Chapter 3: Gas Power Cycle PDF

Mataria Faculty of Engineering Mechanical Power Department POWER STATION CHAPTER GAS POWER CYCLE Assoc. Prof. Dr. Mohamed A. A. Nawar Dr. Eng. Ahmed T. M. Kotb Mechanical Power Engineering Department Mechanical...

Mataria Faculty of Engineering Mechanical Power Department POWER STATION CHAPTER GAS POWER CYCLE Assoc. Prof. Dr. Mohamed A. A. Nawar Dr. Eng. Ahmed T. M. Kotb Mechanical Power Engineering Department Mechanical Power Engineering Department Faculty of Engineering-Mattaria Faculty of Engineering-Mattaria Helwan University Helwan University Cairo 2024 PLEASE  Lecture Outlines 1. Introduction 2. Brayton cycle 3. Evaluating Principal Work and Heat Transfers 4. Effect of pressure ratio on performance 5. Gas turbine irreversibilities and losses 6. Gas Turbines with Regeneration 7. Gas Turbines with Reheat 8. Gas Turbines with Compression with Intercooling 9. Regeneration, Reheat, and Intercooling 10. Gas Turbines for Aircraft Propulsion 11. Other Applications 12. Combined Gas Turbine–Vapor Power Cycle 1- Introduction In comparison to the vapor power plants covered in earlier chapters, gas turbines are often lighter and more compact. Gas turbines are highly suited for transportation applications (plane propulsion, maritime power plants, etc.) because of their advantageous power output-to-weight ratio. Gas turbines are frequently employed for the generation of stationary power. 2- Brayton cycle Gas turbines usually operate on an open cycle, as shown in following figure. Fresh air in ambient conditions is drawn into the compressor, where its temperature and pressure are raised. The high-pressure air proceeds into the combustion chamber, where the fuel is burned at constant pressure. 2- Brayton cycle The resulting high-temperature gases then enter the turbine, where they expand to the atmospheric pressure while producing power. The exhaust gases leaving the turbine are thrown out (not recirculated), causing the cycle to be classified as an open cycle. The open gas-turbine cycle just described can be modeled as a closed cycle, as shown in following figure, by using the air-standard assumptions. An idealization often used in the study of open gas turbine power plants is that of an air-standard analysis. 2- Brayton cycle In an air-standard analysis two assumptions are always made: 1. The working fluid is air, which behaves as an ideal gas. 2. The temperature rise that would be brought about by combustion is accomplished by a heat transfer from an external source. Here the compression and expansion processes remain the same, but the combustion process is replaced by a constant-pressure heat-addition process from an external source, and the exhaust process is replaced by a constant- pressure heat-rejection process to the ambient air. 2- Brayton cycle The ideal cycle that the working fluid undergoes in this closed loop is the Brayton cycle, which is made up of four internally reversible processes: 1-2 Isentropic compression (in a compressor) 2-3 Constant-pressure heat addition 3-4 Isentropic expansion (in a turbine) 4-1 Constant-pressure heat rejection 2- Brayton cycle With an air-standard analysis, we avoid dealing with the complexities of the combustion process and the change of composition during combustion. An air-standard analysis simplifies the study of gas turbine power plants considerably. However, numerical values calculated on this basis may provide only qualitative indications of power plant performance. Sufficient information about combustion and the properties of products of combustion is known and the study of gas turbines can be conducted without the foregoing assumptions. Still, we can learn some important aspects of gas turbine operation by proceeding based on an air-standard analysis, as follows. 