Drag Coefficient Of Particles Research Articles

Drag, lift and torque coefficients for ellipsoidal particles: From low to moderate particle Reynolds numbers

An accurate prediction of the translational and rotational motion of ellipsoidal particles can be only given if a complete set of correlations of the drag, lift and pitching torque coefficients is known. The present study is thus devoted to the assessment of the available correlations in the literature through a comparison with numerical results of the forces acting on a particle given by a full body-fitted direct numerical simulation (DNS) in the case of a uniform flow, for three different ellipsoidal particles, and for Reynolds number ranging from 0.1 to 290. The comparison between the computed force (or hydrodynamic coefficients) and the literature correlations shows clearly that certain precautions must be taken. The mean deviation of the most accurate correlation considered in the present study from our full DNS results can be of the order of 20% for the drag coefficient. For the lift and pitching torque coefficients, the deviations can increase up to roughly 25%. This comparison shows that further works are definitively necessary to develop a complete set of correlations for ellipsoidal particles outside Stokes regime.

Experimental investigation of non-stationary motion of single small spherical particles in an upward flow with different velocities

This experimental investigation focuses on carefully determining the drag coefficient of single spherical particles with considerable small diameters in non-stationary motion. A low-speed wind tunnel and a set of high-speed photography system are employed to confirm the displacement of each particle from its trajectory. Moreover, spherical particles of two different densities are used and the minimum diameter of these particles reaches 0.1mm. Meanwhile, the Basset force generated from the relative acceleration in the gas-particle flow is calculated approximately. The experimental results show that the maximum proportion of Basset force does not exceed 2.2%. In addition, the relationship of CD−Re for the experimental data is also determined. This research offers fundamental experimental results for industrial applications and also contributes to the research of non-stationary gas-particle flow.

Biofilm effects on size gradation, drag coefficient and settling velocity of sediment particles

Sediment particles are often colonized by biofilm in a natural aquatic ecological system, especially in eutrophic water body. A series of laboratory experiments on particle size gradation, drag coefficient and settling velocity were conducted after natural sediment was colonized by biofilm for 5, 10, 15 and 20 days. Particle image acquisition, particle tracking techniques of Particle Image Velocimetry and Particle Tracking Velocimetry were utilized to analyze the changes of these properties. The experimental results indicate that the size gradation, the drag force exerted on bio-particles, and the settling velocity of bio-particles underwent significant change due to the growth of biofilm onto the sediment surface. The study proposes a characteristic particle size formula and a bio-particle settling velocity formula based on the regression of experiment results, that the settling velocity is only 50% to 60% as the single particle which has the same diameter and density. However, biofilm growth causes large particle which the settling velocities are approximately 10 times larger than that of primary particles. These results may be specifically used in the low energy reservoir or lake environment.

Impact of Basset force on threshold values of particle drag coefficient and density parameter in standing sinusoidal wave

A one-dimensional drift of spherical particle in standing sinusoidal wave is studied numerically. The impact of stationary and non-stationary forces of viscous drag, as well as Archimedes, added masses and Basset forces on particle drift direction is investigated. For various Reynolds and Strouhal numbers the dependencies of the threshold particle drag coefficient on density parameter have been found. These dependencies show that with increasing Reynolds and Strouhal numbers the threshold value of the squared drag coefficient decreases markedly. Impact of Basset force on threshold values is especially strong for low- density particles.

