Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session KL: General Fluid Dynamics II |
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Chair: Jean-Marc Vanden-Broeck, University of East Anglia Room: Hilton Chicago Astoria |
Monday, November 21, 2005 4:10PM - 4:23PM |
KL.00001: Two-dimensional sails in a uniform potential flow Michael Booty, Jean-Marc Vanden Broeck We consider a spatially two-dimensional potential flow model for the shape of and lift generated by a single or a pair of inextensible membranes or `sails' in a uniform stream. The problem is solved numerically via the boundary integral method. Of interest are (i) the `luffing' of a sail, which occurs when it is nearly aligned with the oncoming stream, (ii) the interaction of a pair of sails that share a common near-field, and (iii) possible optimal distributions of chord between two sails and relative orientations that can maximize the total lift generated. [Preview Abstract] |
Monday, November 21, 2005 4:23PM - 4:36PM |
KL.00002: Cavitation inception on rudder models with smooth and scalloped leading edges Mark Murray, Laurens Howle We present experimental results, based on water channel testing, comparing the lift and drag characteristics of rudder models with a smooth and scalloped leading edge at velocities which induce cavitation at the low pressure areas of the foils. We also compare the point of cavitation inception. We have found that leading edge cavitation occurs sooner in the scalloped leading edge model, but never progresses over the entire leading edge as it does with the smooth leading edge model. [Preview Abstract] |
Monday, November 21, 2005 4:36PM - 4:49PM |
KL.00003: Exact solutions of the Navier-Stokes equations having steady vortex structures Martin Z. Bazant, H.K. Moffatt We present two classes of exact solutions of the Navier-Stokes equations, which describe steady vortex structures with two-dimensional symmetry in an infinite fluid. The first is a class of similarity solutions obtained by conformal mapping of the Burgers vortex sheet to produce wavy sheets, stars, flowers and other vorticity patterns. The second is a class of non-similarity solutions obtained by continuation and mapping of the classical solution to steady advection-diffusion around a finite circular absorber in a two-dimensional potential flow, resulting in more complicated vortex structures that we describe as avenues, fishbones, wheels, eyes and butterflies. These solutions exhibit a transition from `clouds' to `wakes' of vorticity in the transverse flow with increasing Reynolds number. Our solutions provide useful test cases for numerical simulations, and some may be observable in experiments, although we expect instabilities at high Reynolds number. For example, vortex avenues may be related to counter-rotating vortex pairs in transverse jets, and they may provide a practical means to extend jets from dilution holes, fuel injectors, and smokestacks into crossflows. [Preview Abstract] |
Monday, November 21, 2005 4:49PM - 5:02PM |
KL.00004: The Interplay of Solvation Forces with Lubrication Forces in Thin Gaps Sivakumar Challa, Frank van Swol We report on the motion of a planar sphere approaching a smooth planar surface in a Lennard--Jones fluid using molecular dynamics simulations to understand the effect of solvation forces on the hydrodynamic drag experienced by the sphere. The hydrodynamic theory is found to be well representative of the force experienced by the sphere, even as close as 5--6 molecular lengths from the surface. Close to the surface, the solvation force is observed to be prominent in two regards, in the presence of molecular--length oscillations in the total force, and in some cases being also the predominant contributor to the total force on the sphere. The density distribution of the fluid particles close to the surface is characterized by strong layering, indicative of a breakdown of the continuum approximation in the hydrodynamic theory. Studies employing a range of sphere sizes and approach velocities indicate that the effect of the solvation force is most pronounced for slow approach velocities and for large spheres. Additionally, for analyzing experimental total force data, we suggest a phenomenological approach to decompose the total force on the sphere into a static component (``solvation force'') and a dynamic component (``lubrication force'',) which should be of interest in sedimentation processes and Atomic Force Microscopy. [Preview Abstract] |
Monday, November 21, 2005 5:02PM - 5:15PM |
KL.00005: Mode-Locking of Passive Scaler Transport to Chaotic Flows in a Disk Guy Metcalfe, Daniel Lester, Murray Rudman We study transport of a passive scaler in a bounded 2-dimensional, chaotic flow, specifically a disk with flow generated by tangential boundary motion over finite arcs of the disk, the RAM flow.\footnote{Metcalfe et al, to appear AIChE J (2005).} We calculate a spectral solution to the advection-diffusion equation, such that for a fixed Pecl{\'e}t number the full spectrum of eigensolutions---the so-called ``strange'' eigenmodes for the spatial distribution of the scaler\footnote{Pierrehumbert Chaos {\bf 10} 61 (2000).} and their decay rates---can be obtained for the entire space of controlling flow parameters with just a few additional matrix multiplies. Over this parameter space the dominant strange eigenmode symmetry locks to the wavenumber of the chaotic flow. For low values of stretching the eigenmode is symmetric. As stretching increases, the locked intervals grow, showing Arnol'd tongues and a transition to asymmetry of the scaler distribution. Preliminary experiments using an infrared camera to image temperature in a thin fluid layer show similar patterns and decay rates. [Preview Abstract] |
