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PROBLEMARIO MÁQUINAS DE FLUIDOS COMPRESIBLES E J E R C I C I O S P R O P U E S TO S



CICLO RANKINE I D E A L , R E A L , R E C A L E N TA M I E N T O R E G E N E R AT I V O .



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IDEAL • Steam is the working fluid in the ideal Rankine cycle 1–2– 3–4–1 and in the Carnot cycle 1–2–3’–4’–1 that both operate between pressures of 1.5 bar and 60 bar as shown in the T–s diagram in Fig. P8.3. Both cycles incorporate the steady flow devices shown in Fig. 8.2. For each cycle determine (a) the net power developed per unit mass of steam flowing, in kJ/kg, and (b) the thermal efficiency. Compare results and comment.



IDEAL • Figure P8.13 provides steady-state operating data for a solar power plant that operates on a Rankine cycle with Refrigerant 134a as its working fluid. The turbine and pump operate adiabatically. The rate of energy input to the collectors from solar radiation is 0.3 kW per m2 of collector surface area, with 60% of the solar input to the collectors absorbed by the refrigerant as it passes through the collectors. Determine the solar collector surface area, in m2 per kW of power developed by the plant. Discuss possible operational improvements that could reduce the required collector surface area.



REAL • Una central eléctrica de vapor opera en el ciclo que se muestra en la figura 10-5. Si las eficiencias isentrópicas de la turbina y la bomba son de 87 por ciento y de 85 por ciento, respectivamente, determine a) la eficiencia térmica del ciclo y b) la salida de potencia neta de la central para un flujo másico de 15 kg/s.



REAL • The ideal Rankine cycle 1–2–3–4–1 of Problem 8.3 is modified to include the effects of irreversibilities in the adiabatic expansion and compression processes as shown in the T–s diagram in Fig. P8.15. Let T0 = 300 K, p0 = 1 bar.



• Determine (a) the isentropic turbine efficiency. (b) the rate of exergy destruction per unit mass of steam flowing in the turbine, in kJ/kg. (c) the isentropic pump efficiency. (d) the thermal efficiency.



RECALENTAMIENTO IDEAL • Steam is the working fluid in the ideal reheat cycle shown in Fig. P8.27 together with operational data. If the mass flow rate is 1.3 kg/s, determine the power developed by the cycle, in kW, and the cycle thermal efficiency.



RECALENTAMIENTO REAL • Steam is the working fluid in the vapor power cycle with reheat shown in Fig. P8.35 with operational data. The mass flow rate is 2.3 kg/s, and the turbines and pump operate adiabatically. Steam exits both turbine 1 and turbine 2 as saturated vapor. If the reheat pressure is 15 bar, determine the power developed by the cycle, in kW, and the cycle thermal efficiency.



RECALENTAMIENTO • An ideal Rankine cycle with reheat uses water as the working fluid. As shown in Fig. P8.36, the conditions at the inlet to the first turbine stage are 1600 lbf/in.2, 1200°F and the steam is reheated to temperature T3 between the turbine stages at a pressure of 200 lbf/in.2 For a condenser pressure of 1 lbf/in.2, plot the cycle thermal efficiency versus reheat temperature and plot the cycle thermal efficiency versus quality of the steam at the second-stage turbine exit for the reheat temperature ranging from 600°F to 1200°F.



REGENERATIVO (ABIERTO)



REGENERATIVO • Water is the working fluid in an ideal regenerative Rankine cycle. Superheated vapor enters the turbine at 10 MPa, 480°C, and the condenser pressure is 6 kPa. Steam expands through the first-stage turbine to 0.7 MPa where some of the steam is extracted and diverted to an open feedwater heater operating at 0.7 MPa. The remaining steam expands through the second-stage turbine to the condenser pressure of 6 kPa. Saturated liquid exits the feedwater heater at 0.7 MPa. Determine for the cycle (a) the heat addition, in kJ per kg of steam entering the firststage turbine. (b) the thermal efficiency. (c) the heat transfer from the working fluid passing through the condenser to the cooling water, in kJ per kg of steam entering the first-stage turbine. Reconsider the analysis assuming the pump and each turbine stage have an isentropic efficiency of 80%. Investigate the effects on cycle performance as the feedwater heater pressure takes on other values. Construct suitable plots and discuss for the cycle



REGENERATIVO • A power plant operates on a regenerative vapor power cycle with one open feedwater heater. Steam enters the first turbine stage at 12 MPa, 560°C and expands to 1 MPa, where some of the steam is extracted and diverted to the open feedwater heater operating at 1 MPa. The remaining steam expands through the second turbine stage to the condenser pressure of 6 kPa. Saturated liquid exits the open feedwater heater at 1 MPa. The net power output for the cycle is 330 MW. For isentropic processes in the turbines and pumps, determine: (a) the cycle thermal efficiency. (b) the mass flow rate into the first turbine stage, in kg/s. (c) the rate of entropy production in the open feedwater heater, in kW/K.



