4 results
Three-dimensional flow structures in laminar falling liquid films
- Georg F. Dietze, W. Rohlfs, K. Nährich, R. Kneer, B. Scheid
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- Journal:
- Journal of Fluid Mechanics / Volume 743 / 25 March 2014
- Published online by Cambridge University Press:
- 04 March 2014, pp. 75-123
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Full numerical simulations of the Navier–Stokes equations for four cases of vertically falling liquid films with three-dimensional surface waves have been performed. Flow conditions are based on several previous experimental studies where the streamwise and spanwise wavelengths were imposed, which we exploit by simulating periodic wave segments. The considered flows are laminar but approach conditions at which intermittent wave-induced turbulence has been observed elsewhere. Working liquids range from water to silicone oil and cover a large interval of the Kapitza number (
$\textit {Ka}=18\mbox{--}3923$), which relates capillary to viscous forces. Simulations were performed on a supercomputer, using a finite-volume code and the volume of fluid and continuum surface force methods to account for the multiphase nature of the flow. Our results show that surface waves, consisting of large horseshoe-shaped wave humps concentrating most of the liquid and preceded by capillary ripples on a thin residual film, segregate the flow field into two regions: an inertia-dominated one in the large humps, where the local Reynolds number is up to five times larger than its mean value, and a visco-capillary region, where capillary and/or viscous forces dominate. In the inertial region, an intricate structure of different-scale vortices arises, which is more complicated than film thickness variations there suggest. Conversely, the flow in the visco-capillary region of large-
$\textit {Ka} $ fluids is entirely governed by the local free-surface curvature through the action of capillary forces, which impose the pressure distribution in the liquid film. This results in flow separation zones underneath the capillary troughs and a spanwise cellular flow pattern in the region of capillary wave interference. In some cases, capillary waves bridge the large horseshoe humps in the spanwise direction, coupling the two aforementioned regions and leading the flow to oscillate between three- and two-dimensional wave patterns. This persists over long times, as we show by simulations with the low-dimensional model of Scheid et al. (J. Fluid Mech., vol. 562, 2006, pp. 183–222) after satisfactory comparison with our direct simulations at short times. The governing mechanism is connected to the bridging capillary waves, which drain liquid from the horseshoe humps, decreasing their amplitude and wave speed and causing them to retract in the streamwise direction. Overall, it is observed that spanwise flow structures (not accounted for in two-dimensional investigations) are particularly complex due to the absence of gravity in this direction.
Contributors
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- By Kateri Berasi, Carol A. Boyer, Diane R. Brown, Robyn Lewis Brown, Tony N. Brown, Padraic J. Burns, Cleopatra Howard Caldwell, Daniel L. Carlson, Cheryl Corcoran, Manuela Costa, Stephen Crystal, Gary S. Cuddeback, William W. Eaton, Adrianne Frech, Virginia Aldigé Hiday, Stevan E. Hobfoll, Allan V. Horwitz, Robert J. Johnson, Verna M. Keith, Ronald C. Kessler, Corey L. M. Keyes, Jacinta P. Leavell, Harriet P. Lefley, Mary Clare Lennon, Laura Limonic, Bruce G. Link, Athena McLean, David Mechanic, Elizabeth G. Menaghan, Barret Michalec, John Mirowsky, Shirin Montazer, Joseph P. Morrissey, Carles Muntaner, Bernice A. Pescosolido, Christopher Peterson, Jo C. Phelan, Michael Polgar, Sarah Rosenfield, Catherine E. Ross, Ebony Sandusky, Jaime C. Sapag, Teresa L. Scheid, Mark F. Schmitz, Sharon Schwartz, Dena Smith, David T. Takeuchi, Peggy A. Thoits, R. Jay Turner, Edwina S. Uehara, Jerome C. Wakefield, James Walkup, Emily Walton, Blair Wheaton, David R. Williams, Kristi Williams
- Edited by Teresa L. Scheid, University of North Carolina, Charlotte, Tony N. Brown, Vanderbilt University, Tennessee
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- Book:
- A Handbook for the Study of Mental Health
- Published online:
