1. Overview of Combustion

2. Ignition Three things must be present at the same time
in order to produce fire:
Enough oxygen to provide combustion,
Enough heat to raise the material temperature to its ignition temperature,
Fuel or combustible material which produces high exothermic reaction to propagate heat to not-yet- burnt material nearby

4. Activation energy

5. Flammability limit

7. Different flame types of Bunsen Burner depending on air flow through the throat holes (holes on the side of the bunsen burner). 1. air baffle closed (Safety flame) 2. air baffle half open 3. air baffle nearly fully open 4. air baffle fully open
Premixed flame

8. Diffusion flame
A burning candle. Within the bluer, hotter region near the base of the wick, hydrogen separates from the wax vapor, burns and forms water vapor. Within the brighter, yellower part of the flame, carbon soot oxidizes, and forms carbon dioxide.

9. Spectrum of flame colour

11. Flame stabilisation

12. Stabilisation using swirling

13. Burning fossil fuels produces > 2/3 of our energy production today and probably still will in a century.
Combustion is encountered in many practical systems such as boilers, heaters, domestic and industrial furnaces, thermal power plants, waste incinerators, automotive and aeronautic engines, rocket engines and even in refrigeration plants

14. In most applications, combustion occurs in
gaseous flows and is characterized by:
A strong and irreversible heat release. Heat is released in very thin fronts (typical flame thicknesses are usually < 0.5 mm) inducing strong temperature gradients (temperature ratios between burnt and fresh gases are of the order of 5 to 7).

15. Highly nonlinear reaction rates . These rates follow Arrhenius laws:
where the Yk are the mass fractions of the N species involved in the reaction and Ta is an activation temperature. Ta is generally large so that reaction rates are extremely sensitive to temperature.

16. Combustion strongly modifies the flow field
Combustion strongly modifies the flow field. In simple one-dimensional flames, burnt gases are accelerated because of thermal expansion but more complex phenomena occur in turbulent flows: depending on the situation, turbulence may be either reduced or enhanced by flames .
Fuel oxidation is generally faster compared to flow time scales but pollutant formation (nitric oxides, soot) may be quite slower.

17. Various coupling mechanisms occur in combusting
flow fields:
Chemical reaction schemes deal with the fuel consumption rate, the formation of combustion products and pollutant species and should handle ignition, flame stabilization and quenching (full chemical schemes for usual hydrocarbon fuels involve hundreds of species and thousands of reactions).
Mass transfers of chemical species by molecular diffusion, convection and turbulent transport also occur.

18. The heat released by chemical reactions induces strong conductive, convective or radiative heat transfer inside the flow and with the surrounding walls.

19. For two (liquid fuel) and three (solid fuel) phase reacting systems, some other aspects must also be involved: spray formation, vaporization, droplet combustion.
Even for gaseous combustion, multiphase treatments may be needed: for example, soot particles (which can be formed in all flames) are carbon elements of large size transported by the flow motions.
Some of these phenomena are illustrated in Fig. 1 in the simple configuration, but very complex case, of a candle.

20. Figure 1. A very delicate flame: the candle.
Straight arrows correspond to mass transfer
Broken arrows denote heat transfer.

21. The solid stearin fuel is first heated by heat transfer induced by combustion. The liquid fuel reaches the flame by capillarity along the wick and is vaporized.
Fuel oxidation occurs in thin blue layers (the color corresponds to the spontaneous emission of the CH radical).
Unburnt carbon particles are formed because the fuel is in excess in the reaction zone. Soot, which is produced by imperfect combustion, is welcomed in the case of the candle because it is the source of the yellow light emission.
Flow (entrainment of heavy cold fresh air and evacuation of hot light burnt gases) is induced by natural convection (a candle cannot burn in zero-gravity environment).

22. To describe the various possible states observed in
reacting flows it is useful to introduce a classification
based on combustion regimes. Flames can be (see
Table 1):
premixed, non-premixed or partially premixed in terms of how fuel and oxidiser are contacted
laminar or turbulent in terms of the shape of fluid flow
stable or unstable in terms of maintaining the combustion phenomena

23. Table 1. Some examples of practical applications in terms of premixed/non-premixed flame and laminar/turbulent flow field.

