Encyclopedia of Wildfires and Wildland-Urban Interface (WUI) Fires

Living Edition
| Editors: Samuel L. Manzello

Combustion

  • Forman A. WilliamsEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-51727-8_60-1

Definition and Introduction

Since combustion is an essential part of all fires, including wildfires and fires at the wildland-urban interface, thorough knowledge of combustion is a significant underlying element in addressing the topic of this encyclopedia. A chemical process that liberates heat, combustion typically involves finite-rate chemistry in fluid flow with heat and mass transfer. The science of combustion is focused on obtaining basic descriptions of combustion phenomena by experimental and mathematical methods. The principles are sufficiently well developed that the subject qualifies as an applied science.

Unwanted fires involve specifically the combustion of available fuels in air. Combustion studies contribute to the development of methods for fire prevention, fire detection, fire hazard evaluation, fire damage assessment, and fire suppression. For example, investigations of mechanisms for extinction of combustion suggest elements of operation for fire extinguishers employed in fire suppression. Identification of fire retardant materials is aided by combustion knowledge. Strategies for controlling large fires employ estimates of combustion behavior. In general, much of the field of fire control research concerns combustion research.

Fundamentals of Combustion

Concepts of thermodynamics are of fundamental importance in combustion. Thermodynamic properties of fuels that pertain specifically to combustion include heats of combustion and adiabatic flame temperatures. One definition of the heat of combustion of a fuel is the heat released when the fuel reacts isothermally in air at a given pressure and temperature to form gaseous carbon dioxide and liquid water as reaction products. This is often termed the higher heating value of the fuel, the lower heating value being that reached if the final products contain steam instead of liquid water, so that the heat of vaporization of water is not recovered. The standard heat of combustion, the heat of combustion at normal atmospheric pressure and at standard room temperature, is given in Table 1 for a number of fuels.
Table 1

Selected heats of combustion and flame temperatures for various fuels (From Williams 2002)

Fuel

State

Formula

Standard heat of combustion at 298.15 K (kJ/g)

Oxidizer

Pressure (atm)

Adiabatic flame temperature (K)

Carbon

Solid (graphite)

C

32.8

Hydrogen

Gas

H2

141.8

Air

1

2400

O2

 

3080

Carbon monoxide

Gas

CO

10.1

Air

1

2400

Methane

Gas

CH4

55.0

Air

1

2220

Air

20

2270

O2

1

3030

O2

20

3460

Ethane

Gas

C2H6

51.9

Air

1

2240

Ethylene

Gas

C2H4

50.3

Air

1

2370

Acetylene

Gas

C2H2

48.2

Air

1

2600

O2

1

3410

Propane

Gas

C3H8

50.4

Air

1

2260

Heptane

Liquid

C7H16

48.4

Air

1

2290

Dodecane

Liquid

C12H26

47.7

Air

1

2300

Benzene

Liquid

C6H6

41.8

Air

1

2370

Fuel oil

Liquid

42–47

Air

1

2300

Coal

Solid

20–36

Air

1

2200

Wood

Solid

19–23

Air

1

2100

Also listed in that table are the adiabatic flame temperatures of the fuels, defined as the temperature reached in a fuel-air mixture containing the right amount of air required for burning to the specified products at constant pressure in a system initially at standard room temperature. The right amount of air is termed the stoichiometrically required amount, and if there is more air present, as in fuel-lean systems, or less, as in fuel-rich systems, then in most cases the final flame temperature achieved under adiabatic conditions lies below the value in the table. For acetylene, the values listed are maxima, which occur under fuel-rich conditions. For hydrogen, methane, and acetylene, adiabatic flame temperatures are also listed for combustion in pure oxygen rather than in air, and for methane values are given for an elevated pressure; these different values are seen to be higher. Fuel oils, coal, and wood vary in composition, and so the entries in the last three rows of Table 1 are average estimates. All of the listed flame temperatures here exceed 2000 K, which is why rates of heat transfer from fires are so large, although, because of dilution and measurement difficulties in turbulent flames; maximum observed temperatures generally are less than this, but still above 1000 K, sufficiently high to generate rapid fire spread.

