Density distribution in the flow past a sphere descending in a salt-stratified fluid

2021 ◽  
Vol 927 ◽  
Author(s):  
Shinya Okino ◽  
Shinsaku Akiyama ◽  
Koki Takagi ◽  
Hideshi Hanazaki
Keyword(s):  
Reynolds Number ◽  
Density Distribution ◽  
Stratified Fluid ◽  
Buoyant Jet ◽  
Jet Formation ◽  
Initial Development ◽  
Density Distributions ◽  
Image Velocimetry ◽  
Moderate Reynolds Number ◽  
Short Time

The density distribution around a sphere descending in a salt-stratified fluid is measured by the laser-induced fluorescence (LIF) method. The corresponding velocity distribution is measured by particle image velocimetry (PIV), and numerical simulation is also performed to supplement the observations by LIF and PIV. In steady flow, LIF observes a thin and vertically long structure which corresponds to a buoyant jet. The bell-shaped structure, which appears under strong stratification and moderate Reynolds number (Froude number $Fr \lesssim 3$ , Reynolds number $50 \lesssim Re \lesssim 500$ ), is also identified. The measured density distributions in the salinity boundary layer and in the jet agree with the numerical simulations which use the Schmidt number of the fluorescent dye ( $Sc \sim 2000$ ). The initially unsteady process of the jet formation is also investigated. Under weak stratification, the LIF shows an initial development of an axisymmetric rear vortex as observed in homogeneous fluids. However, as time proceeds and the effect of stratification becomes significant, the vortex shrinks and disappears, while the jet extends vertically upward. Under strong stratification, a thin jet develops without generating a rear vortex, since the effect of stratification becomes significant in a short time before the vortex is generated.

Unstable jets generated by a sphere descending in a very strongly stratified fluid

2019 ◽  
Vol 867 ◽  
pp. 26-44 ◽  
Author(s):  
Shinsaku Akiyama ◽  
Yusuke Waki ◽  
Shinya Okino ◽  
Hideshi Hanazaki
Keyword(s):  
Froude Number ◽  
Particle Image ◽  
Stratified Fluid ◽  
Turbulent Jet ◽  
Homogeneous Fluid ◽  
Image Velocimetry ◽  
Low Froude Number ◽  
Long Time ◽  
Short Time ◽  
Unstable States

The flow around a sphere descending at constant speed in a very strongly stratified fluid ($Fr\lesssim 0.2$) is investigated by the shadowgraph method and particle image velocimetry. Unlike the flow under moderately strong stratification ($Fr\gtrsim 0.2$), which supports a thin cylindrical jet, the flow generates an unstable jet, which often develops into turbulence. The transition from a stable jet to an unstable jet occurs for a sufficiently low Froude number $Fr$ that satisfies $Fr/Re<1.57\times 10^{-3}$. The Froude number $Fr$ here is in the range of $0.0157<Fr<0.157$ or lower, while the Reynolds number $Re$ is in the range of $10\lesssim Re\lesssim 100$ for which the homogeneous fluid shows steady and axisymmetric flows. Since the radius of the jet can be estimated by the primitive length scale of the stratified fluid, i.e. $l_{\unicode[STIX]{x1D708}}^{\ast }=\sqrt{\unicode[STIX]{x1D708}^{\ast }/N^{\ast }}$ or $l_{\unicode[STIX]{x1D708}}^{\ast }/2a^{\ast }=\sqrt{Fr/2Re}$, this predicts that the jet becomes unstable when it becomes thinner than approximately $l_{\unicode[STIX]{x1D708}}^{\ast }/2a^{\ast }=0.028$, where $N^{\ast }$ is the Brunt–Väisälä frequency, $a^{\ast }$ the radius of the sphere and $\unicode[STIX]{x1D708}^{\ast }$ the kinematic viscosity of the fluid. The instability begins when the boundary-layer thickness becomes thin, and the disturbances generated by shear instabilities would be transferred into the jet. When the flow is marginally unstable, two unstable states, i.e. a meandering jet and a turbulent jet, can appear. The meandering jet is thin with a high vertical velocity, while the turbulent jet is broad with a much smaller velocity. The meandering jet may persist for a long time, or develop into a turbulent jet in a short time. When the instability is sufficiently strong, only the turbulent jet could be observed.

