Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session D28: Free-Surface Flows II |
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Chair: Enrique Rame, National Center for Space Exploration Room: Spirit of Pittsburgh Ballroom B/C |
Sunday, November 24, 2013 2:15PM - 2:28PM |
D28.00001: Free surface shapes in rigid body rotation Enrique Rame, R. Balasubramaniam When a given volume of fluid in a container spins as a rigid body, the shape of the free surface can be found from the normal stress balance because the pressure field is known up to an additive constant. The properties of periodic (tubular) free surface shapes in rigid rotation have been studied in the past. In this talk we present results for the more practical case of shapes produced by a fixed fluid volume in a cylindrical container of given radius. We will discuss the shapes of vortices spanning the whole cylinder cross section and developing in an infinitely long container, as a function of rotation number. A critical state develops as the rotation rate approaches a critical value, where the vortex depth exhibits a logarithmic asymptotic growth rate with rotation. We will discuss the relation of these critical values to properties previously discovered by D.D. Joseph \& colleagues. We will also present properties of shapes in finite-height containers. First, we discuss the case of a vortex of given volume whose free surface contacts the container bottom and wall; next, the case when the free surface contacts the top and bottom lids of a rotating container, in the asymptotic limit of large rotation numbers. [Preview Abstract] |
Sunday, November 24, 2013 2:28PM - 2:41PM |
D28.00002: The Interaction of a Turbulent Ship-Hull Boundary Layer and a Free Surface N. Masnadi, N. Washuta, A. Wang, J.H. Duncan The free-surface deformation pattern caused by subsurface turbulent velocity fluctuations in the boundary layer at the mid-length of a naval ship is studied with a novel laboratory scale experimental technique. In this technique, the boundary layer is created in a large tank (13.4 m long, 1.3 m tall, and 2.4 m wide) with a surface-piercing meter-wide stainless steel belt that travels in a horizontal loop around two vertically oriented rollers whose axes are separated by 7.5 m. The device is enclosed in a dry box except for one of the two lengths between the rollers where a straight 6-meter-long section is exposed to the water and represents one side of the ship hull. The belt operates at full-scale ship speeds (up to 15 m/s) in order to match the Reynolds, Froude, and Weber numbers to those of naval ships, thus faithfully modeling the interaction of the turbulence with the free surface at laboratory scale. The water surface profile history midway between the rollers is recorded cinematically in a vertical plane normal to the belt using a Laser Induced Fluorescence (LIF) technique. This surface profile data is used to study the near-wall and far-field frequency content and propagation behavior of the surface ripples. [Preview Abstract] |
Sunday, November 24, 2013 2:41PM - 2:54PM |
D28.00003: The effect of bed roughness on the free surface of an open channel flow and implications for remotely monitoring river discharge Erika Johnson, Edwin Cowen The effect of increased bed roughness on the free surface turbulence signature of an open channel flow is investigated with the goal of incorporating the findings into a methodology to remotely monitor volumetric flow rates. Half of a wide (B$=$2 m) open channel bed is covered with a 3 cm thick layer of loose gravel (D$_{\mathrm{50}}=$0.6 cm). Surface PIV (particle image velocimetry) experiments are conducted for a range of flow depths (B/H$=$10-30) and Reynolds numbers (Re$_{\mathrm{H}}=$10,000-60,000). It is well established that bed roughness in wall-bounded flows enhances the vertical velocity fluctuations (e.g. Krogstad et al. 1992). When the vertical velocity fluctuations approach the free surface they are redistributed (e.g. Cowen et al. 1995) to the surface parallel component directions. It is anticipated and confirmed that the interaction of these two phenomena result in enhanced turbulence at the free surface. The effect of the rough bed on the integral length scales and the second order velocity structure functions calculated at the free surface are investigated. These findings have important implications for developing new technologies in stream gaging. [Preview Abstract] |
Sunday, November 24, 2013 2:54PM - 3:07PM |
D28.00004: Rivulet between two planes: effect of inlet angle Peter Vorobieff, Nima Fathi The behavior of gravity-driven rivulets flowing down between two vertical planes has attracted considerable recent attention, driven both by practical interest and by the attractiveness of the problem from the point of view of nonlinear physics. In this investigation, we study the effects of Reynolds number and variations of the inlet boundary conditions on the rivulet flow. The latter include variation in the entrance angle of the inlet with respect to vertical in the plane containing the rivulet. The experimental arrangement allows to create or eliminate fluctuations in the discharge that drives the rivulet, which leads to changes in the flow patterns we observe, including transitions between different flow regimes, and in some cases coexistence of straight and meandering flow. For a wide range of flow regimes, elimination of fluctuations in the discharge rate leads to emergence of stable, straight, non-meandering flow. While a similar observation had been previously made for flows down an inclined plane, this result is interesting, because of differences in the boundary conditions. [Preview Abstract] |
Sunday, November 24, 2013 3:07PM - 3:20PM |
D28.00005: Flow around the corner in the water impact problem Rouslan Krechetnikov In this work we discuss an effect of three dimensionality of the impacting body on the ejecta evolution in the water impact problem as inspired by recent experimental data. The main finding of this study is the revealed and quantified influence of the geometry of a flat plate corner on the ejecta properties. The systematic approach taken here provides a generalization of the classical two-dimensional results. [Preview Abstract] |
Sunday, November 24, 2013 3:20PM - 3:33PM |
