Particle Reynolds Number Research Articles

Direct numerical simulation of moderate‐Reynolds‐number flow past arrays of ellipsoids

AbstractThrough particle‐resolved direct numerical simulations of flow past arrays of ellipsoids, the hydrodynamic force on ellipsoids depends on the particle orientation, aspect ratio, particle Reynolds number, and solid volume fraction is revealed at moderate Reynolds numbers. The results show that the mean drag force on arrays of prolate/oblate ellipsoids decreases/increases as the Hermans orientation factor increases when flows are in the reference direction defined by the average symmetric axis of particles. The individual drag force on a prolate/oblate ellipsoid increases/decreases with the increase of incidence angle, and it is also affected by the orientation of surrounding particles. The individual lift force is also significant when the aspect ratio is away from unity at large particle Reynolds numbers. Based on simulation results, correlations for the hydrodynamic force on ellipsoids at arbitrary particle Reynolds numbers, solid volume fractions, Hermans orientation factors, incidence angles, and aspect ratios are formulated.

The effect of electric double layers, zeta potential and pH on apparent viscosity of non‐Brownian suspensions

AbstractWe carried out 3D simulations of monodisperse particle suspensions subjected to a constant shear rate with the view to investigate the effect of electrical double layers around the particles on apparent suspension viscosities. To this end, expressions for Debye length, zeta potential, and ionic strength (pH) of the liquid were incorporated into our in‐house lattice Boltzmann code that uses the immersed boundary method and includes subgrid lubrication models. We varied the solids concentration and particle radius, keeping the particle Reynolds number equal to 0.1. We report on results with respect to the effect of pH in the range 9 through 12 and of Debye length on apparent viscosity and spatial suspension structures, particularly at higher solids volume fractions, and on the effect of flow reversals.

Homogeneous drag models in gas–solid fluidization: Big data analytics and conventional correlation

AbstractThe drag force model is vital for capturing gas–solid flow dynamics in many simulation approaches. Most of the homogeneous drag models in the literature are expressed as a function of phase fraction (ε) and particle Reynolds number (Res). In this work, we use a “big data” approach to analyze ~108 data points for drag coefficient (Fd) for Geldart Group A particles at atmospheric pressure and find that the contribution of Res on Fd is much less than ε based on the Maximal information coefficient analysis. Thus, these drag models are separately reduced to machine learning and conventional expressions only related to ε. The reduced models achieve almost the same predictive performance as the originals in bubbling, turbulent, and jet fluidizations. Moreover, the reduced models provide better numerical stability for coarse grid simulations. These findings provide new insights into the drag coefficient for Geldart Group A particles under full fluidization conditions.

Modeling and simulation of supersonic nozzle gas jet laden with polydisperse fire suppressant particles injected from a bypass injector

Dry powder fire extinguishing techniques are widely used due to the environmental friendliness and high efficiency. An Eulerian-Lagrangian interphase coupled modeling is performed for 2D axisymmetric nozzle supersonic gas jets laden with polydisperse fire suppressant particles complying with a Rosin-Rammler distribution injected from a bypass injector. A corrected drag model is developed applicable for very large ranges of particle Reynolds and Mach numbers. A parametric study on performance indexes of jet determining the fire extinguishment efficiency indicates that an increase in injected particle velocity vp,inj, mean diameter dp,m or spread parameter ns, or decrease in mass flow rate qm,p usually causes a monotonous increase of particle streamwise average velocity vp,a, decrease of velocity inhomogeneity Φvp and dispersion Ψp. However, the monotonicity of parametric dependency is probably violated under extreme conditions. It is exemplified by the vp,a, Φvp or Ψp at very large vp,inj, or the Ψp at extremely large ns.