3- Evaluating Principal Work and Heat Transfers The following expressions for the work and heat transfers of energy that occur at steady state are readily derived by reduction of the control volume mass and energy rate balances. Assuming the turbine operates adiabatically and with negligible effects of kinetic and potential energy, the work developed per unit of mass is Ẇ𝒕 = 𝒉𝟑 − 𝒉𝟒 (𝟏) ṁ where ṁ denotes the mass flow rate. With the same assumptions, the compressor work per unit of mass is Ẇ𝒄 = 𝒉𝟐 − 𝒉𝟏 (𝟐) ṁ 3- Evaluating Principal Work and Heat Transfers The heat added to the cycle per unit of mass is 𝑸𝒊𝒏 = 𝒉𝟑 − 𝒉𝟐 (𝟑) ṁ The heat rejected per unit of mass is 𝑸𝒐𝒖𝒕 = 𝒉𝟒 − 𝒉𝟏 (𝟒) ṁ The thermal efficiency of the cycle is Ẇ𝒕ൗ Ẇ𝒄ൗ ṁ − ṁ = 𝒉𝟑 − 𝒉𝟒 − 𝒉𝟐 − 𝒉𝟏 (𝟓) 𝜼= 𝑸𝒊𝒏ൗ 𝒉𝟑 − 𝒉 𝟐 ṁ 3- Evaluating Principal Work and Heat Transfers The back-work ratio for the cycle is Ẇ𝐜ൗ ṁ 𝒉𝟐 − 𝒉𝟏 𝒃𝒘𝒓 = = (𝟔) Ẇ𝐭ൗ 𝒉𝟑 − 𝒉𝟒 ṁ For the same pressure rise, a gas turbine compressor would require a much greater work input per unit of mass flow than the pump of a vapor power plant because the average specific volume of the gas flowing through the compressor would be many times greater than that of the liquid passing through the pump. Hence, a relatively large portion of the work developed by the turbine is required to drive the compressor. Typical back-work ratios of gas turbines is about 66%. In comparison, the back work ratios of vapor power plants are normally only 1 or 2%. 3- Evaluating Principal Work and Heat Transfers If the temperatures at the numbered states of the cycle are known, the specific enthalpies required by the foregoing equations are readily obtained from the ideal gas table for air properties. Alternatively, with the sacrifice of some accuracy, the variation of the specific heats with temperature can be ignored and the specific heats taken as constant. Since Eqs. 1 through 6 have been developed from mass and energy rate balances, they apply equally when irreversibilities are present and in the absence of irreversibilities. Although irreversibilities and losses associated with the various power plant components have a pronounced effect on overall performance, it is instructive to consider an idealized cycle in which they are assumed absent. Such a cycle establishes an upper limit on the performance of the air-standard Brayton cycle. 3- Evaluating Principal Work and Heat Transfers Ignoring irreversibilities as the air circulates through the various components of the Brayton cycle, there are no frictional pressure drops, and the air flows at constant pressure through the heat exchangers. If stray heat transfers to the surroundings are also ignored, the processes through the turbine and compressor are isentropic. The ideal cycle shown in the p–v and T–s diagrams in following figure adheres to these idealizations. 3- Evaluating Principal Work and Heat Transfers Areas on the T–s and p–v diagrams of following figure can be interpreted as heat and work, respectively, per unit of mass flowing. On the T–s diagram, area 2–3–a–b–2 represents the heat added per unit of mass, and area 1–4–a–b–1 is the heat rejected per unit of mass. On the p–v diagram, area 1–2–a–b–1 represents the compressor work input per unit of mass, and area 3–4–b–a–3 is the turbine work output per unit of mass. The enclosed area on each figure can be interpreted as the network output or, equivalently, the net heat added. 3- Evaluating Principal Work and Heat Transfers When air table data are used to conduct an analysis involving the ideal Brayton cycle, the following relationships apply to the isentropic processes 1–2 and 3–4 Since the air flows through the heat exchangers of the ideal cycle at constant pressure, it follows that 𝒑𝟒Τ𝒑𝟑 = 𝒑𝟏Τ𝒑𝟐. When an ideal Brayton cycle is analyzed on a cold air-standard basis, the specific heats are taken as constant. (𝒌−𝟏)ൗ 𝒑𝟐 𝒌 𝑻𝟐 = 𝑻𝟏 𝒑𝟏 (𝒌−𝟏)ൗ (𝒌−𝟏)ൗ 𝒑𝟒 𝒌 𝒑𝟏 𝒌 𝑻𝟒 = 𝑻𝟑 = 𝑻𝟑 𝒑𝟑 𝒑𝟐 𝒄 where k is the specific heat ratio, k = 𝒑ൗ𝒄𝒗. 4- Effect of pressure ratio on performance Conclusions that are qualitatively correct for actual gas turbines can be drawn from a study of the ideal Brayton cycle. The first of these conclusions is that the thermal efficiency increases with increasing pressure ratio across the compressor. For example, referring again to the T–s diagram, we see that an increase in the pressure ratio changes the cycle from 1–2–3–4–1 to 1–2՝–3՝–4–1. Since the average temperature of heat addition is greater in the latter cycle and both cycles have the same heat rejection process, cycle 1–2՝–3՝–4–1 would have the greater thermal efficiency. 