- 05 June 2012
- Print publication:
- 16 November 2009, pp xi-xiv
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6 - Flows with interfaces
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- By A. E. Hasha, J. W. M. Bush, M. F. G. Johnson, M. J. Miksis, R. A. Schluter, S. G. Bankoff, I. L. Kliakhandler, S. H. Davis, S. G. Bankoff, B. J. Fischer, A. A. Darhuber, S. M. Troian, T. Maxworthy, R. Buckingham, J. W. M. Bush, S. T. Thoroddsen, L. Mahadevan, A. A. Vedernikov, B. Scheid, E. Istasse, J. C. Legros
- M. Samimy, Ohio State University, K. S. Breuer, Brown University, Rhode Island, L. G. Leal, University of California, Santa Barbara, P. H. Steen, Cornell University, New York
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- Book:
- A Gallery of Fluid Motion
- Published online:
- 25 January 2010
- Print publication:
- 12 January 2004, pp 63-71
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Summary
We examine the form of the free surface flows resulting from the collision of equal jets at an oblique angle. Glycerol-water solutions with viscosities of 15–50 cS were pumped at flow rates of 10–40 cc/s through circular outlets with diameter 2 mm. Characteristic flow speeds are 1–3 m/s. Figures 2–4 were obtained through strobe illumination at frequencies in the range 2.5–10 kHz.
At low flow rates, the resulting stream takes the form of a steady fluid chain, a succession of mutually orthogonal fluid links, each comprised of a thin oval sheet bound by relatively thick fluid rims (Fig. 1). The influence of viscosity serves to decrease the size of successive links, and the chain ultimately coalesces into a cylindrical stream.
As the flow rate is increased, waves are excited on the sheet, and the fluid rims become unstable (Figs. 2 and 3). Droplets form from the sheet rims but remain attached to the fluid sheet by tendrils of fluid that thin and eventually break. The resulting flow takes the form of fluid fishbones, with the fluid sheet being the fish head and the tendrils its bones. Increasing the flow rate serves to broaden the fishbones.
In the wake of the fluid fish, a regular array of drops obtains, the number and spacing of which is determined by the pinch–off of the fishbones (Fig. 4). At the highest flow rates examined, the flow is reminiscent of that arising in acoustically excited fan-spray nozzles.
Principle of high accuracy for the nonlinear theory of the acceleration of electrons in a vacuum by lasers at relativistic intensities
- H. HORA, M. HOELSS, W. SCHEID, J.W. WANG, Y.K. HO, F. OSMAN, R. CASTILLO
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- Journal:
- Laser and Particle Beams / Volume 18 / Issue 1 / January 2000
- Published online by Cambridge University Press:
- 02 March 2001, pp. 135-144
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Acceleration of electrons by lasers in a vacuum was considered impossible based on the fact that plane-wave and phase symmetric wave packets cannot transfer energy to electrons apart from Thomson or Compton scattering or the Kapitza–Dirac effect. The nonlinear nature of the electrodynamic forces of the fields to the electrons, expressed as nonlinear forces including ponderomotion or the Lorentz force, permits an energy transfer if the conditions of plane waves in favor of the beams and/or the phase symmetry are broken. The resulting electron acceleration by lasers in a vacuum is now well understood as “free wave acceleration”, as “ponderomotive scattering”, as “violent acceleration”, or as “vacuum beat wave acceleration”. The basic understanding of these phenomena relates to an accuracy principle of nonlinearity for explaining numerous discrepancies on the way to the mentioned achievement of “vacuum laser acceleration”, which goes beyond the well-known experience of necessary accuracy in both modeling and experimental work experiences among theorists and experimentalists in the field of nonlinearity. From mathematically designed beam conditions, an absolute maximum of electron energy per laser interaction has been established. It is shown here how numerical results strongly (both essentially and gradually) depend on the accuracy of the used laser fields for which examples are presented and finally tested by the criterion of the absolute maximum.
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