The preceding information pertains to flaming combustion, in which the maximum temperatures occur in the gas phase. Smoldering is another mode of combustion, experienced in particular by cellulosic fuels such as wood and paper, in which oxidation occurs largely heterogeneously after diffusion of oxygen to the surface and interior of the material. Often called glowing combustion, the maximum temperatures for this pathway are lower, roughly in the range of 500–900 K. The two different possible modes arise from two different paths of pyrolysis (thermal decomposition) of the material, illustrated schematically for a carbohydrate (e.g., n = 6 for glucose) as:

where k 1 marks the flaming path and k 2 the glowing path (dehydration). For cellulose, a polymer of C6H10O5, the two competing initial steps may be described as the processes:

in which the “tar” is volatile and vaporizes to form a major gaseous fuel to support a gas-phase flame, while the gases evolved in the dehydration path are mainly noncombustible, and the char that remains can support only a surface oxidation, glowing combustion.

In combustion processes, the chemistry proceeds at finite rates and involves a number of elementary reaction steps. Two principal aspects of the chemical kinetics of combustion are the reaction mechanism (the sequence of elementary steps involved) and the rate of each elementary step. The relative rates of the steps vary with conditions, because they depend on the temperature, pressure, and composition of the system. Thus, steps that are important for some conditions become unimportant for others, which leads to changes in mechanisms as conditions change. Reaction mechanisms are understood well for many but not all combustion processes.

Reaction mechanisms in combustion usually involve chain reactions, in which a reactive intermediate species (such as hydroxyl, OH), called a chain carrier, which is created in some steps and destroyed in others, accelerates the overall rate of conversion of fuel to products. During much of the combustion process, these intermediaries can achieve steady-state concentrations (in which their total rate or creation equals their total rate of destruction), or they can be involved in reaction steps that attain partial equilibrium (in which the forward and backward rates of the steps are equal). If steady-state or partial equilibrium approximations can be verified for a particular combustion process, then improved understanding of its chemical kinetics is obtained, and simplified descriptions of the overall rate of conversion of fuel to products may be developed. The resulting descriptions are called reduced chemical-kinetic mechanisms, and methods for identifying and validating the required approximations in combustion are continually evolving.

When reaction mechanisms are not fully known, but measurements of overall rates of fuel destruction, oxygen consumption, or heat release can be made, then empirical one-step overall reaction rate expression can be obtained. In terms of the fuel concentration f (g/cm3), the oxidizer concentration g (g/cm), pressure p (atm), and temperature T (K), the empirical rate w (g/cm3 sec) often can be fitted to the formula:
$$ w=\mathrm{A}{\mathrm{f}}^l{g}^m{p}^n{e}^{-E/\mathrm{RT}} $$
where R (8.31 J/mol K) is the universal gas constant and the overall activation energy E, reaction orders l and m, pressure exponent l+m+n, and prefactor A are constants. Typically 40 kJ/mol ≤ E ≤200 kJ/mol and 0 ≤ l, m, l+m+n ≤ 2, although values outside these ranges can occur. The exponential factor here is called the Arrhenius factor, and the rate formula is said to be an Arrhenius expression, honoring his early work (1899).

A distinguishing attribute of many combustion processes that gives them a qualitative difference from other chemical rate processes is the tendency for the combustion rate to increase as the combustion proceeds. In chemistry this property often is called autocatalysis. There are two causes for the progressive increase in the rate of combustion. One is chain branching, exemplified by the elementary step H + O2 → OH + O (in a sense, the most important elementary step in all gas-phase combustion in air), where H, O, and OH are chain carriers, so that one carrier thereby generates two; since the combustion rate increases as the concentration of chain carriers increases, branching accelerates the process. The other cause is the increase of most elementary rates with increasing temperature, seen as the exponential factor in the preceding rate formula; since combustion is exothermic (releases heat), the temperature tends to increase as the process proceeds, and therefore the rate increases. The resulting self-acceleratory character of the reaction introduces features such as explosions, characterized as branched-chain explosions if chain branching dominates, or as thermal explosions if the increase in the rate with temperature dominates.

