The Drag on Spheres and Cylinders in a Stream of Dust-Laden Air

1959 ◽  
Vol 26 (4) ◽  
pp. 584-586
Author(s):  
Thomas Gillespie ◽  
A. W. Gunter
Keyword(s):  
Particle Size ◽  
Reynolds Number ◽  
Kinetic Energy ◽  
Drag Coefficient ◽  
Flow Pattern ◽  
Reynolds Numbers ◽  
Dust Concentration ◽  
Phase System ◽  
Two Phase ◽  
Coefficient Versus

Abstract A system has been developed for measuring the drag on small spheres and cylinders in a stream of dust-laden air. The drag was found to be proportional to the kinetic energy of the air plus the kinetic energy of the dust, and to be independent of particle size for particles having diameters in the range of 50 to 400μ. The well-known drag-coefficient versus Reynolds-number plots are the same for dust-free and dust-laden air provided the drag coefficient is calculated using the density of the two-phase system and the Reynolds numbers are calculated using the density of air alone. This suggests that the dust has little effect on the flow pattern. The results indicate that an instrument utilizing the drag principle to measure dust concentration could be developed.

A Numerical Study on Motion of a Sphere Coated With a Thin Liquid Film at Intermediate Reynolds Numbers

1997 ◽  
Vol 119 (2) ◽  
pp. 397-403 ◽  
Author(s):  
S. Kawano ◽  
H. Hashimoto
Keyword(s):  
Reynolds Number ◽  
Liquid Film ◽  
Drag Coefficient ◽  
Flow Pattern ◽  
Numerical Study ◽  
Thin Liquid Film ◽  
Strong Dependence ◽  
Reynolds Numbers ◽  
Rigid Sphere ◽  
Flow Past A Sphere

The steady viscous flow past a sphere coated with a thin liquid film at low and intermediate Reynolds numbers (Re ≤ 200) was investigated numerically. The influences of fluid physical properties, film thickness, and Reynolds number on the flow pattern were clarified. Temperature field around the compound drop was also analyzed. The strong dependence of flow pattern on the characteristics of heat transfer was recognized. The empirical equation of the drag coefficient for the compound drop was proposed. Furthermore, the explicit adaptability of the drag coefficient equation for a gas bubble, a liquid drop, and a rigid, sphere in the range of Reynolds number Re ≤ 1000 was confirmed.

Fully developed MHD turbulence near critical magnetic Reynolds number

1981 ◽  
Vol 104 ◽  
pp. 419-443 ◽  
Author(s):  
J. Léorat ◽  
A. Pouquet ◽  
U. Frisch
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Liquid Sodium ◽  
Turbulent Heat ◽  
Mhd Turbulence

Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L ≈ l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).

Added Mass and In-Line Steady Drag Coefficient of Multiple Risers

1985 ◽  
Vol 107 (1) ◽  
pp. 2-11 ◽  
Author(s):  
T. Overvik ◽  
G. Moe
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Reynolds Numbers ◽  
Added Mass ◽  
Central Cylinder ◽  
Lock In

Part of the results of an investigation with multiple rise configuration exposed to steady currents are presented. These tests were performed on smooth sectional riser models in a water flume at Reynolds numbers in the range 0.5 × 104 to 0.5 × 105. Reynolds number is based upon the diameter of the central cylinder (DC). Both the added mass, the frequency of vibration and the in-line steady drag coefficient are discussed both for vibration in the lock-in range and in the galloping mode.

Particle capture and low-Reynolds-number flow around a circular cylinder

2012 ◽  
Vol 710 ◽  
pp. 362-378 ◽  
Author(s):  
Alexis Espinosa-Gayosso ◽  
Marco Ghisalberti ◽  
Gregory N. Ivey ◽  
Nicole L. Jones
Keyword(s):  
Particle Size ◽  
Reynolds Number ◽  
Larval Settlement ◽  
Capture Rate ◽  
Reynolds Numbers ◽  
Particle Capture ◽  
Particle Size Range ◽  
Reynolds Number Flow ◽  
Number Flow ◽  
First Time

AbstractParticle capture, whereby suspended particles contact and adhere to a solid surface (a ‘collector’), is an important mechanism in a range of environmental processes. In aquatic systems, typically characterized by low collector Reynolds numbers ($\mathit{Re}$), the rate of particle capture determines the efficiencies of a range of processes such as seagrass pollination, suspension feeding by corals and larval settlement. In this paper, we use direct numerical simulation (DNS) of a two-dimensional laminar flow to accurately quantify the rate of capture of low-inertia particles by a cylindrical collector for $\mathit{Re}\leq 47$ (i.e. a range where there is no vortex shedding). We investigate the dependence of both the capture rate and maximum capture angle on both the collector Reynolds number and the ratio of particle size to collector size. The inner asymptotic expansion of Skinner (Q. J. Mech. Appl. Maths, vol. 28, 1975, pp. 333–340) for flow around a cylinder is extended and shown to provide an excellent framework for the prediction of particle capture and flow close to the leading face of a cylinder up to $\mathit{Re}= 10$. Our results fill a gap between theory and experiment by providing, for the first time, predictive capability for particle capture by aquatic collectors in a wide (and relevant) Reynolds number and particle size range.

