VAPOUR POWER CYCLES DEFINITIONS Vapour is the substance that can change its phase during a course of cycle. In the gas power cycles, the working fluid remains gas throughout the entire cycle. But vapour power cycles are external combustion systems in which the working fluid is alternately vaporized and condensed. Steam is the most common working fluid in vapour power cycles since it has several desirable characteristics, such as low cost, easy availability, chemically stable, physiologically harmless and high enthalpy of vaporization. Steam power plants are referred to as coal plants, nuclear plants, or natural gas plants depending on the type of fuel used to supply heat to the steam. But steam goes through the same basic cycle in all of them. In steam power plants water changes into steam and again steam changes into water in different process. Similarly in refrigeration process, refrigerant changes its phase from liquid to vapour and vice versa. If such a substance undergoes cyclic process and generates power, it is known as vapour power cycle. The most famous vapour power cycles are Carnot cycle and Rankine cycle. CARNOT CYCLE Prof. Sadi Carnot developed a cycle with two reversible isothermals and two reversible isentropics with steam as working substance. The pressure-volume and temperature-entropy diagrams are shown below. This reversible cycle consists of the following processes: Process A-B(Reversible isothermal heat addition): Heat is supplied to boiling water in the steam generator (boiler) at reversible constant temperature process. The water gets evaporated until it gets converted into dry saturated steam. The quantity of heat supplied at constant temperature of T1 to increase the entropy of water from S A to S B is given by Q1 hB hA T1 SB S A Process B-C(Reversible adiabatic expansion): The dry saturated steam undergoes frictionless adiabatic expansion in the steam turbine in which work is developed by the shaft. This work is called turbine work or shaft work which is equal to enthalpy drop. During this process, the temperature of steam is reduced to T2 . Therefore, the turbine work developed is given by, Wturbine hB hC Process C-D(Reversible isothermal heat rejection): Heat is removed from the steam leaving the turbine and it condenses the steam at reversible constant temperature process. This condensation process continues up to point D to get initial entropy. The quantity of heat rejected at constant temperature of T2 to decrease the entropy of steam from S B to S A is equal to Q2 hC hD T2 SB S A Process D-A(Reversible adiabatic compression): The wet vapour undergoes frictionless adiabatic compression in the compressor to restore initial temperature of T1 for the water completing thermodynamic cycle. This work required to compress the steam which is equal to raise in enthalpy of water is called compressor work. Therefore, the compressor work is given by, Wcompressor hA hD The net work done is given by, Wnet Wturbine Wcompressor hB hC hA hD The thermal efficiency is given by, Carnot Net work done Wnet h h hA hD 1 hC hD B C Heat supplied Qsup plied hB hA hB hA The thermal efficiency can also be expressed in terms of higher temperature T1 and lower temperature T2 in the cycle as, Net work done Wnet Heat supplied - Heat rejected T1 T2 dS T Carnot 1 2 Heat supplied Qsup plied Heat supplied T1dS T1 Work ratio is defined as the ratio of net work done in the complete cycle to turbine work. Wnet W Wcompressor W rw turbine 1 compressor Wturbine Wturbine Wturbine Specific Steam Consumption (ssc) or steam rate is defined as the flow rate of steam per unit of power Steam flow rate developed in kWh. ssc power output DRAWBACKS OF CARNOT CYCLE Theoretically a Carnot cycle is most efficient; however the following difficulties are associated with it when steam is used as a working substance. 1. Steam condensation is not allowed to proceed to completion. The condensation process is controlled one and to be stopped at point C. 2. The working fluid at point C is both in the liquid and vapour phase, and these do not form a homogeneous mixture which cannot be compressed isentropically. 3. The vapour has a large specific volume and to accommodate greater volumes, the size of the compressor becomes quite big. 4. More power is required for running larger compressors and hence poor plant efficiency is achieved. 5. The cycle has high specific steam consumption, large back work ratio and low work ratio. 