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C OMBUSTION P ROF. S EUNG W OOK B AEK D EPARTMENT OF A EROSPACE E NGINEERING, KAIST, IN KOREA R OOM : Building N7-2 #3304 T ELEPHONE : 3714 Cellphone: 010 – T A : Bonchan Gu R OOM : Building N7-2 #3315 T ELEPHONE : 3754 Cellphone: 010 – P ROF. S EUNG W OOK B AEK D EPARTMENT OF A EROSPACE E NGINEERING, KAIST, IN KOREA R OOM : Building N7-2 #3304 T ELEPHONE : 3714 Cellphone: 010 – T A : Bonchan Gu R OOM : Building N7-2 #3315 T ELEPHONE : 3754 Cellphone: 010 –

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING P HYSICAL P ICTURE OF C OMBUSTION WAVE V ERY S MALL I GNITION E NERGY – E XTINGUISHED V s = SPACE VELOCITY OF THE FLAME ; I.E. RELATIVE TO WALL V u = VELOCITY OF UNBURNED MIXTURE RELATIVE TO WALL V f = VELOCITY OF THE FLAME RELATIVE TO THE UNBURNED MIXTURE V f = V s –V u : BURNING VELOCITY

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING I NSTANTANEOUS G ENERATION OF A C-J D ETONATION STAGNANT BURNED GAS VcVc P(x) V(x) VcVc V CJ P1P1 U = 0

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING S TRUCTURE OF THE D ETONATION W AVE V2V2 CJ (2) COMBUSTION INDUCTION ZONE 2S IGNITION DELAY TIME T2T2 V2V2 V 2S T 2S P 2S V CJ T1T1 P1P1 P CJ P1P1 V CJ UNBURNED

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING U SUALLY G ET Chapman-Jouguet D ETONATION ; P ROPERTIES OF C-J D ETONATION M ASS- M OMENTUM- E NERGY F OR C-J W AVESAND

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING V ALID FOR C-J D ETONATION OR D EFLAGRATION

F OR D ETONATION, P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING OR

C-J D ETONATION V ELOCITY D EPENDS O NLY ON THE H EAT R ELEASE Q, I NDEPENDENT OF. P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING T HEREFORE, V ARIES WITH ONLY B ECAUSE THE S PEED OF S OUND C HANGES. P RESSURE R ATIO, OR

FROM MASS, MOMENTUM, AND ENERGY P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING OR

MACH NUMBER OF BURNED GASES RELATIVE TO THE WALLS P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING FOR C-J (HIGH SUBSONIC)

C OMPARISON BETWEEN P RESSURE BEHIND A S HOCK & C-J D ETONATION FOR THE S AME M ACH N UMBER P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING Q (1) 2S

F OR C-J D EFLAGRATION, ( G OOD FOR C-J D ETONATION & D EFLAGRATION) F OR C-J D EFLGRATION, P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING

( F OR C-J D ETONATION) G ET F OR D EFLAGRATION M= 1/6 P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING E XAMPLE FOR THE C-J D ETONATION OF M IXTURE

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING

D IFFERNTIAL E QUATION OF T RANSPORT OF M ATTER AND E NERGY I NCLUDING C OMBUSTION R EAL C OMBUSTION P HENOMENA I NVOLVE H UNDREDS OF I NTERACTING C HEMICAL R EACTIONS. B UT F OCUS A TTENTION ON A M ODEL OF C OMBUSTION, WHICH A CCORDS WITH R EALITY IN R ESPECT OF THE O VERALL E FFECTS. P URPOSE : Q UANTITATIVE P REDICTIONS OF C OMBUSTION P HENOMENA P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING

S IMPLE C HEMICALLY R EACTING S YSTEM (SCRS) FUEL+OXIDANTPRODUCT 1 S 1+S S : S TOICHIOMETRIC R ATIO R EACTANTS P RODUCE A U NIQUE P RODUCT IN F IXED P ROPORTIONS BY M ASS. P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING INDEPENDENT OF TEMPERATURE

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING H : HEAT OF COMBUSTION IFIF AND

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING F OR S TEADY 1-D D IFFUSION- C ONTROLLED F LAMES T HE F UEL AND O XIDIZER C OMBINE WITH A F IXED S TOICHIOMETRIC R ATIO S : A ND IF

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING O BEYS THE S AME D IFFERENTIAL E QUATION AS THE M ASS F RACTION OF A C HEMICALLY I NERT M ATERIAL D OES. P RECISE K NOWLEDGE OF THE ‘ S IS N OT N ECESSARY. F OR SCRS NO VISCOUS SHEAR WORK NO KINETIC ENERGY EFFECTS NO EXTERNAL ENERGY SOURCES

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING T HE T WO S TREAM M IXING P ROCESS (AN I DEALIZATION OF C OMBUSTION C HAMBER F LOWS) F OR A NY E XTENSIVE P ROPERTY OF A F LUID WHICH IS F REE FROM S OURCES AND S INKS : CONSERVED PROPERTY : MIXTURE FRACTION

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING,, AND A NY L INEAR C OMBINATION OF S UCH C ONSERVED P ROPERTIES: I F THE M IXING P ROCESS IS A DIABATIC AND F REE FROM W ORK I NPUT, S TAGNATION E NTHALPY IS A C ONSERVED P ROPERTY EX) m in : MASS FRACTION OF AN INERT COMPONENT

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING T HE F UEL AND O XIDANT M ASS F RACTION ARE L INKED WITH I F F : FUEL, A : OXYGEN WITH DILUENT

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING A FTER C HEMICAL R EACTION IS C OMPLETED.

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING I T S HOULD B E O BSERVED T HAT THE M IXTURE F RACTION W ILL O BEY THE S AME D IFFERENTIAL E QUATIONS AS D O AND.