Experimental Aerodynamic Characteristics of a Compound Wing in Ground Effect

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Saeed Jamei ◽  
Adi Maimun Abdul Malek ◽  
Shuhaimi Mansor ◽  
Nor Azwadi Che Sidik ◽  
Agoes Priyanto
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Center Of Pressure ◽  
Lift Coefficient ◽  
Angle Of Attack ◽  
Leading Edge ◽  
Ground Effect ◽  
Reynolds Numbers ◽  
Aerodynamic Characteristics ◽  
Ground Clearance

Wing configuration is a parameter that affects the performance of wing-in-ground effect (WIG) craft. In this study, the aerodynamic characteristics of a new compound wing were investigated during ground effect. The compound wing was divided into three parts with a rectangular wing in the middle and two reverse taper wings with anhedral angle at the sides. The sectional profile of the wing model is NACA6409. The experiments on the compound wing and the rectangular wing were carried to examine different ground clearances, angles of attack, and Reynolds numbers. The aerodynamic coefficients of the compound wing were compared with those of the rectangular wing, which had an acceptable increase in its lift coefficient at small ground clearances, and its drag coefficient decreased compared to rectangular wing at a wide range of ground clearances, angles of attack, and Reynolds numbers. Furthermore, the lift to drag ratio of the compound wing improved considerably at small ground clearances. However, this improvement decreased at higher ground clearance. The drag polar of the compound wing showed the increment of lift coefficient versus drag coefficient was higher especially at small ground clearances. The Reynolds number had a gradual effect on lift and drag coefficients and also lift to drag of both wings. Generally, the nose down pitching moment of the compound wing was found smaller, but it was greater at high angle of attack and Reynolds number for all ground clearance. The center of pressure was closer to the leading edge of the wing in contrast to the rectangular wing. However, the center of pressure of the compound wing was later to the leading edge at high ground clearance, angle of attack, and Reynolds number.

Simulation of Flow Around a Cube at Moderate Reynolds Numbers Using the Lattice Boltzmann Method

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Majid Hassan Khan ◽  
Atul Sharma ◽  
Amit Agrawal
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Lattice Boltzmann Method ◽  
Steady Flow ◽  
Flow Regime ◽  
Lattice Boltzmann ◽  
Reynolds Numbers ◽  
Side Force ◽  
Force Coefficients ◽  
Boltzmann Method

Abstract This article reports flow behavior around a suspended cube obtained using three-dimensional (3D) lattice Boltzmann method (LBM)-based simulations. The Reynolds number (Re) range covered is from 84 to 770. Four different flow regimes are noted based on the flow structure in this range of Re: steady axisymmetric (84 ≤ Re ≤ 200), steady nonaxisymmetric (215 ≤ Re ≤ 250), unsteady nonaxisymmetric in one plane and axisymmetric in the other plane (276 ≤ Re ≤ 300), and unsteady nonaxisymmetric in streamwise orthogonal planes (339 ≤ Re ≤ 770). Recirculation length and drag coefficient follow inverse trend in the steady flow regime. The unsteady flow regime shows hairpin vortices for Re ≤ 300 and then it becomes structureless. The nature of force coefficients has been examined at various Reynolds numbers. Temporal behavior of force coefficients is presented along with phase dependence of side force coefficients. The drag coefficient decreases with increase in Reynolds number in the steady flow regime and the side force coefficients are in phase. Drag coefficients are compared with established correlations for flow around a cube and a sphere. The side force coefficients are perfectly correlated at Re = 215 and they are anticorrelated at Re = 250. At higher Reynolds numbers, side force coefficients are highly uncorrelated. This work adds to the existing understanding of flow around a cube reported earlier at low and moderate Re and extends it further to unsteady regime at higher Re.

