Increasing Stokes Number Research Articles

A quickly discrete-continuous phase interaction model for pore-scale motion of droplets in porous foams

The expensive computational cost of pore-scale modeling of droplets in porous foams limits the understanding and application of spray cooling techniques. Thus, a numerical model that can cheaply and quickly predict the interaction of moving droplets with the foam skeleton is valuable. In this work, a novel model based on foam geometry and octree (FGAO) is proposed for the rapid evaluation of discrete-continuous phase interactions in porous foams. The performance of the FGAO model is investigated for different Stokes and Weber numbers, with the full pore-scale model as a benchmark. The results show that the accuracy improves as the Stokes number increases, but the effect of the Weber number on the accuracy is complicated. The accuracy decreases as the We close to the intersection of the interaction region, while it improves as the Weber number is far away from the intersection of the interaction region. To quantitatively assess the error, a relative error (RE) and a weighted mean absolute percentage error (WMAPE) are introduced. The results show that the FGAO model has excellent accuracy with RE < 2.79 % at Stk > 10. At the criteria of WMAPE, the FGAO model performs well at the condition of the initial Weber number is far away from the intersection of the region of the Bai-Gosman model, with WMAPE < 7.3 % at We = 1 Stk = 50 and WMAPE < 3.9 % at We = 400 Stk = 50. Finally, the current method offers a significant advantage in computational speed compared to the full pore-scale model, with an improvement of about 62.9 times for Stk = 50, We = 10.

Clustering, rotation, and swirl of inertial particles in turbulent channel flow

Clustering dynamics of inertial particles in turbulent channel flow are studied via tessellation-based analysis of high-fidelity simulation data at Reτ≈230 with various values of mass loading (10%−100%) and the Stokes number (St+=[1−60]). We then characterise the solenoidal, rotational, and swirling motions of clusters by computing the probability density functions (PDFs) of the divergence, curl, and helicity of the particle velocity, as well as their dependence on wall-normal distance, using the methods of Oujia et al. (2020); Maurel–Oujia et al. (2023). Particle inertia gives heavier tails to the PDFs of divergence and curl, suggesting enhanced intermittency in the convergence/divergence of clusters, and in their rotational motions. The fluctuations of the divergence and curl are most intense in the buffer layer, due to the stronger fluctuations of fluid velocity there. Similarities are identified between the cluster dynamics in the logarithmic region and those in homogeneous isotropic turbulence, including the dependence of divergence, curl, and helicity on Stokes number. The effect of increasing mass loading on cluster dynamics is relatively small except in the viscous sublayer, where attenuation of clustering, rotation, and swirling motions are observed. The effect of increasing Stokes number on the viscous sublayer is different, resulting in more intense convergence/divergence and rotation of particle clusters, as the particles become more independent of the carrier fluid.

Particle transport in turbulent square duct flows with a free surface

Direct numerical simulation combined with a one-way coupled Lagrangian particle tracking technique is employed to investigate dilute particle-laden turbulent flows in open square ducts with a free surface. The focus is on examining the influence of the mean cross-stream secondary flow on particle transport near the wall, free surface, and across the duct cross section. Based on the duct half-width and mean friction velocity, a shear Reynolds number of Reτ = 300 is considered, with the corresponding particle Stokes numbers ranging from St+ = 0.31 to 260. The results reveal that particle concentration near the sidewalls is lower than that near the bottom wall, and the minimum particle concentration is observed at the free surface. Along the bottom wall centerline orientated upward, particle concentration gradually decreases. An exception to this is in the vicinity of the free surface where a slight increase is observed for the heavier particles (St+ ≥ 25), and the amplitude of this increase gradually declines as the Stokes number increases. In the streamwise direction near the free surface, heavier particles tend to preferentially concentrate in regions where the instantaneous transverse secondary flow velocity is negative. As the Stokes number increases, the position of the maximum streamwise velocity for heavier particles is closer to the free surface, and the rotation centers of inner and outer secondary particle motions gradually disappear. The streamwise root mean square velocity for the lightest St+ = 0.31 particles is higher than that for particles with higher inertia in the middle region of the free surface.

