FAYOUM UNIVERSITY FACULTY OF ENGINEERING MECHANICAL ENGINEERING DEPARTMENT THIRD YEAR 2017 – 2018
FIRST TERM
SHEET OF ASSIGNMENTS
Dr. Ahmed Adel
CONVENTIONAL POWER PLANTS 1- Steam Turbines Cycles, Feed Circuit and Performance Analysis 1) In a four stage turbine, the steam expands from 16.3 bar and 270 °C to 0.068 bar. The intermediate stage pressures are 6.1 bar, 1.6 bar and 0.4 bar, respectively and the stage efficiency is 73 %. Draw the condition line of the turbine and then determine: a. The reheat factor. b. The condition of the steam at the end of each stage. c. The internal efficiency of the turbine. d. The thermal power in kW, if the mechanical and generator efficiencies are 94% and 96%, respectively. 2) The following information relate to an impulse steam turbine of 30 MW governed by a simple throttling: - Initial steam pressure at full load = 14 bar. - Initial steam temperature at full load = 275 oC. - Full load steam consumption = 40 kg / sec. - No load steam consumption = 4 kg / sec. - Condenser pressure (assumed constant) = 0.07 bar. - Internal efficiency (assumed constant) = 75 % Calculate the following : a. The power needed to overcome losses in the turbine at no load conditions. b. The steam consumption, nozzle box pressure and exhaust steam condition at 0, 1/3, 1/2 , 3/4 and full load. 3) Steam enters a turbine at 80 bar and 450 oC. The exhaust pressure is 0.06 bar. Compare the following three schemes : a- A simple Rankine cycle with 0.8 relative efficiency. b- A reheat cycle with steam reheated at the pressure where it becomes saturated till its temperature becomes 300 oC. The relative efficiency of each part of the turbine is 0.8. c- A regenerative cycle with one bleeding point at the pressure where the steam becomes saturated. The bled steam just condenses while it heats the feed water in a contact type feed water heater. The relative efficiency of each part of the turbine is 0.8. For each scheme find the net specific work , the cycle efficiency and the condition of the exhaust steam. 4) A steam turbine receives steam at 40 bar and 420 oC. It exhausts at 0.07 bar. The turbine plant has two regenerative feed water heaters of the closed type. The drains are cascaded between heaters back to the condenser. The feed water is heated from 38.6 oC to 150 oC , with equal temperature rise in the two heaters. The difference between the outlet temperature of the feed water and the condensation temperature of the heating steam in each heater is 4 oC. The isentropic efficiency before the first extraction, between the two extractions and after the second extraction are all 0.82. Draw the circuit scheme and then find : a- The bleeding points for the two heaters and the condition of the exhaust steam. b- The thermal efficiency of the cycle. 5) An 850 MW steam turbine plant operates with turbine inlet steam at 80 bar and 540 oC and condenser pressure of 0.07 bar. There are three feed water heaters placed optimally as follows; the high pressure heater is of the closed type with drains cascaded backward. The intermediate pressure heater is of the open type. The low pressure heater is of the closed type with drains pumped forward. Each of the turbine sections have the same internal efficiency of 0.90. The feed pumps have relative efficiencies of 0.80. Calculate : a- The steam mass flow rate at both the turbine stop valve and exhaust flange, in kg/hr. b- The mass flow rate of the condenser cooling water if it undergoes 10 oC temperature rise. c- The cycle efficiency and heat rate, in kJ/kWh. -1–
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6) A 20 MW steam turbine receives steam at 41 bar 425 oC and exhausts at 0.07 bar. The feed circuit of the plant contains three feed water heaters ( including deaerator ), evaporator and ejector heater. Drains are cascaded from heater to the next, than pass through the drain cooler before going to the condenser. Heating of the feed water from the condenser to the boiler drum is shared between the economizer and the feed water heaters in the ratio 1 : 2, respectively. Inlet feed water temperature to the first heater is 10 oC higher than the condensate temperature. Outlet feed water temperature from the economizer is 20 oC lower than the boiling temperature. The total temperature rise in the three heaters is divided equally among them. A difference of 5 oC is allowed between the outgoing feed water temperature and the saturation temperature of steam bled to each closed heater. The steam entering the condenser contains 12% moisture content. The condition line is assumed to be a straight line. The mechanical efficiency is 0.98. Draw the feed circuit diagram, showing the positions of the deaerator heater and the evaporator. Calculate the following : a- Bleeding pressures, condition and amount of steam extracted for the three feed water b- The total steam consumption rate, in ton/hr. c- The thermal efficiency of the plant and the gain in thermal efficiency due to regenerative feed heating. 