稠密气固两相流各向异性颗粒相矩方法

基于气体分子动力学和颗粒动理学方法,考虑颗粒速度脉动各向异性,建立颗粒相二阶矩模型.应用初等输运理论,对三阶关联项进行模化和封闭.考虑颗粒与壁面之间的能量传递和交换,建立颗粒相边界条件模型.采用Koch等计算方法模拟气固脉动速度关联矩.考虑气体-颗粒间相互作用,建立稠密气体-颗粒流动模型.数值模拟提升管内气固两相流动特性,模拟结果表明提升管内颗粒相湍流脉动具有明显的各向异性.预测颗粒速度、浓度和颗粒脉动速度二阶矩与Tartan等实测结果相吻合.模拟结果表明轴向颗粒速度脉动强度约为平均颗粒相脉动强度的1.5倍,轴向颗粒脉动能大约是径向颗粒脉动能3.0倍.     

湍流两相流的脉动速度联合PDF输运方程

概率密度函数（PDF）的方法是构造两相湍流模型的一种重要的方法.构建气体-颗粒速度联合PDF输运方程的关键是颗粒所见气体微团速度的Langevin方程.首先由N-S方程出发,精确推导出颗粒所见气体微团脉动速度的Langevin方程,进而通过理论分析表明,对比通常采用的颗粒所见气体微团瞬时速度的Langevin方程而言,采用前者能有效地减少关联量的统计偏差.最后,给出了颗粒-气体脉动速度的联合PDF输运方程.     

低浓度固液两相流的颗粒相动理学模型

用广义Fokker-Planck扩散模型描述液相湍动对颗粒的挟带作用，用修正的BGK模型描述粒间碰撞效应，建立了封闭的颗粒相PDF输运方程．运用Chapman-Enskog迭代法求得方程的二阶近似解，获得颗粒相脉动速度二阶矩和三阶矩闭合关系．模型与颗粒流模型相容，与液相湍流闭合模型是否相容依赖于扩散模型的具体形式，并据此比较了不同的涡一颗粒作用模型．模型与二维明渠流轻质沙和天然沙试验资料符合很好．表明细小粒径颗粒能够充分跟随水流运动；大粒径颗粒的相间平均速度差和壁面滑移速度明显，近壁区内的颗粒沿流向和垂向脉动强度都可能大于水流，并存在一定程度的颗粒碰撞效应．     

二阶矩两相湍流模型中的改进算法

建立了融合SIMPLEC算法在内的考虑了浓度修正影响的颗粒压力修正方程。提出了二阶矩湍流模型下考虑浓度修正值影响的两相湍流流动的算法,并将它和没有考虑浓度修正值影响的二阶矩湍流模型进行了对照。结果表明在二阶矩模型中是否考虑浓度修正影响会不同程度地影响流场的速度以及浓度等参数分布,考虑浓度修正影响的二阶矩湍流模型更能有效地预测稠密两相湍流流动。     

统一二阶矩模型用于模拟旋流湍流两相流动

用统一二阶矩模型（ＵＳＭ）模拟了旋流数为０４７和１５的气粒两相流动，并和实验结果以及ｋ ε ｋｐ模型的模拟结果进行了对比．研究结果表明，提高旋流数减小了轴向速度反流区，增大了切向速度似固核区．ＵＳＭ和ｋ ε ｋｐ模型预报旋流数为０４７时的两相速度场差别不大，并都和实验结果接近，但前者预报的旋流数为１５的两相速度场比后者有改进，在两种情况下，前者都能揭示出后者无法预报的两相湍流各向异性规律．     

用二阶矩模型研究Richtmyer-Meshkov不稳定性诱导湍流混合

发展了考虑密度脉动和各向异性湍流的二阶矩模型,强调了涉及湍流能量产生项的关联。采用该模型对Poggi等的激波管实验进行了模拟。通过与实验结果的比较分析,验证了采用的模型封闭、模型常数、数值算法和程序实现是合适的。在此基础上,进一步探讨了冲击马赫数和Atwood数对混合的影响。     

