Kinetically Controlled Combustion Phenomena

1. Kinetically Controlled Combustion Phenomena

2. Categorisation of Combustion Phenomena Most of the practical combustion phenomena belong to one of the following three categories: • Phenomena which are primarily controlled by chemical kinetics • Phenomena which are primarily controlled by diffusion, convection and other physical mixing processes • Phenomena in which the roles played by chemical kinetics and physical mixing are more or less of equal importance.

3. Ignition, explosion, extinction and quenching of flames serve as examples of kinetically controlled phenomena • The burning of a gaseous fuel jet, of a liquid fuel spill, spray, or drop, of a carbon sphere and of a candle in which fuel and oxidant are contacted by diffusion illustrate the diffusionally controlled combustion phenomena. • Flames in a gasoline engine, a Bunsen burner and other situations in which the fuel and oxidant are premixed belong to the third category.

4. Let A, B and C denote respectively the fuel, oxidant and product of combustion which are all in gas phase and are uniformly distributed in a combustion chamber • Such a "uniform" distribution may be accomplished by increasing the molecular mixing or turbulent intensity, say, by mechanical stirring • Kinetically controlled phenomena are those in which the reaction rate is slow compared to the rates of heat and species diffusion so that the species and temperature have adequate time available to smooth out any spatial non-uniformities.

5. When reactions are very fast, the spatial nonuniformities of composition and temperature fail to be washed out in the short available time. As a result, gradients of species and temperature are established in space. • Such gradients cause conduction of heat and diffusion of species towards the regions of lower temperatures and concentrations respectively. • The reactants diffuse into the flame zone whereas the products andheat diffuse away from the flame zone. Such a poorly mixed combustion is said to be diffusionally controlled. Explicitly, diffusion controlled phenomena are those in which the rate of reaction is much faster than the rate of diffusion.

6. In a given combustion phenomenon, the fuel and oxidant have to be supplied (by flow, diffusion and mixing) to a station where they react chemically. Heat and products have then to be removed from this station physically. • There are two characteristic rates involved in this problem, the rate of supply and the rate of consumption. The lowest of these two rates governs the overall speed of the process. • In kinetically controlled combustion phenomena, the rate of consumption of the fuel and oxidant by chemical reaction is much smaller than the rate of supply by flow, diffusion or mixing. • In diffusion controlled combustion phenomena, the rate of flow, diffusion and mixing is much smaller than the chemical reaction rate.

7. In kinetically controlled phenomena, the flame occurs more or less uniformly in theentire reaction space • In diffusionally controlled phenomena, flame is located at some distinct station in the space. • This point of distinction is schematically represented in Figure 4. 1.

9. Let the reacting gas mixture of the species A (fuel) and B (oxygen) be confined by a wall in such a way that the characteristic thickness of the body of gas is . • Let YAWbe the mass fraction of A at the wall and Y be some characteristic mean mass fraction of A in the reacting body of gas. • The amount of species A transferred from the wall to the gas phase can be written in terms of a mass transfer coefficient hD (which is proportional to ρD (density x diffusion coeff) as ŴA"= hD(YAW ‑ YA)gm/cm2 /sec • The amount of A consumed in the gas phase reaction is given by a simple rate law which we assume as of order unity and of Arrhenius type ŴA" = k1 YA e-E/(RT) gm/cm2 /sec

10. Solving for YA, • The ratio in the denominator is known as Damkohler number, Da. Case (a): Kinetically controlled regime: • Da → 0, then hD >> k1 e-E/RTand YA YAW • The composition remains nearly uniform throughout the reaction space. • The rate of depletion of the fuel, then, is given by the reaction rate ŴA"  k1 YAW e-E/(RT) (4.4) • The regime arises when the mixing is high, the diffusion coefficient is high, the gas body thickness is small, the pre‑exponential collision factor is small, the activation energy is large and the gas body temperature is low.