7) Steam is supplied to a steam turbine at 170 bar and 550oC with a mass flow rate of 650 kg/s. The steam after expanding in the high pressure turbine down to 36 bar is directed to a reheat section in the steam generator, where its temperature increases to 580oC. The steam then continues expansion in the intermediate pressure turbine to 5 bar. The condensation temperature is 39oC. In the feed circuit of such power plant, there exist six feed water heaters arranged as follows; three closed type heater with drains cascaded backward to the lower pressure heater, followed by an open type deaerator heater, followed by two closed heaters with drains cascaded backward to the open heater. The drains of the lower pressure heater is pumped forward to the feed line. The pressures of the higher and open feed water heaters are 36 and 5 bar, respectively. The inlet feed water temperature to the lower pressure heater is 45oC. The expansion line, in each of the three turbines, is assumed to be a straight line on the h-s chart with an internal efficiency of 0.88. Assume that the steam just condenses in the condenser and feed water heaters. The combined mechanical and generator efficiency is 97 %. The steam generator efficiency is 98 %. Calculate : a- The different feed water heaters extraction pressures. b- The power plant electrical power. c- The power plant overall efficiency, if the fuel used has a calorific value of 42 000 kJ / kg. 8) The following information belong to an 860 MW steam power plant : - Steam conditions at the turbine stop valve = 180 bar and 550 oC - Steam pressure at the high pressure turbine exit = 15 bar - Reheated steam conditions = 15 bar and 550 oC - Steam pressure at the intermediate pressure turbine exit = 1.2 bar - Condenser pressure = 0.07 bar - Internal efficiency of each turbine = 0.87 - Extracted steam pressures for the closed F.W heaters = 15 bar, 1.2 bar and 0.5 bar - Extracted steam pressure for the open F.W. heater = 5 bar - Terminal temperature difference for the closed heaters = 3 oC - Combined mechanical and generator efficiency = 0.95 The drains of the low pressure closed heaters are cascaded back to the condenser and that of the high pressure heater is cascaded back to the open heater. Assume that the expansion line for each turbine to be a straight line on the h-s chart and steam just condenses in the condenser and feed water heaters. Draw the flow diagram of the power plant and then calculate : a. The steam mass flow rate at the turbine stop valve and the power plant thermal efficiency. b. The exhaust steam dryness fraction with and without reheating. c. Calculate the capacity of the suitable steam generator and steam condenser.
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2- Gas Turbine Cycles and Modifications 9) In a gas-turbine power plant, the compressor and the turbine operate with isentropic efficiency of 0.85. The pressure ratio is 6. The temperatures are 25 oC at the compressor inlet, and 700 oC at the turbine inlet. The power output is 10 MW. The exhaust gases from the turbine pass through a waste-heat boiler. Dry saturated steam at 6 bar is generated from feed water at 30 oC. The water absorbs only 97% of the heat removed from the gases. The gases leave the boiler at 180 oC. The calorific value of the fuel used is 43100 kJ/kg, and the efficiency of combustion is 0.98. Assuming the air to be the working fluid in the turbine, find : a- The mass of steam generated in the boiler and the rate of fuel consumption, in kg/hr. b- The overall efficiency of the plant. 10) Atmospheric air at 15 oC and 65% relative humidity enters the compressor of a gas-turbine cycle. The compressor and the turbine have the same pressure ratio of 6 and isentropic efficiencies of 0.80 and 0.90, respectively. Water at 15 oC is injected into the compressor exit air, saturating it. The air then goes through an 85% effectiveness regenerator. The turbine inlet temperature is 1050 oC. If the net power output is 20 MW calculate : a- The air temperature after water injection. b- The original air mass flow rate and the necessary water injection rate. c- The cycle efficiency. Compare these results with those of the case with no water injection. Assume = 1.4 over the cycle. 11) A 5000 kW gas-turbine power plant operates with a low-pressure compressor and a high-pressure one with intercooling stage between them. The overall pressure ratio is 9. A high-pressure turbine is used to drive the compressor, and a low-pressure one drives the electrical generator. The temperature of the gases at entry to the high-pressure turbine is 750 oC, and the gases are reheated to 750 oC after expansion in the first turbine. The exhaust gases leaving the low-pressure turbine are passed through a heat exchanger to heat the air leaving the high-pressure compressor. The intercooler is ideal, and the air inlet temperature to the unit is 27 oC. The isentropic efficiency of each compressor is 0.85 and that of each turbine is 0.87. The heat