Experimental studies on particle behaviour and turbulence modification in horizontal channel flow with different wall roughness

Detailed measurements in a developed particle-laden horizontal channel flow (length 6 m, height 35 mm, the length is about 170 channel heights) are presented using phase-Doppler anemometry for simultaneous determination of air and particle velocity. The particles were spherical glass beads with mean diameters in the range of 60 µm-1 mm. The conveying velocity could be varied between about 10 m/s and 25 m/s, and the particle mass loading could reach values of about 2 (the mass loading is defined as the ratio of particle to gas phase mass flow rates), depending on particle size. For the first time, the degree of wall roughness could be modified by exchanging the wall plates. The influence of these parameters and the effect of inter-particle collisions on the profiles of particle mean and fluctuating velocities and the normalised concentration in the developed flow were examined. It was shown that wall roughness decreases the particle mean velocity and enhances fluctuating velocities due to irregular wall bouncing and an increase in wall collision frequency, i.e. reduction in mean free path. Thereby, the larger particles are mainly more uniformly distributed across the channel, and gravitational settling is reduced. Both components of the particle velocity fluctuation were reduced with increasing mass loading due to inter-particle collisions and the momentum loss involved. Moreover, the effect of the particles on the air flow and the turbulent fluctuations was studied on the basis of profiles in the developed flow and turbulence spectra determined for the streamwise velocity component. In addition to the effect of particle size and mass loading on turbulence modulation, the influence of wall roughness was analysed. It was clearly shown that increasing wall roughness also results in a stronger turbulence dissipation due to two-way coupling.     

Thermo-mechanical modeling of turbulent heat transfer in gas–solid flows including particle collisions

A thermo-mechanical turbulence model is developed and used for predicting heat transfer in a gas–solid flow through a vertical pipe with constant wall heat flux. The new four-way interaction model makes use of the thermal k_θ–τ_θ equations, in addition to the hydrodynamic k–τ transport, and accounts for the particle–particle and particle–wall collisions through a Eulerian/Lagrangian formulation. The simulation results indicate that the level of thermal turbulence intensity and the heat transfer are strongly affected by the particle collisions. Inter-particle collisions attenuate the thermal turbulence intensity near the wall but somewhat amplify the temperature fluctuations in the pipe core region. The hydrodynamic-to-thermal times-scale ratio and the turbulent Prandtl number in the region near the wall increase due to the inter-particle collisions. The results also show that the use of a constant or the single-phase gas turbulent Prandtl number produces error in the thermal eddy diffusivity and thermal turbulent intensity fields. Simulation results also indicate that the inter-particle contact heat conduction during collision has no significant effect in the range of Reynolds number and particle diameter studied.     

Particle resolved direct numerical simulation of a liquid–solid fluidized bed: Comparison with experimental data

Particle-resolved direct numerical simulations of a 3-D liquid–solid fluidized bed experimentally investigated by Aguilar-Corona (2008) have been performed at different fluidization velocities (corresponding to a range of bed solid volume fraction between 0.1 and 0.4), using Implicit Tensorial Penalty Method. Particle Reynolds number and Stokes number are O(100) and O(10), respectively. In this paper, we compare the statistical quantities computed from numerical results with the experimental data obtained with 3-D trajectography and High Frequency PIV. Fluidization law predicted by the numerical simulations is in very good agreement with the experimental curve and the main features of trajectories and Lagrangian velocity signal of the particles are well reproduced by the simulations. The evolution of particle and flow velocity variances as a function of bed solid volume fraction is also well captured by the simulations. In particular, the numerical simulations predict the right level of anisotropy of the dispersed phase fluctuations and its independence of bed solid volume fraction. They also confirm the high value of the ratio between the fluid and the particle phase fluctuating kinetic energy. A quick analysis suggests that the fluid velocity fluctuations are mainly driven by fluid–particle wake interactions (pseudo-turbulence) whereas the particle velocity fluctuations derive essentially from the large scale flow motion (recirculation). Lagrangian autocorrelation function of particle fluctuating velocity exhibits large-scale oscillations, which are not observed in the corresponding experimental curves, a difference probably due to a statistical averaging effect. Evolution as a function of the bed solid volume fraction and the collision frequency based upon transverse component of particle kinetic energy correctly matches the experimental trend and is well fitted by a theoretical expression derived from Kinetic Theory of Granular Flows.     