Combustion Waves

When equations are written for mass, momentum, and energy conservation for planar, steady, adiabatic combustion waves through which reactants are converted to products, it is found that a one-parameter family of waves may exist. The possibilities are conveniently illustrated in the pressure-volume diagram shown in Fig. 1. Here p denotes the ratio of the pressure in the burned gas to that of the initial combustible and v the ratio of the gas volume per unit mass of those combustion products to that of the initial reactants. The locus of the burnt-gas state in this diagram is called the Hugoniot curve, and the negative of the slope of the straight line connecting the burnt state to the initial state (called the Rayleigh line) is found to be proportional to the square of the propagation velocity of the wave. Therefore, the slope must be negative; this divides the Hugoniot curve into two branches, the upper one corresponding to detonations and the lower one to deflagrations. It is seen from the figure that there is a minimum propagation velocity for detonations, exhibiting tangency at the indicated upper Chapman-Jouguet (C-J) point, and a maximum propagation velocity for deflagrations, with tangency at the lower C-J point.
Fig. 1

A schematic diagram of the locus of burnt-gas states for combustion wave, from Williams (1985)

The two dashed lines in the figure illustrate representative intermediate conditions, and each has two intersections, corresponding to weak and strong waves, as indicated in the figure. The waves encountered in combustion are weak (in fact, nearly isobaric) deflagrations and strong, or quite often C-J, detonations. An increase in the heat released in combustion increases the separation between the initial state and the Hugoniot. Additional properties of these waves are summarized in Table 2, where the subscripts + and – refer to upper and lower C-J condition, respectively. In detonations a strong leading shock wave heats the mixture to initiate combustion, while in deflagrations initiation occurs by conduction of heat from the hot products to the cold reactants.
Table 2

A summary of types of combustion waves and their properties (From Williams (1985))

 

Section in Fig. 2–5

Pressure ratio p ≡ (p /p 0)

Velocity and density ratios v ≡ (v /v 0) = (p 0/p

Propagation Mach number M 0 ≡ (v 0/a f,0)

Downstream Mach number M ≡ (v /a e,∞)

Remarks

Strong detonations

Line A–B

p + < p < ∞

v min < v < v + (v min > 0)

M 0+ < M 0 < ∞

M < 1

Seldom observed; requires special experimental arrangement

Upper Chapman-Jouguet point

Point B

p = p + (p + > 1)

v = v + (v + < 1)

M 0 = M 0+ (M 0+ > 1)

M = 1

Usually observed for waves propagating in tubes

Weak detonations

Line B–C

p 1 < p < p + (p 1 > 1)

v + < v < 1

M 0+ < M 0 < ∞

M > 1

Seldom observed; requires very special gas mixtures

Weak deflagrations

Line D–E

p < p < 1

v 1 < v < v (v 1 > 1)

0 < M 0 < M 0−

M < 1

Often observed; p ≈ 1 in most experiments

Lower Chapman-Jouguet point

Point E

p = p (p < 1)

v = v (v > 1)

M 0 = M 0− (M 0− < 1)

M = 1

Not observed

Strong deflagrations

Line E–F

0 < p < p

v < v < v max (v max < ∞)

M 0min < M 0 < M 0− (M 0min > 0)

M > 1

Not observed; forbidden by considerations of wave structure

These combustion waves can occur when the reactants, fuel, and oxidizer are well mixed, termed premixed systems. In fires, the fuel and oxidizer (typically air) usually are not well mixed initially; they are non-premixed systems, also called diffusion flames because the fuel and oxidizer must then mix by diffusion before combustion can begin. The evolution of fires, however, is complex, and the mixing needed for forming combustion waves may well occur during a fire or prior to its initiation, making knowledge of combustion waves essential in evaluation fire hazards. Of the two types of waves, detonations generally are the most destructive because of their associated damaging high pressures. Assessments of possibilities of detonation development therefore become important. If a spark discharge, frictional heating, or a small flame, for example, initiates a deflagration in a confined space such as a long tube, then as the deflagration proceeds, it often undergoes a time-dependent transition to a detonation. Studies of deflagration-to-detonation transitions, which are continuing today because of their complexity, thus become directly relevant.