exchanger thermal ratio is 0.75. A mechanical efficiency of 0.95 may be assumed for both the power shaft and the compressor-turbine shaft. For air; cp = 1.005 kJ/kg K and = 1.4, and for products of combustion; cp = 1.15 kJ/kg K and = 1.333. Neglecting the effect of fuel mass, determine the mass flow rate of the air and the thermal efficiency of the cycle 12) A combined-cycle power plant is designed with four-60 MWe gas turbines and one-150 MWe steam turbine. The fuel of the gas turbine cycle has a stoichiometric air / fuel ratio of 16 with an actual value corresponding to 400% of the theoretical air. Each gas turbine operates with inlet temperature of 15 oC and inlet pressure of 1 bar, turbine inlet temperature of 1040 oC, pressure ratio for both compressor and turbine of 5, and compressor and turbine isentropic and mechanical efficiencies of 0.87 and 0.92, respectively. The temperature of the gases leaving the gas turbine is further raised by supplementary firing to 840 oC and the mixture is changed from 400% to 200% of theoretical air. The gases, then enter a heat recover boiler. The steam cycle has a turbine steam inlet at 80 bar and 540 oC and a deaerating feed water heater which raises the feed water temperature to 240 oC. Condenser pressure is 0.07 bar. All electrical power generation efficiencies are 0.98. Calculate : a- The air mass flow rate in each gas turbine. b- The steam mass flow rate leaving the heat recovery boiler. c- The heat added in the gas-turbine cycle and in the supplementary firing and the stack temperature. d- The efficiencies of gas, steam and combines cycles.
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3- Combined Cycles and Cogeneration 13) Consider a steam generator in a combined cycle of dual pressure steam system. The combustion gases, corresponding to 200% of theoretical air ( stoichiometric air/fuel ratio = 15 ), leave supplementary firing at 650 oC and the steam generator at 176 oC. Steam is generated at 68 bar and 537 oC and 13.6 bar and 260 oC from feed water at 148 oC. The high and low pressure steam mass flow rates are equal. Calculate : a. The mass of gases required per kg of total steam generated. b. The gases exhaust temperature if only high pressure steam is generated for the same gas mass flow rate. 14) In a gas-turbine plant, the compressor and turbine operate with the same isentropic efficiency of 0.85. The pressure ratio is 5. The temperatures are 20 oC at the compressor inlet, and 670 oC at the turbine inlet. The plant output is 8 MW. The exhaust gases passed through a boiler. Steam at 16 bar and 240 o C is generated from feed water at 40 oC. The steam expands in a turbine with isentropic efficiency of 0.75 to a condenser pressure of 0.08 bar. Determine the additional power generated, and the overall thermal efficiency. Assume a boiler efficiency of 0.72 reckoned on a final gas temperature of 20 oC. Also, assume air to be the working fluid in the gas turbine. 15) A textile factory utilizes an average of 18 ton/hr of dry-saturated process steam at a pressure of 3 bar. The factory requires also, at the same time, an average power of 1 MW. For this purpose a small back pressure turbo-generator set is to be used to supply the required power, while the exhaust goes to the factory as process steam at the above conditions. The turbine will be working with an internal efficiency of 0.65, and a combined mechanical and generator efficiency of 0.86. Determine the initial state of the steam required for the turbine. 16) In a topping cycle cogeneration plant using an open cycle gas turbine, the following data are given : - Electrical output 200 MW - Industrial process heat load 600 GJ / hr - Inlet air conditions to compressor 20 oC and 1 bar - Compressor pressure ratio corresponding to maximum work conditions - Compressor isentropic efficiency 0.85 - Inlet fuel temperature to combustion chamber 40 oC - Fuel heating value 40,000 kJ / kg - Average air specific heat 1.02 kJ / kg K - Average fuel specific heat 2.8 kJ / kg K - Average combustion gases specific heat 1.13 kJ / kg K - Average specific heat ratio 1.4 - Maximum cycle temperature 1000 oC - Turbine isentropic efficiency 0.87 - Mechanical efficiency for both power and turbine-compressor shafts 0.95 - Electrical generator efficiency 0.96 Using the above data, calculate : a. The pressure ratio. b. The air / fuel ratio. c. The consumed fuel mass flow rate. d. The exhaust gases contained heat energy. 17) A cogeneration steam plant of the extraction-condensing steam turbine type has turbine inlet flow rate of 12.5 kg/s at 50 bar and 400 oC, extraction for process steam at 220 oC and condensation for both turbine and process steam at 40 oC. Assuming ideal turbine and pump, no feed water heating and 50% fraction of electricity to total energy output, calculate : a. The cogeneration efficiency. b. The combined efficiency if separate electric and steam generation plants are used. For all cases take the steam generator efficiency as 85%.
