1. Ignition
Ignition is a transient process from a nonreactive to a reactive state in which external stimuli lead to thermochemical runaway followed by a rapid transition to self-sustained combustion. The ignition may be spontaneous or forced.
When the temperature and/or pressure of a reactive mixture are raised to a certain value, and the mixture is left alone, it may burst into flame after a certain time. This is called spontaneous ignition, also referred to as self-ignition or autoignition, and occurs without the action of any external source. It occurs, e.g., in Diesel engines.
A process where a mixture, which would not ignite by itself, is ignited locally by an ignition source (such as a spark, a pilot flame or a hot wire) is called forced ignition or induced ignition. It occurs, e.g., in spark-ignition engines.
Although the spontaneous and forced ignition processes are similar, being governed by the same laws, the boundary conditions are different.
Ignition
Combustion

2. Ignition
Many relevant combustion phenomena require the analysis of the ignition process, e.g.:
To investigate the ignitability of a material or a reactive mixture under given initial conditions with a fixed energy input.
To determine the minimum energy required for attainment of ignition.
To study the effect of various physical and chemical parameters on ignition delay.
To determine the time required for ignition to occur.
To prevent fire hazards.
There are many parameters that influence ignition:
initial pressure and temperature of a reactive mixture
chemical composition of the mixture
energy input of an ignition source
spatial and temporal distribution of that energy input
velocity, turbulence intensity and thermal properties of the reactive mixture.
Ignition
Combustion

3. Ignition
In order to attain ignition, three conditions should be met:
The temperature of the reactive mixture should be high enough to allow auto-sustained chemical reactions
The time must be long enough to allow the heat input to be absorbed by the reactants so that a runaway thermochemical process can occur
The mixing between the fuel and the oxidizer, and the heat transfer from the burning mixture to the fresh mixture should be good to allow auto-sustained chemical reactions
Ignition processes are usually very complex, since ignition is inherently transient and detailed chemical kinetics needs to be taken into account, along with convective and diffusive transport.
Hence, unsteady transport equations need to be solved.
Only ignition of gaseous fuels will be addressed in this course.
Ignition
Combustion

4. Spontaneous ignition in a homogeneous and adiabatic system
Let´s consider spontaneous ignition in a homogeneous, isothermal and adiabatic system. The reactive mixture is at rest and the volume is constant. The first law of thermodynamics yields
The conservation equations for the mass fraction of the species and for energy are written as
Let´s further consider a global single-step irreversible reaction. Despite this major simplification, which prevents a quantitative analysis, a qualitative one is feasible
Ignition
Combustion

5. Spontaneous ignition in a homogeneous and adiabatic system
After some algebra, the following results are obtained:
with
Spontaneous ignition of the mixture occurs when the argument of the logarithm approaches zero, so that the temperature increases sharply. This phenomenon is also referred to as thermal explosion.
The time tig, referred to as ignition time or ignition delay time, correspond to the vertical asymptote in the figure. When t approaches tig, the equations above are not valid, and B is no longer a constant (see figure).
Ignition
Combustion

6. Spontaneous ignition in a homogeneous and adiabatic system
The ignition time may be estimated by setting to zero the argument of the logarithm, which yields
The ignition time is inversely proportional to the initial pressure for a reaction of order 2, since tig  B-1 and B  p.
The ignition time decreases with the increase of the initial temperature of the mixture, To. In fact, the activation energy is high enough such that the exponential term dominates: Ea/Ro is close to 2104 K for most fuels, so that exp(Ea/RoT) decreases with the increase of temperature in the relevant range of temperatures.
The ignition time is also inversely proportional to the initial mass fractions of fuel and oxidant via B. This implies that the ignition time increases when there are inerts present in the mixture. However, the equivalence ratio has a marginal influence on the ignition time.
Ignition
Combustion

7. Spontaneous ignition in a homogeneous and adiabatic system
In the case of a system at constant pressure, the energy equation is written as
The previous equations for the ignition time remain valid, but constant B is different.
The analysis of the influence of the initial pressure, temperature and chemical composition of the mixture on the ignition time remain also valid.
In an adiabatic system, spontaneous ignition will always occur, according to the previous analysis. However, it may be very long, in case the activation energy is high and the initial temperature and pressure are low, such that it may not be observed .
In real systems, however, the analysis must be generalized, as we will see next,
Ignition
Combustion

