Geometry Effects on Free Surface Vorticity Flux

1999 ◽  
Vol 121 (3) ◽  
pp. 678-683 ◽  
Author(s):  
Bill Peck ◽  
Lorenz Sigurdson
Keyword(s):  
Free Surface ◽  
Convenient Method ◽  
Gaussian Curvature ◽  
Vortex Lines ◽  
Geometry Effects ◽  
Vorticity Flux

Effects of geometry on the flux of vorticity from a free surface are discussed. Special attention is paid to situations where curvature-dependent contributions to the vorticity flux can be neglected. The geometry of vortex lines embedded in the surface is discussed in this context. These results show that vortex lines can be straight and geometry-induced vorticity flux is produced; conversely vortex lines can be curved and no geometry-induced vorticity flux is produced. A convenient method for assessing vorticity flux from a steady surface based on Gaussian curvature is derived.

Interpreting Vortex Interactions With a Free Surface

1994 ◽  
Vol 116 (1) ◽  
pp. 91-94 ◽  
Author(s):  
E. P. Rood
Keyword(s):  
Free Surface ◽  
Surface Condition ◽  
Viscous Forces ◽  
Vortex Interactions ◽  
Free Surface Condition ◽  
Vortex Loops ◽  
Physical Experiments ◽  
Vorticity Flux ◽  
Tangential Acceleration

An understanding of the process by which vorticity interacts with a free surface is sought by analytical examination of the free-surface condition for the vorticity flux. A novel mechanism is suggested that permits closed vortex loops to evolve into open loops terminating at the free surface. It is hypothesized that abrupt vortex “disconnection,” observed in physical experiments, arises from a smooth diffusion of vorticity through the interface, with a necessary coincident tangential acceleration of the interface attributed to viscous forces.

On the generation of vorticity at a free surface

1999 ◽  
Vol 382 ◽  
pp. 351-366 ◽  
Author(s):  
THOMAS LUNDGREN ◽  
PETROS KOUMOUTSAKOS
Keyword(s):  
Shear Stress ◽  
Free Surface ◽  
Viscous Flows ◽  
Vortex Sheet ◽  
Boundary Integral ◽  
Free Surfaces ◽  
Boundary Integral Formulation ◽  
Pressure Boundary Condition ◽  
Vorticity Flux ◽  
Pressure Boundary Conditions

The mechanism for the generation of vorticity at a viscous free surface is described. This is a free-surface analogue of Lighthill's strategy for determining the vorticity flux at solid boundaries. In this method the zero-shear-stress and pressure boundary conditions are transformed into a boundary integral formulation suitable for the velocity–vorticity description of the flow. A vortex sheet along the free surface is determined by the pressure boundary condition, while the condition of zero shear stress determines the vorticity at the surface. In general, vorticity is generated at free surfaces whenever there is flow past regions of surface curvature. It is shown that vorticity is conserved in free-surface viscous flows. Vorticity which flows out of the fluid across the free surface is gained by the vortex sheet; the integral of vorticity over the entire fluid region plus the integral of ‘surface vorticity’ over the free surface remains constant. The implications of the present strategy as an algorithm for numerical calculations are discussed.

The Analysis of Effects of Curvature Attribute on Interference in Freeform Surface Blade NC Machining

2011 ◽  
Vol 314-316 ◽  
pp. 1783-1787
Author(s):  
Ming Hai Wang ◽  
Xiao Peng Li ◽  
Yue Sun
Keyword(s):  
Free Surface ◽  
Gaussian Curvature ◽  
Cutting Tool ◽  
Nc Machining ◽  
Mapping Method ◽  
Surface Curvature ◽  
Machining Process ◽  
Processing Efficiency ◽  
Intervention Process ◽  
Curvature Parameter

This paper proposes the Gaussian Curvature by analyzing the free surface of the blade surface curvature, which is based on the Gaussian Curvature parameter mapping method to study the Gaussian curvature of free surface NC machining process interference. We introduce the conception of curvature to analyze the curvature and optimize the cutting parameter and cutting tool parameter to avoid interference phenomena happening and improve the processing efficiency and precision. Take the ball end cutter for example to process simulation, it shows that through the analysis of the free surface curvature method to avoid the intervention process is feasible, and has been verified by the experiment.

