Particle Reynolds Number Research Articles

Flow Resistance in Dredged Soil under a Vacuum Preloading System with Vertical Drainage Boards

Zhu, W.; Zhang, M.; Yu, G.; Petukhov, V.; Mymrin, V., and Gidarakos, E., 2020. Flow resistance in dredged soil under a vacuum preloading system with vertical drainage boards. Journal of Coastal Research, 36(2), 327–338. Coconut Creek (Florida), ISSN 0749-0208.Vacuum preloading combined with prefabricated vertical drains is one of the most widely applied methods to improve soft-ground loading capacity in coastal engineering projects. The resistance of solid particles to the pore-water flow in vacuum-preloaded soil plays an important role in the soil consolidation and pore-water dissipation. However, the flow resistance is still not clearly known during the vacuum drainage process. It is not clear whether the formulae for calculating the flow resistance factor for flow in uniform non-deformational porous media are applicable for flow in vacuum-preloaded soils or not. Because of a lack of knowledge on flow resistance in the vacuum-preloaded soil, coastal engineers only rely on their experience to select vacuum pumps. In this paper, the hydraulic resistance to flow in vacuum-preloaded soils was investigated. Energy conservation in the vacuum preloading system during the drainage process was analyzed. Sixteen laboratory tests were conducted, in which the vacuum pressure, flow rate, seepage velocity, and particle Reynolds number were observed or calculated. Results showed that particle size, uniformity coefficient, and porosity of the soil have important effects on resistance in dredged soils under vacuum preloading condition. The flow resistance in the vacuum-preloaded soil behaved quite differently from that in uniform porous medium. The formulae for calculating the flow resistance factor for flow in uniform packed beds were not applicable for flow in vacuum-preloaded soils. A new formula was proposed to calculate the flow resistance factor in vacuum-preloaded soils with acceptable accuracy. Because the vacuum preloading system with fixed pump power consumes much energy, new vacuum preloading systems with low energy consumption are necessarily developed in future work.

Numerical simulation of incipient particle motion

A two-dimensional (2D) computational model for simulation of incipient sediment motion for non-cohesive uniform and non-uniform particles on a horizontal bed was developed using the Discrete Element Method (DEM). The model was calibrated and verified using various experimental data reported in the literature and compared with different theories of incipient particle motion. Sensitivity analysis was done and the effects of relevant parameters were determined. In addition to hydrodynamic forces such as drag, shear lift and Magnus force, the particle-particle interaction effects were included in the model. The asymptotic critical mobility number was evaluated for various critical particle Reynolds numbers (R∗) in the range of very small and very large R*. The obtained curve is classified into four regions. It was found that in the linear region, the drag force has the principal role on the initiation of motion. Moreover, the critical mobility number is independent of particle diameter. A procedure for estimating the critical shear velocity directly from the information on particle diameter and roughness height was developed. Finally, the mechanism of incipient motion for the different regions was studied and the effect of different forces on the incipient particle motion was obtained. It was found that the maximum effects of lift and Magnus forces were, respectively, less than ten and twenty percent of the total force. The drag force, however, was typically the dominant force accounting for majority of the net hydrodynamic force acting on sediment particles at the onset of incipient motion.