Prediction slurry reactor design under uncertainty using CFD model

Mechanically agitated reactors find wide range of applications for solid suspension and mixing in the chemical, biochemical, and mineral processing industries. Understanding the solids dynamics in these reactors is necessary to improve the design and operation of such reactors. Computational fluid dynamic (CFD) models are often useful in this regard, as it can provide significant insights into the flow and mixing of the phases involved. However, the model predictions need extensive evaluation with experimental results before they can be confidently used for the scale-up and optimization of large scale reactors. In the present work the predictive capabilities of CFD techniques as applied to solid-liquid stirred vessels are investigated. Suspensions of sand (diameter equal to 327 m) in water are studied. Eulerian-Granular multiphase model was simulated using FLUNT 6.3.26 to predict the slurry reactor design under uncertainty. The profiles obtained with the Eulerian-Granular approach coupled with the Eulerian, Granular models, and experimental data for comparison purposes. The present model provides an improvement of the predictions in the lower part of the vessel, with respect to the Eulerian model; while the same results can be observed in the rest of the tank where the solid concentration is lower. It seems that the interaction phenomena between the solid and the liquid phases and those among the solid particles do not vary appreciably for low solid concentrations, while at higher concentration some effects become noticeable. It was found that the quasi-steady state behavior of the sand in the mixing tank reached after 20 sec, also after 10 sec were the free surface of the static pressure will be growth until reach peremptory shape after 20 sec. The present model provides a proper representation for the solid distribution, by adopting particle drag coefficient.

Filtered models for bidisperse gas–particle flows

Using the microscopic multi-fluid model as a starting point we perform fine grid simulations of bidisperse gas–particle flows to examine the dependence of the filtered fluid–particle drag coefficient, particle–particle drag coefficient, and particle phase stress on the volume fractions and sizes of the particles and the filter size. Scalings are identified for the filtered fluid–particle drag coefficient, particle–particle drag coefficient, and particle phase pressure that capture the dependence of each filtered correction on the size and volume fraction ratios of the bidisperse assembly.

Drag of Tandem Spheroids in Power-Law Fluids at Moderate Reynolds Numbers

The relative motion between a power-law fluid and two tandem spheroid particles was investigated numerically. The field equations that govern this problem were solved using a commercial computational-fluid-dynamics-based solver. The semi-implicit method for pressure-linked equations (SIMPLE) algorithm and the quadratic upstream interpolation for convective kinematics (QUICK) scheme for convective terms were used. The solver was thoroughly benchmarked through domain and grid studies. Further, extensive new results are presented for the following ranges of conditions: Reynolds number (Re), 1–200; particle aspect ratio (e), 0.5–2; power-law index (n), 0.4–1.6; and interparticle distance (S), 2–5. The main focus of this work was to report the effects of these parameters on the streamlines, surface viscosity, and drag coefficients of the tandem particles. The dependence of the average drag coefficient on the power-law index and Reynolds number had a crossover Reynolds number that was found to be a strong function of the particle aspect ratio and the interparticle distance. Below this crossover Reynolds number, the average drag coefficient increased with decreasing power-law index, whereas for Reynolds numbers greater than the crossover Reynolds number, the average drag coefficient decreased with decreasing power-law index.

Dedicated vertical wind tunnel for the study of sedimentation of non-spherical particles

A dedicated 4-m-high vertical wind tunnel has been designed and constructed at the University of Geneva in collaboration with the Groupe de compétence en mécanique des fluides et procédés énergétiques. With its diverging test section, the tunnel is designed to study the aero-dynamical behavior of non-spherical particles with terminal velocities between 5 and 27 ms(-1). A particle tracking velocimetry (PTV) code is developed to calculate drag coefficient of particles in standard conditions based on the real projected area of the particles. Results of our wind tunnel and PTV code are validated by comparing drag coefficient of smooth spherical particles and cylindrical particles to existing literature. Experiments are repeatable with average relative standard deviation of 1.7%. Our preliminary experiments on the effect of particle to fluid density ratio on drag coefficient of cylindrical particles show that the drag coefficient of freely suspended particles in air is lower than those measured in water or in horizontal wind tunnels. It is found that increasing aspect ratio of cylindrical particles reduces their secondary motions and they tend to be suspended with their maximum area normal to the airflow. The use of the vertical wind tunnel in combination with the PTV code provides a reliable and precise instrument for measuring drag coefficient of freely moving particles of various shapes. Our ultimate goal is the study of sedimentation and aggregation of volcanic particles (density between 500 and 2700 kgm(-3)) but the wind tunnel can be used in a wide range of applications.

