Axisymmetric rotating flow with free surface in a cylindrical tank

2018 ◽  
Vol 861 ◽  
pp. 796-814 ◽  
Author(s):  
Wen Yang ◽  
Ivan Delbende ◽  
Yann Fraigneau ◽  
Laurent Martin Witkowski
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Surface Deformation ◽  
Fluid Layer ◽  
Three Dimensional ◽  
Azimuthal Velocity ◽  
Meridional Plane ◽  
Cylindrical Tank ◽  
Aspect Ratios ◽  
Steady Solutions

The flow induced by a disk rotating at the bottom of a cylindrical tank is characterised using numerical techniques – computation of steady solutions or time-averaged two-dimensional and three-dimensional direct simulations – as well as laser-Doppler velocimetry measurements. Axisymmetric steady solutions reveal the structure of the toroidal flow located at the periphery of the central solid body rotation region. When viewed in a meridional plane, this flow cell is found to be bordered by four layers, two at the solid boundaries, one at the free surface and one located at the edge of the central region, which possesses a sinuous shape. The cell intensity and geometry are determined for several fluid-layer aspect ratios; the flow is shown to depend very weakly on Froude number (associated with surface deformation) or on Reynolds number if sufficiently large. The paper then focuses on the high Reynolds number regime for which the flow has become unsteady and three-dimensional while the surface is still almost flat. Direct numerical simulations show that the averaged flow shares many similarities with the above steady axisymmetric solutions. Experimental measurements corroborate most of the numerical results and also allow for the spatio-temporal characterisation of the fluctuations, in particular the azimuthal structure and frequency spectrum. Mean azimuthal velocity profiles obtained in this transitional regime are eventually compared to existing theoretical models.

scholarly journals Experiments on generation of surface waves by an underwater moving bottom

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150069 ◽  
Author(s):  
Timothée Jamin ◽  
Leonardo Gordillo ◽  
Gerardo Ruiz-Chavarría ◽  
Michael Berhanu ◽  
Eric Falcon
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Surface Deformation ◽  
Fluid Layer ◽  
Fluid Velocity ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Spatio Temporal ◽  
Experimental Findings

We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes an upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics (i.e. its spatio-temporal features) in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal high-pass filter coupled with a spatial low-pass filter. Both filter effects are often neglected in tsunami warning systems, particularly in real-time forecast. Our results display good agreement with a prevailing linear theory without any parameter fitting. Based on our experimental findings, we provide a simple theoretical approach for modelling the rapid kinematics limit that is applicable even for initially non-flat bottoms: this may be a key step for more realistic varying bathymetry in tsunami scenarios.

Three-Dimensional Thermocapillary Convection in Open Cylindrical Annuli

2000 ◽  
Author(s):  
Bok-Cheol Sim ◽  
Abdelfattah Zebib
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Critical Frequency ◽  
Thermocapillary Convection ◽  
Three Dimensional ◽  
Time Dependent ◽  
Infinite Layer ◽  
Aspect Ratios ◽  
Temperature Oscillations ◽  
Good Agreement

Abstract Three-dimensional, time-dependent thermocapillary convection in open cylindrical containers is investigated numerically. Results for aspect ratios (Ar) of 1, 2.5, 8, and 16 and a Prandtl number of 6.84 are obtained to compare the results of numerical simulations with ongoing experiments. Convection is steady and axisymmetric at sufficiently low values of the Reynolds number (Re). Transition to oscillatory states occurs at critical values of Re which depend on Ar. With Ar = 1.0 and 2.5, we observe, respectively, 5 and 9 azimuthal wavetrains travelling clockwise at the free surface near the critical Re. With Ar = 8.0 and 16.0, there are substantially more, but pulsating waves near the critical Re. In the case of Ar = 16.0, which approaches the conditions in an infinite layer, our results are in good agreement with linear theory. While the critical Reynolds number decreases with increasing aspect ratio in the case of azimuthal rotating waves, it increases with increasing aspect ratio in the case of azimuthal pulsating waves. The critical frequency of temperature oscillations is found to decrease linearly with increasing Ar. We have also computed supercritical time-dependent states and find that while the frequency increases with increasing Re near the critical region, the frequency of supercritical convection decreases with Re.

A Comparison Between Weakly-Compressible Smoothed Particle Hydrodynamics (WCSPH) and Moving Particle Semi-Implicit (MPS) Methods for 3D Dam-Break Flows

2021 ◽  
pp. 2050036
Author(s):  
Rubens A. Amaro Junior ◽  
Liang-Yee Cheng ◽  
Sergei K. Buruchenko
Keyword(s):  
Free Surface ◽  
Surface Deformation ◽  
Computational Cost ◽  
Three Dimensional ◽  
Dam Break ◽  
Weakly Compressible ◽  
Highly Nonlinear ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Moving Particle

Lagrangian particle-based methods have opened new perspectives for the investigation of complex problems with large free-surface deformation. Some well-known particle-based methods adopted to solve non-linear hydrodynamics problems are the smoothed parti- cle hydrodynamics (SPH) and the moving particle semi-implicit (MPS). Both methods model the continuum by a system of Lagrangian particles (points), but adopting distinct approaches for the numerical operators, pressure calculation, and boundary conditions. Despite the ability of the particle-based methods in modeling highly nonlinear hydrodynamics, some shortcomings, such as unstable pressure computation and high computational cost remain. In order to assess the performance of these two methods, the weakly-compressible SPH (WCSPH) parallel solver, DualSPHysics, and an in-house incompressible MPS solver are adopted in this work. Two test cases consisting of three-dimensional (3D) dam-break problems are simulated, and wave heights, pressures and forces are compared with the available experimental data. The influence of the artificial viscosity on the accuracy of WCSPH is investigated. Computational times of both solvers are also compared. Finally, the relative benefits of the methods for solving free-surface problems are discussed, therefore providing directions of their applicability.

