VIEWS: 10 PAGES: 70 POSTED ON: 9/14/2012 Public Domain
KARAKTERISTIK BEBERAPA SISTEM TERMODINAMIKA Vapor and Combined Power Cycles (2) 8.2 The carnot vapor cycles Energy reservoir at high temperature, TH 2 3 Boiler W Feed pump W Turbine Condenser 1 4 Energy reservoir at low temperature, TL 8.2 The carnot vapor cycles QIN WTURBINE WPUMP QOUT 8.2 The carnot vapor cycles QIN High temperature heat addition, TH Turbine to obtain work by expansion of working fluid. Work input to compress working fluid WTURBINE Low temperature heat rejection, TL WPUMP QOUT 8.2 The carnot vapor cycles Energy reservoir at high temperature, TH Q1=Q23 Wnet=W34-W12 Q2=Q41 Energy reservoir at low temperature, TL 8.2 The carnot vapor cycles Process T 1-2 Adiabatic compression (work input to system, W1) Q1=QH 2-3 Isothermal expansion TH 2 3 W1 W4 (heat added, Q1) TL 3-4 Adiabatic expansion 1 4 Q2=QL (work out from system, W4) s 4-1 Isothermal compression (heat rejected, Q2) 8.2 The carnot vapor cycles Efficiency of the Carnot cycle, work out wnet net supplied q1 q2 TL 1 1 q1 TH 8.2 The carnot vapor cycles 1. Limiting of heat transfer which severely limits the maximum temperature that can be used in the cycle and the thermal efficiency (Higher power requirement) 2. Not practical to design a compressor that handles two phases (Not homogeneous) 3. Difficult to control the condensation process at the desired quality. 4. High quality of steam decrease or high contents of liquid droplets cause erosion and wear at turbine blades 8.2 Rankine cycle : the ideal cycle for vapor power cycles Elimination of impracticalities of Carnot cycle Superheating the steam in the boiler and condensing it completely in the condenser Rankine cycle 8.2.2 Rankine cycle : the ideal cycle for vapor power cycles Process 1-2 Isentropic compression in a pump 2-3 Isobaric heat addition in a boiler 3-4 Isentropic expansion in a turbine 4-1 Isobaric heat rejection in a condenser 8.2.2 Rankine cycle : the ideal cycle for vapor power cycles 3* T 3 2 1 4 4* s All processes are internally reversible. 8.2.2 Rankine cycle : the ideal cycle for vapor power cycles Isentropic Reversible constant expansion to pressure heat addition 3* produce work T 3 (2 3) (3 4) or (3* 4*) 2 Isentropic compression (1 2) 1 4 4* Reversible constant pressure heat rejection s (4 1) All processes are internally reversible. 8.2.2 Rankine cycle : the ideal cycle for vapor power cycles h 3 Kinetic energy Qin and potential Wturb energy changes Wpump2 4 are usually small 1 Qout and can be neglected. s For steady flow energy equation per unit mass of steam (From first law of Thermodynamics) reduces to qin qout win wout he hi kJ/kg 8.2.2 Rankine cycle : the ideal cycle for vapor power cycles For feed pump (q 0) wpum p h2 h1 v( P2 P ) 1 kJ/kg where h1 h f @ P1 and v v f @ P1 For Boiler ( w 0) qin h3 h2 kJ/kg 8.2.2 Rankine cycle : the ideal cycle for vapor power cycles For turbine (q 0) wturb h3 h4 kJ/kg For condenser( w 0) qout h4 h1 kJ/kg Thermalefficiency of Rankine cycle, wnet qout th 1 qin qin where wnet qin qout wturb wpum p kJ/kg 8.2.2 Rankine cycle : the ideal cycle for vapor power cycles Increased average h temperature of 3* heat addition QH WOUT WIN 2 4 QC 1 s wturb wpum p qin h3* h4 h2 h1 0 h3* h2 h3* 8.3.3 Deviation of actual vapor power cycles from the idealized ones Pressure drop in boiler Irreversibility in the Ideal cycle pump (heat loss) (fluid friction) T 3 Actual cycle 2 4 1 s Pressure drop in condenser Irreversibility in the (fluid friction) turbine (fluid friction) 8.2.3 Deviation of actual vapor power cycles from the idealized ones Isentropic efficiency for pump ws h2 s h1 P wa h2 a h1 Isentropic efficiency for turbine wa h3 h4 a T ws h3 h4 s 8.2.3 Deviation of actual vapor power cycles from the idealized ones Example Steam is the working fluid in an Ideal Rankine cycle. Saturated vapor enter the turbine at 80 bar and saturated liquid exits the condenser at a pressure of 0.08 bar. The turbine and