Ignition, Extinction, and Flammability

Combustible mixtures at low temperatures in principle are reacting, but their rates are so slow that they are negligible. Because of the strong temperature dependence of the rate of heat release, heat losses thus can prevent combustion from the beginning. Rates of heat loss from systems typically increase approximately linearly with increasing temperature, as indicated in Fig. 2. If the thermal conductivity or the surface-to-volume ratio of the system increases, then the slope of the heat loss curve increases. Since there also is a maximum rate of heat release in combustion, there can be three intersections of the heat release and heat loss curves, as illustrated in the figure. The intermediate intersection is, however, statically unstable, so that the two stable intersections are the intersection with the negligible rate of heat release at the bottom and the vigorously burning intersection at the top. Small systems with large rates of heat loss exhibit only the slow reaction intersection, which is the reason that size limits are imposed for storage of exothermic materials. As the size is increased, a tangency condition is approached, which would correspond to extinction if the system were burning rapidly. If, on the other hand, the system had been slowly reacting, then beyond that tangency condition, the unstable intersection would return the system to its state of a negligible rate of reaction. At a still smaller slope, another tangency condition is approached, beyond which there is no longer any intersection for a steady heat balance that is not a rapidly burning intersection. That second tangency thus defines the critical condition for ignition, there being no possibility of slow reactions beyond that condition.
Fig. 2

A schematic illustration of the dependences of the rates of heat release and of heat loss on temperature, illustrating criticality (From Williams 2002)

Extinction is the process in which a combustible system reacting at an appreciable rate is brought to a condition in which it is reacting at a negligible rate, illustrated by approaching the upper tangency condition in the figure. Strategies for achieving extinction of combustion can be classified as isolating the fuel, isolating the oxidizer, cooling the fuel or the gas, inhibiting the chemical reaction, or blowing the flame away. Examples in the first of these categories include mechanical methods, such as the use of shovels to encase fuel in noncombustible material, while a component of the effectiveness of carbon dioxide fire extinguishers falls in the second. Application of water to fires is an example in the third category, and gaseous or powder chemical fire extinguishers operate in the fourth. The development of efficient and effective means to extinguish combustion continues to evolve.

Ignition is the process by which combustible mixtures, reacting at negligible rates, are caused to begin to react rapidly. Ignition can be achieved by external stimuli whenever the high-rate intersection exists. It occurs spontaneously, without external stimuli, (spontaneous combustion) beyond the indicated critical ignition condition, when the only balance is the high-rate balance. The spontaneous process occurs when the system is big enough for the loss rate to depend sufficiently weakly on the temperature of the system.

Conditions for achieving ignition by application of thermal stimuli can be expressed as ignition energies if the rates of application are rapid or as ignition temperatures (variously called spontaneous ignition temperatures or autoignition temperatures) if the rates of application are slow. In the former case, all of the energy applied may contribute to ignition, while in the latter case, some of it is lost, and steady conditions are approached, in which the applied rate equals the loss rate. There are several methods of ignition, for example, exposure to a sufficiently hot surface, to a hot inert gas, to a small flame (piloted ignition), to an electrically heated wire, to a radiant energy source, to an explosive charge, or to an electrical spark discharge. Ignition criteria for the last two of these can be expressed best in terms of ignition energy and for the first two in terms of ignition temperature; the others fall in between. The energy that must be supplied to a system to achieve ignition usually exceeds the ignition energy because of losses; for example, in spark ignition, the electrical energy that must be supplied to the spark (the spark ignition energy) exceeds the ignition energy because of heat conduction to the electrodes and energy carries away in the gas by shock waves.

Ignition energies and ignition temperatures for a few fuels in air are given in Table 3. Values of these quantities can vary appreciably with chemical composition and experimental conditions. Among practical fuels, ignition temperatures tend to be around 700 K for coal and 600 K for newspaper, dry wood, and gasoline.
Table 3

Ignition and flammability properties of selected fuels in air (From Williams 2002)

Fuel

Minimum ignition energy (mJ)

Spontaneous ignition temperature (K)

Lower flammability limit (% by volume of gaseous mixture)

Upper flammability limit (% by volume of gaseous mixture)

Minimum quenching distance (cm)

Maximum burning velocity (cm/s)

