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gasturbine - le'T:I'di'to velops it We strit'f:y of a...

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Unformatted text preview: le 'T :I'di'to velops it] We strit'f, :y of a rnprcs- espo- Ito cn- sel eti- ff ratlltt I a roi- he fol- tl her-ll :1. Hill} .Izu'} 31$ 1' all i1" specif- ierc'EI“ diestl I to all ID—I THE IDEAL BRAYTDN CYCLE AND THE GAS TURBINE ENGINE he jet engine. which extracts energy front a gas turbine. has become a popular [tower- producing device. replacing the reciprocating IC engine wherever higher power per unit engine mass. smoother operation. or increased maintainability is detnanded. We study the thennodynamics of the jet engine and other adaptations of the gas turbine in this chapter. The ideal Brayton cycle. a thermodynamic hear engine cycle, is defined. and its oper- arion is compared to that of the _iet engine. To give the reader a better appreciation of the actual engines. the mechanics of the gas turbine. the compressor. the combustot. and nox- zies and diffusers are presented. These devices are the essential components of the corri- mon jet engine, and a knowledge of their individual functions helps to nitrite the Braytttn cycle more believable. The gas turbine analyses are done using the air-standard analysis. with air being coo- sidereel as a pertect gas. We use many of the perfect gas processes introduced in chapter .r-. and determine how power is mechanically extracted in a gas turbine. We consider three modifications to the Brayttin cycle air-standard analysis to beta-r describe the actual gas turbine operation: [1) use of air rabies to account for specilic heat values. which may vary with temperature: {2] reversible polytropie compression arid es- pansirin processes; and {3] irreversible adiabatic compression and expansion. Regenerative beating. the most common attempt to increase the efficiency of the Bray- ton cycle. is considered iii the contest of a Hrayron eyele application. Finally. the rocket engine is discussed. even though it is neither a gas turbine nor a complete beat engine. An elementary thermodynamic analysis of the solid and liquid recit— ers is then made. New Terms F; Impulse tthra stl ry, Pressure ratio I”. Specific impulse Tip Diffuser efficiency l'ii'f' leass flow rate of fuel 1m Nozzle efficiency ”ta-idle Airr'fuelratio The ideal Brayton cycle is defined by the following four reversible processes; 1—2 Adiabatic compression from state i to state 2 2—3 Constant pressure beat addition 3—4 Adiabatic expansion 4- ] Constant-pressure hear rejection to state I Figure ltL-l shows the p—lr' and T—s diagrams of a typical Brayton cycle with the numbers denoting equilibrium states that correspond to those in the definition of the cycle. A compari son can be made between these diagrams and those for the Due cycle in figure 9—1. The similarities 3'33 3-34 Chapter III Gen Turbinen. .lei Prttpulxiun. and the Brnyton Cycle .7 FIGURE lII—l Property diagrams of ideal Hrttyton cycle one the differences; xhoulcl be readily tipporcnt. The Bmy'ton cycle is most often used to cle- HCTibB the operation of the gin turbine engine. on engine that has been used to power vehicles. such us uircrafi. where it is commonly referred to an; :i jet or turbojet engine. The gun turbine is HIM} need in xtntionur}r uppiiczitione for electrical power generation. either an :1 ate ntiby unit for providing etddit‘lut'tfll power occouiouully or .u; u continuous electric-ti] power generator. Figure ll‘i—E shown a typical arrungernent of the criticul Components of the aircraft gas turbine. or jet engine. The major components of the typicnl gut; turbine ure Ila-ted in :1 out- uwuy view in figure lfl—E: the tune. the comment-or. the ctimbufitlelt chamber or cornbustor. the turbine und turbine nozzles. urtd ll'u: exhauxt nection. in the upcoming Mt) sections, ' . I I'I'N. " .‘x \I'ul'tfi llll'iiE ”1: I ||!-|:1E||.| '--1.2‘i.|- ~ . k —| __ tztaxuii'u || “I'll-“II “H! “Ill 1' I I:- II HI-NM n-‘e _-.'..I."|1II I.I| III ‘1 NI Mali: Wit-amine; l|.'l-I.I'2Ill l — no own '-.:H'-Ji.-1i.|!|1l.'-“' II.-I|I.R_ _ F iii: :ifli: .2. _ l I l l l-4I'II MIA-(:F 'I‘ 1 -- .. '. ‘.|.'RF.|rNE '* - .L I emulsr wri- ‘i.l'_-1i.l'.|'_—.J 5m uncut—l II|I 'H'Iflfii l'l'ii'i 1" . h. .x. |.|'J I“... o i'I-“oio._| '— ' "WM-“L“ 'll. RHHJW - " |'|.|| I'I ihli " ""l I :ml-‘ul \"u IH \.I |c|x FIGL'RE I'll—2 Typical aircraft gen turbine engine {from “The Aircraft Gas Turbine Engine rind [ts Operation." August l'hl'i'fi ed; with iteranihfiion of Pth '3; Whitney Aircraft Dicieioitt Ill-l The ideal lira} tun Cycle and the Gas Turbine Engine 335 we cnnsider in tletail the utttjtii' ctimptinentit.