the pump each have an isentropic efficiency 85%. Determine a. Thermal efficiency b. Mass flow rate of steam in kg/hr for a net power output 100 kW c. Rate of heat transfer into working fluid as it passes through the boiler (MW) d. Rate of heat transfer from condensing steam as it passes through the condenser (MW) e. Mass flow rate of the condenser cooling water in kg/hr if cooling water enter the condenser at 15oC and exits as 35oC 8.2.3 Deviation of actual vapor power cycles from the idealized ones Solution 8.2.3 Deviation of actual vapor power cycles from the idealized ones Solution 8.2.3 Deviation of actual vapor power cycles from the idealized ones Solution 8.2.3 Deviation of actual vapor power cycles from the idealized ones Example Superheated steam at 30 bar and 360oC enter the turbine of steam power plant operating at steady state and expands to a condenser pressure 1.0 bar. Assume the isentropic efficiencies of the turbine and pump 85% and 80% respectively. Determine a. The thermal efficiency b. The heat rate c. The steam supply to deliver 1000kW d. The corresponding Rankine efficiency 8.2.3 Deviation of actual vapor power cycles from the idealized ones Solution 8.2.3 Deviation of actual vapor power cycles from the idealized ones Solution 8.2.3 Deviation of actual vapor power cycles from the idealized ones Solution 8.2.4 How can we increase the efficiency of the Rankine cycle Usage of steam power plants : production of most electric power in the world Basic idea of increasing the thermal efficiency of the steam power plants : 1.Increase the average temperature in the boiler 2.Decrease the average temperature in the condenser 3.4 How can we increase the efficiency of the Rankine cycle Lowering the condenser pressure (Lower Tlow,avg) P mean T , Steam in saturated mixture re thus temperatu of the heat is rejected during condensation Increase in net work output And also the heat input requirements (2 to 2’) but small compare to Wnet Condenser operating pressure is limited by the temperature of the cooling medium Could cause air leakage to condenser and moisture content of the steam in the turbine 8.2.4 How can we increase the efficiency of the Rankine cycle Superheating the steam to high temperatures (Increases Thigh,avg) Steam is superheated at P constant (3 to 3’) which increase the net work output. Decreases the moisture content of the steam at the turbine exit. Steam superheated temperature is limited by metallurgical considerations and material limitation 8.2.4 How can we increase the efficiency of the Rankine cycle Increasing the boiler pressure (Increases Thigh,avg) Pboiler increase which will automatically raises the boiling temperature Instead of increase the net work output, it also increase the moisture content in the turbine 8.2.4 How can we increase the efficiency of the Rankine cycle Example Consider a steam power plant operating on the ideal Rankine cycle. Steam enters the turbine at 3MPa and 350oC and is condensed in the condenser at a pressure of 75kPa. Determine a. The thermal efficiency of this power plant b. The thermal efficiency of this power plant if the condenser pressure decrease to 10kPa. c. The thermal efficiency if steam is superheated to 600oC instead of 350oC d. The thermal efficiency if the boiler pressure is raised to 15MPa while the turbine inlet temperature is maintained at 600oC 8.2.4 How can we increase the efficiency of the Rankine cycle Solution 8.2.4 How can we increase the efficiency of the Rankine cycle Solution 8.2.4 How can we increase the efficiency of the Rankine cycle Solution 8.2.5 The ideal reheat Rankine cycle Objective of reheat the Rankine cycle : Increase the net work output and thus the thermal efficiency without the problem of excessive moisture at the final stage of the turbine Two possible solutions : 1. Superheat the steam to very high temperature before it enters the turbine (limited by metallurgical consideration) 2. Expand the steam in the turbine in two stages, and reheat it in between. 