Effective Drag Coefficient for Gas-Particle Flow in Shock Tubes

1970 ◽  
Vol 92 (1) ◽  
pp. 165-172 ◽  
Author(s):  
George Rudinger
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Particle Motion ◽  
Gas Flow ◽  
Particle Concentration ◽  
Particle Diameter ◽  
Weak Shock ◽  
Average Particle ◽  
Particle Rotation ◽  
Lateral Velocity

Effective drag coefficients for flows of suspensions of spherical glass particles in air were derived from simultaneous measurements of pressure and particle concentration in the flow behind weak shock waves. Average particle diameters were 29 and 62μm. The instantaneous concentration was determined by light scattering, and the results agree well with earlier shock-tube data based on streak records. They exhibit several unexpected features: the correlation between drag coefficient and Reynolds number is much steeper (∝ Re−1.7) than the generally used “standard” curve but approaches it at Reynolds numbers of several hundred; the correlation is independent of the particle concentration over the range of the experiments, that is, for particle-to-gas flow rate ratios between about 0.05 and 0.36; if the Reynolds number immediately behind the shock front is changed by varying the shock strength, the points move along the correlation, but if it is changed by changing the particle size, the entire correlation is shifted although to a smaller extent than would correspond to the direct effect of particle diameter on the Reynolds number. To account for the observations, a flow model is developed which allows for microscopic longitudinal and lateral perturbations of the particle motion that are the result of various causes, such as particle interactions with wakes of other particles, lateral forces caused by particle rotation, or electrostatic forces. Because of the nonlinearity of the equation of motion, the averaged particle motion is different from that of a particle without perturbations. The effective drag coefficient for the average particle motion is therefore different from the standard drag coefficient applied along the actual motion. With this model and plausible assumptions for the average lateral velocity component of the particle motion, all features of the experimental data can be qualitatively explained.

scholarly journals Simulation of Gas Flow Over a Micro Cylinder

2009 ◽  
Author(s):  
Yuan Hu ◽  
Quanhua Sun ◽  
Jing Fan
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Drag Coefficient ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Low Reynolds Number ◽  
Pressure Drag ◽  
Low Reynolds ◽  
Rarefied Gas Effect ◽  
Gas Effect

Gas flow over a micro cylinder is simulated using both a compressible Navier-Stokes solver and a hybrid continuum/particle approach. The micro cylinder flow has low Reynolds number because of the small length scale and the low speed, which also indicates that the rarefied gas effect exists in the flow. A cylinder having a diameter of 20 microns is simulated under several flow conditions where the Reynolds number ranges from 2 to 50 and the Mach number varies from 0.1 to 0.8. It is found that the low Reynolds number flow can be compressible even when the Mach number is less than 0.3, and the drag coefficient of the cylinder increases when the Reynolds number decreases. The compressible effect will increase the pressure drag coefficient although the friction coefficient remains nearly unchanged. The rarefied gas effect will reduce both the friction and pressure drag coefficients, and the vortex in the flow may be shrunk or even disappear.

Settling Behavior of Particles in Bubble Containing Newtonian Fluids: Experimental Study and Model Development

2021 ◽  
Author(s):  
Silin Jing ◽  
Xianzhi Song ◽  
Zhaopeng Zhu ◽  
Buwen Yu ◽  
Shiming Duan
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Volume Concentration ◽  
Settling Velocity ◽  
Particle Density ◽  
Particle Diameter ◽  
Newtonian Fluids ◽  
Spherical Particles ◽  
Bubble Volume ◽  
Particle Reynolds Number

