169 CHAPTER FIVE GAS TURBINES AND JET ENGINES 5.1 Introduction History records over a century and a half of interest in and work on the gas turbine. However, the history of the gas turbine as a viable energy conversion device began with Frank Whittle's patent award on the jet engine in 1930 and his static test of a jet engine in 1937. Shortly thereafter, in 1939, Hans von Ohain led a German demonstration of jet-engine-powered flight, and the Brown Boveri company introduced a 4-MW gas-turbine-driven electrical power system in Neuchatel, Switzerland. The success of the gas turbine in replacing the reciprocating engine as a power plant for high-speed aircraft is well known. The development of the gas turbine was less rapid as a stationary power plant in competition with steam for the generation of electricity and with the spark-ignition and diesel engines in transportation and stationary applications. Nevertheless, applications of gas turbines are now growing at a rapid pace as research and development produces performance and reliability increases and economic benefits. 5.2 An Ideal Simple-Cycle Gas Turbine The fundamental thermodynamic cycle on which gas turbine engines are based is called the Brayton Cycle or Joule cycle. A temperature-entropy diagram for this ideal cycle and its implementation as a closed-cycle gas turbine is shown in Figure 5.1. The cycle consists of an isentropic compression of the gas from state 1 to state 2; a constant pressure heat addition to state 3; an isentropic expansion to state 4, in which work is done; and an isobaric closure of the cycle back to state 1. As Figure 5.1(a) shows, a compressor is connected to a turbine by a rotating shaft. The shaft transmits the power necessary to drive the compressor and delivers the balance to a power-utilizing load, such as an electrical generator. The turbine is similar in concept and in many features to the steam turbines discusssed earlier, except that it is designed to extract power from a flowing hot gas rather than from water vapor. It is important to recognize at the outset that the term "gas turbine" has a dual usage: It designates both the entire engine and the device that drives the compressor and the load. It should be clear from the context which meaning is intended. The equivalent term “combustion turbine” is also used occasionally, with the same ambiguity.
170 Like the simple Rankine-cycle power plant, the gas turbine may be thought of as a device that operates between two pressure levels, as shown in Figure 5.1(b). The compressor raises the pressure and temperature of the incoming gas to the levels of p2 and T2. Expansion of the gas through the turbine back to the lower pressure at this point would be useless, because all the work produced in the expansion would be required to drive the compressor.
171 Instead, it is necessary to add heat and thus raise the temperature of the gas before expanding it in the turbine. This is achieved in the heater by heat transfer from an external source that raises the gas temperature to T3, the turbine inlet temperature. Expansion of the hot gas through the turbine then delivers work in excess of that needed to drive the compressor. The turbine work exceeds the compressor requirement because the enthalpy differences, and hence the temperature differences, along isentropes connecting lines of constant pressure increase with increasing entropy (and temperature), as the figure suggests. The difference between the turbine work, Wt, and the magnitude of the compressor work, |Wc|, is the net work of the cycle. The net work delivered at the output shaft may be used to drive an electric generator, to power a process compressor, turn an airplane propeller, or to provide mechanical power for some other useful activity. In the closed-cycle gas turbine, the heater is a furnace in which combustion gases or a nuclear source transfer heat to the working fluid through thermally conducting tubes. It is sometimes useful to distinguish between internal and external combustion engines by whether combustion occurs in the working fluid or in an area separate from the working fluid, but in thermal contact with it. The combustion-heated, closed-cycle gas turbine is an example, like the steam power plant, of an external combustion engine. This is in contrast to internal combustion engines, such as automotive engines, in which combustion takes place in the working fluid confined between a cylinder and a piston, and in open-cycle gas turbines. 5.3 Analysis of the Ideal Cycle The Air Standard cycle analysis is used here to review analytical techniques and to provide quantitative insights into the performance of an ideal-cycle engine. Air Standard cycle analysis treats the working fluid as a calorically perfect gas, that is, a perfect gas with constant specific heats evaluated at room temperature. In Air Standard cycle analysis the heat capacities used are those for air. A gas turbine cycle is usually defined in terms of the compressor inlet pressure and temperature, p1 and T1, the compressor pressure ratio, r = p2/p1, and the turbine inlet temperature, T3, where the subscripts correspond to states identified in Figure 5.1. Starting with the compressor, its exit pressure is determined as the product of p1 and the compressor pressure ratio. The compressor exit temperature may then be determined by the familiar relation for an isentropic process in an ideal gas, Equation (1.19): T2 = T1( p2 /p1)(k–1)/k [R | K] (5.1) For the two isobaric processes, p2 = p3 and p4 = p1. Thus the turbine pressure ratio, p3/p4, is equal to the compressor pressure ratio, r = p2 /p1. With the turbine inlet temperature T3 known, the turbine discharge temperature can be determined from T4 = T3/( p2/p1)(k–1)/k [R | K] (5.2)
172 and the temperatures and pressures are then known at all the significant states. Next, taking a control volume around the compressor, we determine the shaft work required by the compressor, wc, assuming negligible heat losses, by applying the steady-flow energy equation: 0 = h2 – h1 + wc or wc = h1 – h2 = cp( T1 – T2) [Btu/lbm | kJ/kg] (5.3) Similarly, for the turbine, the turbine work produced is wt = h3 - h4 = cp ( T3 – T4) [Btu/lbm | kJ/kg] (5.4) The net work is then wn = wt + wc = cp ( T3 – T4 + T1 – T2) [Btu/lbm | kJ/kg] (5.5) Now taking the control volume about the heater, we find that the heat addition per unit mass is qa = h3 – h2 = cp ( T3 – T2) [Btu/lbm | kJ/kg] (5.6) The cycle thermal efficiency is the ratio of the net work to the heat supplied to the heater: th = wn /qa [dl] (5.7) which by substitution of Equations (5.1), (5.2), (5.5), and (5.6) may be simplified to th = 1 – ( p2/p1) – (k–1)/k [dl] (5.8) It is evident from Equation (5.8) that increasing the compressor pressure ratio increases thermal efficiency. Another parameter of great importance to the gas turbine is the work ratio, wt /|wc|. This parameter should be as large as possible, because a large amount of the power delivered by the turbine is required to drive the compressor, and because the engine net work depends on the excess of the turbine work over the compressor work. A little algebra will show that the work ratio wt /|wc| can be written as: wt /|wc| = (T3 /T1) / ( p2 /p1) (k–1)/k [dl] (5.9)