A Study on the Turbulent Mixing and Chemical Reaction by the Stochastic Differential Equation and Random Fourier Modes Method

本文的主要研究内容和结果如下：（A）<Simulations by the Stochastic Model>采用概率密度函数法（pdf）对充分发展的圆管湍流中点源轴对称羽流进行了数值模拟。颗粒速度由随机微分方程（圆柱坐标系下的广义朗之万模型）和两种分子混合模型（即，Dopazo的确定性模型和修正的Curl模型。结果表明，这两种模型都能较好地预测平均浓度和波动均方根浓度的径向分布。其次，采用pdf方法模拟了网格湍流中含有二级化学反应的反应混合层。结果表明，二项式朗之万模型作为分子混合模型，适用于反应标量的概率密度函数的预测。此外，新的广义Lange 关于我们 文中建立了轴对称湍流射流模型，并用Dopazo模型模拟了守恒标量场。目标（B）<Simulations by the Random Fourier Modes Method>首先，将随机Fourier模态方法、快速畸变理论和尾涡脱落模型相结合，发展了一种模拟二维圆柱湍流场的新方法。计算了速度场的二阶矩分布和速度谱，并与实验数据进行了比较。计算结果与实验数据吻合较好。其次，采用随机傅立叶模方法和两粒子后向扩散技术或pdf方法中的分子混合模型，对反应标量混合层进行了数值模拟。模拟结果与实验数据吻合较好。在此基础上，发展了各种海崖体湍流的数值模拟方法，并采用随机Fourier模方法研究了均匀各向同性湍流中物质线的统计特性。少

The progress and results of the research are summarized in the following,Object (A) <Simulations by the Stochastic Model>___-The axisimmetric plume from a point source in the fully developed turbulent pipe flow has been simulated by the probability density function method (pdf) method. The particle velocity was modeled by a stochastic differential equation (a generalized Langevin model expressed in the cylindrical coordinates), and the two kinds of molecular mixing model, i.e., the Dopazo's deterministic model and the modified Curl's model have been used. It is found that both models are useful to predict the radial profiles of the mean concentration and fluctuation r.m.s.concentration. Next, the reactive mixing layer with second-order chemical reaction in the grid-turbulence has been simulated by the pdf method. It is found that as the molecular mixing model the binomial Langevin model is suitable to predict the pdf of the reactive scalar quantities. Further, the new generalized Lange … More vin model for the axisymmetric turbulent jet has been developed, and the conserved scalar field has been simulated by the Dopazo's model. Consequently, the scalar moments up to the second-order could be predicted satisfactorily.Object (B) <Simulations by the Random Fourier Modes Method>___-At first, a new method to simulate the turbulent field around a two-dimensional circular cylinder has been developed by the combination of the random Fourier modes method, the rapid distortion theory and the wake vortex shedding model. Then, the distribution of the second-order moment and spectrum of the velocity field have been calculated and compared with the experimetal data. It is found that the simulation results show good agreements with the experimental data. Next, the reactive scalar mixing layer has been simulated by the combination of the randam Fourier modes method and two-particle backward diffusion technique or the molecular mixing model of the pdf method. The agreements between the simulation results and experimental data could be observed. Further, the simulation method of the turbulent flow around the various bluff bodied has been developed, and the statistics of the material line in the homogeneous isotropic turbulence has been investigated by the random Fourier modes method. Less