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.

A fundamental approach to understanding turbulent premixed flames - Advances in Engineering
The cusp-like flame conformation resulting from the Darrieus-Landau instability that propagates (downwards) into a quiescent combustible mixture. The grey surface represents the flame and the color scheme denotes the vorticity magnitude.

About the author

Advitya Patyal received his MS and PhD in Mechanical Engineering from the University of Illinois at Urbana Champaign under Professor Moshe Matalon, where-in he specialized in analytically and computationally modeling thermally reactive flows and understanding the impacts of electric fields on fundamental combustion. Following his graduation, he worked as a Research Engineer at Caterpillar Inc. designing fuel injection systems and new piston designs for ICE’s. Advitya is currently working for Actasys Inc. in the role of Actuator Development Lead where he leverages his background for understanding multiphysics-coupled problems to create the next generation of solid-state actuator systems.

About the author

College of Engineering Caterpillar Distinguished Professor
Mechanical Science and Engineering
University of Illinois at Urbana-Champaign

Moshe Matalon received his B.S. in Applied Mathematics and Physics and a M.S. degree in Engineering Sciences, both from Tel Aviv University and a Ph.D. in Mechanical and Aerospace Engineering from Cornell University. He began his academic career as Assistant Professor in the Aerodynamics Laboratories of the Polytechnic Institute of New York University in 1978, then moved to the McCormick School of Engineering and Applied Science at Northwestern University. Since 2007, he has been in the Grainger College of Engineering at the University of Illinois at Urbana-Champaign in the department of Mechanical Science and Engineering.

Matalon’s research interests are in Combustion Theory, Theoretical Fluid Mechanics and Applied Mathematics. He is a world-renowned theorist on flame dynamic, has reshaped understanding of the complex impacts of fluid dynamics, transport, and chemistry on laminar and turbulent flames, and has established foundations for modern simulations and for interpretation of experiments. Through his publications (nearly 160 archival journal articles) he made significant and long lasting contributions to numerous areas of combustion science including the derivation and formulation of a hydrodynamic theory of premixed flames; derivation of the well-known flame-speed/flame-stretch relation and an invariant formula for the flame stretch rate; clarification of the role of thermal, mass and viscous diffusion on the Darrieus-Landau instability and its nonlinear consequences; consistent criteria for the onset of instability and self-wrinkling of spherically expanding flames; theories of turbulent flames in the flamelet regime of turbulent combustion; description of the reaction zone structure of diffusion (non-premixed) flames for distinct and non-unity Lewis numbers; characterization of thermo-diffusive instabilities in diffusion flames; and substantial contributions to droplet, particle and multi-phase combustion, edge flame dynamics and combustion in porous media and at the microscale.

Matalon was recipient of the distinguished Ya. B. Zeldovich Gold Medal of the Combustion Institute, ICDERS Numa Manson Medal, and AIAA Fluid Dynamics  and Pendray Aerospace Literature Awards. He is Fellow (inaugural class) of the Combustion Institute, the American Institute of Aeronautics and Astronautics AIAA, the Institute of Physics (IOP) in 1999 and the American Physical Society (APS). He was on the editorial board of Combustion Theory and Modelling since its inception in 1997 and serves as Editor-in-Chief of since 2001. He was Associate Editor of the Journal of Fluid Mechanics (2008 – 2019) and served on the Editorial Board of Progress in Energy and Combustion Science (2004 – 2015).


Patyal, A., & Matalon, M. (2022). Isolating effects of Darrieus–Landau instability on the morphology and propagation of turbulent premixed flames. Journal of Fluid Mechanics, 940, 940.

Go To Journal of Fluid Mechanics

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