Dynamics and dispersion of inertial particles in circular cylinder wake flows: A two-way coupled Eulerian–Lagrangian approach

In this paper, the motion of inertial particles in three-dimensional (3D) unsteady cylindrical wake flow is investigated by a two-way coupled Eulerian–Lagrangian approach. At different flow Reynolds numbers (Re), the corresponding striking dynamic property and dispersion mechanism of four particle classes have been studied, with inertia parameterized by means of Stokes number (Sk). It is found that inertial particles with lower Stokes number are expelled from vortex cores, and coherent voids encompass the local Kármán vortex cells. As Stokes number increases, a low velocity particle channel could be formed, which almost coincides with the results in the literature. Moreover, with the increase of Reynolds number, numerous irregular coherent voids are observed in the cylinder wake, and the high-speed particles follow the fluid flow closely when they are contained in the vortices. Although the centrifugal force of Kármán vortex cells significantly affects the dynamics of inertial particles, the fluid flow modulation is believed to be responsible for the distinctive particle dispersion patterns in the vortex streets. For particles with medium inertia, the two-way coupled modulation weakens the centrifugal effect of vortex structures on the particles. This trend declines with the increase of Reynolds number, and vanishes with light particles, while both two-way coupled modulation and the centrifugal effect of vortex structures are almost equally effective with heavy particles. The investigations contribute to a better understanding of the particle-laden flows in practical applications, which will benefit the optimized design of certain machinery and equipment for the industry.

Particle dynamics in compressible turbulent vertical channel flows

In this work, we carry out direct numerical simulations of particle suspensions in the compressible turbulent vertical channel (TVC) flows with Mach number Ma = 1.5 and particle Stokes number St = 1–100. The compressibility effect is considered in the particle dynamic model for the first time in the study of compressible particle-laden wall turbulence. We find that in both incompressible and compressible flow, gravity weakens the wall-normal and spanwise fluctuations of particle velocities as the Stokes number increases. However, compared to the incompressible flow case, the compressible effect amplifies the mean velocity, fluctuations of velocity, and slip velocity of particle in the streamwise direction. The wall-normal and spanwise fluctuations of particle velocities are augmented by the compressible effect in the channel core region. Moreover, in the core region, the effect of fluid compressibility on the wall-normal and spanwise fluctuations of particle velocities attenuates as the Stokes number increases, indicating a competition between the compressible effect and the particle inertia effect. We, furthermore, conduct the quadrant analysis of the local fluctuation velocities of fluid at particle positions and observe preferential distributions in the second and the fourth quadrants at y+ = 12.5–13.5. For compressible TVC flows, the pattern of probability distributions is more elongated, and the percentage is slightly higher in the second and fourth quadrants than that of incompressible flows. This observation implies that more particles locate in the ejection and sweep events in compressible flows than that in incompressible flows, which is anticipated to influence the particle wall-normal transport.

Drop impact dynamic and directional transport on dragonfly wing surface

The ability of dragonflies to fly in the rain without being wetted by raindrops has motivated researchers to investigate the impact behavior of a drop on the superhydrophobic wings of dragonflies. This superhydrophobic surface is used as a reference for the design of directional surfaces and has attracted extensive attention owing to its wide applicability in microfluidics, self-cleaning, and other fields. In this study, the static contact angle and rebound process of a drop impacting a dragonfly wing surface are investigated experimentally, whereas the wetting pressure, Gibbs free energy, and Stokes number vs. coefficient of restitution are theoretically calculated to examine the dynamic and unidirectional transport behaviors of the drop. Results show that the initial inclination angle of the dragonfly wing is similar to the sliding angles along with the drop sliding. The water drop bounces from the bottom of the dragonfly wing to the distal position, demonstrating directional migration. The drop impacts the dragonfly wing surface, and the drop exhibits compression, recovery, and separation phases; in these three phases, the drop morphology evolves. As the Gibbs free energy and cross-sectional area evolve, the coefficient of restitution decreases as the drop continues to bounce, and the Stokes number increases.