D28.00006: Oblique impact of dense granular sheets Jake Ellowitz, Nicholas Guttenberg, Heinrich M. Jaeger, Sidney R. Nagel, Wendy W. Zhang Motivated by experiments showing impacts of granular jets with non-circular cross sections produce thin ejecta sheets with anisotropic shapes, we study what happens when two sheets containing densely packed, rigid grains traveling at the same speed collide asymmetrically. Discrete particle simulations and a continuum frictional fluid model yield the same steady-state solution of two exit streams emerging from incident streams. When the incident angle $\Delta \theta$ is less than $\Delta\theta_c = 120^\circ \pm 10^\circ$, the exit streams' angles differ from that measured in water sheet experiments. Below $\Delta\theta_c$ , the exit angles from granular and water sheet impacts agree. This correspondence is surprising because 2D Euler jet impact, the idealization relevant for both situations, is ill posed: a generic $\Delta \theta$ value permits a continuous family of solutions. Our finding that granular and water sheet impacts evolve into the same member of the solution family suggests previous proposals that perturbations such as viscous drag, surface tension or air entrapment select the actual outcome are not correct. [Preview Abstract] |
Sunday, November 24, 2013 3:33PM - 3:46PM |
D28.00007: Simultaneous Multiphase PIV of Capillary Waves on a High Velocity Liquid Jet Matthieu Andre, Philippe Bardet Relaxation of a laminar boundary layer below the free surface of a jet is inviscidly unstable and can roll-up which generates millimeter size waves. The latter largely modify important characteristics of jets such as heat and mass transfers between phases and can lead to breakup, or air entrainment. Two dimensional linear stability analysis predicts the initial disturbance wavelength and growth rate for inviscid flows; it does not take into account the effects of viscosity, non-linearity, or actual boundary layer profile. Because of the small temporal and spatial scales associated with this flow, few experimental data are available. Data acquisition is further complicated by the presence of a free surface with steep waves. The current experiment consists in a 20.3 mm $\times$ 146.0 mm water slab laminar jet flowing onto a transparent open-channel at a Reynolds number of 2.9 $\times$ 104 to 1.4 $\times$ 105. Two high speed cameras are employed to obtain velocity fields simultaneously in the liquid and in the gas phase with Particle Image Velocimetry (PIV). Fluorescent dye is added in the liquid in order to improve interface detection. Each phase is recorded at 10 kHz, leading to a temporal resolution of 100 $\mu$s and high magnification lenses give a spatial resolution of 200 $\mu$m. The results confirm the mechanism of formation of the short surface waves. Generation of surface vorticity is identified in high curvature regions. Knowledge of the velocities in both phases allows studying vorticity flux through the free surface. The latter stage of wave growth can be accompanied by the formation of a vortex pair in the liquid and air entrapment. [Preview Abstract] |
Sunday, November 24, 2013 3:46PM - 3:59PM |
D28.00008: Ejecta evolution during cone impact Jeremy Marston, Ivan Vakarelski, Sigurdur Thoroddsen We present results from an experimental study of the impact of conical shaped bodies into a pool of liquid. By varying the cone angle, impact speed and liquid physical properties, we examine a broad parameter space and seek to find conditions when self-similarity can be observed during this phenomena. We use high-speed imaging to capture the early-time motion of the liquid ejecta which emanates from the tip of the cone and travels up along the cone surface. Surprisingly, we find that the detachment of the ejecta can be simply described by air entrainment relationships derived from coating experiments. [Preview Abstract] |
Sunday, November 24, 2013 3:59PM - 4:12PM |
D28.00009: Flow-pattern analysis in open and closed square ducts: A comparative investigation of corner vortices Jochen Kriegseis, Markus Vaas, Bettina Frohnapfel In the present study secondary flows in straight square ducts are investigated experimentally for open and closed geometries. The flow of the closed square duct typically consists of a set of eight equal-sized counter-rotating vortices. In contrast, the flow in an open flume of (identical) square geometry is considered, where the development of secondary vortices is strongly affected by the presence of the free surface. Stereo Particle Image Velocimetry (SPIV) experiments have been performed so as to measure the flow in both geometries for varying Reynolds numbers. From the resulting 2D3C velocity information secondary vortices (superimposed onto the mean primary flow) are identified. As expected, the upper bisectors' flow topology differs significantly between open and closed ducts, where typical inner and outer vortices are identified from the open-duct data. Interestingly, the secondary vortices of the lower bisectors of both duct flows reveal a similar topology. In order to study this seeming similarit more rigorously, a modal analysis of the respective flow data is performed by means of proper orthogonal decomposition (POD). As such, similarities and limitations of the comparability of the respective corner vortices are uncovered and discussed as function of Reynolds number. [Preview Abstract] |
Sunday, November 24, 2013 4:12PM - 4:25PM |
D28.00010: Water entry without surface seal: extended cavity formation Mohammad Mansoor, Jeremy Marston, Ivan Vakarelski, Sigurdur Thoroddsen We report results from an experimental study of cavity formation during the impact of hydrophobic spheres onto water. Using a splash-guard mechanism, we block the spray during initial contact from closing thus eliminating the phenomenon known as ``surface seal,'' which typically occurs at \textit{Fr}$= O$(100). As such, we are able to observe the evolution of a smooth cavity in an extended parameter space than has been achieved in previous studies. By systematically varying the tank size and sphere diameter, we examine the influence of increasing wall effects on these guarded impact cavities and note the formation of surface waves with wavelength $\lambda = O$(10) cm and acoustic waves $\lambda_{a} = O(D_{0}) $along the cavity interface, which produce multiple pinch-off points. Acoustic waves are initiated by pressure perturbations, which themselves are generated by the primary cavity pinch-off. Using high-speed particle image velocimetry (PIV) techniques we show the larger waves ($\lambda = O$(10) cm) have a standing nature. We show that previously deduced scalings for the normalised (primary) pinch-off location $H_{p}/H = $1/2 and time $\tau \propto (R_{0}/g)^{1/2}$ do not hold in the presence of strong wall effects for $D_{0}/D_{tank} \ge $ 1/16. [Preview Abstract] |
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