The decay of isotropic turbulence carrying non-spherical finite-size particles

Direct particle–fluid simulations of heavy spheres and ellipsoids interacting with decaying isotropic turbulence are conducted. This is the rigorous extension of the spherical particle analysis in Schneiders et al. (J. Fluid Mech., vol. 819, 2017, pp. 188–227) to $O(10^{4})$ non-spherical particles. To the best of the authors’ knowledge, this represents the first particle-resolved study on turbulence modulation by non-spherical particles of near-Kolmogorov-scale size. The modulation of the turbulent flow is precisely captured by explicitly resolving the stresses acting on the fluid–particle interfaces. The decay rates of the fluid and particle kinetic energy are found to increase with the particle aspect ratio. This is due to the particle-induced dissipation rate and the direct transfer of kinetic energy, both of which can be substantially larger than for spherical particles depending on the particle orientation. The extra dissipation rate resulting from the translational and rotational particle motion is quantified to detail the impact of the particles on the fluid kinetic energy budget and the influence of the particle shape. It is demonstrated that the previously derived analytical model for the particle-induced dissipation rate of smaller particles is valid for the present cases albeit these involve significant finite-size effects. This generic expression allows us to assess the impact of individual inertial particles on the local energy balance independent of the particle shape and to quantify the share of the rotational particle motion in the kinetic energy budget. To enable the examination of this mechanistic model in particle-resolved simulations, a method is proposed to reconstruct the so-called undisturbed fluid velocity and fluid rotation rate close to a particle. The accuracy and robustness of the scheme are corroborated via a parameter study. The subsequent discussion emphasizes the necessity to account for the orientation-dependent drag and torque in Lagrangian point-particle models, including corrections for finite particle Reynolds numbers, to reproduce the local and global energy balance of the multiphase system.

Effect of inertial lift on a spherical particle suspended in flow through a curved duct

We develop a model of the forces on a spherical particle suspended in flow through a curved duct under the assumption that the particle Reynolds number is small. This extends an asymptotic model of inertial lift force previously developed to study inertial migration in straight ducts. Of particular interest is the existence and location of stable equilibria within the cross-sectional plane towards which particles migrate. The Navier–Stokes equations determine the hydrodynamic forces acting on a particle. A leading-order model of the forces within the cross-sectional plane is obtained through the use of a rotating coordinate system and a perturbation expansion in the particle Reynolds number of the disturbance flow. We predict the behaviour of neutrally buoyant particles at low flow rates and examine the variation in focusing position with respect to particle size and bend radius, independent of the flow rate. In this regime, the lateral focusing position of particles approximately collapses with respect to a dimensionless parameter dependent on three length scales: specifically, the particle radius, duct height and duct bend radius. Additionally, a trapezoidal-shaped cross-section is considered in order to demonstrate how changes in the cross-section design influence the dynamics of particles.

Fluid medium effect on stresses in suspensions of high-inertia rod-like particles

The rheology of suspensions of high-inertia (or granular) non-spherical particles characterized by high particle Stokes and Reynolds numbers is rarely investigated. In this study, we investigate the rheology of suspensions of inertial rod-like particles of aspect ratio 4 subjected to shear flow. In particular, the effect of fluid medium (air, water) against dry granular simulations on the developed stresses is assessed. CFD-DEM simulations are performed for a periodic shear box for a range of shear rates and volume fractions of particles. The dependence of rheological properties like shear stress, normal stress difference, pressure and relative viscosity on volume fraction, shear rate, granular temperature and the particle orientation are discussed. These results provide insight into the macroscopic rheology of suspensions of rods and demonstrate that the effect of particle shape and surrounding fluid cannot be completely ignored. Air as a fluid medium shows similar scaling as compared to dry granular simulations, but the stress values are generally lower. We observe drastic change in both scaling and values for water as fluid medium. In all cases, the rods show strong alignment in the direction of shear. This study can be further extended to develop stress closures for use in Eulerian flow models.

Performance Simulation for Gas Flow through a Porous Media in Packed bed Columns using CFD

Two dimensions of Computational Fluid Dynamics simulation for gas flow in the column with filling material as bed at low particle Reynolds numbers and high particle Reynolds numbers have been presented. The simulation test has been done with the column length 0.9 m. Porous media model was used to simulate the gas flow inside porous granular media. Model of standard k-e for the flow turbulent range was used; the difference on the mesh size used to study effect it on the performance of gas flow through porous media. The result of flow rate of the gas was an important variable influencing bed and there are good results between the CFD simulation of pressure drop and the predicted values from Ergun model, and Computational Fluid Dynamics gave us simulation with high details for porous flow in packed bed equipment.