4- Effect of pressure ratio on performance The increase in thermal efficiency with the pressure ratio across the compressor is also brought out simply by the following development, in which the specific heat cp, and thus the specific heat ratio k, is assumed constant. For constant cp, 𝒄𝒑 𝑻 𝟑 − 𝑻 𝟒 − 𝒄𝒑 𝑻 𝟐 − 𝑻 𝟏 𝑻𝟒 − 𝑻𝟏 𝜼= =𝟏− 𝒄𝒑 𝑻 𝟑 − 𝑻 𝟐 𝑻𝟑 − 𝑻𝟐 𝑻𝟒 ൗ 𝑻𝟏 𝑻𝟏 − 𝟏 𝜼= 𝟏− 𝑻𝟐 𝑻𝟑 ൗ − 𝟏 𝑻𝟐 𝑻𝟒൘ = 𝑻𝟑൘ 𝑻𝟏 𝑻𝟐 𝑻𝟏 𝜼= 𝟏− 𝑻𝟐 𝟏 𝜼= 𝟏− 𝒌−𝟏 Τ𝒌 𝒑𝟐ൗ 𝒑𝟏 4- Effect of pressure ratio on performance The cold air-standard ideal Brayton cycle thermal efficiency is a function of the pressure ratio across the compressor. This relationship is shown for k = 1.4. There is a limit of about 1700 K imposed by metallurgical considerations on the maximum allowed temperature at the turbine inlet. It is instructive therefore to consider the effect of compressor pressure ratio on thermal efficiency when the turbine inlet temperature is restricted to the maximum allowable temperature. 4- Effect of pressure ratio on performance The T–s diagrams of two ideal Brayton cycles having the same turbine inlet temperature but different compressor pressure ratios are shown in following figure. Cycle A has a greater pressure ratio than cycle B and thus greater thermal efficiency. However, cycle B has a larger enclosed area, and thus the greater network developed per unit of mass flow. Accordingly, for cycle, A to develop the same net power output as cycle B, a larger mass flow rate would be required, and this might dictate a larger system. 4- Effect of pressure ratio on performance For a fixed turbine inlet temperature, the net work output per cycle increases with the pressure ratio, reaches a maximum, and then starts to decrease. With less work output per cycle, a larger mass flow rate (thus a larger system) is needed to maintain the same power output, which may not be economical. In most common designs, the pressure ratio of gas turbines ranges from about 11 to 16. 4- Effect of pressure ratio on performance 𝑾𝒏𝒆𝒕 = 𝒄𝒑 𝑻𝟑 − 𝑻𝟒 − 𝒄𝒑 𝑻𝟐 − 𝑻𝟏 𝑾𝒏𝒆𝒕 = 𝒄𝒑 𝑻𝟑 − 𝑻𝟒 − 𝑻𝟐 − 𝑻𝟏 𝑻𝟒 𝑻𝟐 𝑾𝒏𝒆𝒕 = 𝒄𝒑 𝑻𝟑 𝟏− − 𝑻𝟏 −𝟏 𝑻𝟑 𝑻𝟏 𝑻𝟑 𝑻𝟒 𝑻𝟐 𝑾𝒏𝒆𝒕 = 𝒄𝒑 𝑻𝟏 𝟏− − −𝟏 𝑻𝟏 𝑻𝟑 𝑻𝟏 𝑾𝒏𝒆𝒕 𝟏−𝒌 𝒌−𝟏 = 𝒕 𝟏 − 𝒑𝒓 𝒌 − 𝒑𝒓 𝒌 − 𝟏 𝒄𝒑 𝑻𝟏 𝑻𝟑 𝒕= 𝑻𝟏 4- Effect of pressure ratio on performance 𝑾𝒏𝒆𝒕 𝟏−𝒌 𝒌−𝟏 = 𝒕 𝟏 − 𝒑𝒓 𝒌 − 𝒑𝒓 𝒌 − 𝟏 𝒄𝒑 𝑻𝟏 1.2 1.0 0.8 Wnet/Cp T1 t=2 t=3 0.6 t=4 0.4 0.2 0.0 0 5 10 15 20 25 pr 5- Gas turbine irreversibilities and losses The principal state points of an air-standard gas turbine might be shown more realistically as in following figure. Because of frictional effects within the compressor and turbine, the working fluid would experience increases in specific entropy across these components. Owing to friction, there also would be pressure drops as the working fluid passes through the heat exchangers. 5- Gas turbine irreversibilities and losses However, because frictional pressure drops are less significant sources of irreversibility, we ignore them in subsequent discussions and for simplicity show the flow through the heat exchangers as occurring at constant pressure. This is illustrated by following figure. Stray heat transfers from the power plant components to the surroundings represent losses, but these effects are usually of secondary importance and are also ignored in subsequent discussions. 5- Gas turbine irreversibilities and losses As the effect of irreversibilities in the turbine and compressor becomes more pronounced, the work developed by the turbine decreases and the work input to the compressor increases, resulting in a marked decrease in the network of the power plant. Accordingly, if an appreciable amount of network is to be developed by the plant, relatively high turbine and compressor efficiencies are required. After decades of developmental effort, efficiencies of 80 to 90% can now be achieved for the turbines and compressors in gas turbine power plants. 5- Gas turbine irreversibilities and losses Designating the states as in following figure, the isentropic turbine and compressor efficiencies are given by Ẇ𝒕 Τ ṁ 𝒉 − 𝒉𝟒 𝜼𝒕 = = 𝟑 Ẇ𝒕 Τ ṁ 𝒔 𝒉𝟑 − 𝒉𝟒𝒔 Ẇ𝒄 Τ ṁ 𝒔 𝒉 − 𝒉𝟏 𝜼𝒄 = = 𝟐𝒔 Ẇ𝒄 Τ ṁ 𝒉𝟐 − 𝒉𝟏 The effects of irreversibilities in the turbine and compressor are important. Still, among the irreversibilities of actual gas turbine power plants, combustion irreversibility is the most significant by far. An air-standard analysis does not allow this irreversibility to be evaluated. 