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 facili- ties. 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-O 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.     

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     

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.     

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...     

Advances in studies on two-phase turbulence in dispersed multiphase flows

Particle/droplet/bubble fluctuation and dispersion are important to mixing, heat and mass transfer, combustion and pollutant formation in dispersed multiphase flows, but are insufficiently studied before the 90 years of the last century. In this paper, the present author reports his systematic studies within nearly 20 years on two-phase turbulence in dispersed multiphase flows, including particle fluctuation in dilute gas-particle and bubble-liquid flows, particle-wall collision effect, coexistence of particle turbulence and inter-particle collisions, fluid turbulence modulation due to the particle wake effect and validation of the two-fluid RANS modeling using large-eddy simulation.     

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.     

A USM-Θ two-phase turbulence model for simulating dense gas-particle flows

A second-order moment two-phase turbulence model for simulating dense gas-particle flows (USM- model), combining the unified second-order moment two-phase turbulence model for dilute gas-particle flows with the kinetic theory of particle collision, is proposed. The interaction between gas and particle turbulence is simulated using the transport equation of two-phase velocity correlation with a two-time-scale dissipation closure. The proposed model is applied to simulate dense gas-particle flows in a horizontal channel and a downer. Simulation results and their comparison with experimental results show that the model accounting for both anisotropic particle turbulence and particle-particle collision is obviously better than models accounting for only particle turbulence or only particle-particle collision. The USM- model is also better than the k--kp- model and the k--kp-p- model in that the first model can simulate the redistribution of anisotropic particle Reynolds stress components due to inter-particle collision, whereas the second and third models cannot.The project supported by the Special Funds for Major State Basic Research of China (G-1999-0222-08), the National Natural Science Foundation of China (50376004), and Ph.D. Program Foundation, Ministry of Education of China (20030007028)     

Measurement and simulation of the two-phase velocity correlation in sudden-expansion gas-particle flows

In this paper the present authors measured the gas-particle two-phase velocity correlation in sudden expansion gas-particle flows with a phase Doppler particle anemometer(PDPA) and simulated the system behavior by using both a Reynolds-averaged Navier-Stokes(RANS) model and a large-eddy simulation(LES).The results of the measurements yield the axial and radial time-averaged velocities as well as the fluctuation velocities of gas and three particle-size groups(30 μ m,50 μ m,and 95 μ m) and the gas-particle velocity correlation for 30 μ m and 50 μ m particles.From the measurements,theoretical analysis,and simulation,it is found that the two-phase velocity correlation of sudden-expansion flows,like that of jet flows,is less than the gas and particle Reynolds stresses.What distinguishes the two-phase velocity correlations of sudden-expansion flow from those of jet and channel flows is the absence of a clear relationship between the two-phase velocity correlation and particle size in sudden-expansion flows.The measurements,theoretical analysis,and numerical simulation all lead to the above-stated conclusions.Quantitatively,the results of the LES are better than those of the RANS model.     

扩展重要抽样法及其在平尾转轴可靠性分析中的应用

提出了扩展重要抽样法，用以计算结构系统的多个失效模式中含有不全相同基本随机变量时的系统失效概率。通过构造扩展重要抽样法的抽样密度函数，给出该方法失效概率的估计值，以及其方差和变异系数的计算公式。并将此方法用于某型飞机平尾转轴的可靠性分析，算例结果表明其优越性。     

Effect of drag force on backward-facing step gas-particle turbulent flows

An improved drag force coefficient of gas-particle interaction based on the traditional Wen’s 1966 model is proposed. In this model, a two-stage continuous function is used to correct the discontinuous switch when porosity less than 0.2. Using this proposed correlation and the Wen’s 1966 model, a gas-particle kinetic energy and particle temperature model is developed to predict the hydrodynamic characteristics in backward-facing step gas-particle two-phase turbulent flows. Numerically results showed that they are in good agreement with experiment measurements and presented model are better due to a improvement of momentum transport between gas and particle phases. Particle dispersions take on the distinctively anisotropic behaviors at every directions and gas phase fluctuation velocity are about twice larger than particle phases. Particle phase has a unique transportation mechanism and completely different from the gas phase due to different density. Furthermore, the correlation values of axial–axial gas-particle are always greater than the radial–radial values at fully flow regions. The gas-particle two-phase interactions will make influence on two-phase turbulent flow behaviors.     

气固两相流动的湍流脉动扩散数学模型及其应用

本文提出了气固两相流动的湍流扩展数学模型，本模型用k-ε双方程模型求解气相湍流场，并根据气流脉动的频谱、能谱曲线提出了随机富工级数来模拟气相脉动速度，用拉氏方法描述颗粒的运动，故称为脉动频谱随机颗粒轨道模型。本文还给出了本模型在气固多相射流和流化床内应用的实例。     

On basic equations of turbulent swirling gas-solid flows and their application in cyclones

The basic equations of turbulent gas-solid flows are derived by using the pseudo-fluid model of particle phase with a refined two-phase turbulence model. These equations are then applied to swirling gas-particle flows for analyzing the collection efficiency in cyclone separators.     