6. The steam at exhaust from the turbine is of low quality, i.e. high moisture content. The liquid water droplets causes pitting and hence erosion of the turbine blades. RANKINE CYCLE Prof. Rankine modified Carnot cycle and presented a technically feasible cycle, called Rankine cycle. It is also a reversible cycle but differs from Carnot cycle in the following respects. The condensation process is allowed to proceed to completion; the exhaust steam from the engine/turbine is completely condensed. At the end of the condensation process, the working fluid is only fluid and not a mixture of liquid and vapour. The pressure of liquid water can be easily raised to the boiler pressure (pressure at which steam is being generated in the boiler) by employing a small sized pump. The steam may be superheated in the boiler so as to obtain exhaust steam of higher quality that can prevent pitting and erosion of turbine blades. The various elements of a steam power plant working on ideal Rankine cycle is shown in the following schematic line diagram. The pressure-volume diagram and temperature-entropy diagram are shown below: The various elements are: A boiler which generates steam at constant pressure. An engine (or) turbine in which steam expands isentropically and work is developed. A condenser in which heat is removed from the exhaust steam and it is completely converted into water at constant pressure. A hot well is used to collect the condensate. A pump which raises the pressure of the liquid water to the boiler pressure and pumps it to boiler for conversion into steam. Process 1–2(Reversible adiabatic pumping (or) compression-PUMP): Reversible adiabatic pumping of condensate water at point 1 from condenser pressure p1 to boiler pressure p2 increases the temperature of feed water as represented by the process 1–2 on temperature–entropy plot. The resulting status is sub-cooled water at high pressure to boiler. The equivalent work W12 is represented by the area under a-b on corresponding p-v diagram. Applying first law of thermodynamics, we have dQ dW dH . Since the process is reversible adiabatic, dQ 0 W12 H mh2 h1 . Therefore, pumping work required, W12 mh2 h1 . This is also equal to flow work given by W12 vdp Since volume of liquid v f remains constant during pumping, Work required for pumping, W12 v f p2 p1 mh2 h1 Process 2–3(Reversible constant pressure heat addition (or) vaporization-BOILER): The sub-cooled liquid at point 2 is now admitted into boiler where it is heated by the hot gases generated due to the combustion of fuel. Water absorbs this heat and converts into saturated liquid and then into superheated steam. The pressure remains constant at p1 during formation of steam and is represented by the process 2-3 (b-c-d-e on temperature-entropy (or) pressure-volume diagrams). Sensible heat addition during process b-c up to saturation liquid point, latent heat addition during c-d up to saturation vapour and superheating during d-e take place. The sensible heating may be done either in economiser or in a special feed heater. Applying first law for any flow process, dQ dW dH . As pressure is kept constant at p1 in a boiler, dW 0 Therefore, heat supplied is given by Q2 3 dH mh3 h2 Process 3–4(Reversible adiabatic expansion-TURBINE): The high energetic and high enthalpy steam is now made to pass through turbine in which reversible adiabatic expansion from high pressure p2 to low pressure p1 takes place imparting its energy to rotating wheel thus developing mechanical work. The resulting steam after expansion process is wet steam and is represented by process 3-4. Applying first law of thermodynamics, we have dQ dW dH Since the process is reversible adiabatic, dQ 0 W3 4 H mh4 h3 Therefore, turbine work developed, W3 4 mh3 h4 Process 4–1(Reversible adiabatic constant pressure heat rejection (or) condensation-CONDENSER): The wet steam at point 4 now enters into condenser through which water is circulated for absorbing latent heat from the wet steam. The steam loses heat and converts into saturated water. This process of reducing the enthalpy and entropy at constant pressure and constant temperature is called condensation. This is represented by the process 4-1. Applying first law for any flow process, dQ dW dH . As pressure is kept constant at p2 in a boiler, dW 0 Therefore, heat supplied is given by Q4 1 dH mh4 h1 The net work done in ideal Rankine cycle is given by Wnet Wturbine Wpump mh3 h4 mh2 h1 Wnet The thermal efficiency of ideal Rankine cycle is given by Rankine Qsup plied Where, Qsup plied mh3 h2 Wnet mh3 h4 mh2 h1 h3 h2 h4 h1 h h Rankine 1 4 1 Qsup plied mh3 h2 h3 h2 h3 h2 Rankine 1 h4 h1 h3 h2 Since the specific volume of liquid water is approximately equal to 1 103 m3 / kg , the pumping work is negligibly small when compared to the turbine work. Therefore by neglecting pump work i.e.h2 h1 , the efficiency of Rankine cycle is given by Rankine h3 h4 h3 h1 COMPARISION OF CARNOT AND RANKINE CYCLES Consider the Carnot and Rankine cycles operating between same boiling and condensation temperatures as shown in the figure. 