6- Gas Turbines with Regeneration Three modifications of the basic gas turbine that increase the network developed are regeneration, multistage expansion with reheat, and multistage compression with intercooling. These modifications can result in substantial increases in thermal efficiency. The turbine exhaust temperature of a gas turbine is normally well above the ambient temperature. Accordingly, the hot turbine exhaust gas has a potential for use (exergy) that would be irrevocably lost were the gas discarded directly to the surroundings. One way of utilizing this potential is using a heat exchanger called a regenerator, which allows the air exiting the compressor to be preheated before entering the combustor, thereby reducing the amount of fuel that must be burned in the combustor. 6- Gas Turbines with Regeneration The combined cycle is another way to utilize the hot turbine exhaust gas. The regenerator shown is a counterflow heat exchanger through which the hot turbine exhaust gas and the cooler air leaving the compressor pass in opposite directions. Ideally, no frictional pressure drop occurs in either stream. The turbine exhaust gas is cooled from state 4 to state y, while the air exiting the compressor is heated from state 2 to state x. 6- Gas Turbines with Regeneration Hence, a heat transfer from a source external to the cycle is required only to increase the air temperature from state x to state 3, rather than from state 2 to state 3, as would be the case without regeneration. The heat added per unit of mass is then given by 𝑸𝒊𝒏 = 𝒉𝟑 − 𝒉𝒙 ṁ The network developed per unit of mass flow is not altered (ideally) by the addition of a regenerator. Thus, since the heat added is reduced, the thermal efficiency increases. 6- Gas Turbines with Regeneration Regenerator effectiveness. The external heat transfer required by a gas turbine power plant decreases as the specific enthalpy hx increases and thus as the temperature Tx increases. There is an incentive in terms of fuel saved for selecting a regenerator that provides the greatest practical value for this temperature. To consider the maximum theoretical value for Tx, refer to following figure, which shows temperature variations of the hot and cold streams of a counterflow heat exchanger. (a) Actual. (b) Reversible 6- Gas Turbines with Regeneration Regenerator effectiveness. First, refer to following figure (a). Since a finite temperature difference between the streams is required for heat transfer to occur, the temperature of the cold stream at each location, denoted by the coordinate z, is less than that of the hot stream. In particular, the temperature of the colder stream as it exits the heat exchanger is less than the temperature of the incoming hot stream. If the heat transfer area were increased, providing more opportunity for heat transfer between the two streams, there would be a smaller temperature difference (a) Actual. at each location. 6- Gas Turbines with Regeneration Regenerator effectiveness. In the limiting case of infinite heat transfer area, the temperature difference would approach zero at all locations, as illustrated in following figure, and the heat transfer would approach reversibility. In this limit, the exit temperature of the colder stream would approach the temperature of the incoming hot stream. Thus, the highest possible temperature that could be achieved by the colder stream is the temperature (b) Reversible. of the incoming hot gas. 6- Gas Turbines with Regeneration Regenerator effectiveness. The maximum theoretical value for the temperature Tx is the turbine exhaust temperature T4, obtained if the regenerator were operating reversibly. The regenerator effectiveness, ηreg, is a parameter that gauges the departure of an actual regenerator from such an ideal regenerator. The regenerator effectiveness is defined as the ratio of the actual enthalpy increase of the air flowing through the compressor side of the regenerator to the maximum