HW6_sol

HW6_sol - (“\Owewof’k Cg Q'OKO’V'PDHS 934/ g_...

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Unformatted text preview: (“\Owewof’k Cg Q'OKO’V'PDHS 934/ g_ (‘Cdu&e, : WHQI‘ «rem/‘43 / TM «9.x QS-fl‘mm paw Cg aN‘Cfa-F-r bomhg (ah/(p1 (70,9er5 or “gum/L Ht a3 'f’i‘e Sam Mm: m WW 9) 'T’ttfi gap-“z V6(Um~(_ 6L9 fave. g2 (Wm #07; (/4514 (“7/53 6?“ )PH 8’00 Him H4 a, W) 57.08% [20/6700 1%; £26, [am 70.? I20)?m A 6? s, 2 9;, /D 7; 1w (my ace/mum £45: 3 '2 6%“) ~0§7yfi g D ark 1m [WWVJ 7!;0013/‘7 (93,7029 "J/xcj C013 52»« gm; may as TPM 9 1 7Z0 L Mia :: O , Z 3 D 62:. fi«( ml) 5‘15) (120)753) /W{ gm " [6/120 M3 (L7) Saw; \Cwefé Vow»; a} TPq L’I )3aseoas Hz. [37?“ MM 1‘- fm WIN»: 0,0827%(2100B : 0.0211 TOW f___,_—- JOTM 3‘75 es (ammlaoflm 07/872010” : W W ' (11‘) H2, MM:— fHL A4qu : 7045’ (ms) 2 I71? mm; £774 £00 The idling engines of a landing turbojet produce forward thrust when operat- ing in a normal manner, but they can produce reverse thrust if the jet is prop- erly deflected. Suppose that while the aircraft rolls down the runway at 150 km/h the idling engine consumes air at 50 kg/s and produces an exhaust velocity of 150 m/s. a. What is the forward thrust of this engine? b. What are the magnitude and direction (Le, forward or reverse) if the ex- haust is deflected 90° without affecting the mass fIOw? c. What are the magnitude and direction of the thrust (forward or reverse) after the plane has come to a stop, with 90° exhaust deflection and an airflow of 40 kg/s? 5'4. After verifying the derivation of Eq. (5.27) for the ideal ramjet find the Mach number M that maximizes 9/"). for Tim = 2500 K, T, = 220K. Evaluate the specific thrust at that Mach number and compare your results with Fig. 5.9. Both Fig. 5.9 (for the ideal ramjet) and Fig. 5.12 (which makes allowance for losses) indicate that at a given flight Mach number the specific fuel con- sumption rises with Tm“. Looking for an explanation of this effect, deter- mine the variation of propulsion, thermal, and overall efficiencres with Tm” for the ideal ramjet for M = 3 and 2000 < Tm“ < 3000 K. Show for the limiting case g/n'zu —> O that f—>O,M—> ; fl_1, 7-17., and 2. __._ __ fl 1 J} 3 °" ‘—l ’°H‘—I-K-—z'm Ea -—-_—- T are. _ To", a“ _ aw To. 220 EL: “5050 =203‘J I an _7;,., striatq 6! 77'» 2.6014320) 7C =__/_9_-s_e__~_mf‘/s_;.Err-4"“. 0 WQM 9a,? "Jag-AT; 3 r: a? 1,3104/5 _ 29.2.3 mg) 3-3:: (AM - E ‘7" “ ’73:): .. "’ "‘5; Ma / W _ M ,9 We CD @ 2'0 3.0%? (9,9,1; ng— 05"??? [7006‘ P“: m 3.0 0_r_a‘/qc/ a??? __ 5“? (Cemfimb _ m _-r_5."_(k_§__f°_fi_ _ _ . 7571!. _ 75¢: __ . 3 9/000 2-47 may; Q;_.S£.s_._fizz__0'fliz_ _Q)_‘f’_?‘23_ __ ‘3 R500 #236 __Q:9m___a..m___§?-6‘3_L__01W atij __ 5. 3M 134%-?“ka _0_:_€/§‘3__@69_2__0"‘/? 0W3 " ___g4a:q__mw_,jz;,_ 52mg ‘ _ 1m..%.0_A1»fs-_____________ __ __ .. MWL_EUT£I -4]; ; @ ga_a;e__¢;o__y__g _ _ " __ TEN..- .—- ._.__.._ __ _I—__ _To: _i_2—5__ fiat. 2-— —} _/-\.. ha. F‘C ‘3 51—90‘ _J~———u , Hilx-rH-‘Sh.’ (M5) t++ or) 5—5. Show that for the ideal turbojet (all efficiencies equal unity), the exhaust Much number M, is given by ‘ M2 = 2 [<fli>h—my(l + 7 _ 1M1) 6 7 ‘ 1 Pin: 2 - l 5 1+ 7 M2 [PM M 2 [0“) 1i 1] TIM/Ta P02 V M is the flight Mach number, P03 . . — is the compressor pressure ratio, P02 T04 —T~ is the ratio of turbine iniet and ambient temperatures, 1 y is the ratio of specific heats (assumed constant). in which The mass flow rates through the compressor and turbine may be assumed equaL . _Tur‘iaoje,r (I) :CD'HST/ (Ch :- Acitéohm 73;. _— For a given work input per unit mass of fluid and given adiabatic efficiency 77:, how does the actual pressure ratio for a compressor differ from the ideal (isentropic) pressure ratio? Derive an expression that relates the actual pres- sure ratio to the ideal one and 77:. As mentioned in Chapter 5, the adiabatic efficiency 77c is usually defined by = he}; - hOZ I103 _ hz ‘ Show the dependence for nc=0,8, 0.9, and ideal pressure ratio 10 < Pas/P02 < 30 and 7 = 1.4. For a diffuser, the adiabatic efficiency cannot be written as a work ratio since the adiabatic work is zero Using the approPriute definition of adiabatic diffuser efficiency 71c _ him ‘ ha "rim—h; show how the actual ratio of exit stagnation pressure to inlet static pressure depends on the diffuser efficiency and the ideal ratio. Show the dependence for m = 0.9, 0.95_,__and flight Machnumber 0.5 < M < 0.9. 