Formation of columnar baroclinic vortices in thermally stratified nonlinear spin-up

2012 ◽  
Vol 702 ◽  
pp. 265-285 ◽  
Author(s):  
J. R. Pacheco ◽  
R. Verzicco
Keyword(s):  
Vortex Core ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Three Dimensional ◽  
Temperature Gradients ◽  
Navier Stokes ◽  
Central Vortex ◽  
Slip Boundary ◽  
Aspect Ratios ◽  
Vorticity Production

AbstractWe investigate the mechanisms that affect the formation of columnar vortices for spin-up in a cylinder where the temperatures at the horizontal walls are prescribed. Numerical results from the three-dimensional Navier–Stokes equations show that a short-lived instability, suppressed by the combined effect of rotation and stratification, generates small temperature variations in the azimuthal direction. Temperature-gradient anomalies produce vorticity, and these vortices stir the fluid at the interface of the central vortex core thus reinforcing the temperature gradients. For sufficiently strong temperature gradients, the central vortex core breaks up into several columnar vortices. It is found, in particular, that small aspect ratios (height over radius of the cylindrical fluid layer) $\Gamma = 1, 2$ tend to inhibit the instability, while larger ones, $\Gamma = 3. 3$, have the opposite effect. The main source of instability is the baroclinic vorticity production and not the presence of a solid sidewall since, counter-intuitively, the flow is more unstable for a free-slip boundary than for a no-slip one. Finally the effect of the temperature boundary conditions (isothermal versus adiabatic) on the horizontal boundaries has been investigated. The adiabatic boundaries help to preserve for longer times the sloping density interfaces that feed, with their potential energy, the baroclinic vorticity production; this results in more unstable flows.

Performance Simulations of Tesla Microfluidic Valves

2007 ◽  
Author(s):  
S. Zhang ◽  
S. H. Winoto ◽  
H. T. Low
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Flow Rate ◽  
Three Dimensional ◽  
Model Performance ◽  
Hydraulic Diameter ◽  
Cross Sectional ◽  
Pressure Flow ◽  
Aspect Ratios ◽  
Tesla Valve

A three-dimensional (3-D) parametric model of Tesla-type valves is proposed. A geometrical relationship is derived for optimization study, and based on the model, performance investigations in terms of diodicity and pressure-flow rate characteristics of the valve are numerically carried out with same hydraulic diameter and different aspect ratios (of the model cross-sectional dimensions) ranging from 0.5 to 4. The 3-D computational simulations show that, for the same hydraulic diameter, the unity aspect ratio gives higher diodicity at Reynolds number less than 500 and higher will be achieved with bigger aspect ratio when the Reynolds number is above 500. Investigations of pressure-flow rate characteristics of the Tesla valve show that Tesla valve with high aspect ratio gives more flow control ability.

The aeroacoustics of finite wall-mounted square cylinders

2017 ◽  
Vol 832 ◽  
pp. 287-328 ◽  
Author(s):  
Ric Porteous ◽  
Danielle J. Moreau ◽  
Con J. Doolan
Keyword(s):  
Boundary Layer ◽  
Experimental Study ◽  
Reynolds Number ◽  
Wind Tunnel ◽  
Three Dimensional ◽  
Flow Structures ◽  
Hot Wire ◽  
Radiated Noise ◽  
Aspect Ratios ◽  
Square Cylinders

This paper presents the results of an experimental study that relates the flow structures in the wake of a square finite wall-mounted cylinder with the radiated noise. Acoustic and hot-wire measurements were taken in an anechoic wind tunnel. The cylinder was immersed in a near-zero-pressure gradient boundary layer whose thickness was 130 % of the cylinder width, $W$. Aspect ratios were in the range $0.29\leqslant L/W\leqslant 22.9$ (where $L$ is the cylinder span), and the Reynolds number, based on width, was $1.4\times 10^{4}$. Four shedding regimes were identified, namely R0 ($L/W<2$), RI ($2<L/W<10$), RII ($10<L/W<18$) and RIII ($L/W>18$), with each shedding regime displaying an additional acoustic tone as the aspect ratio was increased. At low aspect ratios (R0 and RI), downwash dominated the wake, creating a highly three-dimensional shedding environment with maximum downwash at $L/W\approx 7$. Looping vortex structures were visualised using a phase eduction technique. The principal core of the loops generated the most noise perpendicular to the cylinder. For higher aspect ratios in RII and RIII, the main noise producing structures consisted of a series of inclined vortex filaments, where the angle of inclination varied between vortex cells.

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