Gas-particle two-phase turbulent flow in a vertical duct

Two-phase gas-phase turbulent flows at various loadings between the two vertical parallel plates are analyzed. A thermodynamically consistent turbulent two-phase flow model that accounts for the phase fluctuation energy transport and interaction is used. The governing equation of the gas-phase is upgraded to a two-equation low Reynolds number turbulence closure model that can be integrated directly to the wall. A no-slip boundary condition for the gas-phase and slip-boundary condition for the particulate phase are used. The computational model is first applied to dilute gas-particle turbulent flow between two parallel vertical walls. The predicted mean velocity and turbulence intensity profiles are compared with the experimental data of Tsuji et al. (1984) for vertical pipe flows, and good agreement is observed. Examples of additional flow properties such as the phasic fluctuation energy, phasic fluctuation energy production and dissipation, as well as interaction momentum and energy supply terms are also presented and discussed.

Applications to the relatively dense gas-particle turbulent flows in a vertical channel are also studied. The model predictions are compared with the experimental data of Miller & Gidaspow and reasonable agreement is observed. It is shown that flow behavior is strongly affected by the phasic fluctuation energy, and the momentum and energy transfer between the particulate and the fluid constituents.     

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).     

视密度加权的时平均统一二阶矩两相湍流模型

在气粒两相湍流的双流体模型中,颗粒相的视（表观）密度是有脉动的,在时平均的统一二阶矩（USM）模型中出现了和颗粒数密度或视密度脉动有关的项和方程,使模型方程比较复杂。实际上,用LDV或PDPA测量的流体（用小颗粒代表）和颗粒速度都是颗粒数加权平均的结果。因此,在视密度加权平均基础上推导两相湍流模型更为合理。通过推导和封闭了视密度加权平均的统一二阶矩模型（MUSM）方程组,改进了两相速度脉动关联的封闭,并引入了颗粒遇到的气体脉动速度及其输运方程。MUSM模型可以减少所用方程数,节省计算量。视密度加权平均的统一二阶矩两相湍流模型是一种对原有时间平均的统一二阶矩模型和改进和发展。     

大速差射流预燃室内三维回流两相湍流的数值模拟

本文由多流体两相流模型、气相湍流κ-ε模型和颗粒湍流代数模型出发,成功地模拟了真实形状大速差射流预燃室中三维湍流回流两相流动,得到了这类复杂的气固两相流中不同纵横截面上气相速度场、颗粒速度场及浓度场和两相湍流度场的分布,并且获得了与实验定性一致的合理结果,揭示了预燃室中气固两相流动与混合的主要物理特征,探讨了大速差射流技术稳焰和强化燃烧的两相流动机理。     

Modeling of dynamics, heat transfer, and combustion in two-phase turbulent flows: 1. Isothermal flows

This paper presents a review of authors' collective works in the field of two-phase flow modeling done in the past few decades. The paper is aimed at the construction of mathematical models for simulation of particle-laden turbulent flows. A kinetic equation was obtained for the probability density function (PDF) of the particle velocity distribution in turbulent flows. The proposed kinetic equation describes both the interaction of particles with turbulent eddies of the carrier phase and particle-particle collisions. This PDF equation is used for the derivation of different schemes describing turbulent momentum transfer in the dispersed particle phase. The turbulent characteristics of the gaseous phase are calculated on the basis of the k - turbulence model with a modulation effect of particles on the turbulence.

The constructed models have been applied to the calculation of various two-phase gas-particle turbulent flows in jets and channels as well as particle deposition in tubes and separators. For validating the theoretical and numerical results, a wide range of comparisons with experimental data from Russian and foreign sources has been done.     

The setting up of the equations for two-phase flows by the kinetic theory method

The fundamental equations for two-phase flows are deduced from the Boltzmann's equation. The collision terms are treated with a method similar to what is used in the classical kinetic theory for handling the transport properties of dense gases. It is shown that collision pressure and collision thermal flux exist in gas-particle flows in addition to the general partial pressure and partial thermal flux. Their physical natures are quite different from those of the general partial pressure and partial thermal flux. The applicability of the binary collision assumption and the molecular chaos assumption to gas-particle flows is also discussed. Finally, the equations for two-phase flows obtained by the method of the kinetic theory are compared with those obtained by average continuum models and by the model of particle clouds. The results from the kinetic theory show clearly the physical significance of various parameters and clarify some confusing concepts. Institute of Mechanics, Academia Sinica     

大速差射流预燃室内三维回流两相湍流的数值模拟

本文由多流体两相流模型、气相湍流κ-ε模型和颗粒湍流代数模型出发,成功地模拟了真实形状大速差射流预燃室中三维湍流回流两相流动,得到了这类复杂的气固两相流中不同纵横截面上气相速度场、颗粒速度场及浓度场和两相湍流度场的分布,并且获得了与实验定性一致的合理结果,揭示了预燃室中气固两相流动与混合的主要物理特征,探讨了大速差射流技术稳焰和强化燃烧的两相流动机理。