Turbulent particle dispersion in arbitrary wall-bounded geometries: A coupled CFD-Langevin-equation based approach

A Lagrangian continuous random walk (CRW) model is developed to predict turbulent particle dispersion in arbitrary wall-bounded flows with prevailing anisotropic, inhomogeneous turbulence. The particle tracking model uses 3D mean flow data obtained from the Fluent CFD code, as well as Eulerian statistics of instantaneous quantities computed from DNS databases. The turbulent fluid velocities at the current time step are related to those of the previous time step through a Markov chain based on the normalized Langevin equation which takes into account turbulence inhomogeneities. The model includes a drift velocity correction that considerably reduces unphysical features common in random walk models. It is shown that the model satisfies the well-mixed criterion such that tracer particles retain approximately uniform concentrations when introduced uniformly in the domain, while their deposition velocity is vanishingly small, as it should be. To handle arbitrary geometries, it is assumed that the velocity rms values in the boundary layer can locally be approximated by the DNS data of fully developed channel flows. Benchmarks of the model are performed against particle deposition data in turbulent pipe flows, 90° bends, as well as more complex 3D flows inside a mouth-throat geometry. Good agreement with the data is obtained across the range of particle inertia.     

Transport and deposition of neutral particles in magnetohydrodynamic turbulent channel flows at low magnetic Reynolds numbers

The effect of Lorentz force on particle transport and deposition is studied by using direct numerical simulation of turbulent channel flow of electrically conducting fluids combined with discrete particle simulation of the trajectories of uncharged, spherical particles. The magnetohydrodynamic equations for fluid flows at low magnetic Reynolds numbers are adopted. The particle motion is determined by the drag, added mass, and pressure gradient forces. Results are obtained for flows with particle ensembles of various densities and diameters in the presence of streamwise, wall-normal or spanwise magnetic fields. It is found that the particle dispersion in the wall-normal and spanwise directions is decreased due to the changes of the underlying fluid turbulence by the Lorentz force, while it is increased in the streamwise direction. The particle accumulation in the near-wall region is diminished in the magnetohydrodynamic flows. In addition, the tendency of small inertia particles to concentrate preferentially in the low-speed streaks near the walls is strengthened with increasing Hartmann number. The particle transport by turbophoretic drift and turbulent diffusion is damped by the magnetic field and, consequently, particle deposition is reduced.     

Skin-friction drag reduction in turbulent channel flow based on streamwise shear control

It is known that stretching and intensification of a hairpin vortex by mean shear play an important role to create a hairpin vortex packet, which generates the large Reynolds shear stress associated with skin-friction drag in wall-bounded turbulent flows. In order to suppress the mean shear at the wall for high efficient drag reduction (DR), in the present study, we explore an active flow control concept using streamwise shear control (SSC) at the wall. The longitudinal control surface is periodically spanwise-arranged with no-control surface while varying the structural spacing, and an amplitude parameter for imposing the strength of the actuating streamwise velocity at the wall is introduced to further enhance the skin-friction DR. Significant DR is observed with an increase in the two parameters with an accompanying reduction of the Reynolds stresses and vorticity fluctuations, although a further increase in the parameters amplifies the turbulence activity in the near-wall region. In order to study the direct relationship between turbulent vortical structures and DR under the SSC, temporal evolution with initial eddies extracted by conditional averages for Reynolds-stress-maximizing Q2 events are examined. It is shown that the generation of new vortices is dramatically inhibited with an increase in the parameters throughout the flow, causing fewer vortices to be generated under the control. However, when the structural spacing is sufficiently large, the generation of new vortex is not suppressed over the no-control surface in the near-wall region, resulting in an increase of the second- and fourth-quadrant Reynolds shear stresses. Although strong actuating velocity intensifies the near-wall turbulence, the increase in the turbulence activity is attributed to the generation of counter-clockwise near-wall vortices by the increased vortex transport.     