theoretical enthalpy increase. That is, 𝒉𝒙 − 𝒉𝟐 𝜼𝒓𝒆𝒈 = 𝒉𝟒 − 𝒉𝟐 6- Gas Turbines with Regeneration Regenerator effectiveness. As heat transfer approaches reversibility, hx approaches h4 and η_reg tends to unity (100%). In practice, regenerator effectiveness values typically range from 60 to 80%, and thus the temperature Tx of the air exiting on the compressor side of the regenerator is normally well below the turbine exhaust temperature. Increasing the effectiveness above this range would require greater heat transfer area, resulting in equipment costs that might cancel any advantage due to fuel savings. Moreover, the greater heat transfer area that would be required for larger effectiveness can result in a significant frictional pressure drop for flow through the regenerator, thereby affecting overall performance. The decision to add a regenerator is influenced by considerations such as these, and the final decision is primarily an economic one. 6- Gas Turbines with Regeneration Regenerator effectiveness. From the computer data, we see that the cycle thermal efficiency increases from 0.456 (no regenerator) to 0.567 for a regenerator effectiveness of 80%. Regenerator effectiveness is seen to have a significant effect on cycle thermal efficiency. 7- Gas Turbines with Reheat For metallurgical reasons, the temperature of the gaseous combustion products entering the turbine must be limited. This temperature can be controlled by providing air more than the amount required to burn the fuel in the combustor. Therefore, the gases exiting the combustor contain sufficient air to support the combustion of additional fuel. Some gas turbine power plants take advantage of the excess air through a multistage turbine with a reheat combustor between the stages. With this arrangement, the network per unit of mass flow can be increased. Let us consider reheating from the vantage point of an air-standard analysis. 7- Gas Turbines with Reheat The basic features of a two-stage gas turbine with reheat are brought out by considering an ideal air-standard Brayton cycle modified as shown in following figure. After expansion from state 3 to state a in the first turbine, the gas is reheated at constant pressure from state a to state b. The expansion is then completed in the second turbine from state b to state 4. The ideal Brayton cycle without reheat, 1–2–3–4՝–1, is shown on the same T–s diagram for comparison. 7- Gas Turbines with Reheat Because lines of constant pressure on a T–s diagram diverge slightly with increasing entropy, the total work of the two-stage turbine is greater than that of a single expansion from state 3 to state 4՝. Thus, the network for the reheat cycle is greater than that of the cycle without reheat. Despite the increase in network with reheat, the cycle thermal efficiency would not necessarily increase because a greater total heat addition would be required. 7- Gas Turbines with Reheat However, the temperature at the exit of the turbine is higher with reheat than without reheat, so the potential for regeneration is enhanced. When reheat and regeneration are used together, the thermal efficiency can increase significantly. 8- Gas Turbines with Compression with Intercooling The network output of a gas turbine also can be increased by reducing the compressor work input. This can be accomplished by employing multistage compression with intercooling. Let us first consider the work input to compressors at a steady state, assuming that irreversibilities are absent and changes in kinetic and potential energy from inlet to exit are negligible. The p–v diagram of following figure shows two possible compression paths from a specified state 1 to a specified final pressure p2. Path 1–2՝ is for adiabatic compression. Path 1–2 corresponds to compression with heat transfer from the working fluid to the surroundings. 8- Gas Turbines with Compression with Intercooling The area to the left of each curve equals the magnitude of the work per unit mass of the respective process. The smaller area to the left of Process 1–2 indicates that the work of this process is less than for the adiabatic compression from 1 to 2՝. This suggests that cooling gas during compression is advantageous in terms of the work input requirement. Although cooling gas as it is compressed would reduce the work, a heat transfer rate high enough to affect a significant reduction in work is difficult to achieve in practice. 