Numerical study of large particles flowing in non‐Newtonian fluids with nearly neutral buoyancy force

The present work investigates the flow of sauce and food particles in food processing by adopting the Eulerian–Lagrangian approach. To account for the large size of the food particles, subroutines were developed to simulate the particle-wall collision and calculate the pressure gradient force. It was found that the particle-wall collision reduces the average and standard deviation of particle residence time. The standard deviation increases as the Stokes number increases. A critical Stokes number of around 2 is identified where the standard deviation increases dramatically. For a constant Stokes number, as the particle size increases, the standard deviation first increases and then decreases. Furthermore, it was found that the inclusion of the pressure gradient force reduces the average and standard deviation of particle residence time. The effects of this force increase as the particle size increases. These results reveal the nonlinear nature of the interactions between the flow and particles. Practical applications In food processing applications, a mixture of sauce and food particles is to be dispensed onto the meal tray. To ensure even reheating of the packaged food before serving, it is desired that the food particles should be uniformly distributed on the meal tray. Therefore, understanding the particle residence time distribution inside the dispenser is crucial to the design of the dispensing system. Through numerical investigation, the present work investigates the transport of food particles inside a sauce dispenser. The sauce is modeled as a non-Newtonian fluid. The results reveal the nonlinear nature of the interactions between the flow and particles. Based on these findings, better design of the dispensing system can be achieved.

Study of the Dilatancy/Contraction Mechanism of Landslide Fluidization Behavior Using an Initially Saturated Granular Column Collapse Simulation

AbstractFluidlike and integral sliding behaviors can be partly attributed to the dilatancy/contraction behavior of granular materials. A three‐dimensional two‐phase model and smoothed particle hydrodynamics method are applied to study the fluidization behavior by simulating the collapse of an initially fully saturated granular column. The dimensionless numbers (the initial aspect ratio, initial solid volume fraction, and Stokes number associated with the grain size) are varied to examine the collapse process and deposition characteristics. The profiles and front location during collapse highlight that the mechanism changes with the Stokes number and initial solid volume. The granular migration and pore pressure evolution characteristics are presented to clarify the differences in the collapse procedures and mechanisms pertaining to the simulation cases. The dimensionless final runout length and deposition height present monotonically increase and decrease following power laws with increasing initial aspect ratio, respectively; the dimensionless final runout length and deposition height also have monotonically decreasing and increasing relationships with increasing initial solid volume fraction and strongly increasing and decreasing characteristics during the transfer from the viscous flow regime to the inertial flow regime with increasing Stokes number, respectively. The simulation results indicate that the dynamic mechanism of the fluidization transformation is controlled by the Stokes number and initial solid volume fraction. Moreover, the coupling effect of the Stokes number, initial solid volume fraction and initial aspect ratio controls the collapse process of the initially saturated granular column.

An efficient model for the breakage of agglomerates by wall impact applied to Euler-Lagrange LES predictions

The present study completes the development of a model for predicting the effect of wall impacts on agglomerates in turbulent flows. Relying on an Euler-Lagrange hard-sphere approach this physical phenomenon is described in an efficient manner allowing practically relevant multiphase flow simulations at high mass loadings. In a recent study (Khalifa and Breuer, 2020) conditions for the onset of breakage and the resulting fragment size distribution were derived. In the present investigation a data-driven description of the post-breakage kinetics of the fragments is developed based on extensive DEM simulations taking a variety of impact conditions (impact velocity, impact angle, agglomerate size) into account. The description relates the velocity vectors of the fragments after breakage to three parameters: The reflection angle, the spreading angle and a velocity ratio of the magnitude of the fragment velocity to the impact velocity of the agglomerate. Relying on the DEM results Weibull distribution functions are used to describe the parameters of the wall-impact model. The shape and scale parameters of the Weibull distributions are found to mainly depend on the impact angle of the agglomerate. Consequently, relationships between the shape and the scale parameters and the impact angle are established for each of the three parameters based on a fourth-order regression. This allows to determine the velocity vectors of the fragments randomly based on the corresponding Weibull distributions of the reflection angle, the spreading angle and the fragment velocity ratio.The devised model is evaluated in a turbulent duct flow at five Reynolds numbers and three agglomerate strengths given by powders consisting of primary particles of different size. The analysis first concentrates on the pure wall-impact breakage but then also includes agglomerate breakup due to turbulence, drag forces and rotation allowing to determine the shares of the different physical phenomena. It is found that with increasing Stokes number the wall-impact breakage occurs less effectively due to the reduced responsiveness of the agglomerates to the secondary flow motions in the duct. However, in the very high range of St+ other mechanisms such as the turbophoresis and the lift force augment the breakage at walls. Comparing the contributions of the different breakage mechanism reveals that the wall impact is dominant at the lowest Reynolds numbers, whereas the drag stress prevails at high Re.