基于颗粒湍流和颗粒碰撞相互作用规律的湍流模型的研究

颗粒湍流和颗粒碰撞的相互作用规律是两相流动中的核心问题。用颗粒湍流模型和颗粒碰撞的动力论模型叠加的方法在研究两相湍流流动方面取得了一定的成效,但是还有待改进。本文基于颗粒湍流形成大尺度脉动和颗粒间碰撞引起小尺度脉动的概念,从双流体模型出发,建立了两相流动的双尺度kp-pε两相湍流模型。利用该模型对下行床和突扩室内的气固...     

再入飞行器湍流尾迹流场研究

再入飞行器湍流尾迹流场状况，直接关系到飞行器的雷达散射特性。对再入飞行器湍流尾迹等离子体场理论模型，试图通过湍流模式理论来表达，即使用κ－ε－g模型方程来封闭平均化的全Navier-Stokes方程，从而准确获得流动平均场和脉动场信息。使用的N－S平均方程由质量加权平均过程产生，湍流模型方也经过可压缩性修正。真实气体效应重点考察空气处于局部热化学平衡状态。流动控制方程运用一个二阶TVD格式的有限体积法求解，以一典型小钝锥体零攻角再入飞行为例，计算了在两种高程（H－40km和H＝30km)条件下的高超声速湍流尾迹流场。获得的尾迹流场参数与流动物理状况符合，并且湍流脉动参数与已有相应的实验结果定性一致，初步证实该方法合理。     

燃烧室两相流场亚网格燃烧模型的研究

在三维任意曲线坐标系下采用不同的亚网格燃烧模型对环形燃烧室火焰筒气液两相湍流瞬态反应流进行大涡模拟．计算中所采用的数学度模型有：k方程亚网格尺度模型估算亚网格湍流黏性；热通量辐射模型估算辐射换热，分别采用亚网格EBU燃烧模型（E-A model）、亚网格二阶矩输运方程模型（SOM）和亚网格二阶矩代数模型（SOM-A）估算化学反应速率．并在非交错网格系统下气相采用SIMPLE算法和混合差分格式求解，液相采用Lagrange处理，并用PSIC算法对其进行求解．通过实验结果和计算结果的比较，表明在三维任意曲线坐标系下对燃烧室火焰简两相湍流油雾燃烧流场进行大涡模拟，3种不同的亚网格燃烧模型都能真实反映两相湍流化学反应流流动及实际燃烧过程，而采用亚网格二阶矩输运方程模型稍优于其他两种亚网格燃烧模型．     

用PDF方程法分析悬沙垂线浓度分布

从颗粒运动的PDF(概率密度分布函数)输运方程出发。建立颗粒相的质量、动量和脉动速度二阶矩方程．对于明渠二维恒定均匀流。利用垂向动量方程导出了新的泥沙扩散方程。表明颗粒脉动强度梯度、升力、重力沉降和紊动扩散都影响悬沙运动。说明了传统扩散方程的不足．理论分析了水沙两相物理属性和水流条件对泥沙扩散系数和浓度分布特征的影响。并通过细颗粒试验资料的分析进行了定量研究．     

A nonlinear kp-εp particle two-scale turbulence model and its application

A particle nonlinear two-scale turbulence model is proposed for simulating the anisotropic turbulent two-phase flow. The particle kinetic energy equation for two-scale fluctuation, particle energy transfer rate equation for large-scale fluctuation, and particle turbulent kinetic energy dissipation rate equation for small-scale fluctuation are derived and closed. This model is used to simulate gas–particle flows in a sudden-expansion chamber. The simulation is compared with the experiment and with those obtained by using another two kinds of tow-phase turbulence model, such as the single-scale two-phase turbulence model and the particle two-scale second-order moment (USM) two-phase turbulence model. It is shown that the present model gives simulation in much better agreement with the experiment than the single-scale two-phase turbulence model does and is almost as good as the particle two-scale USM turbulence model. The project supported by China Postdoctoral Science Foundation (2004036239).     