8- Gas Turbines with Compression with Intercooling A practical alternative is to separate the work and heat interactions into separate processes by letting compression take place in stages with heat exchangers, called intercoolers, cooling the gas between stages. Following figure illustrates a two-stage compressor with an intercooler. The accompanying p–v and T–s diagrams show the states of internally reversible processes: Process 1– c is an isentropic compression from state 1 to state c where the pressure is pi. Process c–d is constant-pressure cooling from temperature Tc to Td. Process d–2 is an isentropic compression to state 2. 8- Gas Turbines with Compression with Intercooling The work input per unit of mass flow is represented on the p–v diagram by shaded area 1–c–d–2–a–b–1. Without intercooling the gas would be compressed isentropically in a single stage from state 1 to state 2՝ and the work would be represented by enclosed area 1–2՝–a–b–1. The cross-hatched area on the p–v diagram represents the reduction in work that would be achieved with intercooling. Some large compressors have several stages of compression with intercooling between stages. 8- Gas Turbines with Compression with Intercooling The determination of the number of stages and the conditions at which to operate the various intercoolers is a problem in optimization. The use of multistage compression with intercooling in a gas turbine power plant increases the network developed by reducing the compression work. By itself, though, compression with intercooling would not necessarily increase the thermal efficiency of a gas turbine because the temperature of the air entering the combustor would be reduced (compare temperatures at states 2՝ and 2 on the T–s diagram). A lower temperature at the combustor inlet would require additional heat transfer to achieve the desired turbine inlet temperature. 8- Gas Turbines with Compression with Intercooling The lower temperature at the compressor exit enhances the potential for regeneration, however, so when intercooling is used in conjunction with regeneration, an appreciable increase in thermal efficiency can result. The size of the crosshatched area on the p–v diagram representing the reduction in work with intercooling depends on both the temperature Td at the exit of the intercooler and the intercooler pressure pi. By properly selecting Td and pi, the total work input to the compressor can be minimized. For example, if the pressure pi is specified, the work input would decrease (crosshatched area would increase) as the temperature Td approaches T1, the temperature at the inlet to the compressor. 8- Gas Turbines with Compression with Intercooling For air entering the compressor from the surroundings, T1 would be the limiting temperature that could be achieved at state d through heat transfer with the surroundings only. Also, for a specified value of the temperature Td, the pressure pi can be selected so that the total work input is a minimum (the crosshatched area is a maximum). 9- Regeneration, Reheat, and Intercooling The reheat between turbine stages and intercooling between compressor stages provide two important advantages: The network output is increased, and the potential for regeneration is enhanced. Accordingly, when the reheat and intercooling are used together with regeneration, a substantial performance improvement can be realized. One arrangement incorporating reheat, intercooling, and regeneration is shown in following figure. 9- Regeneration, Reheat, and Intercooling This gas turbine has two stages of compression and two turbine stages. The accompanying T–s diagram is drawn to indicate irreversibilities in the compressor and turbine stages. The pressure drops that would occur as the working fluid passes through the intercooler, regenerator, and combustors are not shown. 