scholarly journals Slipping motion of large neutrally buoyant particles in turbulence

2013 ◽  
Vol 735 ◽  
Author(s):  
Mamadou Cisse ◽  
Holger Homann ◽  
Jérémie Bec
Keyword(s):  
Reynolds Number ◽  
Fluid Velocity ◽  
Particle Diameter ◽  
Viscous Sublayer ◽  
Energy Dissipation Rate ◽  
Spherical Particles ◽  
Viscous Boundary Layer ◽  
Average Value ◽  
Wall Flows ◽  
Shadowing Effect

AbstractDirect numerical simulations are used to investigate the individual dynamics of large spherical particles suspended in a developed homogeneous turbulent flow. A definition of the direction of the particle motion relative to the surrounding flow is introduced and used to construct the mean fluid velocity profile around the particle. This leads to an estimate of the particle slipping velocity and its associated Reynolds number. The flow modifications due to the particle are then studied. The particle is responsible for a shadowing effect that occurs in the wake up to distances of the order of its diameter: the particle calms turbulent fluctuations and reduces the energy dissipation rate compared to its average value in the bulk. Dimensional arguments are presented to draw an analogy between particle effects on turbulence and wall flows. Evidence is obtained for the presence of a logarithmic sublayer at distances between the thickness of the viscous boundary layer and the particle diameter ${D}_{p} $. Finally, asymptotic arguments are used to relate the viscous sublayer quantities to the particle size and the properties of the outer turbulence. It is shown in particular that the skin-friction Reynolds number behaves as $R{e}_{\tau } \propto {({D}_{p} / \eta )}^{4/ 3} $.

A strong-interaction theory for the motion of arbitrary three-dimensional clusters of spherical particles at low Reynolds number

1988 ◽  
Vol 197 ◽  
pp. 1-37 ◽  
Author(s):  
Qaizar Hassonjee ◽  
Peter Ganatos ◽  
Robert Pfeffer
Keyword(s):  
Exact Solution ◽  
Reynolds Number ◽  
Low Reynolds Number ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Particle Diameter ◽  
Simple Expression ◽  
Spherical Particles ◽  
Solution Technique ◽  
Low Reynolds

This paper contains an ‘exact’ solution for the hydrodynamic interaction of a three-dimensional finite cluster at arbitrarily sized spherical particles at low Reynolds number. The theory developed is the most general solution to the problem of an assemblage of spheres in a three-dimensional unbounded media. The boundary-collocation truncated-series solution technique of Ganatos, Pfeffer & Weinbaum (1978) for treating planar symmetric Stokes flow problems has been extensively modified to treat the non-symmetric multibody problem. The orthogonality properties of the eigenfunctions in the azimuthal direction are used to satisfy the no-slip boundary conditions exactly on entire rings on the surface of each particle rather than just at discrete points.Detailed comparisons with the exact bipolar solutions for two spheres show the present theory to be accurate to five significant figures in predicting the translational and angular velocity components of the particles at all orientations for interparticle gap widths as close as 0.1 particle diameter. Convergence of the results to the exact solution is rapid and systematic even for unequal-sized spheres (a1/a2 = 2). Solutions are presented for several interesting and intriguing configurations involving three or more spherical particles settling freely under gravity in an unbounded fluid or in the presence of other rigidly held particles. Advantage of symmetry about the origin is taken for symmetric configurations to reduce the collocation matrix size by a factor of 64. Solutions for the force and torque on three-dimensional clusters of up to 64 particles have been obtained, demonstrating the multiparticle interaction effects that arise which would not be present if only pair interactions of the particles were considered. The method has the advantage of yielding a rather simple expression for the fluid velocity field which is of significance in the treatment of convective heat and mass transport problems in multiparticle systems.

