Evaluation of models for the low temperature combustion of alkanes through interpretation of pressure-temperature ignition diagrams

The purpose of this paper is to show the application of global uncertainty analysis to comprehensive and reduced kinetic models as a tool to identify important thermochemical and reaction rate parameters as determinants of the conditions leading to autoignition. Propane oxidation is taken as the test case. The simulation of experimental investigations of the cool flames and two-stage ignitions, via the pressure-temperature ignition diagram, show that existing kinetic models for the low temperature combustion of propane at sub-atmospheric pressures reflect a greater reactivity than seems to be appropriate. That is, the models lead to a prediction of two-stage ignition at pressures somewhat lower and with ignition delays shorter than is found experimentally. The inconsistency between experiment and numerical simulation seems not to be an inherent problem of the qualitative structure of the models, but may derive from uncertainties in the parameters within the mechanism. By use of "brute force", Morris-one-at-a-time and Monte-Carlo simulations, we show that uncertainties in only a small number of parameters, and falling well within the errors that may reasonably be assigned, can shift the response appropriately. Moreover, it appears that in the low temperature combustion regime, thermochemistry is at least as, if not more, important than the reaction rates, yet usually receives less attention within sensitivity studies. In the present case, the main factors controlling the temperature reached in the first stage of two-stage ignition and the time to ignition appear to be connected with the thermochemistry of three specific hydroperoxyalkyl radicals and their derivatives. Other factors, such as heat and mass transport are also addressed, and their effects are mitigated to some extent by evaluation of initial and revised models against experimental data for ignition delay obtained under microgravity. The results highlight more general issues that pertain to the numerical simulation of the combustion of higher hydrocarbons and contribute to the development of the protocol necessary for testing kinetic models before they are ready for use in a predictive capacity.     

Numerical solutions of the orbital equations for diatomic molecules

A basis of Hermite splines is used in conjunction with the collocation method to solve the orbital equations for diatomic molecules. Accurate solutions of the Hartree-Fock equations are obtained using iterative methods over most regions of space, while solving the equations by Gaussian elimination near the nuclear centres. In order to improve the speed and accuracy of our iterative scheme, a new self-adjoint form of the Hartree-Fock equation is derived. Using this new equation, our iterative subroutines solve the Hartree-Fock equations to one part in 10⁶. The Gaussian elimination routines are accurate to better than one part in 10⁸.     

Conditional moment closure modelling of turbulent jet diffusion flames of helium-diluted hydrogen

First-order conditional moment closure (CMC) modelling of NO in non-premixed flames has met with limited success due to the need to consider turbulence influences on the conditional production rate of chemical species. This paper presents results obtained using a second-order approach where such effects are incorporated through solution of a transport equation for the conditional variance. In contrast to earlier work, second-order chemistry is implemented using a more robust numerical technique, with predictions obtained using a Reynolds stress turbulence model. First-order CMC and k–? turbulence model predictions are presented for comparison purposes. For the hydrogen flames examined, results demonstrate small differences between first- and second-order calculations of major species and temperature, although second-order corrections reduce NO and OH levels. Additionally, variations occur between results for these species derived using the two turbulence models due to differences in conditional variance predictions. This and the numerical solution method employed are responsible for deviations with earlier results. It is concluded that while the higher-order CMC model does not significantly improve NO predictions, agreement with OH data is superior. Physical space predictions are sufficiently accurate for assessing flame characteristics, with the Reynolds stress model providing superior results.     

Analysis of kinetic mechanism performance in conditional moment closure modelling of turbulent,non-premixed methane flames

This paper presents results obtained from the application of a first-order conditional moment closure approach to the modelling of two methane flames of differing geometries. Predictions are based upon a second-moment turbulence and scalar-flux closure, and supplemented with full and reduced chemical kinetic mechanisms, ranging from a simple 12-step to a complex 1207-step mechanism. Alongside analysis of the full kinetic schemes' performance, is an appraisal of the behaviour of their derivatives obtained using mechanism-reduction techniques. The study was undertaken to analyse the practicality of incorporating kinetic models of varying complexity into calculations of turbulent non-premixed flames, and to make comparison of their performance. Despite extensive studies of the predictive ability of such schemes under laminar flame conditions, systematic evaluations have not been performed for turbulent reacting flows. This paper reflects upon the impact that selection of chemical kinetics has upon subsequent calculations and concludes that, although application of reduced schemes is more than adequate to reproduce experimental data, selection of the parent mechanism is of paramount importance to the prediction of minor species. Although widely used schemes are well documented and validated, their performances vary considerably. Thus, careful consideration must be made to their application and origins during the evaluation of combustion models.     

ON QUOTIENTS OF BRAID GROUPS

ABSTRACT.

Let G be the group ?[t, t ^?1] x ?. By studying the action of the braid group B_n on the set Gⁿ , we obtain representations of B_n into a wreath product of the symmetric group and the general linear group over ?[t, t ^?1]. This in particular recovers the Burau representation of the braid group. Furthermore, some quotients of the braid group are obtained by using the representations found.     

Mass spectrometric analysis of the S-layer proteins from Clostridium difficile demonstrates the absence of glycosylation

Like many other bacterial cell surfaces, the cell wall of Clostridium difficile is also encapsulated by a proteinaceous paracrystalline layer, the surface (S)-layer. In many bacterial species, the S-layer proteins (SLPs) have been shown to be glycosylated, whereas in other species glycosylation is absent. Unusually, the S-layer of C. difficile is composed of two distinct proteins, the high-molecular weight (HMW) and low-molecular-weight (LMW) SLPs. Previous investigations have reported that one or both of these SLPs are glycosylated, though no definitive study has been conducted. We have used a variety of mass spectrometric approaches to analyse SLPs from a number of strains of C. difficile for the presence of associated glycans. Analysis of intact SLPs by matrix assisted laser desorption/ionisation time of flight (MALDI-ToF) mass spectrometry demonstrated that the observed molecular masses matched the predicted masses of the LMW and HMW SLPs. Furthermore, analysis of Cyanogen bromide (CNBr) and tryptic peptides displayed no evidence of post-translational modification. In the first in-depth study of its kind, we unequivocally demonstrate that the S-layer proteins from the C. difficile strains investigated are not glycosylated.     

A formal total synthesis of the marine diterpenoid diisocyanoadociane

[Structure: see text] A formal total synthesis of diisocyanoadociane, a marine diterpenoid with potent antimalarial properties, has been completed. The synthesis begins with a phenanthrenoid precursor that is transformed into a pyrene-derived intermediate by means of an intramolecular Michael reaction. Nitrogen functionality is introduced via a double Curtius reaction.     

A fourth–order orthogonal spline collocation method for two-dimensional Helmholtz problems with interfaces

Orthogonal spline collocation is implemented for the numerical solution of two-dimensional Helmholtz problems with discontinuous coefficients in the unit square. A matrix decomposition algorithm is used to solve the collocation matrix system at a cost of O(N² log N) on an N × N partition of the unit square. The results of numerical experiments demonstrate the efficacy of this approach, exhibiting optimal global estimates in various norms and superconvergence phenomena for a broad spectrum of wave numbers.