Markov Process Applied to the Study of Turbulent Premixed Flames

The paper provides a detailed description of the mean reaction rate expression derivation within a premixed turbulent combustion flame model based on Reynolds-averaged Navier-Stokes (RANS) equations. This marks the initial crucial step towards adapting the model to a large eddy simulation framework with time filtering, laying the foundation for future development activities. The approach uses a scalar magnitude called c, enabling the depiction of the fluctuating thermodynamic state with a bimodal probability distribution function (c =3D 0 and c =3D 1). The temporal evolution of this scalar variable is modeled as a random telegraphic signal, which is a stationary random function analyzed as a Markov process with two possible states. Additionally, the paper derives the frequency, waiting times in each state, probability functions of each state, auto-correlation function, spectral density, and integral time scale of the process.