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Abstract A cantilever with an open surface crack excited by the pedestal movement with the form of the Gaussian white noise was modeled in this paper. The open crack was simplified as an elastic hinge and the modal functions of the cracked cantilever were obtained. The dynamical equation governing the transverse motion was gained with the Kane's method after sufficient consideration of the geometrical nonlinearity and the axial inertia. Both quasi-conservative stochastic averaging method and the improved energy envelop stochastic averaging method which is effective on strong nonlinearity were applied to analyze the responses of the cantilever model theoretically. The stationary probability density function (PDF) of the amplitude, as well as the joint stationary PDF of the displacement and velocity, was investigated. For the purpose of exploring the reliability of the cantilever, the reliability function was established to avoid the potential fatigue or damage. Numerical simulations were carried out to vindicate the theoretical analysis. The advantage of the improved energy envelop stochastic averaging method was explicated by the digital results of both the stationary PDF of the amplitude and the joint PDF of displacement and velocity. Furthermore, the accuracy of the prediction on the reliability given by the theoretical analysis was also vindicated by the numerical simulation (Monte Carlo method) of the reliability. [ABSTRACT FROM AUTHOR]

Among the combustion products, nitrogen oxides are one of the main contributors to a negative impact on the environment, participating in harmful processes such as tropospheric ozone and acid rains production. The main source of emissions of nitrogen oxides is the human combustion of fossil fuels. Their formation models are investigated and implemented with the goal of obtaining a tool for studying the nitrogen-containing pollutant production. In this work, numerical simulation of solid fuel combustion was carried out on a three-dimensional model of a drop tube furnace by using the commercial software FIRE. It was used for simulating turbulent fluid flow and temperature field, concentrations of the reactants and products, as well as the fluid-particles interaction by numerically solving the integro-differential equations describing these processes. Chemical reactions mechanisms for the formation of nitrogen oxides were implemented by the user functions. To achieve reasonable calculation times for running the simulations, as well as efficient coupling with the turbulent mixing process, the nitrogen scheme is limited to sufficiently few homogeneous reactions and species. Turbulent fluctuations that affect the reaction rates of nitrogen oxides' concentration are modelled by probability density function approach. Results of the implemented model for nitrogen oxides' formation from coal and biomass are compared to the experimental data. Temperature, burnout and nitrogen oxides' concentration profiles are compared, showing satisfactory agreement. The new model allows the simulation of pollutant formation in the real-world applications. [ABSTRACT FROM AUTHOR]

Results related to the filtered non-premixed turbulent flame statistics are presented. Considering non-premixed turbulent combustion modeling in the framework of large eddy simulations (LES), a turbulent flamelet equation is derived based on the filtered governing equations. Using a direct numerical simulation (DNS) data set, the statistical properties of two important parameters, the scalar dissipation and chemical source term, are analyzed in details. Numerical results show that for the scalar dissipation term, the probability density function (PDF) of the magnitude of the mixture fraction gradient changes is strongly dependent on the filter scale, whereas the PDF of the turbulent diffusivity is almost invariant. Theoretically from the scalar structure function a scaling law can be expected for the conditional mean of the difference between the filtered and nonfiltered scalars with respect to the filter scale, which is important for estimating the chemical source in the subgrid scale models. [ABSTRACT FROM AUTHOR]