Investigation of particle-laden turbulent pipe flow at high-Reynolds-number using particle image/tracking velocimetry (PIV/PTV)

An experimental investigation of a high Reynolds number flow (Re = 320 000) of a dilute liquid-solid mixture (<1% by volume) was conducted. The turbulent motion of both the liquid phase (water) and particles (0.5, 1, and 2 mm glass beads) was evaluated in an upward pipe flow using a particle image/tracking velocimetry (PIV/PTV) technique. Results show that the Eulerian mean axial velocity of the glass beads is lower than that of the liquid phase in the central region but higher in the near-wall region. Moreover, the presence of the coarse particles has a negligible effect on the turbulence intensity of the liquid phase. Particles show higher streamwise and radial fluctuations than the liquid-phase at the tested conditions. The profiles of particle concentration across the pipe radius show almost constant concentration in the core of the pipe with a decrease towards the near wall region for 0.5 and 1 mm particles. For the 2 mm particles, a nearly linear concentration gradient from centre to the pipe wall is observed. The results presented here provide new information concerning the effect of a dispersed particulate phase on the turbulence modulation of the liquid carrier phase, especially at high Reynolds numbers. The present study also demonstrates how correlations developed to determine if particles cause turbulence attenuation/augmentation are not applicable for solid-liquid flows at high Reynolds numbers. Finally, the importance of particle-fluid slip velocity on fluid phase turbulence modulation is illustrated.     

Particle and droplet deposition in turbulent swirled pipe flow

In this work we study deposition of particles and droplets in non-rotating swirled turbulent pipe flow. We aim at verifying whether the capability of swirl to enhance particle separation from the core flow and the capability of turbulence to efficiently trap particles at the wall can co-exist to optimize collection efficiency in axial separators. We perform an Eulerian–Lagrangian study based on Direct Numerical Simulation (DNS) of turbulence, considering the effect of different swirl intensities on turbulence structures and on particle transfer at varying particle inertia. We show that, for suitably-chosen flow parameters, swirl may be superimposed to the base flow without disrupting near-wall turbulent structures and their regeneration mechanisms. We also quantify collection efficiency demonstrating for the first time that an optimal synergy between swirl and wall turbulence can be identified to promote separation of particles and droplets.     

Dynamics of disk-like particles in turbulent vertical channel flow

The dynamical behavior of inertial disk-like particles in turbulent vertical channel flow is investigated by an Eulerian–Lagrangian point-particle approach. Gravity effects on distribution, translation, rotation and orientation statistics of non-spherical particles modeled as oblate spheroids have been studied both in an upward and a downward flow and compared with results obtained in the absence of gravity. Altogether 12 different particle classes have been studied, with inertia and shape parameterized by means of Stokes number St and aspect ratio λ ≤ 1. The St = 5 disk-like particles distribute more evenly across the channel in upward than in downward flow. The gravity effect on the particle concentration diminishes with large inertia and the spheroid shape has only a modest influence. Although the gravity significantly affects the streamwise and wall-normal mean slip velocities with increasing inertia, the particle shape rarely has any impact on the translational motion, except for the mean wall-normal velocity. The fluctuations of the velocity of disk-like particles are mainly ascribed to inertia, whereas the gravity and shape only have marginal effects. The presence of gravity is moreover found to have a negligible effect on the particles’ orientation and rotation, in spite of the striking effect of λ on the orientation and rotation seen in the near-wall region. The tendency of the disks to align their symmetry axis orthogonal to the fluid vorticity in the channel center is stronger for particles with modest inertia. In the near-wall region, however, oblate spheroids preferentially align with the fluid vorticity for St >> 1. The observed behavior is believed to be caused by the influence of the gravity force on the turbophoresis; i.e. that inertial particles move towards low-turbulence regions.     

Filtered particle tracking in isotropic turbulence and stochastic modeling of subgrid-scale dispersion

A numerical study based on the Eulerian–Lagrangian formulation is performed for dispersed phase motion in a turbulent flow. The effect of spatial filtering, commonly employed in large-eddy simulations, and the role of the subgrid scale turbulence on the statistics of heavy particles, including preferential concentration, are studied through a priori analysis of DNS of particle-laden forced isotropic turbulence. In simulations where the subgrid scale kinetic energy attains 30–35% of the total we observe the impact of residual fluid motions on particles of a smaller inertia. It is shown that neglecting the influence of subgrid scale fluctuations has a significant effect on the preferential concentration of those particles. A stochastic Langevin model is proposed to reconstruct the residual (or subgrid scale) fluid velocity along particle trajectories. The computation results for a selection of particle inertia parameters are performed to appraise the model through comparisons of particle turbulent kinetic energy and the statistics of preferential concentrations.     

