A Study on the Turbulent Mixing and Chemical Reaction by the Stochastic Process Model and Random Fourier Modes Method

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The progress and results of the research are summarized in the following,Object (A) Simulations by the Stochastic ModelThe reactive mixing layer with second-order chemical reation in the grid-turbulence has been simulated by the probability density function (pdf) method. The particle velocity was modeled by a simplified Langevin model. Three kinds of mixing models, such as the Curl's model, modified Curl's model and binomial Langevin model have been used. It is found that the binomial Langevin model is most suitable to predict the pdf of the reactive scalar quantities. Next, the thermal diffusion field from the axisymmetric heated line source has been simulated by using a generalized Langevin model and the binomial sampling model. The simulation results of the tempareature field up to second-order moment are in good agreement with the experimental data. Further, the plume of matter from the wall point source in the turbulent water pipe flow has been also investigated.Object (B) Simulations the Random Fourier Modes MethodAt first, we investigated the non-reactive plume developed in the grid-turbulence by the random Fourier modes method and two-particle backward diffusion technique. In case of the point source plume, the mean and r.m.s. fluctuation values of scalar quantity show good agreements with the experimetal results. Next the plume around the two-dimensional cylinder in the grid-turbulence has been investigated. The point source plume impinging perpendiculary on the cylinder has been simulated. The simulation results showed that the velocity induced by the wake vortices gives the important role on the spread of the diffusion around the cylinder. From this time on, the non-reative and reactive plume around the cylinder will be investigated by introducing the vortex shedding model into the wake.