A fundamental approach to understanding turbulent premixed flames

Turbulence is an inherently challenging flow problem, which gets further complicated in combustion problems due to a network of complex chemical reactions and substantial heat release. It is mostly classified based on the ratio of turbulent to chemical time scales. In applications involving slow chemistry, it is distributed in the larger portion of the flow. In contrast, it occurs in thin layers or flames embedded within the 3D turbulent flow in applications involving rapid chemistry. The advection of the eddies distorts the flame, thereby manipulating its structure. The surrounding flow is, in turn, affected by the gas expansion induced from the heat generated by chemical reactions. Studying these nonlinear coupled processes remains a big challenge in combustion.

It is important to understand the underlying mechanisms for the topological changes of the flame surface induced by turbulence, including identifying the pertinent parameters responsible for such changes. Other complexities affecting the turbulent flame propagation are caused by intrinsic instabilities responsible for flame distortion, including Darrieus–Landau (DL) instability, which is prevalent in premixed flames.

The need for high enough spatiotemporal resolutions to numerically resolve flame-turbulence interactions renders the problem cost-prohibitive when using DNS, while more affordable approaches, such as RANS and LES, rely on closure assumptions and sub-grid models, making the validity and accuracy of their results difficult to assess. While similar studies in the past provided complex topological configurations, flame folding, and detachment of pockets of unburned gas, they failed to provide vial turbulence features. This is because they were mostly limited to 2D flow, a limitation this study sought to address by extending the hydrodynamic model to studying turbulent flames in 3D.

Herein, Dr. Advitya Patyal and Professor Moshe Matalon from the University of Illinois at Urbana-Champaign adopted a fundamental approach using the hydrodynamic theory of premixed flames. They resorted to a hydrodynamic theory, which has been derived systematically from the general conservation laws by considering the flame thickness to be much smaller than all other fluidynamical length scales. The entire formulation leads to a hydrodynamic free-boundary problem where Navier–Stokes equations was applied to determine the flow at each side of the flame front. Their research work is currently published in the Journal of Fluid Mechanics.

The authors showed that confining the flame to a surface separated the combustion products from the fresh mixture. The flame propagation speed was influenced by flow conditions and the local mixture, while the flow field was altered by the gas expansion due to the temperature increase. Although the flame zone was not resolved numerically and turbulent eddies did not modify the internal flame structure, the combustion processes within the flame zone were governed by two critical lumped parameters: the Markstein length (influenced by the physicochemical properties and the state of the combustible mixture) and the thermal expansion, or unburned-to-burned density ratio (dependent on the heat generated by the chemical reactions). Furthermore, the DL instability had a more significant effect on the incoming turbulent flow than on the underlying combustion processes. For instance, it enhanced the vorticity and the resilience of the mechanisms, suggesting that stronger turbulent flows are needed to reduce anisotropy in the burned gas.

The novelty of this work was demonstrated by using the hydrodynamic model derived in their earlier publications to study turbulent flames in 3D. Unlike other typical numerical approaches, the hydrodynamic model was derived without invoking ad-hoc assumptions or adjusted parameters, making it more feasible and computationally affordable. Thus, it permitted clear and precise calculation of different qualities related to flame surface like strain, speed and degree of wrinkling, which could also be determined by finding an ensemble average over large eddy turnover times. It also allowed robust examination of the morphological changes of the flame surface, the effect of the flame on the turbulent flow and the turbulent flame propagation speed by adjusting the parameters of interest and varying the turbulence levels.

In summary, this is the first study to conduct 3D investigation of premixed flames in homogeneous isotropic turbulent flows from the perspective of hydrodynamic theory. The proposed model was robust and free of phenomenology and turbulence modeling assumptions that often lead to errors. In a statement to Advances in Engineering, distinguished Professor Moshe Matalon, the lead author, said that their fundamental study based on physical first principles makes transparent the mutual interactions between the flame and the fluid flow and advances understanding of the propagation of turbulent premixed flames.