Jets generated by a sphere moving vertically in a stratified fluid

2009 ◽  
Vol 638 ◽  
pp. 173-197 ◽  
Author(s):  
H. HANAZAKI ◽  
K. KASHIMOTO ◽  
T. OKAMURA
Keyword(s):  
Reynolds Number ◽  
Particle Image ◽  
Spiral Structure ◽  
Vertical Plane ◽  
Vertical Motion ◽  
Stratified Fluid ◽  
The Other ◽  
Image Velocimetry ◽  
Weak Stratification ◽  
Flow Past A Sphere

Experiments are performed on the flow past a sphere moving vertically at constant speeds in a salt-stratified fluid. Shadowgraph method and fluorescent dye are used for the flow visualization, and particle image velocimetry is used for the velocity measurement in the vertical plane. Vertical ‘jets’ or columnar structures are observed in the shadowgraph for all the Froude numbers Fr(0.2 ≲ Fr ≲ 70) investigated, and the wake structures in the whole parameter space of Fr and the Reynolds number Re(30 ≲ Re ≲ 4000) are classified into seven types, five of which are newly found. Those include two types of thin jets, one of which is short with its top disturbed by internal waves to have a peculiar ‘bell-shaped’ structure, while the other has an indefinitely long length. There are two other new types of jet with periodically generated ‘knots’, one of which is straight, while the other has a spiral structure. A simply meandering jet has also been found. These wake structures are significantly different from those in homogeneous fluids except under very weak stratification, showing that the stratification effects on vertical motion are much more significant than those on horizontal motion.

Initial development of a free-surface wall jet at moderate Reynolds number

2017 ◽  
Vol 826 ◽  
pp. 235-269 ◽  
Author(s):  
Roger E. Khayat
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Wall Jet ◽  
Ambient Fluid ◽  
Initial Development ◽  
Core Flow ◽  
Moderate Reynolds Number ◽  
Surface Jet ◽  
Infinite Wall ◽  
Steady Laminar

The steady laminar flow of a moderately inertial wall jet is examined theoretically near the exit of a channel. The free-surface jet emerges asymmetrically from the channel as it adheres to an infinite (upper) wall subject to a pressure gradient. The problem is solved using the method of matched asymptotic expansions. The small parameter involved in the expansions is the inverse cubic power of the Reynolds number. The flow field is obtained by matching the inviscid rotational core flow separately with the free-surface and the two wall layers. The upstream influence is examined as well as the break in the symmetry between the two wall layers. The wall jet exhibits a contraction near the channel exit that is independent of inertia, and eventually expands for any Reynolds number. Unlike the flow of a wall jet emerging into the same ambient fluid, the free-surface jet experiences a limited weakening in shear stress along the infinite wall, suggesting the possibility of separation for a jet with relatively low inertia. Significant shearing and elongation ensue at the exit, accompanied by flattening of the velocity profile near the upper wall.

Electronic Cooling Using Synthetic Jet Impingement

2006 ◽  
Vol 128 (9) ◽  
pp. 897-907 ◽  
Author(s):  
Anna Pavlova ◽  
Michael Amitay
Keyword(s):  
Reynolds Number ◽  
Low Frequency ◽  
Jet Impingement ◽  
Constant Heat Flux ◽  
Synthetic Jet ◽  
Synthetic Jets ◽  
Electronic Cooling ◽  
Vortex Rings ◽  
Jet Formation ◽  
Image Velocimetry

The efficiency and mechanisms of cooling a constant heat flux surface by impinging synthetic jets were investigated experimentally and compared to cooling with continuous jets. Effects of jet formation frequency and Reynolds number at different nozzle-to-surface distances (H∕d) were investigated. High formation frequency (f=1200Hz) synthetic jets were found to remove heat better than low frequency (f=420Hz) jets for small H∕d, while low frequency jets are more effective at larger H∕d. Moreover, synthetic jets are about three times more effective in cooling than continuous jets at the same Reynolds number. Using particle image velocimetry, it was shown that the higher formation frequency jets are associated with breakdown and merging of vortices before they impinge on the surface. For the lower frequency jets, the wavelength between coherent structures is larger such that vortex rings impinge on the surface separately.

