Particle subgrid scale modelling in large-eddy simulations of particle-laden turbulence

This study is concerned with particle subgrid scale (SGS) modelling in large-eddy simulations (LESs) of particle-laden turbulence. Although many particle-laden LES studies have neglected the effect of the SGS on the particles, several particle SGS models have been proposed in the literature. In this research, the approximate deconvolution method (ADM) and the stochastic models of Fukagata et al. (Dynamics of Brownian particles in a turbulent channel flow, Heat Mass Transf. 40 (2004), 715–726) Shotorban and Mashayek (A stochastic model for particle motion in large-eddy simulation, J. Turbul. 7 (2006), 1–13) and Berrouk et al. (Stochastic modelling of inertial particle dispersion by subgrid motion for LES of high Reynolds number pipe flow, J. Turbul. 8 (2007), pp. 1–20) are analysed. The particle SGS models are assessed using both a priori and a posteriori simulations of inertial particles in a periodic box of decaying, homogeneous and isotropic turbulence with an initial Reynolds number of Re_λ = 74. The model results are compared with particle statistics from a direct numerical simulation (DNS). Particles with a large range of Stokes numbers are tested using various filter sizes and stochastic model constant values. Simulations with and without gravity are performed to evaluate the ability of the models to account for the crossing trajectory and continuity effects. The results show that ADM improves results but is only capable of recovering a portion of the SGS turbulent kinetic energy. Conversely, the stochastic models are able to recover sufficient SGS energy, but show a large range of results dependent on the Stokes number and filter size. The stochastic models generally perform best at small Stokes numbers, but are unable to predict preferential concentration.     

用改进的随机轨道模型数值模拟突扩液固两相流动

用改进的随机轨道模型数值模拟了突扩湍流液固两相流动。两相的轴向速度和湍动能的预报结果与实验符合得很好,同时还给出了不同计算截面上颗粒数密度和质量流量合理分布．预报结果对计算颗粒数敏感程度的研究表明：与通常的随机轨道不同,改进的随机轨道模型只需要很少的计算颗粒就可以给出合理正确的颗粒相分布。     

考虑双向耦合效应的格子Boltzmann气固两相湍流模型

在流体粒子概率密度函数输运方程中考虑颗粒对流体的反作用力,发展了考虑双向耦合效应的LB气固两相流模型,引入Smagorinsky亚格子模型模拟高雷诺数气相流场.对经典后台阶气固两相流动进行模拟,气相和颗粒相速度分布与实验结果进行比较,发现考虑双向耦合效应的LB气固两相流模型结果明显优于单向耦合结果.进一步研究不同惯性颗粒在流场中的弥散特性,小颗粒(St~O(0.1))对流体的跟随性较好,在流场中分布较为均匀;而St~O(1)的颗粒难被流场涡卷吸进入涡内,呈现倾向性弥散现象;大颗粒(St~O(10))由于自身惯性进入流场涡,在流场中分布较为均匀.     

Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows

The rotational motion and orientational distribution of ellipsoidal particles in turbulent flows are of significance in environmental and engineering applications. Whereas the translational motion of an ellipsoidal particle is controlled by the turbulent motions at large scales, its rotational motion is determined by the fluid velocity gradient tensor at small scales, which raises a challenge when predicting the rotational dispersion of ellipsoidal particles using large eddy simulation (LES) method due to the lack of subgrid scale (SGS) fluid motions. We report the effects of the SGS fluid motions on the orientational and rotational statistics, such as the alignment between the long axis of ellipsoidal particles and the vorticity, the mean rotational energy at various aspect ratios against those obtained with direct numerical simulation (DNS) and filtered DNS. The performances of a stochastic differential equation (SDE) model for the SGS velocity gradient seen by the particles and the approximate deconvolution method (ADM) for LES are investigated. It is found that the missing SGS fluid motions in LES flow fields have significant effects on the rotational statistics of ellipsoidal particles. Alignment between the particles and the vorticity is weakened; and the rotational energy of the particles is reduced in LES. The SGS-SDE model leads to a large error in predicting the alignment between the particles and the vorticity and over-predicts the rotational energy of rod-like particles. The ADM significantly improves the rotational energy prediction of particles in LES.     