8.2.5 The ideal reheat Rankine cycle qprim ary wturb I 1-2 Isentropic compression wturb II in pump 2-3 Isobaric heat addition in boiler qreheat 3-4 Isentropic expansion in high pressure turbine 4-5 Isobaric heat addition in boiler (reheat) qin qprimary qreheat h3 h2 h5 h4 5-6 Isentropic expansion in wturb out wturb I wturb II h3 h4 h5 h6 low pressure turbine qout h6 h1 6-1 Isobaric heat rejection in wpum p h2 h1 condenser 8.2.5 The ideal reheat Rankine cycle wturb I 1-2 Isentropic compression qreheat wturb II in pump 2-3 Isobaric heat addition in qprim ary wturb I boiler wturb II qreheat 3-4 Isentropic expansion in wpum pin high pressure turbine qprim ary 4-5 Isobaric heat addition in boiler (reheat) 5-6 Isentropic expansion in wturb I wturb II wpump th low pressure turbine qprimary qreheat 6-1 Isobaric heat rejection in condenser 8.2.5 The ideal reheat Rankine cycle Increase the number of expansion and reheat stage is limited by : Superheated exhaust which increase the temperature for the heat rejection process (decrease the thermal efficiency) 8.2.5 The ideal reheat Rankine cycle Example Steams are the working fluid in an ideal Rankine cycle with superheat and reheat. Steam enters the first stage turbine at 80 bar 480oC and expands to 7 bar. It is then reheated to 440oC before entering the second stage turbine where it expand to the condenser pressure of 0.08 bar. The net power output is 100 MW. Determine a. The thermal efficiency of the cycle b. The mass flow rate of steam in kg/hr c. The rate of heat transfer Qout from the condensing steam as it passes through the condenser in MW. 8.2.5 The ideal reheat Rankine cycle Solution 8.2.5 The ideal reheat Rankine cycle Solution 8.2.5 The ideal reheat Rankine cycle Solution 3.6 The ideal regenerative Rankine cycle Feed water : liquid that living the pump Regeneration : heat transfer from the expanding steam in a counterflow heat exchanger built in the turbine Regeneration Regenerator : or a feedwater heater (FWH) is a device where heat transfer occur Usage of regeneration : improves cycle efficiency Type of FWH : Open type and Closed type 8.2.6 The ideal regenerative Rankine cycle Open Feedwater Heaters a mixing chamber of steam and feedwater 1-2 Isentropic compression to saturation temperature in pump I. 2-3 Mixing of Feedwater from pump 6-3 with steam from turbine. 3-4 Isentropic compression to the boiler pressure in pump II. 4-5 Isobaric heat addition in boiler. 5-6 Isentropic expansion to intermediate pressure (y portion to FWH). 5-7 Isentropic expansion to the condenser pressure. 7-1 Isobaric heat rejection in condenser. 8.2.6 The ideal regenerative Rankine cycle Open Feedwater Heaters 8.2.6 The ideal regenerative Rankine cycle Closed Feedwater Heaters Heat transfer without mixing taking place 1-2 Isentropic compression in pump I. 2-9 Regeneration (only heat transfer) 3-4 Isentropic compression in pump II 9/4-5 Mixing of feed water and steam 5-6 Isobaric heat addition in boiler. 6-7 Isentropic expansion to intermediate pressure (y portion to FWH). 6-8 Isentropic expansion to the condenser pressure. 7-3 Regeneration (only heat transfer) 8-1 Isobaric heat rejection in condenser. 8.2.6 The ideal regenerative Rankine cycle Closed Feedwater Heaters 8.2.6 The ideal regenerative Rankine cycle yh6 1 y h2 h3 yh6 h2 yh2 h3 h3 h2 y h6 h2 qin h5 h4 qout 1 y h7 h1 h5 wturb yh6 1 y h7 wpump wpump I wpump II h5 wturb yh6 h7 yh7 wpump 1 y h1 h2 h3 h4 wturb h5 h6 1 y h6 h7 8.2.6 The ideal regenerative Rankine cycle Example A steam power plant operates on an ideal regenerative Rankine cycle. Steam enters the turbine at 6MPa and 450oC and is condensed in the condenser at 20kPa. Steam is extracted from the turbine at 0.4 MPa to heat the feedwater in an open feedwater heater. Water leaves the feedwater heater as a saturated liquid. Show the cycle on a T-s diagram, and determine a. The net work output per kilogram of steam flowing through the