Large eddy simulation of a turbulent non-premixed propane-air reacting flame in a cylindrical combustor

Large Eddy Simulation (LES) is applied to investigate the turbulent non-premixed combustion flow, including species concentrations and temperature, in a cylindrical combustor. Gaseous propane (C3H8) is injected through a circular nozzle which is attached at the centre of the combustor inlet. Preheated air with a temperature of 773 K is supplied through the annulus surrounding of this fuel nozzle. In LES a spatial filtering is applied to the governing equations to separate the flow field into large-scale and small-scale eddies. The large-scale eddies which carry most of the turbulent energy are resolved explicitly, while the unresolved small-scale eddies are modelled using the Smagorinsky model with Cs = 0.1 as well as dynamically calibrated Cs. The filtered values of the species mass fraction, temperature and density, which are the functions of the mixture fraction (conserved scalar), are determined by integration over a beta probability density function (β-PDF). The computational results are compared with those of the experimental investigation conducted by Nishida and Mukohara. According to this experiment, the overall equivalence ratio of 0.6, which is calculated from the ratio of the air flow rate supplied to the combustion chamber to that of the stoichiometric reaction, is kept constant so that the turbulent combustion at the fuel nozzle exit starts under the fuel-rich conditions

Singularities of the Effective Fugacity on the Ising Model on the Cayley Tree

. Evidence suggesting a connection between Lee--Yang singularities of the magnetization of the Ising model and the singularities of the effective fugacity is presented. 1 Introduction The study of the Griffiths' singularities in random ferromagnetic Ising models [2] (see [3] and [4] for general discussions) remains one of the most living topics of research in Statistical Mechanics of spin systems. Besides its physical relevance, it involves various mathematical difficulties that make a detailed analysis particularly challenging. One of the main difficulties relies in the almost absence of models where a concrete study of the analytic properties of the magnetization and other thermodynamic quantities, as functions of the (complex) fugacity, could be developed. In [6] a detailed rigorous analysis of the presence of Griffiths' singularities has been performed in a class of layered diluted ferromagnetic Ising models on the Cayley tree. This involved the study of the analytic structure of t..