Response of the streaks, the active and passive eddies in an unsteady channel flow

Spanwise space–time correlations of the wall shear stress and the longitudinal velocity fluctuations in the low buffer layer of an unsteady channel flow are reported. The imposed amplitude is 20% of the centerline velocity and the imposed frequency covers a large range going from the quasi-steady limit to the bursting frequency of the corresponding steady flow. The unsteady spanwise correlation coefficient is investigated both through its own modulation characteristics (amplitude and phase shifts) and those of the resulting streak spacing. A good correspondence is found between the modulation of the streak spacing and that of the ejection period. The data is further analyzed by temporal filtering of the wall shear stress and streamwise velocity fluctuations. It is shown that the large outer-layer structures play a “passive” role in the unsteady response of the near wall turbulence. The inner wall eddies, in return, are amply responsible for the unsteady reaction of both the turbulent wall shear stress and the streamwise velocity intensities in the buffer layer.     

The effect of two-way coupling and inter-particle collisions on turbulence modulation in a vertical channel flow

Turbulence modulation due to its interaction with dispersed solid particles in a downward fully developed channel flow was studied. The Eulerian framework was used for the gas-phase, whereas the Lagrangian approach was used for the particle-phase. The steady-state equations of conservation of mass and momentum were used for the gas-phase, and the effect of turbulence on the flow-field was included via the standard k–ε model. The particle equation of motion included the drag, the Saffman lift and the gravity forces. Turbulence dispersion effect on the particles was simulated as a continuous Gaussian random field. The effects of particles on the flow were modeled by appropriate source terms in the momentum, k and ε equations. Particle–particle collisions and particle–wall collisions were accounted for in these simulations. Gas-phase velocities and turbulence kinetic energy in the presence of 2–100% mass loadings of two particle classes (50 μm glass and 70 μm copper) were evaluated, and the results were compared with the available experimental data and earlier numerical results. The simulation results showed that when the inter-particle collisions were important and was included in the computational model, the fluid turbulence was attenuated. The level of turbulence attenuation increased with particle mass loading, particle Stokes number, and the distance from the wall. When the inter-particle collisions were negligible and/or was neglected in the model, the fluid turbulence was augmented for the range of particle sizes considered.     

Reconstruction of a quasi-instantaneous image of coherent structures from hotwire signals obtained by a multi-point simultaneous measurement system

The turbulent velocity components (u, v) at 11 points in a reciprocating oscillatory turbulent flow have been measured simultaneously by a set of eleven X-type hotwire probes located in a plane perpendicular to the mean flow. Using a conditional sampling technique and a new method of data analysis for the inverse estimation of flow fields called the “virtual plate/load and MASCON model”, a quasi-instantaneous three-dimensional image of coherent structures of turbulence was first reconstructed directly from the experimental velocity data. The quasi-instantaneous image was expressed in terms of the velocity components u, v, w and the vorticity components ω_x ω_y, ω_z and we found that the large-scale coherent structure was composed of a pair of counter-rotating fluid motions with asymmetry which was quite different from that of the ensemble-averaged one. Flow patterns induced by the large-scale structure have been clarified by perspective representations visualized by computer simulations that produce timelines and streaklines of fluid particle traces. Results showed that the new experimental method was applicable for investigating the three-dimensional feature of coherent structures including asymmetry.     

Turbulent transport dissimilarity with modulated turbulence structure in channel flow of viscoelastic fluid

This experimental study investigated the turbulent transport dissimilarity with a modulated turbulence structure in a channel flow of a viscoelastic fluid using simultaneous particle image velocimetry and planar laser-induced fluorescence measurements. An instantaneous dye concentration field with fluctuating velocity vectors showed that mass was transferred by hierarchically large-scale wavy motions with inclination. A co-spectral analysis showed that the spatial phase modulation of the streamwise velocity and dye concentration fluctuations for the wall-normal velocity fluctuation corresponded to the relaxation time. The occurrence of intense dye concentration fluctuation and small streamwise velocity fluctuation in a thin boundary layer caused dissimilar turbulent transport because of the non-zero negative correlation of the streamwise velocity and dye concentration fluctuations for the wall-normal velocity fluctuation only on large scales. This explains the turbulent transport dissimilarity which leads to the zero averaged Reynolds shear stress and non-zero wall-normal turbulent mass flux.     

