Tiago L. Farias

Fractal and projected structure properties of soot aggregates

The structure of soot aggregates was investigated, emphasizing the fractal properties as well as the relationships between the properties of actual and projected soot images. This information was developed by considering numerically simulated soot aggregates based on cluster-cluster aggregation as well as measured soot aggregates based on thermophoretic sampling and analysis by transmission electron microscopy (TEM) of soot for a variety of fuels (acetylene, propylene, ethylene, and propane) and both laminar and turbulent diffusion flame conditions. It was found that soot aggregate fractal properties are relatively independent of fuel type and flame condition, yielding a fractal dimension of 1.82 and a fractal prefactor of 8.5, with experimental uncertainties (95% confidence) of 0.08 and 0.5, respectively. Relationships between the actual and projected structure properties of soot, e.g., between the number of primary particles and the projected area and between the radius of gyration of an aggregate and its projected image, also are relatively independent of fuel type and flame condition.

A RECIPE FOR IMAGE CHARACTERIZATION OF FRACTAL-LIKE AGGREGATES

In the present paper a simple and straightforward recipe for characterizing the structural and fractal properties of aggregates from their projected images is presented. Starting from geometrical properties that are directly measured from the projected image—such as primary particle mean diameter, maximum projected length, projected area, and overlap coefficient—important threedimensional properties including number of primary particles in an aggregate, radius of gyration, aggregate surface, or fractal dimensions, Dfandkg, can be inferred. Expressions proposed in the recipe to relate three dimensional with projected properties were obtained from an extensive investigation of the structure of numerically simulated cluster–cluster fractal-like aggregates. This involved the simulation of statistically significant populations of aggregates having appropriate fractal properties and prescribed numbers of primary particles per aggregate in order to characterize three-dimensional morphological properties of aggregates. Specific ranges of aggregate properties considered were as follows: number of primary particles per aggregate up to 512, fractal dimension, Df≈1.78, overlap coefficient in the range 0–0.33 and fractal pre factor between 1.5 and 3.1.

Range of validity of the Rayleigh-Debye-Gans theory for optics of fractal aggregates.

The range of validity of the Rayleigh-Debye-Gans approximation for the optical cross sections of fractal aggregates (RDG-FA) that are formed by uniform small particles was evaluated in comparison with the integral equation formulation for scattering (IEFS), which accounts for the effects of multiple scattering and self-interaction. Numerical simulations were performed to create aggregates that exhibit mass fractallike characteristics with a wide range of particle and aggregate sizes and morphologies, including x(p) = 0.01-1.0, ‖m - 1‖ = 0.1-2.0, N = 16-256, and D(f) = 1.0-3.0. The percent differences between both scattering theories were presented as error contour charts in the ‖m - 1‖x(p) domains for various size aggregates, emphasizing fractal properties representative of diffusion-limited cluster-cluster aggregation. These charts conveniently identified the regions in which the differences were less than 10%, between 10% and 30%, and more than 30% for easy to use general guidelines for suitability of the RDG-FA theory in any scattering applications of interest, such as laser-based particulate diagnostics. Various types of aggregate geometry ranging from straight chains (D(f) ≈ 1.0) to compact clusters (D(f) ≈ 3.0) were also considered for generalization of the findings. For the present computational conditions, the RDG-FA theory yielded accurate predictions to within 10% for ‖m - 1‖ to approximately 1 or more as long as the primary particles in aggregates were within the Rayleigh scattering limit (x(p) ≤ 0.3). Additionally, the effect of fractal dimension on the performance of the RDG-FA was generally found to be insignificant. The results suggested that the RDG-FA theory is a reasonable approximation for optics of a wide range of fractal aggregates, considerably extending its domain of applicability.

