Lean flame dynamics through a 2D lattice of alkane droplets in air

International audienceFlame propagation along a 1-D array or through a 2D-lattice of fuel droplets has long been suggested to schematize spray-flames spreading in a two-phase premixture. The present numerical work considers the fresh aerosol as a system of individual alkane droplets initially located at the nodes of a face-centered 2D-lattice, surrounded by a variable mixture of alkane and air, in which the droplets can move. The main parameters of the study are s, the lattice path, and phi_ L , the liquid loading, which are both varied, whereas phi_T , the overall equivalence ratio, is maintained lean ( phi_T = 0.85). Main results are as follows: (a) For a large lattice path (or when the droplets are large enough), spreading occurs in two stages: a short time of combustion followed by a long time lag of vaporization and a classical triple flame (with a very short rich wing) spreads around the droplets; (b) spray-flame speed decreases as liquid loading increases; (c) an elementary model invoking both propagation stages allows us to interpret flame speed as a function of the sole parameter s × phi_ L ; (d) when the lattice path shortens, the spray-flame exhibits a pattern that continuously goes from this situation to the plane flame front

Rich Spray-Flame Propagating through a 2D-Lattice of Alkane Droplets in Air

International audienceIn a recent numerical paper (Nicoli et al. Combust. Sci. Technol. vol. 186, pp. 103-119; 2014) [1], a model of isobaric flame propagation in lean sprays has been proposed. The initial state of the monodisperse mists was schematized by a system of individual alkane droplets initially located at the nodes of a face-centered 2D-lattice, surrounded by a saturated mixture of alkane and air. In the present study, the previous model is complemented with an original chemical scheme that allows us to study the combustion of rich alkane/air mixtures

Spray-Flame Dynamics in a Rich Droplet Array

International audienceIn a recent numerical paper (Nicoli et al. Combust. Sci. Technol. vol. 186, pp. 103-119; 2014) [1], a model of isobaric flame propagation in lean sprays has been proposed. The initial state of the monodisperse mists was schematized by a system of individual alkane droplets initially located at the nodes of a face-centered 2D-lattice, surrounded by a saturated mixture of alkane and air. In the present study, the previous model is complemented with an original chemical scheme that allows us to study the combustion of rich alkane/air mixtures

Penalization modeling of a limiter in the Tokamak edge plasma

International audienceAn original penalization method is applied to model the interaction of magnetically confined plasma with limiter in the frame of minimal transport model for ionic density and parallel momentum. The limiter is considered as a pure particle sink for the plasma and consequently the density and the momentum are enforced to be zero inside. Comparisons of the numerical results with one dimensional analytical solutions show a very good agreement. In particular, presented method provides a plasma velocity which is almost sonic at the boundaries obstacles as expected from the sheath conditions through the Bohm criterion. The new system being solved in an obstacle free domain, an efficient pseudo-spectral algorithm based on a Fast Fourier transform is also proposed, and associated with an exponential filtering of the unphysical oscillations due to Gibbs phenomenon. Finally, the efficiency of the method is illustrated by investigating the flow spreading from the plasma core to the Scrape Off Layer at the wall in a two-dimensional system with one then two limiters neighboring

Laminar flow in a two-dimensional plane channel with local pressure-dependent crossflow

International audienceLong ducts (or pipes) composed of transpiring (e.g. porous) walls are at the root of numerous industrial devices for species separation, as tangential filtration or membrane desalination. Similar configurations can also be involved in fluid supply systems, as irrigation or biological fluids in capillaries. A transverse leakage (or permeate flux), the strength of which is assumed to depend linearly on local pressure (as in Starling's law for capillary), takes place through permeable walls. All other dependences, as osmotic pressure or partial fouling due to polarization of species concentration, are neglected. To analyse this open problem we consider the simplest situation: the steady laminar flow in a two-dimensional channel composed of two symmetrical porous walls. First, dimensional analysis helps us to determine the relevant parameters. We then revisit the Berman problem that considers a uniform crossflow (i.e. pressure-independent leakage). We expand the solution in a series of Rt, the transverse Reynolds number. We note this series has a rapid convergence in the considered range of Rt (i.e. Rt ≤ O(1)). A particular method of variable separation then allows us to derive from the Navier-Stokes equations two new ordinary differential equations (ODE), which correspond to first and second orders in the development in Rt, whereas the zero order recovers the Regirer linear theory. Finally, both new ODEs are used to study the occurrence of two undesirable events in the filtration process: axial flow exhaustion (AFE) and crossflow reversal (CFR). This study is compared with a numerical approach

