences and irreversibilities are higher and plant efficiencies are lower. The most economical pinch point temperature difference is obtained by optimization of fixed cost (based on capital costs), and operating costs (based on fuel costs).
Figure 22.7 also shows that overall temperature differences between the combustion gases and water and steam are greater for parallel flow than counter flow heat exchange in steam generators. Heat transfer considerations also favour counter flow as it gives higher overall heat transfer coefficients. The counter flow is thus favoured over parallel flow.
ii. Internal Irreversibilities:
Introduced because of fluid friction and throttling in the turbine and the pump and mixing.
They are result of fluid friction, throttling and mixing in turbines, pumps, and pressure losses in pipes, bends, valves etc.
The actual expansion of steam in the turbine is adiabatic but not adiabatic reversible (isentropic) and during expansion entropy increases. The ideal expansion, which is isentropic is 1 – 2s but the actual expansion is 1 – 2.
The pump pressure P4 has to be more than turbine inlet pressure P1 because of pressure drop in heat exchangers, feed water heaters, pipes, bends and valves etc. Thus P5 is the pressure of steam leaving the steam generator, while P5, is the pressure at turbine inlet. Heat loss in the turbine decreases entropy of steam from 5′ to 1.
As a result, dryness and therefore enthalpy at 2 is more than that at 2s. The irreversible losses in the turbine are represented by turbine isentropic efficiency and are given by the ratio of turbine actual work to the ideal isentropic work. Hence,
Well-designed turbines give efficiencies of around 90%. ηT given above is not to be confused with cycle thermal efficiency. It is also overall isentropic efficiency. The individual turbine stages may have different efficiencies.
The compression of water in the pumps is also adiabatic but not isentropic. The entropy increases. The ideal compression is 3 – 4s while the actual one is 3 – 4. The losses are represented by pump isentropic efficiency which is the ratio of ideal isentropic work to the actual work taken by the pump. Hence –
In both Eqs. (22.14) and (22.16), the smaller quantity is in the numerator. The actual pump work can be obtained by –
Thus we pay penalty for the turbine and pump irreversibilities. The turbine produces less work and the pump absorbs more work.
Mean Temperature of Heat Addition:
In Rankine cycle, heat is added at constant pressure but not at constant temperature. There is a large difference between temperature of water at the entry of the economiser at point 4 and that of steam at the exit of the super-heater at point 1. To find mean temperature of heat addition Tm, construct a rectangle 6-2-3-2-5 on the base 2-3 such that area 6-2-3-5 and area 1-2-3-4-5-1 are equal. Recall a similar construction of a rectangle on indicator diagram of an IC engine to find the mean effective pressure Pm.
Since T2 is fixed by condenser pressure for which very little improvement is possible over present practices, the efficiency largely depends on Tm. Larger the value of Tm greater is the cycle efficiency.
It will be realised now that superheating of steam will raise the value of Tm over the saturated cycle and hence will increase the cycle efficiency.
Lecture Note # 10. Binary Vapour Cycle:
The efficiency of a reversible cycle is given by ηrev = 1 – (T1/T2), where T1 is the average temperature of heat addition and T2 is the average temperature of heat rejection. Higher the value of T1 or lower the value of T2, higher the efficiency.
The irreversibilities of Rankine cycle are least during evaporation than during feed heating or superheating. Thus, higher the saturation temperature of steam, higher the efficiency. However, for steam higher saturation temperature is accompanied by high pressure. Recall that at critical temperature of 374°C, the critical pressure of steam is 221 bar—a very high value. This high pressure poses some design problems and results in thick and heavy boiler and turbine components.
Fluids other than water having better thermodynamic properties were tried. Mercury was most successful of them. The metallurgical limit of steam turbine materials is 560°C. Mercury at 560°C has saturation pressure of only 12 bar. Thus mercury is a better fluid at high pressure end.
But at low pressure end, mercury is a bad fluid. At 30°C which is normal lower limit of a steam cycle, its saturation pressure is only 3.6 x 10-6 bar; and its specific volume is enormously large.
Therefore a plant is designed to use mercury vapour in high pressure cycle which transfers its heat to water vapour in a low pressure cycle. Such a cycle is called Binary vapour cycle.
The “Mercury cycle” abcde is a simple Rankine cycle using saturated mercury vapour. The heat rejected by mercury during condensation (process b-c) is transferred to convert saturated water of “steam cycle” into saturated steam (process 5-6). The saturated steam is superheated in the superheater, using furnace heat (process 6-1) and then admitted to steam turbine. The condensate is heated in the economizer (process 4–5) to convert it into saturated liquid which is then admitted to steam boiler—mercury condenser, where it absorbs its latent heat.
