Chemical and statistical soot modeling

The combustion of petroleum based fuels like kerosene, gasoline, or diesel leads to the formation of several kind of pollutants. Among them, soot particles are particularly bad for their severe consequences on human health. Over the past decades, strict regulations have been placed on car and aircraft engines in order to limit these particulate matter emissions. Designing low emission engines requires the use of predictive soot models which can be applied to the combustion of real fuels. Towards this goal, the present work addresses the formation of soot particles both from a chemical and statistical point of view. As a first step, a chemical model is developed to describe the formation of soot precursors from the combustion of several components typically found in surrogates, including n-heptane, iso-octane, benzene, and toluene. The same mechanism is also used to predict the formation of large Polycyclic Aromatic Hydrocarbons (PAH) up to cyclopenta[cd]pyrene (C_(18)H_(10)). Then, a new soot model which represents soot particles as fractal aggregates is used. In this model, a soot particle is described by three variables: its volume (V), its surface area (S), and the number of hydrogen sites on the surface (H). The Direct Quadrature Method of Moments (DQMOM) is used as a precise representation of the population of soot particles which includes small spherical particles and large aggregates. This model is shown to predict accurately the formation of soot in a wide range of flames including premixed and counter flow diffusion flames, low and high temperature flames and for a wide range of fuels from ethylene to iso-octane. Finally, this model predicts several aggregate properties like the primary particle diameter and gives insight into the reactivity of the soot surface

A cost-effective semi-implicit method for the time integration of fully compressible reacting flows with stiff chemistry

We present a simple method to remove the stiffness associated with the chemical source terms in the fully compressible Navier-Stokes equations when the classical fourth order Runge-Kutta scheme is used

Properties of selected mutations and genotypic landscapes under Fisher's Geometric Model

The fitness landscape - the mapping between genotypes and fitness - determines properties of the process of adaptation. Several small genetic fitness landscapes have recently been built by selecting a handful of beneficial mutations and measuring fitness of all combinations of these mutations. Here we generate several testable predictions for the properties of these landscapes under Fisher's geometric model of adaptation (FGMA). When far from the fitness optimum, we analytically compute the fitness effect of beneficial mutations and their epistatic interactions. We show that epistasis may be negative or positive on average depending on the distance of the ancestral genotype to the optimum and whether mutations were independently selected or co-selected in an adaptive walk. Using simulations, we show that genetic landscapes built from FGMA are very close to an additive landscape when the ancestral strain is far from the optimum. However, when close to the optimum, a large diversity of landscape with substantial ruggedness and sign epistasis emerged. Strikingly, landscapes built from different realizations of stochastic adaptive walks in the same exact conditions were highly variable, suggesting that several realizations of small genetic landscapes are needed to gain information about the underlying architecture of the global adaptive landscape.Comment: 51 pages, 8 figure

A fast, low-memory, and stable algorithm for implementing multicomponent transport in direct numerical simulations

Implementing multicomponent diffusion models in reacting-flow simulations is computationally expensive due to the challenges involved in calculating diffusion coefficients. Instead, mixture-averaged diffusion treatments are typically used to avoid these costs. However, to our knowledge, the accuracy and appropriateness of the mixture-averaged diffusion models has not been verified for three-dimensional turbulent premixed flames. In this study we propose a fast,efficient, low-memory algorithm and use that to evaluate the role of multicomponent mass diffusion in reacting-flow simulations. Direct numerical simulation of these flames is performed by implementing the Stefan-Maxwell equations in NGA. A semi-implicit algorithm decreases the computational expense of inverting the full multicomponent ordinary diffusion array while maintaining accuracy and fidelity. We first verify the method by performing one-dimensional simulations of premixed hydrogen flames and compare with matching cases in Cantera. We demonstrate the algorithm to be stable, and its performance scales approximately with the number of species squared. Then, as an initial study of multicomponent diffusion, we simulate premixed, three-dimensional turbulent hydrogen flames, neglecting secondary Soret and Dufour effects. Simulation conditions are carefully selected to match previously published results and ensure valid comparison. Our results show that using the mixture-averaged diffusion assumption leads to a 15% under-prediction of the normalized turbulent flame speed for a premixed hydrogen-air flame. This difference in the turbulent flame speed motivates further study into using the mixture-averaged diffusion assumption for DNS of moderate-to-high Karlovitz number flames.Comment: 36 pages, 14 figure

Effects of dissipation rate and diffusion rate of the progress variable on local fuel burning rate in premixed turbulent flames

The validity of the premixed flamelet equations and the dependence of the fuel burning rate on the parameters involved in these equations have been investigated using a large series of direct numerical simulations of turbulent premixed flames in the thin reaction zones (TRZ) and the distributed reaction zones (DRZ) regimes. Methane, toluene, n-heptane, and iso-octane fuels were considered over a wide range of unburnt conditions and turbulence characteristics. Flames with unity and non-unity Lewis numbers were investigated separately to isolate turbulence-chemistry interaction from differential diffusion effects. In both cases, the flamelet equations, which rely on the assumption of a thin reaction zone, are locally valid throughout the TRZ regime, more precisely up to a Karlovitz number at the reaction zone of 10 (based on the definition used in this paper). Consistent with this result, in the unity Lewis number limit, the fuel burning rate is strongly correlated with the dissipation rate of the progress variable, the only parameter in the flamelet equations. In the non-unity Lewis number case, the burning rate is a strong function of both the dissipation rate and the diffusion rate, both of which are parameters in the flamelet equations. In particular, the correlation with these parameters is significantly better than with curvature or tangential strain rate