scholarly journals Flow past a cylinder close to a free surface

1997 ◽  
Vol 330 ◽  
pp. 1-30 ◽  
Author(s):  
J. SHERIDAN ◽  
J.-C. LIN ◽  
D. ROCKWELL
Keyword(s):  
Free Surface ◽  
Complete Separation ◽  
Small Scale ◽  
Central Feature ◽  
Flow Past ◽  
Flow Past A Cylinder ◽  
Scale Breaking ◽  
Free Surface Wave ◽  
Submerged Cylinder ◽  
Vorticity Flux

Flow past a cylinder beneath a free surface gives rise to fundamental classes of nearwake structure that are distinctly different from the wake of a completely submerged cylinder. A central feature is the generation of a vorticity layer from the free surface due to: localized separation, in the form of small-scale breaking of a free-surface wave; or complete separation from the free surface. This vorticity layer appears adjacent to a layer from the surface of the cylinder, thereby forming a jet-like flow. It is shown that the instantaneous vorticity flux on either side of this jet is rapidly balanced immediately after the onset of separation from the free surface.

Free Surface of a Rotating HeII Film

1973 ◽  
Vol 51 (21) ◽  
pp. 2283-2286 ◽  
Author(s):  
E. Vittoratos ◽  
M. W. Cole ◽  
P. P. M. Meincke
Keyword(s):  
Thin Films ◽  
Free Surface ◽  
Superfluid Helium ◽  
Vortex Line ◽  
Rotational Frequency ◽  
Experimental Results ◽  
Quantized Vortex ◽  
Bulk Liquid ◽  
Vapor Interface ◽  
Vortex Lines

Stimulated by recent conflicting experimental results, we have investigated the properties of quantized vortex lines in thin films of superfluid helium. The shape of the liquid–vapor interface in the presence of a single line is calculated. The depression of the interface ("dimple") that results is considerably smaller for the film than for the bulk liquid. The critical rotational frequency for the appearance of the first vortex line is only slightly reduced below the bulk value.

Tracking vortex surfaces frozen in the virtual velocity in non-ideal flows

2019 ◽  
Vol 863 ◽  
pp. 513-544 ◽  
Author(s):  
Jinhua Hao ◽  
Shiying Xiong ◽  
Yue Yang
Keyword(s):  
Lorentz Force ◽  
Diffusion Term ◽  
Surface Field ◽  
Vortex Lines ◽  
Body Forces ◽  
Vorticity Flux ◽  
Virtual Velocity

We demonstrate that, if a globally smooth virtual circulation-preserving velocity exists, Kelvin’s and Helmholtz’s theorems can be extended to some non-ideal flows which are viscous, baroclinic or with non-conservative body forces. Then we track vortex surfaces frozen in the virtual velocity in the non-ideal flows, based on the evolution of a vortex-surface field (VSF). For a flow with a viscous-like diffusion term normal to the vorticity, we obtain an explicit virtual velocity to accurately track vortex surfaces in time. This modified flow is dissipative but prohibits reconnection of vortex lines. If a globally smooth virtual velocity does not exist, an approximate virtual velocity can still facilitate the tracking of vortex surfaces in non-ideal flows. In a magnetohydrodynamic Taylor–Green flow, we find that the conservation of vorticity flux is significantly improved in the VSF evolution convected by the approximate virtual velocity instead of the physical velocity, and the spurious vortex deformation induced by the Lorentz force is eliminated.

scholarly journals Experimental investigation of the vorticity generation within a spilling water wave

1997 ◽  
Vol 330 ◽  
pp. 113-139 ◽  
Author(s):  
DANA DABIRI ◽  
MORTEZA GHARIB
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Gravity Wave ◽  
High Speed ◽  
Capillary Waves ◽  
Breaking Wave ◽  
Dominant Source ◽  
First Case ◽  
Surface Jet ◽  
Vorticity Flux

