ME-00 Fall 07 HW-9 / Gven Dffuer and two-tage compreor wth ntercoolng n a turbojet engne Fnd (a) Temperature (K) of ar at the dffuer ext (b) Ma flow rate (/) of ar through the engne (c) Total power nput (kw) for the LPC and HPC (d) Area (m ) and dameter (ft) at the dffuer nlet Sytem/EFD Q cooler m m 4 m m m 5 W LPC W HPC Aumpton - Steady tate, teady flow - One-dmenonal, unform flow - Ar behave a an deal ga - Ignore PE change - Intercooler, LPC, and HPC: Ignore KE change - Neglect preure drop for the ntercooler - Ignore heat tranfer for dffuer, LPC, and HPC: Q 0 - No work for dffuer and ntercooler: W 0 - Neglect effect of ppng between varou component Bac Equaton dm m 4 5 me m m m m m mar dt e de V Ve Q W m h gz me he gze dt e
ME-00 Fall 07 HW-9 / Soluton (a) Conderng energy balance for the dffuer ( I): Ideal ga table for ar: h 0 at T = 0 K h h V (00) h 0 65 000 T 60 65 60 Ideal ga table for ar: 70 60 70 60 T 65 K (b) Conderng energy balance for the ntercooler ( II): Q m h h cooler ar 4 Ideal ga table for ar: h 40. at T = 400 K; h 4 65 at T 4 = T = 65 K Ma flow rate of ar through the engne: m ar Q cooler 6805 65 40. h4 h m ar 50 (c) Conderng energy balance for LPC ( III) and HPC ( IV), total power for the compreor: W LPC WHPC mar h hh4 h 5 50 65 40. W W,60 kw ; negatve gn ndcate power nput LPC HPC (d) Conderng deal ga equaton of tate, pecfc volume of ar at the dffuer nlet: 0.87 0 K RarT -K m v.5 p 0.500 kpa AV Ma flow rate of ar at the dffuer nlet: m v m 50.5 Area of the dffuer nlet ecton: A A 0.4 m m 00 Conderng crcular nlet ecton, the dameter of the dffuer nlet ecton: A D D 0.7 m.4 ft 4
ME-00 Fall 07 HW-0 /4 Gven Power cycle wth two-tage team turbne Fnd (a) Fracton of team extracted from the HPT (b) Total power output (kw) for the HPT and LPT (c) Total power nput (kw) for the LPP and HPP (d) Rate of heat tranfer (kw) for the water n the boler (e) Rate of heat tranfer (kw) for the team n the condener (f) Thermal effcency (%) ung (b), (c), and (d); compare ung (d) and (e) (g) Ma flow rate (/) of the coolng water Sytem/EFD m team 0 y mteam W HPT ym team W LPT Q boler Condener W HPP W LPP Aumpton - Steady tate, teady flow - One-dmenonal, unform flow - Ignore KE and PE change - Neglect preure drop for the boler and condener - Ignore heat tranfer for boler, condener (team and coolng water), mxng chamber, pump, and turbne: Q 0 - No work for boler, condener, and mxng chamber: W 0 - Neglect effect of ppng between varou component
ME-00 Fall 07 HW-0 /4 Bac Equaton dm m 6 7 me m m m mteam; m m4 m5 ( y) m team dt e de V Ve Q W m h gz me he gze dt e Soluton State : p = 80 bar, T = 50ºC T at (p ) = 95.0C T > T at (p ) uperheated vapor Ung uperheated vapor table: h 448.7 State : p = 7 bar, T = 80ºC T at (p ) = 64.95C T > T at (p ) uperheated vapor Ung uperheated vapor table: h 799.4 State : p = 0.08 bar, x = 0.8 h hf pxhg h f 7.84 0.8576. 7.84 9.8 State 4: p 4 = 0.08 bar, x 4 = 0 (aturated lqud) h4 hf p 47.84 State 5: p 5 = 7 bar, T 4 = 4ºC T at (p 5 ) = 64.95C T 5 < T at (p 5 ) ub-cooled (compreed) lqud Ung aturated lqud approxmaton: m h5 hf T5vf T5p5 patt580.07 0.00009 7 0.08650800 kpa 80.77 State 6: p 6 = 7 bar, x 6 = 0 (aturated lqud) h6 hf p 6697 State 7: p 7 = 80 bar, T 7 = 67ºC T at (p 7 ) = 95.0C T 7 < T at (p 7 ) ub-cooled (compreed) lqud Ung double nterpolaton n compreed lqud table: h 7 70.58 State 8: p 8 = bar, T 8 = 0ºC T at (p 8 ) = 99.6C T 8 < T at (p 8 ) ub-cooled (compreed) lqud Ung aturated lqud approxmaton: m h8 hf T8vf T8p8 patt88.94 0.00008 0.0900 kpa 84.0
ME-00 Fall 07 HW-0 /4 State 9: p 9 = bar, T 9 = 0ºC T at (p 9 ) = 99.6C T 9 < T at (p 9 ) ub-cooled (compreed) lqud Ung aturated lqud approxmaton: m h9 hf T9vf T9p9 patt95.7 0.000044 0.0447000kPa 5.8 (a) Conderng energy balance for the mxng chamber ( I): mh mh h6 h5 697 80.77 ym 5 teamh y mteamh mteamh6 y h h5 799.4 80.77 Fracton of team extracted from the HPT: y 0. e e e (b) Conderng energy balance for HPT ( II) and LPT ( III), total power for the W HPT WLPT mteam hh yh h turbne: 0 448.7 799.40.799.4 9.8 W W 5,789 kw ; potve gn ndcate power output HPT LPT (c) Conderng energy balance for LPP ( IV) and HPP ( V), total power for the W LPP WHPP mteam yh4 h5 h6 h7 pump: 0 0.7.84 80.77697 70.58 W W 574 kw ; negatve gn ndcate power nput LPP HPP (d) Conderng energy balance for boler ( VI), rate of heat tranfer for water n the boler: Q boler mteam hh 70 448.7 70.58 Q 8,44 kw ; potve gn ndcate heat tranfer to the bolng water boler (e) Conderng energy balance for condener ( VII) (only tream excludng coolng water), rate of heat tranfer for team n the condener: Q condener y mteam h4 h 0.0 7.84 9.8 Q 46,70 kw ; negatve gn ndcate heat tranfer from the condenng condener team to coolng water
ME-00 Fall 07 HW-0 4/4 (f) Thermal effcency for a power cycle: W W HPT WHPT WLPP WHPP 5, 789 574kW net th th 4.7% Qn Qboler 8,44 kw W 8,44 46, 70kW net Q Qboler Q net condener th th 4% Q Q Q 8,44 kw n n boler Note: Thermal effcency value are wthn 0.5% due to round-off error related to heat tranfer rate and power calculaton (g) Conderng energy balance for condener ( VII) (tream and coolng water): mh mh y m h m h y m h m h e e team coolng water 8 team 4 coolng water 9 e Ma flow rate of coolng water: 0.0 9.8 7.84 y m team hh4 m coolng water h9 h8 5.884.0 m coolng water 7 Note: Coolng water can be modeled a ncompreble lqud: 4.8 0 K 4.8 -K h h u u v v p p c T T 9 8 9 8 8 9 9 8 water 9 8