Direct numerical simulations of oscillatory boundary layers over rough walls

Numerical simulations of turbulent oscillatory flow over a bed made of fixed, identical spherical particles have been performed. Oscillations are imposed through a shear-driven forcing by means of an harmonic velocity boundary condition on the bed. A parametric study on the effect of the particle size and Reynolds number, spanning from the laminar to the fully-turbulent regimes, has been performed. Results show that the temporal evolution of the flow over the rough bed is modified compared to the classical Stokes’ solution for smooth-wall laminar boundary layers. In the turbulent cases, the phase shift in the velocity at various distances from the bed is reduced compared to the laminar case. The phase shift reduction seems predominantly dependent on the Reynolds number rather than the bed morphology, which suggests that a unique curve may exist for large enough values of the Reynolds number. Turbulence is observed during the deceleration phases of the cycle, with the presence of a logarithmic layer in the velocity profile, and “canonical” distribution of Reynolds shear stress and turbulent kinetic energy production. During the acceleration, the logarithmic region is suppressed and the Reynolds shear stress changes sign. Nevertheless, the turbulent kinetic energy production becomes only slightly negative, because the shear is also very small during these phases. A good correlation between Reynolds and shear stresses is also evidenced from the eddy viscosity profiles, which show the presence of plateau in the outer layers approximately constant across the phases of the cycle. Turbulence in the outer layers is related to structures which develop during previous cycles and propagate from the bed to the bulk of the channel. When the flow is fully developed, anisotropy maps show similar distributions to unidirectional wall-bounded flows, while departures from canonical distributions during the transient phases are mild, because the flow responds very rapidly to the time-varying forcing.

A force partitioning method to model spherical particles in liquid flows with low grid resolution

We have extended the traditional point-force method for modeling suspended small particles to include a force partitioning approach for particles that are slightly larger than the grid size. This size range falls between the limits of applicability for both the point-force and immersed-boundary methods. In our approach, we partition the modified term of the momentum exchange between the solid and fluid phases into the grid cells based on the area and volume fraction of the solid particle contained in each cell. We demonstrate that, for particle Reynolds numbers less than 40 and using the relatively coarse grid resolution, our method yields resolution-consistent results for the flow field, which are in good agreement with those obtained using the highly resolved immersed boundary method. By incorporating our method with the immersed-boundary method to handle large-sized particles, we demonstrate the ability to efficiently model the segregation of mixed-sized particles in liquid flows.

Impact of Stefan flow on the interphase scalar transfer in flow past random particle arrays

By using a particle-resolved direct numerical simulation, the impact of Stefan flow on interphase heat transfer in flow past static random particle arrays is investigated. The findings demonstrate that the temperature boundary layer of particles is thickened/thinned by the outward/inward Stefan flow and therefore hinders/improves the contact between main gas flow and particles. With the impact of positive Stefan Reynolds number (Resf), the maximum percentage reduction of Nusselt number could be over 3 times of the maximum percentage reduction of drag coefficient at the same condition. The rise in particle Reynolds number (Re) or solid volume fraction (c) can partially offset the impact of Stefan flow. Finally, the simulation data are used to develop a correction factor for interphase heat transfer considering the impact of Stefan flow for −3 < Resf < 6, 0 < Re < 100, and 0 < c < 0.5. Note that the scalar in current work is chosen to be the dimensionless temperature, but the results are general and applicable to any passive scalar.

Direct numerical simulation of flow past a reactive/inert mixed particle pair

During the pyrolysis and gasification processes inside fluidized bed reactors, a single reactive particle is generally surrounded by multiple inert heat carrier particles. In this work, we focus on the simplest mixed particle pair (one reactive particle: P1, and one inert particle: P2) to investigate the joint effects of the Stefan Reynolds number (Resf), the particle Reynolds number (Re), separation distance normalized by particle diameter (L), and relative orientation (α) on the drag force exerting on each particle by particle-resolved direct numerical simulations. The results show that when particles are placed in a tandem arrangement, the blocking effect on P2 is weakened/strengthened with negative/positive Stefan flow since the effective diameter of P1 is smaller/larger than its real diameter. When L = 1.25, Re = 3, and particles are placed in tandem, the drag force of P1 decreases as Resf increases, but the reduction of the drag force decreases as Re increases. Under such conditions, the positive Stefan flow induces the repulsion between the two particles; thus, the drag force of P2 increases as Resf increases. When Resf = 3 and P2 is located downstream, the repulsive force felt by P1 can partially offset the drag force at L = 1.25, Re = 3. Moreover, the negative/positive Stefan flow enhances/weakens the drag force of P2 when it is located upstream. The Stefan flow has a negligible effect on the drag force of P2 when L = 3.