3-4-5-6-3 represents Carnot cycle whereas 1-3-4-5-1 represents Rankine cycle in which pumping work has been neglected. On a temperature-entropy diagram, the area enclosed by cyclic processes represents the net work done in the cycle and the area under the line representing heat addition gives the heat supplied to the cycle. The net work done in Carnot cycle is equal to the enclosed area c and that of Rankine cycle is b+c and heat input in Carnot cycle is equal to the area under line 3-4 & that of Rankine cycle is 1-3-4. Net work done c Therefore efficiency of Carnot cycle is equal to Carnot Heat supplied cd Let 1-2-4-5-1 is another reversible cycle which will have thermal efficiency given by Net work done abc Carnot Heat supplied abcd e From Carnot theorem, two reversible cycles operating between same temperature limits have same efficiency. Therefore, efficiency of Carnot cycle is also equal to Net work done abc Carnot Heat supplied abcd e d e (or) 1 Carnot (1) abcd e Net work done bc The efficiency of Rankine cycle is given by Rankine Heat supplied bcd e d e (or) 1 Rankine (2) bcd e From equations (1) and (2), it is obvious that 1 Carnot 1 Rankine (or) Carnot Rankine (3) i.e. The efficiency of Carnot cycle is more than that of Rankine cycle when both are operating under same temperature limits. From equations (3), it is known that for the Carnot cycle, the entire heat input is during constant temperature process 3-4 which takes place at maximum cycle temperature. But for Rankine cycle, head addition does not take place during constant temperature process. The temperature during sensible heating is much lower and continuously changing, and that lowers the average temperature at which heat is supplied and accordingly efficiency of Rankine cycle goes down. Consider the figure where, Rankine cycle without superheat: 1 – A – 2 – 3 – 4 – 1. Rankine cycle with superheat: 1 – A – 2 – 2'– 3' – 4 – 1. Carnot cycle without superheat: A – 2 – 3 –4'' – A. Carnot cycle with superheat: A – 2'' – 3' – 4² – A. Temperature of heat supply to Carnot cycle is equal to t A Mean temperature of heat supply to Rankine cycle is equal to t m t1 t 2 / 2 Carnot cycle needs a compressor to handle wet steam mixture whereas in Rankine cycle, a small pump is used. The steam can be easily superheated at constant pressure along 2 - 2' in a Rankine cycle. Superheating of steam in a Carnot cycle at constant temperature is accompanied by a fall of pressure which is difficult to achieve in practice because heat transfer and expansion process should go side by side. Therefore Rankine cycle is used as ideal cycle for steam power plants. RANKINE CYCLE USING STEAM WITH AND WITHOUT SUPERHEAT ACTUAL RANKINE CYCLE VS IDEAL RANKINE CYCLE (EFFECT OF IRREVERSIBILITIES) WORKING FLUID FOR A RANKINE CYCLE METHODS OF IMPROVING RANKINE CYCLE EFFICIENCY EFFECT OF PRESSURE AND TEMPERATURE ON RANKINE CYCLE EFFECT OF TEMPERATURE: The basic Rankine cycle can be enhanced through processes such as superheating, reheating and regeneration. Superheating: Figure illustrates the Rankine cycle with superheat. Superheat causes a net increase in temperature at which heat is being received past the point of vapour saturation, in other words the vapour is heated so that its temperature is higher than the saturation temperature associated with Pa Pb Pc Pd . This does several things. First, it increases the mean temperature at which heat is added Tmean thus increasing the efficiency of the cycle. Second is that the quality of the two-phase mixture leaving the turbine during the expansion is higher with superheating, so that there is less moisture content in the mixture as it flows through the turbine. (The moisture content at e is less than that at e’) This is an advantage in terms of decreasing the mechanical deterioration of the turbine blades. However, in order to make use of superheat, one must have a high temperature