10- Gas Turbines for Aircraft Propulsion Gas turbines are particularly suited for aircraft propulsion because of their favorable power-to-weight ratios. The turbojet engine is commonly used for this purpose. As illustrated in following figure, this type of engine consists of three main sections: the diffuser, the gas generator, and the nozzle. The diffuser placed before the compressor decelerates the incoming air relative to the engine. A pressure rise known as the ram effect is associated with this deceleration. 10- Gas Turbines for Aircraft Propulsion The gas generator section consists of a compressor, combustor, and turbine, with the same functions as the corresponding components of a stationary gas turbine power plant. In a turbojet engine, the turbine power output need only be sufficient to drive the compressor and auxiliary equipment. The gases leave the turbine at a pressure significantly greater than atmospheric and expand through the nozzle to a high velocity before being discharged to the surroundings. 10- Gas Turbines for Aircraft Propulsion The overall change in the velocity of the gases relative to the engine gives rise to the propulsive force or thrust. Some turbojets are equipped with an afterburner, as shown in following figure. This is essentially the reheat device in which additional fuel is injected into the gas exiting the turbine and burned, producing a higher temperature at the nozzle inlet than would be achieved otherwise. Consequently, a greater nozzle exit velocity is attained, resulting in increased thrust. 10- Gas Turbines for Aircraft Propulsion The T–s diagram of the processes in an ideal turbojet engine is shown in following figure. Following the assumptions of an air-standard analysis, the working fluid is air modeled as an ideal gas. The diffuser, compressor, turbine, and nozzle processes are isentropic, and the combustor operates at constant pressure. Process a–1 shows the static pressure rise that occurs in the diffuser as the air decelerates isentropically through this component. 10- Gas Turbines for Aircraft Propulsion Process 1–2 is an isentropic compression. Process 2–3 is a constant-pressure heat addition. Process 3–4 is an isentropic expansion through the turbine during which work is developed. Process 4–5 is an isentropic expansion through the nozzle in which the air accelerates and the pressure decreases. 11- Other Applications Turboprop Engine The turboprop engine shown in following figure consists of a gas turbine in which the gases are allowed to expand through the turbine to atmospheric pressure. The net power developed is directed to a propeller, which provides thrust to the aircraft. Turboprops are efficient propulsion devices for speeds of up to about 600 km/h (400 miles/h). 11- Other Applications Turbofan Engine In the turbofan shown in following figure, the core of the engine is much like a turbojet, and some thrust is obtained from expansion through the nozzle. However, a set of large-diameter blades attached to the front of the engine accelerates air around the core. This bypass flow provides additional thrust for takeoff, whereas the core of the engine provides the primary thrust for cruising. Turbofan engines are commonly used for commercial aircraft with flight speeds of up to about 1000 km/h (600 miles/h). 11- Other Applications Turboprop vs. Turbofan Both turboprop and turbofan engines are gas turbine engines, meaning that thermodynamically they function identically. The differentiation is in how exhaust energy is used; turboprops use the exhaust drive a propeller, and turbofans accelerate the exhaust to produce thrust. Turboprop Turbofan 11- Other Applications Turboprop vs. Turbofan Turboprops extract virtually all the kinetic energy and a larger portion of the thermal energy via expansion turbines to drive the propeller, while turbofans utilize an expansion nozzle to create high speed exhaust (thrust). For turboprops, very little thrust is produced by the exhaust directly (2%- 3% of total thrust output), the propeller does the work of converting heat to thrust via a gearbox driven by the expansion turbine. Turboprop Turbofan 11- Other Applications Ramjet A particularly simple type of engine known as a ramjet is shown in following figure. This