http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node27.ht ml 3.7 Brayton Cycle [VW, S & B: 9.8-9.9, 9.12] The Brayton cycle (or Joule cycle) represents the operation of a gas turbine engine. The cycle consists of four processes, as shown in Figure 3.13 alongside a sketch of an engine: a - b Adiabatic, quasi-static (or reversible) compression in the inlet and compressor; b - c Constant pressure fuel combustion (idealized as constant pressure heat addition); c - d Adiabatic, quasi-static (or reversible) expansion in the turbine and exhaust nozzle, with which we 1. take some work out of the air and use it to drive the compressor, and 2. take the remaining work out and use it to accelerate fluid for jet propulsion, or to turn a generator for electrical power generation; d - a Cool the air at constant pressure back to its initial condition. Figure 3.13: Sketch of the jet engine components and corresponding thermodynamic states The components of a Brayton cycle device for jet propulsion are shown in Figure 3.14. We will typically represent these components schematically, as in Figure 3.15. In practice, real Brayton cycles take one of two forms. Figure 3.16(a) shows an ``open'' cycle, where the working fluid enters and then exits the device. This is the way a jet propulsion cycle works. Figure 3.16(b) shows the alternative, a closed cycle, which recirculates the working fluid. Closed cycles are used, for example, in space power generation. 1992). Figure 3.Figure 3.15: Thermodynamic model of gas turbine engine cycle for power generation [Open cycle operation] [Closed cycle operation] . Top: turbojet with afterburning.14: Schematics of typical military gas turbine engines. bottom: GE F404 low bypass ratio turbofan with afterburning (Hill and Peterson. Treating the working fluid as a perfect gas with constant specific heats.10) 3.7.Figure 3. The heat exchange can be expressed in terms of enthalpy differences between the relevant states.. the first law gives (writing the equation in terms of a unit mass).3. Here is zero because is a function of state.4) or by remembering the definition of . The net work done is therefore where . the heat absorbed. and any cycle returns the system to its starting state3.1 Work and Efficiency The objective now is to find the work done. Tracing the path shown around the cycle from . are defined as heat received by the system ( need to evaluate the heat transferred in processes . For a constant pressure.2. quasi-static process the heat exchange per unit mass is We can see this by writing the first law in terms of enthalpy (see Section 2. similarly.. The heat rejected is. for the heat addition from the combustor.and back to .and is negative). The net work per unit mass is given by . and the thermal efficiency of the cycle. We thus .16: Options for operating Brayton cycle gas turbine engines Muddy Points Would it be practical to run a Brayton cycle in reverse and use it as refrigerator? (MP 3. or. Using this relation in the expression for thermal efficiency. In terms of compressor temperature ratio.8) yields an expression for the thermal efficiency of a Brayton cycle: (3. The other two legs of the cycle are Therefore .. .. finally. .10) .The thermal efficiency of the Brayton cycle can now be expressed in terms of the temperatures: (3. so . Eq.. We know that points and are on a constant pressure process as are points and .8 ) To proceed further.9) The temperature ratio across the compressor. (3. . and using the relation for an adiabatic reversible process we can write the efficiency in terms of the compressor (and cycle) pressure ratio. and adiabatic and reversible. we need to examine the relationships between the different temperatures. which is the parameter commonly used: (3. which powers the 747 and the 767).17: Gas turbine engine pressures and temperatures Figure 3.17 shows pressures and temperatures through a gas turbine engine (the PW4000.18: Gas turbine engine pressure ratio trends (Jane’s Aeroengines.Figure 3. Figure 3. 1998) . doesn't that reduce the internal energy of the flow and therefore the enthalpy? (MP 3.7. Note the relation between the gas .13) If the gas undergoes constant pressure cooling in the exhaust outside the engine. is that still within the system boundary? (MP 3.18 shows the history of aircraft engine pressure ratio versus entry into service.Figure 3. Figure 3.2 Gas Turbine Technology and Thermodynamics The turbine entry temperature.) Figures 3. The thermodynamic concepts apply to the behavior of real aerospace devices! Muddy Points When flow is accelerated in a nozzle.14) Does it matter what labels we put on the corners of the cycle or not? (MP 3. is fixed by materials technology and cost.21 show the progression of the turbine entry temperatures in aeroengines.15) Is the work done in the compressor always equal to the work done in the turbine plus work out (for a Brayton cyle)? (MP 3.20 and 3.21 is from Pratt & Whitney. the blades fail.19: Trend of Brayton cycle thermal efficiency with compressor pressure ratio Equation (3.10) says that for a high cycle efficiency.19.11) Why do we say the combustion in a gas turbine engine is constant pressure? (MP 3.20 is from Rolls Royce and Figure 3.16) 3. . the pressure ratio of the cycle should be increased.12) Why is the