两相湍流色噪声扩维法PDF模型及数值模拟

由颗粒运动的朗之万方程出发,对流体脉动速度采用扩维方法,得到两个不同层次的PDF输运方程.通过对颗粒运动方程求解和高斯分布假设,解决PDF方程的封闭问题,获得颗粒二阶矩模型,然后将颗粒应力方程简化成代数方程,建立代数应力模型.将对流扩散方程的有限分析法运用到求解两相流模型中,对壁面两相射流进行数值模拟,对比分析数值结果与实验结果.     

钝体后湍流预混燃烧的PDF模拟

本文采用PDF方法对矩形燃烧室内钝体后的湍流预混火焰进行了数值模拟。脉动速度-频率-标量联合的PDF输运方程用Monte Carlo方法求解,质量、动量和能量的平均值由基于无结构网格的有限体积法求解,压力通过状态方程获得。PDF方程中所需的平均密度、平均速度和压力由有限体积法提供,并将用Monte Carlo方法求出的雷诺应力、化学反应源项和比热比传递给有限体积法。本文对丙烷和空气燃烧的不同简化化学反应机理进行了研究,并与实验结果进行比较,获得满意的结果。     

DSM-LPDF两相湍流模型及旋流两相流动的模拟

本文由流体－颗粒速度的拉氏联合概率密度函数（ＰＤＦ）输运方程出发,用Ｓｉｍｏｎｉｎ建议的Ｌａｎｇｅｖｉｎ模型封闭颗粒所遇到流体瞬时速度的条件期望项,并用Ｍｏｎｔｅ Ｃａｒｌｏ方法直接求解 ＰＤＦ输运方程,将其和求解流体雷诺应力方程模型的有限差分方法结合,建立了雷诺应力－拉氏ＰＤＦ（ＤＳＭ－ＬＰＤＦ,简称ＤＬ）两相湍流模型．用此模型模拟了旋流数为０．４７的突扩旋流气粒两相流动,并与文献中ＰＤＰＡ实验和用类似于单相流动湍流模型封闭方法的时平均统一二阶矩（ＵＳＭ）模型的预报进行了对比．     

基于拉氏概率密度的两相湍流二阶矩模型

用颗粒运动的拉氏分析和PDF方法,改进了颗粒相的二阶矩模型。由拉氏两相运动的随机微分方程出发,采用随机过程分析和信号分析法得到湍流两相流动的PDF输运方程,双流体模型方程和两相脉动速度相关的基本模式的封闭式,和用其它方法导出的方程与封闭式的结果一致,对封闭式作了重要的改进,在分析颗粒轨道上的流体湍流作用时间时,全面地引入拉氏分析的轨道穿越效应、惯性效应、连续效应和湍流的各向异性。     

基于小关联时间两相湍流色噪声的近似模型及数值模拟

从一般高斯型色噪声模型出发,通过泛函导数,应用小关联时间,近似计算多维色噪声,得到有效Fokker-Planck方程.将其应用到两相湍流中得到颗粒相的概率密度函数输运方程,从而得到颗粒相的二阶矩模型.将颗粒应力方程简化成代数方程,建立代数应力模型.将对流扩散方程的有限分析法运用到求解两相流模型中,对壁面两相射流进行数值模拟,并将求解结果与实验结果进行对比分析.     

湍流两相流动有燃烧颗粒相概率密度函数输运方程理论

由有燃烧的湍流气粒两相流动的瞬态方程和统计力学概率密度函数概念出发,推导了有燃烧颗粒相的质量－动量－能量联合概率密度函数（ＰＤＦ）输运方程,并对方程中条件期望项用梯度模拟概念进行了模拟封闭。封闭后的ＰＤＦ方程可作为建立颗粒拟流体模型方程和封闭二阶矩模型的基础,也可以通过Ｍｏｎｔｅ－Ｃａｒｌｏ 法求解用以直接计算颗粒雷诺应力和湍流动能,以便和二阶 矩模型的结果相对照,改善二阶矩模型。     

下降管中稠密两相湍流的数值模拟

本文将统一二阶矩两相湍流模型和颗粒动力学理论结合,推导并封闭了稠密两相流考虑颗粒间碰撞的统一二阶矩两相湍流模型。该模型用颗粒动力学理论模拟颗粒之间的碰撞,用各向异性的统一二阶矩模型考虑气相和颗粒相的湍流脉动,并用输运方程描述气固两相湍流之间的相互作用。最后用该模型对下降管中的气粒两相流动进行了模拟,模拟所得的沿径向颗粒浓度分布和速度分布与实验吻合较好,预报结果也反应出了颗粒雷诺应力的各向异性。     