Fluid Flow Analysis in a Pebble Bed Modular Reactor Using RANS Turbulence Models

2008 ◽  
Author(s):  
Margaret Mkhosi ◽  
Richard Denning ◽  
Audeen Fentiman
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulence Intensity ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Pebble Bed ◽  
Rans Turbulence Models ◽  
Flow Domain

The computational fluid dynamics code FLUENT has been used to analyze turbulent fluid flow over pebbles in a pebble bed modular reactor. The objective of the analysis is to evaluate the capability of the various RANS turbulence models to predict mean velocities, turbulent kinetic energy, and turbulence intensity inside the bed. The code was run using three RANS turbulence models: standard k-ε, standard k-ω and the Reynolds stress turbulence models at turbulent Reynolds numbers, corresponding to normal operation of the reactor. For the k-ε turbulence model, the analyses were performed at a range of Reynolds numbers between 1300 and 22 000 based on the approach velocity and the sphere diameter of 6 cm. Predictions of the mean velocities, turbulent kinetic energy, and turbulence intensity for the three models are compared at the Reynolds number of 5500 for all the RANS models analyzed. A unit-cell approach is used and the fluid flow domain consists of three unit cells. The packing of the pebbles is an orthorhombic arrangement consisting of seven layers of pebbles with the mean flow parallel to the z-axis. For each Reynolds number analyzed, the velocity is observed to accelerate to twice the inlet velocity within the pebble bed. From the velocity contours, it can be seen that the flow appears to have reached an asymptotic behavior by the end of the first unit cell. The velocity vectors for the standard k-ε and the Reynolds stress model show similar patterns for the Reynolds number analyzed. For the standard k-ω, the vectors are different from the other two. Secondary flow structures are observed for the standard k-ω after the flow passes through the gap between spheres. This feature is not observable in the case of both the standard k-ε and the RSM. Analysis of the turbulent kinetic energy contours shows that there is higher turbulence kinetic energy near the inlet than inside the bed. As the Reynolds number increases, kinetic energy inside the bed increases. The turbulent kinetic energy values obtained for the standard k-ε and the RSM are similar, showing maximum turbulence kinetic energy of 7.5 m2·s−2, whereas the standard k-ω shows a maximum of about 20 m2·s−2. Another observation is that the turbulence intensity is spread throughout the flow domain for the k-ε and RSM whereas for the k-ω, the intensity is concentrated at the front of the second sphere. Preliminary analysis performed for the pressure drop using the standard k-ε model for various velocities show that the dependence of pressure on velocity varies as V1.76.

The Role of Surface Tension Effects During Methanol Droplet Combustion

2006 ◽  
Author(s):  
Vasudevan Raghavan ◽  
Daniel N. Pope ◽  
George Gogos
Keyword(s):  
Surface Tension ◽  
Reynolds Number ◽  
Liquid Phase ◽  
Water Absorption ◽  
Flow Pattern ◽  
Liquid Droplet ◽  
Reynolds Numbers ◽  
Droplet Combustion ◽  
Complex Flow ◽  
Suspended Droplet

A numerical investigation of methanol droplet combustion in a zero-gravity and low-pressure convective environment is presented. Simulations have been carried out using a predictive, transient and axisymmetric model, which includes droplet heating, liquid-phase circulation and water absorption. First, a suspended droplet (constant relative velocity) burning in an ambient of air at 300K is considered. A nearly quiescent environment (initial Reynolds number Re0=0.01) is used to impose a weak gas-phase convective flow, introducing a deviation from spherical symmetry. The resulting weak liquid-phase circulation is greatly enhanced due to surface tension effects, which create a complex, time-varying, multicellular flow pattern within the liquid droplet. The complex flow pattern, which, in the presence of surface tension, results in nearly perfect mixing, causes increased water absorption within the droplet, leading to larger extinction diameters. Surface tension effects are shown to be dominant in causing water absorption, even at initial Reynolds numbers as high as 5. Results for combustion in a nearly quiescent environment (Re0=0.01) with varying initial droplet diameters, (d0 = 0.16 to 1.72 mm), show that predictions of droplet extinction diameters, although they are still below the experimental data, do improve substantially when surface tension effects are included. Next, results for suspended droplets and for moving droplets burning in an ambient of air at 1200K, for a range of initial Reynolds numbers that are of interest in spray combustion (Re0=1-100) are presented. It is shown that, for moving droplets, due to the presence of an envelope flame at some stage during the droplet lifetime, surface tension is important over the entire range of Re0 considered; the extinction diameter decreases with increasing Re0. Extinction is not observed for a moving droplet when surface tension effects are neglected. For suspended droplets, when transition or envelope flame is present, which corresponds to Re0 less than approximately 15, surface tension is important; when an envelope flame is present (Re0 less than approximately 10), the extinction diameter increases with Re0. The variation of droplet lifetime with Re0 is much stronger for suspended droplets than for moving droplets. Depending on the Reynolds number, results on methanol droplet lifetimes and extinction diameters measured through suspended droplet experiments may not be applicable to moving droplets.