Transport of particles in a turbulent rough-wall pipe flow

Abstract

Mechanisms of particle preferential concentration induced by secondary motions in a dilute turbulent square duct flow

Particle-laden turbulent square duct flows at Reτ = 300 (based on the duct half-width and the mean friction velocity) are investigated using direct numerical simulation with one-way coupled Lagrangian particle tracking. Four particle-to-fluid density ratios are considered with the corresponding shear Stokes number St+ = 0.31, 25, 125, and 260. Particle motion is governed by drag, lift, added-mass, and pressure gradient forces. The main purpose of this work is to examine the effect of the turbulence-driven secondary flows on particle preferential accumulation and their dependence on the Stokes number. Results obtained indicate that the cross-stream secondary motions encourage inertial particles to accumulate preferentially in the duct corners, where the maximum of the cross-sectional particle concentration occurs. The extent of accumulation here is strongly dependent on the Stokes number, with the greatest accumulation found at St+ = 25. Interestingly, the maximum of the intensity of the secondary particle velocity along the corner bisector is also achieved at St+ = 25, whereas in the region adjacent to the wall, it is found to decrease with a particle Stokes number. Additionally, it is observed that the higher inertia particles are more easily trapped in the stagnation zone of secondary flows with low turbulence intensity in the corner region. In the near-wall region, the heavier particles (St+ ≥ 25) are prone to reside and form elongated clusters along the low-speed streamwise velocity streaks, with this trend less pronounced with the increasing Stokes number. Along the wall, away from the corner where the secondary motion is attenuated, particle accumulation is dominated by the near-wall coherent vortices. This phenomenon is further discussed using a region-based correlation analysis between the particle spatial distribution and local flow topology. An in-depth particle dynamic analysis determines that the average cross-sectional drag force resulting from the secondary flow is mainly responsible for the particle motion throughout the duct cross section, which tends to push particles away from the walls in the near-wall region but shows the exact opposite trend in the bulk flow region. Moreover, the pressure gradient force also plays an important role for low-inertia particles. As the Stokes number is increased, the lift force becomes progressively dominant in the viscous sublayer, acting to pull particles toward the corners and walls of the duct.

Evaporating droplets in shear turbulence

This paper investigates droplets that evaporate and cluster in shear turbulence with direct numerical simulations. The flows are statistically stationary and homogeneous, which reduces the physical complexity and simplifies the statistical analysis. The mass loadings are about 0.1, the Stokes numbers are about 1, and the Taylor-scale Reynolds numbers are about 60. The simulations show that the clusters are anisotropic and inclined toward the flow direction on large scales, but isotropic on small scales. When the mass loading increases, the clusters contain more droplets, but their size remains unchanged, and the droplets in clusters experience higher vapor mass fractions. When the Stokes number increases, the clusters contain fewer droplets and become larger, and the droplets in clusters experience lower vapor mass fractions. When the Reynolds number increases, the clusters contain more, smaller droplets and become smaller, and the inclination angles of the clusters change.