8. Semenov analysis for homogeneous, non-adiabatic systems
The analysis of Semenov considers a homogeneous system and a global reaction in a system whose boundary is maintained at the initial temperature of the mixture, To, such that there is heat transfer from the mixture to the walls of the system.
The energy equation may be written as
qr – Energy released per unit of time due to chemical reaction
ql – Energy loss per unit time (through the boundary)
Since both qr and ql are positive, spontaneous ignition may either occur or not, depending on how large ql is compared with qr. Spontaneous ignition will occur if qr > ql
Ignition
Combustion

9. Semenov analysis for homogeneous, non-adiabatic systems
The evolutions represented in the figure may correspond, e.g., to three different pressures, since qr  pa+b-1. They may also correspond to the same pressure, but for different fuels, with different activation energies.
qr increases with the temperature. A peak should appear at high temperatures, as in the evolution of the reaction rate vs. temperature, but we are only concerned with lower temperatures, far from the peaks of qr and Rfu.
ql increases linearly with the increase of temperature (neglecting the small influence of temperature on the convective coefficient)
Case 1: qr=qr1
There are two stationary points (qr=ql)
Point a: Stable stationary point
Point b: Unstable stationary point
Ignition
Combustion

10. Semenov analysis for homogeneous, non-adiabatic systems
If T< Ta then qr > ql and the temperature will increase until T=Ta and qr = ql. Spontaneous ignition does not occur since dT/dt = 0 at this temperature.
Point a is stable because a temperature perturbation will cause the system to evolve until T=Ta is achieved again (why?).
If T > Tb then qr > ql and spontaneous ignition will occur.
Point b is unstable. The system may remain indefinitely at T=Tb, but any temperature perturbation will cause the system to evolve either to T=Ta or to spontaneous ignition (why?).
Case 2 - qr=qr2
There is one stationary point (qr=ql) :
Point c: Metastable point
Ignition
Combustion

11. Semenov analysis for homogeneous, non-adiabatic systems
If T< Tc then qr > ql and the temperature will increase until T=Tc and qr = ql. Spontaneous ignition does not occur since dT/dt = 0 at this temperature.
If T > Tc then qr > ql and spontaneous ignition will occur.
Point c is metastable because a temperature perturbation will cause the system to evolve either until T=Tc (if the temperature of the system decreases due to the perturbation) or spontaneous ignition (if the temperature of the system increases due to the perturbation) .
Case 3 - qr=qr3
Spontaneous ignition always occurs, since qr > ql and dT/dt > 0, no matter the initial temperature of the system
Ignition
Combustion

12. Semenov analysis for homogeneous, non-adiabatic systems
In case 2, the transition between the occurrence and the no occurrence of spontaneous ignition is defined by point c. The temperature at that point is the ignition temperature, Tig = Tc. At that temperature, the heat release rate is equal to the rate of heat loss, and is mathematically defined by:
and
Hence,
The following approximate result may be obtained from these equations:
Ignition
Combustion

13. Semenov analysis for homogeneous, non-adiabatic systems
In general, Tig exceeds To by 10 to 25 ºC. The difference Tig – To is the maximum temperature increase that may occur in the combustion system without spontaneous ignition.
Spontaneous ignition in a system at initial temperature To occurs if the pressure is greater than a critical value. This pressure may be determined by inserting the equation for Tig in the equation This yields, after some algebra, the Semenov equation.
The constant in Semenov’s equation depends on several factors, such as the geometry of the system, and the ratio volume/area of the surface.
The ignition temperature experimentally obtained for well-defined conditions should not be extrapolated to other conditions.
Ignition
Combustion

14. Chain spontaneous ignition
In the spontaneous ignition cases considered so far, the temperature increases continuously along the time, but the increase is initially small, and becomes abrupt after some time (the ignition time or ignition delay time). These are purely thermal ignition processes, also referred to as thermal explosions.
Spontaneous ignition may also occur after a period during which the temperature remains constant (the ignition time or ignition delay time) as a result of chain-branching reactions. This is referred to as chain spontaneous ignition or chain explosion.
In practice, since the combustion reactions are exothermic and take place at molecular level by means of formation and multiplication of radicals, both thermal and chain-branching reaction mechanisms occur simultaneously and contribute to spontaneous ignition.
Ignition
Combustion

15. Ignition delay time Ignition
The precise definition of the ignition delay time depends on the criterion used (e.g., consumption of fuel, formation of CO, formation of OH, increase of pressure in a constant volume vessel, increase of temperature in an adiabatic vessel, etc.)
However, the ignition delay time experimentally obtained is little sensitive to the selected criterion, since all the above phenomena occur when ignition takes place, and they happen almost simultaneously.
The ignition delay time is strongly dependent on To, being inversely proportional to To (see figure), as predicted from the theory
The slope of the lines is equal to Ea/Ro
The fuel significantly influences tig.
Ignition
Combustion

