How To Calculate The Power Of A Power Of Two
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1 MAE41-Enrgy Systm Prsntation Topic: Introduction to Brayton Cycl Prpard by: L Lng Fng
2 1. Gas Turb powr Plant.. History of Brayton Cycl.. Air standard Brayton Cycl 4. Work and Hat Transfr Brayton cycl. -Idal Air-Standard Brayton Cycl. 5. Prssur Ratio ffct on t fficincy of Brayton cycl. 6. Irrvrsibility ffct on t fficincy. 7. Rgnrativ gas turb.
3 Introduction: 1. Gas Turb Powr Plant Tr basic componnts: 1. Comprssor. Combustor. Turb
4 1. Gas Turb Powr Plant -Modlg Gas Turb Powr Plant 1. Workg Fluid is air.. Combustion procss modl by a Hat Excangr.. No composition cang t air.
5 1. Gas Turb Powr Plant Modl of t Gas Turb Powr Plant- Brayton Cycl
6 . History of Brayton Cycl Invntd by Gorg Baily Brayton. Not commrcially succssful. Rasons: Not compact and fficint as t Otto cycl availabl at t sam tim. Frank Wittl, a young cadt sows t limitation of t piston drivn ngs for ig spd air craft is trm papr. H sowd tat a contuous flow turb basd ng wic combustion occurrd at constant prssur could ovrcom ts limitations. Tis cycl, of cours, is t Brayton cycl.
7 . Air Standard Brayton Cycl Assumptions: Modl combustion as a at xcangr. Air is an Idal Gas Modl as a clos systm. Undrgos a trmodynamic Cycl.
8 . Air Standard Brayton Cycl P-v Diagram and T-s Diagram of Brayton Cycl Procss 1-: Isntropic comprssion t comprssor Procss -: Hat Addition at a constant prssur Procss -4: Isntropic xpansion a turb Procss 4-1: Hat Rjction at a constant prssur.
9 4.Work and Hat Transfr Brayton Cycl Analysis Tools: 1. Mass Rat Balanc Equation. m out m out. Enrgy Rat Balanc Equation. de dt CV Q CV W m V gz m V gz
10 4. Work and Hat Transfr Brayton Cycl Stat 1 to Stat : Isntropic Comprssion Procss t Comprssor. Assumptions: Stady Stat Exists. Ktic and Potntial Enrgy ar ngligibl t procss No Hat Transfr t comprssion procss.
11 4. Work and Hat Transfr Brayton Cycl Matmatical modl: Stat 1 to Stat - 1. Apply Mass Balanc Equation, m m m 1 out m m. Apply Enrgy Rat Balanc Equation, out de dt CV Q CV W m V gz m V gz Wit t givn assumptions, w av: W comprssor m ( 1
12 4. Work and Hat Transfr Brayton Cycl Stat to stat : -Isobaric Expansion Procss t Hat Excangr. Assumptions: Stady Stat Conditions xists. Ktic nrgy and potntial nrgy is ngligibl No work is bg don durg tis procss.
13 4. Work and Hat Transfr Brayton Cycl Matmatical modl: Stat to Stat - 1. Apply Mass Balanc Equation, m out m m m out m. Apply Enrgy Rat Balanc Equation, de dt CV Q CV W m V gz m V gz Wit t givn assumptions, w av: Q Q m m m
14 4. Work and Hat Transfr Brayton Cycl Stat to Stat 4: Isntropic Expansion Procss t Turb Similar to t procss from Stat 1 to Stat, t Work output is: W turb m ( 4
15 4. Work and Hat Transfr Brayton Cycl Stat 4 to Stat 1: -Isobaric Hat Transfr Procss t Hat Excangr Similar to t procss from Stat to Stat, t Hat Transfr is: Q out m ( 4 1
16 4. Work and Hat Transfr Brayton Cycl Trmal Efficincy of Brayton Cycl: Trmal Efficincy, η = dsird rquird work output at put η = W turb / m W Q / m comprssor / m (Part of t work Output was usd to driv t comprssor. η = ( 4 ( 1
17 4. Work and Hat Transfr Brayton Cycl -Idal Air-Standard Brayton Cycl. Usg Idal Gas Equation to furtr idaliz t Brayton Cycl Advantags: 1. W can avoid usg Air tabl to fd t rspctiv ntalpy.. Can provid an uppr limit to t prformanc of Brayton Cycl Assumptions: 1. Tr is no frictional prssur drop t t cycl.. Tr is no irrvrsibility t cycl.. Hat Transfr to t surroundg is also ignord. Basic Equations: Idal gas Equation for Isntropic Procss: k k P1 V1 PV or T P T1 P 1 ( k1 k
18 4. Work and Hat Transfr Brayton Cycl -Idal Air-Standard Brayton Cycl. W will gt t followg rlations for Brayton Cycl: V1 V P 4 T 1 P4 T and and V4 V P P T1 T
19 5. Prssur Ratio Effct on t Efficincy of Brayton cycl. Usg Spcific Hat Equation for Idal Gas, d C p ( T dt T Trmal Efficincy of t Brayton Cycl can now b calculatd trms of tmpratur: W av, And Fally, η = η = η = ( 4 ( 1 C ( T p 4 C ( T T C p p T 1 ( T T 1 ( k1 P P k / 1 -Rlation btwn prssur ratio and trmal fficincy. 1
20 5. Prssur Ratio Effct on t Efficincy of Brayton cycl. Rstrictions on t prssur ratio: 1. Mtallurgical considration at t Turb Inlt.. Siz of t Gas Turb.
21 6. Effct of Irrvrsibility on Efficincy -Incras of ntropy comprssor and Turb du to frictional ffct. -Exprinc prssur drop Hat Excangr du to Friction. Tus, Isntropic Efficincy of t Turb and Hat Excangr bcom:, turb = ( W ( W turb turb / m / m s 4 4, s, comprssor = ( W ( W comprssor Comprssor / m / m s, s 1 1
22 7. Rgnrativ Gas Turb -Us of Enrgy of t air xaustd from t Turb to partly at t air from t comprssor. -T at xcang btwn t Exaust air and t air from t comprssor occurs t Rgnrator.
23 7. Rgnrativ Gas Turb T-s diagram of a Rgnrativ Gas Turb. -T xaust gas is coold from stat 4 to stat 6 t rgnrator. -Air xitg t comprssor is atd from stat to stat 5 t rgnrator. -T xtra at from t xaustd air will vntually go to stat 1. -Air xistg t comprssor was atd from stat 5 to stat Now, t fficincy of t Brayton Cycl bcoms: η = ( 4 ( 1 5'
24 Gas Turb Powr Plant Opn mod, Clos mod. History of Brayton Clcl Summary Air Standard Brayton Cycl Assumptions, Modl as Two Isntropic Procsss and two Isobaric Procsss. Work and Hat Transfr Brayton Cycl Work: W comprssor m ( 1 W turb m ( 4 Hat: Q m ( Q out m ( 4 1 Trmal Efficincy: ( 4 ( 1
25 Summary (contu Prssur Effct on t Efficincy of t Brayton Cycl Effct of Irrvrsibility on Efficincy Isntropic fficincy: Rgnrativ Gas Turb Incras Efficincy: k k P P 1 ( 1 / 1 1 s s turb turb turb m W m W 4, 4 / ( / ( 1 1, / ( / ( m W m W s comprssor s Comprssor comprssor 5 ' 1 4 ( ( End- Tank you.
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