Modeling and Implementation of a Flamelet Based Model With Presumed Shaped Probability Distribution Function Integration in Fortran for Non-Premixed Flame Dynamics

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Abstract Numerical modeling of combustion dynamics for various applications is a complex problem that involves flow-chemistry interaction and requires the implementation of efficient numerical schemes. Computational modeling of turbulent combustion is essential in predicting different combustion attributes like flame stability and heat release. Despite being a reasonable alternative to the experimental data, the modeling approach also requires tremendous computational resources. Various strategies have been introduced over the year to minimize computational time. This study reports on a Fortran-based Computational Fluid Dynamics (CFD) code to investigate non-premixed flame applications, utilizing a fourth-order accurate compact finite difference scheme. The CFD code incorporates the flamelet model combined with the Navier-Stokes (NS) equations to solve for various variables, including velocity, pressure, temperature, mixture fraction, mixture fraction variance, and scalar dissipation rate. Flamelet model uses laminar flame components in turbulent flame, where the laminar flamelet characterizes the local structure at each point on the flame front. The reactant fluxes depend on the gradients of flow velocity and are controlled by the scalar dissipation rate. The flamelet model and the β(beta)-pdf integration for species transport and temperature distribution are incorporated into the code. The laminar diffusion flame provides unique relationships for all thermochemical variables (such as temperature, species concentrations, and heat release rate) in terms of the mixture fraction. These relationships can be averaged for the non-premixed flame using an assumed probability distribution function of the conserved scalar. The steady-state flamelet libraries are generated from a zero-dimensional chemical kinetics solver with dependencies on mixture fraction and scalar dissipation rate.