Josette Bellan

A model of smoldering combustion applied to flexible polyurethane foams

Smoldering combustion, particularly in upholstery and bedding materials, has been proven a serious life hazard. The simplest representation of this hazard situation is one-dimensional downward propagation of a smolder wave against a buoyant upflow (cocurrent smolder); the configuration treated here is identical in all respects to this except for the presence of a forced flow replacing the buoyant one. The complex degradation chemistry of the polyurethanes is here reduced to the two major overall reactions of char formation and char oxidation. The model solutions, which are in reasonable agreement with experimental results, show the smolder process to be oxygen-limited, which leads to some very simple trends. More subtle behavior aspects determine actual propagation velocity, fraction of fuel consumed, and apparent equivalence ratio (all of which are variable). The self-insulating character of the smolder wave makes it viable in a wide-ranging set of conditions if the igniting stimulus is sufficiently long. These results have significant implications regarding the problem of smolder prevention or hindrance.

A Theory of Turbulent Flame Development and Nitric Oxide Formation in Stratified Charge Internal Combustion Engines

A theoretical model of turbulent flame propagation in a reciprocating stratified charge engine is developed and calculations of temperature and species concentrations as functions of space and time are made. Also pressure is calculated as a function of time. A spacial variation of mixture ratio is considered such that there is a fuel-rich region in the center of the cylinder and a fuel-lean region near the cylinder walls. The spark in the fuel-rich region results in a premixed-type of flame propagating toward the walls. A diffusion-type flame results in the wake of the other flame due to the mixing of the excess air and fuel.

Theoretical examination of assumptions commonly used for the gas phase surrounding a burning droplet

A finite reaction-rate model is compared to three commonly used flame-sheet models. The latter differ in their treatment of the evaporation from the surface and the value used for the molecular weights in the evaporation law. All four models are applicable to both steady and unsteady burning of droplets. Further, they account for variations of droplet radii and allow for differences in ambient conditions. Numerical results (obtained forn-decane) show that if the radius of the droplet is 10^(−2) cm the thin-flame approximation is excellent at 10 atm if the droplet surface temperature is not close to either the boiling point or the ambient temperature. However, this approximation is unacceptable at 1 atm. Among the three flame-sheet models, the one using non equilibrium evaporation at the surface and individual molecular weights best approximates the finite reaction-rate theory. However, this agreement breaks down for smaller droplets with lower surface temperatures, or for air with a larger oxygen content. These conclusions are independent of the chosen kinetics. The Clausius-Clapeyron approximation is shown to be excellent away from the boiling point for R = 10^(−2) cm. However, as the droplet surface temperature approaches the boiling point, or the droplet radius decreases, this assumption leads to considerable errors in the evaporation rate and also distortion of the thermal layer. Even larger errors are obtained when an average molecular weight is used. Here, large underestimates of the evaporation rate and great distortions of the thermal layer of the droplet are obtained. In spite of these errors, all models agree well at wet-bulb conditions.

Combustion and NO Formation in a Stratified-Charge Engine: a Two-Turbulent Equations Model

A theoretical model of turbulent flame propagation in reciprocating stratified-charge engines is developed and compared to a previous model. A spacial variation of mixture ratio is considered such that there is a fuel-rich region in the center of the cylinder and a fuel lean-region near the cylinder walls. The spark in the fuel-rich region results in a premixed type of flame propagating toward the walls. A diffusion-type flame results in the wake of the other flame due to the mixing of the excess air and fuel. n nThe first model which was presented in a previous paper is based upon a prescribed time variation of the turbulent diffusivity depending upon the piston velocity. In the present work, a two-turbulent-equations model is developed and the turbulent diffusivity varies in space and time as well. Without experimental data it is difficult to ascertain that the second model is superior to the first one. However, because of the coupling of the turbulence phenomenon to the combustion itself, the second model is believed to be better than the first one. In both models calculations of the temperature and species mass fractions as functions of time and space are made. Also, the pressure is calculated as a function of time. n nA parametric study is performed with the second model. Parameters concerning both the engine and the mixture are varied. In particular a comparison with an engine operating with a premixed gas mixture is made. Trends indicate methods to “optimize” the combustion process so that a “satisfactory” reduction in NO could be achieved with a “small” drop in the pressure level.