Turbulence modulation model for gas–particle flow based on probability density function approach

The paper focuses on the turbulence modulation problem in gas–particle flow with the use of probability density function(PDF) approach. By means of the PDF method, a general statistical moment turbulence modulation model without considering the trajectory difference between two phases is derived from the Navier–Stokes equations. A new turbulence production term induced by the dispersed-phase is analyzed and considered. Furthermore, the trajectory difference between two media is taken into account. Subsequently, a new k–ε turbulence modulation model in dilute particle-laden flow is successfully set up. Then, the changes to several terms, including the turbulence production, dissipation, and diffusion terms, are well described consequently. The promoted model provides a more probable explanation for the modification of particles on the turbulence. Finally, we applied the model to simulate a gas–particle turbulence flow case in a wall jet, and found that the simulation results agree well with the experimental data.     

固体粒子在直流式除尘器中湍流脉动的数值模拟

本文对直流除尘器涡室内固体粒子的湍流脉动现象进行了数值分析,通过气体速度随机脉动谱,把气相湍流运动对固体粒子运动的影响引入粒子的运动平衡方程中,用拉格朗日法模拟了粒子的轨迹及其扩散运动,应用四阶龙科库塔方法求解粒子的运动方程。计算结果表明对粒子的数值模拟可以较好地预测除尘器的性能,如除尘器的切割粒径。     

Ultrasonic particle size fractionation in a moving air stream

Identification of bio-aerosol particles may be enhanced by size sorting before applying analytical techniques. In this paper, the use of ultrasonic acoustic radiation pressure to continuously size fractionate particles in a moving air stream is described. Separate particle-laden and clean air streams are introduced into a channel and merged under laminar flow conditions. An ultrasonic transducer, mounted flush to one wall of the channel, excites a standing ultrasonic wave perpendicular to the flow of the combined air stream. Acoustic radiation forces on the particles cause them to move transverse to the flow direction. Since the radiation force is dependent upon the particle size, larger particles move a greater transverse distance as they pass through the standing wave. The outlet flow is then separated into streams, each containing a range of particle sizes. Experiments were performed with air streams containing glass microspheres with a size distribution from 2-22 μm, using a centerline air stream velocity of approximately 20 cm/s. An electrostatic transducer operating at a nominal frequency of 50 kHz was used to drive an ultrasonic standing wave of 150 dB in pressure amplitude. The microsphere size distributions measured at the outlet were compared with the predictions of a theoretical model. Experiments and theory show reasonable correspondence. The theoretical model also indicates an optimal partitioning of the particle-laden and clean air inlet streams.     

A numerical scheme for particle-laden thin film flow in two dimensions

The physics of particle-laden thin film flow is not fully understood, and recent experiments have raised questions with current theory. There is a need for fully two-dimensional simulations to compare with experimental data. To this end, a numerical scheme is presented for a lubrication model derived for particle-laden thin film flow in two dimensions with surface tension. The scheme relies on an ADI process to handle the higher-order terms, and an iterative procedure to improve the solution at each timestep. This is the first paper to simulate the two-dimensional particle-laden thin film lubrication model. Several aspects of the scheme are examined for a test problem, such as the timestep, runtime, and number of iterations. The results from the simulation are compared to experimental data. The simulation shows good qualitative agreement. It also suggests further lines of inquiry for the physical model.     

A high-order WENO-Z finite difference based particle-source-in-cell method for computation of particle-laden flows with shocks