Evolution of the age-included nearest pair distribution in disperse multiphase flows

The age of the nearest particle pair is introduced as the difference between the current time and the most recent time when the nearest particle pair was formed. The evolution equation for the age-included nearest pair distribution function is derived. With the assumption of random destruction of the nearest particle pairs, the evolution equation predicts the exponential probability distribution of the ages of the nearest particle pairs. Particle-resolved numerical simulations with moving particles are performed to verify this prediction. The equation is then used to derive the evolution equation for the particle–fluid–particle (PFP) stress, which is known to be related to hyperbolicity of the two-fluid equations. It is found that the relaxation time of the age probability distribution is also the relaxation time for the PFP stress. Guided by the closure terms in the PFP stress evolution equation, we study kinematics of the nearest particle pairs in the particle-resolved simulations for flows caused by sedimentation of the particles with initially isotropic and homogeneous particle distributions. At the steady states, the particle Reynolds numbers are around 20. Anisotropy and inhomogeneity of particle distributions are seen to develop in these flows. The mean distances to the nearest particles and evolution of the distribution of the Voronoi cell volumes are studied. We also found the PFP stress is closely related to the changes in these inter-particle scale quantities.

Drag model of finite-sized particle in turbulent wall-bound flow over sediment bed

Drag force acting on a particle is vital for the accurate simulation of turbulent multiphase flows, but the robust drag model is still an open issue. Fully resolved direct numerical simulation (DNS) with an immersed boundary method is performed to investigate the drag force on saltating particles in wall turbulence over a sediment bed. Results show that, for saltating particles, the drag force along the particle trajectories cannot be estimated accurately by traditional drag models originally developed for an isolated particle that depends on the particle-wall separation distance or local volume fraction in addition to the particle Reynolds number. The errors between the models and DNS are especially clear during the descending phase of the particles. Through simple theoretical analysis and DNS data fitting, we present a corrected factor using the classical, particle Reynolds number dependent drag force model as the benchmark model. The new drag model, which takes the particle vertical velocity into account, can reasonably predict the mean drag force obtained by DNS along a particle trajectory.

Leading-Edge Erosion and Floating Particles: Stagnation Point Simulation in Particle-Laden Turbulent Flow via Lagrangian Particle Tracking

Since the stagnation point is subject to straining motion, this 3D experiment is an effort to simulate the stagnation plane, which applies to studying the particle erosion in rotary machine blades, such as wind turbines, gas turbines, and compressors. Wind turbine blade erosion, caused by particles such as sand, ice, insects, raindrops, and snowflakes, can significantly impact turbine efficiency, as with other rotary machines. Previous research has indicated that flow geometry and gravity can influence particle dynamics statistics. The current study’s laboratory experiment simulates the airfoil’s stagnation plane to investigate how floating particles cause erosion. The experiment involves seeding tracers and inertial particles in a strained turbulent flow with specific turbulent intensity, strain rate, and the presence of gravity. It is conducted on initially homogeneous turbulence undergoing a sudden axisymmetric expansion. The flow was generated in 100&lt;Reλ&lt;160. The Lagrangian particle tracking technique based on the 4-frame best estimate method was employed to measure the velocity field. The obtained results are with two different mean strain rates and Reynolds–Taylor microscales in the presence of gravity, which has not been considered in most numerical studies in a particle-laden turbulent flow. It provides a transparent window to investigate how particles of different sizes with distinct strain rates flow and their relationship to the turbulence intensity affects the erosion. Two most important issues are observed in the presence of gravity: Increasing the turbulence intensity from Reλ=100 to 160 led to a 10–23% increase in the erosion ratio, depending on the particle type and the flow strain rate. Likewise, a doubled mean strain rate of the flow (caused by deformation/shear flow) resulted in a 3–10% increase in erosion, depending on the particle type and Reynolds number. Moreover, the influence of gravity could potentially play a significant role in this observation.

