Three different methods to introduce turbulence in the computational domain of Direct Numerical Simulations (DNS) of statistically planar turbulent premixed flame configurations have been reviewed and their advantages and disadvantages in terms of run time, natural flame development, control of turbulence parameters and convergence of statistics extracted from the simulations have been discussed in detail. It has been found that there is no method, which is clearly superior to the other two alternative methods. An analysis has been performed to explain why Lundgren's physical space linear forcing results in an integral length scale which is, independent of the Reynolds number, a constant fraction of the domain size. Furthermore, an evolution equation for integral length scale has been derived, and a scaling analysis of its terms has been performed to explain the evolution of integral length scale in the context of Lundgren's physical space linear forcing. Finally, a modification to Lundgren's forcing approach has been suggested which ensures that the integral length scale settles to a predetermined value so that Direct Numerical Simulations of statistically planar turbulent premixed flames with physical space forcing can be conducted for prescribed values of Damköhler and Karlovitz numbers.
The local flow topology analysis of the primary atomization of liquid jets has been conducted using the invariants of the velocity-gradient tensor. All possible small-scale flow structures are categorized into two focal and two nodal topologies for incompressible flows in both liquid and gaseous phases. The underlying direct numerical simulation database was generated by the one-fluid formulation of the two-phase flow governing equations including a high-fidelity volume-of-fluid method for accurate interface propagation. The ratio of liquid-to-gas fluid properties corresponds to a diesel jet exhausting into air. Variation of the inflow-based Reynolds number as well as Weber number showed that both these non-dimensional numbers play a pivotal role in determining the nature of the jet break-up, but the flow topology behaviour appears to be dominated by the Reynolds number. Furthermore, the flow dynamics in the gaseous phase is generally less homogeneous than in the liquid phase because some flow regions resemble a laminar-to-turbulent transition state rather than fully developed turbulence. Two theoretical models are proposed to estimate the topology volume fractions and to describe the size distribution of the flow structures, respectively. In the latter case, a simple power law seems to be a reasonable approximation of the measured topology spectrum. According to that observation, only the integral turbulent length scale would be required as an input for the a priori prediction of the topology size spectrum.
Compared to Large Eddy Simulation (LES) of single-phase flows, which has become a mature and viable turbulence modelling technique, the LES of two-phase flows with moving immiscible interfaces is at a rather early development stage. There is no standard set of governing equations for two-phase flow LES, but rather a variety of different formulations, all with advantages and disadvantages. This paper discusses and analyses in detail the governing equations for two-phase flow LES in the context of the Volume of Fluid method, as well as suitable Subgrid Scale closures for the different unknown terms. A particular focus is on the Favre filtered one fluid formulation of the momentum equations, but a comparison with the filtered and the volume averaged version of the balance equations is made as well. Differences and commonalities between the different approaches are discussed and, based on a priori analysis of explicitly filtered Direct Numerical Simulation data, suitable closure models for a posteriori analysis are identified.
The Favre-averaged scalar dissipation rate transport conditional on local flow topologies in premixed turbulent flames has been analysed based on a detailed chemistry Direct Numerical Simulation database of statistically planar turbulent hydrogen-air premixed flames with an equivalence ratio of 0.7 representing the corrugated flamelets, thin reaction zones and broken reaction zones regimes of premixed turbulent combustion. The local flow topologies have been categorised by the values of the three invariants of the velocity gradient tensor and the statistical behaviour of the Favre-averaged scalar dissipation rate conditional on these flow topologies has been analysed in detail for different choices of reaction progress variable. The qualitative behaviour of the scalar-turbulence interaction term in the Favre-averaged scalar dissipation rate transport equation has been found to be affected by the regime of combustion, whereas the chemical reaction rate gradient contribution to the scalar dissipation rate transport has been found to be affected by the choice of the reaction progress variable. The topologies, which exist for all values of dilatation rate, contribute significantly to the Favre-averaged scalar dissipation rate transport in premixed turbulent flames for all regimes of combustion. In addition, the flow topologies, which are obtained only for positive values of dilatation rate, contribute significantly to the Favre-averaged scalar dissipation rate transport in the case representing the corrugated flamelets regime combustion. An unstable nodal flow topology, which is representative of a counter-flow configuration, has been found to be a dominant contributor to the Favre-averaged scalar dissipation rate transport for all regimes of combustion irrespective of the choice of reaction progress variable.
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