A high-order particle-source-in-cell (PSIC) algorithm is presented for the computation of the interaction between shocks, small scale structures, and liquid and/or solid particles in high-speed engineering applications. The improved high-order finite difference weighted essentially non-oscillatory (WENO-Z) method for solution of the hyperbolic conservation laws that govern the shocked carrier gas flow, lies at the heart of the algorithm. Finite sized particles are modeled as points and are traced in the Lagrangian frame. The physical coupling of particles in the Lagrangian frame and the gas in the Eulerian frame through momentum and energy exchange, is numerically treated through high-order interpolation and weighing. The centered high-order interpolation of the fluid properties to the particle location is shown to lead to numerical instability in shocked flow. An essentially non-oscillatory interpolation (ENO) scheme is devised for the coupling that improves stability. The ENO based algorithm is shown to be numerically stable and to accurately capture shocks, small flow features and particle dispersion. Both the carrier gas and the particles are updated in time without splitting with a third-order Runge–Kutta TVD method. One and two-dimensional computations of a shock moving into a particle cloud demonstrates the characteristics of the WENO-Z based PSIC method (PSIC/WENO-Z). The PSIC/WENO-Z computations are not only in excellent agreement with the numerical simulations with a third-order Rusanov based PSIC and physical experiments in [V. Boiko, V.P. Kiselev, S.P. Kiselev, A. Papyrin, S. Poplavsky, V. Fomin, Shock wave interaction with a cloud of particles, Shock Waves, 7 (1997) 275–285], but also show a significant improvement in the resolution of small scale structures. In two-dimensional simulations of the Mach 3 shock moving into forty thousand bronze particles arranged in the shape of a rectangle, the long time accuracy of the high-order method is demonstrated. The fifth-order PSIC/WENO-Z method with the fifth-order ENO interpolation scheme improves the small scale structure resolution over the third-order PSIC/WENO-Z method with a second-order central interpolation scheme. Preliminary analysis of the particle interaction with the flow structures shows that sharp particle material arms form on the side of the rectangular shape. The arms initially shield the particles from the accelerated flow behind the shock. A reflected compression wave, however, reshocks the particle arm from the shielded area and mixes the particles.     

自由剪切流动中颗粒扩散的自相似特性

为了研究自由剪切流动中颗粒扩散的统计特性,对空间发展模式的三维气固两相射流和时间发展模式的三维气固两相混合层进行了直接数值模拟.其中对气相不可压缩Navier-Stokes方程的求解分别采用有限容积方法和拟谱方法,对离散惯性颗粒的跟踪采用单向耦合的拉格朗日方法.统计结果显示,当流场进入自相似状态后,以流场速度梯度二阶不变量Q为自变量的颗粒数的概率分布函数也呈现出与颗粒尺寸和时间发展无关的自相似特性.     

Soot-velocity measurements by particle vaporization velocimetry

We demonstrate a new imaging technique for velocity measurements in particle-laden flows. The technique, particle vaporization velocimetry, is a form of flow tagging based on laser vaporization of absorbing particles at defined locations in the flow. The locations of these tagged regions are then interrogated after a known delay to determine the convective velocity. Results are presented for vaporization of carbonaceous (soot) particles in a nonreacting gas jet and a hydrocarbon flame, with interrogation provided by either elastic scattering or laser-induced incandescence from the soot. The long lifetime of the tagged soot regions (>2 ms) allows measurements to be made over a wide range of velocities.     

固体粒子通过叶尾激波的运动特性

含尘叶轮机械如烟气轮机。高炉余气透平已得到广泛的使用。其内部是含有固体粒子的气固两相流动,又是有激波的跨音流动。叶片近尾缘区内的固粒运动受到激波的作用,使用常规的理论方法来预测气固两相流的流场会产生误差。本文通过粒子的受力分析建立了固体粒子通过激波时的运动模型。通过数值模拟可以明显的见到固体粒子受到激波的作用,粒子在激波后运动有明显的折转。获得了粒子通过激波的运动特性。     

A Modeling Study on Particle Dispersion in Wall-Bounded Turbulent Flows

Three physical mechanisms which may affect dispersion of particle's motion in wall-bounded turbulent flows, including the effects of turbulence, wall roughness in particle-wall collisions, and inter-particle collisions, are numerically investigated in this study. Parametric studies with different wall roughness extents and with different mass loading ratios of particles are performed in fully developed channel flows with the Eulerian-Lagrangian approach. A low-Reynolds-number $k-\epsilon$ turbulence model is applied for the solution of the carrier-flow field, while the deterministic Lagrangian method together with binary-collision hard-sphere model is applied for the solution of particle motion. It is shown that the mechanism of inter-particle collisions should be taken into account in the modeling except for the flows laden with sufficiently low mass loading ratios of particles. Influences of wall roughness on particle dispersion due to particle-wall collisions are found to be considerable in the bounded particle-laden flow. Since the investigated particles are associated with large Stokes numbers, i.e., larger than $\mathcal{O}(1)$, in the test problem, the effects of turbulence on particle dispersion are much less considerable, as expected, in comparison with another two physical mechanisms investigated in the study.     