REGENERATIVO • Reconsider the cycle of previous Problem as the feedwater heater pressure takes on other values. Plot the cycle thermal efficiency, cycle work per unit mass entering the turbine, in kJ/kg, the heat transfer into the cycle per unit mass entering the turbine, in kJ/kg, the fraction of steam extracted and sent to the feedwater heater, the mass flow rate into the first turbine stage, in kg/s, and the rate of entropy production in the open feedwater heater, in kW/K, versus feedwater heater pressure ranging from 0.3 to 10 MPa.



REGENERATIVO • Water is the working fluid in an ideal regenerative Rankine cycle with one closed feedwater heater. Superheated vapor enters the turbine at 10 MPa, 480°C, and the condenser pressure is 6 kPa. Steam expands through the first-stage turbine where some is extracted and diverted to a closed feedwater heater at 0.7 MPa. Condensate drains from the feedwater heater as saturated liquid at 0.7 MPa and is trapped into the condenser. The feedwater leaves the heater at 10 MPa and a temperature equal to the saturation temperature at 0.7 MPa. Determine for the cycle (a) the heat transfer to the working fluid passing through the steam generator, in kJ per kg of steam entering the firststage turbine. (b) the thermal efficiency. (c) the heat transfer from the working fluid passing through the condenser to the cooling water, in kJ per kg of steam entering the first-stage turbine.



REGENERATIVO • As indicated in Fig. P8.52, a power plant similar to that in Fig. 8.11 operates on a regenerative vapor power cycle with one closed feedwater heater. Steam enters the first turbine stage at state 1 where pressure is 12 MPa and temperature is 560°C. Steam expands to state 2 where pressure is 1 MPa and some of the steam is extracted and diverted to the closed feedwater heater. Condensate exits the feedwater heater at state 7 as saturated liquid at a pressure of 1 MPa, undergoes a throttling process through a trap to a pressure of 6 kPa at state 8, and then enters the condenser. The remaining steam expands through the second turbine stage to a pressure of 6 kPa at state 3 and then enters the condenser. Saturated liquid feedwater exiting the condenser at state 4 at a pressure of 6 kPa enters a pump and exits the pump at a pressure of 12 MPa. The feedwater then flows through the closed feedwater heater, exiting at state 6 with a pressure of 12 MPa. The net power output for the cycle is 330 MW. For isentropic processes in each turbine stage and the pump, determine. (a) the cycle thermal efficiency. (b) the mass flow rate into the first turbine stage, in kg/s. (c) the rate of entropy production in the closed feedwater heater, in kW/K. (d) the rate of entropy production in the steam trap, in kW/K.



REGENERATIVO • Reconsider the cycle of the previous Problem, but include in the analysis that each turbine stage and the pump have isentropic efficiencies of 83%.



EXAMEN 1 • Figure P8.79 provides steady-state operating data for a cogeneration cycle that generates electricity and provides heat for campus buildings. Steam at 1.5 MPa, 280°C, enters a two-stage turbine with a mass flow rate of 1 kg/s. A fraction of the total flow, 0.15, is extracted between the two stages at 0.2 MPa to provide for building heating, and the remainder expands through the second stage to the condenser pressure of 0.1 bar. Condensate returns from the campus buildings at 0.1 MPa, 60°C and passes through a trap into the condenser, where it is reunited with the main feedwater flow. Saturated liquid leaves the condenser at 0.1 bar. Determine (a) the rate of heat transfer to the working fluid passing through the boiler, in kW. (b) the net power developed, in kW. (c) the rate of heat transfer for building heating, in kW. (d) the rate of heat transfer to the cooling water passing through the condenser, in kW.



EXAMEN 2 • Consider a cogeneration system operating as shown in Fig. P8.80. Steam enters the first turbine stage at 6 MPa, 540°C. Between the first and second stages, 45% of the steam is extracted at 500 kPa and diverted to a process heating load of 5x108 kJ/h. Condensate exits the process heat exchanger at 450 kPa with specific enthalpy of 589.13 kJ/kg and is mixed with liquid exiting the lower-pressure pump at 450 kPa. The entire flow is then pumped to the steam generator pressure. At the inlet to the steam generator the specific enthalpy is 469.91 kJ/kg. Saturated liquid at 60 kPa leaves the condenser. The turbine stages and the pumps operate with isentropic efficiencies of 82% and 88%, respectively. Determine (a) the mass flow rate of steam entering the first turbine stage, in kg/s. (b) the net power developed by the cycle, in MW. (c) the rate of entropy production in the turbine, in kW/K.