heat source or reduce boiler pressure. Reheating: The maximum and minimum temperatures are the same, but the average temperature at which heat is absorbed is lower for the Rankine cycle. To alleviate the problem of having moisture in the turbine, one can heat again after an initial expansion in a turbine, as shown in Figure for space power application. This process is known as reheating. The main practical advantage of reheating (and of superheating) is the decrease in moisture content in the turbine by increasing the effective temperature of heat addition because most of the heat addition in the cycle occurs in the vaporization part of the heat addition process. High pressure, superheated steam is expanded in a high pressure turbine to an intermediate pressure and the fluid then returned to a second stage boiler and super- heater and reheated to state 2`. The reheated steam is then expanded in a low-pressure turbine to the final exhaust pressure. Regeneration: Modifications to the cycle can also be made to reduce cycle irreversibility. One of the principle sources is the sensible heat addition required to bring the boiler feed-water up to saturation temperature. This is accomplished by using some of the flow through the turbine to heat the feed- water. To achieve reversibility, the setup would be as in figure but this is impractical. A practical setup is shown in figure. EFFECT OF PRESSURE: We can also examine the effect of variations in design parameters on the Rankine cycle such as effect of exit pressure and maximum boiler pressure. Effect of maximum boiler pressure on Rankine cycle efficiency: The effect of increasing the boiler pressure on Rankine cycle efficiency is shown on the T-s diagram. Increasing boiler pressure results in an increase in net work done with a corresponding decrease in heat rejected. However, for the indirect power cycle, the downside of raising the boiler pressure (and temperature since the steam is saturated) is that it forces the primary side temperature up to provide sufficient ∆T to transfer the heat from the primary to secondary side. This higher primary side temperature pushes the fuel closer to its limits and increases the tendency for the fluid to boil. To counter this, if necessary, the primary side pressure would have to be increased and pressure vessel walls would have to be thicker. Figure shows a comparison of two cycles with different maximum pressure but the same maximum temperature, which is set by material properties. The average temperature at which the heat is supplied for the cycle with a higher maximum pressure is increased over the original cycle, so that the efficiency increases. Effect of exit pressure on Rankine cycle efficiency: Consider first the changes in cycle output due to a decrease in exit pressure. In terms of the cycle shown in Figure, the exit pressure would be decreased from P4 to P4' . The original cycle is 1 2 3 4 1 and the modified cycle is 1' 2 ' 3 4 ' 1' . The consequences are that the cycle work, which is the cyclic integral of Tds, is increased. In addition, as drawn, although the levels of the mean temperature at which the heat is absorbed and rejected both decrease, the largest change is the mean temperature of the heat rejection, so that the thermal efficiency increases. REHEAT CYCLE In a reheat cycle, the expansion of steam is carried out in two or more stages. After partial expansion to an intermediate pressure in the high pressure turbine, the steam is withdrawn and reheated to the original temperature at the same intermediate pressure. Steam is then returned to low pressure turbine and further expanded to the required condenser pressure. The layout of a reheat Rankine cycle with two stages of expansion and the corresponding t-s diagram are also shown below. Considering unit mass of steam, Turbine work = Work done in high pressure turbine + Work done in low pressure turbine Wturbine h1 h2 h3 h4 Pump work = Work required for pumping W pump h6 h5 Heat supplied = Heat supplied in boiler + Heat supplied in reheater Qsup plied h1 h6 h3 h2 reheat h1 h2 h3 h4 h6 h5 h1 h6 h3 h2 The reheat cycle reduces the moisture content at low pressure turbine and accordingly the erosion and corrosion problems in the turbine are eliminated. It also increases the output of the turbine and also overall efficiency of the plant. However, reheating requires more maintenance. Increase in thermal efficiency is also not appreciable in comparison to the expenditure incurred