Maximum Solid Phase Concentration in Geophysical Turbulent Gas‐Particle Flows: Insights From Laboratory Experiments

AbstractThe maximum solid phase concentration in geophysical turbulent gas‐particle mixtures is essential for understanding the flow dynamics but is poorly known. We present laboratory experiments on turbulent mixtures of air and ceramic particles generated in a vertical pipe. The mixtures had maximum bulk concentrations Cmax = 0.7–2.4 vol. % set by the onset of clustering and that increased with the degree of turbulence. Comparison with results of similar experiments with less dense (glass) particles reveals that Cmax increases with the particle Reynolds number according to Cmax = 0.78 × Rep0.17. Published results of experiments at specific Rep in different configurations are consistent with our data, suggesting that the model for Cmax may be generally applicable to turbulent mixtures. From our empirical laws we infer that natural turbulent gas‐particle flows with Rep ~ 102–105 have maximum solid concentrations of ~2–5 vol. %.

Rotational dynamics of a particle in a turbulent stream

The paper presents results for the resolved numerical simulation of a turbulent flow past a homogeneous sphere and a spherical shell of equal mass and radius (and, therefore, with a larger moment of inertia) free to rotate around a fixed center. This situation approximates the behavior of a particle whose relative motion with respect to the fluid is driven by external forces, such as a density difference in a gravitational field. Holding the center fixed makes it possible to have precise information on the turbulent flow incident on the particle by repeating the same simulations without the particle. Two particle Reynolds numbers based on the mean velocity, Rep=80 and 150, are investigated; the incident turbulence has Reλ=36 and 31, respectively. The particle diameter is an order of magnitude larger than the Kolmogorov length scale and close to the integral length scale. The turbulent eddies that interact most strongly with the particle are characterized. Their size is found to increase with Rep due to the interplay of the convection timescale, the particle timescale, and the eddy timescale, but it remains of the order of the particle diameter. The sign of the hydrodynamic torque is likely to persist much less than the convection time, although longer durations are also found, revealing the effect of occasional interactions with larger eddies. The autocorrelation of the torque changes sign at shorter and shorter fractions of the convection time as the Reynolds number increases. Significant cross-stream forces are found. An analysis of their magnitude shows that they are mostly due to induced vortex shedding combined with a weaker Magnus-like mechanism.

Particle-Vane Interaction Probability in Gas Turbine Engines

Abstract Engine durability tests are used by manufacturers to demonstrate engine life and minimum performance when subjected to doses of test dusts, often Arizona Road Dust. Grain size distributions are chosen to replicate what enters the engine; less attention is paid to other properties such as composition and shape. We demonstrate here the differences in the probability of interaction of a particle of a given particle Reynolds number on to a vane if particle shape, vane geometry, and flow Reynolds number are varied and discuss why the traditional definition of Stokes number is inadequate for predicting the likelihood of interaction in these flows. We develop a new generalized Stokes number for nozzle guide vanes and demonstrate its use through application to 2D sections of the General Electric E3 nozzle guide vane. The new Stokes number is used to develop a reduced-order probability curve to predict the interaction efficiency of spherical and nonspherical particles, independent of flow conditions and vane geometry. We show that assuming spherical particles instead of more realistic sphericity of 0.75 can lead to as much as 25% difference in the probability of interaction at Stokes numbers of around unity. Finally, we use a hypothetical size distribution to demonstrate the application of the model to predict the total mass fraction of dust interaction with a nozzle guide vane at design point conditions and highlight the potential difference in the accumulation factor between spherical and nonspherical particles.