16. Forced ignition Ignition
The spontaneous ignition of a reactive mixture does not occur when the heat release rate is insufficient to compensate the heat losses to the surroundings or when the initial temperature of the mixture is so low, and therefore tig so long, that it is not reasonable to wait until spontaneous ignition occurs.
In such a case, a heat source is used. The minimum heat source required to ignite a reactive mixture is the minimum ignition energy.
Forced ignition, similarly to spontaneous ignition, may be explained either by the formation of large number of radicals yielding a chain explosion or by the energy added to the mixture (e.g., by a spark) to accelerate the chemical reactions yielding a thermal explosion.
The spark is the most common form of forced ignition. Spark ignition is highly reliable and is used, e.g., in spark-ignition and gas turbine engines, various industrial, commercial and residential burners.
Ignition
Combustion

17. Spark ignition Ignition
In spark ignition, a high potential difference is applied between two electrodes separated by a small gap. That potential difference causes an electrical discharge across the reactive mixture between the electrodes, heating that mixture.
The heat source causes a local significant increase of temperature, igniting the mixture, with the subsequent propagation of the flame to the fresh mixture.
Several ignition criteria have been used in the literature:
i) Ignition occurs when the heat release rate in the ignition region becomes equal to the heat loss to the surroundings.
ii) Ignition occurs when the characteristic cooling time of the mixture at adiabatic flame temperature exceeds the characteristic reaction time.
iii) Ignition occurs when enough energy is added to the mixture to heat a slab as thick as a steadily propagating laminar flame to the adiabatic flame temperature
Ignition
Combustion

18. Minimum ignition energy
Let’s consider a spherical gas volume, which represents the incipient propagating flame created by a spark, and let rcrit be the critical radius of that volume below which the flame does not propagate, i.e., ignition does not occur.
The minimum ignition energy is the energy required to heat a gas volume with radius equal to rcrit up to the adiabatic flame temperature. According to criterion i), the following equation may be written:
The solution of the steady state heat conduction equation for rcrit  r <  subjected to T=Tad at r = rcrit and T=To at r   yields
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Combustion

19. Minimum ignition energy
The minimum ignition energy may also be expressed as
Eliminating the critical radius from the previous equations leads to
(note that Rfu<0)
The minimum ignition energy depends on the pressure and on the initial temperature of the reactive mixture. It may be concluded that Eig  p1-3n/2 , where n is the order of the global reaction, since Rfu  pn
In the case of a global reaction of order 2,
Eig  p-2
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Combustion

20. Minimum ignition energy
The minimum ignition energy decreases significantly with the increase of the initial temperature of the mixture (mainly due to the increase of Rfu)
Fuel
To(K)
Eig(mJ)
n-heptane
298
14,5
Propane
233
11,7
373
6,7
243
9,7
444
3,2
iso-octane
27,0
253
8,4
11,0
5,5
4,8
331
4,2
n-pentane
45,0
356
3,6
7,8
3,5
477
1,4
2,3
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Combustion

21. Minimum ignition energy
Influence of f on Eig
(Eig )min depends on a of the fuel.
Fuel with lower M has higher a, implying that (Eig)min shifts to lower f.
Ignition
Combustion

22. Minimum ignition energy
The theory presented above is qualitative and does not allow an accurate prediction of the minimum ignition energy.
Experience shows that only part of the electrical energy of the spark is used to heat the reactive mixture, while another part is dissipated by thermal and electromagnetic radiation and conduction through the electrodes.
The minimum ignition energy depends on the geometry and material of the electrodes.
In the case of electrodes without flanges, the minimum ignition energy is obtained for a moderate distance between the electrodes, and increases if the distance is too small (due to heat loss to the electrodes) or too high (due to the need to heat a higher gas volume)
In the case of electrodes with flanges, ignition only occurs if the distance between the electrodes exceeds a minimum distance, referred to as quenching distance, dq. It has been experimentally found that
Ignition
Combustion

23. Minimum ignition energy
Combustion

24. Minimum ignition energy
There is a pressure below which spark ignition is not possible, regardless of the energy of spark
If the mixture is not at rest, ignition is affected:
The heated region is larger, particularly for turbulent flows
Heat losses increase
The quenching distance increases
The overall effect is the increase of Eig when the mean flow velocity or the turbulence intensity increase.
Mixture of methane/air
Ignition
Combustion