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# Airbreathing Engines MAE 4261

Florida Tech

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This 8 page Class Notes was uploaded by Marie Nicolas on Monday October 12, 2015. The Class Notes belongs to MAE 4261 at Florida Institute of Technology taught by Daniel Kirk in Fall. Since its upload, it has received 141 views. For similar materials see /class/221696/mae-4261-florida-institute-of-technology in Mechanical and Aerospace Engineering at Florida Institute of Technology.

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Date Created: 10/12/15

MAE 4261 AIR BREATHING PROPULSION RAMJET ANALYSIS Overview Recall that all aircraft engines are heat engines in that they use the thermal energy derived from combustion of fossil fuels to produce mechanical energy in the form of kinetic energy of an exhaust jet The excess momentum of the exhaust jet over that of the incoming air ow results in thrust which is used to propel the aircraft In class we have shown that using a control volume approach the general expression for thrust may be written as shown in Equation 1 TmUmgUgppgz4 1 m 1fm mf We also showed that this expression may be written in a convenient dimensionless form as shown in Equation 2 U A 2 i1f721h amp1 moU U0 moUg pa 0 In the modeling of aircraft engines if we assume that the exhaust pressure is equal to the ambient pressure pep0 and thatfltlt 1 then the expression becomes U 3 M0 2 1 ma7 U7 0 In this expression we have introduced the nondimensional Mach number M0U0a0 where a0 is the local speed of sound 1 It should be noted that the behavior of the nozzle can be much more complex and that deviation from ideal expansion becomes important for supersonic ight This aspect will be looked at in more detail when we examine the nozzle portion of the engine in detail We represent a gas turbine engine using a Brayton cycle and are able to derive expressions for work as functions of temperature or pressure at various points in the cycle We now seek to perform an ideal cycle analysis which is a method for expressing thrust and thermal efficiency of engines in terms of useful design variables The objective of cycle analysis for various propulsion devices ramjets turbojets turbofans is to estimate the thrust T and the thermal efficiency nthem al or alternatively Isp as a function of l typical design limiters 2 ight conditions and 3 design choices so that we can analyze the performance of various enginesz To do so we will employ the following methodology 1 Estimate the ingested mass ow mu and the exhaust to inlet velocity ratio UeU0 in terms of temperature ratios 2 Use a power balance to relate turbine parameters to compressor parameters not used in ramj et analysis where there is no compressor or turbine 3 Use an energy balance across the burner combustor to relate the combustor temperature rise to the fuel ow rate and fuel energy content We can write the ratio of exhaust to inlet velocity ratio as U M URT M g UM2RTM T It is most efficient to find the exit Mach number Me and temperature Te by keeping track of the stagnation temperatures and pressures through several components In general it is the stagnation properties that most conveniently represent the effect of the components on the uid as it ows through the engine The relations for stagnation temperature and pressure are given below3 2 Note that ideal cycle analysis addresses only the thermodynamics of the air ow within the engine and does not concern itself with the detailed design of the components such as blading rotational speed or any other geometry Instead the analysis is focused on the results that the various components produce such as temperature and pressure ratios Later in the course we will look at the detailed geometry and operation of these components to see how they work to produce given results 3 The terms stagnation temperature and total pressure are synonyms meaning exactly the same thing In this document stagnation temperatures and pressures are denoted by T and pt respectively In other texts such as Mechanics and Thermodynamics of Propulsion by Hill and Peterson the stagnation temperature and pressure are denoted by To and p0 respectively Both forms of the notation are comm on in the literature The subscript t is chosen to avoid confusion with the location upstream of the engine designated as 0 zero Notation and Station Numbering It is very helpful to de ne a set of symbols that represent ratios of stagnation properties as distinguished from static or thermodynamic properties of the working uid Also note that stagnation properties T1 and p are more easily measured than static properties T and p The table below summarizes this set of useful symbols pressures across component Ratio of total temperatures across component to to The ow upstream of the engine station 0 may be written as T A1L 1Mga0 T 2 0 L 1L 1M77150 po 2 l V V L o H a f a II o Vl Ideal Assumptions Inlet or Diffuser ndl rdl adiabatic isentropic Combustor or Burner and Afterburner nbl 1131 Nozzle 11 1 Inl For the compressor and for the turbine we can write T L p23 n 23 T 771 p c T c If r 22 22 T L P25 n 25 T 71 p 2 T 2 It rt 24 24 This quantity is used so frequently that it gets its own special designation 91 It is also one of the most important metrics for aircraft engine performance Ramjet