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 studies of the viscous boundary layer properties in turbulent Rayleigh–Bénard convection

2008 ◽  
Vol 605 ◽  
pp. 79-113 ◽  
Author(s):  
CHAO SUN ◽  
YIN-HAR CHEUNG ◽  
KE-QING XIA
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Rayleigh Number ◽  
Power Law ◽  
Thermal Boundary Layer ◽  
Viscous Sublayer ◽  
Viscous Boundary Layer ◽  
Velocity Boundary Layer ◽  
Viscous Boundary

We report high-resolution measurements of the properties of the velocity boundary layer in turbulent thermal convection using the particle image velocimetry (PIV) technique and measurements of the temperature profiles and the thermal boundary layer. Both velocity and temperature measurements were made near the lower conducting plate of a rectangular convection cell using water as the convecting fluid, with the Rayleigh number Ra varying from 109 to 1010 and the Prandtl number Pr fixed at 4.3. From the measured profiles of the horizontal velocity we obtain the viscous boundary layer thickness δυ. It is found that δυ follows the classical Blasius-like laminar boundary layer in the present range of Ra, and it scales with the Reynolds number Re as δυ/H = 0.64Re−0.50±0.03 (where H is the cell height). While the measured viscous shear stress and Reynolds shear stress show that the boundary layer is laminar for Ra < 2.0 × 1010, two independent extrapolations, one based on velocity measurements and the other on velocity and temperature measurements, both indicate that the boundary layer will become turbulent at Ra ~ 1013. Just above the thermal boundary layer but within the mixing zone, the measured temperature r.m.s. profiles σT(z) are found to follow either a power law or a logarithmic behaviour. The power-law fitting may be slightly favoured and its exponent is found to depend on Ra and varies from −0.6 to −0.77, which is much larger than the classical value of −1/3. In the same region, the measured profiles of the r.m.s. vertical velocity σw(z) exhibit a much smaller scaling range and are also consistent with either a power-law or a logarithmic behaviour. The Reynolds number dependence of several wall quantities is also measured directly. These are the wall shear stress τw ~ Re1.55, the viscous sublayer δw ~ Re−0.91, the friction velocity uτ ~ Re0.80, and the skin-friction coefficient cf ~ Re−0.34. All of these scaling properties are very close to those predicted for a classical Blasius-type laminar boundary layer, except that of cf. Similar to classical shear flows, a viscous sublayer is also found to exist in the present system despite the presence of a nested thermal boundary layer. However, velocity profiles normalized by wall units exhibit no obvious logarithmic region, which is likely to be a result of the very limited distance between the edge of the viscous sublayer and the position of the maximum velocity. Compared to traditional shear flows, the peak position of the wall-unit-normalized r.m.s. profiles is found to be closer to the plate (at z+ = z/δw ≃ 5). Our overall conclusion is that a Blasius-type laminar boundary condition is a good approximation for the velocity boundary layer in turbulent thermal convection for the present range of Rayleigh number and Prandtl number.

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.

scholarly journals Experimental investigation of turbulent suspensions of spherical particles in a square duct

2018 ◽  
Vol 857 ◽  
pp. 748-783 ◽  
Author(s):  
Sagar Zade ◽  
Pedro Costa ◽  
Walter Fornari ◽  
Fredrik Lundell ◽  
Luca Brandt
Keyword(s):  
Particle Size ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Single Phase ◽  
Volume Fraction ◽  
Particle Diameter ◽  
Spherical Particles ◽  
Particle Sizes ◽  
Duct Flow ◽  
Square Duct

