Numerical Model for Fluid Spin-Up From Rest in a Partially Filled Cylinder

1987 ◽  
Vol 109 (2) ◽  
pp. 194-197 ◽  
Author(s):  
G. F. Homicz ◽  
N. Gerber
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Numerical Model ◽  
Froude Number ◽  
Numerical Investigation ◽  
Cylindrical Cavity ◽  
Ekman Layer ◽  
Bottom Wall ◽  
Fill Ratio ◽  
Liquid Free Surface

A numerical investigation is presented for the axisymmetric spin-up of fluid in a partially filled cylindrical cavity. It is an extension of earlier analyses to those cases where the liquid free surface intersects one or both endwalls. Previous models of the laminar Ekman layer pumping are modified heuristically for situations where the layer(s) no longer covers the entire wall. Numerical results for a range of Reynolds number, Froude number, and fill ratio have been obtained. They clearly demonstrae that it is the bottom wall Ekman layer which is primarily responsible for spin-up.

Turbulent structure in free-surface jet flows

1995 ◽  
Vol 291 ◽  
pp. 223-261 ◽  
Author(s):  
D. T. Walker ◽  
C.-Y. Chen ◽  
W. W. Willmarth
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Froude Number ◽  
Tangential Velocity ◽  
Rate Of Change ◽  
Normal Velocity ◽  
Reynolds Stresses ◽  
Velocity Fluctuations ◽  
Surface Normal ◽  
Surface Disturbances

Results of an experimental study of the interaction of a turbulent jet with a free surface when the jet issues parallel to the free surface are presented. Three different jets, with different exit velocities and jet-exit diameters, all located two jet-exit diameters below the free surface were studied. At this depth the jet flow, in each case, is fully turbulent before significant interaction with the free surface occurs. The effects of the Froude number (Fr) and the Reynolds number (Re) were investigated by varying the jet-exit velocity and jet-exit diameter. Froude-number effects were identified by increasing the Froude number from Fr = 1 to 8 at Re = 12700. Reynolds-number effects were identified by increasing the Reynolds number from Re = 12700 to 102000 at Fr = 1. Qualitative features of the subsurface flow and free-surface disturbances were examined using flow visualization. Measurements of all six Reynolds stresses and the three mean velocity components were obtained in two planes 16 and 32 jet diameters downstream using a three-component laser velocimeter. For all the jets, the interaction of vorticity tangential to the surface with its ‘image’ above the surface contributes to an outward flow near the free surface. This interaction is also shown to be directly related to the observed decrease in the surface-normal velocity fluctuations and the corresponding increase in the tangential velocity fluctuations near the free surface. At high Froude number, the larger surface disturbances diminish the interaction of the tangential vorticity with its image, resulting in a smaller outward flow and less energy transfer from the surface-normal to tangential velocity fluctuations near the surface. Energy is transferred instead to free-surface disturbances (waves) with the result that the turbulence kinetic energy is 20% lower and the Reynolds stresses are reduced. At high Reynolds number, the rate of evolution of the interaction of the jet with the free surface was reduced as shown by comparison of the rate of change with distance downstream of the local Reynolds and Froude numbers. In addition, the decay of tangential vorticity near the surface is slower than for low Reynolds number so that vortex filaments have time to undergo multiple reconnections to the free surface before they eventually decay.

Large Eddy Simulation of Flow Past Free Surface Piercing Circular Cylinders

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
G. Yu ◽  
E. J. Avital ◽  
J. J. R. Williams
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Large Eddy Simulation ◽  
Froude Number ◽  
Drag Force ◽  
Surface Effect ◽  
Circular Cylinders ◽  
Near Wake ◽  
Eddy Simulation ◽  
Large Eddy

