1. COMBUSTION ENGINEERING
PROF. SEUNG WOOK BAEK
DIV. OF AEROSPACE ENGINEERING, KAIST, IN KOREA
ROOM : 3304
TELEPHONE : 3714

2. BURNING OF A FUEL DROPLET IN AN OXIDIZED ATMOSPHERE
PROBLEMS
HOW TO PRODUCE SPRAYS
CHARACTERISTICS OF THE SPRAY
BURNING RATE OF SPRAY?
OXIDIZER
PRESSURE
AMBIENT TEMPERATURE
EFFECTS OF
MICRO EXPLOSION
METAL PARTICLE
SLURRY
IGNITION
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

3. COMBUSTION ENGINEERING
DROPLET MAY INTERACT IF CLOSE TOGETHER
GROUP COMBUSTION
INDIVIDUAL DROPLET COMBUSTION
EFFECT OF CONVECTION
EFFECT OF BUOYANCY
OXIDIZER
FUEL
BURNING OF AN INDIVIDUAL DROPLET
FLAME SURFACE
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

4. COMBUSTION ENGINEERING
TYPICAL EXPERIMENTS
EXCESSIVELY LARGE SIZE
PRECLUSION OF TRANSIENT
PHENOMENA
QUARTZ FILAMENT
DISTORTION HEAT LOSS
SUSPENSION TECHNIQUE
SUSPENDED DROPLET
FUEL
POROUS SPHERE
(A)
(B)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

5. COMBUSTION ENGINEERING
FREE FALLING DROPS
ZERO g EXPERIMENTS
FORCED CONVECTION
(C)
(D)
BUOYANCY EFFECT
(1) BURNING RATE IS INCREASED DUE TO ENHANCED TRANSPORT RATES
(2) FLAME SHAPE IS SEVERELY DISTORTED: NOT MEANINGFUL TO IDENTIFY A FLAME DIAMETER
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

6. COMBUSTION ENGINEERING
IN (A)
FOR STEADY BURNING
(1)
: SPHERE RADIUS
IN (B) AND (C) AFTER AN INITIAL UNSTEADY PERIOD
(2)
: DROPLET DIAMETER
: EVAPORATION CONSTANT(BURNING CONSTANT)
LAW: ALSO VALID FOR PURE VAPORIZATION
ANALYSIS
DERIVATION OF EQUATION (2): PREDICTS BURNING RATE: FLAME SHAPES: TEMPERATURE AND CONCENTRATION PROFILES
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

7. COMBUSTION ENGINEERING
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

8. COMBUSTION ENGINEERING
ASSUMPTION
(1) SPHERICAL SYMMETRY
(2) USE SINGLE STEP REACTION
(3) Shvab-Zeldovitch FORMULATION
(4) STEADY COMBUSTION
(i) HEATING AND IGNITION PERIODS NEGLECTED (THE FLOW VARIABLES ARE CONSTANT INSIDE THE DROPLET)
(ii) CHANGES AS DROPLET VAPORIZES: AT MOST USING QUASI STEADY THEORY
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

9. COMBUSTION ENGINEERING
BECAUSE OF THE SIGNIFICANT DENSITY DISPARITY BETWEEN LIQUID AND GAS, THE PROPERTIES AT THE DROPLET SURFACE SUCH AS THE REGRESSION RATE, SPECIES CONCENTRATIONS, AND TEMPERATURE IN LIQUID PHASE CHANGE AT RATES MUCH SLOWER THAN THOSE FOR THE GAS PHASE TRANSPORT PROCESSES
(3)
(4) IF
(5)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

10. COMBUSTION ENGINEERING
THE BURNING RATE?
(6)
WILL BE AN EIGENVALUE OF
(7)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

11. COMBUSTION ENGINEERING
COMBINE (6) AND (7)
(8)
( IS INDEPENDENT OF r )
LET
(9)
(10)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

12. COMBUSTION ENGINEERINGIF
(11)
FROM (5)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

13. COMBUSTION ENGINEERING
CONSIDER THERMAL COUPLING FCN
B.C.
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

14. COMBUSTION ENGINEERING
DROPLET SURFACE
SPECIES CONSERVATION (GO TO APPENDIX)
NO SURFACE REACTION
INTERFACE IS NOT MOVING.
NO EXCESS MASS AT SURFACE
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

15. COMBUSTION ENGINEERING
(12)
FOR OXIDIZER (NO DISSOLUTION INTO DROPLET)
USE
(13)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

16. COMBUSTION ENGINEERING
INTERFACE CONDITION ON T FOR UNIFORM AND CONSTANT DROPLET TEMPERATURE
(14)
L = LATENT HEAT OF VAPORIZATION
INTRODUCE
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

17. COMBUSTION ENGINEERING
(15)
BY MAKING
TERM INVOLVING DROPS OUT
COMBINE RESULTS (13) & (15),
(16)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

18. COMBUSTION ENGINEERING
APPLY FOR
(17)
(18) AS
(19)
(20)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

19. COMBUSTION ENGINEERING
(20)
FROM DEFINITION OF
(21)
USING DEFINITION OF
FROM EQUATION (20),
(22)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