Collisions and caustics frequencies of long flexible fibers in two-dimensional flow fields

The present work analyzes numerical simulations of long flexible fibers in two-dimensional flows. The focus is on the frequency at which caustics occur and the characterization of the collisions among fibers. The continuous flexible fibers are modeled as a set of connected rigid cylinders, where forces are applied to the center of mass of each cylinder determining their motion and fiber deformation. A domestic numerical code, which implements a fourth-order Runge–Kutta method to solve the system of ordinary differential equations, was validated against experimental data in a previous study. The two-dimensional steady analytical velocity fields correspond to the Arnold–Beltrami–Childress flows. Simulations are performed for a wide range of Stokes numbers ranging from 0.05 to 10.87. In a previous study, the frequency of caustics formation was shown to correlate strongly with fiber clustering. Now, a dimensionless caustics frequency is related to the Stokes number. The number of collisions correlates negatively with the Stokes number and positively with the clustering and the frequency of caustics formation. At low Stokes numbers, collisions are preferentially perpendicular, decreasing the angle of collision as the Stokes number increases. Most of the collisions occur at low relative velocities between the two colliding fibers. The angle of collision is strongly determined by vorticity and inertia, while the relative velocities of the fibers colliding seem to be determined by the characteristic velocity field.

Clustering behaviour and settling velocity of bidisperse inertial particles in turbulent open channel flow

The clustering behaviour and settling velocity of bidisperse inertial particles with sub-millimetre diameters travelling in a turbulent open channel flow are investigated using the simultaneous particle image velocimetry and particle tracking velocimetry measurement technique. Instantaneous images of flow field and inertial particles are separated based on different wavelengths of light emitted by fluorescent seeding particles and inertial particles. Four flow configurations of turbulence are generated by turbulence grids with different sizes in the open channel. The clustering behaviour of monodisperse and bidisperse inertial particles and the discrepancy between them in the different flow cases are studied. We found that bidisperse inertial particles have weaker clustering phenomenon as compared with corresponding monodisperse inertial particles and this weak clustering phenomenon is almost consistent when the Taylor microscale Reynolds number Reλ changes from 90 to 267. The relationship between settling velocity and local concentration of inertial particles is then investigated. The results support the preferential concentration as the mechanism for the enhancement of settling velocimetry when the normalized particle concentration is in the range of 0.1~10. However, the anisotropy property and large eddy effect in turbulence will greatly change the interaction between inertial particles and turbulent flows and further alter their settling velocity, such as the average settling velocity decreasing with increasing Stokes number which depends on the dissipation time scale. Accordingly, we propose a new dimensionless multiscale parameter SvηReL1/2 to take into account the effect of large eddies and turbulence anisotropy on the settling velocity. With the simultaneous measurement of particle settling velocities and fluid velocities, we also analyse the unsteady force term in the particle dynamic equation. When the turbulence intensity is small and/or the particle inertia related to particle diameter and density ratio between inertial particle and fluid is small, the unsteady term can have a large contribution and it should not be neglected in the particle dynamic equation for the point-particle method in the numerical simulations of particle-laden flows.

Acceleration of small heavy particles in homogeneous shear flow: direct numerical simulation and stochastic modelling of under-resolved intermittent turbulence