H2

0.02

850

4

75

0.06

300

CH4

0.29

810

5

15

0.21

45

C2H6

0.24

790

3

12

0.18

47

C2H4

0.09

760

2.7

36

0.12

78

C2H2

0.03

580

2.5

100

0.07

160

C3H8

0.24

730

2.1

9.5

0.18

45

C7H16

0.24

500

1.1

6.7

0.18

42

C6H6

0.21

840

1.3

8

0.18

47

CH3OH

0.14

660

6.7

36

0.15

54

In gas mixtures of fuel and oxidizer, it has been found experimentally that ignition cannot be achieved if the fuel or oxidizer concentration is too low. The critical concentration of either fuel or oxidizer, below which ignition is impossible, is the flammability limit of the mixture. These limits can be expressed as minimum and maximum fuel percentages, between which the fuel percentage must lie for the mixture to be combustible. The minimum percentage is called the lower flammability limit (LFL), and the maximum is the upper flammability limit (UFL). Flammability limits for a few fuels in air at atmospheric pressure and room temperature are listed in Table 3. If the intent is to burn the mixture, then it is necessary to keep the fuel percentage between the LFL and the UFL. To handle mixtures safely, without the possibility of combustion occurring, the fuel percentage should be kept below the LFL or above the UFL. In partially filled gasoline tanks of automobiles, for example, the fuel percentage in the air above the liquid usually is above the UFL (which is about 6%).

The LFL and the UFL vary with pressure and temperature and normally tend to approach each other as either of these quantities is decreased. Thus, as the pressure is reduced, the LFL and UFL converge and meet each other at a critical pressure, the minimum pressure limit of flammability. At pressures below this critical value, the mixture does not burn at any fuel percentage. The pressure limit of flammability for any given mixture decreases with increasing temperature. At pressures well above this limit, if the temperature is high enough, the mixture will experience autoignition, without any external ignition stimulus; the minimum critical value for this higher pressure is the explosion limit. The pressure at the explosion limit usually decreases with increasing temperature, although for many fuels, such as hydrogen and hydrocarbons, the opposite trend occurs over an intermediate range of conditions in many experimental situations, for chemical-kinetic reasons. Between the flammability limit and the explosion limit, the mixture can be ignited by an external stimulus but does not ignite spontaneously.

A standard apparatus in which the LFL and UFL are measured is a vertical tube 5 cm in diameter and 100 cm in length, with its ends either closed or open to the atmosphere. The tube is filled with the gas mixture, and a strong spark is discharged either at the top or at the bottom of the tube. The result of the experiment depends on whether the tube is open or closed and on whether the spark is at the top (downward propagation) or at the bottom (upward propagation). The limits usually are widest for upward propagation in a closed tube. The limits usually reported are the widest because the results are used most often in connection with safety. Since the limits depend on the experiment, they are properties not only of the gas mixture but also of the configuration of the system. Limits generally widen as the size of the gas container increases. Tabulations of limits are useful only if the dependence on the configuration is not too great. This condition usually is satisfied because differences in the UFL for upward or downward propagation in closed or open tubes seldom exceed a few percent; corresponding changes in the LFL seldom reach a factor of two. In addition, when tubes greater than 5 cm are employed, the widening of the limits is generally found to be small. One reason for selecting 5 cm is that, when smaller diameters are employed, the flammability range begins to narrow appreciably. If the tube diameter is too small, then combustion cannot be achieved at any fuel percentage. The critical diameter below which combustion is impossible is the quenching diameter of the mixture.

If a deflagration propagating through a gas meets a tubular restriction with a diameter less than the quenching diameter, then combustion fails to penetrate into the tube. Similarly, if the deflagration encounters parallel plates whose separation distance is less than a critical value (the quenching distance), then combustion fails to proceed between the plates. Experimentally, the quenching diameter is about 20–50% greater than the quenching distance. Quenching distances for a few fuels in air at atmospheric pressure and room temperature are given in Table 3. The values listed there are those for the fuel percentage that gives the minimum value; the quenching distance increases significantly as the fuel percentage departs from the optimum. There is a corresponding dependence of the ignition energy on the fuel percentage. Values of quenching diameters are employed in the design of flame arrestors, in which fine grids are placed in gas lines to prevent flames from propagating through them.