A two-scale second-order moment two-phase turbulence model for simulating dense gas-particle flows

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the single-scale second-order moment two-phase turbulence model superposed with a particle collision model (USM-θ model) in most regions. The project supported by the Special Funds for Major State Basic Research, China (G-1999-0222-08), and the Postdoctoral Science Foundation (2004036239) The English text was polished by Keren Wang     

Two-phase turbulence models for simulating dense gas–particle flows

The two-fluid model is widely adopted in simulations of dense gas–particle flows in engineering facilities. Present two-phase turbulence models for two-fluid modeling are isotropic. However, turbulence in actual gas–particle flows is not isotropic. Moreover, in these models the two-phase velocity correlation is closed using dimensional analysis, leading to discrepancies between the numerical results, theoretical analysis and experiments. To rectify this problem, some two-phase turbulence models were proposed by the authors and are applied to simulate dense gas–particle flows in downers, risers, and horizontal channels; Experimental results validate the simulation results. Among these models the USM-Θ and the two-scale USM models are shown to give a better account of both anisotropic particle turbulence and particle–particle collision using the transport equation model for the two-phase velocity correlation.     

EFFECT OF EMPIRICAL COEFFICIENTS ON SIMULATION IN TWO-SCALE SECOND-ORDER MOMENT PARTICLE-PHASE TURBULENCE MODEL

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. The proposed model is used to simulate gas-particle downer reactor flows. The computational results of both particle volume fraction and mean velocity are in agreement with the experimental results. After analyzing effects of empirical coefficient on prediction results, we can come to a conclusion that, inside the limit range of empirical coefficient, the predictions do not reveal a large sensitivity to the empirical coefficient in the downer reactor, but a relatively great change of the constants has important effect on the prediction.     

Calculation of a turbulent two-phase isobaric jet

A numerical calculation is carried out by the finite-difference method based on proposed equations for a turbulent submerged jet containing an admixture of solid particles. The relative longitudinal particle velocity and the influence of particles on the turbulence intensity are taken into account. The calculated results adequately agree with available experimental data. A turbulent two-phase jet is examined in [1] on the basis of the theory for a variable density jet, assuming equal mean velocities for the gas and particles and not considering the influence of particles on the turbulence intensity. Particles are analogously taken into account by a noninertial gas mixture in [2, 3], and a particle Schmidt number of 1.1 is assumed in [4]. A model is proposed in [5] which takes into account the influence of particles on the turbulence intensity of the gas phase. Problems concerning the initial and main sections of a submerged jet were solved in [6] by the integral method on the basis of this model and the assumed equality of the mean velocities of the gas and particles. Turbulent mixing of homogeneous two-phase flows with allowance made for dynamic nonequilibrium of the phases is considered in [7]. However, the neglect of turbulent transfer of particle mass and momentum led to a physically unrealistic solution for the particle concentration in the far field of the mixture. A two-phase jet is considered in the present work on the basis of the theory of a two-velocity continuous medium [8, 9] with allowance made for turbulent transfer of particle mass and momentum. The influence of particles on the turbulence intensity of the gas phase is taken into account with the model of [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 57–63, September–October, 1976.The author acknowledges useful comments and discussion.of the work by G. N. Abramovich and participants of his seminar. The author sincerely thanks I. N. Murzinov for scientific supervision of the work.     

Characterization of particle-laden, confined swirling flows by phase-doppler anemometry and numerical calculation

The particle dispersion characteristics in a confined swirling flow with a swirl number of approx. 0.5 were studied in detail by performing measurements using phase-Doppler anemometry (PDA) and numerical predictions. A mixture of gas and particles was injected without swirl into the test section, while the swirling airstream was provided through a co-flowing annular inlet. Two cases with different primary jet exit velocities were considered. For these flow conditions, a closed central recirculation bubble was established just downstream of the inlet.

