Turbulent premixed flame fronts: Fractal scaling and implications for les modeling

Abstract

Large Eddy Simulation in turbulent combustion is a promising approach for simulation of high Reynolds number flows, typical of industrial combustion appliances. Self-similarity of reactive turbulent fronts emerges from their fractal properties, which can be suitably exploited to model the unresolved sub-grid contribution of combustion, see [1] and ref. therein. Following those authors, with appropriate hypotheses, the filtered progress variable equation reads $$\frac{\partial \overline{\rho}\widetilde{c}}{\partial t} + \nabla \cdot (\overline{\rho}\widetilde{u}\widetilde{c}) + \nabla \cdot (\overline{\rho}\widetilde{uc} - \overline{\rho}\widetilde{u}\widetilde{c}) = \nabla \cdot (\overline{\rho D \nabla c}) + \overline{\dot{\omega}} = \rho_{u}S_{L} \Xi \left|\nabla\overline{c}\right|,$$ Where \(\Xi = \left|\overline{\nabla_{c}}\right|/\left|\nabla_{\overline{c}}\right|\) is the wrinkling factor, strictly related to the flame surface density concept \(\sum = \left|\overline{\nabla_{c}}\right|.\) The model can be closed using the fractal behavior of flames, i.e. \(\Xi (\Delta) = (\Delta/\epsilon_{i})^{D - 2}\), where D is the fractal dimension of the flame front and \(\epsilon_{i}\) is the scale below which the fractal scaling is lost (\(\Delta\) is the mesh spacing). A crucial issue of this model is the determination of the fractal dimension D and of the inner cut-off \(\epsilon_{i}\) and their dependence on turbulence/chemistry conditions.