11. Case (b): Diffusionally (or Diffusion or Flow or Physically) Controlled Regime: • Da , hD <<k1 e-E/RT • The physical rate (of supply flow, mixing and diffusion) is much smaller than the chemical rate (of the reaction) • Equation 4.2 then gives i.e. the gas body mass fraction of species A is negligible compared with the mass fraction at the wall. • The rate of fuel depletion is given by the mass transfer rate as ŴA"  hD YAW(4.5) • These phenomena arise when the mixing is poor, the flow and diffusion are slow, the gas body thickness is large and the chemical reaction is fast

12. Diffusion flames can be converted into kinetic flames by either increasing the chemical time or decreasing the physical time. • For example, if we blow out a match or a candle, or send a burning droplet into a fast moving air stream, the flame is extinguished due to the chemical reaction rate << the increased rate of diffusion of the fuel and oxygen into the reaction zone (fuel is diluted). Kinetically controlled • Similarly, if we increase the flow velocity of fuel in any diffusion flame, a point is reached where the flame lifts away from the tube through which the fuel issues (heat is “swallowed”)

14. Ignition • Most of the energy released in a combustion reaction is in thermal form while a fraction is released in the form of light. • Emission of light is either due to incandescent solid particles such as carbon in the flames (hot light = incandescence) or due to some unstable (excited) intermediate species (colt light = chemiluminence). • Of the heat generated, part is lost from the reacting mixture and part is retained by it.

15. (a) Thermal Ignition • Under certain conditions of heating brought about by an external source of energy such as a spark, hot vessel walls, compression, etc., there is always some temperature of the reacting mixture at which the rate of heat generation exceeds the loss rate. • The excess heat increases the mixture temperature which in turn leads to higher reaction rate. The mixture temperature rises continuously and acceleratively until a high heat evolution rate is attained. Ignitionis then said to have occurred.

16. In reality, the accelerative rise of temperature is quite abrupt; the previously invisible slow reaction suddenly becomes visible and measurable. • An uncontrollably fast reaction is known as an explosion.Closed vessel explosions are very common in practice. • At ignition, any combustion reaction seems as though it were an explosion. For this reason, superficially, the terms "explosion" and "ignition" are used synonymously in the combustion literature.

17. (b) Chemical Chain Ignition • If the combustion reaction involves intermediate chain carriers, ignition is possible even under isothermal conditions. If the rate of chain carrier generation exceeds the rate of their termination, the reaction becomes progressively fast and subsequently leads to ignition. • The chain initiation itself may require an external source of thermal or photon energy. Once the chain is initiated, the external source may be removed and ignition may be expected if the above criterion of positive chain carrier balance is fulfilled. • Determination of the conditions under which a given combustible mixture ignites, is an important topic in the design of combustion engines as well as in fire prevention.

18. (c) Scope of the Present Chapter • A major part of the rest of this chapter deals with ignition and extinction from a thermal viewpoint. • The concepts of ignition delay, flammability limits, and minimum ignition energy are presented through this thermal theory.

19. (d) Two Types of Ignition • Experience shows that there are two general modes of ignition ‑ spontaneous and forced. Spontaneous ignition • Spontaneous ignitionis sometimes called as auto‑ignition or self‑ignition. Spontaneous ignition occurs as a result of raising the temperature of a considerable volume of a combustible gas mixture by containing it in hot boundaries or by subjecting it to adiabatic compression. • Because the heat generation rate is a strong exponential function of temperature whereas the heat loss rate is a simple linear function, even a slight increase in the temperature of the reacting mixture would greatly increase the rate of its temperature rise.

20. As a consequence, once the generation rate exceeds the loss rate, ignition occurs in the whole volume almost instantaneously. • The reaction then proceeds by itself without any further external heating. Forced ignition • Forced ignition occurs as a result of local energy addition from an external source such as an electrically heated wire, an electric spark, an incandescent particle, a pilot flame, etc. • A flame is initiated locally near the ignition source and it propagates into the rest of the mixture.

