A numerical study of the dynamics of a particle settling at moderate Reynolds numbers in a linearly stratified fluid

2014 ◽  
Vol 750 ◽  
pp. 5-32 ◽  
Author(s):  
A. Doostmohammadi ◽  
S. Dabiri ◽  
A. M. Ardekani
Keyword(s):  
Settling Velocity ◽  
Peak Velocity ◽  
Numerical Study ◽  
Maximum Velocity ◽  
Reynolds Numbers ◽  
Stratified Fluid ◽  
Settling Particle ◽  
Settling Behaviour ◽  
Prandtl Numbers ◽  
Neutrally Buoyant

AbstractIn this paper, the transient settling dynamics of a spherical particle sedimenting in a linearly stratified fluid is investigated by performing fully resolved direct numerical simulations. The settling behaviour is quantified for different values of Reynolds, Froude and Prandtl numbers. It is demonstrated that the transient settling dynamics is correlated to the induced Lagrangian drift of flow around the settling particle. A simplified model is provided to predict the maximum velocity of the settling particle in linearly stratified fluids. The peak velocity can be followed by the oscillation of the settling velocity and the particle can even reverse its direction of motion before reaching to its neutrally buoyant level. The frequency of oscillation of settling velocity scales with the Brunt–Väisälä frequency and the motion of the particle can lead to the formation of secondary and tertiary vortices following the primary vortex.

Velocity distribution around a sphere descending in a linearly stratified fluid

2017 ◽  
Vol 826 ◽  
pp. 759-780 ◽  
Author(s):  
Shinya Okino ◽  
Shinsaku Akiyama ◽  
Hideshi Hanazaki
Keyword(s):  
Boundary Layer ◽  
Velocity Distribution ◽  
High Speed ◽  
Particle Image ◽  
Maximum Velocity ◽  
Reynolds Numbers ◽  
Stratified Fluid ◽  
Velocity Variation ◽  
Image Velocimetry ◽  
Wave Patterns

The flow around a sphere descending at constant speed in a salt-stratified fluid is observed by particle image velocimetry. A unique characteristic of this flow is the appearance of a thin and high-speed rear jet whose maximum velocity can reach more than five times the sphere velocity. In this study we have investigated how the velocity distributions, especially those in the jet and in the boundary layer of the sphere, vary when the Froude number $Fr(=W^{\ast }/N^{\ast }a^{\ast })$ or the Reynolds number $Re(=W^{\ast }(2a^{\ast })/\unicode[STIX]{x1D708}^{\ast })$ ($W^{\ast }$: vertical velocity of the sphere, $N^{\ast }$: Brunt–Väisälä frequency, $a^{\ast }$: radius of the sphere, $\unicode[STIX]{x1D708}^{\ast }$: kinematic viscosity of the fluid) is changed. The results show that the radius of the jet and the thickness of the boundary layer are comparable, and they decrease for smaller Froude numbers and larger Reynolds numbers. Both of them are estimated at moderate Reynolds numbers by the primitive length scale of the stratified fluid ($l_{\unicode[STIX]{x1D708}}^{\ast }=\sqrt{\unicode[STIX]{x1D708}^{\ast }/N^{\ast }}$), or in non-dimensional form by $l_{\unicode[STIX]{x1D708}}^{\ast }/2a^{\ast }=(Fr/2Re)^{1/2}$. The overall velocity distribution in the lee of the sphere is measured to identify the internal wave patterns and their effect on the velocity variation along the jet. Corresponding numerical simulation results using the axisymmetry assumption are in agreement with the experimental results.

Experimental and Numerical Studies of Cold Inflow at the Exit of Buoyant Channel Flows

1987 ◽  
Vol 109 (2) ◽  
pp. 392-399 ◽  
Author(s):  
Vijay Modi ◽  
K. E. Torrance
Keyword(s):  
Boundary Layer ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Critical Value ◽  
Ambient Fluid ◽  
Buoyant Jet ◽  
Wall Boundary Layer ◽  
Numerical Studies ◽  
Turbulent Flow Regime ◽  
Neutrally Buoyant

Experimental and numerical studies of the separation of a smooth attached buoyant flow from the inner wall of a duct, as the duct discharges into a quiescent environment, are reported. The associated penetration of neutrally buoyant ambient fluid into the duct is called cold inflow. The experimental study was carried out for air flows over ranges of Reynolds and Froude numbers, based on duct radius, of Re = 2400 to 3300 and Fr = 0.68 to 2.69. The experiments provide information on the onset and extent of cold inflow in a turbulent flow regime. Spatial profiles of fluctuating temperature reveal a wedge-shaped cold inflow region at the wall near the exit when Fr is decreased below a critical value. The numerical study examines the influence of Re and Fr on the structure of the cold inflow phenomenon at moderate Reynolds numbers (Re = 200 to 500 and Fr = 1 to 5). Steady-state, two-dimensional, laminar flow solutions reveal a region of downward-flowing cold air near the wall of the duct which leads to premature separation of the wall boundary layer. The separated boundary layer merges into the buoyant jet above the duct exit.