Brayton cycle less efficient than the Carnot cycle? (MP 3. This trend is plotted in Figure 3. (If the temperature is too high. Figure 3. and it can be seen that there has been a large increase in cycle pressure ratio. Figure 3. which shows two Brayton cycles. For maximum efficiency we would like as high as possible.22.temperature coming into the turbine blades and the blade melting temperature.21: Turbine blade cooling technology [Pratt & Whitney] For a given level of turbine technology (in other words given maximum temperature) a design question is what should the compressor be? What criterion should be used to decide this? Maximum thermal efficiency? Maximum work? We examine this issue below. Figure 3.20: Rolls-Royce high temperature technology Figure 3. This means that the compressor .22: Efficiency and work of two Brayton cycle engines The problem is posed in Figure 3. The conclusion from either of these arguments is that a cycle designed for maximum thermal efficiency is not very useful in that the work (power) we get out of it is zero. evaluated in traversing the cycle.11). as the net work. . This is the area enclosed by the curves. We know that . The work per unit mass is given by: where is the maximum turbine inlet temperature (a design constraint) and atmospheric temperature. The design variable is the compressor exit temperature. (3. This leads to compact propulsion devices.exit temperature approaches the turbine entry temperature.11) To use Eq. and to find the maximum as this is varied. The maximum work occurs where the derivative of work with respect to is zero: (3. as is the atmospheric temperature). The net work will be less than the heat received. the heat received approaches zero and so does The net work in the cycle can also be expressed as . we differentiate the : is expression for work with respect to The first and the fourth terms on the right hand side of the above equation are both zero (the turbine entry temperature is fixed. we need to relate and . A more useful criterion is that of maximum work per unit mass (maximum power per unit mass flow). which is seen to approach zero as .. 23. (3. compressor pressure ratio.11) gives the compressor exit temperature for maximum work as . In terms of temperature ratio. Plugging this expression for the derivative into Eq. for different temperature ratios . we need to multiply the work per unit mass by the mass flow rate: (3.12 ) The trend of work output vs.Hence.. The role of the temperature ratio can be seen if we examine the work per unit mass which is delivered at this condition: Ratioing all temperatures to the engine inlet temperature. To find the power the engine can produce. . is shown in Figure 3. The condition for maximum work in a Brayton cycle is different than that for maximum efficiency. turbine entry temperature] Figure 3.24(a) shows the gas turbine engine layout including the core (compressor.24(b) shows the core power for . for different temperature ratios [Gas turbine engine core] [Core power vs.24: Aeroengine core power [Koff/Meese.Figure 3.23: Trend of cycle work with compressor pressure ratio. Figure 3. Figure 3. burner. and turbine).24 shows the expression for power of an ideal cycle compared with data from actual jet engines. 1995] Figure 3. 17) Question about the assumptions made in the Brayton cycle for maximum efficiency and maximum work (MP 3. The analysis not only shows the qualitative trend very well but captures much of the quantitative behavior too. the Brayton cycle is therefore less efficient than a Carnot cycle. Muddy Points What are the units of in ? (MP 3. Figure 3. L.18) You said that for a gas turbine engine modeled as a Brayton cycle the work done is . except for the conversion factors.7.19) 3. (MP 3. A final comment (for this section) on Brayton cycles concerns the value of the thermal efficiency.25: Ideal ramjet [J. Kerrebrock. The Brayton cycle thermal efficiency contains the ratio of the compressor exit temperature to atmospheric temperature. Does this suggest that the work that you get out of the engine doesn't depend on how good your compressor and turbine are? since the compression and expansion were modeled as adiabatic.3 Brayton Cycle for Jet Propulsion: the Ideal Ramjet A schematic of a ramjet is given in Figure 3. so that the ratio is not based on the highest temperature in the cycle. as the Carnot efficiency is. For a given maximum cycle temperature.25. The equation in the figure for horsepower (HP) is the same as that which we just derived. Aircraft Engines and Gas Turbines] In the ramjet there are ``no moving parts. where is the heat added and is the heat rejected.'' The processes that occur in this .a number of different engines as a function of the turbine rotor entry temperature. why does Douglas Quattrochi 2006-08-06 ? (MP 3. The ramjet thermodynamic cycle efficiency can be written in terms of flight Mach number. as follows: and so See also Section 11. with a decrease in Mach number. Muddy Points Why don't we like the numbers 1 and 2 for the stations? Why do we go 0-3? (MP 3.3 for other figures of merit.6. : Constant pressure combustion.20) For the Brayton cycle efficiency.propulsion device are: : Isentropic diffusion (slowing down) and compression. . . : Isentropic expansion through the nozzle.21) .