The acceleration of inertial particles in a homogeneous shear flow may vigorously respond to the intense flow structures induced by the mean shear. In this study, by direct numerical simulation (DNS) of particle-laden shear flow, we observe the statistical properties of those accelerations, and then we assessed the recently proposed simulation approach in which the effect of intermittency on residual scales is linked directly with coarsely resolved flow turbulence. First, we focused on the acceleration statistics of fluid particles in a homogeneous shear flow. Consistent with previous findings in homogenous isotropic turbulence, the norm and the direction of fluid acceleration in shear flow are shown to be conditioned by the dynamics of intermittent long-lived vortical structures. The averaged acceleration norm of the fluid particle exhibits a pseudo-cyclic behaviour, which is a signature of the periodic action of the largest confined vortices against the mean shear. The long correlation time of the acceleration norm, of the order of the integral time, the high level of fluctuations of the acceleration norm (very close to the magnitude of the mean norm of acceleration) and the log-normality in its statistical distribution reflect the impact of intense flow structures in shear flow. The presence of these zones results also in highly non-Gaussian statistics of the acceleration of a fluid particle and its velocity increments at small time lags. Contrary to the acceleration norm, the acceleration direction of a fluid particle is observed to be short, of the order of the Kolmogorov time, and to be statistically independent of the acceleration norm. The short-time correlation of the acceleration direction is attributed usually to effects of centripetal forces in intense vorticity filaments. We suggest that, in homogeneous shear turbulence, there may be a supplementary effect on the acceleration direction: the vortex, stretched by the mean shear, may exert the preferential direction of fluid particle acceleration. As evidence, our DNS shows that fluid particles are accelerated preferentially in the direction of longitudinal vortical tubes, effectively stretched by the imposed mean shear. Concerning simulations with heavy point-wise particles, it is shown that, when the inertia of a particle is not high, its acceleration closely follows all the aforementioned properties of the fluid particle acceleration. Particularly, an inertial particle is also entrained by accelerating motion in the direction of the effectively stretched vortical tubes. Although with increasing Stokes number of the inertial particle, the effects of strong intermittency in the flow are filtered, it is shown that the alignment of the particle acceleration direction with vortical tubes is amplified – particles with higher inertia respond to solicitations of stronger vortical structures. An alternative to the Maxey (J. Fluid Mech., vol. 174, 1987, pp. 441–465) preferential sweeping mechanism is discussed in this paper. When the shear turbulence is under-resolved, we employed the large-eddy simulation (LES) equations with a forcing term on the smallest resolved scales in order to simulate stochastically the effects of the dynamics on the residual scales. The forcing term is expressed with two independent stochastic processes, one for its norm and another for its direction. While the norm of acceleration is modelled using Pope’s log-normal process with the integral time for correlation, its direction is modelled in the framework of an Ornstein–Uhlenbeck process on the unit sphere. Consistently with our DNS, the latter process contains two presumed times: the homogeneous strain rate is specified as typical time of relaxation towards the direction of resolved vorticity, and the Kolmogorov time is presumed as a typical time of the diffusion process on the unit sphere. The high efficiency of this approach is demonstrated in prediction of the small-scale dynamics observed in DNS, even in the case when the shear length scale is not resolved by LES.

Numerical study on characteristics of particle deposition efficiency on different walls of 90° square bend

A better understanding of the characteristics of particle deposition in bend would help in designing a sampling bend. In this paper, gas-solid flow in 90° bend was simulated using the RNG k-ɛ turbulence model and the Lagrangian particle-tracking model. The preliminary results show that the deposition efficiency in 90° square bend is lower than that in 90° circular bend. Afterwards, the flow field, particle trajectories, and effect of curvature ratio on deposition efficiency on different walls were analyzed in 90° square bend. The results show that the main deposition location is related to the Stokes number. On inner wall, the deposition efficiency increases first and then decreases as the Stokes number increases, and particles mainly deposit in middle deflection angles range. Moreover, increasing the curvature ratio changes the flow field in the bend and, in turn, the deposition efficiency on inner wall and distributions of deposition efficiency on outer wall.

Particles in turbulent separated flow over a bump: Effect of the Stokes number and lift force

Particle-laden turbulent flow that separates due to a bump inside a channel is simulated to analyze the effects of the Stokes number and the lift force on the particle spatial distribution. The fluid friction Reynolds number is approximately 900 over the bump, the highest achieved for similar computational domains. The presence of the bump creates a complex background flow with a recirculating region and a strong shear layer. A range of particle Stokes numbers are considered, each simulated with and without the lift force in the particle dynamic equation. The effect of the lift force on the particle concentration is dominant in regions of high spanwise vorticity, particularly at the walls and in the shear layer. The concentration change is of the order of thousands when compared to cases where the lift force is omitted. At a low Stokes number, the particles segregate at both top and bottom walls and are present in the recirculating region. As the Stokes number increases, particles bypass the recirculating region and their redistribution is mostly affected by the strong shear layer. Particles segregate at the walls and particularly accumulate in secondary recirculating regions behind the bump. At higher Stokes numbers, the particles create reflection layers of high concentration due to their inertia as they are diverted by the bump. The fluid flow is less influential, and this enables the particles to enter the recirculating region by rebounding off walls and create a focused spot of high particle concentration.