Buoyancy-driven bubbly flows: role of meso-scale structures on the relative motion between phases in bubble columns operated in the heterogeneous regime

The hydrodynamics of bubble columns in the heterogeneous regime is investigated from experiments with bubbles at large particle Reynolds numbers and without coalescence. The void fraction field $\varepsilon$ at small scales, analysed with Voronoï tessellations, corresponds to a random Poisson process (RPP) in homogeneous conditions but it significantly differs from an RPP in the heterogeneous regime. The distance to an RPP allows identifying meso-scale structures, namely clusters, void regions and intermediate regions. A series of arguments demonstrate that the bubble motion is driven by the dynamics of these structures. Notably, bubbles in clusters (respectively in intermediate regions) are moving up faster, up to 3.5 (respectively 2) times the terminal velocity, than bubbles in void regions whose absolute velocity equals the mean liquid velocity. In addition, the mean unconditional relative velocity of bubbles is recovered from mean relative velocities conditional to meso-scale structures, weighted by the proportion of bubbles in each structure. Assuming buoyancy–inertia equilibrium for each structure, the relative velocity is related to the characteristic size and concentration of meso-scale structures. By considering the latter quantity's values at large gas superficial velocities, a cartoon of the internal flow structure is proposed. Arguments are proposed to help understanding why the relative velocity scales as $(gD\varepsilon )^{1/2}$ (with $D$ the column's diameter and $g$ gravity's acceleration). The proposed cartoon seems consistent with a fast-track mechanism that, for the moderate Rouse numbers studied, leads to liquid velocity fluctuations proportional to the relative velocity. The potential impact of coalescence on the above analysis is also commented.

Effect of channel dimensions and Reynolds numbers on the turbulence modulation for particle-laden turbulent channel flows

The addition of particles to turbulent flows changes the underlying mechanism of turbulence and leads to turbulence modulation. The important parameters are particle Stokes number, mass loading, particle Reynolds number, fluid bulk Reynolds number, etc., that act together and affect the fluid phase turbulence intensities. In the present study, simulations are carried out for different system sizes (2δ/dp=54,81, and 117) and fluid bulk Reynolds numbers (Reb = 5600 and 13 750) to quantify the extent of turbulence attenuation. Here, δ is the half-channel width, dp is the particle diameter, and Reb is the fluid Reynolds number based on the fluid bulk velocity and channel width. Our study shows that system size and fluid bulk Reynolds number are the two crucial parameters that affect the particle feedback force and turbulence modulation more significantly than the other. The extent of turbulence attenuation increases with an increase in system size for the same volume fraction while keeping the Reynolds number fixed. However, for the same volume fraction and fixed channel dimension, the extent of attenuation is low at a higher Reynolds number. The streamwise turbulent structures are observed to become lengthier and fewer with an increase in system size for the same volume fraction and fixed bulk Reynolds number. However, the streamwise high-speed streaks are smaller, thinner, and closely spaced for higher Reynolds numbers than the lower ones for the same volume fraction. Particle phase velocity statistics for different cases have also been reported.

Impacts of Particle Shape, Skeletal Porosity and Density on the Settling Velocity of Gravel‐Size Coral Debris

AbstractKnowledge of the hydrodynamic behavior of carbonate bioclasts is essential for solving coastal morphodynamic problems in marine carbonate depositional environments. Marine carbonate grains are produced within the sedimentary system itself and are deformed by subsequent hydrodynamics, resulting in particle densities, sizes and shapes that are distinct from those of terrigenous sediments. In this study, we investigated the shapes and settling characteristics of gravel‐size natural coral debris collected from the coasts of Okinawa Prefecture, Japan. Based on the shape parameters and settling velocities obtained using image analysis techniques and settling tube experiments, respectively, a correlation model for predicting the settling velocity of coral gravel particles was developed by extending the previous formula of Dietrich (1982, https://doi.org/10.1029/wr018i006p01615) over particle Reynolds number values ranging from 384.23 to 4439.76. The model determines the settling velocity as a function of particle nominal diameter, form, roundness, and surface texture parameters that were selected after examining several other shape descriptors. Compared with other models, the proposed model showed better settling velocity predictive skills for coral gravel particles classified into four shape types. The proposed model also determines how the drag coefficient of coral gravel particles should be modified from that for spherical particles, by accounting for the abovementioned coral gravel particle shape parameters. The obtained data set of settling velocity and modification of the drag coefficient can be used for quantitative interpretation of suspension, transport, and sedimentation processes in marine carbonate depositional environments.