Abstract Accurate description of cuttings slippage in the gas-liquid phase is of great significance for wellbore cleaning and the control accuracy of bottom hole pressure during MPD. In this study, the wellbore bubble flow environment was simulated by a constant pressure air pump and the transparent wellbore, and the settling characteristics of spherical particles under different gas volume concentrations were recorded and analyzed by highspeed photography. A total of 225 tests were conducted to analyze the influence of particle diameter (1–12mm), particle density (2700–7860kg/m^3), liquid viscosity and bubble volume concentration on particle settling velocity. Gas drag force is defined to quantitatively evaluate the bubble’s resistance to particle slippage. The relationship between bubble drag coefficient and particle Reynolds number is obtained by fitting the experimental results. An explicit settling velocity equation is established by introducing Archimedes number. This explicit equation with an average relative error of only 8.09% can directly predict the terminal settling velocity of the sphere in bubble containing Newtonian fluids. The models for predicting bubble drag coefficient and the terminal settling velocity are valid with particle Reynolds number ranging from 0.05 to 167 and bubble volume concentration ranging from 3.0% to 20.0%. Besides, a trial-and-error procedure and an illustrative example are presented to show how to calculate bubble drag coefficient and settling velocity in bubble containing fluids. The results of this study will provide the theoretical basis for wellbore cleaning and accurate downhole pressure to further improve the performance of MPD in treating gas influx.

Experimental Investigation of Convective Melting of Granular Packed Bed Under Microgravity

2002 ◽  
Vol 124 (3) ◽  
pp. 516-524 ◽  
Author(s):  
J. Jiang ◽  
Y. Hao ◽  
Y.-X. Tao
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Froude Number ◽  
Average Particle Size ◽  
Particle Diameter ◽  
Packed Bed ◽  
Melting Rate ◽  
Solid Particles ◽  
Average Particle ◽  
Stefan Number

To improve the understanding of convective melting of packed solid particles in a fluid, an experimental investigation is conducted to study the melting characteristics of a packed bed by unmasking the buoyancy forces due to the density difference between the melt and solid particles. A close-loop apparatus, named the particle-melting-in-flow (PMF) module, is designed to allow a steady-state liquid flow at a specified temperature. The module is installed onboard NASA’s KC-135 reduced gravity aircraft using ice particles of desired sizes and water as the test media. Experimentally determined melting rates are presented as a function of upstream flow velocity, temperature and initial average particle size of the packed bed. It is found that the melting rate is influenced mainly by the ratio of the Reynolds number (Re, based on the initial particle diameter) to the square of the Froude number (Fr), and the Stefan number (Ste). In general, the dimensionless melting rate decreases as Re/Fr2 increases and increases as Ste increases. With the absence of gravity, i.e., as the Froude number approaches infinity, a maximum melting rate can be achieved. The increase in the melting rate proportional to the Stefan number also becomes more pronounced under the zero gravity condition. The trend of average and local Nusselt number of the melting packed bed under microgravity, as a function of Reynolds number and Prandtl number, is discussed and compared with the case of nonmelting packed bed.

Influence of Particle Shape on the Drag Coefficient for Isometric Particles

1994 ◽  
Vol 59 (12) ◽  
pp. 2583-2594 ◽  
Author(s):  
Miloslav Hartman ◽  
Otakar Trnka ◽  
Karel Svoboda ◽  
Václav Veselý
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Drag Coefficient ◽  
Fluidized Beds ◽  
Fluid Velocity ◽  
Particle Diameter ◽  
Free Fall ◽  
Fall Velocity ◽  
Gas Cleaning ◽  
Explicit Formulae

A comprehensive correlation has been developed of the drag coefficient for nonspherical isometric particles as a function the Reynolds number and the particle sphericity on the basis of data reported in the literature. The proposed formula covers the Stokes, the transitional and the Newton region. The predictions of the reported correlation have been compared to experimental data measured in this work with the dolomitic materials in respect to their use in calcination and gas cleaning processes with fluidized beds. Approximative explicit formulae have also been reported that make it possible to estimate the terminal free-fall velocity of a given particle or to predict the particle diameter corresponding to a fluid velocity of interest.

