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A premixed flame is a flame formed under certain conditions during the
combustion Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combus ...
of a premixed charge (also called pre-mixture) of fuel and
oxidiser An oxidizing agent (also known as an oxidant, oxidizer, electron recipient, or electron acceptor) is a substance in a redox chemical reaction that gains or " accepts"/"receives" an electron from a (called the , , or ). In other words, an oxid ...
. Since the fuel and oxidiser—the key chemical reactants of combustion—are available throughout a homogeneous
stoichiometric Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equ ...
premixed charge, the combustion process once initiated sustains itself by way of its own heat release. The majority of the chemical transformation in such a combustion process occurs primarily in a thin interfacial region which separates the unburned and the burned gases. The premixed flame interface propagates through the mixture until the entire charge is depleted. The propagation speed of a premixed flame is known as the
flame speed The flame speed is the measured rate of expansion of the flame front in a combustion reaction. Whereas ''flame velocity'' is generally used for a fuel, a related term is explosive velocity, which is the same relationship measured for an explosive. ...
(or burning velocity) which depends on the convection-diffusion-reaction balance within the flame, i.e. on its inner chemical structure. The premixed flame is characterised as laminar or turbulent depending on the velocity distribution in the unburned pre-mixture (which provides the medium of propagation for the flame).


Premixed flame propagation


Laminar

Under controlled conditions (typically in a laboratory) a laminar flame may be formed in one of several possible flame configurations. The inner structure of a laminar premixed flame is composed of layers over which the decomposition, reaction and complete oxidation of fuel occurs. These chemical processes are much faster than the physical processes such as vortex motion in the flow and, hence, the inner structure of a laminar flame remains intact in most circumstances. The constitutive layers of the inner structure correspond to specified intervals over which the temperature increases from the specified unburned mixture up to as high as the
adiabatic flame temperature In the study of combustion, the adiabatic flame temperature is the temperature reached by a flame under ideal conditions. It is an upper bound of the temperature that is reached in actual processes. There are two types adiabatic flame temperature: ...
(AFT). In the presence of volumetric heat transfer and/or aerodynamic stretch, or under the development intrinsic flame instabilities, the extent of reaction and, hence, the temperature attained across the flame may be different from the AFT.


Laminar burning velocity

For a one-step irreversible chemistry, i.e., \nu_F \rm + \nu_O \rm_2 \rightarrow \rm, the planar, adiabatic flame has explicit expression for the burning velocity derived from
activation energy asymptotics Activation energy asymptotics (AEA), also known as large activation energy asymptotics, is an asymptotic analysis used in the combustion field utilizing the fact that the reaction rate is extremely sensitive to temperature changes due to the large ...
when the Zel'dovich number \beta\gg 1. The reaction rate \omega (number of moles of fuel consumed per unit volume per unit time) is taken to be Arrhenius form, :\omega = B \left(\frac\right)^m \left(\frac\right)^n e^, where B is the
pre-exponential factor In chemical kinetics, the pre-exponential factor or A factor is the pre-exponential constant in the Arrhenius equation (equation shown below), an empirical relationship between temperature and rate coefficient. It is usually designated by A when ...
, \rho is the
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
, Y_F is the
fuel mass fraction In combustion physics, fuel mass fraction is the ratio of fuel mass flow to the total mass flow of a fuel mixture. If an air flow is fuel free, the fuel mass fraction is zero; in pure fuel without trapped gases, the ratio is unity. As fuel is burne ...
, Y_ is the oxidizer mass fraction, E_a is the
activation energy In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules p ...
, R is the
universal gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
, T is the
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
, W_F\ \& \ W_ are the
molecular weights The molecular mass (''m'') is the mass of a given molecule: it is measured in daltons (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quanti ...
of fuel and oxidizer, respectively and m\ \& \ n are the reaction orders. Let the unburnt conditions far ahead of the flame be denoted with subscript u and similarly, the burnt gas conditions by b, then we can define an equivalence ratio \phi for the unburnt mixture as :\phi = \frac\frac. Then the planar laminar burning velocity for fuel-rich mixture (\phi>1 ) is given by :S_L=\left\^ e^ + O(\beta^), where :G(n,m,a) = \int_0^\infty y^n (y+a)^m\ dy and a=\beta(\phi-1)/\mathrm_F. Here \lambda is the
thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...
, c_p is the
specific heat In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
at constant pressure and \mathrm is the
Lewis number The Lewis number (Le) is a dimensionless number defined as the ratio of thermal diffusivity to mass diffusivity. It is used to characterize fluid flows where there is simultaneous heat and mass transfer. The Lewis number puts the thickness of the ...
. Similarly one can write the formula for lean \phi<1 mixtures. This result is first obtained by T. Mitani in 1980. Second order correction to this formula with more complicated transport properties were derived by
Forman A. Williams Forman Arthur Williams (born January 12, 1934) is an American academic in the field of combustion and aerospace engineering who is Emeritus Professor of Mechanical and Aerospace Engineering at the University of California San Diego. Education Wil ...
and co-workers in the 80s. Variations in local propagation speed of a laminar flame arise due to what is called flame stretch. Flame stretch can happen due to the straining by outer flow velocity field or the curvature of flame; the difference in the propagation speed from the corresponding laminar speed is a function of these effects and may be written as: :U_L = S_L - S_L \mathcal_c\delta_L \kappa + \mathcal_a \delta_L\mathbf\cdot\nabla\mathbf\cdot\mathbf where \delta_L is the laminar flame thickness, \kappa is the flame curvature, \mathbf is the unit normal on the flame surface pointing towards the unburnt gas side, \mathbf is the flow velocity and \mathcal_c\ \& \ \mathcal_a are the respective
Markstein number In combustion engineering and explosion studies, the Markstein number characterizes the effect of local heat release of a propagating flame on variations in the surface topology along the flame and the associated local flame front curvature. The di ...
s of curvature and strain.


