The problem of non-perturbative description of stationary flames with arbitrary gas expansion is considered. A general method for deriving equations for the flame front position is developed. On the basis of the Thomson circulation theorem an implicit integral of the flow equations is constructed. With the help of this integral the flow structure near the flame front is determined, and a closed system of equations for the flame front position and a set of auxiliary quantities is obtained. This system is shown to be quasi-local, and its transverse representation is found. This representation allows reduction of the system to a single equation for the flame front position. The developed approach is applied to the case of zero-thickness flames.
An experimental study of methane, propane and dimethyl ether (DME) pre-mixed flames propagating in a quasi-two-dimensional Hele-Shaw cell placed horizontally is presented in this paper. The flames are ignited at the open end of the combustion chamber and propagate towards the closed end. Our experiments revealed two distinct propagation regimes depending on the equivalence ratio of the mixture as a consequence of the coupling between the heat-release rate and the acoustic waves. The primary acoustic instability induces a small-amplitude, of around 8 mm, oscillatory motion across the chamber th…
Premixed flames propagating within small channels show complex combustion phenomena that differ from flame propagation at conventional scales. Available experimental and numerical studies have documented stationary/non-stationary and/or asymmetric modes that depend on properties of the incoming reactant flow as well as channel geometry and wall temperatures. The present work seeks to illuminate mechanisms leading to symmetry-breaking and limit cycle behavior that are fundamental to these combustion modes. Specifically, four cases of lean premixed methane/air combustion -- two equivalence ratio…
The early stages of flames propagation in tubes with no-slip walls and the inversion of the flame front from a convex shape directed towards unburned gas to a concave shape with a cusp directed to the burned gas, known as a tulip flame, was investigated for closed and half-open tubes by solving the fully compressible reactive Navier-Stokes equations with a one-step Arrhenius chemical model for the highly reactive hydrogen/air and slowly reacting methane/air mixtures. The development of the tulip flame in hydrogen/air obtained in simulations with a one-step Arrhenius model was compared with sim…
Spark ignition of ethanol droplet/vapor/air mixture is studied with a Eulerian-Eulerian method and detailed chemical mechanism. The flame kernel-droplet interaction is quantified with an evaporation completion front (ECF). Two categories of spray flames can hence be defined based on the relative location between the ECF and flame front, i.e., homogeneous and heterogeneous spray flames. An element-based equivalence ratio (ER) at the flame front (flame ER for short) is introduced to measure the gas composition in evaporating sprays. For overall fuel-lean mixtures, quasi-stationary spherical flam…
The present work investigates forced ignition and oscillating propagation of spray flame in a mixture of fine ethanol droplets and air. Eulerian-Eulerian method with two-way coupling is used and detailed chemical mechanism is considered. Different droplet diameters and liquid fuel equivalence ratios (ER) are studied. The evaporation completion front (ECF) is defined to study the interactions between the evaporation zone and flame front. The gas composition at the flame front is quantified through an effective ER. The results show that the kernel trajectory is considerably affected by droplet s…
Significant progress has been made on the model development for simulating turbulent reacting flows. As a consequence, we are currently in a position where key-physical aspects of fairly complex combustion processes are well understood at a qualitative and -- in many cases -- also at a quantitative level. Examples are the prediction of temperature and major species, statistically stationary flames, gas-phase combustion, turbulent transport, and turbulence/flame coupling. However, current challenges lie in capturing transient processes and stability boundaries, minor species and emissions, mult…
The Euler equations describing two-dimensional steady flows of an inviscid fluid are studied. These equations are reduced to one equation for the stream function and then, using the Hirota function, solutions of three nonlinear elliptic equations are found. %: Sine-Gordon, Sinh-Gordon and Tzitzéica. The solutions found are interpreted as sources in a rotating fluid, jets, chains of sources and sinks, vortex structures. We propose a new simple method for constructing solutions in the form of rational expressions of elliptic functions. It is shown that the flux of fluid across a closed curve is …