突扩湍流气粒流动两相脉动速度关联和颗粒速度概率密度分布的实验研究

本文用PDPA对突扩气粒两相流动中的两相脉动速度关联进行了测量,得到了30和50微米颗粒的两相脉动速度关联,其空间分布和气体及颗粒的雷诺应力分布一致．同时发现,气粒两相速度概率密度分布并不都是高斯分布。     

各向异性颗粒PDF输运方程及其颗粒湍流扩散

根据Minier的模型,获得颗粒所见流体脉动速度的朗之万模型,并推导颗粒所见流体湍流脉动速度自关联函数,该函数具有各向异性的特征,进一步由流体脉动速度朗之万模型和颗粒运动方程获得相应的颗粒PDF输运方程.为描述在网格生成湍流中的颗粒扩散运动,将颗粒PDF输运方程作相应的简化,获得一个具有颗粒湍流各向异性的解析解,将方程的解与Wellsand Stock的颗粒湍流扩散实验结果进行比较,获得了很好的结果.揭示了具有各向异性特征的颗粒PDF输运方程的优越性.     

颗粒增强湍流的新模型和气粒流动的湍流变动

用雷诺应力方程模型和极细的网格系对单个颗粒受湍流气体绕流进行了数值模拟,研究了改变颗粒直径和气体相对速度时颗粒增强气体湍流的规律.据此构造了颗粒尾涡增强气体湍流的新模型.将此子模型加入到两相流动模型中,对竖直和水平通道内气粒两相流动进行了数值模拟,和实验结果的对照表明,考虑颗粒尾涡增强气体湍流效应得到的气体湍流脉动速度的模拟结果比不考虑此效应的模拟结果好得多.     

Stochastic modeling of evaporating sprays within a consistent hybrid joint PDF framework

In the present study, a framework for modeling two-phase evaporating flow is presented, which employs an Eulerian–Lagrangian–Lagrangian approach. For the continuous phase, a joint velocity-composition probability density function (PDF) method is used. Opposed to other approaches, such PDF methods require no modeling for turbulent convection and chemical source terms. For the dispersed phase, the PDF of velocity, diameter, temperature, seen gas velocity and seen gas composition is calculated. This provides a unified formulation, which allows to consistently address the different modeling issues associated with such a system. Because of the high dimensionality, particle methods are employed to solve the PDF transport equations. To further enhance computational efficiency, a local particle time-stepping algorithm is implemented and a particle time-averaging technique is employed to reduce statistical and bias errors. In comparison to previous studies, a significantly smaller number of droplet particles per grid cell can be employed for the computations, which rely on two-way coupling between the droplet and gas phases. The framework was validated using established experimental data and a good overall agreement can be observed.     

Improvement of the pressure algorithm of the stand-alone PDF method to treat unsteady three-dimensional turbulent reacting flows

This paper deals with the particle-mesh probability density function (PDF) method. It shows how an existing but less precise pressure algorithm for the stand-alone method can be improved. The present algorithm is able to handle the general case of an unsteady three-dimensional turbulent reacting flow. The transport equation of the joint PDF of velocity and composition is solved with a particle method. Open boundary conditions are realized and for statistical reasons a simple but effective particle splitting procedure is applied.

Based on a simple configuration, the properties of the presented improved pressure algorithm are analysed. It is shown which numerical condition must be taken care of so that the algorithm is able to correct the particle positions such that the normalization condition is fulfilled as accurately as specified.

To verify the algorithm the combustion of a methane–air mixture enclosed in an open simulation volume is calculated. It is shown that the simple particle splitting algorithm works very effectively in the studied case. The behaviour of the improved pressure algorithm is examined by different calculations. To analyse the convergence of the algorithm, the particle number per cell and the grid spacing are varied. To demonstrate the accuracy, a statistically stationary inflow/outflow configuration is used and the numerical solution is compared to an analytical one. For a less symmetric test case, the previous unsteady combustion problem is simulated, including an additional mean velocity in one direction.