Finite-length effects on dynamical behavior of rod-like particles in wall-bounded turbulent flow

Combined Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) measurements have been performed in dilute suspensions of rod-like particles in wall turbulence. PIV results for the turbulence field in the water table flow apparatus compared favorably with data from Direct Numerical Simulations (DNS) of channel flow turbulence and the universality of near-wall turbulence justified comparisons with DNS of fiber-laden channel flow. In order to examine any shape effects on the dynamical behavior of elongated particles in wall-bounded turbulent flow, fibers with three different lengths but the same diameter were used. In the logarithmic part of the wall-layer, the translational fiber velocity was practically unaffected by the fiber length l. In the buffer layer, however, the fiber dynamics turned out to be severely constrained by the distance z to the wall. The short fibers accumulated preferentially in low-speed areas and adhered to the local fluid speed. The longer fibers (l/z > 1) exhibited a bi-modal probability distribution for the fiber velocity, which reflected an almost equal likelihood for a long fiber to reside in an ejection or in a sweep. It was also observed that in the buffer region, high-speed long fibers were almost randomly oriented whereas for all size cases the slowly moving fibers preferentially oriented in the streamwise direction. These phenomena have not been observed in DNS studies of fiber suspension flows and suggested l/z to be an essential parameter in a new generation of wall-collision models to be used in numerical studies.     

Antisymmetric quadrupole mode of coherent structures in wall-bounded turbulence

Experiments were conducted in a water tunnel by tomographic time-resolved particle image velocimetry (Tomo-TRPIV). The Reynolds number Re_θ is 2460 on the base of momentum thickness. According to the physical mechanism of the stretch and compression of multi-scale vortex structures in the wall-bounded turbulence, the topological characteristics of turbulence statistics in logarithmic layer were illustrated by local-averaged velocity structure function. During coherent structures bursting, results reveal that the topological structures of velocity gradients, velocity strain rates and vorticities behave as antisymmetric quadrupole modes. A three-layer antisymmetric quadrupole vortex packet confirms that there is a tight relationship between the outer layer and the near-wall layer.     

多孔介质壁面剪切湍流速度时空关联的研究

作为一个基础统计量,时空关联函数在湍流问题的研究中有着广泛的应用,是研究湍流噪声、湍流中物质扩散和大涡模拟亚格子模型等问题的重要参考.本文通过建立三维多孔结构壁面剪切湍流模型,采用含Darcy-Brinkman-Forchheimer作用力项的格子Boltzmann方程对无穷大多孔介质平行板之间壁湍流进行了数值模拟,进而研究其速度脉动时空关联函数的统计特性.一方面,根据计算得到的流场数据,对比分析了常规槽道湍流与多孔介质壁面槽道湍流的时间关联函数.另一方面,计算并讨论了不同孔隙率和渗透率的多孔介质壁面对速度脉动时空关联性的影响.通过研究表明:多孔结构壁面剪切湍流的时空关联函数等值线与椭圆理论相符;在研究参数范围内,多孔介质壁面的速度时空关联系数随着孔隙率增大而增大,随着渗透率增大而减小.同时发现在槽道壁面的近壁区、过渡区、对数律区和中心区等不同位置处,速度时空关联呈现较大差异性:越远离壁面位置(对数律区和中心区),其时空关联函数所呈现的关联等值线椭圆越细长,高值相关等值线越集中.多孔介质主要改变速度时空关联椭圆图像的椭圆率,说明多孔介质壁面主要影响湍流横扫速度.     

A stochastic Langevin model of turbulent particle dispersion in the presence of thermophoresis