A penalization method for the simulation of weakly compressible reacting gas-particle flows with general boundary conditions

In this paper, the Brinkman penalization method is extended to the weakly compressible formulation of the Navier–Stokes equations to study gas-particle flows with reactions and coupled heat and mass transfer. The weakly compressible approximation removes the acoustic modes from the solution while allowing a variable density. The Brinkman volume penalization method describes the solid phase as a porous medium with a vanishing permeability. The method is validated with literature benchmarks for a fixed or moving particle. Various reaction scenarios are then investigated. First, the capability of the method to deal with intra-particle diffusion and reaction is evaluated. The impact on the conversion of the particle Reynolds number based on the slip velocity is assessed, for a range of Reynolds numbers encountered in fluidization. Next, surface reactions are focused on, with infinite or finite rate. A Dirichlet-type condition is imposed on the particle surface to treat an infinite reaction rate and a high solid thermal conductivity while a finite-rate surface reaction requires Neumann and Robin surface conditions for the temperature and species mass fractions. The impact of density changes induced by heat release and molecular weight changes is assessed in these different cases. It is shown that the combination of the weakly compressible approximation and the penalization method allows to treat the presence of the solid phase and reactions in an efficient manner and to take into account the effects of compressibility in commonly encountered situations in reaction engineering.

Motion of a non-axisymmetric particle in viscous shear flow

We examine the motion in a shear flow at zero Reynolds number of particles with two planes of symmetry. We show that in most cases the rotational motion is qualitatively similar to that of a non-axisymmetric ellipsoid, and characterised by a combination of chaotic and quasiperiodic orbits. We use Kolmogorov–Arnold–Moser (KAM) theory and related ideas in dynamical systems to elucidate the underlying mathematical structure of the motion and thence to explain why such a large class of particles all rotate in essentially the same manner. Numerical simulations are presented for curved spheroids of varying centreline curvature, which are found to drift persistently across the streamlines of the flow for certain initial orientations. We explain the origin of this migration as the result of a lack of symmetries of the particle’s orientation orbit.

Evaluation of empirical equations to predict bridge pier scour in a non-cohesive bed under clear-water conditions

Pier scour has been cited as the main mechanism responsible for the failure of bridges spanning rivers. Despite extensive research since the 1950s, there is no universally agreed upon procedure to accurately predict the equilibrium scour depth. Experimental data was generated by 48 tests with four flows and three pier shapes to evaluate the capability of 30 empirical equations to predict the local scour depth. Fine sand and crushed peach pips were used to address the scaling challenges of the equations by means of an equivalent movability number. The equations yielded a wide range of mostly unreliable results, particularly for the non-cylindrical pier shapes. Nevertheless, the HEC-18 models are recommended, in conjunction with Shen et al (1969), and Ali and Karim (2002), because they rely on the pier Reynolds number, a parameter which is significant in the vortex formation. Prediction models taking the horseshoe vortex into consideration could offer better scour depth predictions. Field data was analysed to improve the HEC-18 equation with new factors for pier shape and armouring for different confidence intervals. The armouring factor is based on the particle Reynolds number as opposed to the widely adopted critical velocity, and achieves considerably less scatter about the line of equality despite under-predictions for the cylindrical piers. Alternatively, a diagram comparable to the Modified Liu Diagram has the potential to predict bridge pier scour even though the pier structure parameters are omitted. Further research and improved prediction models should be considered, particularly advanced numerical models which are becoming increasingly feasible.

Effect of particle size ratio on shear-induced onset of particle motion at low particle Reynolds numbers: From high shielding to roughness

We study incipient motion of single beads on regular substrates made of spherical particles of a different size in steady shear flow at small particle Reynolds numbers. We cover a large range of sizes: from small beads that are highly shielded from the shear flow by the substrate spheres, and hence, are susceptible to the flow through the interstices of the substrate, to beads fully exposed to the flow, where the substrate rather acts like roughness of an otherwise flat surface. Numerical and experimental studies agree within measurement uncertainty. To describe the findings, we extend a recently derived model for particles of equal size which was validated over a wide range of substrates [Agudo et al., “Shear-induced incipient motion of a single sphere on uniform substrates at low particle Reynolds numbers,” J. Fluid Mech. 825, 284–314 (2017)]. The extended model covers the entire spectrum of size ratios, where the critical Shields number varies from about zero to infinity. The model properly describes the numerical and experimental data. For well exposed beads, we find a scaling law between the critical Shields number and the size ratio between mobile bead and substrate spheres with an exponent of −1.

