COMBUSTION. TA : Donggi Lee ROOM: Building N7-2 #3315 TELEPHONE : 3754 Cellphone : PROF.

Transcription

1 COMBUSIO ROF. SEUG WOOK BAEK DEARME OF AEROSACE EGIEERIG, KAIS, I KOREA ROOM: Buldng 7- #334 ELEHOE : 3714 Cellphone : swbaek@kast.a.kr A : Dongg Lee ROOM: Buldng 7- #3315 ELEHOE : 3754 Cellphone : kngdongg@kast.a.kr

2 HE Shvah-Zeldovth FORMULAIO OF EQUAIOS OF MULI-COMOE REACIG GASES ASSUMIO EGLEC (A) BODY FORCE (B) HERMAL DIFFUSIO (SORE EFFEC) (C) RESSURE GRADIE DIFFUSIO (D) BULK VISCOSIY (E) RADIAIO SEADY FLOW OVERALL COIUIY ( v ) I MOS OF LOW SEED COMBUSIO ROBLEMS VISCOUS ERMS ARE EGLECED, IF M 1 ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

3 MOMEUM EQUAIO : JUSIFICAIO OE DIMESIOAL SECIES EQUAIO ( v V ) y v y V dy d v ( yv ) dx dx y ( v ) v y ~ CHEMICAL IME t ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

4 IF v IS A CHARACERISIC VELOCIY, v t o v l : CHARACERISIC CHEMICAL LEGH ROULSIO AD COMBUSIO LABORAORY l ~ ORDER OF DISACE I WHICH REACIO IS COMLEED ~ REACIO ZOE HICKESS (MAY MOLECULAR COLLISIOS ARE EEDED) IEGRAE 1D MOMEUM EQUAIO OCE 4 3 dv dx u j u u j X p v p onst 1 j, x j p u j u j j ( ) ( ) x j x 3 j COMBUSIO EGIEERIG j u j x k k

5 v Op ( ) x ROULSIO AD COMBUSIO LABORAORY I REGIO WHERE VISCOUS EFFECS ARE IMORA dv dv Dv v p dx p v dx p v Dt t ~ O( ) : VISCOUS IME p v v o t v l v vl v v M R ~ O(1) v R v VISCOUS LEGH p R R l l v : LEGH I WHICH RASLAIOAL AD RAAIOAL MODES ARE EQUILIBRIAED: OE OR WO COLLISIOS ~ MEA FREE AH v COMBUSIO EGIEERIG

6 l l v 1 l 1 ~ 1 m : I AMOSHERE l 5 v ~ 3 1 m v lv vt o v v p R DIMESIOLESS VARIABLES ROULSIO AD COMBUSIO LABORAORY l v t o v p p, ~ v ~ v,, ~ x x x ; why l? C p v l v dy d v ( yv ) dx dx COMBUSIO EGIEERIG

7 vl v v M R l v t o v v lv vt o v v p R WHY l? BECAUSE COIUIY dy d v ( yv ) dx dx MOMEUM v l ROULSIO AD COMBUSIO LABORAORY ~~ dy v dx ~ 3 4 dv p v v O(1) p p dx v M, p 4 lv dv p M v O(1) 3 l dx t l p t l v v ~~ dy v dx ~ l O(1) v COMBUSIO EGIEERIG

8 p onstant: momentum ( v ) : MASS If M 1 ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

9 D v ( e ) v p p v ( v ) Dt q X v V ) Q s s ( s SEADY SAE EERGY EQUAIO p EGLEC KIEIC EERGY VISCOUS WORK BODY FORCE RADIAIO vu q pv u = SECIFIC IERAL EERGY q = HEA FLUX = h yv 1 vu( ) ( hyv ) pv 1 (1) () ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

10 vu( ) ( hyv ) pv 1 u 1 v ( hy 1 ROULSIO AD COMBUSIO LABORAORY p h y ) [ v 1 p p v vp v vp pv p SUBSIUE IO h onst y ] ( v onstant) v vv vu( ) ( hyv ) pv 1 COMBUSIO EGIEERIG

11 EERGY EQUAIO BECOMES [ v h y ] v p pv 1 ( h y V ) p v ( ) 1 1 SECIES COSERVAIO, yh ( v V ) h h p ) d y ( v V (3) (4) (5) ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

12 ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG U (5) I (4), h d yv d v 1 1 (6) y 1

13 v d yv 1 SECOD ERM I (6), USE USE d dx B ( x ) V D ln y yv 1 Dy y d D y 1 d ( LEIBIZ RULE) d y d ( ) y d p 1 f ( x, t) x f ( x, t) dt dt f ( x, B) A( x ) B ( x) A( x) d db dx 1 h f ( x, A) da dx (6) (7) (8) (9) ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