Computational Evaluation of Approximate Rayleigh-Debye-Gans/ Fractal-Aggregate Theory for the Absorption and Scattering Properties of Soot

A computational evaluation of an approximate theory for the optical properties of soot is described, emphasizing the small-angle (Guinier) regime. The approximate theory (denote RDG-FA theory) is based on the Rayleigh-Debye-Gans scattering approximation while treating soot as mass-fractal aggregates of spherical primary particles that have constant diameters and refractive indices. The approximate theory was evaluated by more exact predictions from the solution of the volume integral equation formulation of the governing equations, using the method of moments, and based on the ICP algorithms of Iskander et al. (1989). Numerical simulations were used to constructs statistically significant populations of soot aggregates having appropriate fractal properties and prescribed numbers of primary particles per aggregate. Optical properties considered included absorption, differential scattering, and total scattering cross sections for conditions typical of soot within flame environments at wavelengths in the visible and the infrared. Specific ranges of aggregate properties were as follows: primary particle optical size parameters up to 0.4, numbers of primary particles per aggregate up to 512, mean fractal dimensions of 1.75, mean fractral prefactors of 8.0, and refractive indices typical of soot. Over the range of the evaluation, ICP and RDG-FA predictions generally agreed within numerical uncertainties (ca. 10 percent) within the Guinier regime, complementing similar performance of RDG-FA theory in the power-law regime based on recent experiments. Thus, the use of approximate RDG-FA theory to estimate the optical properties of soot appears to be acceptable-particularly in view of the significant uncertainties about soot optical properties due to current uncertainties about soot refractive indices

Numerical characterization of the morphology of aggregated particles

Abstract The structures of both cluster–cluster and particle–cluster fractal-like aggregates were investigated in the present study. Statistically significant populations of numerically simulated aggregates having appropriate fractal properties and prescribed number of primary particles per aggregate were generated in order to characterize three-dimensional morphological properties of aggregates, such as fractal dimension, fractal pre-factor, coordination number distribution function, and distribution of angles between triplets. Effects of aggregation mechanisms (i.e., cluster–cluster or particle–cluster) and aggregate size were taken into consideration. In addition, the morphological properties of aggregates undergoing partial sintering and restructuring were also investigated. To fulfill these objectives, aggregates were initially built without considering sintering or restructuring effects. Partial sintering of primary particles was then considered by introducing a penetration coefficient that allows touching particles to approach each other. Restructuring of aggregates was modeled during the process of building the cluster–cluster aggregates. For each pair of clusters that were attached together due to the normal aggregation procedure, a further mechanism was included that allowed the cluster to collapse until a more compact and stable position was achieved. The population studied was composed of ca. 450 simulated aggregates having a number of primary particles per aggregate between 8 and 1024. Calculations were performed for aggregates having a penetration coefficient in the range of 0–0.25 with and without restructuring. The following properties were investigated: fractal dimension, fractal pre-factor, coordination number distribution function, angle between triplets, and aggregate radius of gyration.

MODELLING OF HEAT TRANSFER IN RADIATING AND COMBUSTING SYSTEMS

The solution of reactive flow problems with radiative heat transfer requires a radiation model which is simultaneously accurate, fast and compatible with the algorithm employed to solve the transport equations. In the present paper, a review of the most commonly used methods to predict radiative heat transfer in combustion chambers is presented. Among them, three methods that satisfy the above requirements are described in more detail; namely the discrete transfer, the discrete ordinates and the finite volume method. Some examples of results obtained for simple test cases are presented where predictions obtained with some of the most well known models are compared. An important issue within the radiation modelling domain is the evaluation of the radiative properties of gases and particulate matter that are commonly found in the combustion products. Therefore, in the second part of the paper, the problems related to the evaluation of the radiative properties of the combustion products, i.e. participating gaseous species and particles, are focused and the methods used to solve these problems are described.