We report experimental observations of turbulent flow with spherical particles in a square duct. Three particle sizes, namely $2H/d_{p}=40$ , 16 and 9 ( $2H$ being the duct full height and $d_{p}$ being the particle diameter), are investigated. The particles are nearly neutrally buoyant with a density ratio of 1.0035 and 1.01 with respect to the suspending fluid. Refractive index matched–particle image velocimetry (RIM–PIV) is used for fluid velocity measurement even at the highest particle volume fraction (20 %) and particle tracking velocimetry (PTV) for the particle velocity statistics for the flows seeded with particles of the two largest sizes, whereas only pressure measurements are reported for the smallest particles. Settling effects are seen at the lowest bulk Reynolds number $Re_{2H}\approx$ 10 000, whereas, at the highest $Re_{2H}\approx 27\,000$ , particles are in almost full suspension. The friction factor of the suspensions is found to be significantly larger than that of single-phase duct flow at the lower $Re_{2H}$ investigated; however, the difference decreases when increasing the flow rate and the total drag approaches the values of the single-phase flow at the higher Reynolds number considered, $Re_{2H}=27\,000$ . The pressure drop is found to decrease with the particle diameter for volume fractions lower than $\unicode[STIX]{x1D719}=10\,\%$ for nearly all $Re_{2H}$ investigated. However, at the highest volume fraction $\unicode[STIX]{x1D719}=20\,\%$ , we report a peculiar non-monotonic behaviour: the pressure drop first decreases and then increases with increasing particle size. The decrease of the turbulent drag with particle size at the lowest volume fractions is related to an attenuation of the turbulence. The drag increase for the two largest particle sizes at $\unicode[STIX]{x1D719}=20\,\%$ , however, occurs despite this large reduction of the turbulent stresses, and it is therefore due to significant particle-induced stresses. At the lowest Reynolds number, the particles reside mostly in the bottom half of the duct, where the mean velocity significantly decreases; the flow is similar to that in a moving porous bed near the bottom wall and to turbulent duct flow with low particle concentration near the top wall.

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 Deep Learning Based Instance Segmentation of Titanium Dioxide Particles in the Form of Agglomerates in Scanning Electron Microscopy

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 968
Author(s):  
Paul Monchot ◽  
Loïc Coquelin ◽  
Khaled Guerroudj ◽  
Nicolas Feltin ◽  
Alexandra Delvallée ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Titanium Dioxide ◽  
Learning Community ◽  
Spherical Particles ◽  
Average Value ◽  
Size Characterization ◽  
Scanning Electron

The size characterization of particles present in the form of agglomerates in images measured by scanning electron microscopy (SEM) requires a powerful image segmentation tool in order to properly define the boundaries of each particle. In this work, we propose to use an algorithm from the deep statistical learning community, the Mask-RCNN, coupled with transfer learning to overcome the problem of generalization of the commonly used image processing methods such as watershed or active contour. Indeed, the adjustment of the parameters of these algorithms is almost systematically necessary and slows down the automation of the processing chain. The Mask-RCNN is adapted here to the case study and we present results obtained on titanium dioxide samples (non-spherical particles) with a level of performance evaluated by different metrics such as the DICE coefficient, which reaches an average value of 0.95 on the test images.

scholarly journals Influence of Macroscopic Wall Structures on the Fluid Flow and Heat Transfer in Fixed Bed Reactors with Small Tube to Particle Diameter Ratio

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 689
Author(s):  
Thomas Eppinger ◽  
Nico Jurtz ◽  
Matthias Kraume
Keyword(s):  
Heat Transfer ◽  
Fixed Bed ◽  
Particle Diameter ◽  
Diameter Ratio ◽  
Spherical Particles ◽  
Reactor Wall ◽  
Entry Length ◽  
Fixed Bed Reactors ◽  
Wall Structures ◽  
Small Tube

Fixed bed reactors are widely used in the chemical, nuclear and process industry. Due to the solid particle arrangement and its resulting non-homogeneous radial void fraction distribution, the heat transfer of this reactor type is inhibited, especially for fixed bed reactors with a small tube to particle diameter ratio. This work shows that, based on three-dimensional particle-resolved discrete element method (DEM) computational fluid dynamics (CFD) simulations, it is possible to reduce the maldistribution of mono-dispersed spherical particles near the reactor wall by the use of macroscopic wall structures. As a result, the lateral convection is significantly increased leading to a better radial heat transfer. This is investigated for different macroscopic wall structures, different air flow rates (Reynolds number Re = 16 ...16,000) and a variation of tube to particle diameter ratios (2.8, 4.8, 6.8, 8.8). An increase of the radial velocity of up to 40%, a reduction of the thermal entry length of 66% and an overall heat transfer increase of up to 120% are found.

