Propagation of large scale premixed turbulent flames

We examine premixed turbulent combustion within the context of a hydrodynamic model derived from physical first principles. This is an asymptotic model that exploits the multi-scale nature of the problem, characterized by two disparate length scales: the diffusion length scale representing the flame thickness and the hydrodynamic length scale associated with the dimensions of the combustion chamber. It treats the flame as a surface of density discontinuity that separates the burned gas from the fresh combustible mixture and propagates relative to the unburned gas at a speed that depends on the local stretch rate - a measure of the deformation of the flame front that depends on the local curvature and hydrodynamic strain rate that it experiences. The dependency on stretch rate is modulated by a Markstein length, a parameter of the order of flame thickness that mimics the effects of diffusion, mixture strength and stoichiometry. In an experimental setting, a change in the value of Markstein length can be brought about by varying the fuel type and mixture composition or through variations in system pressure. A numerical methodology was developed for the implementation of this model that requires a surface tracking algorithm for the evolution of the flame front combined judiciously to a Navier-Stokes solver for the variable density fluid-dynamical equations. Such a hybrid algorithm is developed and utilized to study premixed turbulent flame propagation, with an aim of providing a deeper insight into the mechanisms governing flame-turbulence interactions. In particular, this approach is used to systematically address the fundamental problem of determining the turbulent flame speed, a problem that has been at the forefront of combustion research for several decades. The turbulent flame speed, defined as the mean propagation speed of a premixed flame in a turbulent environment, is of great practical importance being directly related to the mean fuel consumption rate in a given combustor. The relatively simplistic nature of our methodology allows us to span a wide parameter space, typically not possible via experiments or direct numerical simulations. One of our primary findings is that depending on the composition of the combustible mixture and the intensity of turbulence, the turbulent flame can have markedly different shapes with dramatically different turbulent flame speeds. The flames can either be statistically planar, corrugated with increasing sharp crests pointing towards the burnt gas that are generated through hydrodynamic effects resulting from the expansion of the hot products or highly corrugated with instances of the flame folding on itself and forming pockets of unburnt gases that detach from the flame surface and get consumed. Characterization of the turbulent flame is done via statistics of quantities such as thickness of the flame brush, flame curvature and the hydrodynamic strain exerted by the flow, which includes contributions from turbulence and the induced flow due to the flame. Another important aspect of our work is the formulation of scaling laws governing the turbulent flame speed. These scaling laws are free of any modeling assumptions and ad-hoc parameters commonly used in turbulent studies. In particular, they exhibit explicit dependence on various functional parameters, including: turbulence parameters, such as turbulence intensity and length scale; combustion parameters, such as mixture composition and heat release; and flow parameters, such as hydrodynamic strain. All the aforementioned parameters can either be calculated or measured experimentally. The scaling laws obtained show very good agreement with the experimental scaling laws, which typically contain one or more adjustable parameters, available in the literature. This work and its results further our understanding about the complexities of the intricate mechanisms that govern flame- turbulence interactions and can be used to guide ongoing experimental and large-scale numerical simulation efforts in this field. Also, accurate scaling laws for the turbulent flame speed are central to the design and optimization of internal combustion engines leading to improved performance, and for improving predictive capabilities of existing software that model and simulate the complex turbulent field within combustion devices