The presented improved pressure algorithm provides the opportunity to calculate unsteady three-dimensional turbulent reacting flows with a stand-alone method, and offers an alternative to the complex hybrid finite-volume/particle PDF method.     

A PDF projection method: A pressure algorithm for stand-alone transported PDFs

In this paper, a new formulation of the projection approach is introduced for stand-alone probability density function (PDF) methods. The method is suitable for applications in low-Mach number transient turbulent reacting flows. The method is based on a fractional step method in which first the advection–diffusion–reaction equations are modelled and solved within a particle-based PDF method to predict an intermediate velocity field. Then the mean velocity field is projected onto a space where the continuity for the mean velocity is satisfied. In this approach, a Poisson equation is solved on the Eulerian grid to obtain the mean pressure field. Then the mean pressure is interpolated at the location of each stochastic Lagrangian particle. The formulation of the Poisson equation avoids the time derivatives of the density (due to convection) as well as second-order spatial derivatives. This in turn eliminates the major sources of instability in the presence of stochastic noise that are inherent in particle-based PDF methods. The convergence of the algorithm (in the non-turbulent case) is investigated first by the method of manufactured solutions. Then the algorithm is applied to a one-dimensional turbulent premixed flame in order to assess the accuracy and convergence of the method in the case of turbulent combustion. As a part of this work, we also apply the algorithm to a more realistic flow, namely a transient turbulent reacting jet, in order to assess the performance of the method.     

Comparisons of Lagrangian and Eulerian PDF methods in simulations of non-premixed turbulent jet flames with moderate-to-strong turbulence-chemistry interactions

Transported probability density function (PDF) methods have been applied widely and effectively for modelling turbulent reacting flows. In most applications of PDF methods to date, Lagrangian particle Monte Carlo algorithms have been used to solve a modelled PDF transport equation. However, Lagrangian particle PDF methods are computationally intensive and are not readily integrated into conventional Eulerian computational fluid dynamics (CFD) codes. Eulerian field PDF methods have been proposed as an alternative. Here a systematic comparison is performed among three methods for solving the same underlying modelled composition PDF transport equation: a consistent hybrid Lagrangian particle/Eulerian mesh (LPEM) method, a stochastic Eulerian field (SEF) method and a deterministic Eulerian field method with a direct-quadrature-method-of-moments closure (a multi-environment PDF-MEPDF method). The comparisons have been made in simulations of a series of three non-premixed, piloted methane–air turbulent jet flames that exhibit progressively increasing levels of local extinction and turbulence-chemistry interactions: Sandia/TUD flames D, E and F. The three PDF methods have been implemented using the same underlying CFD solver, and results obtained using the three methods have been compared using (to the extent possible) equivalent physical models and numerical parameters. Reasonably converged mean and rms scalar profiles are obtained using 40 particles per cell for the LPEM method or 40 Eulerian fields for the SEF method. Results from these stochastic methods are compared with results obtained using two- and three-environment MEPDF methods. The relative advantages and disadvantages of each method in terms of accuracy and computational requirements are explored and identified. In general, the results obtained from the two stochastic methods (LPEM and SEF) are very similar, and are in closer agreement with experimental measurements than those obtained using the MEPDF method, while MEPDF is the most computationally efficient of the three methods. These and other findings are discussed in detail.     

Solving the Boltzmann equation in a 2-D-configuration and2-D-velocity space for capacitively coupled RF discharges

A new kinetic scheme, the generalized Monte Carlo flux (GMCF) method, provides the electron particle distribution function in phase space, f(ν, μ, r, z, t) (ν: speed, μ: velocity angle, r: radial position, z: axial position, and t: time), for solving the Boltzmann equation in modeling capacitively coupled RP discharges. For a simulation with spatial- and temporal-varying fields in RF discharges, the GMCF method handles the collision terms of the Boltzmann equation by using one transition matrix to compute the collision transition between velocity space cells. An anti-diffusion flux transport scheme is developed to overcome the numerical diffusion in the velocity and configuration spaces. The major advantages of the GMCF method are the increase in resolution in the tail of distribution functions and the decrease of computation time. The GMCF calculation results in terms of microscopic electron distribution function and macroscopic quantities of density, electric field and ionization rate, are presented for RF discharges and compared with other kinetic and fluid simulation and experimental results. The effects of the induced radial electric field in the sheath close to the radial wall in a cylindrically symmetric parallel-plate geometry are discussed