14 v d yv d h 1 1 (6) COMBIE (8) & (9) 1 yv d D D d ( ransport of hermal Energy by Dffuson) HE (6) BECOMES, v d D Le Lews D umber d DC 1 h (1) ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

15 h d d v 1 ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG ASSUME 1 Le DC HE REUR O SECIES, COMBIE EQUAIOS (5) & (7) (11) y D V V v y ln ) ( p y y v (1) REMARKS : 1) Shvah-Zeldovth FORM OF EQUAIOS. ) Cp s & Cp s ARE O ECESSARILY COSA. h d D D d v 1

16 SIGLE REACIO SE k m m 1 1 LAW OF MASS ACIO C ˆ HE RAE OF RODUCIO OF A CHEMICAL SECIES IS ROORIOAL O HE RODUCS OF HE COCERAIO OF EACH REACA WIH EACH COCERAIO RAISED O A OWER EQUAL O IS SOICHIOMERIC COEFFICIE. = COCERAIO OF SECIES = MOLES ER UI VOLUME ER SECOD FORMED OF SECIES ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

17 ˆ W ALSO WE CA WRIE, k = SECIFIC REACIO RAE COSA ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG C k 1 ) ( ˆ ) ( ) ( ˆ 1 C k

18 ˆ ( ) ˆ j j j... = RAE OF RODUCIO FOR AY SECIES (MOLES/UI VOLUME/S) Wˆ W ) ( W = MOLECULAR WEIGH OF SECIES ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

19 ] [ ) ( ) ( D v L L W h d C 1 '' ' ) ( ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG FOR SECIES AD EERGY EQUAIOS WIH SIGLE REACIO, EACH CA BE REDUCED O HE FORM FOR EERGY EQUAIO ) ( ' '' W y FOR SECIES EQUAIO h d d v 1 p y y v ) ( W

20 m m ox '' ' fu s W ( ) y L OFE : A LIEAR OERAOR : O LIEAR: IVOLVES RODUCS OF S k E / R ~ e : ARRHEIUS YE y SICE L( ) L( 1 ) L( ) L( 1) L( ) L() ROULSIO AD COMBUSIO LABORAORY 1 REMARKS ) MAY BE IMLICILY O-LIEAR BECAUSE OF DEEDECE OF V O D COMBUSIO EGIEERIG

21 DIFFUSIO FLAME AY FLAME I WHICH FUEL AD OXIDIZER ARE ORIGIALLY UMIXED EXAMLES) CADLE FLAME ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

22 DROLE BURIG IDIVIDUAL DROLE BURIG OXIDIZER ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

23 BOUDARY LAYER ADJACE O FUEL SURFACE OXIDIZER FUEL OXIDIZER ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

24 JE FLAME ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

25 LAMIAR DIFFUSIO FLAMES ARE CHARACERIZED BY (1) REACIO RAES FAS COMARED O RAES OF MASS AD EERGY RASFERS BY DIFFUSIO AD COVECIO () REACIO EDS O BE COCERAED I HI FROS WHERE FUEL AD OXIDIZER ARE I SOICHIOMERIC ROORIO. (3) RAE OF COVERSIO OF MIXURE IS SLOWER HA HA I REMIXED FLAME ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

26 (4) WHE JE VELOCIY EXCEEDS A CERAI VALUE HE FLAME BECOMES URBULE LARMIAR RASIIO URBULE Hottel and Hawtherns FLAME HEIGH 3 RD SYMOSIUM O COMBUSIO (1949) JE VELOCIY ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

27 QUALIAIVE AALYSIS r L RELAIO BEWEE FLAME HEIGH L UBE DIAMEER d d OXIDIZER FUEL VELOCIY V (OR FLOW RAE ) V MASS FLOW V d ROULSIO AD COMBUSIO LABORAORY ~ RAE A WHICH FUEL AD OXIDIZER MIX BY DIFFUSIO A Flame D dy dr 1 ~ LdD d COMBUSIO EGIEERIG

28 d ~ D d ~ t dffuson LD FOR GIVE FUEL D IDEEDE OF L ~ t L ~ dffuson FOR URBULE FLOW L ~ L ~ d v d D v d D RELACE D BY A URBULE DIFFUSIO COEFFICIE, ~ LD d Dt ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG

29 D t (URBULE SCALE)(URBULE IESIY) SIZE OF LARGES EDDY L d IDEEDE OF JE VELOCIY d ~ LD t ~ ~ d Ld L ~ ROULSIO AD COMBUSIO LABORAORY COMBUSIO EGIEERIG