Dynamic coupling of fluid and structural mechanics for simulating particle motion and interaction in high speed compressible gas particle laden flow

In this work, structural finite element analyses of particles moving and interacting within high speed compressible flow are directly coupled to computational fluid dynamics and heat transfer analyses to provide more detailed and improved simulations of particle laden flow under these operating conditions. For a given solid material model, stresses and displacements throughout the solid body are determined with the particle–particle contact following an element to element local spring force model and local fluid induced forces directly calculated from the finite volume flow solution. Plasticity and particle deformation common in such a flow regime can be incorporated in a more rigorous manner than typical discrete element models where structural conditions are not directly modeled. Using the developed techniques, simulations of normal collisions between two 1 mm radius particles with initial particle velocities of 50–150 m/s are conducted with different levels of pressure driven gas flow moving normal to the initial particle motion for elastic and elastic–plastic with strain hardening based solid material models. In this manner, the relationships between the collision velocity, the material behavior models, and the fluid flow and the particle motion and deformation can be investigated. The elastic–plastic material behavior results in post collision velocities 16–50% of their pre-collision values while the elastic-based particle collisions nearly regained their initial velocity upon rebound. The elastic–plastic material models produce contact forces less than half of those for elastic collisions, longer contact times, and greater particle deformation. Fluid flow forces affect the particle motion even at high collision speeds regardless of the solid material behavior model. With the elastic models, the collision force varied little with the strength of the gas flow driver. For the elastic–plastic models, the larger particle deformation and the resulting increasingly asymmetric loading lead to growing differences in the collision force magnitudes and directions as the gas flow strength increased. The coupled finite volume flow and finite element structural analyses provide a capability to capture the interdependencies between the interaction of the particles, the particle deformation, the fluid flow and the particle motion.     

Single-Fluid Model of a Mixture for Laminar Flows of Highly Concentrated Suspensions

A model of laminar flow of a highly concentrated suspension is proposed. The model includes the equation of motion for the mixture as a whole and the transport equation for the particle concentration, taking into account a phase slip velocity. The suspension is treated as a Newtonian fluid with an effective viscosity depending on the local particle concentration. The pressure of the solid phase induced by particle-particle interactions and the hydrodynamic drag force with account of the hindering effect are described using empirical formulas. The partial-slip boundary condition for the mixture velocity on the wall models the formation of a slip layer near the wall. The model is validated against experimental data for rotational Couette flow, a plane-channel flow with neutrally buoyant particles, and a fully developed flow with heavy particles in a horizontal pipe. Based on the comparison with the experimental data, it is shown that the model predicts well the dependence of the pressure difference on the mixture velocity and satisfactorily describes the dependence of the delivered particle concentration on the flow velocity.     

Experimental and mechanistic study of dispersed micrometer-sized particle resuspension in a square straight duct with rough walls

The resuspension of graphite dust is an important phenomenon in the release of radioactivity and the safety of nuclear reactors during severe accidents. In this study, a visualization experimental platform is constructed to study effects of particle size, flow velocity, and wall roughness on the resuspension characteristics of graphite particles. A statistical model of particle resuspension applicable to monolayer dispersed particles is developed based on the moment equilibrium of the particles and the flow field characteristics, as calculated by the large-eddy simulation framework. The results show that particle resuspension can be divided into short- and long-term resuspension stages. Most particle resuspension occurs during the short-term stage. With increases in flow velocity and particle diameter, the aerodynamic or adhesion force acting on the particles increases, and corresponding particle resuspension fraction increases. The influence of rough walls on particle resuspension is related to both the force on the particles and the arm ratio between the wall morphology and the particle diameter. A comparison with the experimental results demonstrates that the particle resuspension model developed in this study accurately predicts the impact of flow velocity, particle size, and wall roughness on particle resuspension.     

Statistical models for predicting the effect of bidisperse particle collisions on particle velocities and stresses in homogeneous anisotropic turbulent flows

The purpose of this paper is to present and compare two statistical models for predicting the effect of collisions on particle velocities and stresses in bidisperse turbulent flows. These models start from a kinetic equation for the probability density function (PDF) of the particle velocity distribution in a homogeneous anisotropic turbulent flow. The kinetic equation describes simultaneously particle–turbulence and particle–particle interactions. The paper is focused on deriving the collision terms in the governing equations of the PDF moments. One of the collision models is based on a Grad-like expansion for the PDF of the velocity distributions of two particles. The other model stems from a Grad-like expansion for the joint fluid–particle PDF. The validity of these models is explored by comparing with Lagrangian simulations of particle tracking in uniformly sheared and isotropic turbulent flows generated by LES. Notwithstanding the fact that the fluid turbulence may be isotropic, the particle velocity fluctuations are anisotropic due to the impact of gravitational settling. Comparisons of the model predictions and the numerical simulations show encouraging agreement.     