in reheating. REGENERATIVE CYCLE PRACTICAL REGENERATIVE SYSTEM The average temperature at which heat is added to the working fluid can be increased by preheating teh feed water before it enters the boiler. For this purpose, part of the steam is withdrawn or extracted at some intermediate stage during expansion in the turbine. The rest of the steam expands in the turbine to the condenser pressure. The steam thus extracted is mixed with feed water coming from the hot well. The system of abstracting steam from any point in the turbine and subsequently using it for heating the feed water is called bleeding. The figure shows the layout & t-s diagrams of cycle employing open type feed water heating. Considering unit mass of steam, Heat supplied in the boiler, Qsup plied h1 h5 Turbine work = Work done in turbine Wturbine 1h1 h2' 1 mh2' h4 Pump work = Work input to pump-1 + Work input to pump-2 Wpump h2 h1 h8 h7 h1 h2 1 mh2 h4 h2 h1 h8 h7 regerativ ' h1 h5 In regenerative cycle, 1. There is improvement in cycle economy with relatively much smaller capital expenditure. 2. With the infinite number of heaters, the heating process becomes reversible and the efficiency approaches to Carnot efficiency. 3. The supply of feed water to the boiler is at increased temperature. That reduces the temperature range in the boiler and keeps thermal stresses low. 4. However, the work done per kg of steam decreases and as such large capacity boiler is needed for a given output. 5. The system also becomes complicated, less flexible and involves greater maintenance and capital cost due to installation of feed water heaters. REQUIREMENTS FOR A GOOD WORKING FLUID The working fluid for Rankine cycle should be cheap, universally available, chemically stable and harmless. The main requirements of an ideal working fluid for Rankine cycle are: (1) Large latent heat of vaporization (2) Critical temperature should be well above the metallurgical limit so that latent heat can be supplied at maximum temperature of the cycle (3) The condensation pressure should not be too low so that leakage problems are minimized (4) The freezing point should be below the room temperature to facilitate the filling and draining of the equipment. (5) Highest saturation temperature for a moderate pressure (6) Low specific heat (7) High density (8) Steep saturated vapour line (9) Higher saturation pressure than atmospheric pressure at the minimum cycle temperature (10) Non-toxic, non-corrosive and not excessively viscous BINARY VAPOUR CYCLE In the steam power plant, most of the steam supplied in the boiler by spending lot of fuel is wasted and is rejected in the condenser. If the heat that is rejected in the condenser can be used to generate vapours of some other working substances at high pressure, another Rankine cycle can be run and can produce work. Such a cycle works with two working substances producing dual work but at only one heat supply is called binary vapour power cycle. To run a binary vapour power cycle, the two working fluids should have high temperature difference. The substance having high boiling point acts as topping cycle and the other as bottoming cycle. The substance in the bottoming cycle absorbs the required heat of vaporization from the condensing fluid in topping cycle. Water is better than any other working fluid, however, in high temperature range, there are a few other better substances namely diphenyl ether, aluminium bromide, mercury. And other liquid metals like sodium and potassium. From amongst those mentioned above, only mercury has actually been used in practice. At pressure of 12 bar, the saturation temperatures for water, aluminium bromide and mercury are 187C, 482.5C, 560C. So, mercury is a better fluid than any other in the high temperature range. Because of high temperature, its vaporization pressure is relatively low. Its critical pressure and temperature are 1080 bar and 1460C respectively. For the above reasons, mercury vapour leaving the mercury turbine is condensed at a higher temperature and the heat released during the condensation of mercury is utilized in evaporating the water to form steam to operate a conventional turbine. The flow diagram of mercury-steam binary cycle and the corresponding temperature-entropy diagram are shown below. The mercury cycle (high temperature cycle) 1-2-3-4 is a simple Rankine type of cycle using saturated vapour. Heat is supplied to the mercury during the process 1-2. The mercury expands in a turbine