Let ṁ represent the flow rate of mercury in the mercury cycle per kg of steam circulating in the steam cycle. Then for 1 kg of steam,
To vapourise 1 kg of water from its saturation temperature, about 7 to 8 kg of mercury need to be condensed.
Other fluids which are used in place of mercury are:
1. Diphenyl ether (C6H5)2O
2. Aluminium bromide AlBr3.
3. Zinc ammonium chloride Zn(NH3)2Cl.
4. Liquid metals like sodium, potassium.
However, mercury vapour cycles are not very widely used because:
1. Mercury is toxic, highly expensive and difficult to procure.
2. It has low latent heat and hence about 8-10 kg of mercury is required to evaporate 1 kg of water.
3. It does not wet the tube surface, so addition of magnesium or titanium is necessary.
Binary Vapour Engine:
We know that maximum possible efficiency of any engine working between the temperature limits of T2 and T1 is given by the equation –
(Atmospheric temperature)
Since T2, is fixed by atmospheric conditions, the thermal efficiency of a plant can only be improved by increasing T1. In a steam plant an increase of T1 may entail the use of a corresponding higher pressure, which is one of the limiting factors in its design. By using mercury vapour in place of steam in the high temperature range of the cycle, an increase in T1 is obtained without any increase in maximum pressure. The heat rejected by mercury in condensing can be utilized in raising superheated steam for the low temperature range of the cycle. A power plant using two vapours in this way is known as binary vapour plant.
On the T-s diagram are shown the liquid and saturated steam lines for water and steam, meeting at the critical temperature which occurs at a steam pressure of 221 bars. The lines ab and be represent the heating and evaporation of liquid mercury plotted to the same temperature scale as the steam, the scale of corresponding pressures is lower for mercury. The mercury vapour at c has a much higher temperature than steam at the same pressure. At c the mercury expanded adiabatically through a separate mercury vapour turbine to d; from d it is condensed to a, its latent heat being utilized for evaporating a corresponding amount of steam. The mercury has thus described the cycle abcd.
The steam cycle is represented by gadef, ga represents the heating of the feed water, ad its evaporation by the condensing mercury, and de the superheating of the steam by the flue gases At e the steam is expanded adiabatically through a steam turbine to f; fg represents the condensing of the exhaust steam in the condenser. This completes the steam cycle.
To obtain the correct amount of heat from the condensing mercury for evaporating the steam, it is found that 8.196 (8.2 Approx.) kg of mercury are required per kg of steam. It will be seen from the areas of T-s diagram that the use of mercury for the high temperature range of the cycle gives a higher efficiency than that obtainable from steam with the same addition of heat. Using pressure limits of 24 bar and. 0.07 bar, a steam plant gives an efficiency of 24-25% whilst that of the binary vapour plant is 50%.
A diagrammatic view of a binary vapour plant is shown below. The hot gases from the furnace pass through the mercury boiler, through the liquid mercury heater, then through the steam super-heater and finally through the feed water economiser, after which they are exhausted to the chimney.
The liquid mercury passes from the mercury liquid heater to the mercury vapour boiler where it is evaporated. It then flows to the mercury turbine through which it is expanded to its low pressure limit. From here it exhausts to the mercury condenser steam boiler where its latent heat is given upto the hot feed water; this operation condenses the mercury whilst at the same time the feed water is evaporated to steam. The mercury is then returned to the mercury liquid boiler, thus completing its cycle.
The feed water from the economiser (not shown) is evaporated to steam in the mercury condenser steam boiler and then passes to the super-heater where it is superheated by the hot flue gases. From the super-heater the superheated steam passes to the steam turbine in which it is expanded down to the steam condenser pressure, it is then condensed in the steam condenser and passes back to the economiser, thus completing the cycle of the water and steam.
At the Hartford-USA-binary vapour plant, erected by the General Electric Co., the weight of mercury in use in the plant is 60 tonnes. A higher efficiency is obtained than is possible from a steam plant of the same output. Daily saving of 150 T of coal compared with the consumption of an equivalent steam plant. Five binary vapour plants have been erected by the General Electric Co.
In the early stages of the development of the mercury boiler, it was found that the liquid mercury did not wet the heating surface of the tubes. There was a tendency for a film of mercury vapour to form at the tube surface which prevented a good heat transfer to the liquid. The difficulty was overcome by a 0.002 percent solution of magnesium and titanium being used in the boiler as a surface wetting agent.
The chief objection to the mercury vapour plant is the danger due to poisonous fumes if any leakage of mercury vapour occurs, and special precautions are taken to prevent this.