Simulation of particles released near the wall in a turbulent boundary layer

A direct numerical simulation was used along with a Lagrangian particle tracking technique to study particle motion in a horizontal, spatially developing turbulent boundary layer along an upper-wall (with terminal velocity directed away from the wall). The objective of the research was to study particle diffusion, dispersion, reflection, and mean velocity in the context of two parametric studies: one investigated the effect of the drift parameter (the ratio of particle terminal velocity to fluid friction velocity) for a fixed and finite particle inertia, and the second varied the drift parameter and particle inertia by the same amount (i.e. for a constant Froude number). A range of drift parameters from 10⁻⁴ to 10⁰ were considered for both cases. The particles were injected into the simulation at a height of four wall units for several evenly distributed points across the span and a perfectly elastic wall collision was specified at one wall unit.Statistics collected along the particle trajectories demonstrated a transition in particle movement from one that is dominated by diffusion to one that is dominated by gravity. For small and intermediate sized particles (i.e. ones with outer Stokes numbers and drift parameters much less than unity) transverse diffusion away from the wall dominated particle motion. However, preferential concentration is seen near the wall for intermediate-sized particles due to inhomogeneous turbulence effects (turbophoresis), consistent with previous channel flow studies. Particle–wall collision statistics indicated that impact velocities tended to increase with increasing terminal velocity for small and moderate inertias, after which initial conditions become important. Finally, high relative velocity fluctuations (compared to terminal velocity) were found as particle inertia increased, and were well described with a quasi-one-dimensional fluctuation model.     

The effects of surface roughness geometry of flow undergoing Poiseuille flow by molecular dynamics simulation

Numerical simulation of Poiseuille flow of liquid Argon in a rough nano-channel using the non-equilibrium molecular dynamics simulation is performed. Density and velocity profiles across the channel are investigated in which roughness is implemented only on the lower wall. The Lennard–Jones potential is used to model the interactions between all particles. The effects of surface roughness geometry, gap between roughness elements (or roughness periodicity), surface roughness height and surface attraction energy on the behavior of the flow undergoing Poiseuille flow are presented. Results show that surface shape and roughness height have a decisive role on the flow behaviors. In fact, by increasing the roughness ratio (height to base ratio), the slip velocity and the maximum velocity in the channel cross section are reduced, and the density fluctuations near the wall increases. Results also show that the maximum density near the wall for a rough surface is less than a smooth wall. Moreover, the simulation results show that the effect of triangle roughness surface on the flow behavior is more than the cylindrical ones.     

表面粗糙度对微细管内气体流动特性的影响

采用了表面粗糙度粘性系数模型对微细管内的气体流动进行数值模拟，以研究微管内壁表面粗糙度对微管内气体流动的影响。运用本文改进的表面粗糙度粘性系数模型，数值模拟与实验数据十分吻合。计算结果表明，进出口压力一定时，表面粗糙度对流场的压力、密度及温度分布的影响不大，但是对速度场的影响十分显著，表面粗糙度使气体流动速度减小，并使壁面附近的速度梯度减小，从而使通过管道的气体质量流量减小，在微管内的气体流动中，表面粗糙度的影响是不能被忽略的。     

Particle collisions in a turbulent flow

An equation for the two-point probability density function of the two-particle the coordinate and velocity distribution is obtained. A closed system of equations for the first and second two-point moments of the velocity fluctuations of a pair of particles with allowance for the turbulent flow inhomogeneity is given. Boundary conditions for the equations of the particle concentration and the intensity of the relative random velocity during particle collision are obtained. A unified formula describing the interparticle collision process as a result of turbulent motion and the average relative particle velocity slip is obtained for the kernel of the coagulation equation. The effect of the average velocity slip of the particles and the carrier phase on the parameters of motion of the dispersed admixture and its coagulation is investigated on the basis of a two-point two-time velocity fluctuation autocorrelation function with two time and space scales representing the energy-bearing and small-scale motion of the fluid phase.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 104–116, March–April, 1996.     

