Critical Stokes Number for Gas-Solid Flow Erosion of Wind Turbine Airfoil

Wind turbine blades are inevitable to be eroded in wind-sand environment,so it is crucial to identify the flow conditions under which the erosion happens.Here,the effect of the sand diameter on wind turbine airfoil is first investigated.When the sand diameter is less than 3μm,the sands will bypass the airfoil and no erosion occurs.When the sand diameter is larger than 4μm,the sand grains collide with the airfoil and the erosion happens.Thus,there must be a critical sand diameter between 3μm and 4μm,at which the erosion is initiated on the airfoil surface.To find out this critical value,aparticle Stokes number is introduced here.According to the range of the critical sand diameter mentioned above,the critical value of particle Stokes number is reasonably assumed to be between 0.007 8and 0.014.The assumption is subsequently validated by other four factors influecing the erosion,i.e.,the angle of attack,relative thickness of the airfoil,different series airfoil,and inflow velocity.Therefore,the critical range of Stokes number has been confirmed.

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.

Effect of Stokes number on energy modulation of the fluid in turbulent particle-laden channel flows

The effect of Stokes number on the kinetic energy(KE)budget in particle-laden turbulent channel flows is examined by conducting two-way coupled direct numerical simulations using the Eulerian-Lagrangian approach.The friction Reynolds number of the single phase channel flow is Re_(τ)=180,the particle mass loading and volume fraction areφ_(m)=0.2,φ_(v)≈10−4,and the Stokes numbers range from St^(+)=14–92.The statistics show that due to the presence of solid particles,the mean velocity is reduced in the vicinity of the wall but enhanced in the outer region,and the off-streamwise intensity of fluctuated velocity and the Reynolds stress are reduced in the whole channel.The analysis on the budgets of turbulent kinetic energy(TKE)finds that the presence of particles induces a significant reduction on both the production and dissipation rates.With increasing Stokes number St^(+),both the production and dissipation rates exhibit non-monotonical trends,i.e.,both initially decrease for St^(+)<40 and then transit to growth after St^(+)>40.This suggests that the particle-induced suppression on TKE production and dissipation is the strongest nearly at St^(+)=40.It is also found that particles act as an additional sink/source term in the budgets of both mean-flow kinetic energy(MKE)and TKE.In addition,we investigate the influence of St^(+)on the“zero point”which indicates the balance of exchanging energy between the particle and fluid phases.It is shown that with increasing St^(+),the“zero point”moves toward the wall,suggesting that the position of perfect following between particle and fluid is closer to the wall with larger St^(+).The present results reveal the Stokes number effects on the spatial transport mechanisms of MKE,TKE in turbulent channel flows laden with inertial particles.

Numerical simulation of slurry jets using mixture model

Slurry jets in a static uniform environment were simulated with a two-phase mixture model in which flow-particle interactions were considered. A standard k-e turbulence model was chosen to close the governing equations. The computational results were in agreement with previous laboratory measurements. The characteristics of the two-phase flow field and the influences of hydraulic and geometric parameters on the distribution of the slurry jets were analyzed on the basis of the computational results. The calculated results reveal that if the initial velocity of the slurry jet is high, the jet spreads less in the radial direction. When the slurry jet is less influenced by the ambient fluid （when the Stokes number St is relatively large）, the turbulent kinetic energy k and turbulent dissipation rate e, which are relatively concentrated around the jet axis, decrease more rapidly after the slurry jet passes through the nozzle. For different values of St, the radial distributions of streamwise velocity and particle volume fraction are both self-similar and fit a Gaussian profile after the slurry jet fully develops. The decay rate of the particle velocity is lower than that of water velocity along the jet axis, and the axial distributions of the centerline particle streamwise velocity are self-similar along the jet axis. The pattern of particle dispersion depends on the Stokes number St. When St = 0.39, the panicle dispersion along the radial direction is considerable, and the relative velocity is very low due to the low dynamic response time. When St = 3.08, the dispersion of particles along the radial direction is very little, and most of the particles have high relative velocities along the streamwise direction.

Turbulent Modulation in Particulate Flow: A Review of Critical Variables

A review of the main mechanisms influencing turbulent modulation in the presence of spherical and non-spherical particles is presented. The review demonstrates the need for more numerical and experimental work with higher accuracy than obtained so far and the need to resolve the flow near the surface of particles with the aim to re-evaluate the quantitative effect of different parameters on turbulent modulation. The review reveals that non-spherical particles have more adverse effect on turbulence as compared to spherical ones, for the same ambient conditions.

Flow instability of nanofuilds in jet

The flow instability of nanofluids in a jet is studied numerically under various shape factors of the velocity profile, Reynolds numbers, nanoparticle mass loadings,Knudsen numbers, and Stokes numbers. The numerical results are compared with the available theoretical results for validation. The results show that the presence of nanoparticles enhances the flow stability, and there exists a critical particle mass loading beyond which the flow is stable. As the shape factor of the velocity profile and the Reynolds number increase, the flow becomes more unstable. However, the flow becomes more stable with the increase of the particle mass loading. The wavenumber corresponding to the maximum of wave amplification becomes large with the increase of the shape factor of the velocity profile, and with the decrease of the particle mass loading and the Reynolds number. The variations of wave amplification with the Stokes number and the Knudsen number are not monotonic increasing or decreasing, and there exists a critical Stokes number and a Knudsen number with which the flow is relatively stable and most unstable,respectively, when other parameters remain unchanged. The perturbation with the first azimuthal mode makes the flow unstable more easily than that with the axisymmetric azimuthal mode. The wavenumbers corresponding to the maximum of wave amplification are more concentrated for the perturbation with the axisymmetric azimuthal mode.

