Document 6603547
Transcription
Document 6603547
L 31 Rankine Cycle with Enhancements Dr. Gore Example 520°C, 140 bar 520°C (40 bar) 1 3 Turbine 2 5 Turbine 1 0.08 bar 4 40 bar 2 250°C (140 bar) 7 bar H. P. F. W. Pump 140 bar 7 bar 7 bar 12 0.08 bar O.F. W.H. 9 10 • • L. P. F. W. Pump Throttle 40 bar • 7 8 C. F.W.H. • 6 7 bar 11 The components of a modern Rankine cycle power plant include a steam generator, multiple reheaters, multiple stages of turbines, a condenser, a cooling tower, multiple feed water pumps, an open feed-water heater and multiple closed feed water heaters, multiple feed water pumps, and throttling devices for feeding back of the extracted steam into the feed water system. The example shown above is for illustration purposes and each plant is typically custom designed for the local conditions and customer requirements. In the example shown above, superheated steam at state 1 is generated by the steam generator that is receiving of heat from a combustion furnace typically burning coal, natural gas, oil, biomass or all of the above depending on the fuel availability, prices, power management needs, environmental requirements, incentives and subsidies, and management decisions. The heat generated by combustion of the fuel is transferred to the feed water which enters the steam generator as a sub-cooled liquid at state 12 (140 bar and 250 oC) and leaves as superheated vapor at state 1 (140 bar and 520 oC). The processes in the steam generator include sub-cooled heating from (140 bar and 250 oC) to (140 bar and 336.75 oC) in a gas to liquid heat exchanger, boiling from saturated liquid to saturated vapor state at a fixed temperature of 336.75 oC in a drum and tube or a tube and tube boiler, and then superheating from 336.75 oC to 520 oC in a gas to gas extended surface shell and finned tube heat exchanger portion of the steam generator. The transfer of heat from the combustion gases at high temperature to the water and steam at lower temperature involves significant net entropy production and loss of exergy. One of the areas of opportunity is to reduce the temperature difference across which combustion gases transfer heat to the steam and water. 1 • • • • • • • • The superheated steam at high temperature and pressure is expanded in the high pressure turbine to produce work by conversion of enthalpy to kinetic energy in an impulse stage of nozzles and then of the kinetic energy to work represented by the rate of change of angular momentum multiplied by the angular displacement per unit time of the turbine wheel. The turbine rotor drives the rotor of a generator which supplies electricity to the consumers. In steady state, the work of the turbine matches the work of the generator. In a real system, the steam flow is modulated at many frequencies by a complex interconnected control system that also includes depositing and recovering stored energies from a flywheel system to maintain the 60 Hz frequency of electrical power even in the face of fluctuating load demand. With the introduction of renewable energy sources into the grid, power plant controls engineering has become a great area of opportunity for ME300 graduates. The high pressure turbine expands the steam from 140 bar to 40 bar in as close to an isentropic manner as possible. If the expansion can be accomplished in an isentropic manner, the exit temperature is 320 oC and the state is superheated (Tsat = 250.4 oC). The exit steam flow from the HPT is divided into two streams. One stream flows to a steam reheater which raises the temperature to 520 oC but now at a lower pressure. The other stream flows into a closed feed water heater which reduces the temperature by heating the 140 bar high pressure feed water that is flowing through tubes of the heat exchanger. The shell side steam cools to the saturated liquid state in the process and the liquid is extracted to flow through a throttle for mixing in the low pressure (8 bar) open feed water heater. The portion of the steam at 40 bar reheated to 520 oC expands to 7 bar through the first stage of the low pressure turbine producing work. At this stage, a portion of the steam is extracted for open system heating of the feed water pumped to 7 bar pressure. The remaining steam expands through the final stage of the low pressure turbine to the condenser pressure of 0.08 bar