Radial lift on a suspended finite-sized sphere due to fluid inertia for low-Reynolds-number flow through a cylinder

2013 ◽  
Vol 722 ◽  
pp. 159-186 ◽  
Author(s):  
Sukalyan Bhattacharya ◽  
Dil K. Gurung ◽  
Shahin Navardi
Keyword(s):  
Reynolds Number ◽  
Particle Diameter ◽  
Axial Direction ◽  
Perturbation Scheme ◽  
Fluid Inertia ◽  
Regular Perturbation ◽  
Cross Sectional ◽  
First Order ◽  
Reynolds Number Flow ◽  
Freely Suspended

AbstractThis article describes the radial drift of a suspended sphere in a cylinder-bound Poiseuille flow where the Reynolds number is small but finite. Unlike past studies, it considers a circular narrow conduit whose cross-sectional diameter is only $1. 5$–$6$ times the particle diameter. Thus, the analysis quantifies the effect of fluid inertia on the radial motion of the particle in the channel when the flow field is significantly influenced by the presence of the suspended body. To this end, the hydrodynamic fields are expanded as a series in Reynolds number, and a set of hierarchical equations for different orders of the expansion is derived. Accordingly, the zeroth-order fields in Reynolds number satisfy the Stokes equation, which is accurately solved in the presence of the spherical particle and the cylindrical conduit. Then, recognizing that in narrow vessels Stokesian scattered fields from the sphere decrease exponentially in the axial direction, a simpler regular perturbation scheme is used to quantify the first-order inertial correction to hydrodynamic quantities. Consequently, it is possible to obtain two results. First, the sphere is assumed to follow the axial motion of a freely suspended sphere in a Stokesian condition, and the radial lift force on it due to the presence of fluid inertia is evaluated. Then, the approximate motion is determined for a freely suspended body on which net hydrodynamic force including first-order inertial lift is zero. The results agree well with the available experimental results. Thus, this study along with the measured data would precisely describe particle dynamics inside narrow tubes.

Law of bounded dissipation and its consequences in turbulent wall flows

2021 ◽  
Vol 933 ◽  
Author(s):  
Xi Chen ◽  
Katepalli R. Sreenivasan
Keyword(s):  
Dissipation Rate ◽  
Scaling Law ◽  
Random Variable ◽  
Energy Dissipation Rate ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Wall Flows ◽  
Maximum Value ◽  
Turbulent Wall ◽  
Promising Perspective

The dominant paradigm in turbulent wall flows is that the mean velocity near the wall, when scaled on wall variables, is independent of the friction Reynolds number $Re_\tau$ . This paradigm faces challenges when applied to fluctuations but has received serious attention only recently. Here, by extending our earlier work (Chen & Sreenivasan, J. Fluid Mech., vol. 908, 2021, p. R3) we present a promising perspective, and support it with data, that fluctuations displaying non-zero wall values, or near-wall peaks, are bounded for large values of $Re_\tau$ , owing to the natural constraint that the dissipation rate is bounded. Specifically, $\varPhi _\infty - \varPhi = C_\varPhi \,Re_\tau ^{-1/4},$ where $\varPhi$ represents the maximum value of any of the following quantities: energy dissipation rate, turbulent diffusion, fluctuations of pressure, streamwise and spanwise velocities, squares of vorticity components, and the wall values of pressure and shear stresses; the subscript $\infty$ denotes the bounded asymptotic value of $\varPhi$ , and the coefficient $C_\varPhi$ depends on $\varPhi$ but not on $Re_\tau$ . Moreover, there exists a scaling law for the maximum value in the wall-normal direction of high-order moments, of the form $\langle \varphi ^{2q}\rangle ^{{1}/{q}}_{max}= \alpha _q-\beta _q\,Re^{-1/4}_\tau$ , where $\varphi$ represents the streamwise or spanwise velocity fluctuation, and $\alpha _q$ and $\beta _q$ are independent of $Re_\tau$ . Excellent agreement with available data is observed. A stochastic process for which the random variable has the form just mentioned, referred to here as the ‘linear $q$ -norm Gaussian’, is proposed to explain the observed linear dependence of $\alpha _q$ on $q$ .

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