24. Criterion (a) depends on the way how to introduce the reactants into the combustion zone and is one of the main parameters controlling the flame regime.
Fuel and oxidizer may be mixed before the reaction takes place (premixed flames, Fig. 2a) or enter the reaction zone separately (non-premixed or diffusion flames, Fig. 2b).

25. Figure 2. Classification of the combustion regime as a function of the reactant introduction scheme.

26. Criterion (b) corresponds to the usual definition of turbulent states in which large Re numbers lead to unsteady flows. Most practical flames correspond to turbulent flows: turbulence enhances combustion intensity and allows the design of smaller burners.
Criterion (c) is more specific of reacting flows: in some situations, a flame may exhibit strong unsteady periodic motions (combustion instabilities) due to a coupling between acoustics, hydrodynamics and heat release.

27. Premixed flames
In premixed combustion, the reactants, fuel and oxidizer, are assumed to be perfectly mixed before entering the reaction zone (Fig. 2a).
Premixed flames propagate towards the fresh gases by diffusion/reaction mechanisms: the heat released by the reaction preheats the reactants by diffusion until reaction starts (reaction rates increase exponentially with temperature).

28. A one dimensional laminar premixed flame propagates relatively to the fresh gases at the so-called laminar flame speed sl depending on the reactants, the fresh gases temperature and the pressure (Fig. 3). For usual fuels, the laminar flame speed is about 0.1 to 1 m/s.
When fresh gases are turbulent, the premixed flame propagates faster. Its speed sT is called the turbulent flame speed and is larger than the laminar flame speed (sT >> sl).

29. Figure 3. Structure of a one-dimensional premixed laminar flame.

30. For typical flames, the flame thickness, including preheat zone, is about 0.1 to 1 mm whereas the reaction zone itself is ten times thinner. In this figure, the oxidizer is assumed to be in excess.
The correlation between sT, sl and the turbulence intensity of the incoming flow u’:
(1)

31. where  and n are two model parameters of the order of unity
where  and n are two model parameters of the order of unity. Unfortunately, sT is not a well defined quantity (Gouldin,1996) and depends on various parameters (chemistry characteristics, flow geometry).
Eq. (1) is consistent with the experimental observation that the turbulent flame speed increases with the turbulence intensity.

32. Premixed flames offer high burning efficiency as the reactants are already mixed before combustion.
The burnt gases temperature, which plays an important role in pollutant formation, can be easily controlled by the amount of fuel injected in the fresh gases.

33. But these flames may be difficult to design because reactants should be mixed in well defined proportions (fuel/oxidizer mixtures burn only for a limited range of fuel mass fraction).
A premixed flame may also develop as soon as the reactants are mixed, leading to possible safety problems.

34. Non-premixed flames
In non-premixed flames (also called diffusion flames), reactants are introduced separately in the reaction zone.
The prototype of this situation is the fuel jet discharging in atmospheric air (Fig. 5). This configuration is very simple to design and to build: no pre-mixing is needed and it is safer: the flame cannot propagate towards the fuel stream because it contains no oxidizer and vice versa.

35. Nevertheless, diffusion flames are less efficient because fuel and oxidizer must mix by molecular diffusion before burning.
The maximum burnt gases temperature is given by the temperature of fuel and oxidizer burning in stoichiometric proportions and cannot be controlled easily.
The structure of a one-dimensional non-premixed laminar flame is sketched in Fig. 4.

36. Figure 4. Structure of a one-dimensional non-premixed laminar flame
Figure 4. Structure of a one-dimensional non-premixed laminar flame. Here fuel and oxidizer streams are assumed to have the same temperature.

37. Turbulence is also found to enhance combustion processes in non-premixed flames as evidenced by Hottel and Hawthorne (1949) who measured the length of a diffusion flame burning a fuel jet discharging in ambient air as a function of the fuel flow rate (Fig. 5).
The flame length increases linearly with the fuel flow rate as long as the flow remains laminar.

38. Figure 5. Non-premixed jet flame
Figure 5. Non-premixed jet flame. A fuel jet discharges in the ambient air. Top: flow configuration; Bottom: flame length versus fuel jet velocity. (Hottel and Hawthorne, 1949.