21. There are many instances in which a fuel and an oxidant are rapidly mixed at a high temperature which can result in a spontaneous ignition. • For example, a spray of diesel fuel into the hot compressed air is in part vaporized and mixed with the air in a very short time. Following a definite delay, the reaction would proceed rapidly enough to be considered a flame. • There are technically important instances of spontaneous ignition where it is not vvanted, i.e. fire such as that occuring on oil splashed on hot surfaces and the knock in a gasoline engine.

22. SpontaneousIgnition Spontaneous Ignition Delay (a) The Criterion Consider a vessel of volume V and surface S containing a combustible mixture. Let T0 be the initial temperature of the mixture. Assume that the temperature at any later time in the mixture is spatially uniform. Let the vessel walls be kept at T0 for all times.

23. Eq. (4.7) applies to adiabatic combustion system • Eq. (4.8) takes into account the heat transfer from flame to the wall • First term represents heat generation by reactions • Second term represents accumulation of heat in the vessel • Third term represents heat transfer

24. If the heat transfer coefficient is constant, at a very low pressure the reaction rate will be small because the system then practically remains at T = To • At a very high pressure, the heat generation overwhelms the loss term (i.e. the system approaches adiabatic conditions). The temperature and the reaction rate, then, enhance one another until spontaneous ignition occurs. • Therefore, it is reasonable to expect that there exists a critical pressurebelow which the reaction behaves more like an isothermal (non-explosive) process and above which it behaves like a spontaneously exploding (abrupt temperature) adiabatic process.

25. (b) Ignition delay • The criterion of positive heat balance is required for spontaneous ignition • When the limiting case of adiabaticity isapproached, Eq. 4.8 with 3rd term = 0 can be used to deduce the concept of ignition delay (sometimes called ignition lag, induction time, or ignition time). • The strong influence of temperature on a simple thermal reaction rate is often expressed by the conventional Arrhenius exponential or by a simple power law.

26. The power m is of the order 20 to 30 for most combustible mixtures whereas the activation energy E is of the order 20 to 60 kilocalories per mole. • Incorporating Eq. 4.15 into Eq. 4.7 and integrating, the time history of temperature is obtained as

27. Equation 4.16 indicates that as the time the temperature T of the reacting mixture rises very steeply. • The critical time is called ignition delay

28. Eq. 4.17 shows that the ignition delay is short if the mixture has a low volumetric heat capacity, high temperature dependence of the rate, high heat of combustion and high initial reaction rate.

29. Incorporating Eq. 4.15a into Eq. 4.7 and integrating, the time history of temperature is obtained as with the assumption of negligible reactant consumption during the ignition delay, the time history of temperature is where

30. Figure 4.5 illustrates mixture temperature at fraction of delay time for various values of E/RT0

31. Semenov Theory of Spontaneous Ignition • Eq. 4.8 can be rewritten in the following eq. • Keeping the pressure fixed, (T)will be a steeply rising function as shown in Figure 4.6(a) • (T) isa linear function of Twith a slope of hS cal/(sec K). Keeping hS fixed, three different (T) functions are also shown in Figure 4.6(a) corresponding to three values of the wall temperature T0. T is mixture temperature. • The right hand side ofEq. 4.8 as a function of T is shown in Figure 4.6(b) for the three values of T0

33. Case: Wall temperature relatively low • When T0 = T03, the curve and line intersect at two points, a and b; at a and b thus dT/dt =zero. • If the starting (i.e., T at time t = 0) reacting mixture temperature T < Ta, (and by Eq. 4.8, dT/dt) > 0 and < 0. So, a mixture with T < Ta slowly heats up until Ta (or dT/dt > 0), at a rate which continuously decreases with time (d2 T/dt2 < 0). Curves of such heating for four different values of the starting temperature are shown in Figure 4.7(a).