Direct numerical simulation (DNS) and experimental data have shown that inertial particles exhibit concentration peaks in isothermal turbulent boundary layers, whereas tracer-like particles remain well mixed in the domain. It is therefore expected that the interactions between turbulence and thermophoresis will be strong in particle-laden flows where walls and carrier fluid are at significantly different temperatures. To capture turbulent particle dispersion with active thermophoresis, a coupled CFD-Lagrangian continuous random walk (CRW) model is developed. The model uses 3D mean flow velocities obtained from the Fluent 6.3 CFD code, to which are added turbulent fluid velocities derived from the normalized Langevin equation which accounts for turbulence inhomogeneities. The mean thermophoretic force is included as a body force on the particle following the Talbot formulation. Validation of the model is performed against recent integral thermophoretic deposition data in long pipes as well as the TUBA TT28 test with its detailed local deposition measurements. In all cases, the agreement with the data is very good. In separate parametric studies in a hypothetical cooled channel flow, it is found that turbulence strongly enhances thermophoretic deposition of particles with dimensionless relaxation times τ⁺ of order 1 or more. On the other hand, the thermophoretic deposition of very small inertia particles (τ⁺ < 0.2) in the asymptotic region far from the injection point tends to that which characterizes stagnant flow conditions, in agreement with the DNS results of Thakurta et al.     

Compressibility effects due to turbulent fluctuations

This paper deals with intrinsic effects of compressibility, i.e. with dilatation fluctuations in response to pressure fluctuations. Three different types of turbulent flows are considered in more detail: homogeneous turbulent shear flow, wall-bounded turbulent shear flow and shock/turbulence interaction. A survey of the present knowledge in this field, mainly based on DNS data, is given. Using the linear inviscid perturbation equations a direct link between fluctuations of dilatation and of velocity in the direction of mean shear is presented for homogeneous shear flow. This relation might form the basis for a more universal pressure-dilatation model. It is conjectured that the insignificance of intrinsic compressibility effects in wall-bounded supersonic shear flow is mainly due to the impermeability constraint of the wall. To this end, a linear stability analysis of supersonic channel flow along cooled, but permeable walls has been performed based on Coleman et al.'s [5] mean flow data. It shows an increase in the moduli of eigenfunctions related to compressibility, like pressure, and in moduli of quantities derived from eigenfunctions such as ‘pressure dilatation’ and squared dilatation. Although these results do not prove our hypothesis they provide hints in this direction. Shock/turbulence interaction is viewed as a source of compressibility. Former DNS data of Hannappel and Friedrich [10] for shock/isotropic turbulence interaction showing the effect of compressibility on the amplification of fluctuations are interpreted based on linear perturbation equations.     

Interactions of particles and microbubbles with turbulence

Dilute, dispersed two-phase flows arise in many contexts ranging from solid particles or droplets in gas flows to bubbles in liquids. Many of the flows of interest are turbulent, which presents a complex problem to analyze or to determine the dominant physical processes contributing to the observed phenomena. Advances in experimental techniques have made it possible to measure directly turbulent and particle velocity fluctuations in dilute systems. This has provided a counterpart to advances in computational and analytical models and a basis on which to test these models. Three specific areas are considered: the fluctuating forces on an individual particle in an unsteady flow, the response of a solid particle to a turbulent air flow, and the corresponding response of a small bubble in turbulent liquid flows. Results from direct numerical simulations are presented for each of these, including the nonuniform distribution of particles generated by local instantaneous features of the flow. The issue of turbulence modulation at low to moderate void fractions is discussed.     

壁湍流相干结构和减阻控制机理

剪切湍流中相干结构的发现是上世纪湍流研究的重大进展之一,这些大尺度的相干运动在湍流的动力学过程中起重要作用,也为湍流的控制指出了新的方向.壁湍流高摩擦阻力的产生与近壁区流动结构密切相关,基于近壁区湍流动力学过程的减阻控制方案可以有效降低湍流的摩擦阻力,但是随着雷诺数的升高, 这些控制方案的有效性逐渐降低.近年来研究发现, 在高雷诺数情况下外区存在大尺度的相干运动,这种大尺度运动对近壁区湍流和壁面摩擦阻力的产生有重要影响,为高雷诺数湍流减阻控制策略的设计提出了新的挑战.该文将对壁湍流相干结构的研究历史加以简单的回顾,重点介绍近壁区相干结构及其控制机理、近年来高雷诺数外区大尺度运动的研究进展,在此基础上提出高雷诺数减阻控制研究的关键科学问题.      