EFFECTS OF POLYDISPERSITY OF AGGREGATES AND PRIMARY PARTICLES ON RADIATIVE PROPERTIES OF SIMULATED SOOT

Abstract The effects of primary particle (particle) and cluster (aggregate) size distributions on absorption and scattering properties of simulated soot were studied both computationally and theoretically. Computational methods involved the solution of the volume integral equation formulation of Maxwells equations using the method of moments, based on the ICP algorithm. The theoretical methods employed Rayleigh-Debye-Gans approximation for mass fractal-like aggregates (RDG-FA) formed by small particles. An extension of the RDG-FA formulation was proposed to account for polydisperse particle sizes, based on a volume correction approach. Differential and total scattering as well as absorption cross sections were considered for morphologies representative of soot found in flame environments. Aggregates were constructed using a sequential algorithm which mimics mass fractal-like structures. Log-normal and normal (Gaussian) probability density functions were employed to consider polydisperse populations of aggregates and particles, respectively. Over the range of evaluation, the effects of aggregate and particle polydispersity were negligible for the angular scattering pattern in the power-law regime. Furthermore, absorption cross section was similarly affected by polydispersity of aggregates and particles. Finally, the RDG-FA predictions generally agreed with the ICP results within 10%, confirming its applicability to predict mean optical properties of polydisperse populations of soot aggregates and particles.

Quantification of technical impacts and environmental benefits of electric vehicles integration on electricity grids

In this paper a typical electricity distribution network for a residential area in Portugal is used in order to assess the impact of integrating different levels of pure electric vehicles and plug-in hybrid vehicles in the grid and in pollutants emissions. First, the amount of vehicles that can be safely accommodated in the grid will be determined. Second, changes in pollutants emissions will be evaluated, by applying a vehicle full life cycle analysis.

Measuring and Modeling Emission Effects for Toll Facilities

At conventional pay tolls, vehicles joining a queue must come to a stop and undergo several stop-and-go cycles until payment is completed. As a result, emissions increase because of excessive delays, queuing, and speed change cycles for approaching traffic. The main objective of this research is to quantify traffic and emission impacts of toll facilities in urban corridors. As a result of experimental measurements of traffic and emissions, the impact of traffic and emission performance of conventional and electronic toll facilities is presented. The approach attempts to explain the interaction between toll system operational variables (traffic demand, service time, and service type) and system performance variables (stops, queue length, and emissions). The experimental data for validating the numerical traffic model were gathered on pay tolls located in three main corridors that access the city of Lisbon, Portugal. The emissions model is based on real-world onboard measurements of vehicle emissions. With the appropriate speed profiles of vehicles in pay tolls, onboard emission measurements were carried out to quantify the relationships between vehicle dynamics and emissions. The main conclusion of this work is that there are two different types of stop-and-go driving cycles for vehicles joining the queue at a conventional toll booth: short and long. The length of each cycle depends on the expected queue length at the toll booth and the frequency of each cycle directly affects the level of vehicle emissions. The greatest percentage of emissions for a vehicle that stops at a pay toll is due to its final acceleration back to cruise speed after leaving the pay toll.

Radiative heat transfer in soot-containing combustion systems with aggregation

Abstract The effects of soot shape on radiative transfer predictions in soot-containing flames were quantitatively analyzed by using a realistic simulation of the aggregation process. Various spectral properties (phase function, albedo, extinction coefficient, and emissivity) of fractal soot aggregates were computed using the integral equation formulation for scattering (IEFS) for a broad wavelength spectrum from ultraviolet (0.2 μm) to infrared (6.2 μm). Total emissions from uniform clouds of aggregates of small spherical pa:rticles were then estimated for typical soot volume fractions and flame temperatures. All spectral and total radiative transfer properties computed using IEFS were normalized by the predictions based on the primary (unaggregated) particles. The spectral variation of the extinction coefficient of aggregates relative to that of primary particles has a somewhat unexpected and complex behavior in the ultraviolet and infrared wavelength regions due to the opposite effects of morphology and soot refractive indices. The effects of soot aggregation on spectral and total emissivities are found to be less than 25 and 13%, respectively, for typical particle volume fractions and flame temperatures. The results suggest that the shape effects on emission predictions in soot-laden flames can be neglected, vastly simplifying the engineering treatment of radiation modeling of combustion devices.