Particles In Turbulent Flow Research Articles

A novel method measuring the clustering of particles: Pseudo-gravitation

A novel pseudo-gravitation method is proposed to quantitatively measure the degree of the preferential concentration of particles in turbulent flows, where virtual gravitations are employed to evaluate the extent of particle accumulation. The pseudo-gravitation method introduces a nondimensional “Gravitation Index” (GĨ) to estimate the local concentration of particles and a nondimensional “Global Gravitation Index” (GGĨ) to quantify the degree of particle clustering across the whole domain. This method can effectively characterize both the Eulerian and Lagrangian properties of the particle preferential concentration, without the need for any predefined artificial parameters. Additionally, it is not only robust to the variation in the number of particles but also sensitive to the change in physical parameters, such as the Stokes number (St) and Reynolds number (Re).

Lagrangian particle tracking at large Reynolds numbers.

In the study of fluid turbulence, the Lagrangian frame of reference represents the most appropriate methodology for investigating transport and mixing. This necessitates the tracking of particles advected by the flow over space and time at high resolution. In the past, the purely spatial counterpart, the Eulerian frame of reference, has been the subject of extensive investigation utilizing hot wire anemometry that employs Taylor's frozen flow hypotheses. Measurements were reported for Taylor scale Reynolds number Rλ > 104 in atmospheric flows, which represent the highest strength of turbulence observed on Earth. The inherent difficulties in accurately tracking particles in turbulent flows have thus far constrained Lagrangian measurements to Taylor scale Reynolds numbers up to approximately Rλ = 103. This study presents the Lagrangian particle tracking setup in the MaxPlanck Variable Density Turbulence Tunnel (VDTT), where Taylor scale Reynolds numbers between 100 and 6000 can be reached. It provides a comprehensive account of the imaging setup within the pressurized facility, the laser illumination, the particles used, and the particle seeding mechanism employed, as well as a detailed description of the experimental procedure. The suitability of KOBO Cellulobeads D-10 particles as tracers within the VDTT is illustrated. The results demonstrate that there is no significant charge exhibited by the particles and that the impact of their inertia on the results is negligible across a wide range of experimental conditions. Typical data are presented, and the challenges and constraints of the experimental approach are discussed in detail.

Numerical investigation on the tracer followability of nitrogen droplets over the airfoil in cryogenic wind tunnel

Cryogenic wind tunnels (CWT) achieve high Reynolds number aerodynamic performance measurements by cooling the medium with liquid nitrogen. Utilization of naturally-occurring liquid nitrogen droplets as tracer particles for non-intrusive measurement applications in CWT shows great potential in the previous work. However, the droplet motion characteristics over the airfoil remain to be investigated, and the followability evaluation approach is lacking. Accordingly, an Euler-Lagrange model for transonic particle flow over the NACA0012–64 airfoil was established. The effect of flow characteristics on the particle motion was explored. The results reveal that the flow separation and shock wave phenomenon over the airfoil causing velocity deviation between airflow and droplet. The shock wave is the main deviation driver, and flow separation causing trace blind zones. Droplets larger than 10 μm fail to effectively follow the variation of airflow. The blind zone enlarges with angle of attack (AoA), particularly when AoA exceeding 10 degrees. Moreover, Stokes number is found to be inadequate for characterizing the followability of tracer particles in turbulent flow. Consequently, an evaluation method based on the Basset-Boussinesq-Oseen equation was developed. This research provides theoretical and technical support for advancing the use of nitrogen droplets as tracer particles in CWT.

Modified stochastic diffusion particle tracking model driven by skew Brownian motion: Analysis of sediment particle motion in turbulent flow under the effects of ejection and sweep.

Turbulent bursting events have been classified into outward interactions (Q1), ejections (Q2), inward interactions (Q3), and sweeps (Q4) in various studies. Ejections (Q2) and sweeps (Q4) have been identified as significant contributors to time consumption, momentum flux, and sediment flux. Additionally, research has shown that the distribution of these events varies nonuniformly at different bed elevations. Despite extensive investigations into the nonuniform distribution of turbulent bursting events, their impact on sediment transport has been rarely explored. In this work, we developed a modified stochastic diffusion particle tracking model (SD-PTM) driven by skew Brownian motion (SBM) using the stochastic Lagrangian approach to scrutinize sediment particle movement in turbulent flows. The model incorporates turbulent characteristics derived from a direct numerical simulation dataset, allowing for a comprehensive analysis of sediment particle dynamics. Moreover, the proposed model accounts for the nonuniform spatial distribution of ejection and sweep events, as well as the particle movement direction during these events. Numerical simulations of the model were conducted to trace sediment particle trajectories in the streamwise and vertical directions. The analysis of sediment transport involved calculating the variance of particle trajectories to examine anomalous diffusion. The model's performance was evaluated by comparing it with flow velocity and sediment concentration profiles obtained from measurements in previous studies. In conclusion, our study suggests that the motion of sediment particles in turbulent flow can be thoroughly investigated under extreme flow conditions using the modified SD-PTM driven by SBM.