Effect of Starch on the Flocculation and Settling Behaviour of Titanium Dioxide Suspensions

1974 ◽  
Vol 9 (1) ◽  
pp. 154-171
Author(s):  
S.N. Ray ◽  
C. Hsi ◽  
B.C. -Y. Lu
Keyword(s):  
Titanium Dioxide ◽  
Suspended Solids ◽  
Settling Velocity ◽  
Pollution Abatement ◽  
Paper Mills ◽  
Paper Making ◽  
Jar Test ◽  
Settling Behaviour ◽  
Dimensionless Function ◽  
Flocculation Rate

Abstract This study concerns the problem of removal of suspended solids from the effluent streams of paper mills by chemical treatment. As titanium dioxide is one of the ingredients used in paper mills and present in the effluent streams, its flocculation and settling behaviour were investigated. Jar test experiments were conducted using alum and organic polyelectrolyte as the flocculants. As starch is also used in the paper making process, its influence on the flocculation and settling behaviour of titanium dioxide was conducted with the concentration of starch varying between 0–3% of the dry solids. The experimental results on flocculation are expressed in terms of dimensionless function Gθϕ and flocculation rate constants. The fraction of solids settled is presented in terms of the settling velocity. Concentration of starch was found to have a significant influence. The amount of alum required could be reduced by 75% by using starch 0.6% of the amount of titanium dioxide in the suspension and at the same time improving the settling velocity two folds. A possible application of this finding in pollution abatement is discussed.

An Experimental and Numerical Study of Heat Transfer and Pressure Loss in a Rectangular Channel With V-Shaped Ribs

2006 ◽  
Author(s):  
Michael Maurer ◽  
Jens von Wolfersdorf ◽  
Michael Gritsch
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Thermal Performance ◽  
Pressure Loss ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Reynolds Numbers ◽  
Transfer Enhancement ◽  
High Reynolds Numbers ◽  
High Reynolds

An experimental and numerical study was conducted to determine the thermal performance of V-shaped ribs in a rectangular channel with an aspect ratio of 2:1. Local heat transfer coefficients were measured using the steady state thermochromic liquid crystal technique. Periodic pressure losses were obtained with pressure taps along the smooth channel sidewall. Reynolds numbers from 95,000 to 500,000 were investigated with V-shaped ribs located on one side or on both sides of the test channel. The rib height-to-hydraulic diameter ratios (e/Dh) were 0.0625 and 0.02, and the rib pitch-to-height ratio (P/e) was 10. In addition, all test cases were investigated numerically. The commercial software FLUENT™ was used with a two-layer k-ε turbulence model. Numerically and experimentally obtained data were compared. It was determined that the heat transfer enhancement based on the heat transfer of a smooth wall levels off for Reynolds numbers over 200,000. The introduction of a second ribbed sidewall slightly increased the heat transfer enhancement whereas the pressure penalty was approximately doubled. Diminishing the rib height at high Reynolds numbers had the disadvantage of a slightly decreased heat transfer enhancement, but benefits in a significantly reduced pressure loss. At high Reynolds numbers small-scale ribs in a one-sided ribbed channel were shown to have the best thermal performance.

A Numerical and Experimental Investigation of Turbulent Heat Transport Downstream From an Abrupt Pipe Expansion

1983 ◽  
Vol 105 (4) ◽  
pp. 862-869 ◽  
Author(s):  
R. S. Amano ◽  
M. K. Jensen ◽  
P. Goel
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Separated Flow ◽  
Flow Region ◽  
Reynolds Numbers ◽  
Turbulent Heat ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Pipe Expansion

An experimental and numerical study is reported on heat transfer in the separated flow region created by an abrupt circular pipe expansion. Heat transfer coefficients were measured along the pipe wall downstream from an expansion for three different expansion ratios of d/D = 0.195, 0.391, and 0.586 for Reynolds numbers ranging from 104 to 1.5 × 105. The results are compared with the numerical solutions obtained with the k ∼ ε turbulence model. In this computation a new finite difference scheme is developed which shows several advantages over the ordinary hybrid scheme. The study also covers the derivation of a new wall function model. Generally good agreement between the measured and the computed results is shown.

A numerical study on free-fall of a torus with initial inclination angle at low Reynolds numbers

2021 ◽  
Vol 107 ◽  
pp. 103389
Author(s):  
Tao Huang ◽  
Haibo Zhao ◽  
Sai Peng ◽  
Jiayu Li ◽  
Yang Yao ◽  
...  
Keyword(s):  
Inclination Angle ◽  
Numerical Study ◽  
Free Fall ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Low Reynolds

A Numerical Study of Heat Transfer and Flow Structure in Channels With Miniature V Rib-Dimple Hybrid Structure on One Wall

2018 ◽  
Author(s):  
Peng Zhang ◽  
Yu Rao ◽  
Yanlin Li
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Numerical Simulations ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Hybrid Structure ◽  
Transfer Enhancement ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Flow Mixing

This paper presents a numerical study on turbulent flow and heat transfer in the channels with a novel hybrid cooling structure with miniature V-shaped ribs and dimples on one wall. The heat transfer characteristics, pressure loss and turbulent flow structures in the channels with the rib-dimples with three different rib heights of 0.6 mm, 1.0 mm and 1.5 mm are obtained for the Reynolds numbers ranging from 18,700 to 60,000 by numerical simulations, which are also compared with counterpart of a pure dimpled and pure V ribbed channel. The results show that the overall Nusselt numbers of the V rib-dimple channel with the rib height of 1.5 mm is up to 70% higher than that of the channels with pure dimples. The numerical simulations show that the arrangement of the miniature V rib upstream each dimple induces complex secondary flow near the wall and generates downwashing vortices, which intensifies the flow mixing and turbulent kinetic energy in the dimple, resulting in significant improvement in heat transfer enhancement and uniformness.

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