Two-phase micro-and macro-time scales in particle-laden turbulent channel flows

The micro- and macro-time scales in two-phase turbulent channel flows are investigated using the direct nu- merical simulation and the Lagrangian particle trajectory methods for the fluid- and the particle-phases, respectively. Lagrangian and Eulerian time scales of both phases are cal- culated using velocity correlation functions. Due to flow anisotropy, micro-time scales are not the same with the theo- retical estimations in large Reynolds number （isotropic） tur- bulence. Lagrangian macro-time scales of particle-phase and of fluid-phase seen by particles are both dependent on particle Stokes number. The fluid-phase Lagrangian inte- gral time scales increase with distance from the wall, longer than those time scales seen by particles. The Eulerian inte- gral macro-time scales increase in near-wall regions but de- crease in out-layer regions. The moving Eulerian time scales are also investigated and compared with Lagrangian integral time scales, and in good agreement with previous measure- ments and numerical predictions. For the fluid particles the micro Eulerian time scales are longer than the Lagrangian ones in the near wall regions, while away from the walls the micro Lagrangian time scales are longer. The Lagrangian integral time scales are longer than the Eulerian ones. The results are useful for further understanding two-phase flow physics and especially for constructing accurate prediction models of inertial particle dispersion.

Collection efficiency in a three-dimensional randomly arranged dual-layer granular bed filter

The dual-layer granular bed filter packed with randomly arranged granules was simulated to study the effects of bed depth of the lower layer of fine granules and the inlet gas velocity on the collection mechanism.The computational results show that the collection efficiency is much better from this granular bed than a single-layer granular bed,especially for particle diameters of 1-10μm.The inlet gas velocity has less effect on the grade collection efficiency of the dual-layer granular bed than of the single-layer granular bed.The dual-layer granular bed provides a high collection efficiency and low pressure drop.The relationship between the grade collection efficiency and the Stokes number(St)based on the inlet gas velocity is obtained.If St is below a threshold,the grade collection efficiency remains stable;if St is in value above threshold,the grade collection efficiency increases linearly with lg(St).As the bed depth of the lower layer of fine granules increases,the threshold for St shifts forward.

Numerical study of gas-solid two-phase flow and erosion in a cavity with a slope

Gate valve is mainly used to turn on or turn off the pipeline in pneumatic conveying.When the gate valve is fully open,the particles are easy to collide with the cavity rear wall and enter into the cavity,resulting in particles’accumulation in the cavity.The particles in cavity will accumulate between the cavity bottom and the flashboard bottom wall and prevent the gate from turning off normally.Meanwhile,the particles’collision with cavity rear wall will cause serious erosion.Both the particles’accumulation and erosion will cause the poor sealing of the gate valve,further resulting in the leakage of the pipeline system.To reduce the particles’accumulation in cavity and erosion on cavity when the gate valve is fully open,we simplify the gate valve into a cavity structure and study it.We find that adding a slope upstream the cavity can effectively reduce the particles’accumulation in the cavity and the erosion on the cavity rear wall.In this work,Eulerian-Lagrangian method in commercial code(FLUENT)was used to study the gas-solid two-phase flow and erosion characteristics of a cavity with a slope.The particle distribution shows that the particles with Stokes number St=1.3 and St=13 cannot enter the cavity due to the slope,but the particles with St=0.13 enter the cavity following the gas.For St=13,the particles collide with the wall many times in the ideal cavity.Erosion results show that the slope can transfer the erosion on cavity rear wall to the slope and reduce the maximum erosion rate of the wall near the cavity to some degrees.

Dynamic modeling of micro- and nano-sized particles impinging on the substrate during suspension plasma spraying

Suspension plasma spraying （SPS） can be utilized to manufacture finely structured coatings. In this process, liquid suspended with microor nano-sized solid particles is injected into a plasma jet. It involves droplet injection, solvent evaporation, and discharge, acceleration, heating, and melting of the solid particles. The high-speed and high-temperature particles final- ly impact on the substrate wall, to form a thin layer coating. In this study, a comprehensive numerical model was developed to simulate the dynamic behaviors of the suspension droplets and the solid particles, as well as the interactions between them and the plasma gas. The plasma gas was treated as compressible, multi-component, turbulent jet flow, using Navier-Stokes equations solved by the Eulerian method. The droplets and solid particles were treated as discrete Lagrangian entities, being tracked through the spray process. The drag force, Saffman lift force, and Brownian force were taken into account for the aerodynamic drag force, aerodynamic lift force, and random fluctuation force imposed on the particles. Spatial distributions of the micro- and nano-sized particles are given in this paper and their motion histories were observed. The key parameters of spray distribution, including particle size and axial spray distance, were also analyzed. The critical size of particle that follows well with the plasma jet was deduced for the specified operating conditions. Results show that in the downstream, the substrate influences the flow field structure and the particle characteristics. The appropriate spray distances were obtained for different microand nano-sized particles.

Micropaticle transport and deposition from electrokinetic microflow in a 90° bend

In this study, the irreversible deposition of microparticles from electrokinetic microfluidic flow in a 90° bend was exami- ned both computationally and theoretically. The flow and electric fields were firstly simulated by the finite volume method, and then a large number of microparticles were injected and traced by the one-way coupling Lagrangian model, incorporating the electrical, hydrodynamic and near-wall repulsive forces exerted on the microparticles. The simulation results indicate that the microparticles with larger size are repelled to close to the upper region of the outer wall under the effect of dielectrophoresis （DEP） force, and the near-wall repulsive force which prevented particles from colliding with the wall would decrease the particles＇ ultimate deposition efficiency. In addition, the specified exponential relationship between the particle deposition efficiency and its relaxation time or par- ticle Stokes number are theoretically derived when the near-wall repulsive force is considered or not.