Vincent Giovangigli

Thermal diffusion effects in hydrogen-air and methane-air flames

The influence of thermal diffusion on the structure of hydrogen-air and methane-air flames is investigated numerically using complex chemistry and detailed transport models. All the transport coefficients in the mixture, including thermal diffusion coefficients, are evaluated using new algorithms which provide, at moderate computational costs, accurate approximations derived rigorously from the kinetic theory of gases. Our numerical results show that thermal diffusion is important for an accurate prediction of flame structure. §E-mail address: ern@cermics.enpc.fr ∥E-mail address: giovangi@cmapx.polytechnique.fr

Convergent iterative methods for multicomponent diffusion

Abstract We investigate iterative methods for solving consistent linear systems arising from the kinetic theory of gases and for providing multicomponent diffusion coefficients for gaseous mixtures. Various iterative schemes are proved to be convergent by using the properties of matrices with convergent powers and the properties of nonnegative matrices. In particular, we investigate Stefan-Maxwell diffusion equations and we express the multicomponent diffusion matrix as a symmetric convergent series. We also rigorously justify the accuracy of Hirschfelder-Curtiss approximations with mass correctors often used to approximate diffusion velocities in gas mixtures.

Impact of Detailed Multicomponent Transport on Planar and Counterflow Hydrogen/Air and Methane/Air Flames

Abstract Freely propagating and counterflow laminar premixed steady hydrogen/air and methane/air flames are investigated numerically using complex chemistry and detailed transport models. All the transport coefficients in the mixture, including thermal diffusion coefficients, are evaluated using cost-effective, accurate algorithms derived recently by the authors from the kinetic theory of gases. Our numerical results provide a quantitative assessment of the impact of thermal diffusion on planar flame speed as a function of equivalence ratio and on extinction limits of counterflow flames as a function of either strain rate or equivalence ratio. In some cases, such as rich hydrogen/air flames, the effect of thermal diffusion is actually opposite to the one expected from a qualitative viewpoint or obtained with empirical models. In addition, we observe relevant effects of thermal diffusion on extinction of methane/air counterflow flames

Towards polyalgorithmic linear system solvers for nonlinear elliptic problems

The authors investigate the performance of several preconditioned conjugate gradient-like algorithms and a standard stationary iterative method (block-line successive overrelaxation (SOR)) on linear systems of equations that arise from a nonlinear elliptic flame sheet problem simulation. The nonlinearity forces a pseudotransient continuation process that makes the problem parabolic and thus compacts the spectrum of the Jacobian matrix so that simple relaxation methods are viable in the initial stages of the solution process. However, because of the transition from parabolic to elliptic character as the timestep is increased in pursuit of the steady-state solution, the performance of the candidate linear solvers spreads as the domain of convergence of Newton’s method is approached. In numerical experiments over the course of a full nonlinear solution trajectory, short recurrence or optimal Krylov algorithms combined with a Gauss–Seidel (GS) preconditioning yield better execution times with respect to the s...

Comparison between experimental measurements and numerical calculations of the structure of counterflow, diluted, methane-air, premixed flames

In this paper we investigate experimentally and numerically the structure and extinction of counterflow methane-air flames in the fresh reactant-hot product configuration. The flame is formed in the neighborhood of the stagnation point produced by the counterflow of fresh mixture and hot combustion products. Temperature and species profiles are measured using radiatively corrected thermocouple measurements together with a quartz microproble and a gas chromatograph. The governing conservation equations are solved numerically by employing adaptive continuation techniques. The model includes detailed transport and complex kinetics.

Projected iterative algorithms with application to multicomponent transport

Abstract We investigate projected iterative algorithms for solving constrained symmetric singular linear systems. We discuss the symmetry of generalized inverses and investigate projected standard iterative methods as well as projected conjugate-gradient algorithms. Using a generalization of Steins theorem for singular matrices, we obtain a new proof of Kellers theorem. We also strengthen a result from Neumann and Plemmons about the spectrum of iteration matrices. As an application, we consider the linear systems arising from the kinetic theory of gases and providing transport coefficients in multicomponent gas mixtures. We obtain low-cost accurate approximate expressions for the transport coefficients that can be used in multicomponent flow models. Typical examples for the species diffusion coefficients and the volume viscosity are presented.

Impact of volume viscosity on a shock–hydrogen-bubble interaction

We investigate the influence of volume viscosity on a planar shock–hydrogen-bubble interaction. The numerical model is two dimensional and involves complex chemistry and detailed transport. All transport coefficients are evaluated using algorithms which provide accurate approximations rigourously derived from the kinetic theory of gases. Our numerical results show that volume viscosity has an important impact on the velocity distribution – through vorticity production – and therefore on the flame structure.

Analytical and numerical modeling of flame-balls in hydrogen-air mixtures

Abstract Flame-balls are stationary spherical premixed flames observed in certain near-limit mixtures. It is believed that radiative heat losses are an important stabilizing influence. Numerical solutions of flame balls are constructed for hydrogen-air mixtures using an accurate description of the chemical kinetics, diffusive transport, and radiation losses. A lean limit equivalence ratio of 0.0866 is predicted and a rich limit of 2.828. For any equivalence ratio between the two limits there are two solutions. One is characterized by a small flame, incomplete reactant consumption, and negligible radiation losses. The other by a large flame, complete consumption of one of the reactants, and significatn radiation losses. The maximum temperature varies between 1200 and 900 K as the two solution branches are traversed. Much of our discussion is a reprise and modification of previously published analytical results, for these provide physical insight into the nature of the solutions, and suggest that a portion of the large flame branch near the lean limit is stable and so corresponds to observable flames.

The kinetic chemical equilibrium regime

We investigate reactive gas mixtures in the kinetic chemical equilibrium regime. Our starting point is a generalized Boltzmann equation with a chemical source term valid for arbitrary reaction mechanisms and yielding a positive entropy production. We first study the Enskog expansion in the kinetic chemical equilibrium regime. We derive a new set of macroscopic equations in the zeroth- and first-order regimes, expressing conservation of element densities, momentum and energy. The transport fluxes arising in the Navier–Stokes equilibrium regime are the element diffusion velocities, the heat flux vector and the pressure tensor and are written in terms of transport coefficients. Upon introducing species diffusion velocities, the kinetic equilibrium regime appears to be formally equivalent to the one obtained for gas mixtures in chemical nonequilibrium and then letting the chemical reactions approach equilibrium. The actual values of the transport coefficients are, however, different. Finally, we derive the entropy conservation equation in the Navier–Stokes equilibrium regime and show that the source term is positive and that it is compatible with Onsager’s reciprocal relations.

ASYMPTOTIC STABILITY OF EQUILIBRIUM STATES FOR MULTICOMPONENT REACTIVE FLOWS

We consider the equations governing multicomponent reactive flows derived from the kinetic theory of dilute polyatomic reactive gas mixtures. Using an entropy function, we derive a symmetric conservative form of the system. In the framework of Kawashima and Shizutas theory, we recast the resulting system into a normal form, that is, in the form of a symmetric hyperbolic–parabolic composite system. We also characterize all normal forms for symmetric systems of conservation laws such that the null space associated with dissipation matrices is invariant. We then investigate an abstract second-order quasilinear system with a source term, around a constant equilibrium state. Assuming the existence of a generalized entropy function, the invariance of the null space naturally associated with dissipation matrices, stability conditions for the source term, and a dissipative structure for the linearized equations, we establish global existence and asymptotic stability around the constant equilibrium state in all space dimensions and we obtain decay estimates. These results are then applied to multicomponent reactive flows using a normal form and the properties of Maxwellian chemical source terms.