Flammability limits and quenching distances are manifestations of the same general phenomena and are associated with heat loss and with the strong dependence of heat release rates on temperature. Because of this strong dependence, rates of heat loss that are only roughly 10% of the rate of heat release can cause extinction of a deflagration. Qualitatively, it is as if a system at an upper intersection in Fig. 2 were to be subject to heat loss lines with slopes that generally increase until the upper tangency condition is reached, beyond which only a slow reaction intersection is possible.

Since it is the ratio of the rate of heat loss to the rate of heat release that is of significance in extinction, reduction of the rate of heat release is an alternative way to extinguish deflagrations. This can be achieved by adding flame inhibitors to the combustible to reduce the rate, by reducing the temperature (through dilution, e.g., by addition of water or an inert gas to extinguish the combustion), or by slowing the chemical kinetics at a constant flame temperature (through chemical inhibition that interferes with the branched-chain reaction, e.g., by introducing bromine-containing species that combine with chain carriers to reduce their concentrations in the reaction zone). An extreme version of slowing the chemical kinetics can arise if a change in conditions produces an abrupt change in the kinetic mechanism to one that releases heat at a much slower rate. An example of this may be found in hydrogen-oxygen combustion, in which the influence of the less reactive radical HO2 acts as a sink for chain carriers by combining with the much more reactive radical H, removing it to form the stable molecules H2 and O2, thereby killing the main chain-branching step, as becomes dominant at flame temperatures below about 900 K.

Approximate correlations between quenching distances and minimum ignition energies have been developed. It can be stated that, to ignite a combustible, an amount of energy must be deposited locally that is roughly sufficient to raise the temperature to the adiabatic flame temperature in a disk-shaped volume of diameter equal to the quenching diameter and of a thickness equal to the deflagration thickness, defined below. The resulting ignition criterion can be expressed solely in terms of either the quenching diameter or the deflagration thickness by using the result that the quenching diameter generally lies between about 20 and 60 times the deflagration thickness (essentially because heat loss rates that are roughly 10% of the heat release rates cause extinction, as indicated earlier). The basis of this ignition energy criterion is that if it is not satisfied, then the heat loss to the cool combustible surrounding the ignition point causes extinction after the energy is deposited.

Premixed Flames

Deflagrations exhibit thicknesses and propagation velocities that depend on their structures, as can be reasoned by dimensional analysis, in terms of a thermal diffusivity (dimensions length squared divided by time) and an overall chemical reaction time; resulting typical deflagration thicknesses generally are around a fraction of a millimeter at normal atmospheric conditions. The corresponding propagation velocity, for any given fuel, at given atmospheric conditions, is termed the laminar burning velocity. It can be obtained from measurements the dependence of the cone angle of a flame above a Bunsen burner on the flow rate into the burner, for example, or from measurements of the flow rate for liftoff of a flat horizontal flame formed on a flat-flame burner. The laminar burning velocity depends on the equivalence ratio, the ratio of the fuel-to-oxidizer mass (or mole) ratio to the value of that ratio for stoichiometric conditions (conditions under which no fuel or oxidizer is left over after combustion). Burning velocities exhibit maxima near equivalence ratios of unity (actually, usually somewhat greater than unity because of variation in the chemical kinetics and transport properties). Table 3 lists in the last column these maximum burning velocities for the fuels included there.

Gaseous planar premixed flames are subject to instabilities. There is a hydrodynamic instability resulting from the fact that the density of the burnt gas is less than that of the reactants, but diffusion effects usually overcome this instability. Exceptions are found in fuel-lean hydrogen flames and in fuel-rich flames of propane and higher hydrocarbons, for which high molecular diffusion coefficients of the reactant that is present in deficient quantities lead locally to the mixtures becoming more nearly stoichiometric as that reactant diffused preferentially toward the hot reaction zone; this phenomenon produces cellular flame structures in these mixtures. In detonations, on the other hand, diffusion effects are very small because of the high flow velocities with respect to the wave, but the finite-rate chemistry that occurs behind the leading shock wave leads to a convective-acoustic instability that results in most detonations exhibiting cellular structures; diamond-like patterns result from this, there being narrow lines of very high pressures that can leave traces on smoked foils, as well as often on shreds of debris, which are helpful in forensic analyses to determine whether a detonation occurred in an accident scenario.
Fig. 3