Anisotropic Mean Flow Enhancement and Anomalous Transport of Finite-Size Spherical Particles in Turbulent Flows.

We investigate the influence of dispersed solid spherical particles on the largest scales of the turbulent Arnold-Beltrami-Childress (ABC) flow. The ABC flow is an ideal instance of a complex flow: it does not have solid boundaries, but possesses an inhomogeneous and three-dimensional mean shear. By tuning the parameters of the suspension, we show that particles modulate the largest scales of the flow toward an anisotropic, quasi-two-dimensional and more energetic state. In this regime, particles move along quasistraight trajectories and exhibit anomalous transport.

Polarity switch of PMMA powder transported through a PMMA duct

During pneumatic conveying, powder electrifies rapidly due to the high flow velocities. In our experiments, the particles even charge if the conveying duct is made of the same material, which might be caused by triboelectrification between two asymmetric contact surfaces. Surprisingly, we found the airflow rate to determine the polarity of the overall powder charge. This study investigates the charging of microscale PMMA particles in turbulent flows passing through a square PMMA duct. The particles are spherical and monodisperse. A Faraday at the duct outlet measured the total charge of the particles. At low flow velocities, the particles charged negatively after passing through the duct. However, the powder’s overall charge switched to a positive polarity when increasing the flow velocity.

Reduced Sediment Settling in Turbulent Flows Due To Basset History and Virtual Mass Effects

AbstractThe behavior of suspended particles in turbulent flows is a recalcitrant problem spanning wide‐ranging fields including geomorphology, hydrology, and dispersion of particulate matter in the atmosphere. One key mechanism underlying particle suspension is the difference between particle settling velocity (ws) in turbulence and its still water counterpart (wso). This difference is explored here for a range of particle‐to‐fluid densities (1–10) and particle diameter to Kolmogorov micro‐eddy sizes (0.1–10). Conventional models of particle fluxes that equate ws to wso result in eddy diffusivities and turbulent Schmidt numbers contradictory to laboratory experiments. Incorporating virtual mass and Basset history forces resolves these inconsistencies, providing clarity as to why ws/wso is sub‐unity for the aforementioned conditions. The proposed formulation can be imminently used to model particle settling in turbulence, especially when sediment distribution outcomes over extended time scales far surpassing turbulence time scales are sought.

Transport of inertial ellipsoidal particles in turbulent flow over rough walls

Transport of inertial ellipsoidal particles in turbulent flow over rough walls

Eulerian–Eulerian RSTM-PDF Modeling of Turbulent Particulate Flow

A novel 3D computational model was developed for the turbulent particulate two-phase flow simulation in the rectangular channel. The model is based on the Eulerian approach applied to 3D Reynolds-averaged Navier–Stokes modeling and statistical Probability Distribution Function method. The uniqueness of the method lies in the direct calculation of normal and transverse components of the Reynolds stresses for both gas and particles. Two cases were examined: a conventional channel flow and grid-generated turbulence flow. The obtained numerical results have been verified and validated by the experimental data, received from the turbulent particle dispersion test. The computed values of the particles’ turbulent dispersion and the maximum value of the particulate concentration distribution show good agreement with the experimental results. The examples are ranged from coal and other bulk material pneumatic transport, vertical fluidized beds, coal gasifiers, and chemical reactors.

Dynamical regimes and clustering of small neutrally buoyant inertial particles in stably stratified turbulence

We consider the Maxey-Riley equation for small neutrally buoyant inertial particles in the Boussinesq approximation. The main motivation is the study of phytoplankton and oceanic particles in turbulent flows. We show that particles behave as forced damped oscillators, with different regimes depending on the particles Stokes number and the fluid Brunt-V\"ais\"al\"a frequency. Using direct numerical simulations we study their dynamics and show that small neutrally buoyant particles in these flows tend to cluster in regions of low local vorticity.

