Chapter 9

Is the effect of turbine and compressor irreversibilities of a turbojet engine to reduce \((a)\) the net work, \((b)\) the thrust, or \((c)\) the fuel consumption rate?

A turbojet is flying with a velocity of \(900 \mathrm{ft} / \mathrm{s}\) at an altitude of \(20,000 \mathrm{ft}\), where the ambient conditions are 7 psia and \(10^{\circ} \mathrm{F}\). The pressure ratio across the compressor is \(13,\) and the temperature at the turbine inlet is 2400 R. Assuming ideal operation for all components and constant specific heats for air at room temperature, determine ( \(a\) ) the pressure at the turbine exit, \((b)\) the velocity of the exhaust gases, and \((c)\) the propulsive efficiency.

A turbofan engine operating on an aircraft flying at \(200 \mathrm{m} / \mathrm{s}\) at an altitude where the air is at \(50 \mathrm{kPa}\) and \(-20^{\circ} \mathrm{C}\) is to produce \(50,000 \mathrm{N}\) of thrust. The inlet diameter of this engine is \(2.5 \mathrm{m} ;\) the compressor pressure ratio is \(12 ;\) and the mass flow rate ratio is \(8 .\) Determine the air temperature at the fan outlet needed to produce this thrust. Assume ideal operation for all components and constant specific heats at room temperature.

A turbojet aircraft is flying with a velocity of \(280 \mathrm{m} / \mathrm{s}\) at an altitude of \(9150 \mathrm{m},\) where the ambient conditions are \(32 \mathrm{kPa}\) and \(-32^{\circ} \mathrm{C} .\) The pressure ratio across the compressor is \(12,\) and the temperature at the turbine inlet is 1100 K. Air enters the compressor at a rate of \(50 \mathrm{kg} / \mathrm{s}\), and the jet fuel has a heating value of \(42,700 \mathrm{kJ} / \mathrm{kg}\). Assuming ideal operation for all components and constant specific heats for air at room temperature, determine ( \(a\) ) the velocity of the exhaust gases, \((b)\) the propulsive power developed, and \((c)\) the rate of fuel consumption.

Consider an aircraft powered by a turbojet engine that has a pressure ratio of \(9 .\) The aircraft is stationary on the ground, held in position by its brakes. The ambient air is at \(7^{\circ} \mathrm{C}\) and \(95 \mathrm{kPa}\) and enters the engine at a rate of \(20 \mathrm{kg} / \mathrm{s}\) The jet fuel has a heating value of \(42,700 \mathrm{kJ} / \mathrm{kg},\) and it is burned completely at a rate of \(0.5 \mathrm{kg} / \mathrm{s}\). Neglecting the effect of the diffuser and disregarding the slight increase in mass at the engine exit as well as the inefficiencies of engine components, determine the force that must be applied on the brakes to hold the plane stationary.

Air at \(7^{\circ} \mathrm{C}\) enters a turbojet engine at a rate of \(16 \mathrm{kg} / \mathrm{s}\) and at a velocity of \(300 \mathrm{m} / \mathrm{s}\) (relative to the engine). Air is heated in the combustion chamber at a rate \(15,000 \mathrm{kJ} / \mathrm{s}\) and it leaves the engine at \(427^{\circ} \mathrm{C}\). Determine the thrust produced by this turbojet engine. (Hint: Choose the entire engine as your control volume.

Calculate the exergy destruction for each process of Stirling cycle of Prob. \(9-74,\) in \(\mathrm{kJ} / \mathrm{kg}\)

A gas-turbine power plant operates on the regenerative Brayton cycle between the pressure limits of 100 and \(700 \mathrm{kPa}\). Air enters the compressor at \(30^{\circ} \mathrm{C}\) at a rate of \(12.6 \mathrm{kg} / \mathrm{s}\) and leaves at \(260^{\circ} \mathrm{C}\). It is then heated in a regenerator to \(400^{\circ} \mathrm{C}\) by the hot combustion gases leaving the turbine. A diesel fuel with a heating value of \(42,000 \mathrm{kJ} / \mathrm{kg}\) is burned in the combustion chamber with a combustion efficiency of 97 percent. The combustion gases leave the combustion chamber at \(871^{\circ} \mathrm{C}\) and enter the turbine whose isentropic efficiency is 85 percent. Treating combustion gases as air and using constant specific heats at \(500^{\circ} \mathrm{C}\), determine (a) the isentropic efficiency of the compressor, ( \(b\) ) the effectiveness of the regenerator, \((c)\) the air-fuel ratio in the combustion chamber, \((d)\) the net power output and the back work ratio, \((e)\) the thermal efficiency, and \((f)\) the second-law efficiency of the plant. Also determine \((g)\) the second-law efficiencies of the compressor, the turbine, and the regenerator, and \((h)\) the rate of the energy flow with the combustion chamber with a combustion efficiency of 97 percent. The combustion gases leave the combustion chamber at \(871^{\circ} \mathrm{C}\) and enter the turbine whose isentropic efficiency is 85 percent. Treating combustion gases as air and using constant specific heats at \(500^{\circ} \mathrm{C}\), determine (a) the isentropic efficiency of the compressor, (b) the effectiveness of the regenerator, (c) the air-fuel ratio in the combustion chamber, \((d)\) the net power output and the back work ratio, \((e)\) the thermal efficiency, and \((f)\) the second-law efficiency of the plant. Also determine \((g)\) the second-law efficiencies of the compressor, the turbine, and the regenerator, and \((h)\) the rate of the energy flow with the combustion gases at the regenerator exit.

A four-cylinder, four-stroke, 1.8 -liter modern, highspeed compression- ignition engine operates on the ideal dual cycle with a compression ratio of \(16 .\) The air is at \(95 \mathrm{kPa}\) and \(70^{\circ} \mathrm{C}\) at the beginning of the compression process and the engine speed is 2200 rpm. Equal amounts of fuel are burned at constant volume and at constant pressure. The maximum allowable pressure in the cycle is 7.5 MPa due to material strength limitations. Using constant specific heats at \(1000 \mathrm{K}\) determine \((a)\) the maximum temperature in the cycle, \((b)\) the net work output and the thermal efficiency, (c) the mean effective pressure, and \((d)\) the net power output. Also, determine \((e)\) the second-law efficiency of the cycle and the rate of energy output with the exhaust gases when they are purged.

An Otto cycle with a compression ratio of 10.5 begins its compression at \(90 \mathrm{kPa}\) and \(35^{\circ} \mathrm{C}\). The maximum cycle temperature is \(1000^{\circ} \mathrm{C}\). Utilizing air-standard assumptions, determine the thermal efficiency of this cycle using (a) constant specific heats at room temperature and (b) variable specific heats.