Two-dimensional dynamics of a mobile elliptical cylinder in an upward flow

The fully resolved dynamics of an elliptical particle suspended in an upward flow in an expanding channel, with successively increasing degrees of freedom of motion from a completely fixed state to an eventually fluidized state, are examined using particle resolved direct numerical simulation. The signed distance function immersed boundary method (sdfibm), implemented in OpenFOAM, is validated against results from COMSOL for the case of a pinned ellipse. The aspect ratio of the ellipse (defined as the ratio of the major to the minor axis (γ=Ra/Rb) is held constant at 2, while the minor axis is kept as Rb=0.15 (with respect to the inlet width, Wi = 1). A particle Reynolds number defined as Rep=(2Ra)Vmax/ν (where Vmax = 1 is the centerline velocity) is varied up to 300. The simulations exhibit rich dynamical behavior with stable, steady solutions up to Rep around 67, above which vortex shedding begins, with the ellipse responding with its oscillatory motion in response to the stresses and torques acting on it by the fluid. For the case of free translation in the x direction, multiple oscillatory states are found, where the particle is confined in the left or right half of the flow domain, depending on the initial placement of the particle. The forces on the particle get progressively complicated as the degree of freedom of movement of the ellipse increases, indicating that traditional drag correlations with fixed particles may not be valid in situations when they have mobility if one desires higher fidelity in coarse-grained models.

Comparing two IBM implementations for the simulation of uniform packed beds

Nowadays, the design of fixed packed bed reactors still relies on empirical correlations, which, especially for small tube to particle diameter ratios, are mostly too inaccurate because of the presence of wall effects. Therefore, the simulation of fixed packed bed reactors plays an important role to predict and control the flow and process parameters in such, nowadays and in the future. Because of its straightforward applicability to non-uniform packings with particles of arbitrary shapes, the immersed boundary method (IBM) has advantages over other numerical methods and is used more and more frequently. This paper compares two approaches of IBMs for the simulation of fixed bed reactors with spherical shaped particles. The classic, smooth approach is compared to the straightforward to implement blocked-off method for velocity fields above the fixed bed for particle Reynolds numbers of 300 and 500. Results from experimental inline PIV-measurements of the reactor to be simulated serve as a basis for comparison. Very good agreement with the experiment is found for both simulation methodologies with higher resolutions, considering the more stable flow at a particle Reynolds number of 300. Differences in the different IBM approaches occurred for the more unsteady flow at a particle Reynolds number of 500. Compared to the blocked-off method, the smooth IBM reflects the formation of additional jets and recirculation zones better right above the bed, though increasing the fluid mesh resolution improves the accuracy of the blocked-off method. Overall, a more diffusive behaviour is found for the blocked-off simulations due to the stairstep representation, which is avoided by using interpolation stencils as in the smooth IBM. With higher mesh refinement in the blocked-off IBM this effect can be reduced, but this also increases the computational effort.

Analysis of Variables Influencing Scour on Large Sand-Bed Rivers Conducted Using Field Data

Throughout the lifespan of a bridge, morphological changes in the riverbed affect the variable action-imposed loads on the structure. This emphasizes the need for accurate and reliable data that can be used in model-based projections targeted for the identification of risk associated with bridge failure induced by scour. The aim of this paper is to provide an analysis of scour depth estimation on large sand-bed rivers under the clear water regime, detect the most influential (i.e., explanatory) variables, and examine the relationship between them and scour depth as a response variable. A dataset used for the analysis was obtained from the United States Geological Survey’s extensive field database of local scour at bridge piers, i.e., the Pier-Scour Database (PSDB-2014). The original database was filtered to exclude the data that did not reflect large sand-bed rivers, and several influential variables were omitted by using the principal component analysis. This reduction process resulted in 10 influential variables that were used in multiple non-linear regression scour modeling (MNLR). Two MNLR models (i.e., non-dimensional and dimensional models) were prepared for scour estimation; however, the dimensional model slightly overperformed the other one. According to the Pearson correlation coefficients (r), the most influential variables for estimating scour depth were as follows: Effective pier width (r = 0.625), flow depth (r = 0.492), and critical and local velocity (r = 0.474 and r = 0.436), respectively. In the compounded hydraulic-sediment category, critical velocity had the greatest impact (i.e., the highest correlation coefficient) on scour depth in comparison to densimetric Froude and critical Froude numbers that were characterized by correlation coefficients of r = 0.427 and r = 0.323, respectively. The remaining four variables (local and critical bed shear stress, Froude number, and particle Reynolds number) exhibited a very weak correlation with scour depth, with r &lt; 0.3.