‘ the turbine. the L'flTl'lpt'iffi'Sfll'. and the cnmhuxtnr. in seetiun I'D—5. we cunt-cider the enmplcte engine and in; cycle. Keep in mind that [him he cunt} an example and that there are many ether engines 1which have physical characteristics differ- ent from thme of the gar- turbine but which cnuld hc apprtmimaled h} the Bruy'mn cycle. A schematic diagram of Lhe gas turbine nperutittg 011 .‘1 Bray-tern cycle iii Sl'IUWII in figure ]U—3_ If we apply the steady-flew energy equation to the indit idual components. and anxunie t'E‘tEf‘thlé pTMtl'Ht-iflh. and nn significant kinetic ur pntential energ}r change}; we nh- min the fi‘illnwing: . Fur the Etllttpt'urfilun 1-3. h: - in = —tt‘ltmmp till—It 2. For the ctilnhua-ititin la}. n] " ill; = thud [Ill—2| .3. F111" the turbine cxpaniziun 3—4. .I'u '- tr; = —tt‘.i.',.”h Hill-3} For the enclosed area in the p—l'diagram ut' figure IEl—I. which is the net work cf the cycle. we get it‘ll-3m- : tel-mm + italic...“II Hill—4t “I" with...“ = It; — In 1- II. - It; till—5| 'I'he cncluyed area in the T—.-. diagram must he the net heat added to the cycle. and Ifi"rpel = qHIJIJ + t.lret 11M] Thih also can be identified ill! ql‘llfl = u'l‘ctcle [I'll-Tl If we inaume a perfect gar. as the u'nrkhtg medium. then equations. I Ill—1 J. t ill—2 t. [ 1t1—3L and t I'D—5t can he thither itlteted. In particular. the thennndynamic efficiency Iii-1' L'}|.'lL' X III} ”Hi {Jada FIfiL'RE Ill—3 Schematic tit' Btaytnn etch: _~__-a~' turbine .131? Chapter It] Gas Turbines. Je1 Propulsion. and the Brsyton Cycle n} reduces to 1 r Fttil _ = _ i intpui a]; |:1 —lr lit-lift] >< lflfl Hill—9} ~ r for perfect gases and reversible conditions [see problem 10—h}. tit-here rt, is the pressure ratio given by py‘pl or yam-"F4. 3 EXAMPLE 10-1 A tdfld-hp gas turbine operates with a perfect gas on the Breyten cycle and has an inlet i pressure of 14.? pets. The oomhuetor pressure is tut] psis. and the ratio of the spear-tic J heats of the perfect gas is 1.4. Determine the thermal efficiency of the engine and the rate r of heat addition that is required. Solution We assume that the perfect gas has constant specific heats. and the efficiency can then he i found from equation [10—9]. where rp - 1m psia.I 14.? psle = 6.303. Then ! 1 : Answer Hr = 1 — — =- 42.2% {5.303 39.431 .4 l The rate of heat addition may he Found from the definition oi thermal efficiency equa- 3 tion {1 tit-El}. We have I - wkcycle llSlade = 1 Ti?“ — 101:!) hp — ears h ' +1422 ' p or. expressed in more customary heat transfer uniter Ci _ E_'Et_?fl hp-Btu 3“” ' 1.41 hpvs Answer = 1680 Btuy's 1 0-2 The manner by which thermal energy is converted into mechanical energy. thereby provid— THE GAS TURBINE ing work in the gas turbine. is shown in the schematic diagram of figure Iii—4. Here Lhe high velocity stream of gas tor liquid] is directed against the paddle wheel. thus inducing a mtorien of Lhe wheel. This arrangement is called an impulse turbine and is one of the two FIGURE 10-4 Basic ]) _ FIGL' principle of impulse turbine hill: winder ' [11Fh1l‘le 5:35 % induced We °' “W N. Ill-1 The Gas Turbine FIGURE 10-5 Typical 1111pulse turbine turbine blade types of turbines. Figure lfl—S shows an isometric diagram of how an actual impulse ti bine may be configured. The other type of turbine. the reaction turbine. is depicted figure Ill—6: here the fluid is ejected at a. high velocity from nozzles attached to the turbi wheel. This causes a reaction that propels the turbine wheel in the opposite direction of t fluid stream. Both typos oi‘turhincs are utilized in practice. and if more than one Iwheel used in a turbine tthen called a multistage turbine]. the rescuon principle has many i herent advantages. Figure lfl—‘i‘ shows a typical turbine stage in which entrance stationn nozzle vanes act to increase the kinetic energy of hot gases and direct them toward the r lining turbine blades. The hot gases pass through this smtion and are redirected toward a other downstream turbine stage or to the atmosphere. FIG L'RE Ill-ti Reaction turbine 333 Chapter II] Gas Turbines. Jet Propulsion. and the Etaytbn Cyeie direction of Inter bindee I’CIEIN blade )) (t t j entrance rater blade exit statiemry nozzle section stationery nozzle vane section vane Beeliun FIGURE 10-? Typical gas. or steam turbine stage. I-lnt gases enter an entrance nozzle section from a supply or upstrc directed against rotor blades. and leave at a luwer pressure and tempm'amre through exit nozzle vanes to another dnwne the atmesphe're For an adiabatic turbine. neglecting potential energy changes. we ener t7” — 1.72 ¥ + a3 — ha = —wicm, and we can sirnnlif},r this by noting that 17” and 173 are negiigible. Then if”; — #1 = ”Hf-km which is the wink prmlueed in a turbine if the process is adiabatic and if ' changes are neglected. The power ia then tbuml frurn an: — F11}= me, This equminn is gem} with either SI or Engiish units. ...
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