A schematic illustration of different possible mechanisms of flame spread (From Williams 1982)

Diffusion Flames

In fires, the fuel and oxidizer usually are not initially premixed, and hence they involve diffusion flames. Diffusion flames may spread through arrays of solid or liquid fuels. The process of flame spread usually involves heating of the nonburning fuel to a temperature at which it begins to give off combustible gas that can participate in the combustion process. A surface of fire inception can be defined as a conceptual surface separating burning and nonburning fuel. A spread velocity can then be defined as the velocity at which this surface moves through the fuel array and can be estimated from the heat flux q imparted by the combustion and the energy required to bring the virgin fuel into participation. Many different physical phenomena can be involved in flame spread (radiation, conduction, convection, flame contact, firebrand transport, buoyancy, surface tension, etc.), some of which are illustrated in Fig. 3. Although there have been many studies of flame spread, understanding of the most important phenomena that arise is still progressing.

Energy balances also can be useful for estimating steady burning rates of condensed fuels in fires that burn with diffusion flames. The fundamental balance involved there is that the feedback energy flow rate from the flames to the fuel must equal the energy required to generate the combustible gases from the fuel, there being possible radiative, convective, and conductive components in the feedback. The flow processes occurring may be laminar or turbulent, depending on the size of the fire. An idea of whether the flow will be laminar or turbulent can be formed by considering the simpler configuration of a laminar gaseous jet flame in an open oxidizing atmosphere.

There are correlations (based on experiment and on theory) between energy emission rates and flame heights of diffusion flames of gaseous jets. Flame heights and shapes usually are defined from visual observations, but in more scientific studies, they often are related to the position at which the mixture is stoichiometric, since it varies from being very fuel rich at the jet exit to very fuel lean in the atmosphere. Flame heights defined in different ways typically differ by amounts on the order of 10%, although differences between average and maximum heights in turbulent situations can exceed a factor of two. Figure 4 is a schematic illustration of the dependence of the average flame height on the exit velocity of the fuel jet; the numbers in the figure would apply roughly to a methane jet issuing from a tube 0.5 cm in diameter into air at atmospheric pressure and room temperature.
Fig. 4

A schematic illustration of the flame height for open-jet diffusion flames, showing laminar and turbulent regimes, liftoff heights, and blowoff velocity (From Williams 2002)

At low exit velocities, the diffusion flame is laminar, and its height increases in proportion to the exit velocity u. Theory and experiment agree in showing the laminar height to be proportional to ud 2 /D, where d is the exit diameter and D is the thermal diffusivity of the gas. Buoyancy can play an important role, and it causes departures from this type of dependence if the exit is not round. Transition to turbulence begins at exit velocities above a critical value, and the portion of the flame that is turbulent then rapidly increases with u. The dashed line in the figure marks the lower boundary of the turbulent portion. The height of the turbulent flame is independent of u and proportional to d, as predicted if the molecular diffusivity D is replaced by a turbulent diffusivity proportional to ud.

The base of the flame is observed to be lifted abruptly to an appreciable distance above the jet exit when u exceeds another critical value. This value depends somewhat on the exit geometry of the jet, and depending on the fuel and the oxidizer, it may occur in the laminar or turbulent regime. The liftoff is caused by extinction of the diffusion flame in the region of high rates of strain at the base of the flame. At greater heights, the rate of strain is less because the jet has spread, and the flame again can begin. The height at which the lifted flame begins, called the liftoff height, increases approximately linearly with u. At a large enough exit velocity, the liftoff height is nearly equal to the flame height, and blowoff of a roughly spherical flame occurs at a third critical exit velocity, the blowoff velocity. If u exceeds the blowoff velocity, then a diffusion flame cannot be stabilized by the jet. Even in this relatively simple experiment, then, diffusion flames behave in complex ways that currently are largely but not completely understood.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of California San DiegoLa JollaUSA

Section editors and affiliations

  • Sayaka Suzuki
    • 1
  1. 1.National Research Institute of Fire and Disaster (NRIFD)TokyoJapan