20. COMBUSTION ENGINEERING
DISCUSSION (EQUATION (22))
CAN BE VARIABLE
DOES NOT DEPEND ON FLAME SURFACE APPROXIMATION
( : FLAME SURFACE APPROXIMATION)
: BASIC FUEL PROPERTIES GENERALLY KNOWN
: FOR BURNING DROPS
: USUALLY KNOWN IF AMBIENT ATMOSPHERE IS SPECIFIED
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

21. COMBUSTION ENGINEERING
Tl IS DETERMINED BY THERMODYNAMIC CONDITION, SUCH THAT AT THE SURFACE =
THEREFORE, WE NEED TO KNOW
FREQUENTLY USED ONE IS Clausius-Clapeyron RELATION.
: NORMAL ATMOSPHERIC PRESSURE & BOILING TEMPERATURE
: PREVAILING PRESSURE
FUEL BOILING TEMPERATURE, (GOOD APPROXIMATION)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

22. COMBUSTION ENGINEERING
(23)
(24)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

23. COMBUSTION ENGINEERING
(25)
(ACCURATE KNOWLEDGE OF Tb IS NOT ESSENTIAL)
(SIMILARITY BETWEEN VAPORIZATION & COMBUSTION) B
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

24. COMBUSTION ENGINEERING
FROM EQUATION (5)
(26)
REMARKS
INSENSITIVE TO PRESSURE, WEAKLY DEPENDENT ON TEMPERATURE
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

25. COMBUSTION ENGINEERING
OTHER CHARACTERISTICS OF BURNING DROPLETS
SOLVED FOR
2nd ORDER EQUATIONS
3 B.C’s
FLAME LOCATION?
(27)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

26. COMBUSTION ENGINEERINGAS
ASSUME AS
(28)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

27. COMBUSTION ENGINEERING
AT DROPLET SURFACE,
(29)
BECAUSE OF
AT DROPLET SURFACE,
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

28. COMBUSTION ENGINEERING
(20)
(21)
(28)
(29)
(30)
COMBINE : (28), (29), (30) FOR UNKNOWNS
SOLVE FOR
(31)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

29. COMBUSTION ENGINEERING
CONCENTRATION PROFILE AND TEMPERATURE
FLAME SURFACE APPROXIMATION
AT FLAME
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

30. COMBUSTION ENGINEERING
PROFILES 1
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

31. COMBUSTION ENGINEERING
(32)
(27)
WHEN
(33)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

32. COMBUSTION ENGINEERING
ASSUME
USE EXPRESSION FOR IF
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

33. COMBUSTION ENGINEERING
REMARK
INDEPENDENT OF (DROPLET RADIUS)
TOO LARGE BY A FACTOR OF 2
BECAUSE NATURAL CONVECTION IS NEGLECTED
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

34. COMBUSTION ENGINEERING
MODERN DEVELOPMENTS
NOT SPHERICALLY SYMMETRIC, BUT MULTIDIMENSIONAL
TRANSIENT EFFECTS IN SURFACE REGRESSION RATE AND INTERIOR DROPLET HEATING
MULTICOMPOSITIONAL WITH VARYING VOLATILITIES
DROPLET INTERACTIONS
THERMODYNAMIC NON-IDEALITY: DISSOLUTION OF AMBIENT GA IN LIQUID DROPLET, REAL EQUATION OF STATE, REAL THERMODYNAMIC PROPERTIES
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

35. COMBUSTION ENGINEERING
APPENDIX
CONDITION AT FLAME SURFACE AND THE NATURE OF THE FLAME SURFACE APPROXIMATION
OXIDIZER
FUEL
ai = INTERFACE AREA
v = VOLUME OF CONTROL VOLUME
FROM Leibnitz RULE WITH
USING
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

36. COMBUSTION ENGINEERING
MOTION OF THE C.V.
USING DIVERGENCE RULE
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

37. COMBUSTION ENGINEERING
WHEN THE INTERFACE (C.V.) DOES NOT MOVE
CONSERVATION OF SPECIES BECOMES
(*)
FOR i = F,
(**)
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

38. COMBUSTION ENGINEERING
ALL FUEL FLOWING TOWARD THE FLAME FRONT + SIDE IS CONSUMED AT THE FLAME SURFACE
FOR i = 0
(***)
FOR SINGLE STEP CHEMICAL REACTION
: RATE OF PRODUCTION
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

39. COMBUSTION ENGINEERING
DIVIDE
(**) BY
(***) BY
AND SUBTRACT
WHEN FUEL + OXIDIZER FLOW INTO FLAME FROM OPPOSITE SIDES IN STOICHIOMETRIC PROPORTIONS,
AT FLAME
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

40. COMBUSTION ENGINEERING
CONCENTRATION GRADIENTS REMAIN FINITE AT THE FLAME
DIFFUSION FLUX IN STOICHIOMETIC PROPORTIONS
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING

41. COMBUSTION ENGINEERING
REMARKS
TEMPERATURE?
SOLVE FOR
AND
PRODUCT?
SOLVE FOR
AND
BASIC PROPERTIES OF DIFFUSION FLAME ARE ESTABLISHED WITHOUT CONSIDERATION OF REACTION RATES I.E. CHEMICAL KINETICS
PROPULSION AND COMBUSTION LABORATORY
COMBUSTION ENGINEERING