engine requires neither a compressor nor a turbine. A sufficient pressure rise is obtained by decelerating the high-speed incoming air in the diffuser (ram effect). For the ramjet to operate, therefore, the aircraft must already be in flight at high speed. The combustion products exiting the combustor are expanded through the nozzle to produce the thrust. Ramjet 11- Other Applications Ramjet In each of the engines mentioned thus far, combustion of the fuel is supported by air brought into the engines from the atmosphere. For very high-altitude flight and space travel, where this is no longer possible, rockets may be employed. In these applications, both fuel and an oxidizer (such as liquid oxygen) are carried on board the craft. Thrust is developed when the high-pressure gases obtained on combustion are expanded through a nozzle and discharged from the rocket. Ramjet 12- Combined Gas Turbine–Vapor Power Cycle A combined power cycle couples two power cycles such that the energy discharged by heat transfer from one cycle is used partly or wholly as the input for the other cycle. In the present section, a combined gas turbine–vapor power cycle is considered. The stream exiting the turbine of a gas turbine is at a high temperature. One way the potential (exergy) of this high-temperature gas stream can be used, thereby improving overall fuel utilization, is by a regenerator that allows the turbine exhaust gas to preheat the air between the compressor and combustor. Another method is provided by the combined cycle shown in following figure, involving a gas turbine cycle and a vapor power cycle. 12- Combined Gas Turbine–Vapor Power Cycle The two power cycles are coupled so that the heat transfer to the vapor cycle is provided by the gas turbine cycle, which may be called the topping cycle. The combined cycle has the gas turbine’s high average temperature of heat addition and the vapor cycle’s low average temperature of heat rejection, and thus a thermal efficiency greater than either cycle would have individually. For many applications combined cycles are economical, and they are increasingly being used worldwide for electric power generation. The thermal efficiency of the combined cycle is Ẇ𝒈𝒂𝒔 + Ẇ𝒗𝒂𝒑 𝜼= 𝑸𝒊𝒏 12- Combined Gas Turbine–Vapor Power Cycle The relation for the energy transferred from the gas cycle to the vapor cycle is obtained by applying the mass and energy rate balances to a control volume enclosing the heat exchanger. For steady-state operation, negligible heat transfer with the surroundings, and no significant changes in kinetic and potential energy, the result is ṁ𝒗 𝒉 𝟕 − 𝒉 𝟔 = ṁ𝒈 𝒉 𝟒 − 𝒉 𝟓 In this cycle, energy is recovered from the exhaust gases by transferring it to the steam in a heat exchanger that serves as the boiler. In general, more than one gas turbine is needed to supply sufficient heat to the steam. Also, the steam cycle may involve regeneration as well as reheating. Energy for the reheating process can be supplied by burning some additional fuel in the oxygen-rich exhaust gases. 12- Combined Gas Turbine–Vapor Power Cycle The temperature difference between the saturation temperature of water and the gas temperature leaving the evaporator is called pinch point. The lowest temperature difference between the water and the gas temperature is called the pinch point. Approach point is the temperature difference between the temperature of steam corresponding to drum operating pressure and water temperature leaving the economizer. 12- Combined Gas Turbine–Vapor Power Cycle Both these variables affect the steam production, the cost, and effectiveness of heat recovery steam generator (HRSG). If the pinch point is lower, total heat recovered in HRSG is higher, and steam generation is also high. However, lowering the pinch point necessitates a larger heat exchange surface, which in turn increases the cost. Its optimum value is 8- 10°C. When the approach temperature is lower, the economizer produces more steam due to flashing, which must be avoided for the tubes' long life. Higher approach temperature increases the surface in the evaporator section and assures higher stability. Its optimum value is 10°C.