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18) A new power station project ( 3 x 25 MW ) is intended to supply process steam for petroleum refinery and electrical power as well. Each turbo-generator unit is to be fed with steam at 90 bar and 535 oC, and exhausts at 0.07 bar. Process steam amounting to 100 ton/hr is to be extracted from each turbine at about 13 bar. The fed water is pumped to the economizer after being heated from 50 oC to 215 oC in three feed water heaters having equal temperature rise with drain cascading system. If the expansion line is assumed to be a straight line, ending with 12 % moisture at the exhaust flange, draw a sketch for the feed circuit. Assume a terminal temperature difference of about 3 oC for each heater between outgoing feed water and saturation temperature of heating steam. Calculate the following : a. Bleeding pressures and amount of steam bled for each heater per kilogram of supplied steam. b. The total steam consumption rate of each turbine to supply 25 MW and 100 ton/hr process steam. c. The capacity of the suitable boiler and the capacity of the suitable condenser for each unit. d. The efficiency of utilization of the plant if all the process steam is utilized down to 40 oC. e. The steam rate and the heat rate per kWh. 19) A combined cycle for a nuclear power plant uses helium in the gas-turbine cycle. The compressor and turbine have the same pressure ratio of 2, the same isentropic efficiency of 0.85 and inlet temperatures of 60 oC and 1115 oC, respectively. The regenerator effectiveness is 0.85. The steam cycle operates with 68 bar and 537 oC supply steam and 0.06 bar condenser pressure. The steam turbine internal efficiency is 0.85. The feed water heater in the steam cycle has a terminal temperature difference of 15.5 oC. Calculate : a. The helium mass flow rate, for a combined output of 200 MW. b. The gas, steam and combined cycle efficiencies. For helium take : cp = 5.23 kJ/kg K and = 1.66. 20) A 100 MW ( thermal ) binary-vapour cycle uses saturated mercury vapour at 1300 oC at the top turbine inlet. The mercury condenses at 700 oC in a mercury condenser–steam boiler in which saturated steam is generated at 28 bar. The steam is further superheated to 880 oC in the mercury-boiler-steam superheater. The steam condenses at 0.07 bar. Assume that both the mercury and steam turbines have the same isentropic efficiency of 0.85 and the pumping work is neglected. Draw the flow sheet and the T-s diagram of the binary cycle and find : a. The mass flow rates of the mercury and the steam. b. The heat added and heat rejected. c. The mercury, steam and binary cycles thermal efficiencies. 21) A 3000 BHP diesel-engine power plant consumes 0.19 kg of fuel oil per BHP hr. The air-to-fuel ratio is 22 by mass. The exhaust gases leave the engine at 450 oC. The cooling water enters the cylinder jackets at 20 oC and leaves at 80 oC. It is desired to utilize the heat available in the exhaust gases and a part of the cooling water to obtain distilled water, by using an evaporator and a condenser. The cooling water leaving the engine jackets is directed to the evaporator to produce dry-saturated steam at 1.05 bar. This steam is then condensed in the condenser. The heating gases leave the evaporator at 140 oC. The specific heat of the gases is 1.088 kJ/kg K. Neglecting blow down and heat losses, find the amount of distilled water obtained per hour. 22) A power grid has a load pattern during one 24-hours period that averages 600 MW during 18 hours and 1200 MW during 6 hours. A turbine-pump storing system, with an elevation of 40 m is considered. Calculate : a. The power output of the plant, in MW, that would meet the load demand with and without storage, b. The volume, in m3, of water that must be pumped to meet the storage demand, if the overall efficiency of the hydro-electric plant is 0.75.