Microscopic Analysis of Sand Shear Band in Direct Shear Test Based on Particle Flow Theory

2012 ◽  
Vol 170-173 ◽  
pp. 83-87
Author(s):  
Yang Liu ◽  
Jie Hu ◽  
Shun Chuan Wu
Keyword(s):  
Shear Band ◽  
Direct Shear Test ◽  
Shear Test ◽  
Displacement Vector ◽  
Particle Diameter ◽  
Average Particle ◽  
Direct Shear ◽  
Particle Rotation ◽  
Principal Stresses ◽  
Shear Process

In order to analyze the microscopic shear mechanics behavior of sands, a numerical simulation is carried out in sand direct shear test with commercial DEM software PFC2D. By compiling FISH function, PFC2D is able to visualize principal stresses and their inclination inside the sample. In the simulation, particle rotation gradient and particle displacement vector are observed to analyze the microscopic formation mechanism of shear band. The strain and deformation is concentrated in a band whose thickness is about 10 times of average particle diameter and the band is close to the shear plane. The porosity ratio in shear band is higher than other parts of the sample with shear process.

An Immersed Boundary Direct Numerical Simulation Study of the Wall Effect on the Dynamics of a Rigid Sphere

2017 ◽  
Author(s):  
Jason Gatewood ◽  
Zhi-Gang Feng
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Drag Coefficient ◽  
Particle Diameter ◽  
Laminar Flows ◽  
Wall Effect ◽  
Immersed Boundary ◽  
Rigid Sphere ◽  
Rigid Spheres

The presence of a wall near a rigid sphere is known to disturb the particle fore and aft flow field and thereby affect particle drag and lift. This effect has wide ranging implications in particulate flows such as the dynamics of blood cells in microvessels or the transport of particulates in channel and pipe flows. In this study, an Immersed Boundary Direct Numerical Simulation (IB-DNS) is used to predict the dynamics of a rigid spherical body in the presence of a wall at laminar flows. The wall effect is shown to be significant when the dimensionless ratio (L/D) of the particle diameter (D) to the wall distance (L) is less than 3, and when particle Reynolds number is less than 10. Based on the IB-DNS results, a correlation for the wall effect on drag coefficient is derived that can be used to predict the actual drag coefficient for rigid spheres under the influence of a wall for L/D between 0.75 and 3 and Reynolds number between 0.18 and 10. The data underlying the correlation developed herein is validated by comparison to published experimental, numerical, and analytical correlations. The application of the IB-DNS method to study the wall effect is both novel and significant. It is novel in that such an application is not yet demonstrated. It is significant in that it; (1) utilizes a uniform Cartesian fluid mesh and (2) requires no sub domains of higher grid resolution in the wall gap.

Particle motion and erosion morphology of the spool orifice in an electro-hydraulic servo valve under a small opening

2021 ◽  
pp. 095440622110349
Author(s):  
Xinqiang Liu ◽  
Hong Ji ◽  
Fei Liu ◽  
Nana Li ◽  
Jianjun Zhang ◽  
...  
Keyword(s):  
Wear Rate ◽  
Particle Motion ◽  
Particle Diameter ◽  
Pressure Differential ◽  
Erosion Wear ◽  
Particle Rotation ◽  
Small Opening ◽  
Servo Valve ◽  
Typical Particle ◽  
Hydraulic Servo

To explore the spool orifice’s particle motion and erosion morphology in an electro-hydraulic servo valve under a small opening, a modeled particle motion visualization test and CFD calculation were conducted to study typical particle trajectory. The influence of pressure differential, particle shape, and particle diameter on the erosion rate along the working edges was discussed. The erosion characteristic morphology and working edges’ fillet diameter distribution were measured and analyzed. There are four typical particle motions: translation and spin on the wall faced the flow, translation and turn on the backflow wall, carried motion by the mainstream and particle rotation in a vortex. A model of the erosive particle motion of the spool orifice was built based on the visualization test and CFD. During these motions, the microscopic scraping and collision of particles with the working edges are the main causes of erosion wear. The erosion wear rate of the working edge is proportional to the pressure differential and the non-roundness of the particles. The fillet of a working edge periodically increases or decreases with the circumferential angle, which occurs due to the morphology and is consistent with the erosion wear rate distribution along the working edge.