producing additional work. In the condenser the mass of steam leaving the final low pressure turbine stage is cooled by a circulating water stream in a noncontact heat transfer process to generate saturated liquid at 0.08 bar and 41.51oC. The heat rejected in the condenser is an important part of the overall system energy balance. Further, the second law of thermodynamics requires that a certain percentage of the heat added in the steam generator plus the heat added in the reheater must be rejected in the condenser. The saturated liquid stream leaving the condenser at 0.08 bar is pumped by the low pressure feed water pump to 7 bar before entering the open feed water heater. The three streams mixing in the open feed water heater restore the mass flow rate of water flowing through the high pressure feed water pump to that of the flow rate through the indirect contact feed water heater and the steam generator. The heat rejected by the condenser is deposited into the environment by either a cooling tower or a flowing river stream in the vicinity of the power plant. Many auxiliary devices are necessary for metering, controlling, regulating various pressures, temperatures and flows. These are not shown or considered here in the first level of power plant analysis. The plant definition summarized above allows the first level of cycle analysis on the basis of balance equations for mass, energy and exergy. The analysis and insights can be improved by studying the processes on a T-s diagram. 2 1 3 12 9 10 2s 11 8 4s 7 6 5s T-s diagram for the Rankine cycle showing two turbine stages with reheating and extractions for feed water heating are depicted above. • • • • • • Isentropic turbines assumed for simplicity 4, 11, 7 mix in the open feed water heater to make 8. 9 is Heated to 12 using energy given up in the process 2 to 10 Note the mass of cold substance in feed water heaters is much higher that the mass of hot substance. (Unlike regenerators in Brayton cycle where the masses are similar). Pitting of turbine blades is caused by impinging drops at relatively high velocities, when expansion process leads to condensation of liquid drops. A part of the (small) expanded steam is used to preheat the water going into the boiler. This action increases the average temperature of heat addition and efficiency. (This is analogous to using exhaust gasses of a turbine to preheat air in a Brayton cycle). Fully expanded steam can’t be used for this purpose because it is already at a very low temperature and heat recovery from it for regeneration is impossible. 3 • • Pump work is generally very small compared to turbine work. Typically pumps are driven using small steam turbines attached to them rather than connected mechanically to the shaft of the main steam turbine. Electrical motors may also be used to drive pumps. Cogeneration plants tap steam off at an appropriate location (lower the pressure the better) for heating for processing applications. State p, bar 1 140 2s 40 T, oC 3 4 5 6 7 8 9 40 7 0.08 0.08 7 7 140 520 10 11 12 40 7 140 • (1 • 7.15 • Remark 520 320 3378.7 3015.4 Use Given , 320°% & '() *+,()(- ./+') (40 bar) 3490.0 2975.0 41.51 2240.5 41.51 173.88 ~42 174.58 ~165 697.22 ~165 711.25 6.4610 6.4610 (6.4553) 7.15 7.15 7.15 0.5926 - 250.4 1087.3 ~165 1087.3 ~ 1175 - Energy analysis on F.W.H. performed Energy analysis on F.W.H. performed Energy analysis on F.W.H. performed 71 8( 9 : ;1 < 71 =(> 0.86 B ST .∆V 1 : ;1 < 0.86= 0.86 H. IJ 0.86;2577= : ;0.14=173.88 > ;1.0084 W 10 0 =;7 < 0.08=100 0.6978 ⁄ LLMH. N OP/OR (Note pump work is small.) (-)/Y /- 1 & Y[ /- 11 & Y\ /- 4 & ,V)] ^))_ S/-)` )/-)` /]/+a(b(. ;1 < Y[ < Y\ = G ;C. 1 D.1E F= ;G. GC D.1E F= 71 ;8.2287= : ;1 < 71 =0.5926 B 71 71 Assume 1 Use given 0 , 0 (approximate interpolation) approximate interpolation Use (1 7.15 , (Saturated because (1 6 ( ) Saturated liquid (0.08 bar) Pump work is added Energy analysis on F.W.H. performed using these Energy analysis on F.W.H. performed using > /- 7 c/`( ],S], D > dD efg C d b( : Y[ : Y\ ],S], C b( d 1; G= ],S]. Y\ , Y[ , h 1087.3 Still 2 Unknowns: Closed feed water heater analysis 1; < E= Y[ ; < D= 250°% Use Table A-5 Compressed Liquids Table 1175 /]_, Y\ ;ijk il = ;ik ijm = ; Y[ 0.152 697.22 : ; E . DG ;140 DDD G 0.241 : ST < 7=100 G : .G ;140 < 7=100 697.22 : 14.73 4 711.95 /`) /- - b( V,b]- ']' ],S].