Flows past a free surface piercing cylinder are studied numerically by large eddy simulation at Froude numbers up to FrD=3.0 and Reynolds numbers up to ReD=1×105. A two-phase volume of fluid technique is employed to simulate the air-water flow and a flux corrected transport algorithm for transport of the interface. The effect of the free surface on the vortex structure in the near wake is investigated in detail together with the loadings on the cylinder at various Reynolds and Froude numbers. The computational results show that the free surface inhibits the vortex generation in the near wake, and as a result, reduces the vorticity and vortex shedding. At higher Froude numbers, this effect is stronger and vortex structures exhibit a 3D feature. However, the free surface effect is attenuated as Reynolds number increases. The time-averaged drag force on the unit height of a cylinder is shown to vary along the cylinder and the variation depends largely on Froude number. For flows at ReD=2.7×104, a negative pressure zone is developed in both the air and water regions near the free surface leading to a significant increase of drag force on the cylinder in the vicinity of the free surface at about FrD=2.0. The mean value of the overall drag force on the cylinder increases with Reynolds number and decreases with Froude number but the reduction is very small for FrD=1.6–2.0. The dominant Strouhal number of the lift oscillation decreases with Reynolds number but increases with Froude number.

An implicit scheme for simulation of free surface non-Newtonian fluid flows on dynamically adapted grids

2021 ◽  
Vol 36 (3) ◽  
pp. 165-176
Author(s):  
Kirill Nikitin ◽  
Yuri Vassilevski ◽  
Ruslan Yanbarisov
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Newtonian Fluid ◽  
Viscoelastic Fluid ◽  
Fluid Flows ◽  
Numerical Results ◽  
Implicit Scheme ◽  
New Approach

Abstract This work presents a new approach to modelling of free surface non-Newtonian (viscoplastic or viscoelastic) fluid flows on dynamically adapted octree grids. The numerical model is based on the implicit formulation and the staggered location of governing variables. We verify our model by comparing simulations with experimental and numerical results known from the literature.

A note on the instabilities of a horizontal shear flow with a free surface

2000 ◽  
Vol 406 ◽  
pp. 337-346 ◽  
Author(s):  
L. ENGEVIK
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Shear Flow ◽  
Velocity Profile ◽  
Froude Number ◽  
The Other ◽  
Algebraic Equations ◽  
Horizontal Shear ◽  
Analytical Treatment ◽  
Unstable Region

The instabilities of a free surface shear flow are considered, with special emphasis on the shear flow with the velocity profile U* = U*0sech2 (by*). This velocity profile, which is found to model very well the shear flow in the wake of a hydrofoil, has been focused on in previous studies, for instance by Dimas & Triantyfallou who made a purely numerical investigation of this problem, and by Longuet-Higgins who simplified the problem by approximating the velocity profile with a piecewise-linear profile to make it amenable to an analytical treatment. However, none has so far recognized that this problem in fact has a very simple solution which can be found analytically; that is, the stability boundaries, i.e. the boundaries between the stable and the unstable regions in the wavenumber (k)–Froude number (F)-plane, are given by simple algebraic equations in k and F. This applies also when surface tension is included. With no surface tension present there exist two distinct regimes of unstable waves for all values of the Froude number F > 0. If 0 < F [Lt ] 1, then one of the regimes is given by 0 < k < (1 − F2/6), the other by F−2 < k < 9F−2, which is a very extended region on the k-axis. When F [Gt ] 1 there is one small unstable region close to k = 0, i.e. 0 < k < 9/(4F2), the other unstable region being (3/2)1/2F−1 < k < 2 + 27/(8F2). When surface tension is included there may be one, two or even three distinct regimes of unstable modes depending on the value of the Froude number. For small F there is only one instability region, for intermediate values of F there are two regimes of unstable modes, and when F is large enough there are three distinct instability regions.

Three-dimensional numerical model for open-channels with free-surface variations

2003 ◽  
Vol 41 (1) ◽  
pp. 110-112
Author(s):  
ZhixiaN. Cao ◽  
Rodney Day ◽  
Sarah Liriano
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Three Dimensional ◽  
Open Channels
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