Influences of the Darrieus-Landau instability on premixed turbulent flames

Patyal, Advitya

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https://hdl.handle.net/2142/99405 Copy

Description

Title

Influences of the Darrieus-Landau instability on premixed turbulent flames

Author(s)

Patyal, Advitya

Issue Date

2017-12-08

Director of Research (if dissertation) or Advisor (if thesis)

Matalon, Moshe

Doctoral Committee Chair(s)

Matalon, Moshe

Committee Member(s)

• Fischer, Paul
• Pantano, Carlos
• Panesi, Marco

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Darrieus-Landau instability
• Gas expansion
• Level-set methodology
• Premixed flames
• Turbulent combustion
• Scalar mixing
• Vortex stretching
• Cusp-like flames
• Three-dimensional flames

Abstract

The hydrodynamic instability which results from large density variations between the fresh mixture and the hot combustion products was discovered by Darrieus and Landau over seventy years ago, and has been named after its inventors. The instability, which prevents flames from being too flat, was thought to lead immediately to turbulent flames. Recent studies, initiated by weakly nonlinear analyses and extended by two-dimensional simulations suggest that this is not the case. It was established that the flame, beyond the onset of instability develops into a cusp-like structure pointing towards the burned gas region that propagates at a speed substantially large than the laminar flame speed. In this work, we present for the first time a systematic study of the bifurcation phenomena in the more realistic \textit{three-dimensional flow} and extend this analysis to homogeneous isotropic turbulent flows. The computations are carried out within the context of the hydrodynamic theory where the flame is treated as a surface of density discontinuity separating burned gas from the fresh mixture, and propagates at a speed that depends on the local curvature and hydrodynamic strain rate. The asymptotic model derived from first principles exploits the multi-scale nature of the problem, specifically the difference between the flame thickness representing the diffusion length scale and the hydrodynamic length which is characteristic of the dimensions of the domain. The dependence of the local stretch rate experienced by the flame - a measure of the local flame surface curvature and the strain rate, is modulated by the Markstein length, which mimics effects of reaction and diffusion occurring inside the flame. This parameter is of the order of the flame thickness and for an experimental setting can be changed by varying the fuel type or its equivalence ratio or the ambient system pressure. A low Mach-number Navier-Stokes solver modified by an appropriate source term is used to determine the flow field that results from the gas expansion and the flame is tracked using a level-set methodology with a surface parameterization method employed to accurately capture the local velocity and stretch rate. Under laminar flow conditions, the hybrid numerical scheme is shown to recover the known exact solutions predicted in the weak gas expansion limit and corroborates the bifurcation results from linear stability analysis. The new conformations that evolve beyond the instability threshold have a sharp crest pointing towards the burned gas with ridges along the troughs, and propagate nearly 40\% faster than planar flames. Indeed, the appearance of sharp folds and creases, which are some manifestations of the Darrieus-Landau instability, have been observed on the surface of premixed flames in various laminar and turbulent settings. The understanding from laminar flames is extended to practical three-dimensional homogeneous isotropic turbulent flows, to study premixed flame propagation, with an aim of providing a deeper insight into the mechanisms governing flame-turbulence interactions. The impact of the Darrieus-Landau instability on the topology of the flame surface is studied and it is shown that similar to passive interfaces, the complex conformations formed on the flame surface due to turbulence are locally not spherical in shape, rather cylindrical, similar to shapes resulting from two-dimensional unsteady flame-vortex interactions, which can be thought as simplifications of three-dimensional problems. Furthermore, probability distribution functions of flame surface curvature, strain and mean flame position show that the presence of the Darrieus-Landau instability can have visibly different effects on the topology of the flame. The presence of a flame is also observed to create significant anisotropy in the burned gas in terms of restructuring the intense vortical structures, which weakens as the turbulence intensity increases. The changes in density across the flame are also responsible for vorticity destruction and generation in terms of dilatation, vortex stretching and baroclinic torque. In particular, alignments between the vorticity vector, flame surface normal and eigenvectors of the strain rate tensor are used to identify the impact of the strain rate tensor on vortex stretching and transport of scalar gradients, while changes in flame topology due to the Darrieus-Landau instability are shown to significantly impact vorticity generation through the baroclinic torque using enstrophy budgets. The turbulent flame speed, defined as the mean propagation speed of a premixed flame in a turbulent environment is of great importance in the design of combustors. The relatively robust methodology of the current approach allows us to study the turbulent flame speed for a wide parametric space at a reasonable computational cost. One of the primary findings reported in this work is that the Darrieus-Landau instability can have a dramatic impact on the propagation speed of turbulent premixed flames. Further, contrary to prior studies in the literature, the turbulent flame speed doesn't scale with the mean area ratio of the flame and is reduced by an increase in the mean flame stretch, which makes accurate computations of flame stretch important.

Graduation Semester

2017-12

Type of Resource

text

Permalink

http://hdl.handle.net/2142/99405

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Copyright 2017 Advitya Patyal

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