Combustion Theory and Modelling

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Starting from a Rakib–Sivashinsky type of equation for the local amplitude of wrinkling of premixed flames propagating upward or downward, we numerically study how the ensemble-averaged cell wavelengths (crest-to-crest, or from spectral density of wrinkling) evolve from random initial conditions, when the gravity is weak. Tentative theories yield simple scaling laws that are in good agreement with the numerical results; yet some lack of universality suggests that such laws are merely accurate and not exact. Open problems, e.g. relating to noise, are finally evoked.

This work deals with the numerical simulation on an unstructured mesh of the ignition and burning in an oxidizing atmosphere of a fuel droplet heated on one side. This is relevant for studying the ignition of droplets in a spray when they are crossing a flame zone stabilized in it. The droplet here is replaced by a porous cylinder, and the flame by a hot solid wall. The reaction is assumed to be described by a single step, A + νB → P. The cell-centred finite volume scheme considered here uses a generalized Roe's approximate Riemann solver with the monotonic upwind scheme for conservative laws (MUSCL) technique for the convective part and Green–Gauss type interpolation for the viscous part. The thinness of the reaction zone is taken into account by using an adaptive refinement–unrefinement procedure. It has been found that the process of droplet ignition takes place by means of a propagation of a triple flame around the 'droplet' when the chemical reaction is sufficiently fast with respect to the molecular heat and mass diffusion process.

A two-dimensional numerical model is developed to simulate combustion and heat transfer in 'Swiss roll' combustors (SRC). This model couples heat transfer and chemical reaction in the gas and heat diffusion in the conducting walls. The goal of the model is to gain insight into micro-scale combustion to prevent the occurrence of extinction. In the numerical modelling, the 'Swiss roll' geometry is unwrapped into a straight channel, with heat recirculation between the unburnt and burnt gas being appropriately taken into account. The simulation is carried out using a fourth-order scheme to discretize the spatial variables, with time integration to steady state, based on a first-order Runge–Kutta scheme. We investigate the extinction mechanisms and heat transfer characteristics in the combustor, and perform parametric studies to examine their effects on combustion and extinction. Numerical predictions of extinction limits agree well with experimental data.

Premixed laminar combustion in closed vessels has been widely used for the determination of laminar burning velocities. A novel multiple burnt gas zone model has been developed to describe the different aspects of premixed laminar combustion in a closed spherical vessel. The mixture is divided into burnt and unburnt gases with the flame front as a discontinuity. Unburnt gases are assumed to be in a frozen chemical state. However, burnt gases are divided into a number of burnt gas zones. For the methane–air mixture the model is used to determine the temperature distribution within the burnt gas, the relationship between the pressure rise and mass fraction burnt, the variation of the combustion products with temperature and pressure, the spatial distribution of the gas density, the influence of elevated initial temperature, pressure and molecular structure. This computation allows for the variation in heat capacity of the constituents, and solves the equilibrium combustion equation for the ten major species (N₂, O₂, H₂, CO, CO₂, H₂O, O, H, NO, OH). This eliminates some of the simplifications made by Bradley and Mitcheson (1976 Combust. Flame 26 201–17) or Takeno and Iijima (1979 7th Int. Colloq. on Gas Dynamics of Explosions and Reactive Systems (Göttingen, Germany) pp 20–4), such as the constant specific heat for the burnt and unburnt gases, incorporation of the flame front thickness, use of the Rankine–Hugoniot relation for finding the burnt gas state.