An Altered Paradigm for Modelling Turbulent Premixed Combustion within the Context of the Two-fluid Approach - Vladimir L. Zimont (Research Aspects in Chemical and Materials Sciences Vol. 3, 2022)
We consider and develop the altered paradigm that refers to the use of the two-fluid approach to the problem of the turbulent premixed combustion in the flamelet regime, which enable to exclude the challenge of modelling the counter-gradient scalar transport phenomenon and its transition to the gradient one, as well as the peculiarities of the mean stress tensor in the turbulent flame describing among other things abnormally large for turbulent flow velocity fluctuations in the flame. We formulate conditionally averaged mass and momentum equations where the unknowns that need to be modelled are only the conditional Reynolds stresses in the unburned and burned gases, and the mean chemical source. To avoid the requiring modelling surface-averaged parameters appearing in the known in the literature conditionally averaged momentum equations, we propose an altered statistical-physical model of one-step transformation of the unburned gas with the conditional mean parameters \(u_u\), \(p_u\) into the burned gas with the parameters \(u_b\), \(p_b\). To derive two-fluid conditionally averaged mass and momentum equations, we propose a simple method of splitting of the Favre ensemble averaged mass and momentum equations of the problem into two-fluid conditionally averaged equations, which allowed us to avoid commonly used for derivation generalized functions. The unknowns in the altered unclosed equations that need modelling are the conditions Reynolds stresses \(τ_ij,u\), \(τ_ij,b\) and the mean chemical source \(ρ W\). We discuss the unclosed differential equations for these unknowns, which can be used for their advanced modelling, and propose more simple modelling the conditional Reynolds stresses using spitted conditional equations of the standard " K - \(ε\) " turbulence model and an expression for the mean chemical source derived by us elsewhere. The developed altered two-fluid conditional averaging paradigm can be a feasible alternative to the widely used Favre averaging paradigm.