during the process 2-3 and is then condensed during the process 3-4. The feed pump completes the cycle during the process 4-1. The heat rejected by the mercury during its condensation is transferred to boil water and form saturated vapour (process 8-5). The superheated steam expands in turbine (process 5-6) and is then condensed (process 6-7). The feed water (condensate) is then pumped (process 7-8) and heated till it is saturated liquid in the economiser (process 8-9) before going to the mercury condenser-steam boiler where latent heat is absorbed. Let mHg be the rate of mercury in the topping cycle and mst be the rate of steam circulating in the bottoming cycler. Therefore, Heat supplied, Q1 mHg h2 h1 , and Total work done in the cycle, Wnet mHg h2 h3 mst h5 h6 Wnet mHg h2 h3 mst h5 h6 Thermal efficiency, binary Q1 mHg h2 h1 Similarly, applying energy balance equation in the heat exchanger, we get mHg h3 h4 mst h5 h9 that gives mass of steam generated per kg of mercury supplied. Therefore, thermal efficiency of binary vapour cycle is more than that of Rankine cycle. Let Hg be the efficiency of mercury circuit and st be the efficiency of steam circuit, then combined efficiency is given by combined 1 1 Hg 1 st EFFECT OF IRREVERSIBILITIES ON CYCLE EFFICIENCY Actual work required for pumping, Wpump actual h2' h1 Ideal work required for pumping, Wpump ideal h2 h1 Isentropic efficiency of pump is given by, Wpump ideal h2 h1 pump isentropic Ideal work required Actual wor k required Wpump actual h2 ' h1 Actual work developed from turbine, Wturbineactual h1 h2' Ideal work developed from turbine, Wturbineideal h1 h2 Isentropic efficiency of turbine is given by, Wturbineactual h1 h2 turbineisentropic Actual wor k developed ' Ideal work developed Wturbineideal h1 h2 PROBLEMS ON VAPOUR POWER CYCLES 1. A basic steam power plant works on ideal Rankine cycle operating between 30 bar and 0.04 bar. The initial condition of steam being dry saturated, calculate pumping work required, work developed from turbine, cycle efficiency, work ratio and specific steam consumption. Assume the flow rate of steam as 10 kg/s. (Ans: 30.07 kW, 9402.2 kW, 35%, 0.9968, 3.84 kg/kWh) 2. A steam turbine working on Rankine cycle is supplied with dry saturated steam at 25 bar and the exhaust takes place at 0.2 bar. For a steam flow rate of 10 kg/s, determine quality of steam after expansion, work developed, work required, work ratio, cycle efficiency and heat flow in the condenser. (Ans: 0.776, 7392.8 kW, 25.52 kW, 0.996, 28.9%, 18.1 MW) 3. In a Rankine cycle thermal power plant, superheated steam is supplied at 1.5 MPa and 300C to a turbine and expands to a condenser pressure of 80 kPa. The saturated liquid coming out from condenser is pumped back to the boiler by a feed pump. Assuming ideal processes, determine the condition of steam after expansion, cycle efficiency, mean effective pressure, ideal steam consumption per unit kWh and actual steam consumption per unit kWh. Take relative efficiency as 0.6 and neglect pump work. (Ans: 0.916, 21.27%, 293.63 kPa, 6.39 kg/kWh, 10.66 kg/kWh) 4. 9 kg/hr of steam is supplied to a steam power plant operating between 30 bar and 0.06 bar. Neglecting pump work, calculate the net work done in the cycle and Rankine cycle efficiency if steam is supplied to turbine (i) at dry saturated and (ii) at 30 bar and 400C. (Ans: (i) 2.24 kW, 33.8% (ii) 2.623 kW, 34.07%) 5. In a reheating cycle, steam at a pressure of 90 bar & 480C is expanded in a steam turbine in first stage up to 12 bar and reheated to its original temperature before expanding to the condenser pressure of 0.07 bar. If the mass flow rate of steam is 0.5 kg/s, find the power developed and efficiency neglecting pump work. (Ans: 791 kW, 41.76%) 6. A steam power plant operates on a theoretical reheat cycle. Steam at 25 bar and 400C is supplied to the high pressure turbine. After its expansion to dry state, the steam is reheated to its original temperature at constant pressure. Subsequent expansion occurs in the low pressure turbine to a condenser pressure of 0.04 bar. Considering pumping work, make calculations to determine quality of steam at entry to condenser, thermal efficiency and specific stema consumption. (Ans: 0.945, 37%, 2.652 kg/kWh) 7. In a single heater regenerative cycle, the steam enters the turbine at 30 bar, 400C and exhaust pressure is 0.1 bar. The feed water heater is a direct contact type which operates at 5 bar. Find (i) efficiency and steam rate