Adsorption of safranine T from aqueous medium by nano mesoporous MCM-41: adsorption equilibrium, kinetics, and thermodynamics

2020 ◽  
Vol 10 ◽  
Author(s):  
Xiao-Dong Li ◽  
Qing-Zhou Zhai
Keyword(s):  
Electron Microscopy ◽  
Ph Value ◽  
Particle Diameter ◽  
Spherical Particles ◽  
Practical Significance ◽  
Average Particle ◽  
Average Pore ◽  
Kinetics And Thermodynamics ◽  
Safranine T ◽  
Mcm 41

Introduction: In industrial production, a small amount of saffron T emissions will cause increase of water color and increase of chemical oxygen consumption, so study of the decolorization of saffron T wastewater has an important practical significance. Methods: MCM (Mobil Composition of Matter)-41 molecular sieve was synthesized by hydrothermal method. Power Xray diffraction and scanning electron microscopy were used to characterize the sample. Safranine T dye was adsorbed from water by the MCM-41 prepared. Kinetics and thermodynamics of the adsorption were studied. Results: The MCM-41 sample presented spherical particles and regular. The BET (Brunner-Emmett-Teller) specific surface area of the sample determined by 77 K low temperature nitrogen adsorption-desorption isotherm was 932 m2 /g. Its average particle diameter was 110 nm. TEM (transmission electron microscopy) results showed that the sample structure presented a honeycomb pore structure and the average pore diameter was 3.0 nm. The results showed that when room temperature was 20 ± 1 ℃, adsorbate safranine T: adsorbent MCM-41 = 20 : 1，the optimum pH value of adsorption was 4.0 and contact time was 20 min, the adsorption rate reached 98.29% and the adsorption capacity was 19.66 mg/g. The entropy change and enthalpy change of the adsorption system are respectively ΔS0 = 157.5 J/(mol·K); ΔH0 = 21.544 kJ/mol. When temperature was 277.15, 293.15, 303.15 K，the free energy change was respectively △G1 0 = -22.107 kJ/mol, △G2 0 = -24.627 kJ/mol, △G3 0 = -26.202 kJ/mol. Conclusion: The adsorption of safranine T by MCM-41 belongs to a pseudo-second-order adsorption. This adsorption accords with the Freundlich equation and belongs to a heterogeneous adsorption. The adsorption is an endothermic reaction of entropy increase, being spontaneous.

scholarly journals A Comparative Evaluation of Nanohydroxyapatite-Enriched Hydrogen Peroxide Home Bleaching System on Color, Hardness and Microstructure of Dental Enamel

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3072
Author(s):  
Riccardo Monterubbianesi ◽  
Vincenzo Tosco ◽  
Tiziano Bellezze ◽  
Giampaolo Giuliani ◽  
Mutlu Özcan ◽  
...  
Keyword(s):  
Hydrogen Peroxide ◽  
Particle Diameter ◽  
Dental Enamel ◽  
Sem Analysis ◽  
Control Group ◽  
Average Particle ◽  
Color Analysis ◽  
Enamel Microstructure ◽  
Prismatic Structure ◽  
20 Nm

This study aimed to evaluate two hydrogen peroxide (HP)-based at-home bleaching systems in order to analyze whether nano-hydroxyapatite (nHA) addition may represent a reliable and safe solution for tooth whitening without altering dental microstructure and hardness. Human third molars (N = 15) were treated with two bleaching agents, one containing 6%HP (6HP) and the other 6% HP nHA-enriched (6HP-nHA) with average particle diameter ranging from 5–20 nm. Their effects on enamel were assessed using a spectrophotometer, Vickers microhardness (VMH) test and Scanning Electron Microscopy (SEM), comparing the treated groups with the non-treated control group (CTR). Color analysis revealed improvement in whiteness in both groups compared to CTR. VMH test results showed no differences among the groups. SEM analysis highlighted no evident changes in the enamel microstructure of tested groups compared to CTR. At high magnification, in 6HP group, a slight increase in irregularities of enamel surface morphology was observed, while 6HP-nHA group displayed removal of the aprismatic layer but preservation of the intact prismatic structure. These results suggest that the 6HP-nHA agent may be recommended to provide reliable whitening treatment, without damaging the enamel micromorphology and hardness.

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