34. If the starting temperature of the mixture is Ta < T < Tb, both and < 0 so that the mixture cools down to Ta at a continuously decreasing rate. Such cooling curves are shown in Figure 4.7(a) for three different values of the starting temperature. • If the starting temperature of the mixture T > Tb, both dT/dt and d2T/dt2 > 0 so that the temperature of the reacting gases increases at an accelerating rate as shown by four curves in Figure 4.7(a).

35. Case: Wall temperature relatively high • When To = To1, curve and line never intersect. Thus, is always > 0. As shown in Figure 4.7(c), the temperature of the gases increases acceleratively. Case: Wall temperature moderate: • As the wall temperatures progressively > T03 are considered, the points a and b approach one another when ultimately they coincide at the point c corresponding to a critical wall temperature T02 in Figure 4.6(a). • The heat balance curve for this situation is shown in 4.6(b). The heating curves are shown in Figure 4.7(b).

37. Important criteria concerning spontaneous ignition • The wall temperature T02 is a limiting one beyond which the reaction progressively accelerates. The corresponding temperature Tc is called spontaneous ignition temperature of the reactant gas mixture in the given vessel. • Tc is not a fundamental property of the given fuel/oxidant mixture. The vessel in which such a mixture is contained has quite a strong influence on it.

38. At the critical point, c, the curve and the line are tangential. The interrelationship between pressure, temperature and composition at the ignition threshold hence is given by the following two equations. • In the above analysis, the pressure (i.e. the reaction) and the heat transfer coefficient are kept fixed and the critical wall temperature is deduced

39. Keeping the reaction (=pressure) and wall temperature fixed while seeking for the critical heat transfer coefficient results in Fig. 4.8

40. Keeping the wall temperature and the heat transfer coefficient fixed and while seeking for the critical reaction (=critical pressure) results in Fig. 4.9

41. Application of Semenov Theory to Predict Ignition Range • The critical point c in Figure 4.6(a) marks the transition of a slow stable reaction into one that is explosive. Assuming Arrhenius type rate law, Eqs. 4.18 and 4.19 become

42. Eliminating H Vkn CAcn/hSfrom these two equations and with an assumption that the amount of reactant consumed in the ignition delay is negligible, This quadratic has two roots; the lower one applies to ignition and the upper one to extinction.

43. Substituting Eq. 4.20 in Eq. 4.18(a) we obtain for a simple second order thermal reaction (applies to most of HC/air reactions) • Since RTc/E << 1, • If the gases are assumed perfect and if Pc and PA are respectively the total pressure and the species A partial pressure, where XA is the mole fraction of the species A.

44. Equation 4.22 thus becomes, • If the composition X, is kept fixed, Eq. 4.23 relates the critical pressure with the critical temperature. • Logarithmically,

45. Eq. 4.24 is known as Semenov Equation. Plotting ln (Pc/Tc2) on the y‑axis and (I/Tc) on the x‑axis, Eq. 4.24 gives a straight line with a slope of E/2R (see Figure 4.10).

46. Pc ‑ Tc plane, as shown in Figure 4.11, delineates the ignitable from non-ignitable conditions. • At low pressures, very high temperatures are needed to accomplish ignition and vice versa.

47. Equation 4.24 can also be used to construct the ignition ranges on a T ‑ XA plane at a fixed total pressure and on a P ‑ XA plane at a fixed temperature (see Figures 4.12 and 4.13) • In general, these graphs are U‑shaped. The conditions lying inside the U result in an ignition whereas those lying outside, do not. • Several inferences can be drawn from these figures (see T ‑ XA relation given by Figure 4.12)

50. Firstly, there exist a lower and an upper concentration limits for ignition; if the mixture is too fuel‑lean or too fuel‑rich, ignition is not possible no matter what the temperature is. The critical fuel concentration, below which ignition is impossible, is known as the lower limit of ignitability; and that above which ignition is impossible, is known as the upper limit. • Secondly, as the temperature is lowered, these two limits approach one another, thus narrowing the range of ignition. • Thirdly, if the temperature is very low, ignition is impossible at any composition.