of cycle (ii) the increase in mean temperature of heat addition, efficiency and steam rate as compared to Rankine cycle without regeneration. Neglect pump work. (Ans: (i) 35.36%, 3.93 kg/kWh (ii) 27.4C, 1.18%, 0.476 kg/kWh) 8. In a single feed water regenerative cycle, the saturated steam enters a turbine at a pressure of 30 bar and the condenser pressure is 0.04 bar. The steam is initially dry saturated and enough steam is bled off at the optimum pressure to heat the feed water. Determine the amount of bled steam and cycle efficiency neglecting pump work. (Ans: 0.1896 kg/s per kg of steam, 37.3%) 9. A power generating plant uses steam as a working fluid and operates on ideal Rankine cycle between a source temperature of 311.1C (boiler pressure of 100 bar) & a sink temperature of 32.9C (condenser pressure of 0.05 bar). (i) Determine the cycle efficiency and work ratio. Also determine the rate of steam generation if the power output of the plant is 1 MW. (ii) How the cycle efficiency and work ratio would be affected if isentropic efficiency of turbine is 0.8 and the saturated liquid coming out of the condenser is compressed to the boiler pressure with an isentropic efficiency of 0.9. (Ans: (i) 38.9%, 0.99, 3585 kg/MWh (ii) 31%, 0.9869, 4500 kg/MWh) 10. In a Rankine cycle, the steam enters the turbine at a saturation pressure of 20 bar and exhaust pressure of 0.04 bar. Determine pump work required, turbine work developed and Rankine efficiency assuming the flow rate as 10 kg/s. Calculate the above parameters if pump efficiency is 80% and turbine efficiency is 85%. (Ans: (i) 20 kW, 8892 kW, 33.18% (ii) 25.03 kW, 7533.3 kW, 28.27%) 11. A binary vapour plant uses mercury between temperatures 205C and 540C. The mercury is dry and saturated at high temperature. The steam cycle works between 17.35 bar and 73.66 mm of mercury. Steam is supplied to boiler at 370C and feed water is used at 200C in economiser and is evaporated to dry steam in the condenser and is superheated by gases. Assume ideal cycle, find mass of mercury circulated per kg of steam generated, the work done by mercury and steam per kg separately and plant efficiency. Use following properties for mercury. (Ans: 9.42 kg/s per kg of steam generated, 1210.47 kW/kg of steam, 1152.7 kW/kg of steam, 66%) Tsat hf hg sf sg (C) (kCal/kg) (kCal/kg) (kCal/kgK) (kCal/kgK) 540 1.80 87.3 0.0360 0.1217 205 6.92 78.7 0.0188 0.1675 12. A binary vapour cycle operates on mercury and steam. Saturated mercury vapour at 4.5 bar is supplied to the mercury turbine from which it exhaust at 0.04 bar. The mercury condenser generates saturated steam at 15 bar which is expanded in a steam turbine to 0.04 bar. (i) Find overall efficiency of the cycle. (ii) If 50 tons per hour of steam flows through the steam turbine, what is the flow through the mercury turbine? (iii) Assuming that all the processes are reversible, what is the useful work done in the binary vapour cycle for the specified steam flow? (iv) If the steam leaving the mercury condenser is superheated to a temperature of 300C in a super-heater located in the mercury boiler, and if the internal efficiencies of mercury and steam turbines are 0.85 and 0.87 respectively, calculate the overall efficiency of the cycle. Take following properties of saturated mercury. (Ans: (i) 52.94% (ii) 59.35×104 kg/hr (iii) 28.49 MW (iv) 46.2%) Psat Tsat hf hg sf sg vf vg (bar) (C) (kJ/kg) (kJ/kg) (kJ/kgK) (kJ/kgK) (m3/kg) (m3/kg) 4.50 450.0 62.93 355.98 0.1352 0.5397 79.9×10-6 0.068 0.04 216.9 29.98 329.85 0.0808 0.6925 76.5×10-6 5.178 QUESTIONS ON VAPOUR POWER CYCLES 1. Explain the operations of a Rankine cycle with a neat sketch. 2. Differentaite between Rankine cycle and Carnot cycle. 3. Derive expression for heat and work quantities in a Rankine cycle. hence derive expression for thermal efficiency. 4. Explain the effect of temperature and pressure on Rankine cycle. 5. State and explain different methods of improving thermal efficiency of a Rankine cycle. 6. Explain with a neat sketch a reheat cycle. Derive expression for thermal efficiency. 7. Explain with a neat sketch a regenerative cycle. Derive expression for thermal efficiency. 8. Explain with a neat sketch a practical regenerative cycle. Derive expression for thermal efficiency. 9. Differentiate between ideal Rankine cycle and actual rankine cycle with neat diagrams. 10. Explain with a neat diagram the working of a binary vapour power cycle.
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