Predicting the drag coefficient and settling velocity of spherical particles

Abstract This paper presents a relationship for calculating the drag coefficient of a spherical particle. The results obtained were validated using experimental data, including comparison with results from other relationships such as certainty analysis. The validation indicated that the proposed relationship is easier to apply and produces the best results. In addition, a relationship based on the characteristics of both the fluid and the particles was established to calculate directly the settling velocity of a spherical particle in a fluid at rest. The settling velocity values obtained with the proposed relationship were validated using experimental data and the model proved to be reliable and precise.

Explosively driven particle fields imaged using a high speed framing camera and particle image velocimetry

A high speed framing camera and a particle image velocimetry instrument were used to determine the properties of explosively driven particle fields in early microsecond and later millisecond times. Test items were configured in a two inch long cylindrical shape with a half inch diameter core of organic explosive. The core was surrounded by a particle bed of aluminum or tungsten powder of a specific particle size distribution. Position data from the leading edge of the particle fronts for each charge was recorded with a high speed framing camera at early time and with a particle image velocimetry (PIV) instrument at later time to determine particle velocity. Using a PIV image, a velocity gradient along the length of the particle field was established by using the mean particle velocity value determined from three separate horizontal bands that transverse the particle field. The results showed slower particles at the beginning of the particle field closest to the source and faster ones at the end. Differences in particle dispersal, luminescence, and agglomeration were seen when changes in the initial particle size and material type were made. The aluminum powders showed extensive luminescence with agglomeration forming large particle structures while the tungsten powder showed little luminescence, agglomeration and no particle structures. Combining velocity data from the high speed framing camera and PIV, the average drag coefficient for each powder type was determined. The particle field velocities and drag coefficients at one meter showed good agreement with the numerical data produced from a computational fluid dynamics code that takes advantage of both Eulerian and Lagrangian solvers to track individual particles after a set post detonation time interval.

Shock tube investigation of quasi-steady drag in shock-particle interactions

A reassessment of historical drag coefficient data for spherical particles accelerated in shock-induced flows has motivated new shock tube experiments of particle response to the passage of a normal shock wave. Particle drag coefficients were measured by tracking the trajectories of 1-mm spheres in the flow induced by incident shocks at Mach numbers 1.68, 1.93, and 2.04. The necessary data accuracy is obtained by accounting for the shock tube wall boundary layer growth and avoiding interactions between multiple particles. Similar to past experiments, the current data clearly show that as the Mach number increases, the drag coefficient increases substantially. This increase significantly exceeds the drag predicted by incompressible standard drag models, but a recently developed compressible drag correlation returns values quite close to the current measurements. Recent theoretical work and low particle accelerations indicate that unsteadiness should not be expected to contribute to the drag increase over the relatively long time scales of the experiments. These observations suggest that elevated particle drag coefficients are a quasi-steady phenomenon attributed to increased compressibility rather than true flow unsteadiness.

Remote control of DNA-acting enzymes by varying the Brownian dynamics of a distant DNA end

Enzyme rates are usually considered to be dependent on local properties of the molecules involved in reactions. However, for large molecules, distant constraints might affect reaction rates by affecting dynamics leading to transition states. In single-molecule experiments we have found that enzymes that relax DNA torsional stress display rates that depend strongly on how the distant ends of the molecule are constrained; experiments with different-sized particles tethered to the end of 10-kb DNAs reveal enzyme rates inversely correlated with particle drag coefficients. This effect can be understood in terms of the coupling between molecule extension and local molecular stresses: The rate of bead thermal motion controls the rate at which transition states are visited in the middle of a long DNA. Importantly, we have also observed this effect for reactions on unsupercoiled DNA; other enzymes show rates unaffected by bead size. Our results reveal a unique mechanism through which enzyme rates can be controlled by constraints on macromolecular or supramolecular substrates.

PTV measurement of drag coefficient of fibrous particles with large aspect ratio

Abstract The aerodynamic behaviour of long aspect ratio nylon fibrous particles has been investigated experimentally while settling in air under super dilute conditions without any influence of secondary flows and at fibre Reynolds numbers of 0.5–2 based on fibre diameter. A method for laser-based measurement of the orientations and velocities of fibrous particles is also presented. The experimental apparatus employs a two-dimensional Particle Tracking Velocimetry (PTV) to calculate orientation and velocity based on the two end-points. The controlling length scale in the relationship between Reynolds number and drag coefficient was investigated and the equivalent diameter of settling fibre in air was reported. Finally the influence of volume fraction and fibre straightness were assessed.

