Triple flame structure and diffusion flame stabilization

The stabilization of diffusion ñames is studied using asymptotic techniques and numerical tools. The configuration studied corresponda to parallel streams of cold oxidizer and fuel initially separated by a splitter píate. It is shown that stabilization of a diffusion flame may only occur in this situation by two processes. First, the flame may be stabilized behind the flame holder in the wake of the splitter píate. For this case, numerical simulations confirm scalings previously predicted by asymptotic analysis. Second, the flame may be lifted. In this case a triple flame is found at longer distanees downstream of the flame holder. The structure and propagation speed of this flame are studied by using an actively controlled numerical technique in which the triple flame is tracked in its own reference frame. It is then possible to investigate the triple flame structure and velocity. It is shown, as suggested from asymptotic analysis, that heat reléase may induce displacement speeds of the triple flame larger than the laminar flame speed corresponding to the stoichiometric conditions prevailing in the mixture approaching the triple flame. In addition to studying the characteristics of triple flames in a uniform flow, their re-sistance to turbulence is investigated by subjecting triple flames to different vortical configurations

Effects of pressure gradients on turbulent premixed flames

The influence of a constant acceleration on a turbulent premixed flame is studied by direct numerical simulation. This acceleration induces a mean pressure gradient across the flame brush, leading to a modification of the turbulent flame structure due to differential buoyancy mechanisms between heavy cold fresh and light hot burnt gases. Such a pressure gradient may be encountered in practical applications in ducted flames. A favorable pressure gradient, i.e. the pressure decreases from unburnt to burnt gases, is found to decrease the flame wrinkling, the flame brush thickness, and the turbulent flame speed. A favorable pressure gradient also promotes counter-gradient turbulent transport. On the other hand, adverse pressure gradients tend to increase the flame brush thickness and turbulent flame speed, and promote classical gradient turbulent transport. The balance equation for the turbulent flux of the Favre averaged progress variable is also analyzed. The first results show that the fluctuating pressure term, cannot be neglected as generally assumed in models. Simple models assuming that a high mean pressure gradient may only be balanced by the cross-dissipation term seem too approximate. This analysis has to be continued to compare simulation data and closure schemes proposed for the transport equation. The analysis developed by Veynante et al.(1995) has been extended to imposed acceleration and mean pressure gradients. A simple model for the turbulent flux is proposed and validated from simulation data. Then, a modified criterion is derived to delineate between counter-gradient and gradient turbulent diffusion. In fact, counter-gradient diffusion may occur in most practical applications, especially for ducted flames

DNS and modeling of the interaction between turbulent premixed flames and walls

The interaction between turbulent premixed flames and walls is studied using a two-dimensional full Navier-Stokes solver with simple chemistry. The effects of wall distance on the local and global flame structure are investigated. Quenching distances and maximum wall heat fluxes during quenching are computed in laminar cases and are found to be comparable to experimental and analytical results. For turbulent cases, it is shown that quenching distances and maximum heat fluxes remain of the same order as for laminar flames. Based on simulation results, a 'law-of-the-wall' model is derived to describe the interaction between a turbulent premixed flame and a wall. This model is constructed to provide reasonable behavior of flame surface density near a wall under the assumption that flame-wall interaction takes place at scales smaller than the computational mesh. It can be implemented in conjunction with any of several recent flamelet models based on a modeled surface density equation, with no additional constraints on mesh size or time step

Hydrodynamic instabilities in gaseous detonations: comparison of Euler, Navier–Stokes, and large-eddy simulation

A large-eddy simulation is conducted to investigate the transient structure of an unstable detonation wave in two dimensions and the evolution of intrinsic hydrodynamic instabilities. The dependency of the detonation structure on the grid resolution is investigated, and the structures obtained by large-eddy simulation are compared with the predictions from solving the Euler and Navier–Stokes equations directly. The results indicate that to predict irregular detonation structures in agreement with experimental observations the vorticity generation and dissipation in small scale structures should be taken into account. Thus, large-eddy simulation with high grid resolution is required. In a low grid resolution scenario, in which numerical diffusion dominates, the structures obtained by solving the Euler or Navier–Stokes equations and large-eddy simulation are qualitatively similar. When high grid resolution is employed, the detonation structures obtained by solving the Euler or Navier–Stokes equations directly are roughly similar yet equally in disagreement with the experimental results. For high grid resolution, only the large-eddy simulation predicts detonation substructures correctly, a fact that is attributed to the increased dissipation provided by the subgrid scale model. Specific to the investigated configuration, major differences are observed in the occurrence of unreacted gas pockets in the high-resolution Euler and Navier–Stokes computations, which appear to be fully combusted when large-eddy simulation is employed

Numerical simulations of turbulent premixed H2/O2/N2 flames with complex chemistry

Premixed stoichiometric H2/O2/N2 flames propagating in two-dimensional turbulence were studied using direct numerical simulation (simulations in which all fluid and thermochemical scales are fully resolved) including realistic chemical kinetics and molecular transport. Results are compared with earlier zero-chemistry (flame sheet) and one-step chemistry simulations. Consistent with the simpler models, the turbulent flame with realistic chemistry aligns preferentially with extensive strain rates in the tangent plane and flame curvature probability density functions are close to symmetric with near-zero means. By contrast to simple-chemistry results with non-unity Lewis numbers (ratio of thermal to species diffusivity), local flame structure does not correlate with curvature but rather with tangential strain rate. Turbulent straining results in substantial thinning of the flame relative to the steady unstrained laminar case. Heat release and H2O2 contours remain thin and connected ('flamelet-like') while species including H-atom and OH are more diffuse. Peak OH concentration occurs well behind the peak heat-release zone. The feasibility of incorporating realistic chemistry into full turbulence simulations to address issues such as pollutant formation in hydrocarbon-air flames is suggested

Mod/Resc Parsimony Inference

We address in this paper a new computational biology problem that aims at understanding a mechanism that could potentially be used to genetically manipulate natural insect populations infected by inherited, intra-cellular parasitic bacteria. In this problem, that we denote by \textsc{Mod/Resc Parsimony Inference}, we are given a boolean matrix and the goal is to find two other boolean matrices with a minimum number of columns such that an appropriately defined operation on these matrices gives back the input. We show that this is formally equivalent to the \textsc{Bipartite Biclique Edge Cover} problem and derive some complexity results for our problem using this equivalence. We provide a new, fixed-parameter tractability approach for solving both that slightly improves upon a previously published algorithm for the \textsc{Bipartite Biclique Edge Cover}. Finally, we present experimental results where we applied some of our techniques to a real-life data set.Comment: 11 pages, 3 figure

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017