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 (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{F} + \nu_O \rm{O}_2 \rightarrow \rm{Products}, the planar, adiabatic flame has explicit expression for the burning velocity derived from
activation energy asymptotics 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{\rho Y_F}{W_{F}}\right)^m \left(\frac{\rho Y_{O_2}}{W_{O_2}}\right)^n e^{-E_a/RT}, where B is the
pre-exponential factor, \rho is the
density, Y_F is the
fuel mass fraction, Y_{O_2} is the oxidizer
mass fraction, E_a is the
activation energy, R is the
universal gas constant, T is the
temperature, W_F\ \& \ W_{O_2} are the
molecular weights 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{\nu_{O_2} W_{O_2}}{\nu_F W_F}\frac{Y_{F,u}}{Y_{O_2,u}}. Then the planar laminar burning velocity for fuel-rich mixture (\phi>1 ) is given by :S_L=\left\{\frac{2 B\lambda_b \rho_b^{m+n} \nu_F^m Y_{O_2,u}^{m+n-1} G(n,m,a)}{ c_{p,b} \rho_u^2 \nu_{O_2} W_{O_2}^{m+n-1} \beta^{m+n+1} \mathrm{Le}_{O_2}^{-n} \mathrm{Le}_F^{-m}}\right\}^{1/2} e^{-E_a/2RT_b} + O(\beta^{-1}), where :G(n,m,a) = \int_0^\infty y^n (y+a)^m\ dy and a=\beta(\phi-1)/\mathrm{Le}_F. Here \lambda is the
thermal conductivity, c_p is the
specific heat at constant pressure and \mathrm{Le} is the
Lewis number. Similarly one can write the formula for lean \phi 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 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: :S_T=S_L + \mathcal{M}_c \delta_L (S_L-\mathbf{v}\cdot\mathbf{n}) \nabla \cdot \mathbf{n} - \mathcal{M}_t \delta_L \nabla_t\cdot \mathbf{v}_t where \mathbf{n} is the unit normal to the flame surface (pointing towards the burnt gas side), \mathbf{v} is the flow velocity field evaluated at the flame surface and \nabla_t\cdot \mathbf{v}_t is the surface divergence of the tangential velocity \mathbf{v}_t=(\mathbf{I}-\mathbf{n}\otimes\mathbf{n})\mathbf{v}; with flow being incompressible outside the flame, \nabla_t\cdot \mathbf{v}_t=-\mathbf{n}\otimes\mathbf{n}:\nabla\mathbf{v}-(\mathbf{v}\cdot\mathbf{n})\nabla\cdot\mathbf{n}. Moreover, \mathcal{M}_c and \mathcal{M}_t are the two
Markstein numbers, associated with the curvature and tangential straining.
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 for a scalar G as: : \frac{\partial G}{\partial t} + \mathbf{v} \cdot \nabla G = S_T |\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 S_T. 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 ==