EXAMEN 3 • Figure P8.82 shows a cogeneration cycle that provides power and process heat. In the steam cycle, superheated vapor enters the turbine at 40 bar, 440°C and expands isentropically to 1 bar. The steam passes through a heat exchanger, which serves as a boiler of the Refrigerant 134a cycle and the condenser of the steam cycle. The condensate leaves the heat exchanger as saturated liquid at 1 bar and is pumped isentropically to the steam generator pressure. The rate of heat transfer to the working fluid passing through the steam generator of the steam cycle is 13 MW. The Refrigerant 134a cycle is an ideal Rankine cycle with refrigerant entering the turbine at 16 bar, 100°C. The refrigerant passes through a heat exchanger, which provides process heat and acts as a condenser for the Refrigerant 134a cycle. Saturated liquid exits the heat exchanger at 9 bar. Determine (a) the mass flow rate of steam entering the steam turbine, in kg/s. (b) the mass flow rate of Refrigerant 134a entering the refrigerant turbine, in kg/s. (c) the percent of total power provided by each cycle. (d) the rate of heat transfer provided as process heat, in kW.



PROYECTO 1 • Referring to Fig. 8.12, if the fractions of the total flow entering the first turbine stage (state 1) extracted at states 2, 3, 6, and 7 are y2, y3, y6, and y7, respectively, what are the fractions of the total flow at states 8, 11, and 17?



PROYECTO 2 • Data for a power plant similar in design to that shown in Fig 8.12 are provided in the table below. The plant operates on a regenerative vapor power cycle with four feedwater heaters, three closed and one open, and reheat. Steam enters the turbine at 16,000 kPa, 600°C, expands in three stages to the reheat pressure of 2000 kPa, is reheated to 500°C, and then expands in three more stages to the condenser pressure of 10 kPa. Saturated liquid exits the condenser at 10 kPa. Between the first and second stages, some steam is diverted to a closed feedwater heater at 8000 kPa. Between the second and third stages, additional steam is diverted to a second closed feedwater heater at 4000 kPa. Steam is extracted between the fourth and fifth turbine stages at 800 kPa and fed into an open feedwater heater operating at that pressure. Saturated liquid at 800 kPa leaves the open feedwater heater. Between the fifth and sixth stages, some steam is diverted to a closed feedwater heater at 200 kPa. Condensate leaves each closed feedwater heater as saturated liquid at the respective extraction pressures. For isentropic processes in each turbine stage and adiabatic processes in the pumps, all closed feedwater heaters, all traps, and the open feedwater heater show that (a) the fraction of the steam diverted between the first and second stages is 0.1000. (b) the fraction of the steam diverted between the second and third stages is 0.1500. (c) the fraction of the steam diverted between the fourth and fifth stages is 0.0009. (d) the fraction of the steam diverted between the fifth and sixth stages is 0.1302.



… CONTINUA PROYECTO 2



PROYECTO 3 • Data for a regenerative vapor power cycle using an open and a closed feedwater heater similar in design to that shown in Fig P8.60 are provided in the table below. Steam enters the turbine at 14 MPa, 560°C, state 1, and expands isentropically in three stages to a condenser pressure of 80 kPa, state 4. Saturated liquid exiting the condenser at state 5 is pumped isentropically to state 6 and enters the open feedwater heater. Between the first and second turbine stages, some steam is extracted at 1 MPa, state 2, and diverted to the closed feedwater heater. The diverted steam leaves the closed feedwater heater as saturated liquid at 1 MPa, state 10, undergoes a throttling process to 0.2 MPa, state 11, and enters the open feedwater heater. Steam is also extracted between the second and third turbine stages at 0.2 MPa, state 3, and diverted to the open feedwater heater. Saturated liquid at 0.2 MPa exiting the open feedwater heater at state 7 is pumped isentropically to state 8 and enters the closed feedwater heater. Feedwater exits the closed feedwater heater at 14 MPa, 170°C, state 9, and then enters the steam generator. If the net power developed by the cycle is 300 MW, determine (a) the cycle thermal efficiency. (b) the mass flow rate into the first turbine stage, in kg/s. (c) the rate of heat transfer from the working fluid as it passes through the condenser, in MW.



…CONTINUA PROYECTO 3 • Data for a regenerative vapor power cycle using an open and a closed feedwater heater similar in design to that shown in Fig P8.60 are provided in the table below. Steam enters the turbine at 14 MPa, 560°C, state 1, and expands isentropically in three stages to a condenser pressure of 80 kPa, state 4. Saturated liquid exiting the condenser at state 5 is pumped isentropically to state 6 and enters the open feedwater heater. Between the first and second turbine stages, some steam is extracted at 1 MPa, state 2, and diverted to the closed feedwater heater. The diverted steam leaves the closed feedwater heater as saturated liquid at 1 MPa, state 10, undergoes a throttling process to 0.2 MPa, state 11, and enters the open feedwater heater. Steam is also extracted between the second and third turbine stages at 0.2 MPa, state 3, and diverted to the open feedwater heater. Saturated liquid at 0.2 MPa exiting the open feedwater heater at state 7 is pumped isentropically to state 8 and enters the closed feedwater heater. Feedwater exits the closed feedwater heater at 14 MPa, 170°C, state 9, and then enters the steam generator. If the net power developed by the cycle is 300 MW, determine



… • Reconsider the cycle of the previous Problem, but include in the analysis that each turbine stage and the pump have isentropic efficiencies of 83%.