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.

scholarly journals Turbulence Measurements in Pipe Flow With Drag Reducing Polymer Additives

2016 ◽  
Author(s):  
L. Marylin Pumisacho ◽  
Luis Fernando A. Azevedo
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Velocity Fields ◽  
Instantaneous Velocity ◽  
Shear Stresses ◽  
Normal Velocity ◽  
Reynolds Stresses ◽  
Velocity Fluctuations ◽  
Turbulent Reynolds Number ◽  
Viscous Shear

Pressure drop and instantaneous velocity fields were measured for fully developed turbulent pipe flow of water and a solution of water and long chain polymer at low concentration. Two-dimensional Particle Image Velocimetry technique — PIV, coupled with a particle tracking technique was employed to yield velocity fields with high spatial resolution. Turbulence statistics were obtained from a series of approximately 2500 instantaneous velocity fields measured for each flow configuration characterized by the turbulent Reynolds number and the polymer concentration. Tests were conducted for a turbulent Reynolds number range from Reτ≈1764 to Reτ≈3154, and for 20 wppm of Superfloc A110 polymer in water. Time-averaged, rms velocity fluctuations and turbulent shear stresses profiles were measured. Drag reductions of the order of 50% were measured. Changes in the axial and wall-normal velocity fluctuations were measured and linked to the presence of the polymer. Reynolds stresses were also shown to decrease in the buffer layer of polymer solution flows as a result of a decrease in the correlation of axial and wall normal fluctuations. A deficit of the viscous shear stress and Reynolds stresses in relation to the total stress was measured close to the wall and attributed to the polymer stresses exerted on the fluid. All the results obtained were in agreement with the available literature, which serve to validate the procedures and test section employed in the experiments.

A P.I.V. Processing Technique for Directly Measuring Surface-Normal Velocity Gradient at a Free Surface

2005 ◽  
Author(s):  
Tuy N. M. Phan ◽  
Chuong V. Nguyen ◽  
John C. Wells
Keyword(s):  
Free Surface ◽  
Channel Flow ◽  
Velocity Gradient ◽  
Open Channel ◽  
Open Channel Flow ◽  
Processing Technique ◽  
High Mass ◽  
Normal Velocity ◽  
Uniform Compression ◽  
Surface Normal

Compressive surface-normal velocity gradient at a free surface leads to high mass transfer across a free surface. Our research aims to directly measure this velocity gradient at the free surface by proposing an advanced Particle Image Velocimetry (PIV) technique and simultaneously evaluate its applicability. This technique, PIV/IG (Interface Gradiometry), was proposed by Nguyen et al. (2004) to directly measure wall velocity gradient with high S.N.R. Herein, we adapt this technique to measure the compressive surface-normal velocity gradient at the free surface of open channel flow with minimal fluctuation of water surface. We validate this technique in a two-component PIV configuration by synthetic PIV images corresponding to uniform compression, linearly-varying compression, and a velocity field based on DNS data of open channel flow at friction Reynolds number Reτ = 240 and zero Froude number. The results clearly show that this technique works much better than the velocity differentiation method. The effect of template size on the measured value is evaluated.

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.

Prediction of Solid/Free-Surface Juncture Boundary Layer and Wake of a Surface-Piercing Flat Plate at Low Froude Number

1998 ◽  
Vol 120 (2) ◽  
pp. 354-362 ◽  
Author(s):  
Madhu Sreedhar ◽  
Fred Stern
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Flat Plate ◽  
Froude Number ◽  
Secondary Flows ◽  
Wall Region ◽  
Normal Stresses ◽  
Streamwise Vorticity ◽  
Reynolds Stresses ◽  
Mean Velocity

Results are reported of a RANS simulation investigation on the prediction of turbulence-driven secondary flows at the free-surface juncture of a surface-piercing flat plate at low Froude numbers. The turbulence model combines a nonlinear eddy viscosity model and a modified version of a free-surface correction formula. The different elements of the model are combined and the model constants calibrated based on the premises that the anisotropy of the normal stresses is mainly responsible for the dynamics of the flow in the juncture region, and an accurate modeling of the normal-stress anisotropy as obtained from the data is a primary requirement for the successful prediction of the overall flow field. The predicted mean velocity, streamwise vorticity, turbulent kinetic energy, and other quantities at the juncture are then compared with data and analyzed with regard to findings of related studies. In agreement with the experimental observations, the simulated flow at large depths was essentially two-dimensional and displayed all the major features of zero pressure gradient boundary layer and wake, including the anisotropy of normal stresses in the near-wall region. In the boundary-layer free-surface juncture region, the major features of interest that were predicted include the generation of secondary flows and the thickening of the boundary layer near the free surface. In the wake free-surface juncture region, even though secondary flows and a thickening of the wake width near the free surface were predicted in accordance with the experimental observations, the overall comparison with the experiment was not as satisfactory as the boundary-layer juncture. This is partly due to the lack of a strong coherent flow structure in the wake juncture and the presence of possible wave effects in the wake in the experiments. An examination of the terms in the Reynolds-averaged streamwise vorticity equation reconfirmed the importance of the anisotropy of the normal Reynolds stresses in the production of streamwise vorticity. The free-surface wave elevations were negligible for the present model problem for the nonzero Froude number studied. Finally, concluding remarks are presented with regards to extensions for practical geometries such as surface ship flows.

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.

An example of steady laminar flow at large Reynolds number

1960 ◽  
Vol 9 (4) ◽  
pp. 593-602 ◽  
Author(s):  
Iam Proudman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Tangential Velocity ◽  
Fluid Flows ◽  
The Other ◽  
Large Reynolds Number ◽  
Rotational Flows ◽  
Flow Domain ◽  
Source Of Information

The purpose of this note is to describe a particular class of steady fluid flows, for which the techniques of classical hydrodynamics and boundary-layer theory determine uniquely the asymptotic flow for large Reynolds number for each of a continuously varied set of boundary conditions. The flows involve viscous layers in the interior of the flow domain, as well as boundary layers, and the investigation is unusual in that the position and structure of all the viscous layers are determined uniquely. The note is intended to be an illustration of the principles that lead to this determination, not a source of information of practical value.The flows take place in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. When fluid is extracted through both walls there are boundary layers on both walls and the flow outside these layers is irrotational. When fluid is extracted through one wall and injected through the other, there is a boundary layer only on the former wall and the inviscid rotational flow outside this layer satisfies the no-slip condition on the other wall. When fluid is injected through both walls there are no boundary layers, but there is a viscous layer in the interior of the channel, across which the second derivative of the tangential velocity is discontinous, and the position of this layer is determined by the requirement that the inviscid rotational flows on either side of it must satisfy the no-slip conditions on the walls.

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.

Pure Design Method for Aerofoils in Cascade

1969 ◽  
Vol 11 (5) ◽  
pp. 454-467 ◽  
Author(s):  
K. Murugesan ◽  
J. W. Railly
Keyword(s):  
Exact Solution ◽  
Velocity Distribution ◽  
Design Problem ◽  
Design Method ◽  
Tangential Velocity ◽  
Surface Velocity ◽  
Normal Velocity ◽  
Blade Design ◽  
Blade Shape

An extension of Martensen's method is described which permits an exact solution of the inverse or blade design problem. An equation is derived for the normal velocity distributed about a given contour when a given tangential velocity is imposed about the contour and from this normal velocity an initial arbitrarily chosen blade shape may be successively modified until a blade is found having a desired surface velocity distribution. Five examples of the method are given.

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