Etude en boucle ouverte de l’action d’une onde acoustique sur une flamme de brouillard

Lorsque l'échelle de réaction-diffusion est plus grande que la distance inter-goutte, le brouillard est homogénéïsable. Sa combustion peut donner lieu à des flammes pulsantes. La possible résonance de cet oscillateur est étudiéee quand la flamme est soumise à une onde acoustique. Le critère de Rayleigh prédit l’apparition d’une instabilité thermo-acoustique. Si la fréquence s'approche de la fréquence intrinsèque de pulsation, le transfert d’énergie est trouvé maximal

Non-linear CFL Conditions Issued from the von Neumann Stability Analysis for the Transport Equation

International audienceThis paper presents a theory of the possible non-linear stability conditions encountered in the simulation of convection dominated problems. Its main objective is to study and justify original CFL-like stability conditions thanks to the von Neumann stability analysis. In particular, we exhibit a wide variety of stability conditions of the type t ≤ C x α with t the time step, x the space step, and α a rational number within the interval [1, 2]. Numerical experiments corroborate these theoretical results

Natural convection along a heated vertical plate immersed in a nonlinearly stratified medium: application to liquefied gas storage

International audienceWe consider free convection driven by a heated vertical plate immersed in a nonlinearly stratified medium. The plate supplies a uniform horizontal heat flux to a fluid, the bulk of which has a stable stratification, characterized by a non-uniform vertical temperature gradient. This gradient is assumed to have a typical length scale of variation, denoted Z0, while Ψ0 is the order of magnitude of the related heat flux that crosses the medium vertically. We derive an analytic solution to the Boussinesq equations that extends the classical solution of Prandtl to the case of nonlinearly stratified media. This novel solution is asymptotically valid in the regime Ras " 1, where Ras denotes the Rayleigh number of nonlinear stratification, based on Z0, Ψ0, and the physical properties of the medium. We then apply the new theory to the natural convection affecting the vapour phase in a liquefied pure gas tank (e.g. the cryogenic storage of hydrogen). It is assumed that the cylindrical storage tank is subject to a constant uniform heat flux on its lateral and top walls. We are interested in the vapour motion above a residual layer of liquid in equilibrium with the vapour. High-precision axisymmetric numerical computations show that the flow remains steady for a large range of parameters, and that a bulk stratification characterized by a quadratic temperature profile is undoubtedly present. The application of the theory permits a comparison of the numerical and analytic results, showing that the theory satisfactorily predicts the primary dynamical and thermal properties of the storage tank

A Helmholtz--Hodge projection method using an iterative gauge computation to solve the 3D generalized Stokes problem

International audienceThe generalized Stokes problem (GSP) is broadly recognized as a keystone in implicit or semi-implicit discretizations of the Navier--Stokes equations (NSE), either incompressible or of low Mach number type, i.e., for which there exists a constraint on the vector field. The GSP is also known as the steady Darcy--Brinkman model for flows in porous media or in Hele--Shaw configurations. Up to now, only pressure- (preconditioned) Uzawa methods claimed to solve the three-dimensional (3D) GSP exactly (i.e., without introducing an error due to some time stepping). In the present article, we present another exact 3D solver that is developed in the particular context of the Helmholtz--Hodge projection in $(H^1)^d$. Instead of working iteratively with the pressure operator (i.e., the Schur complement), we are interested here in using an alternative scalar field, which performs the projection and is called the gauge. It turns out that iterative computation of the gauge presents efficient properties in terms of operator conditioning. To prove the relevance of the gauge method, we demonstrate several mathematical properties of the operator acting on the gauge, especially when preconditioned in an appropriate way. In particular, we prove that the gauge operator can be solved efficiently with any gradient method. The convergence properties of the continuous preconditioned operator are quantitatively estimated in the context of a semiperiodic two-dimensional (2D) domain. We then study the discrete gauge operator implemented in the framework of Chebyshev 2D-3D pseudospectral methods. It exhibits the same favorable properties as those found for the continuous operator. Finally, we perform numerical experiments that corroborate our analyses