Effects of particle velocity fluctuations on inter-phase heat transfer in gas-solid flows

Heat transfer in gas-solid flows has been numerically investigated via an immersed boundary-thermal lattice Boltzmann method. Stationary random assemblies of spheres are adopted in the simulations. The effect of particle velocity fluctuations whose magnitude is represented by the so-called granular temperature is accounted for by implementing velocity fluctuations obeying the isotropic Maxwellian distribution on spheres. It is found that particle fluctuations enhance the heat transfer between the gas and solid phases. This enhancement increases with increasing granular temperature-based Reynolds number and becomes less significant as the particle Reynolds number and the solid volume fraction increase. It is also found that the Nusselt numbers on individual particles follow the Log-Normal distribution at both zero and finite granular temperature conditions. The long tail of this distribution is caused by the existence of a non-negligible portion of the domain with fast local gas velocities that could significantly promote heat transfer.

Investigation on convective heat transfer and friction factor of silver–water nanofluid under laminar flow – an experimental study

Laminar flow forced convective heat transfer and friction factor of silver-water nanofluids were experimentally examined under uniform heat flux condition in a horizontal circular pipe. Heat transfer coefficient and friction factor of nanofluids were experimentally evaluated as a function of particle volume concentration and Reynolds number. Reynolds number was varied from 500 to 2300 for the different particle volume fraction of 0.01, 0.05 and 0.1%. The experimental results indicate that both Nusselt number and heat transfer coefficient of the nanofluid increase with the increasing particle volume concentration and Reynolds number. The maximum enhancement of 36.1% in heat transfer coefficient was obtained for 0.1% volume fraction of nanoparticles at Reynolds number of 2300. Also, there is an increase in friction factor of nanofluid with the increase in nano-particle volume concentration. New correlations of Nusselt number and friction factor of nanofluids are proposed using the experimental data. The estimation of Nusselt number and friction factor of nanofluids using the proposed correlations are in good agreement with the experimental results.

Dynamic particle ordering in oscillatory inertial microfluidics

Particles suspended in conduit flows at small and intermediate Reynolds numbers cluster on specific focal positions while also forming particle pairs and trains due to flow-mediated interactions. The recent introduction of oscillatory inertial microfluidics has enabled the creation of virtually infinite channels, allowing the manipulation of particles at extremely low particle Reynolds numbers (Rep ≪ 1). Here, we investigate experimentally the dynamics of formation, the robustness and the stability of particle pairs, and the precision of the inter-particle distance in an oscillatory flow field, in microchannels with a rectangular cross section. Our results indicate that the cross-sectional arrangement of the particles is fundamental in determining the characteristics of the resulting particle pair.

Analysis of mixed convection heat transfer of nanofluids in a minichannel for aiding and opposing flow conditions

In this study, mixed convection heat transfer characteristics of nanofluid flow in a circular minichannel were investigated experimentally. The effects of the particle volume ratio (0, 0.25, and 0.75%) and Reynolds number (200-60) on heat transfer by mixed convection were investigated for aiding and opposing flow conditions. Water and water based SiO2 nanofluids were used as working fluid in a minichannel with a diameter of 1.9 mm, and constant heat flux was applied to the outer surface of the minichannel. Temperature-dependent thermophysical properties such as thermal conductivity and viscosity, obtained by experimental measurements, were used in heat transfer calculations. Pressure based numerical computations for all experimental cases were also made by using single phase approach. The results were analyzed separately for aiding flow condition in which secondary flows originating from natural convection are in the same direction with the forced flow, and for opposing flow condition in which secondary flows are in the opposite direction with forced flow. For detailed analysis of mixed convection heat transfer, temperature contours and velocity profiles were obtained by the numerical computations which were compared and validated with the experimental results. According to the data obtained, it was determined that the addition of nanoparticles into the pure water increased the Nusselt number by around 21–64% for the aiding flow, and 18–58% for the opposing flow. The heat transfer in the aiding flow was observed to be minimum 4% and maximum 16% higher in comparison with the opposing flow condition. It was concluded that the direction of secondary flows significantly affects heat transfer.