Sources of vorticity are examined for a laboratory-generated spilling breaking wave. Two cases are studied. For the first case, based on the breaker height, the Reynolds and Froude numbers are 7370 and 2.04, respectively. The breaker is preceded by 1 mm wavelength capillary waves, with the largest amplitude-to-wavelength ratio equal to 0.18. For this case, it is found that the dominant source of vorticity flux is a viscous process, due to the deceleration of a thin layer of the surface fluid. For the second case, the Reynolds and Froude numbers based on the wave height are 1050 and 1.62, respectively. No breaking is observed for this case; rather a capillary–gravity wave is observed with 4 mm wavelength capillaries preceding the gravity wave. The largest amplitude-to-wavelength ratio of these capillaries is 0.28. This case shows that capillary waves do not contribute to the vorticity flux; rather the only dominant source of the vorticity flux into the flow is the free-surface fluid deceleration.Lastly, a thin free-surface jet that is relatively vorticity-free is found to precede the spilling breaker. Analyses suggest that our wave-breaking phenomena can be modelled by a hydraulic jump phenomenon where the Froude number is based on the thickness of the free-surface jet, and on the velocity of the free-surface jet just prior to breaking. We believe this to be a more physically descriptive value of the Froude number. For the high-speed case, the Froude number based on the thickness of the free-surface jet is 4.78, while for the lower-speed case it is 2.14.

Vortex reconnection in the late transition in channel flow

2016 ◽  
Vol 802 ◽  
Author(s):  
Yaomin Zhao ◽  
Yue Yang ◽  
Shiyi Chen
Keyword(s):  
Channel Flow ◽  
Fluid Motion ◽  
Wall Friction ◽  
Sudden Increase ◽  
Mean Flow ◽  
Vortex Sheets ◽  
Vortex Reconnection ◽  
Vortex Lines ◽  
Symmetric Plane ◽  
Vorticity Flux

Vortex reconnection, as the topological change of vortex lines or surfaces, is a critical process in transitional flows, but is challenging to accurately characterize, particularly in shear flows. We apply the vortex-surface field (VSF), whose isosurface is the vortex surface consisting of vortex lines, to study vortex reconnection in the Klebanoff-type temporal transition in channel flow. The VSF evolution can capture the reconnection of the hairpin-like vortical structures evolving from the initial vortex sheets in opposite halves of the channel. The incipient vortex reconnection is characterized by the vanishing minimum distance between a pair of vortex surfaces and the reduction of vorticity flux through the region enclosed by the wall and the VSF isoline of the channel half-height on the spanwise symmetric plane. We find that the surge of the wall-friction coefficient begins at the identified reconnection time. From the Biot–Savart law, the rapid reconnection of vortex lines can induce a velocity opposed to the mean flow, which partially blocks the flow near the central region and generally accelerates the near-wall fluid motion in the flow with constant mass flux. Therefore, the vortex reconnection appears to play an important role in the sudden increase of wall friction in transitional channel flows.

The viscous vortex induced by a sink on the axis of a circulating fluid in the presence of a plane free surface

1969 ◽  
Vol 36 (2) ◽  
pp. 219-238 ◽  
Author(s):  
T. J. Pedley
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Stagnation Point ◽  
Velocity Fields ◽  
First Order ◽  
The Core ◽  
Meridional Velocity ◽  
Vortex Lines ◽  
Burgers Vortex ◽  
Made In

The flow under discussion represents an idealization of the bath-tub vortex; distortions of the free surface, finite sink size, and all rigid boundaries have been eliminated from the problem in order to isolate the effect of the non-uniform stretching of vortex lines produced by the sink flow. A boundary-layer type of approximation is made about the axis, which requires that the meridional Reynolds number (N) be large, and since the problem is still intractable, an expansion is made in powers ofK=R2/N(whereRis the swirl Reynolds number), which measures the strength of the interaction between the swirl and meridional velocity fields. In the limit of zeroKthe flow is a modified Burgers vortex whose radius decreases to zero at the sink. For non-zeroK, the interaction is not restricted to the vortex core, because the presence of the vortex modifies the outer irrotational flow, inducing a radial mass flux into the core, whose dependence on the axial co-ordinate is calculated to the first order inK.The structure of the core is obtained, again to the first order inK, from two co-ordinate expansions, one near the stagnation point on the axis, and the other near the sink, although only the first few terms of the latter can be determined explicitly. It is shown how the methods can be extended not only to higher orders inK, but also to any other narrow viscous vortex in which the vortex lines are stretched non-uniformly away from an internal stagnation point.

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