boiler b. The thermal efficiency of the cycle 8.2.6 The ideal regenerative Rankine cycle Solution 8.2.6 The ideal regenerative Rankine cycle Solution 8.2.6 The ideal regenerative Rankine cycle Solution 8.2.6 The ideal regenerative Rankine cycle Example A regenerative vapor power cycle with one open feedwater heater. Steam enters the turbine at 80 bar 480oC and expands to 7 bar, where some of the steam is extracted and diverted to the open feedwater heater operating at 7 bar. The remaining steam expands through the second stage turbine to the condenser pressure 0.08 bar. Saturated liquid exits the open feedwater heater at 7 bar. The isentropic efficiency of each turbine stage is 85% and each pump operates isentropically. If the net power output of the cycle is 100 MW. Determine 1. The thermal efficiency 2. The mass flow rate of steam entering the first turbine stage in kg/hr 8.2.6 The ideal regenerative Rankine cycle Solution 8.2.6 The ideal regenerative Rankine cycle Solution 8.2.6 The ideal regenerative Rankine cycle Solution 8.2.6 The ideal regenerative Rankine cycle Example A steam power plant operates on an ideal reheat-regenerative Rankine cycle and has a net power of 80MW. Steam enters the high pressure turbine at 10MPa and 550oC and leaves at 0.8MPa. Some steam is extracted at this pressure to heat the feedwater in an open feedwater heater. The rest of the steam is reheated to 500oC and is expanded in the low pressure turbine to the condenser pressure of 10kPa. Show the cycle on a T-s diagram with respect to saturation lines, and determine 1. The mass flow rate of steam through the boiler 2. The thermal efficiency of the cycle 8.2.6 The ideal regenerative Rankine cycle Solution 8.2.6 The ideal regenerative Rankine cycle Solution 8.2.6 The ideal regenerative Rankine cycle Solution 8.2.7 combined gas-vapor cycles Combined cycle of Brayton gas power cycle and Rankine vapor power cycle Purpose of combination : To achieve higher thermal efficiency Gas turbine engine Regeneration, 500oC (Temperature limit 1500oC) Steam turbine engine (Temperature limit 620oC) 8.2.7 combined gas-vapor cycles 8.2.7 combined gas-vapor cycles Example The gas turbine portion of a combined gas-steam power plant has a pressure ratio of 16. air enters the compressor at 300K at a rate of 14kg/s and is heated to 1500K in the combustion chamber. The combustion gases leaving the gas turbine are used to heat the steam to 400oC at 10MPa in a heat exchanger. The combustion gases leave the heat exchanger at 420K. The steam leaving the turbine is condensed at 15kPa. Assuming all the compression and expansion processes to be isentropic, determine a. The mass flow rate of the steam b. The net power output c. The thermal efficiency of the combined cycle For air, assume constant specific heats at room temperature. 8.2.7 combined gas-vapor cycles Solution 8.2.7 combined gas-vapor cycles Solution 8.2.7 combined gas-vapor cycles Solution 8.2.7 combined gas-vapor cycles Example Consider a combined gas-steam power cycle. The topping cycle is a simple Brayton cycle that has a pressure ratio of 7. Air enters the compressor at 15oC at a rate of 10kg/s and the gas turbine at 950oC. The bottoming cycle is a reheat Rankine cycle between the pressure limits of 6MPa and 10kPa. Steam is heated in a heat exchanger at a rate if 1.15 kg/s by the exhaust gases leaving the gas turbine and the exhaust gases leave the heat exchanger at 200oC. Steam leaves the high-pressure turbine at 1.0MPa and is reheated to 400oC in the heat exchanger before it expands in the low pressure turbine. Assuming 80% isentropic efficiency for all pumps and turbine, determine a. The moisture content at the exit of the low pressure turbine b. The steam temperature at the inlet of high pressure turbine c. The net power output and the thermal efficiency of the combined plant 8.2.7 combined gas-vapor cycles Solution 8.2.7 combined gas-vapor cycles Solution 8.2.7 combined gas-vapor cycles Solution