The heating and acceleration dynamics of Al2O3 particles in the axisymmetric heterogeneous flow emanating from a plasma torch with inter-electrode inserts

Measured data on the temperature and velocity of Al₂O₃ particles of size fraction 34±6 μm in the jet emanating from a DC plasma torch with inter-electrode inserts under conditions of axisymmetric heterogeneous flow are reported. The velocity and temperature of individual particles were measured using a laser-optical diagnostic complex, which was a combination of a bifocal laser anemometer and a pyrometer based on a compact spectrometer. For measuring the temperature of individual particles in the particle-laden plasma jet, three-color pyrometry was used. The obtained data on the characteristics of particles in the jet emanating from the plasma spray torch with inter-electrode inserts equipped with a unit for radial-annular injection of powder into the plasma jet show that the implemented conditions for processing powder materials allow reaching a high homogeneity of the aggregate state of particles in the jet flow (～ 100 % of melted particles).     

A numerical method for fully resolved simulation (FRS) of rigid particle–flow interactions in complex flows

A fictitious-domain based formulation for fully resolved simulations of arbitrary shaped, freely moving rigid particles in unsteady flows is presented. The entire fluid–particle domain is assumed to be an incompressible, but variable density, fluid. The numerical method is based on a finite-volume approach on a co-located, Cartesian grid together with a fractional step method for variable density, low-Mach number flows. The flow inside the fluid region is constrained to be divergence-free for an incompressible fluid, whereas the flow inside the particle domain is constrained to undergo rigid body motion. In this approach, the rigid body motion constraint is imposed by avoiding the explicit calculation of distributed Lagrange multipliers and is based upon the formulation developed by Patankar [N. Patankar, A formulation for fast computations of rigid particulate flows, Center for Turbulence Research Annual Research Briefs 2001 (2001) 185–196]. The rigidity constraint is imposed and the rigid body motion (translation and rotational velocity fields) is obtained directly in the context of a two-stage fractional step scheme. The numerical approach is applied to both imposed particle motion and fluid–particle interaction problems involving freely moving particles. Grid and time-step convergence studies are performed to evaluate the accuracy of the approach. Finally, simulation of rigid particles in a decaying isotropic turbulent flow is performed to study the feasibility of simulations of particle-laden turbulent flows.     

Polarization imaging of multiply-scattered radiation based on integral-vector Monte Carlo method

A new integral-vector Monte Carlo method (IVMCM) is developed to analyze the transfer of polarized radiation in 3D multiple scattering particle-laden media. The method is based on a “successive order of scattering series” expression of the integral formulation of the vector radiative transfer equation (VRTE) for application of efficient statistical tools to improve convergence of Monte Carlo calculations of integrals. After validation against reference results in plane-parallel layer backscattering configurations, the model is applied to a cubic container filled with uniformly distributed monodispersed particles and irradiated by a monochromatic narrow collimated beam. 2D lateral images of effective Mueller matrix elements are calculated in the case of spherical and fractal aggregate particles. Detailed analysis of multiple scattering regimes, which are very similar for unpolarized radiation transfer, allows identifying the sensitivity of polarization imaging to size and morphology.     

