Problem 91
A gas-turbine power plant operates on a simple Brayton cycle with air as the working fluid. The air enters the turbine at 120 psia and \(2000 \mathrm{R}\) and leaves at 15 psia and \(1200 \mathrm{R} .\) Heat is rejected to the surroundings at a rate of 6400 \(\mathrm{Btu} / \mathrm{s},\) and air flows through the cycle at a rate of \(40 \mathrm{lbm} / \mathrm{s}\) Assuming the turbine to be isentropic and the compresssor to have an isentropic efficiency of 80 percent, determine the net power output of the plant. Account for the variation of specific heats with temperature.
Problem 93
A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 800 kPa. Air enters the compressor at \(30^{\circ} \mathrm{C}\) and leaves at \(330^{\circ} \mathrm{C}\) at a mass flow rate of \(200 \mathrm{kg} / \mathrm{s}\). The maximum cycle temperature is \(1400 \mathrm{K}\). During operation of the cycle, the net power output is measured experimentally to be 60 MW. Assume constant properties for air at \(300 \mathrm{K}\) with \(c_{\mathrm{v}}=0.718 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}, c_{p}=\) \(1.005 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}, R=0.287 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}, k=1.4\) (a) Sketch the \(T\) -s diagram for the cycle. (b) Determine the isentropic efficiency of the turbine for these operating conditions. (c) Determine the cycle thermal efficiency.
Problem 94
A gas-turbine power plant operates on a modified Brayton cycle shown in the figure with an overall pressure ratio of \(8 .\) Air enters the compressor at \(0^{\circ} \mathrm{C}\) and \(100 \mathrm{kPa}\) The maximum cycle temperature is 1500 K. The compressor and the turbines are isentropic. The high pressure turbine develops just enough power to run the compressor. Assume constant properties for air at \(300 \mathrm{K}\) with \(c_{v}=0.718 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}\) \(c_{p}=1.005 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}, R=0.287 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}, k=1.4\) (a) Sketch the \(T\) -s diagram for the cycle. Label the data states. (b) Determine the temperature and pressure at state \(4,\) the exit of the high pressure turbine. (c) If the net power output is \(200 \mathrm{MW}\), determine mass flow rate of the air into the compressor, in \(\mathrm{kg} / \mathrm{s}\)
Problem 95
How does regeneration affect the efficiency of a Brayton cycle, and how does it accomplish it?
Problem 96
Somebody claims that at very high pressure ratios, the use of regeneration actually decreases the thermal efficiency of a gas-turbine engine. Is there any truth in this claim? Explain.
Problem 98
In \(1903,\) Aegidius Elling of Norway designed and built an 11 -hp gas turbine that used steam injection between the combustion chamber and the turbine to cool the combustion gases to a safe temperature for the materials available at the time. Currently there are several gas-turbine power plants that use steam injection to augment power and improve thermal efficiency. For example, the thermal efficiency of the General Electric LM5000 gas turbine is reported to increase from 35.8 percent in simple-cycle operation to 43 percent when steam injection is used. Explain why steam injection increases the power output and the efficiency of gas turbines. Also, explain how you would obtain the steam.
Problem 99
A gas turbine for an automobile is designed with a regenerator. Air enters the compressor of this engine at \(100 \mathrm{kPa}\) and \(30^{\circ} \mathrm{C}\). The compressor pressure ratio is \(10 ;\) the maximum cycle temperature is \(800^{\circ} \mathrm{C} ;\) and the cold air stream leaves the regenerator \(10^{\circ} \mathrm{C}\) cooler than the hot air stream at the inlet of the regenerator. Assuming both the compressor and the turbine to be isentropic, determine the rates of heat addition and rejection for this cycle when it produces 115 kW. Use constant specific heats at room temperature.
Problem 103
The idea of using gas turbines to power automobiles was conceived in the 1930 s, and considerable research was done in the \(1940 \mathrm{s}\) and \(1950 \mathrm{s}\) to develop automotive gas turbines by major automobile manufacturers such as the Chrysler and Ford corporations in the United States and Rover in the United Kingdom. The world's first gasturbine-powered automobile, the 200 -hp Rover Jet \(1,\) was built in 1950 in the United Kingdom. This was followed by the production of the Plymouth Sport Coupe by Chrysler in 1954 under the leadership of G. J. Huebner. Several hundred gas- turbine-powered Plymouth cars were built in the early 1960 s for demonstration purposes and were loaned to a select group of people to gather field experience. The users had no complaints other than slow acceleration. But the cars were never mass-produced because of the high production (especially material) costs and the failure to satisfy the provisions of the 1966 Clean Air Act. A gas-turbine-powered Plymouth car built in 1960 had a turbine inlet temperature of \(1700^{\circ} \mathrm{F}\), a pressure ratio of \(4,\) and a regenerator effectiveness of \(0.9 .\) Using isentropic efficiencies of 80 percent for both the compressor and the turbine, determine the thermal efficiency of this car. Also, determine the mass flow rate of air for a net power output of 130 hp. Assume the ambient air to be at \(510 \mathrm{R}\) and 14.5 psia.
Problem 107
A Brayton cycle with regeneration using air as the working fluid has a pressure ratio of \(7 .\) The minimum and maximum temperatures in the cycle are 310 and 1150 K. Assuming an isentropic efficiency of 75 percent for the compressor and 82 percent for the turbine and an effectiveness of 65 percent for the regenerator, determine \((a)\) the air temperature at the turbine exit, \((b)\) the net work output, and \((c)\) the thermal efficiency.
Problem 108
A stationary gas-turbine power plant operates on an ideal regenerative Brayton cycle \((\epsilon=100 \text { percent })\) with air as the working fluid. Air enters the compressor at \(95 \mathrm{kPa}\) and \(290 \mathrm{K}\) and the turbine at \(880 \mathrm{kPa}\) and \(1100 \mathrm{K}\). Heat is transferred to air from an external source at a rate of \(30,000 \mathrm{kJ} / \mathrm{s}\) Determine the power delivered by this plant (a) assuming constant specific heats for air at room temperature and ( \(b\) ) accounting for the variation of specific heats with temperature.
