An Approach to Generalization of the TFC Turbulent Combustion Model Implemented in the Ansys Fluent and CFX Commercial CFD Codes

The TFC model of turbulent premixed combustion implemented in Ansys Fluent and CFX solvers is based on the theoretical concept of the microturbulent (thickened) flamelet combustion regime and the concept of transient Intermediate Steady Propagation (ISP) flame derived from the original theory of the premixed turbulent flame developed within the Kolmogorov-type hypothesis-based method. At the intermediate stage of flame propagation, when the small-scale wrinkles of the flamelet sheet, which determine the turbulent flame speed
t , reach statistical equilibrium and the large-scale wrinkles, which determine the flame width
t remain in nonequilibrium, the constant flame speed is determined by a theoretical formula directly used in the TFC model, and the increase in flame width is controlled by turbulent diffusion. The basic TFC model was developed mainly for numerical simulation of stabilized flames in turbulent flows, where the initial stage of combustion is not important and the final stage is practically unattainable (burners of gas turbines and boilers with lean mixtures, laboratory flames with high turbulence levels, where the combustion regime of thickened flamelets prevails). The TFC model corresponds to the two-parametric Kolmogorov "
-
" turbulence model or conceptually similar "
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" model, in which small-scale turbulence is assumed to be statistically equilibrium and large-scale turbulence is usually statistically nonequilibrium. The basic TFC model does not describe the initial stage of flame propagation, at which the formation of the ISP flame with statistically equilibrium small-scale combustion structures occurs) as well as the final stage, at which large-scale combustion structures reach statistical equilibrium. In developing a generalized TFC model, we hypothesized that the evolution of flame velocity and width at the initial stage of flame development can be expressed in terms of an increasing turbulent diffusion coefficient described by Taylor's theory. This led to the possibility of modeling the initial stage of combustion without involving additional empirical constants. In modeling the final stage of combustion, we used the result of our original study of the steady-state flame speed in the context of a hyperbolic differential equation describing the leading edge of a turbulent flame, which confirmed and refined Damköhler's classical result
The developed generalized TFC model describes three stages of turbulent premixed combustion:The relatively short initial stage of combustion in which a developed turbulent flame is formed (modeling this stage is important, e.g., in SI engines); An intermediate stage of combustion, observed in real burners, where the transition flame is typically of increasing width with an approximately constant angle of inclination to the flow;The final stage of combustion, when the flame has a constant speed and width, is practically unattainable and therefore cannot prevail in real burners, However, the transition from the transient ISP flame to the steady state flame along the burner may occur, for example, in the case of very lean mixtures.The developed generalized TFC combustion model describes the gasdynamic effects arising from different pressure-driven accelerations of cold reactants and hot products. They lead to non-gradient and often counter-gradient scalar flux in the flame, strong anisotropy of velocity fluctuation, effects on mean stresses, and chemical source. The generalized TFC combustion model is presented in the form of a three-dimensional Favre averaged differential equation for the reaction progress variable. which has a standard form for a CFD solver.