The spanwise spectra in wall-bounded turbulence

The pre-multiplied spanwise energy spectra of streamwise velocity fluctuations are investigated in this paper. Two distinct spectral peaks in the spanwise spectra are observed in low-Reynolds-number wall-bounded turbulence.The spectra are calculated from direct numerical simulation(DNS) of turbulent channel flows and zero-pressure-gradient boundary layer flows. These two peaks locate in the nearwall and outer regions and are referred to as the inner peak and the outer peak, respectively. This result implies that the streamwise velocity fluctuations can be separated into large and small scales in the spanwise direction even though the friction Reynolds number Reτ can be as low as 1000. The properties of the inner and outer peaks in the spanwise spectra are analyzed. The locations of the inner peak are invariant over a range of Reynolds numbers. However, the locations of the outer peak are associated with the Reynolds number,which are much higher than those of the outer peak of the pre-multiplied streamwise energy spectra of the streamwise velocity.     

A model for tracking inertial particles in a lattice Boltzmann turbulent flow simulation

A computationally inexpensive model for tracking inertial particles through a turbulent flow is presented and applied to the turbulent flow through a square duct having a friction Reynolds number of Re_τ = 300. Prior to introducing particles into the model, the flow is simulated using a lattice Boltzmann computation, which is allowed to evolve until a steady state turbulent flow is achieved. A snapshot of the flow is then stored, and the trajectories of particles are computed through the flow domain under the influence of this static probability field. Although the flow is not computationally evolving during the particle tracking simulation, the local velocity is obtained stochastically from the local probability function, thus allowing the dynamics of the turbulent flow to be resolved from the point of view of the suspended particles. Particle inertia is modeled by using a relaxation parameter based on the particle Stokes number that allows for a particle velocity history to be incorporated during each time step. Wall deposition rates and deposition patterns are obtained and exhibit a high level of agreement with previously obtained DNS computational results and experimental results for a wide range of particle inertia. These results suggest that accurate particle tracking through complex turbulent flows may be feasible given a suitable probability field, such as one obtained from a lattice Boltzmann simulation. This in turn presents a new paradigm for the rapid acquisition of particle transport statistics without the need for concurrent computations of fluid flow evolution.     

A Dissipation Rate Equation for Low-Reynolds-Number and Near-Wall Turbulence

Two-equation turbulence models are usually formulated for specific flow types and are seldom validated against a variety of flows to account for near-wall and low-Reynolds-number effects simultaneously. In addition to low-Reynolds-number effects, near-wall flows also experience wall blocking, which is absent in free flows. Consequently, near-wall modifications to two-equation models could be quite different from low-Reynolds-number corrections. Besides, it is known that existing two-equation models perform poorly when used to calculate plane wall jets and two-dimensional backstep flows. These problems could be traced to the modeling of the dissipation rate equation. In this paper an attempt is made to improve the modeling of the dissipation rate equation so that it could successfully predict both free and wall-bounded shear flows including plane wall jets and backstep flows. The predictions are compared with experimental and direct numerical simulation data whenever available. Most of the data used are obtained at low Reynolds numbers. Good correlation with data is obtained. Therefore, for the first time, a model capable of correctly predicting free and wall-bounded shear flows, backstep flows, and plane wall jets is available. Received: 12 December 1995 and accepted 12 November 1996     

A low Reynolds number variant of partially-averaged Navier-Stokes model for turbulence

A low Reynolds number (LRN) formulation based on the Partially Averaged Navier-Stokes (PANS) modelling method is presented, which incorporates improved asymptotic representation in near-wall turbulence modelling. The effect of near-wall viscous damping can thus be better accounted for in simulations of wall-bounded turbulent flows. The proposed LRN PANS model uses an LRN k-ε model as the base model and introduces directly its model functions into the PANS formulation. As a result, the inappropriate wall-limiting behavior inherent in the original PANS model is corrected. An interesting feature of the PANS model is that the turbulent Prandtl numbers in the k and ε equations are modified compared to the base model. It is found that this modification has a significant effect on the modelled turbulence. The proposed LRN PANS model is scrutinized in computations of decaying grid turbulence, turbulent channel flow and periodic hill flow, of which the latter has been computed at two different Reynolds numbers of Re = 10,600 and 37,000. In comparison with available DNS, LES or experimental data, the LRN PANS model produces improved predictions over the standard PANS model, particularly in the near-wall region and for resolved turbulence statistics. Furthermore, the LRN PANS model gives similar or better results - at a reduced CPU time - as compared to the Dynamic Smagorinsky model.