Second-Order Semi-Discretized Schemes for Solving Stochastic Quenching Models on Arbitrary Spatial Grids

Reaction-diffusion-advection equations provide precise interpretations for many important phenomena in complex interactions between natural and artificial systems. This paper studies second-order semi-discretizations for the numerical solution of reaction-diffusion-advection equations modeling quenching types of singularities occurring in numerous applications. Our investigations particularly focus at cases where nonuniform spatial grids are utilized. Detailed derivations and analysis are accomplished. Easy-to-use and highly effective second-order schemes are acquired. Computational experiments are presented to illustrate our results as well as to demonstrate the viability and capability of the new methods for solving singular quenching problems on arbitrary grid platforms

Ignition and Extinction Behavior of Fuels in a Microcombustor

Conventional fuel testing device-CFR engine requires large quantities of fuels, which makes it unsuitable for research of small samples of fuels. This current study seeks to address this limitation by using an externally heated microcombustor as an alternative fuel testing device. Mainly three combustion behaviors have been observed inside a microcombustor: strong flames at higher flow rates, Flames with Repetitive Extinction and Ignition (FREI) at intermediate flow rates, and weak flames at marginal flow rates. In previous studies, weak combustion behavior has been proven suitable to study fuel properties from small samples of fuels. Microcombustor experiments typically rely on flame images. Imaging of weak flame needs long camera exposures due to reduced CH* emissions, hence weak flame experiments are not suitable for high throughput testing. FREI and strong flames give stronger CH* emission signals and can provide high throughput testing ability. The objective of this work is to investigate the potential of FREI and strong flames for fuel research and screening purposes. A major novelty of this work is to evaluate FREI behavior through lowspeed imaging and a microphone. FREI ignition and extinction temperatures of methane, ethane, propane, dimethyl ether and ethylene are shown to be fuel specific. The strong flame behavior is used to obtain insights into laminar flame speed of fuels. The respective impacts of microcombustor diameter, external heating, and unburned mixture equivalence ratio have been studied well. The open-source CFD package OpenFOAM with the detailed chemistry solver LaminarSMOKE is used to study FREI behavior of stoichiometric propane-air mixtures at engine relevant pressures. In simulations, critical fuel properties - i.e., FREI ignition and extinction temperatures, quenching diameter, and flame thickness, are found to decrease with increasing pressure similar to conventional IC engine behavior. Overall, fuel specific behavior of microcombustion and elevated pressure simulation results have shown microcombustion potential for fuel characterization for IC engines

The role of conductive heat losses on the formation of isolated flame cells in Hele-Shaw chambers

The propagation of low-Lewis-number premixed flames is analyzed in a partially confined Hele-Shaw chamber formed by two parallel plates separated a distance h apart. An asymptotic-numerical study can be performed for small gaps compared to the flame thickness deltaT . In this narrow-channel limit, the prob- lem formulation simplifies to a quasi-2D description in which the velocity field is controlled by domi- nant viscous effects. After accounting for conductive heat losses through the plates in our formulation, we found that the reaction front breaks into one or several isolated flame cells where the temperature is large enough to sustain the reaction, both in absence and in presence of buoyancy effects. Under these near-limit conditions, the isolated flame cells either travel steadily or undergo a slow random walk over the chamber in which the reacting front splits successively to form a tree-like pathway, burning only a small fraction of the fuel before reaching the end of the chamber. The production of quasi-2D circular or comet-like flames under specific favorable conditions is demonstrated in this paper, with convection, conductive heat losses and differential diffusion playing an essential role in the formation of the isolated one and two-headed flame cells.This work was supported by the project ENE2015-65852-C2-1-R (FV,MSS,DMR) and ENE2015-65852-C2-2-R (DFG,VK) (MINECO/FEDER, UE). Daniel Martínez-Ruiz would like to thank Amable Liñán for fruitful discussions

Front propagation directed by a line of fast diffusion: large diffusion and large time asymptotics

The system under study is a reaction-diffusion equation in a horizontal strip, coupled to a diffusion equation on its upper boundary via an exchange condition of the Robin type. This class of models was introduced by H. Berestycki, L. Rossi and the second author in order to model biological invasions directed by lines of fast diffusion. They proved, in particular, that the speed of invasion was enhanced by a fast diffusion on the line, the spreading velocity being asymptotically proportional to the square root of the fast diffusion coefficient. These results could be reduced, in the logistic case, to explicit algebraic computations. The goal of this paper is to prove that the same phenomenon holds, with a different type of nonlinearity, which precludes explicit computations. We discover a new transition phenomenon, that we explain in detail

Time-dependent computational studies of flames in microgravity

The research performed at the Center for Reactive Flow and Dynamical Systems in the Laboratory for Computational Physics and Fluid Dynamics, at the Naval Research Laboratory, in support of the NASA Microgravity Science and Applications Program is described. The primary focus was on investigating fundamental questions concerning the propagation and extinction of premixed flames in Earth gravity and in microgravity environments. The approach was to use detailed time-dependent, multispecies, numerical models as tools to simulate flames in different gravity environments. The models include a detailed chemical kinetics mechanism consisting of elementary reactions among the eight reactive species involved in hydrogen combustion, coupled to algorithms for convection, thermal conduction, viscosity, molecular and thermal diffusion, and external forces. The external force, gravity, can be put in any direction relative to flame propagation and can have a range of values. A combination of one-dimensional and two-dimensional simulations was used to investigate the effects of curvature and dilution on ignition and propagation of flames, to help resolve fundamental questions on the existence of flammability limits when there are no external losses or buoyancy forces in the system, to understand the mechanism leading to cellular instability, and to study the effects of gravity on the transition to cellular structure. A flame in a microgravity environment can be extinguished without external losses, and the mechanism leading to cellular structure is not preferential diffusion but a thermo-diffusive instability. The simulations have also lead to a better understanding of the interactions between buoyancy forces and the processes leading to thermo-diffusive instability

A computational approach to flame hole dynamics

Turbulent diffusion flames at low strain rates sustain a spatially continuous flame surface. However, at high strains, which may be localized in a flow or not, the flame can be quenched due to the increased heat loss away from the reaction zone. These quenched regions are sometimes called flame holes. Flame holes reduce the efficiency of combustion, can increase the production of certain pollutants (e.g. carbon monoxide, soot) as well as limit the overall stability of the flame. We present a numerical algorithm for the calculation of the dynamics of flame holes in diffusion flames. The key element is the solution of an evolution equation defined on a general moving surface. The low-dimensional manifold (the surface) can evolve in time and it is defined implicitly as an iso-level set of an associated Cartesian scalar field. An important property of the method described here is that the surface coordinates or parameterization does not need to be determined explicitly; instead, the numerical method employs an embedding technique where the evolution equation is extended to the Cartesian space, where well-known and efficient numerical methods can be used. In our application of this method, the field defined on the surface represents the chemical activity state of a turbulent diffusion flame. We present a formulation that describes the formation, propagation, and growth of flames holes using edge-flame modeling in laminar and turbulent diffusion flames. This problem is solved using a high-order finite-volume WENO method and a new extension algorithm defined in terms of propagation PDEs. The complete algorithm is demonstrated by tracking the dynamics of flame holes in a turbulent reacting shear layer. The method is also implemented in a generalized unstructured low-Mach number fluid solver (Sandia's SIERRA low Mach Module ``Nalu") and applied to simulate local extinction in a piloted jet diffusion flame configuration