Vortex shedding from a circular cylinder in moderate-Reynolds-number shear flow

1980 ◽  
Vol 101 (4) ◽  
pp. 721-735 ◽  
Author(s):  
Masaru Kiya ◽  
Hisataka Tamura ◽  
Mikio Arie
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Shear Flow ◽  
Vortex Shedding ◽  
Transverse Velocity ◽  
Number Range ◽  
Uniform Shear ◽  
Reynolds Number Range ◽  
Moderate Reynolds Number ◽  
Shear Parameter

The frequency of vortex shedding from a circular cylinder in a uniform shear flow and the flow patterns around it were experimentally investigated. The Reynolds number Re, which was defined in terms of the cylinder diameter and the approaching velocity at its centre, ranged from 35 to 1500. The shear parameter, which is the transverse velocity gradient of the shear flow non-dimensionalized by the above two quantities, was varied from 0 to 0·25. The critical Reynolds number beyond which vortex shedding from the cylinder occurred was found to be higher than that for a uniform stream and increased approximately linearly with increasing shear parameter when it was larger than about 0·06. In the Reynolds-number range 43 < Re < 220, the vortex shedding disappeared for sufficiently large shear parameters. Moreover, in the Reynolds-number range 100 < Re < 1000, the Strouhal number increased as the shear parameter increased beyond about 0·1.

scholarly journals Die zeitliche Änderung der radialen Elektronendichteverteilung beim Theta-Pinch

1963 ◽  
Vol 18 (8-9) ◽  
pp. 895-900
Author(s):  
Franz Peter Küpper
Keyword(s):  
Density Distribution ◽  
Electron Density ◽  
Electron Density Distribution ◽  
Electron Distribution ◽  
Radial Symmetry ◽  
Zero Order ◽  
Time Interval ◽  
Interferometric Method ◽  
Density Distributions ◽  
Theta Pinch

In a θ-pinch the radial symmetry of the electron density distribution as a function of time has been measured by a MACH—ZEHNDER interferometer. In a time interval of 400 nsec during a discharge an image converter made three pictures (exposure times of 10 nsec each) . Up to 100 nsec after the first compression, the experimental results show different density distributions for the cases of trapped parallel and antiparallel magnetic fields. Complete radial symmetry of the electron density distribution was not found.Another interferometric method for measuring the radial symmetry of the electron distribution by observing “zero order” fringes is described.

Models of the scalar spectrum for turbulent advection

1978 ◽  
Vol 88 (3) ◽  
pp. 541-562 ◽  
Author(s):  
R. J. Hill
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Schmidt Number ◽  
Temperature Fluctuations ◽  
Limited Extent ◽  
Temperature Spectrum ◽  
One Dimensional ◽  
Moderate Reynolds Number ◽  
Temperature Spectra ◽  
High Reynolds

Several models are developed for the high-wavenumber portion of the spectral transfer function of scalar quantities advected by high-Reynolds-number, locally isotropic turbulent flow. These models are applicable for arbitrary Prandtl or Schmidt number, v/D, and the resultant scalar spectra are compared with several experiments having different v/D. The ‘bump’ in the temperature spectrum of air observed over land is shown to be due to a tendency toward a viscous-convective range and the presence of this bump is consistent with experiments for large v/D. The wavenumbers defining the transition between the inertial-convective range and viscous-convective range for asymptotically large v/D (denoted k* and k1* for the three- and one-dimensional spectra) are determined by comparison of the models with experiments. A measurement of the transitional wavenumber k1* [denoted (k1*)s] is found to depend on v/D and on any filter cut-off. On the basis of the k* values it is shown that measurements of β1 from temperature spectra in moderate Reynolds number turbulence in air (v/D = 0·72) maybe over-estimates and that the inertial-diffusive range of temperature fluctuations in mercury (v/D ≃ 0·02) is of very limited extent.

Moderate Reynolds Number Mixing in a T-Channel

2010 ◽  
Author(s):  
Susan Thomas ◽  
Tim Ameel
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Large Body ◽  
Experimental Studies ◽  
Numerical Work ◽  
Moderate Reynolds Number ◽  
Wide Range ◽  
Particle Imaging ◽  
Experimental Trials

An experimental investigation of water flow in a T-shaped channel with rectangular cross section (20 × 20 mm inlet ID and 20 × 40 mm outlet ID) has been conducted for a Reynolds number Re range of 56 to 422, based on inlet diameter. Dynamical conditions and the T-channel geometry of the current study are applicable to the microscale. This study supports a large body of numerical work, and resolution and the interrogation region are extended beyond previous experimental studies. Laser induced fluorescence (LIF) and particle imaging velocimetry (PIV) are used to characterize flow behaviors over the broad range of Re where realistic T-channels operate. Scalar structures previously unresolved in the literature are presented. Special attention is paid to the unsteady flow regimes that develop at moderate Re, which significantly impact mixing but are not yet well characterized or understood. An unsteady symmetric topology, which develops at higher Re and negatively impacts mixing, is presented, and mechanisms behind the wide range of mixing qualities predicted for this regime are explained. An optimal Re operating range is identified based on multiple experimental trials.

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