39. When the jet becomes turbulent, the flame length remains constant even when the flow rate increases, showing an increase of the combustion intensity.
Very large flow rates will lead to lifted flames (the flame is no more anchored to the jet exit) and then to blow-off or flame quenching.

40. Partially premixed flames
The previously described premixed and non-premixed flame regimes correspond to idealized situations.
In practical applications, fuel and oxidizer cannot be perfectly premixed.
In some situations, an imperfect premixing is produced on purpose to reduce fuel consumption (toward premixed) and to reduce pollutant emissions (toward diffusion).

41. For example, in spark-ignited stratified charge internal combustion engines, the fuel injection is tuned to produce a quasi-stoichiometric mixture in the vicinity of the spark to promote ignition but a lean mixture in the rest of the cylinder.
In non-premixed flames, fuel and oxidizer must meet to burn and ensure flame stabilization, leading to partially premixed zones.
A small premixed flame develops and stabilizes a diffusion flame as shown in Fig. 6. As a consequence, partially premixed flames have now become topics of growing interest

42. Figure 6. Structure of a triple flame
Figure 6. Structure of a triple flame. The flame is stabilized by a premixed flame burning imperfectly premixed reactants (rich and lean wings). A diffusion flame develops downstream.

43. Stable and unstable flames: Thermodiffusive instabilities
Laminar premixed flames exhibit intrinsic instabilities depending on the relative importance of reactant molecular diffusion and heat diffusion. An example of such phenomena, studied in details in numerous papers (see, for example Williams, 1985) is illustrated in Fig. 7.

44. Assume that the molecular diffusivity of reactants is higher than the thermal diffusivity (i.e. the Lewis number Le = k/( Cp D), comparing thermal and species diffusivities, < 1).
When the flame front is convex towards the fresh gases, reactants diffuse towards burnt gases faster than heat diffuse towards cold fresh gases.
These reactants are heated and then burn faster in reduced convex region, increasing the local flame speed sl (sl > slo) with time

45. On the other hand, for fronts convex towards the burnt gases, reactants diffuse in a large zone thus increasing convex region and the flame velocity is decreased compared to slo (sl < slo). This situation is unstable: the flame front wrinkling increases.
When the species molecular diffusivity < the heat diffusivity (Lewis number > 1), a similar analysis shows that the flame is stable: the flame front wrinkling decreases.

46. Figure 7. Sketch of thermo-diffusive instabilities (in laminar premixed flames). For Le < 1, molecular diffusion (red arrows) > heat diffusion (blue arrows) and the wrinkling of the flame front is enhanced by differential flame speeds (left figure).
For Le > 1 (right figure), a stable planar flame is obtained in which molecular diffusion (blue arrows) < heat diffusion (red arrows)

47. Stable and unstable flames: Flame/acoustic interactions
Thermodiffusive instabilities (laminar premixed flames) are rarely observed in industrial devices.
However, another type of instability may develop in confined flames. These instabilities come from a coupling between hydrodynamics, heat release and acoustics.
Strong unsteady motions develop producing noise, enhancing combustion intensity and leading sometimes to the system destruction.

48. In some cases, such instabilities may be generated on purpose to increase efficiency like in pulse combustors, but generally undesired.
A simple example of such combustion instability is provided in Fig. 8 for a premixed turbulent laboratory burner (Poinsot et al., 1987). Without combustion instabilities, a turbulent reacting jet stabilized by recirculation zones is observed (Fig. 9 left).
Changing the equivalence ratio  (i.e. the amount of fuel in the air stream) leads to a strong instability (Fig. 9 right): large mushroom vortices are formed at a frequency of 530 Hz, increasing the combustion intensity by about 50 %.

49. The mechanism of such an instability may be summarized as follows (Poinsot et al., 1987): a vortex is generated at the jet inlet and convected downstream. It induces an unsteady reaction rate, producing an acoustic wave moving upstream to generate a new vortex at the burner inlet.

50. Figure 8. Experimental turbulent premixed burner of Poinsot et al

51. Figure 9. Combustion instabilities in a turbulent premixed flame
Figure 9. Combustion instabilities in a turbulent premixed flame. Schlieren views of the central jet through the quartz window of Fig. 8: stable (left) and unstable (right) regimes. The flow is going from the right to the left (Poinsot et al., 1987).