Modelling of gas–solid turbulent channel flow with non-spherical particles with large Stokes numbers

This paper describes a complete framework to predict the behaviour of interacting non-spherical particles with large Stokes numbers in a turbulent flow. A summary of the rigid body dynamics of particles and particle collisions is presented in the framework of Quaternions. A particle-rough wall interaction model to describe the collisions between non-spherical particles and a rough wall is put forward as well. The framework is coupled with a DNS-LES approach to simulate the behaviour of horizontal turbulent channel flow with 5 differently shaped particles: a sphere, two types of ellipsoids, a disc, and a fibre. The drag and lift forces and the torque on the particles are computed from correlations which are derived using true DNS.The simulation results show that non-spherical particles tend to locally maximise the drag force, by aligning their longest axis perpendicular to the local flow direction. This phenomenon is further explained by performing resolved direct numerical simulations of an ellipsoid in a flow. These simulations show that the high pressure region on the acute sides of a non-spherical particle result in a torque if an axis of the non-spherical particle is not aligned with the flow. This torque is only zero if the axis of the particle is perpendicular to the local direction of the flow. Moreover, the particle is most stable when the longest axis is aligned perpendicular to the flow.The alignment of the longest axis of a non-spherical particle perpendicular to the local flow leads to non-spherical particles having a larger average velocity compared to spherical particles with the same equivalent diameter. It is also shown that disc-shaped particles flow in a more steady trajectory compared to elongated particles, such as elongated ellipsoids and fibres. This is related to the magnitude of the pressure gradient on the acute side of the non-spherical particles. Finally, it is shown that the effect of wall roughness affects non-spherical particles differently than spherical particles. Particularly, a collision of a non-spherical particle with a rough wall induces a significant amount of rotational energy, whereas a corresponding collision with a spherical particle results in mostly a change in translational motion.     

Motion of a sphere down an inclined plane in a viscous flow

The motion of a rigid particle near a wall in a fluid flow is an important element of particle transport by fluids. The aim of this study was to carry out an experimental and theoretical investigation of the gravity-induced motion of a rigid sphere in a viscous fluid in the presence of a transverse flow. The experimental study of this configuration is a way of understanding the specific features of the hydrodynamically constrained particle motion. It is established that the transverse motion of the fluid substantially increases the particle settling velocity, which grows with increase in the transverse flow velocity. This effect is most pronounced for small angles of inclination of the plane. The difference in the particle settling velocities in the presence and absence of the transverse flow could reach a factor of two.     

Large Eddy Simulations of turbulent particle-laden channel flow

This paper scrutinises the Large Eddy Simulation (LES) approach to simulate the behaviour of inter-acting particles in a turbulent channel flow. A series of simulations that are fully (four-way), two-way and one-way coupled are performed in order to investigate the importance of the individual physical phenomena occurring in particle-laden flows. Moreover, the soft sphere and hard sphere models, which describe the interaction between colliding particles, are compared with each other and the drawbacks and advantages of each algorithm are discussed. Different models to describe the sub-grid scale stresses with LES are compared. Finally, simulations accounting for the rough walls of the channel are compared to simulations with smooth walls. The results of the simulations are discussed with the aid of the experimental data of Kussin J. and Sommerfeld M., 2002, Experimental studies on particle behaviour and turbulence modification in horizontal channel flow with different wall roughness, Exp. in Fluids, 33, pp. 143–159 of Reynolds number 42,000 based on the full channel height. The simulations are carried out in a three-dimensional domain of 0.175 m × 0.035 m  × 0.035 m where the direction of gravity is perpendicular to the flow. The simulation results demonstrate that rough walls and inter-particle collisions have an important effect in redistributing the particles across the channel, even for very dilute flows. A new roughness model is proposed which takes into account the fact that a collision in the soft sphere model is fully resolved and it is shown that the new model is in very good agreement with the available experimental data.     

An analytical approach for the closure equations of gas–solid flows with inter-particle collisions

This work examines the effect of inter-particle collisions on the motion of solid particles in two-phase turbulent pipe and channel flows. Two mechanisms for the particle–particle collisions are considered, with and without friction sliding. Based on these collision mechanisms, the correlations of the various velocity components of colliding particles are obtained analytically by using an averaging procedure. This takes into account three collision coordinates, two angles and the distance between the centers of colliding particles. The various stress tensor components are obtained and then introduced in the mass, linear momentum and angular momentum equations of the dispersed phase. The current approach applies to particle–particle collisions that result from both the average velocity difference and the turbulent velocity fluctuations. In order to close the governing equations of the dispersed phase, the pseudo-viscosity coefficients are defined and determined by the time of duration of the inter-particle collision process. The model is general enough to apply to both polydisperse and monodisperse particulate systems and has been validated by comparisons with experimental data.