Particle clusters and drag coefficients in gas–solid downer units

This manuscript reports “individual” particle cluster information obtained using a Chemical Reactor Engineering Centre Gas–Solid Optical Probe (CREC-GS-Optiprobe) equipped with a Graded Refractive Index (GRIN) lens. The CREC-GS-Optiprobe is used to study the fluid dynamics in the developed region of a co-current gas solid down flow fluidized bed unit. The CREC-GS-Optiprobe forms a 118±34μm diameter highly illuminated light region at 8.05mm distance in front of the sensor tip. Experiments are carried out in a circulating fluidized bed downer cold model unit of 3.0m height and 0.0257m internal diameter. The solid used is a fluid catalytic cracking (FCC) catalyst with a mean particle diameter of 84.42μm and a particle density of 1722kg/m3. The superficial gas velocity and solid mass fluxes are varied from 0.95 to 2.53m/s and from 10 to 106kg/m2s, respectively. Analysis of the data obtained involves a rigorous methodology for setting the data baseline in compliance with solid mass balances. The application of this method allows the simultaneous measurement of (i) cluster solid concentrations, (ii) individual cluster slip velocities and (iii) individual cluster sizes. These data also allow calculation of cluster size frequency distribution at various radial positions in the downer unit. On the strength of these experimental data, particle cluster drag coefficients are calculated as a function of the cluster Reynolds’ number and average particle number in the cluster. Drag coefficients determined using the proposed method provide close range values. These findings support a particle string configuration for clusters in downer units.

Aerodynamic flow around a sport utility vehicle—Computational and experimental investigation

Standard CFD methods require a mesh that fits the boundaries of the computational domain. For a complex geometry the generation of such a grid is time-consuming, and often requires modifications to the model geometries particularly when one begins with the “raw” CAD data. This paper evaluates the newly developed Immersed Boundary (IB) approach which does not require mesh to be conformal to body and thus would speed up the process of the grid generation. The IB approach starts directly from CAD (STL) files, and has the potential in mitigating the process of CAD cleanup and surface meshing for the CFD simulations. The Reynolds-Averaged Navier–Stokes (RANS) solver based on the Immersed Boundary technique is used to investigate the aerodynamic flow field around a generic Sport Utility Vehicle (SUV). The simulations are compared with the experimental data for the same vehicle geometries. The experimental data include particle image velocimetry (PIV) velocity, surface pressure and drag coefficient measurements. The results show that the CFD simulations were able to track the flow very well for the generic SUV (both qualitatively and quantitatively). The predicted drag coefficients for the generic SUV model was within 5% of the measured values. Finally, the IB approach was used to predict the flow structures and the drag coefficient for a production SUV (Chevy Tahoe). In addition, the same geometry was simulated using the standard body-fitted approach for direct comparison with the IB simulations. The flow results of both simulations were similar. The simulated drag coefficients for the IB and the body-fitted approaches were within 3% and 3–7% of the measured value, respectively. It should be noted that, the paper is about a comparison of the IB to body-fitted approaches for automotive aerodynamics, and these approaches are simulations of wind tunnel measurements. Since the wind tunnel testing is a cold process using an “engine-off” condition, there was no need to perform the simulations with thermal boundary conditions activated for engines, exhaust, heat exchangers, etc.

A new definition of bed expansion index and voidage for fluidized biofilm-coated particles

Experimental data available in the literature for bed voidage and bed expansion index of biofilm-coated particles in a fluidized bed was extracted, sorted and used to study the validation of the proposed bed expansion index equations in the literature. Drag coefficients of biofilm-coated particles for all the aforementioned data were calculated using a new proposed equation [1] that describes drag forces as a function of Archimedes numbers. Archimedes number was proposed to be superior to Reynolds number for bed expansion definition. New equations based on Archimedes number and physical properties of biofilm-coated particles were proposed to calculate the bed expansion index of fluidized biofilm-coated particles as well as bed voidage in fluidized bed bioreactors. The new equations predicted the existing experimental bed expansion index and voidage with less standard average error than all other literature equations that related bed expansion to Reynolds number.

