In the next lecture... Tutorial on ideal cycles and component performance.
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2 In the next lecture... utoril on idel cycles nd component performnce. rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby
3 roblem # Lect-9 A Bryton cycle opertes with regenertor of 75% effectiveness. he ir t the inlet to the compressor is t 0. M nd 30 o C, the pressure rtio is 6.0 nd the mximum cycle temperture is 900 o C. If the compressor nd the turbine hve efficiencies of 80% ech, find the percentge increse in the cycle efficiency due to regenertion. rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby 3
4 roblem # Lect-9 s 6 5 4s M 0 3 K 73 K π c 6 η c, η t 0.8 s rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby 4
5 Solution: roblem # Let us first consider the Bryton cycle without the regenertor: 0s 0s of 0 ( γ ) compressor, s η C 73 04s 705K.668 From the definition of / γ 0 04s isentropic efficiency rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby 505K 6 0.4/.4 5K 5
6 For herefore, w w t c h h Now, Hence, Q η Lect-9 Solution: roblem # turbine we hve, η ( ( ( K h h 6.09 kj/kg 04 t 0 wt w Q h c c c p p h 04s 0 0 ) 0.8(73 705) 375K 04 0 ) kj/kg ) kj/kg.005 (73 555) % 6.09 rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby 6
7 Let us 04 or, Now, Q Lect-9 Solution: roblem # now consider the regenertor Regenertor effectiveness K 0.75( ) h h ( 798K ( ) c p ) 0 0 : kj/kg rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby 7
8 Solution: roblem # Since η w Q w net net or or he percentge increse due to regenertion : remins the sme, % 4. 56% rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby 8
9 roblem # Lect-9 A gs turbine operting t pressure rtio of.34 produces zero net work output when kj of het is dded per kg of ir. If the inlet ir temperture is 300 K nd the turbine efficiency if 7%, find the compressor efficiency. rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby 9
10 Solution: roblem # Since the net work output is zero, w c w t or, c 0s 0s p 0 or, ( ) K K Given tht het dded kj/kg ( γ )/ γ /.4 0.4/.4 rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby 0
11 We know tht 04 he or, Lect-9 Solution: roblem # + ( turbine efficiency is η 0 04s 0s 0 ( 04 ( / ) / ) ) 04s % nd 774 / K / nd 774K 04s or 70.4% 0.4/ K rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby
12 roblem # 3 Lect-9 An ircrft flies t Mch number of 0.75 ingesting n irflow of 80 kg/s t n ltitude where the mbient temperture nd pressure re K nd 0 k, respectively. he inlet design is such tht the Mch number t the entry to the inlet is 0.60 nd tht t the compressor fce is he inlet hs n isentropic efficiency of Find () the re of the inlet entry (b) the inlet pressure recovery (c) the compressor fce dimeter. rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby
13 Solution: roblem # 3 Mch number is 0.75, hence, the flight speed is u γ otl pressure, 0 + M Sttic temperture t inlet entry, ρ M 0 / γr R he totl temperture, / γ M.4 87 kg / m rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby K γ M 4 γ /( γ ) m / s 46 K
14 Solution: roblem # 3 Sttic pressure t inlet entry, ρ 0 / / + R γ M 0.7 γ /( γ ) kg / m herefore, re t the inlet entry, A m u ρ m M m γr ρ rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby 4
15 Now, Lect-9 Solution: roblem # 3 Substituting the vlues, 0 0s ressure recovery, 0 0 he sttic pressure t the compressor 0 Diffuser efficiency, 0 0 γ / + M η γ / ( ) ( γ / ) 300 d fce, rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby 0s 0 0s 45.75K 39.3K γ /( γ )
16 Solution: roblem # 3 ρ / R 0.893kg / m 3 Velocity t the compressor fce, u Are of the compressor fce, 4. m / m the dimeter, d.08 m A M m / u ρ γr s rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby 6
17 roblem # 4 Lect-9 A turbojet engine opertes t n ltitude where the mbient temperture nd pressure re 6.7 K nd k, respectively. he flight mch number is 0.9 nd the inlet conditions to the convergent nozzle re 000 K nd 60 k. If the nozzle efficiency is 0.98, the rtio of specific het is.33, determine whether the nozzle is operting under choked condition or not. Determine the nozzle exit pressure. rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby 7
18 Solution: roblem # 4 he nozzle efficiency is η n or, 7 7s ( 7 7s Under choked condition, η n h h ( /( γ + )) ( / ) c h h c ( γ )/ γ defined s M 7 7s, / / (/ η )(( γ ) /( γ + ))) n γ /( γ ) 7 7s / / 07 rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby 8
19 Lect-9 Solution: roblem # 4 Substituting the vlues, e c Also, We cn see tht herefore, c.45 he exit pressure would therefore be equl > the nozzle is 3.95k operting under choked condition. rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby to 9
20 Exercise roblem # A Bryton cycle with two stges of compression nd two stges of expnsion hs n overll pressure rtio of 8.0. Air enters ech stge of the compressor t 300 K nd ech stge of the turbine t 300 K. Determine the therml efficiency () with no regenertor (b) with n idel regenertor (c) if compressor nd turbine hve 80% efficiency, no regenertor. Ans: () 35%, (b) 69.6 %, (c) 6 % rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby 0
21 Exercise roblem # In gs turbine plnt, the ir t the inlet is t 7 o C, 0. M. he pressure rtio is 6.5 nd the mximum temperture is 800 o C. he turbine nd compressor efficiencies re 80% ech. Find () the compressor work per kg of ir (b) the turbine work per kg of ir (c) het supplied per kg of ir nd (d) the cycle efficiency. Ans: () 59.4 kj/kg, (b) kj/kg (c) kj/kg (d)6. % rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby
22 Exercise roblem # 3 An ircrft is flying t Mch number of 0.8 t n ltitude where the mbient sttic pressure is 40 k. If the diffuser pressure recovery is 0.9, determine the isentropic efficiency of the diffuser. Ans: rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby
23 Exercise roblem # 4 he nozzle of turbojet engine develops thrust of 590 Ns/kg. he ircrft is flying t 40 m/s. he pressure nd temperture t the nozzle entry re.84 k nd 993 K, respectively. If the rtio of specific het is 0.33, determine the nozzle efficiency. he nozzle cn be ssumed to be operting under choked condition. Ans: 0.95 rof. Bhskr Roy, rof. A M rdeep, Deprtment of Aerospce, II Bomby 3
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