Lagrangian stochastic model for the orientation of inertialess spheroidal particles in turbulent flows: An efficient numerical method for CFD approach

In this work, we propose a model for the orientation of inertialess spheroidal particles suspended in turbulent flows. This model consists in a stochastic version of the Jeffery equation that can be included in a statistical Lagrangian description of particles suspended in a flow. It is compatible and coherent with turbulence models that are widely used in CFD codes for the simulation of the flow field in practical large-scale applications. In this context, we propose and analyze a numerical scheme based on a splitting scheme algorithm that decouples the orientation dynamics into its main contributions: stretching and rotation. We detail its implementation in an open-source CFD software. We analyze the weak and strong convergence of both the global scheme and of each sub-part. Subsequently, the splitting technique yields to a highly efficient hybrid algorithm coupling pure probabilistic and deterministic numerical schemes. Various numerical experiments were implemented and the results were compared with analytical predictions of the model to assess the algorithm efficiency and accuracy.

Dust Settling From Turbulent Layers in the Free Troposphere: Implications for the Saharan Air Layer

AbstractDesert dust accounts for a substantial fraction of the total atmospheric aerosol loading. It produces important impacts on the Earth system due to its nutrient content and interactions with radiation and clouds. However, current climate models greatly underestimate its airborne lifetime and transport. For instance, super coarse Saharan dust particles (with diameters greater than 10 µm) have repeatedly been detected in the Americas, but models fail to reproduce their transatlantic transport. In this study, we investigated the extent to which vertical turbulent mixing in the Saharan Air Layer (SAL) is capable of delaying particle deposition. We developed a theory based on the solution to a one‐dimensional dust mass balance and validated our results using large‐eddy simulation (LES) of a turbulent shear layer. We found that eddy motion can increase the lifetime of suspended particles by up to a factor of 2 when compared with laminar flows. Moreover, we found that the increase in a lifetime can be reliably estimated solely as a function of the particle Peclet number (the ratio of the mixing timescale to the settling timescale). By considering both the effects of turbulent mixing and dust asphericity, we explained to a large extent the presence of super coarse Saharan dust in the Caribbean observed during the Saharan Aerosol Long‐Range Transport and Aerosol‐Cloud‐Interaction Experiment (SALTRACE) field campaign. The theory for the lifetime of coarse particles in turbulent flows developed in this study is also expected to be applicable in other similar geophysical problems, such as phytoplankton sinking in the ocean mixed layer.

Modeling the resuspension of small inertial particles in turbulent flow over a fractal-like multiscale rough surface

A generalized dynamic resuspension model for particles rolling on a surface with fractal-like multiscale roughness elements is introduced and compared with experimental measurements. Second, nonGaussian stochastic models for the flow velocity seen by a particle are compared with a Gaussian stochastic model. Third, particle resuspension is predicted using large-eddy simulations with a stochastic model for the subgrid-scale flow velocity. The present results confirm the importance of including the multiscale asperity model, nonGaussian flow velocity model, and particle subgrid-scale model to accurately predict resuspension dynamics.

Clusters of heavy particles in two-dimensional Keplerian turbulence

Protoplanetary disks are gaseous systems in Keplerian rotation around young stars, known to be turbulent. They include a small fraction of dust from which planets form. In the incremental scenario for planet growth, the formation of kilometer-size objects (planetesimals) from pebbles is a major open question. Clustering of particles is necessary for solids to undergo a local gravitational collapse. To address this question, the dynamic of inertial particles in turbulent flows with Keplerian rotation and shear is studied. Two-dimensional direct numerical simulations are performed to explore systematically two physical parameters: the rotation rate, which depends on the distance to the star, and the particle response time, which relates to their size. Shear is found to drastically affect the characteristics of the turbulent flow destroying cyclones and favoring the survival of anticyclones. Faster Keplerian rotation enhances clustering of particles. For intermediate sizes, particles concentrate in anticyclones. These clusters form in a hierarchical manner and merge together with time. For other parameter values, solids concentrate on fractal sets that get more singular with rotation. The mass distribution of particles is then found to be multifractal with small dimensions at large orders, intriguing for triggering their gravitational collapse. Such results are promising for a precise description and better understanding of planetesimal formation.