Regularization of the Lagrangian point force approximation for deterministic discrete particle simulations

The current article presents a regularization procedure of the Lagrangian point-force approach commonly used to account for the perturbation of a fluid phase by a dispersed particle phase. The regularization procedure is based on a nonlinear diffusion equation to naturally ensure parallel efficiency when the regularization length scale extends over several grid cells. The diffusion coefficient thus becomes a function of the particle source term gradient and expressions allowing to approximately adjust the regularization length scale according to the local particle to mesh size ratio are proposed, so that mesh refinement or polydisperse sprays may be handled. Elementary numerical test cases confirm the convergence of the present procedure under mesh refinement and its ability to locally adapt the regularization length scale. Furthermore, the chosen regularization length scale allows to match the leading order term of the perturbation flow field set by the particle beyond approximately two particle diameters in the Stokes regime.When applying the presented source term regularization procedure, the terminal velocity of a particle settling under gravity in the Stokes regime becomes relatively insensitive to mesh refinement. However, errors with respect to the theoretical settling velocity remain substantial and removal of the particle’s self induced velocity appears necessary to recover the undisturbed fluid velocity at the particle location and correctly evaluate the drag force. As the current regularization procedure yields source terms that are close to Gaussian, an analytic expression from the literature is used to estimate the particle’s self induced velocity. When combining source term regularization and removal of the particle’s self induced velocity, good results are obtained for the terminal settling speed in the Stokes regime. Results obtained for horizontally separated particle pairs settling under gravity in the Stokes regime show equally good agreement with theoretical results. Because analytic expressions for the particle’s self-induced velocity are no longer available at finite particle Reynolds numbers, correlations recently proposed in the literature are used to obtain correct settling velocities beyond the Stokes regime.

Experimental study on the wall factor for spherical particles settling in parallel plates filled with power-law fluids

Hydraulic fracturing is a widespread stimulation technology in the petroleum industry. The retardation due to the fracture wall existence impacts the efficient placement of the proppant in fractures. Accurate prediction of the wall factor for proppant settling in fractures filled with Power-law fluids is important in predicting the transport distance and bed height of proppant in hydraulic fractures. However, few studies were conducted to analyze the wall factor of fracture on the settling proppant. In this study, a set of transparent parallel plates and a high-speed camera were used to record the settling behaviors of the proppant in the fracture. A total of 756 tests were carried out to analyze the effects of fluid properties, the dimensionless diameter, particle size, particle density, and the particle Reynolds number on the wall factor, involving the ranges of the dimensionless diameter and the particle Reynolds number are 0.04–0.9 and 0.0001–144.25, respectively. Results indicate that the wall factor is a function of both the dimensionless diameter and the particle Reynolds number. And a new model with 1.23% relative error was developed to predict the wall factor of the parallel plates on the spherical particles settling in the Power-law fluid. Finally, it was found that the wall effect vanishes when the dimensionless diameter is smaller than 0.057. The results of this study could help field engineers optimize proppant size and fracturing parameters.

Analysis of the Particle Clustering Phenomenon in the Fluid Catalytic Cracking of Gasoil in a Downer Reactor

AbstractA large eddy simulation (LES)‐discrete element method (DEM) investigation was carried out to study particle clusters in a canonical downer reactor during the fluid catalytic cracking of gasoil. The analysis considered two cases: with and without chemical reactions. The results of the system under cold‐flow conditions for the frequency and mean lifetime of clusters were in good agreement with experimental data. The changes in the hydrodynamic conditions generated by the cracking reactions led to clusters with shorter mean lifetime but higher frequency compared to the system without chemical reactions. Additionally, the frequency and mean lifetime of clusters were successfully correlated to an empirical expression as a function of the particle Reynolds number and the Stokes number, which summarize the hydrodynamic conditions of the downer.