The PDA measurements allowed the correlation between particle size and velocity to be obtained and also the spatial change in the particle size distribution throughout the flow field. For these results, the behaviour of different size classes in the entire particle size spectrum, ranging from about 15 to 80 μm, could be studied, and the response of the particles to the mean flow and the gas turbulence could be characterized. Due to the response characteristics of particles with different diameters to the mean flow and the flow turbulence, a considerable separation of the particles was observed which resulted in a streamwise increase in the particle mean number diameter in the core region of the central recirculation bubble. For the lower particle inlet velocity (i.e. low primary jet exit velocity), this effect is more pronounced, since here the particles have more time to respond to the flow reversal and the swirl velocity component. This also gave a higher mass of recirculating particle material.

The numerical predictions of the gas flow were performed by solving the time-averaged Navier-Stokes equations in connection with the well known kε turbulence model. Although this turbulence model is based on the assumption of isotropic turbulence, the agreement of the calculated mean velocity profiles compared to the measured gas velocities is very good. The gas-phase turbulent kinetic energy, however, is considerably underpredicted in the initial mixing region. The particle dispersion characteristics were calculated by using the Lagrangian approach, where the influence of the particulate phase on the gas flow could be neglected, since only very low mass loadings were considered. The calculated results for the particle mean velocity and the mass flux are also in good agreement with the experiments. Furthermore, the change in the particle mean diameter throughout the flow field was predicted approximately, which shows that the applied simple stochastic dispersion model also gives good results for such very complex flows. The variation of the gas and particle velocity in the primary inlet had a considerable impact on the particle dispersion behaviour in the swirling flow and the particle residence time in the central recirculation bubble, which could be determined from the numerical calculations. For the lower particle inlet velocity, the maximum particle size-dependence residence time within the recirculation region was considerably shifted towards larger particles.     

Numerical modeling of a two-dimensional vertical turbulent two-phase jet

The results of numerically modeling two-dimensional two-phase flow of the “gas-solid particles” type in a vertical turbulent jet are presented for three cases of its configuration, namely, descending, ascending, and without account of gravity. Both flow phases are modeled on the basis of the Navier-Stokes equations averaged within the framework of the Reynolds approximation and closed by an extended k-? turbulence model. The averaged two-phase flow parameters (particle and gas velocities, particle concentration, turbulent kinetic energy, and its dissipation) are described using the model of mutually-penetrating continua. The model developed allows for both the direct effect of turbulence on the motion of disperse-phase particles and the inverse effect of the particles on turbulence leading to either an increase or a decrease in the turbulent kinetic energy of the gas. The model takes account for gravity, viscous drag, and the Saffman lift. The system of equations is solved using a difference method. The calculated results are in good agreement with the corresponding experimental data which confirms the effect of solid particles on the mean and turbulent characteristics of gas jets.     

Nanoparticle coagulation in a planar jet via moment method

Large eddy simulations of nanoparticle coagulation in an incompressible pla- nar jet were performed.The particle is described using a moment method to approximate the particle general dynamics equations.The time-averaged results based on 3000 time steps for every case were obtained to explore the influence of the Schmidt number and the Damkohler number on the nanoparticle dynamics.The results show that the changes of Schmidt number have the influence on the number concentration of nanoparticles only when the particle diameter is less than 1 nm for the fixed gas parameters.The number concentration of particles for small particles decreases more rapidly along the flow di- rection,and the nanoparticles with larger Schmidt number have a narrower distribution along the transverse direction.The smaller nanoparticles coagulate and disperse easily, grow rapidly hence show a stronger polydispersity.The smaller coagulation time scale can enhance the particle collision and coagulation.Frequented collision and coagulation bring a great increase in particle size.The larger the Damkohler number is,the higher the particle polydispersity is.