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4- Nuclear Power Plants 22) A PWR power plant producing 1260 kg/s of 75 bar saturated steam uses reheating. The high and low pressure turbines exhaust at 17 bar and 0.07 bar, respectively. For simplicity, assume that both the expansion in turbines and pumping are isentropic, there are no feed water heaters, and the reheater drain is returned to the steam generator. Calculate : a- The fraction of the live steam that is diverted to the reheater, if steam is reheated to 290oC. b- The cycle net power. c- The cycle efficiency. 23) A PWR has water inlet and exit temperatures at 290oC and 320oC, respectively. It has a 30 m3 vapour pressurizer which is normally 60% full of water at a pressure of 140 bar. A case of an insurge occurred during which 0.25 m3 of water entered the pressurizer from the primary circuit hot leg 0.05 m3 entered through the spray and 50 kWh was added by the electric heaters. Determine the internal energy of the pressurizer contents before and after the event, in kJ. Neglect heat losses to the ambient. 24) A pressurized-water reactor operating at 138 bar has primary water entering at 288oC and leaving at 320oC. A 28 m vapour pressurizer is normally half full of water. During a transient the pressure rose to 145 bar, 90 kg of spray water entered the pressurizer, and the pressurizer became 60% full of water. Ignoring heat losses to ambient, calculate the amount of heat added by the electric heaters. 25) A sodium cooled reactor has 140 m3 of primary coolant at an average temperature of 505oC. A cover gas of argon acts as a pressurizer. Calculate the volume of argon necessary to limit the pressure rise to 1% for a coolant temperature rise of 55oC. Assume the gas is compressed : a- Isothermally. b- Isentropically. 26) A boiling water reactor operating at a pressure of 70 bar produces 1200 kg/sec of saturated steam from feed water at 200oC. The average core exit quality is 10%. Calculate : a- The recirculation ratio. b- The core inlet enthalpy and temperature. c- The degree of subcooling. d- The heat generated in the reactor. 27) A 1000 MW boiling water reactor power plant with 33% efficiency was operating at 75% of rated load with steam mass flow rate of 1150 kg/sec, a reactor core pressure of 70 bar, and an average exit quality of 13.6%. The plant uses recirculation control. Calculate : a. The feed water temperature. b- The core degree of sub-cooling. c- The downcomer flow at 75% load. d- The average exit quality, immediately after initiation of load change to 80%, and when load has changed. e- The steam and downcomer flows after load change. 28 ) In a HTGR power plant, helium is used as a primary loop coolant. Helium circulators force it to the reactor top at 240 oC and 48 bar and leaves at the bottom at 760 oC. Helium then goes through the steam generators to the circulators inlet. The total pressure drop in the primary loop is 3 bar. In the working fluid loop, there are six typical steam generators. Each steam generator consists of an economizer, evaporation section, superheater and a reheater. Steam is generated at 166 bar and 510 oC. The steam expands in the high pressure turbine down to 38 bar. The steam then expands in an expander, derives the helium circulator, to 30 bar and goes to the reheater section, where its temperature increases to 538 oC. The steam then expands in intermediate and low pressure turbines to a condenser pressure of 0.09 bar. The internal efficiencies of the high pressure, intermediate pressure, low pressure turbines and expander are all 0.87. In the feed circuit, there are three feed water heaters, to rise the feed water temperature from 60 oC to 270 oC, with equal temperature rise. Draw the power plant flow sheet and then calculate : a. The temperature reached at the various points. b. The steam and helium mass flow rates, assuming combined mechanical and generator efficiency of 0.96. c. The heat generated in the reactor and the helium circulator power, for plant output of 1170 MW.
