Developing theory of probability density function for stochastic modeling of turbulent gas-particle flows

Turbulent gas-particle flows are studied by a kinetic description using a prob- ability density function （PDF）. Unlike other investigators deriving the particle Reynolds stress equations using the PDF equations, the particle PDF transport equations are di- rectly solved either using a finite-difference method for two-dimensional （2D） problems or using a Monte-Carlo （MC） method for three-dimensional （3D） problems. The proposed differential stress model together with the PDF （DSM-PDF） is used to simulate turbulent swirling gas-particle flows. The simulation results are compared with the experimental results and the second-order moment （SOM） two-phase modeling results. All of these simulation results are in agreement with the experimental results, implying that the PDF approach validates the SOM two-phase turbulence modeling. The PDF model with the SOM-MC method is used to simulate evaporating gas-droplet flows, and the simulation results are in good agreement with the experimental results.

Auxiliary error and probability density function based neuro-fuzzy model and its application in batch processes

This paper focuses on resolving the identification problem of a neuro-fuzzy model(NFM) applied in batch processes. A hybrid learning algorithm is introduced to identify the proposed NFM with the idea of auxiliary error model and the identification principle based on the probability density function(PDF). The main contribution is that the NFM parameter updating approach is transformed into the shape control for the PDF of modeling error. More specifically, a virtual adaptive control system is constructed with the aid of the auxiliary error model and then the PDF shape control idea is used to tune NFM parameters so that the PDF of modeling error is controlled to follow a targeted PDF, which is in Gaussian or uniform distribution. Examples are used to validate the applicability of the proposed method and comparisons are made with the minimum mean square error based approaches.

ON THE PDF MODELS FOR ATMOSPHERIC DIFFUSION IN BOUNDARY LAYER

In this paper, taking its turbulent exchange coefficient as a function of the Lagrangian time scale and standard variance of the turbulence in atmosphere, the atmospheric dispersion PDF models are obtained on the basis of atmospheric diffusion K-theory. In the model the statistics of wind speed are directly used as its parameters instead of classic dispersion parameters. The bi- Gaussian PDF is derived in convective boundary layer (CBL), from the statistics of vertical velocity in both of the downdraft and updraft regions that are investigated theoretically in the other part of this paper. Giving the driven parameters of the CBL (including the convective velocity scale w* and the mixing depth h_i) and the time-averaged wind speed at release level, the PDF model is able to simulate the distribution of concentration released at any levels in the CBL. The PDF's simulations are fairly consistent with the measurements in CONDORS experiment or the results brought out by some numerical simulations.