Drag force of compressible flows past random arrays of spheres

We perform particle-resolved simulations of subsonic and transonic flows past random arrays of spherical particles. The particle Reynolds number is held at Re≈300 to ensure the flow remains in the continuum regime. At low volume fractions, the drag force increases sharply near a critical Mach number due to the formation of shock waves and reaches a maximum value when the bulk flow is supersonic. Neighbor-induced aerodynamic interactions reduce the critical Mach number at higher volume fractions. An effective Mach number is introduced to capture the increase in compressibility effects on drag. A new drag correlation is proposed valid for subsonic and weakly supersonic flow from dilute to moderately dense suspensions.

Drag force modification model for turbulent suspended-load sediment solid–liquid two-phase flow

The calculation accuracy of a solid–liquid two-phase flow numerical simulation is related directly to the reliability of the results obtained. The interphase drag force significantly affects the calculation results of the solid concentration distribution of suspended-load sediment solid–liquid two-phase flow. However, the conventional Wen–Yu drag force model is obtained by adding solid concentration to the standard drag force coefficient curves. The model does not consider the influence of turbulence, which is a comprehensive reflection of particle inertia and liquid turbulence intensity. To improve the calculation accuracy of the Wen–Yu model, the particle inertia and turbulence intensity factors are introduced to express the comprehensive influence of the particle inertia and liquid turbulent intensity on the drag force coefficient for the suspended-load sediment solid–liquid two-phase flow. The turbulence modification function preliminary expression is determined and further modified to improve the calculation accuracy for a particle Reynolds number of less than 100 by combining experimental data and the least square method through experiments and theoretical research. Then, the final expression of the turbulence modification function is proposed to help modify the drag force coefficient of the Wen–Yu model, and finally establish the modified turbulence effect (MTE)-Wen–Yu drag force modification model. The calculations for the suspended-load sediment solid–liquid two-phase flow in the circular tubes show that the solid-phase concentration values calculated by the MTE-Wen–Yu drag force model are considerably closer to the experimental results than those obtained by the Wen–Yu drag force model in the suspended-load sediment solid–liquid two-phase flow calculation for different inlet velocities, inlet solid concentrations, and particle diameters. Hence, the calculation accuracy of the MTE-Wen–Yu model is higher than that of the Wen–Yu drag force model. The calculation precision of the solid-phase concentration distribution calculated using the MTE-Wen–Yu drag force model decreases with the increase in particle diameter owing to the high quality and large inertia of large particles. Therefore, it is more suitable for the numerical simulation of suspended-load sediment solid–liquid two-phase flow with a small particle diameter.

Computational fluid dynamics study of hydrogen production by sorption enhanced steam ethanol reforming process in fluidized bed

As a renewable resource, hydrogen plays a pivotal role in the energy transition of the current world. A promising route for hydrogen production is the sorption enhanced steam ethanol reforming (SE-SER), which is characterized by the complex multi-scale characteristics. This paper aims to explore the hydrodynamic (e.g., gas and solid flux, solid dispersion and velocity) and thermodynamic (e.g., particle temperature and heat transfer coefficient) characteristics on the micro-level together with the effect of operating parameters on the SE-SER performance. Accordingly, the reactive multiphase particle-in-cell (MP-PIC) model has been developed under the Lagrangian manner for studying the SE-SER process in the bubbling fluidized bed. In this model, it is assumed that uniform temperature appears inside the particle, and particles with similar properties are packed into a parcel to reduce computational cost. This model has been well validated with experimental data. The results indicate that along the bed height, the solid temperature decreases while the heat transfer coefficient increases. H2 and CO2 have similar distribution in the bed, mainly accumulating in the upper part of the reactor. Enlarging the ratio of H2O to C2H6O in the gas mixture promotes the yields of H2 and CO2. The relationships between key particle variables are explored. It is found that increasing the slip velocity enlarges the particle heat transfer coefficient, and large particle Reynolds number mainly appears with small solid volume fraction. The explored results provide valuable insights into deeply understanding complex multiphase flow and optimizing actual operation of the SE-SER field.