Remote Control of DNA-Acting Enzymes by Molecular Boundary Conditions

The rate of action of an enzyme at a point along a long DNA molecule is usually assumed to be determined by the local properties of that region of the nucleic acid chain such as its sequence, flexibility, and molecular stress. Here we show that enzymes that relax DNA torsional stress display rates which strongly depend on how the distant ends of the molecule are constrained: experiments with different size colloidal particles tethered to the end of 10 kb DNAs reveal enzyme rates that are inversely correlated with particle drag coefficient. This effect can be understood in terms of the coupling between molecule extension and local molecular stresses: the rate of bead thermal motion controls the rate at which transition states are visited in the middle of a long DNA. Torsional stress is not a requirement for this effect. Importantly, some enzymes show rates unaffected by bead size. Our results reveal a new mechanism through which variation in chromosome domain architecture, and more generally, large-scale architecture of large thermally fluctuating substrates, can control enzyme rates.

Prediction of Drag Coefficient and Secondary Motion of Free-Falling Rigid Cylindrical Particles with and without Curvature at Moderate Reynolds Number

Laboratory experiments have been conducted to understand the behavior of negatively buoyant cylindrical particles of density ρ, length L, diameter d, with and without curvature, freely falling in a fluid of density ρw at Reynolds numbers based on d of 200–6,000. The paper proposes a parameter based on the cylinder density ratio S=ρ/ρw and aspect ratio E=L/d that is able to predict the onset of different modes of secondary motion ranging from oscillations to tumbling. The same parameter can also predict the maximum amplitude of the oscillations of the cylinder, on the basis of comparing the magnitudes of the oscillation velocity with the fall velocity. Contrary to previous work that has treated the oscillations and drag coefficient dependence as independent phenomena, this paper argues that the secondary motion reduces the time-averaged projected surface area of the cylinder during its descent, leading to a lower observed drag coefficient CD computed using the nominal projected area of length times diamete...

LDV measurements and analysis of gas and particulate phase velocity profiles in a vertical jet plume in a 2D bubbling fluidized bed Part II: Mass and momentum transport

A Laser Doppler Velocimetry (LDV) technique was implemented to simultaneously measure the gas and particulate phase velocities in a high-speed jet plume in a two-dimensional (2D) bubbling fluidized bed. The gas and particulate phase velocity profiles are presented and analyzed. This includes similarity profile scaling as well as volume fraction, mass flow, and momentum transport calculations for the two phases. Furthermore, applying the Eulerian equation of motion to the particulate phase with the measured velocity profiles, the bed particle drag coefficient is recovered and is found to be consistent with the established empirical value.

LDV measurements and analysis of gas and particulate phase velocity profiles in a vertical jet plume in a 2D bubbling fluidized bed Part III: The effect of fluidization

In the present work, the effect of emulsion fluidization on the gas and particle phase transport in a high-speed gas jet plume in a bubbling bed is examined. Implementing a Laser Doppler Velocimetry (LDV) technique, the gas and particulate phase velocities of a gas jet injected into a bubbling bed of 838μm high-density polyethylene (HDPE) micropellets were measured. These velocity profiles were used to determine the volume fraction, mass flow, and momentum transport rate for each phase at various axial locations as well as an average particle drag coefficient in the measurement region of the plume. Maintaining consistent gas jet inlet conditions, the HDPE emulsion fluidization was varied from a spouted bed to 50% beyond minimum fluidization. In addition to the integral flow values, centerline phase velocity scaling is also examined. The scaling is based on the development of similarity velocity profiles for the two phases. Additional experiments to investigate this idea were carried out with 1) the particle emulsion and fluidization level is held constant while the jet inlet velocity is varied and 2) the jet inlet velocity and fluidization ratio is held constant while the bed particles are varied.