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Diffusion flame streets, observed in non-premixed micro-combustion devices, align parallel to a shear flow. They are observed to occur in mixtures with high Lewis number ($Le$) fuels, provided that the flow Reynolds number, or the Peclet…

Fluid Dynamics · Physics 2024-07-03 Prabakaran Rajamanickam , Aiden Kelly , Joel Daou

We provide a mathematical analysis of a thermo-diffusive combustion model of lean spray flames, for which we prove the existence of travelling waves. In the high activation energy singular limit we show the existence of two distinct…

Classical Analysis and ODEs · Mathematics 2017-03-06 Pierre Berthonnaud , Komla Domelevo

The problem of premixed flame propagation in wide horizontal tubes is revisited. Employing the on-shell description of flames with arbitrary gas expansion, a nonlinear second-order differential equation for the front position of steady…

Fluid Dynamics · Physics 2015-05-30 Kirill A. Kazakov

In order to reduce CO2 emissions, hydrogen combustion has become increasingly relevant for technical applications. In this context, lean H2-air flames show promising features but, among other characteristics, they tend to exhibit…

This work is dedicated to the analysis of the delicate details of the effect of upstream velocity fluctuations on the flame propagation speed. The investigation was carried out using the Sivashinsky model of cellularisation of…

Fluid Dynamics · Physics 2013-05-29 V. Karlin

The structure of flame filaments resulting from chaotic mixing within a combustion reaction is considered. The transverse profile of the filaments is investigated numerically and analytically based on a one-dimensional model that represents…

Chaotic Dynamics · Physics 2007-05-23 Istvan Zoltan Kiss , J. H. Merkin , S. K. Scott , P. L. Simon , S. Kalliadasis , Zoltan Neufeld

Thermal-diffusional pulsation behaviors in planar as well as outwardly and inwardly propagating white dwarf carbon flames are systematically studied. In the 1D numerical simulation, the asymptotic degenerate equation of state and simplified…

High Energy Astrophysical Phenomena · Physics 2017-05-31 Guangzheng Xing , Yibo Zhao , Mikhail Modestov , Cheng Zhou , Yang Gao , Chung K. Law

We consider flame front propagation in channel geometries. The steady state solution in this problem is space dependent, and therefore the linear stability analysis is described by a partial integro-differential equation with a space…

Pattern Formation and Solitons · Physics 2011-08-19 Oleg Kupervasser , Zeev Olami , Itamar Procaccia

The problem of non-perturbative description of stationary flames with arbitrary gas expansion is considered. On the basis of the Thomson circulation theorem an implicit integral of the flow equations is constructed. With the help of this…

Fluid Dynamics · Physics 2009-11-10 Kirill A. Kazakov

We study traveling waves in a coordinate-free model of flame fronts. The flame front is the interface between the burnt and unburnt phases of a gas undergoing combustion. The front therefore moves in a preferred direction, as the unburnt…

Analysis of PDEs · Mathematics 2025-07-29 Sultan Aitzhan , Benjamin F. Akers , David M. Ambrose

This study presents a systematic characterization of burner-stabilized lean hydrogen flame morphology across a wide range of equivalence ratios, dilution factors, and flow rates. Spatially resolved measurements of three-dimensional…

Fluid Dynamics · Physics 2025-09-17 Zeyu Yan , Xiangyu Nie , Shuoxun Zhang , Shengkai Wang

The problem of deflagration-to-detonation transition in an unconfined environment is revisited. With a freely expanding self-accelerating hydrogen-oxygen flame as an example, it is shown that deflagration-to-detonation transition is indeed…

Fluid Dynamics · Physics 2019-06-28 Andrey Koksharov , Leonid Kagan , Gregory Sivashinsky

The main goal of this paper is to prove $L^1$-comparison and contraction principles for weak solutions (in the sense of distributions) of Hele-Shaw flow with a linear Drift. The flow is considered with a general reaction term including the…

Analysis of PDEs · Mathematics 2023-12-27 Noureddine Igbida

The problem of linear stability of confined V-flames with arbitrary gas expansion is addressed. Using the on-shell description of flame dynamics, a general equation governing propagation of disturbances of an anchored flame is obtained.…

Fluid Dynamics · Physics 2009-02-26 Hazem El-Rabii , Guy Joulin , Kirill A. Kazakov

Computed flame motion through and between swirling eddys exhibits a maximum advancement rate which is related to the time duration of flame motion between eddys. This eddy spatial structure effect upon the apparent turbulent flame speed…

chao-dyn · Physics 2008-02-03 Wm. T. Ashurst

Shock waves are steep wave fronts that are fundamental in nature, especially in high-speed fluid flows. When a shock hits an obstacle, or a flying body meets a shock, shock reflection/diffraction phenomena occur. In this paper, we show how…

Analysis of PDEs · Mathematics 2016-02-17 Gui-Qiang G. Chen , Mikhail Feldman

Hydrogen-air deflagrations with venting at the end of obstructed tubes are studied experimentally and numerically. A shockless transition to the so-called chocked regime of the flame propagation is reported. Mixtures with 13% vol. of…

Fluid Dynamics · Physics 2012-09-03 J. Yanez , M. Kuznetsov , V. Bykov

A three-dimensional flamelet model considering vortex stretching with unitary Lewis number is used to simulate diluted hydrogen-oxygen diffusion flames. Non-reacting nitrogen is used as the diluent gas in the fuel stream. Unitary Lewis…

Fluid Dynamics · Physics 2024-10-08 Wes Hellwig , Xian Shi , William A. Sirignano

The present study is devoted to the detailed numerical analysis of the combustion waves propagation through the lean hydrogen-air mixtures with suspended micro-droplets of water. Considered gaseous mixtures are characterized by a relatively…

Fluid Dynamics · Physics 2019-09-20 I. S. Yakovenko , A. D. Kiverin

Bubbles of inviscid fluid surrounded by a viscous fluid in a Hele-Shaw cell can merge and break-off. During the process of break-off, a thinning neck pinches off to a universal self-similar singularity. We describe this process and reveal…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Seung-Yeop Lee , Eldad Bettelheim , Paul Wiegmann