Understanding flame-wall interactions and developing high-fidelity near-wall turbulent combustion models is important to build a submodel for predictive simulations of combustion devices. Recent studies have investigated the characteristics of back-on quenching (BOQ), where premixed flames quench against a cold wall on its burned gas side. It was reported that turbulence induces multimodal local quenching, and such a non-canonical quenching configuration needs to be understood. This presentation provides an overview of our recent numerical studies on laminar and turbulent flame-wall interaction to provide insights into the physics of the BOQ process, in order to propose strategies for near-wall turbulent combustion modeling. Several important aspects, namely the roles differential diffusion, surface reaction and flow transients, are studied.
Premixed propane flames propagating in large Hele-Shaw cells are strongly unstable, leading to a large number of cells on the flame front. It is possible to measure experimentally the growth rate of the instability, for downward or upward propagating flames, and the effect of gravity on the growth rate seems small in both cases. However the nonlinear behavior of the flames is completely changed by gravity, new cells are constantly created on the front for downward propagating flames whereas the amplitude of the flame is strongly increased for upward propagating flames. We give a nonlinear description of these effects, based on a modified Sivashinsky equation.
(1) An investigation of the coupling between the Darrieus-Landau and Saffman-Taylor hydrodynamic instabilities in the presence of an imposed flow following Darcy's law. A linear stability analysis is carried out leading to an explicit dispersion relation of the form s = a k - b k2 where s and k are the growth rate and wave number of a normal-mode perturbation. The coefficients a and b identified incorporate in a transparent way the coupling between the Darrieus-Landau, Saffman-Taylor and Rayleigh-Taylor instabilities combined with the effect of the imposed mean flow and the flame speed dependence on its curvature. The implications of the dispersion relation are discussed.
(2)
An
investigation of how the flame diffusive-thermal instabilities (or
similar Turing-type instabilities of a diffusion-reaction front) are
influenced in narrow channels by the direction of a shear flow relative
to that of front propagation. The study is motivated by the fact that
shear flows lead to Taylor dispersion (flow enhanced diffusion) in the
flow direction, but not in orthogonal directions. This leads
effectively to anisotropic diffusion whose influence on flame
instabilities is conducive to surprising conclusions. In particular, a
cellular long-wave instability is identified even in mixtures with Lewis
number larger than unity, which is described (near onset) by a modified
Kuramoto-Sivashinsky equation including a dispersion term (a third-order
spatial derivative) as well as a drift term (first-order derivative).
Hele-Shaw
cells are interesting tools for quasi-2D quantitative analysis of the
premixed flames propagation, allowing precise measurements of linear
growth rates and structural morphology, like cell size statistics, to
name a few. However, specific phenomenon’s appear in this configuration,
like vibro-acoustic coupling, or dynamics within the thickness.
Ultra-lean
hydrogen flame is closely related to hydrogen safety. Recently
unexpected flame regimes in ultra-lean hydrogen/air mixtures have been
observed in experiments. However, the evolution and propagation of
ultra-lean hydrogen flames are still not well understood. This study
aims to investigate the evolution and propagation of ultra-lean
hydrogen/air flames in an open Hele-Shaw cell. 3D simulations are
conducted by considering detailed chemistry and transport model. By
changing the equivalence ratio, different flame regimes reported in
previous experiments are observed in simulations. Specifically, regimes
including two-headed branching, two-headed finger and one-headed finger
are observed as the equivalence ratio increases. The flame cell
evolution is analyzed.
The
deflagration-to-detonation transition (DDT) on the tip of an elongated
flame in a tube is analyzed in the double limit of large activation
energy and small Mach number of laminar flames. A spontaneous transition
of a self-accelerated laminar flame taking the form of a dynamical
saddle-node bifurcation of the flow inside the inner structure of the
laminar flame is exhibited by the asymptotic analysis. The predicted
critical conditions for the finite-time pressure runaway are in
good agreement with the experimental data of the DDT onset in tubes.
Premixed hydrogen-air flames that propagate in slender channels have been recently found to be bistable in the limit of fuel-lean mixtures and non-negligible conductive heat losses. In particular, two stable configurations conformed by either a circular or a double-cell flame front arise for the same combination of controlling parameters (fuel mixture, channel size and thermal conductivity). In this work, detailed analyses are performed over the unsteady evolution of a set of numerical simulations. Specifically, the initial temperature profiles (distribution and peak value) and subsequent expansion of the flow field prescribe the early growth of the flame front leading to different curvatures and sizes of the kernel that control the evolution into each of the canonical structures.
The highly non-linear multiscale nature of combustion presents a challenge for numerical methods, necessitating methods which are both highly accurate and fast. Consequently, direct numerical simulations of combustion have long been dominated by high-order finite difference methods, which whilst extremely fast and accurate, are limited to simplified geometries. In this talk I'll introduce an alternative approach, based on a mesh-free discretisation, yielding high-order simulations in complex confined geometries. I will present results for a range of laminar and turbulent flame simulations in non-trivial geometries, where the method has potential to shed new light on fundamental flame dynamics.
Strong shear flows confined to narrow channels induce Taylor diffusion, leading to an anisotropic diffusion medium where transport is preferential in the streamwise direction. This phenomenon has significant implications for the stability of planar flames residing within these channels. We show that for flames aligned parallel to the shear flow, Taylor diffusion does not influence the flame structure itself, but rather plays a critical role in its stability. This talk will explore the impact of Taylor diffusion on diffusive-thermal and Darrieus-Landau instabilities, a key factor in the previously unexplained phenomenon of flame-street formation observed in micro-burners. Our research provides novel insights that elucidate this captivating behaviour.
Bifurcation
theory is a powerful tool in applied mathematics for systematically
extracting solution structures including evolutionary systems regardless
of stabilities of solutions. This talk addresses applications of
bifurcation theory to flame dynamics through recent works on premixed
flame morphology in the presence of Darrieus-Landau instability and the
effect of gravity, based on joint works with Prof. Moshe Matalon (UIUC),
as well as further directions.
Our study numerically investigates triple-flame propagation in a two-dimensional mixing layer in the presence of a Poiseuille flow using a thermo-diffusive model. We extend recent asymptotic results obtained for infinitely large Zeldovich number (β) to finite values and examine the impact of the flow amplitude (A) and the flame-front thickness (ɛ). Key findings include the inversion of flame front concavity towards the unburnt gas and the emergence of flame-tips for small values of ɛ and large values A.
Flame propagation and stability in
two-dimensional channels are investigated with a focus on 2D and 3D
diffusive-thermal (Turing) flame instabilities in a Poiseuille flow.
This talk explores the effect of flow amplitude (Peclet number Pe),
channel width (Damkohler number Da) and differential diffusion (Lewis
number Le) on the stability of the flame, in both adiabatic and
isothermal wall conditions. In the adiabatic case, steady flame
solutions exist for all Le, Pe and Da, whereas in the isothermal case,
they are limited by a minimum value of the Damkohler number (quenching
distance). For the instability analysis, we focus on those
steady solutions which are symmetric. The instability experienced by
these flames appears as a combination of the traditional
diffusive-thermal instability of planar flames and the recently
identified instability corresponding to a transition from symmetric to
asymmetric flames. Instability regions are identified in the parameter
space for selected channel widths by computing the eigenvalues of a
linear stability problem. In the cold isothermal wall case, it is
found that shear flows against the propagation of the flame increase
the quenching distance, while shear flows aiding the propagation of
the flame increase the quenching distance. Adiabatic stability results
closely resemble isothermal stability results.