Vorticity isotropy in high Karlovitz number premixed flames

The isotropy of the smallest turbulent scales is investigated in premixed turbulent combustion by analyzing the vorticity vector in a series of high Karlovitz number premixed flame direct numerical simulations. It is found that increasing the Karlovitz number and the ratio of the integral length scale to the flame thickness both reduce the level of anisotropy. By analyzing the vorticity transport equation, it is determined that the vortex stretching term is primarily responsible for the development of any anisotropy. The local dynamics of the vortex stretching term and vorticity resemble that of homogeneous isotropic turbulence to a greater extent at higher Karlovitz numbers. This results in small scale isotropy at sufficiently high Karlovitz numbers and supports a fundamental similarity of the behavior of the smallest turbulent scales throughout the flame and in homogeneous isotropic turbulence. At lower Karlovitz numbers, the vortex stretching term and the vorticity alignment in the strain-rate tensor eigenframe are altered by the flame. The integral length scale has minimal impact on these local dynamics but promotes the effects of the flame to be equal in all directions. The resulting isotropy in vorticity does not reflect a fundamental similarity between the smallest turbulent scales in the flame and in homogeneous isotropic turbulence

Thermochemical properties of polycyclic aromatic hydrocarbons (PAH) from G3MP2B3 calculations

In this article, we present a new database of thermodynamic properties for polycyclic aromatic hydrocarbons (PAH). These large aromatic species are formed in very rich premixed flames and in diffusion flames as part of the gas-phase chemistry. PAH are commonly assumed to be the intermediates leading to soot formation. Therefore, accurate prediction of their thermodynamic properties is required for modeling soot formation. The present database consists of 46 species ranging from benzene (C_6H_6) to coronene (C_(24)H_(12)) and includes all the species usually present in chemical mechanisms for soot formation. Geometric molecular structures are optimized at the B3LYP/6-31++G(d,p) level of theory. Heat capacity, entropy, and energy content are calculated from these optimized structures. Corrections for hindered rotor are applied on the basis of torsional potentials obtained from second-order Møller-Plesset perturbation (MP2) and Dunning's consistent basis sets (cc-pVDZ). Enthalpies of formation are calculated using the mixed G3MP2//B3 method. Finally, a group correction is applied to account for systematic errors in the G3MP2//B3 computations. The thermodynamic properties for all species are available in NASA polynomial form at the following address: http://www.stanford.edu/group/pitsch/

Predicting aromatic exciplex fluorescence emission energies

PAH dimerization has been widely posited to play an important, even rate-determining role in soot nucleation, despite scanty experimental evidence of the existence of PAH dimers in flames. Laser-induced fluorescence (LIF) offers a promising in situ method of identifying PAH dimers, if dimer fluorescence can be distinguished from the fluorescence of the constituent monomers and other species present. Predicting transition energies for excited dimers (excimers) and excited complexes (exciplexes) represents a significant challenge for theory. Nonempirically tuned LC-BLYP functionals have been used to compute excited-state geometries and emission energies for a database of 81 inter- and intramolecular PAH excimers and exciplexes. Exciplex emission energies depend sensitively on the topology of the PAHs involved, but a linear relationship between the mean monomer bandgap and the computed exciplex emission means that dimer electronic properties can be predicted based on the properties of the constituent monomers. The range of fluorescence energies calculated for structures containing small to moderately-sized PAHs indicates that either noncovalent or aliphatically-linked complexes could generate the visible-range fluorescence energies observed in LIF experiments

Predicting the photoresponse of soot nuclei: Spectroscopic characteristics of aromatic aggregates containing five-membered rings

Establishing the mechanism for soot nucleation will require in situ experimental characterization of the identity and intermolecular interactions of the initial precursors, and electronic spectroscopy methods have the potential to do both. However, the optical response of polycyclic aromatic hydrocarbon (PAH) dimers and complexes differs significantly from that of the constituent monomers, and studies of soot precursor complexes have largely been limited to PAHs containing only six-membered aromatic rings. Hydrocarbons containing unsaturated five-membered rings are also present in high concentration in flames, and the photoresponse of complexes containing five-membered rings has not yet been examined. In this work, we elucidate the spectroscopic properties of small hydrocarbon complexes containing cyclopentadienyl groups or cyclopenta-fused groups, calculating ground- and excited-state binding energies, optimal excited-state geometries, repulsion energies, and fluorescence emission wavelengths. We show that excited-state distortion of cyclopentadienyl groups allows strong binding and low-energy fluorescence emission compared to similar-sized PAHs, and that a cyclopenta-fused group dramatically lowers the absorption and emission energies for acenaphthylene, dominating excited-state noncovalent interactions—findings that could shed light on the complex electronic properties of flames

Isolating effects of large and small scale turbulence on thermodiffusively unstable premixed hydrogen flames

Lean turbulent premixed hydrogen/air flames have substantially increased flame speeds, commonly attributed to differential diffusion effects. In this work, the effect of turbulence on lean hydrogen combustion is studied through Direct Numerical Simulation using detailed chemistry and detailed transport. Simulations are conducted at six Karlovitz numbers and three integral length scales. A general expression for the burning efficiency is proposed which depends on the conditional mean chemical source term and gradient of a progress variable. At a fixed Karlovitz number, the normalized turbulent flame speed and area both increase linearly with the integral length scale ratio. The effect on the mean source term profile is minimal, indicating that the increase in flame speed can solely be attributed to the increase in flame area. At a fixed integral length scale, both the flame speed and area first increase with Karlovitz number before decreasing. At higher Karlovitz numbers, the diffusivity is enhanced due to penetration of turbulence into the reaction zone, significantly dampening differential diffusion effects