Numerical simulation of instantaneous flow structure of swirling and non-swirling coaxial-jet particle-laden turbulence flows

A subgrid scale two-phase second-order-moment (SGS-SOM) model based on the two-fluid continuum approach is presented for the analysis of the instantaneous flow structures of swirling and non-swirling coaxial-jet particle-laden turbulence flows. Since the interaction between the two-phase subgrid scale stresses and the anisotropy of two-phase subgrid scale stresses is fully considered, it is superior to the conventional subgrid scale model on the basis of single gas phase or together with their similar forms for the particle phase for not taken these characters thoroughly into account. The swirling numbers s=0.47 and s=0 of coaxial-jet particle-laden turbulence flows (measured by M. Sommerfeld, H.H. Qiu, Detailed measurements in a swirling particulate two-phase flow by a phase Doppler anemometer, Int. J. Heat Fluid Flow 12 (1991) 20-28) are numerically simulated by large eddy simulation using this model, together with a Reynolds-averaged Navier-Stokes model using the unified second-order-moment two-phase turbulence model (RANS-USM). The instantaneous results show that the multiple recirculating gas flow structure is similar to that of single-phase swirling flows; but the particle flow structure contains less vortices. Both SGS-SOM and RANS-USM predicted that the two-phase time-averaged velocities and the root-mean-square fluctuation velocities are validated and are in good agreement with the experimental results. It is seen that for the two-phase time-averaged velocities both the models give almost the same results, hence the RANS-USM modeling is validated by large eddy simulation. For the two-phase root-mean-square fluctuation velocities the SGS-SOM results are obviously better than the RANS-USM results.     

近红外离散波长光谱基线漂移校正方法研究

微分是(近)红外光谱多元分析校正中最常使用也是最有效的光谱基线漂移校正方法。由于数据数目较少及相邻数据在光谱意义或数学意义上缺乏连续性,微分不能直接用于离散波长光谱消除基线漂移。为此,提出了一种结合插值拟合和微分校正离散光谱基线漂移的新方法。思路是采用三次样条插值法对离散波长光谱进行拟合,然后对拟合光谱进行Savitaky-Golay卷积求导,再从微分光谱中取出对应于原离散波长光谱数值的数值,构成离散波长光谱的微分光谱,从而实现离散波长光谱的基线漂移校正。通过分别由模拟离散波长光谱数据和实际的离散波长光谱数据建立多元校正模型检验新方法效果。采用ABC干粉灭火剂和土壤的近红外光谱数据及性质建立了PLS和MLR模型。结果表明,新方法能有效消除离散波长光谱的基线漂移对多元分析校正产生的不利影响,明显地提高了多元分析校正模型的准确性,对改善离散波长光谱仪器分析准确度具有重要的理论意义和实际应用价值。     

Effect of gravity on the development of homogeneous shear turbulence laden with finite-size particles

Fully resolved simulations of homogeneous shear turbulence (HST) laden with sedimenting spherical particles of finite size have been performed to clarify the effects of gravity on the development of particle-laden turbulent shear flows. We consider turbulence in a horizontal flow subjected to vertical or horizontal shear. Numerical results show that the development of HST laden with finite-size particles are significantly altered by gravity. The effects of gravity lead to a slower increase in the Taylor-microscale Reynolds number, whose value is found to be well correlated with the average particle Reynolds number. The gravity also causes a slower increase in the turbulence kinetic energy (TKE) through the enhancement of energy dissipation. The change in the Reynolds shear stress (RSS) due to particles also significantly contributes to the relative change in TKE. In vertically sheared cases, RSS has high values between counter-rotating trailing vortices behind the particles, which causes a transient relative increase in TKE. In horizontally sheared cases, on the other hand, RSS is reduced in the wakes of particles, which contributes to a significant relative reduction in TKE.     

Deposition of inertial particles from turbulent flow in channels at high Reynolds numbers

On the basis of the previously developed asymptotic theory of turbulent particle-laden flow with particle deposition in channels coupled with the transport model for the particle Reynolds stress, an asymptotic solution to the problem on the deposition of particles in the limit of high Reynolds numbers was obtained. The numerical calculations confirmed the presence, in the region of the transition from the diffusion-impaction regime of particle sedimentation to the inertia-moderated regime, bifurcation phenomenon of a solution found previously in earlier studies. Features of particle accumulation in the viscous sublayer are analyzed. On the basis of the numerical solution, correlations for particle deposition velocity were obtained. Boundary conditions of the wall-function type for particle concentration whose use allows widening the applicability limits of the equilibrium Eulerian models in terms of particle inertia are proposed.