Experimental Measurements of the Wake of a Sphere at Subcritical Reynolds Numbers

2021 ◽  
Vol 143 (6) ◽  
Author(s):  
Robert Muyshondt ◽  
Thien Nguyen ◽  
Y. A. Hassan ◽  
N. K. Anand
Keyword(s):  
Reynolds Number ◽  
Spectral Analysis ◽  
Kinetic Energy ◽  
Cross Correlation ◽  
Reynolds Numbers ◽  
Velocity Fields ◽  
Stereoscopic Particle Image Velocimetry ◽  
Recirculation Region ◽  
Flow Structures ◽  
Vortex Identification

Abstract This work experimentally investigated the flow phenomena and vortex structures in the wake of a sphere located in a water loop at Reynolds numbers of Re = 850, 1,250, and 1,700. Velocity fields in the wake region were obtained by applying the time-resolved stereoscopic particle image velocimetry (TR-SPIV) technique. From the acquired TR-SPIV velocity vector fields, the statistical values of mean and fluctuating velocities were computed. Spectral analysis, two-point velocity–velocity cross-correlation, proper orthogonal decomposition (POD) and vortex identification analyses were also performed. The velocity fields show a recirculation region that decreases in length with an increase of Reynolds numbers. The power spectra from the spectral analysis had peaks corresponding to a Strouhal number of St = 0.2, which is a value commonly found in the literature studies of flow over a sphere. The two-point cross-correlation analysis revealed elliptical structures in the wake, with estimated integral length scales ranging between 12% and 63% of the sphere diameter. The POD analysis revealed the statistically dominant flow structures that captured the most flow kinetic energy. It is seen that the flow kinetic energy captured in the smaller scale flow structures increased as Reynolds number increased. The POD modes contained smaller structure as the Reynolds number increased and as mode order increased. In addition, spectral analysis performed on the POD temporal coefficients revealed peaks corresponding to St = 0.2, similar to the spectral analysis on the fluctuating velocity. The ability of POD to produce low-order reconstructions of the flow was also utilized to facilitate vortex identification analysis, which identified average vortex sizes of 0.41D for Re1, 0.33D for Re2, and 0.32D for Re3.

Sensitivity of stratified turbulence to the buoyancy Reynolds number

2013 ◽  
Vol 725 ◽  
pp. 1-22 ◽  
Author(s):  
P. Bartello ◽  
S. M. Tobias
Keyword(s):  
Reynolds Number ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Froude Number ◽  
Relative Size ◽  
Stratified Flow ◽  
Reynolds Numbers ◽  
Stratified Turbulence ◽  
Integral Scale

AbstractIn this article we present direct numerical simulations of stratified flow at resolutions of up to $204{8}^{2} \times 513$, to explore scalings for the dynamics of stably stratified turbulence. Recent work suggests that for strong enough stratification, the vertical integral scale of the turbulence adjusts to yield a vertical Froude number, ${F}_{v} $, of order unity at high enough Reynolds number, whilst the horizontal Froude number, ${F}_{h} $, decreases as stratification is increased. Our numerical simulations are consistent with predictions by Lindborg (J. Fluid Mech., vol. 550, 2006, pp, 207–242), and with numerical simulations at lower resolution, in that the horizontal kinetic energy spectrum follows a Kolmogorov spectrum (after replacing the wavenumber with the horizontal wavenumber) and that the horizontal potential energy spectrum similarly follows the Corrsin–Obukhov spectrum for a passive scalar. Most importantly, we build upon these previous results by thoroughly exploring the dependence of the horizontal spectrum of horizontal kinetic energy on both the stratification and the relative size of the vertical dissipation terms, as quantified by the buoyancy Reynolds number. Our most important result is that variations in the power-law exponent scale entirely with the buoyancy Reynolds number and not with the stratification itself, lending considerable support to the Lindborg (2006) hypothesis that horizontal spectra are independent of stratification at large Reynolds numbers. We further demonstrate that even at the large numerical resolution of this study, the spectrum and hence the dynamics are affected by the buoyancy Reynolds number unless it is larger than $O(10)$, indicating that extreme care must be taken when assessing claims made from previous numerical simulations of stratified flow at low or moderate resolution and extrapolating the results to geophysical or astrophysical Reynolds numbers.

Sign in / Sign up

Export Citation Format

Share Document