Statistical Descriptions of Inhomogeneous Anisotropic Turbulence

Descriptions are given of the Langevin and diffusion equation of passively marked fluid particles in turbulent flow with spatially varying and anisotropic statistical properties. The descriptions consist of the first two terms of an expansion in powers of C0−1, where C0 is an autonomous Lagrangian-based Kolmogorov constant: C0≈7. Solutions involve the application of methods of stochastic analysis while complying with the basic laws of physics. The Lagrangian-based descriptions are converted into Eulerian-based fixed-point expressions through asymptotic matching. This leads to novel descriptions for the mean values of the fluctuating convective terms of the conservation laws of continua. They can be directly implemented in CFD codes for calculating fluid flows in engineering and environmental analysis. The solutions are verified in detail through comparison with direct numerical simulations of turbulent channel flows at large Reynolds numbers.

Particle deposition and characteristics of turbulent flow in converging and diverging nozzles using Eulerian-Lagrangian approach

The current study conducts a thorough assessment of the deposition of aerosol particles in turbulent flows in both converging and diverging nozzles using the Lagrangian particle tracking model and the RNG k-ε turbulence model. The air-particle interaction depends on flow velocity, particle diameter, and types of flow sections when the particles are injected into the airflow. For the parametric simulation, Stokes number is varied from 0.0354 to 0.8265 with the corresponding particle diameter ranging from 2.00 to 10.00 μm, whereas Reynolds number is varied from 5000 to 10,000. Computational results show how the particle deposition efficiency in converging and diverging nozzles is influenced by Stokes number, diameter ratio of pipe, particle diameter, and Reynolds number. The deposition efficiency of a diverging nozzle is found to be lower than that of a converging nozzle, and the flow Reynolds number increases the deposition efficiency slightly in the diverging nozzle but gradually in the converging nozzle.

Clustering in laboratory and numerical turbulent swirling flows

We study the three-dimensional clustering of velocity stagnation points, of nulls of the vorticity and of the Lagrangian acceleration, and of inertial particles in turbulent flows at fixed Reynolds numbers, but under different large-scale flow geometries. To this end, we combine direct numerical simulations of homogeneous and isotropic turbulence and of the Taylor–Green flow, with particle tracking velocimetry in a von Kármán experiment. While flows have different topologies (as nulls cluster differently), particles behave similarly in all cases, indicating that Taylor-scale neutrally buoyant particles cluster as inertial particles.

On the agglomeration and breakage of particles in turbulent flows through pipe bends using CFD-PBE

Predicting the agglomeration and breakage of solid particles is important when designing a compact and efficient water purification process. A coupled computational fluid dynamics model is presented where the population balance equation is applied to track the particle size distribution for a periodic turbulent pipe flow with 180° bends for fluid Reynolds numbers of 15,000<Ref<35,000 and pipe bend radii of rB=dh,rB=1.5dh and rB=2.5dh. The critical parameters in the Euler-Euler model are analysed and values are chosen to describe the agglomeration of soot particles based on an experimentally obtained particle size distribution measured using a Malvern Mastersizer 3000. It is concluded that the particle Sauter mean diameter converges to a constant value independent of the pipe bend radius when Ref>30,000. The Sauter mean diameter increases from d32=42.7μm to d32=95μm without changing the total length of the static flocculator by choosing rB=dh and Ref=15,000.

Bayesian comparison of stochastic models of dispersion

Stochastic models of varying complexity have been proposed to describe the dispersion of particles in turbulent flows, from simple Brownian motion to complex temporally and spatially correlated models. A method is needed to compare competing models, accounting for the difficulty in estimating the additional parameters that more complex models typically introduce. We employ a data-driven method, Bayesian model comparison, which assigns probabilities to competing models based on their ability to explain observed data. We focus on the comparison between the Brownian and Langevin dynamics for particles in two-dimensional isotropic turbulence, with data that consist of sequences of particle positions obtained from simulated Lagrangian trajectories. We show that, while on sufficiently large time scales the models are indistinguishable, there is a range of time scales on which the Langevin model outperforms the Brownian model. While our set-up is highly idealised, the methodology developed is applicable to more complex flows and models of particle dynamics.

Study of preferential concentration in turbulent flows using combined graph theory and Voronoï analysis

Collisions between particles in turbulent flows may be enhanced by the formation of clusters due to the preferential concentration effect. However, the internal sub-structure of the clusters remains unclear. This paper describes using the “degree of a node” and the “shortest path length” from graph theory, in combination with Voronoï analysis, to gain further insight into both the structure and internal sub-structure of a cluster. This is demonstrated on experimental measurements obtained from a confined counter-flow/jet system. A minority of the particles, which comprise large clusters, are found to have a significantly large number of neighboring particles for collisions. However, particles which comprise small clusters typically have a random number of neighbors.