A preliminary theoretical study of droplet extinction by depressurization

Depressurization-induced extinction of droplets is demonstrated using an unsteady liquid-phase theory and a previously presented quasisteady gas-phase model. Numerical results show that depressurization of the gas phase causes extinction of both regressing and nonregressing droplets. For nonregressing droplets it is found that at fixed droplet size the extinction pressure is a decreasing function of the initial depressurization rate; thus results are explained in terms of the time lag needed by a droplet to respond to a change in pressure. Regressing droplets, which extinguish more rapidly than constant-size ones, show the same type of behavior. Extinction boundaries, evaluated as functions of the initial temperature profile, show that whereas for constant-size droplets the extinction pressure is a strong decreasing function of the temperature, for regressing droplets this dependence is very weak and an asymptote is reached as the temperature increases. Results obtained by varying the initial pressure show that the extinction pressure is an increasing function of the initial pressure for regressing droplets. For constant-size droplets this function is nonmonotonic and reaches a maximum at the initial pressure for which the initial temperature profile is the wet-bulb state. The thermal conductivity of the liquid phase has almost no influence on the extinction boundary.

Quasi-Steady Gas Phase Assumption for a Burning Droplet

Sedimentation Potential and Rate in Gravitational Fields The irreversible thermodynamics of sedimentation phenomena have been discussed by de Grott, and Rastogi and Misra. When insoluble solid particles are allowed to fall under gravity, potential energy is converted into electrical energy and a sedimentation current flows. Moreover, in such a system, when an electric field is applied the particles move, giving rise to electrophoresis. The phenomenological relations can be written as

Model for Studying Unsteady Droplet Combustion

The concept of a reduced boundary condition at the surface of a droplet is used to develop a theory of unsteady droplet burning. This theory utilizes a quasi-steady gas-phase assumption, which has been shown to be realistic for a wide range of droplet sizes at low pressures. The most significant consequence of the theory is that the problem of unsteady droplet burning is reduced to the solving of a single diffusion-type nonlinear partial differential equation having one of its boundary conditions determined by an algebraic function of the quasi-steady gas-phase variables. This reduced boundary condition incorporates the entire dependence of the solution on fuel characteristics, chemical kinetics, and thermal properties of the gases. An experiment is proposed for determining this boundary condition so that the nonsteady droplet combustion problem can be solved for a realistic situation. By using additional assumptions, a numerical estimate of the boundary condition has been made.

Linear finite-element numerical techniques for combustion problems requiring variable step size

Combustion problems frequently pose situations nin which the dependent variables (temperature, nspecies concentrations, etc.) vary rapidly in some nlocal domain and much more slowly throughout nthe remaining region of interest. Such situations narise for both fluid-mechanical (e.g., boundary-layer nbehavior) and chemical reasons (i.e., Arrhenius- ntype temperature dependence of chemical reaction nrates). In any case, they present a particular ndifficulty in the numerical solution of the governing nconservation equations: if a fixed space-step is nto be used, its magnitude is dictated by stability nand/or accuracy requirements of the limited but nrapidly varying domain. Outside this narrow domain, nmany more space steps are taken than are required; ncomputing costs are thus magnified. n nVarious means to avoid this difficulty have nbeen used in the past, but none has proved generally nsatisfactory or convenient. Finite-element methods nare substantially more convenient than the classical nfinite-difference techniques for approximating nspatial dependencies in certain combustion problems. nWe discuss only linear finite-element (LFE) nmethods here. A discussion of this and more ngeneral finite-element methods can be found in nseveral sources [1-3]; we briefly outline the application nof the LFE method and illustrate its advantages.