Accumulation of heavy particles in circular bounded vortex flows induced by two small rotating cylinders

In the present study, we adopt an Eulerian–Lagrangian CFD model based on the discrete element method (DEM) and immersed boundary method (IBM) to numerically investigate the accumulation behavior of heavy particles in circular bounded vortex flows induced by two small rotating cylinders. Both one-way and two-way couplings combined with the particle-particle and particle-wall collisions which are resolved by a hard-sphere approach are analyzed and effects of Stokes number, Reynolds number, the center-to-center distance between the circular domain and each small cylinder (r1) and particle number are also comprehensively explored. It is found that, under one-way coupling, there is always a stable state for the accumulation of particles trapped inside the circular domain. Moreover, five different particle accumulation patterns are identified as the two small rotating cylinders move away from the domain center and the critical values of r1 are also reported. However, under two-way coupling, the motion of the particles is irregular and the stable closed trajectories or accumulation points appearing in cases under one-way coupling cease to exist, due to the intense interaction between particles and the gas phase. In addition, many more particles accumulate on the wall under two-way coupling than under one-way coupling at the same conditions, demonstrating that the influence of particles on the flow will in turn strongly affect the particle motion and push more particles to the wall. The percentage of particles accumulated on the wall increases with increasing Stokes number and Reynolds number, whereas it decreases as the center-to-center distance between the circular domain and each small rotating cylinder increases under both one-way and two-way couplings.

Effects of the particle Stokes number on wind turbine airfoil erosion

Under natural conditions, wind turbines are inevitably eroded by the action of sand-wind flow. To further investigate the effects of dust drift on the erosion of the wind turbine blades in sand-wind environments, the effects of the wind velocity, particle diameter, and particle density on the erosion of wind turbine airfoils are studied, and the effects of the particle Stokes number on the airfoil erosion are discussed. The results show that, when the angle of attack (AOA) is 6.1°, there will be no erosion on the airfoil surface if the particle Stokes number is lower than 0.013 5, whereas erosion will occur if the particle Stokes number is higher than 0.015 1. Therefore, there exists a critical range for the particle Stokes number. When the particle Stokes number is higher than the maximum value in the critical range, airfoil erosion will occur. The result is further confirmed by changing the particle diameter, particle density, and inflow speed. It is shown that the erosion area on the airfoil and the maximum erosion rate are almost equal under the same particle Stokes number and AOA. The extent of airfoil erosion increases when the particle Stokes number increases, and the critical particle Stokes number increases when the AOA increases. Moreover, the geometric shape of the airfoil pressure surface greatly affects the airfoil erosion, especially at the curvature near the leading edge.

Accumulation of heavy particles in a circular bounded vortex flow: Parameter influence and comparison

In this work, the accumulation behavior of heavy particles in a circular bounded viscous vortex flow has been explored by an Euler–Lagrange CFD model. Inter-particle and particle-wall collisions are resolved by a hard-sphere model. Effects of Stokes number, the size and the location of the small rotating cylinder are investigated under both one-way and two-way couplings. Results show that, under one-way coupling, most particles will accumulate at one point inside the domain and the accumulation point will move farther away from the stagnation point of the flow field as Stokes number increases. However, under two-way coupling, there is no accumulation point inside the domain. Instead the majority of particles accumulate on the circular wall. As Stokes number enhances, more particles will accumulate on the wall under both one-way and two-way couplings. The slight change of the rotating cylinder's size has little influence on the results, implying the reliability of using the small rotating cylinder to induce the vortex flow. However, the variation in the rotating cylinder's location has a significant impact on the results. As the small cylinder moves farther away from the center of the circular domain, the accumulation point can extend to an accumulation circle under one-way coupling, and less particles will accumulate on the wall under both one-way and two-way couplings.