Analysis A picture of the BOMARCA missile which employs a ramjet thruster is shown in Figure 1a a cutaway picture of a conventional ramjet engine is shown in Figure 1b and a cutaway drawing of a similar device is shown in Figure 1c Afi gure 1b Bristl Siddeley Thor Ramjet 1 skomer J39 M m mmcrmluur smhum aimch 1m sinmm mu minimum lnnm39 NIUy mu can Figure 1c CutAway Schematic of a Conventional Ramjet Layout from Mechanics and Thermodynamics of Propulsion 2nd Edition Figure 57 A schematic representation taken from Hill amp Peterson is shown below in Figure 2a and the accompanying TS diagram is shown in Figure 2b a DilTuscr Hr Combustion chamber quot w Nozzle We Fuel inlet 4 1 lt gt lt WW Exllausl jet 1m 4i ii ltigtcigtm 2M Supersonic Subsonic compression compression Figure 2a Ramjet Schematic from Mechanics and Thermodynamics ofPropulsion 2 d Edition Figure 56 Figure 2b Temperature or Enthalpy versus Entropy Diagram for a Ramjet Engine Figure 56 Mechanics and Thermodynamics ofPropulsion 2 d Edition The notion in this schematic and TS diagram may seem somewhat strange since the combustor is divided into two regions region 2 and region 3 The reason that this is done is to keep the numbering convention consistent with the turbojet and turbofan engines which are far more common propulsion devices than the ramjet In the turbojet and turbofan the diffuser exit compressor inlet is always station 2 the compressor exit combustor inlet is always station 3 and the combustor exit turbine inlet is always station 4 Station 2 is kept as the exit of the diffuser but since there is no rotating machinery compressor station 3 is kept as the inlet to the combustor We can think of the region between 2 and 3 as the fuel injectors although that region will not appear in particular in our analysis Station 4 is then kept as the exit of the combustor but again recall that there is no mechanical turbine in the ramjet engine Examining the TS diagram we can make several modeling approximations l The compression and expansion processes are taken to be isentropic ie the process is reversible and there is no heat transfer adiabatic On the TS diagram this corresponds to legs a02 and 046 For all isentropic processes the total temperature and total pressure is a constant The combustion process between 02 and 04 or neglecting the fuel injectors between 03 and 04 is done at low speed Mlt03 and is modeled as constant pressure heat addition Thus the stagnation pressure remains constant although the stagnation temperature increases due to the heat addition combustion Items 1 and 2 imply that the stagnation pressure remains constant throughout the ramjet engine We will make use of this observation in modeling the ramj et engine We can now use the notation from Table l to develop expressions for the Thrust T and Speci c Impulse 15p of the ramjet engine For this engine where the stagnation pressure is a constant throughout the deVice we can write4 N Pm Pm 7 1 i 1771A402 P0 2 7 ii 17122 471 P6 P 2 Where M0 is the ight Mach number and Me is the exit plane Mach number If we assume that the nozzle is ideally expanded then PeP0 and we can write 111 Po P MM0 5 This implies that UegLn 6 U0 610 E Tao Tn Now substitute this result into the thrust equation Equation 3 U 3 M0 2 1 m a U0 T M L1 7 1000 0 T3 4 Note the approximation in this expression Again we are dealing with ideal cycle analysis so we will assume that specific heat ratios and gas constants remain fixed throughout the engine The ratio Tt4T13 is the total temperature ratio across the combustor which can be written in shorthand as 1b So the thrust equation becomes Mg1 81 T m0 610 This equation may also be written as 82 T M0 mad 6 0 0 These equations point out some interesting aspects of the ramjet engine 1 Ramjets or scramjets develop no static thrust they must be moving to develop thrust This will be in direct contrast to turbojets and turbofans 2 The device relies on ram compression of the air and has no moving parts no spinning compressor to compress the air prior to combustion To have efficient compression of the air the ramj et requires high ight speeds 3 The performance of the device relies in the stagnation temperature rise across the burner Some performance results are summarized in Figure 59 which shows that the maximum thrust of the ramjet is developed for ight speeds around Mach 3 Energy Heat Balance Across the Burner Combustor The final step involves writing the specific impulse thrust specific fuel consumption and other measures of efficiency using these same parameters We begin by writing the First Law across the combustor to relate the fuel ow rate and heating value of the fuel to the total enthalpy rise mfhmacp714jls 9 m m CFTG Ti TA f 0 h To To m m LTO 6 T 73T 7 f 0 4 The specific impulse is The thrust specific fuel consumption can be written as mf 12 TSFC 7 T These are the desired results We have expressed the speci c impulse in terms of typical design parameters such as the ight Mach number design variables and fuel and atmospheric properties Lastly the overall efficiency of the ramjet engine is given by T U 0 l3 novemll 7 mf h These results are plotted in Hill and Peterson Figures 59 and 510 Note that Hill and Peterson use QR for the heating value of the fuel and these expressions simply use h

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