Laminar flamelet model

The laminar flamelet model is one of the methods of modelling turbulent combustions apart from SCRS, eddy flamelet model and others. Combustion is a very important thermochemical process with significant material and aerodynamic implications and thus CFD modeling of combustion has become indispensable. The laminar flamelet model is basically for non pre-mixed fuel (the system in which the fuel and oxygen is supplied from two different pipes). ∂ Y k ∂ t = χ 2 1 L e k ( ∂ 2 Y k ∂ Z 2 ) + ω k ρ {displaystyle {partial Y_{k} over partial t}={chi over 2}{1 over Le_{k}}{iggl (}{partial ^{2}Y_{k} over partial Z^{2}}{iggr )}+{omega _{k} over ho }}     (1) c p ∂ T ∂ t = χ 2 ( ∂ 2 h ∂ Z 2 ) − ∑ k = 1 N h k { χ 2 ∂ 2 Y k ∂ Z 2 + ω k ρ } {displaystyle {c_{p}}{partial T over partial t}={chi over 2}{iggl (}{partial ^{2}h over partial Z^{2}}{iggr )}-{sum _{k=1}^{N}h_{k}}{iggl {}{chi over 2}{partial ^{2}Y_{k} over partial Z^{2}}+{omega _{k} over ho }{iggr }}}     (2) χ ~ s t = χ ~ ∫ 0 1 F ( Z ) F ( Z s t )   P ( Z ) d Z {displaystyle {{widetilde {chi }}_{st}}={{widetilde {chi }} over int limits _{0}^{1}{frac {F(Z)}{F(Z_{st})}} P(Z),dZ}}     (3) F ( Z ) = exp ⁡ ( − 2 [ erfc − 1 ⁡ ( 2 Z ) ] 2 ) {displaystyle F(Z)=exp {igl (}-2{igl }^{2}{igr )}}     (3) The laminar flamelet model is one of the methods of modelling turbulent combustions apart from SCRS, eddy flamelet model and others. Combustion is a very important thermochemical process with significant material and aerodynamic implications and thus CFD modeling of combustion has become indispensable. The laminar flamelet model is basically for non pre-mixed fuel (the system in which the fuel and oxygen is supplied from two different pipes). The concept of ensemble of laminar flamelets was first introduced by Forman A. Williams in 1975, while the theoretical foundation was developed by Norbert Peters in the early 80s. The flamelet concept considers the turbulent flame as an aggregate of thin, laminar (Re < 2000), locally one-dimensional flamelet structures present within the turbulent flow field. Counterflow diffusion flame is a common laminar flame which is used to represent a flamelet in a turbulent flow. Its geometry consists of opposed and axi-symmetric fuel and oxidizer jets. As the distance between the jets is decreased and/or the velocity of the jets is increased, the flame is strained and departs from its chemical equilibrium until it eventually extinguishes. The mass fraction of species and temperature fields can be measured or calculated in laminar counterflow diffusion flame experiments. When calculated, a self-similar solution exists, and the governing equations can be simplified to only one dimension i.e. along the axis of the fuel and oxidizer jets. It is in this direction where complex chemistry calculations can be performed affordably. The following assumptions are made in the study of all the flamelet models:– 1. While modelling only a single mixture fraction are allowed. Modelling of two-mixture-fraction flamelet models is not possible.2. It is assumed that the mixture fraction follow the β-function PDF, and scalar dissipation fluctuations are not considered.3. Empirically-based streams cannot be used.