Thermodynamics (ME22002), IIT Kharagpur, Spring 2006
Problem Set on Air Standard Cycles 1.
A stoichiometric mixture of gasoline and air has an energy release upon combustion of approximately 2800 kJ/kg of the mixture. To approximate an actual spark- ignition engine using such a mixture, consider an air-standard Otto cycle that has a heat addition of 2800 kJ/kg of air, a compression ratio of 7, and a pressure and temperature at the beginning of the compression process of 90 kPa, 10°C. Assuming constant specific heat, with the value from Table A.l0, determine a) The maximum pressure and temperature of the cycle. b) The thermal efficiency of the cycle. c) The mean effective pressure.
2. In the air-standard Otto cycle, all the heat transfer qh occurs at constant volume. It would be more realistic to assume that part of qh occurs after the piston has started its downward motion in the expansion stroke. Therefore, consider a cycle identical to the Otto cycle, except that the first two-thirds of the total qh occurs at constant volume and the last one-third occurs at constant pressure. Assume that the total qh is 2400 kJ/kg, that the pressure and temperature at the beginning of the compression process are 90 kPa, 20°C, and that the comparison ratio is 7 Calculate the maximum pressure and temperature and the thermal efficiency of this cycle. Compare the results with those of a conventional Otto cycle having the same given variables. 3. Consider an ideal air-standard diesel cycle in which the state before the compression process is 95 kPa, 290 K, and the compression ratio is 20. What maximum temperature must the cycle have to have a thermal efficiency of 60%? 4. An air-standard Ericsson cycle has an ideal regenerator. Heat is supplied at
1600 K. The minimum pressure in the cycle is 100 kPa, and the compressor pressure ratio is 14 to 1. a) Calculate the power output of the turbine. What fraction of the turbine output is required to drive the compressor? b) What is the thermal efficiency of the cycle? 7. Repeat Problem 6, but assuming that the compressor has an isentropic efficiency of 85% and the turbine an isentropic efficiency of 88%. 8. The gas turbine cycle shown in the figure below is to be used as an automotive engine. In the first turbine, the gas expands to a pressure P5, just low enough for this turbine to drive the compressor. The gas is then expanded through the second turbine connected to the drive wheels. The data for this engine are shown in the figure. Consider the working fluid to be air throughout the entire cycle, and assume that all processes are ideal. Determine. a) The intermediate pressure P5. b) The net specific work output of the engine, and the mass flow rate through the engine. c) The air temperature entering the burner T3, and the thermal efficiency of the engine. 7
=150 kW
Thermodynamics (ME22002), IIT Kharagpur, Spring 2006
Problem Set on Vapour Cycles 0
1. A steam power plant has a boiler exit at 4MPa, 500 C and a condenser exit 0 temperature of 45 C. Assume all components are ideal and find the cycle efficiency and the specific work and heat transfer in the components. 2. Consider a simple ideal Rankine cycle that uses steam as the working fluid. The high–pressure side of the cycle is at a supercritical pressure. Such a cycle has a potential advantage of minimizing local temperature differences between the fluids in the steam generator, such as the instance in which the high–temperature energy source is the hot exhaust gas from a gas–turbine engine. Calculate the 0 thermal efficiency of the cycle if the state entering the turbine is 25 MPa, 500 C, and the condenser pressure is 5 kPa. What is the steam quality at the turbine exit? 3. Consider an ideal steam regenerative cycle in which steam enters the turbine at 3.5 MPa, 400°C, and exhausts to the condenser at 10 kPa. Steam is extracted from the turbine at 0.8 MPa and also at 0.2 MPa for heating the boiler feed water in two open feed water heaters. The feed water leaves each heater at the temperature of the condensing steam. The appropriate pumps are used for the water leaving the con- denser and the two feed water heaters. Calculate the thermal efficiency of the cycle and the net work per kilogram of steam. 4. Consider an ideal steam combined reheat and regenerative cycle in which steam enters the high-pressure turbine at 3.5 MPa, 400°C, and is extracted for feed water heating at 0.8 MPa. The remainder of the steam is reheated to 400°C at this pressure, 0.8 MPa, and is fed to the low-pressure turbine. Steam is extracted from the low-pressure turbine at 0.2 MPa for feed water heating. The condenser pressure is 10 kPa. Both feed water heaters are open heaters. Calculate the thermal efficiency of the cycle and the net work per kilogram of steam.
6.
Steam leaves a power plant steam generator at 3.5 MPa, 400°C, and enters the turbine at 3.4 MPa, 375°C. The isentropic turbine efficiency is 88%, and the turbine exhaust pressure is 10 kPa. Condensate leaves the condenser and enters the pump at 35°C, 10 kPa. The isentropic pump efficiency is 80%, and the discharge pressure is 3.7 MPa. The feed water enters the steam generator at 3.6 MPa, 30°C. Calculate the following. a. The thermal efficiency of the cycle. b. The irreversibility of the process in the line between the steam generator exit and the turbine inlet, assuming an ambient temperature of 25°C.
7.
For the steam power plant described in Problem 1, assume the isentropic efficiencies of the turbine and pump are 85% and 80%, respectively. Find the component specific work and heat transfers and the cycle efficiency.
8.
Find the availability .of the water at all the states in the steam power plant described in the previous problem. Assume. The heat source in the boiler is at 600"C and the low-temperature reservoir is at 25°C. Give the second law efficiency of all the components.
9.
In a particular reheat-cycle power plant, steam enters the high-pressure turbine at 5 MPa, 450°C and expands to 0.5 MPa, after which it is reheated to 450°C. The steam is then expanded through the low-pressure turbine to 7.5 kPa. Liquid water leaves the condenser at 30°C, is pumped to 5 MPa, and then returned to the steam generator. Each turbine is adiabatic with an isentropic efficiency of 87% and the pump efficiency is 82%. If the total power outpu t of the turbines is 10 MW, determine a. The mass flow rate of steam b. The pump power input c. The thermal efficiency of the power plant