Turbulent

In practical scenarios, turbulence is inevitable and, under moderate conditions, turbulence aids the premixed burning process as it enhances the mixing process of fuel and oxidiser. If the premixed charge of gases is not homogeneously mixed, the variations on equivalence ratio may affect the propagation speed of the flame. In some cases, this is desirable as in stratified combustion of blended fuels. A turbulent premixed flame can be assumed to propagate as a surface composed of an ensemble of laminar flames so long as the processes that determine the inner structure of the flame are not affected. Under such conditions, the flame surface is wrinkled by virtue of turbulent motion in the premixed gases increasing the surface area of the flame. The wrinkling process increases the burning velocity of the turbulent premixed flame in comparison to its laminar counterpart. The propagation of such a premixed flame may be analysed using the field equation called as
G equation In Combustion, G equation is a scalar G(\mathbf,t) field equation which describes the instantaneous flame position, introduced by Forman A. Williams in 1985 in the study of premixed turbulent combustion. The equation is derived based on the Level-s ...
for a scalar G as: : \frac + \mathbf \cdot \nabla G = U_L , \nabla G, , which is defined such that the level-sets of G represent the various interfaces within the premixed flame propagating with a local velocity U_L. This, however, is typically not the case as the propagation speed of the interface (with resect to unburned mixture) varies from point to point due to the aerodynamic stretch induced due to gradients in the velocity field. Under contrasting conditions, however, the inner structure of the premixed flame may be entirely disrupted causing the flame to extinguish either locally (known as local extinction) or globally (known as global extinction or blow-off). Such opposing cases govern the operation of practical combustion devices such as SI engines as well as aero-engine afterburners. The prediction of the extent to which the inner structure of flame is affected in turbulent flow is a topic of extensive research.


Premixed flame configuration

The flow configuration of premixed gases affects the stabilization and burning characteristics of the


Bunsen flame

In a Bunsen flame, a steady flow rate is provided which matches the flame speed so as to stabilize the flame. If the flow rate is below the flame speed, the flame will move upstream until the fuel is consumed or until it encounters a
flame holder A flame holder is a component of a jet engine designed to help maintain continual combustion. In a scramjet engine the residence time of the fuel is very low and complete penetration of the fuel into the flow will not occur. To avoid these conditio ...
. If the flow rate is equal to the flame speed, we would expect a stationary flat flame front normal to the flow direction. If the flow rate is above the flame speed, the flame front will become conical such that the component of the velocity vector normal to the flame front is equal to the flame speed.


Stagnation flame

Here, the pre-mixed gases flow in such a way so as to form a region of stagnation (zero velocity) where the flame may be stabilized.


Spherical flame

In this configuration, the flame is typically initiated by way of a spark within a homogeneous pre-mixture. The subsequent propagation of the developed premixed flame occurs as a spherical front until the mixture is transformed entirely or the walls of the combustion vessel are reached.


Applications

Since the equivalence ratio of the premixed gases may be controlled, premixed combustion offers a means to attain low temperatures and, thereby, reduce NOx emissions. Due to improved mixing in comparison with
diffusion flame In combustion, a diffusion flame is a flame in which the oxidizer and fuel are separated before burning. Contrary to its name, a diffusion flame involves both diffusion and convection processes. The name diffusion flame was first suggested by S. ...
s, soot formation is mitigated as well. Premixed combustion has therefore gained significance in recent times. The uses involve lean-premixed-prevaporized (LPP) gas turbines and SI engines.


See also

* Flamelet generated manifold *
Luminous flame A luminous flame is a burning flame which is brightly visible. Much of its output is in the form of visible light, as well as heat or light in the non-visible wavelengths. An early study of flame luminosity was conducted by Michael Faraday and bec ...
* Oxy-fuel


References

{{Reflist Combustion Fire