'Low 1 {was *i/Iaa )Sstimate the propulsion and thermal efficiencies of a turboth engine during subsonic cruise. The flight Mach number is 0.8, and the amMflEeLzL-Iflprj~ / ture is 225 K. The compressor pressure ratiéis 12, and the turbine inlet tem- Bfl‘ perature is 1300 K. The respective adiabatic efficiencies of the diffuser, compressor, turbine, and nozzle are 0.92, 0.85, 0.85, and 0.95. The burner stagnation pressure ratio is 097, and the average specific heat during and utter combustion is 1.1 kJ/kg' K, and the average molecular weight is 2‘). 7:93 3 filfl r. ” rflgflr,[[/+p—’;—-r€ lat/zsfl‘é _: 5%‘31K 3°}. 7. £32,903 : (542(11) : (2.5; Pa Pa P02 9Z1: = 0.?8 7;, : Bank ‘1, r: 0'91 Qe‘cwe COMLOH'NM: ES :(H/ (,ip 33:64: R =l-ODS‘fL: Dan/W6 8/ MW Combushmi 4/; : l-l K37¢; -/< 1‘ 5,23? ue=fim For :: 2 0, 1 N _t__ [/5337 T Q C qswvvmomfl (I‘m) 7 1 / (A 2 WWW; : C) r?) 'IM (Magyar) = 2W3”; “75 72/0 .: ZC!+S.>C/Le. "—M—EU [amt/«2% “Ml/2 =‘ HOWWMM 2%: Dow; (WJV/L » 2qo.§"Z/z_l 53,47,161 9Z7; : (NH M52/2 ~M7a : z.m<z<a’2z.nz/z ,zqo.r73 4am 0761??”CL65/Tmn/m ': O)‘/62 720 :oz/ a; :DJVQQ(0‘%2) : @337 '5 <5: 4g Compare the specific fuel consumption of a turbojet and a ramjet that are being considered for flight at M = 1,5 and 50,000 it altitude (ambient pres- sure and temperature: 11.6 kPa and 205 K, respectively). The turbojet pressure ratio is 12 and the maximum allowable tempera- ture is 1400 K. For the ramjet the maximum temperature is 2500 K. For sim— plicity ignore aerodynamic IOSSes in both engines Conventional hydrocarbon fuels are to be used (heating value 45,000 kJ/kg). Assume y = 1.4 and c,, = 1.0 kJ/(kg ' K). luv—1.9 T4: 105K a 1 MW Pa 21116: APR ‘ = (-5 l:¥(2&7?)(20r) A; = 4630 . 5‘ "4/; [Kama/+5 To}. 2 T; (1+IgT-(ML) 3205174, 2 29%3K 3 2 CE (1 T“, 4733) rim-22ng -297~.3:l &« “(WA/(rows ‘l 0.0‘f'2‘t Pe, _ Pa Z/T" N11_%’t / TDD/7: 7‘ P03 Me : ‘U aorfigfpifiafi‘ = “llQWTDBZ—tfi Had/1473 = 20/0003t2m3fl"(/+ £59)"’ "2 b24637? Rite : 0.5%“? (1 m :l@,&rm HDWH 22%} ’ é‘las‘ 1.. . ...———-~ lurbojej—C 7'2; 3 5197.3 0.3 b-QAQOWC 7—5? 2 7:1 63) 3% : 2?;z.3( HAY/«'1‘ :gamk 7392. QSSOM‘? “56 4% 1“ M7: 977.“ “gr u: 7;? — [7,; -7731) 2 below «(Ml/.1 e 52%;) c (8%).6 K [SF— 3 (0}(1Xa,éfl?‘r) an} . K f Consider two versions of a jet engine. The first is a standard engine run with a turbine inlet temperature of 1200 K. The second is identical, except that its E”? turbine is cooled by bleeding air from the compressor; in this way the allow- able turbine inlet temperature may be raised to 1600 K. The basic engine and the bleed air line are indicated in the figure. To make an estimate of the ef— fect of this modification on the thrust, suppose that the engine is flying at Mach 2 at an altitude where the ambient temperature is 200 K and that com- pressor pressure ratio is 9: 1. Suppose also that for the second engine 10% of the airflow is bled from the compressor at a point where the pressure ratio is 4:1. After cooling the turbine, the bleed air is exhausted from the engine with no appreciable velocity. For simplicity assume all components of both engines to be reversible. Let 'y = 1.4 and c,, = 1.0 kJ/(kg ‘ K). 3. Determine the thrust of the two engines per unit mass flow of air enter- ing the compressor. b. What is the ratio of the thrust specific fuel consumption of the second engine to that of the first? r—————’ Bleed air ICN‘ — ( l+93me —_(:‘_, 0.6;f0'3 [\ /@ ma *— ...
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HW6_sol - (“\Owewof’k Cg Q'OKO’V'PDHS 934/ g_...

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