Monday, November 21, 2005 5:15PM - 5:28PM |
KL.00006: Residence time of a buoyant ball in a hydraulic jump Richard Keane, Michael Dameron, Gustavo Gioia, Pinaki Chakraborty We study experimentally the residence time required for a buoyant ball to cross upstream of a hydraulic jump. The experimental results indicate that the the distribution of residence times is exponential, and therefore history-independent. Based on this insight, we formulate a model in which an attempt at crossing the hydraulic jump is made at regular time intervals $\tau$ and with a constant probability of success $p$, use phenomenological theory of turbulence to obtain an expression for $\tau$, and ascertain that $p$ depends on a single dimensionless variable, which we identify. Last, we show that the predictions of this model are in good accord by the experimental data over a broad range of Froude numbers, ball sizes, and ball densities. [Preview Abstract] |
Monday, November 21, 2005 5:28PM - 5:41PM |
KL.00007: Bounds on the enstrophy growth rate for solutions of the 3-d Navier-Stokes equations Lu Lu, Charles Doering It is still an open problem whether smooth solutions to the 3-d Navier-Stokes equations lose regularity in finite time. But it is known that if enstrophy ($\|\mathbf{\omega}\|^2$) remains finite, the solution is regular. The growth rate of enstrophy can be estimated from the Navier-Stokes equations by Sobelev inequalities. In general form, $d\|\mathbf{\omega}\|^2/dt \le c(\|\mathbf{\omega}\|^2)^\alpha$, where $c$ is a constant. In 2d, the exponent $\alpha$ is 2 and leads to regularity. However, $\alpha=3$ in 3d, which shows only finite-time regularity of the solutions. In these types of estimates, incompressibility is not used. We formulate the search for the maximal enstrophy growth rate as a variational problem and include incompessibility as a constraint. The variational problem is solved numerically by a gradient-flow type algorithm. Our preliminary results show that $\alpha\approx 1.75$, which hints that solutions of the 3-d Navier-Stokes equations are regular for all time. [Preview Abstract] |
Monday, November 21, 2005 5:41PM - 5:54PM |
KL.00008: Vorticity Dynamics in Soap Films Petri Fast, Pak-Wing Fok Fast flowing soap films offer an experimental realization of two-dimensional flow that allows studies of fluid-structure interaction and vortex shedding mechanisms. The thickness of a gravity driven soap film can undergo significant variations in experiments but most modeling work in the past has focused on incompressible results that correspond to constant thickness films. We discuss a viscous compressible model of soap film flow that is equivalent to the Navier-Stokes equations with a film thickness dependent viscosity. A new vorticity transport equation for compressible soap film flow suggests effects unique to soap films and not predictible by a constant density incompressible theory. New exact solutions for the soap film model will be presented. Numerical simulations are shown to illustrate vortex shedding in soap film experiments. [Preview Abstract] |
Monday, November 21, 2005 5:54PM - 6:07PM |
KL.00009: Drag Reduction Method using Combination of Hydrophobic and Hydrophilic Coatings Hirotaka Sakaue, Ryujiro Sakakibara, Katsuaki Morita A new drag reduction method for a moving model in water is presented. This method applies a flow control using a combination of hydrophobic and hydrophilic coatings on the model surface. The flow is passively controlled by changing a chemical property on a model surface. As a preliminary result, a sphere with 2 mm in diameter is used as a basic model. The sphere is dropped in a 1 m height water tube, which has 100 mm in diameter. A flash lamp with 10 ms interval is used to capture the sphere motion at the terminal velocity. The drag coefficients, Cd, of different surface coatings are compared. Hydrophobic coating on the sphere increases drag with Cd of 0.49, while non-hydrophobic coated one shows Cd of 0.44. A sphere with hydrophilic coating gives Cd of 0.42. This tells that the hydrophilic coating on a sphere reduces drag instead of applying hydrophobic coating. In the final version, the time interval of dropping motion will be included. Besides a sphere model, other basic shapes, such as flat plate and cone, will be investigated. For a flat plate and a cone model, a combination of hydrophobic and hydrophilic coatings will be separately applied on a model surface to discuss the efficiency of a new drag reduction method. [Preview Abstract] |
Monday, November 21, 2005 6:07PM - 6:20PM |
KL.00010: Fronts in high-temperature laminar jets Mario Sanchez-Sanz, Antonio Sanchez, Amable Linan This paper addresses the slender laminar flow resulting from the discharge of a low-Mach-number hot gas jet of radius $a$ and moderately large Reynolds number $R_j$ into a cold atmosphere of the same gas. We give the boundary-layer solution for plane and round jets with very small values of the ambient-to-jet temperature ratio $\varepsilon$ accounting for the temperature dependence of the viscosity and conductivity typical of real gases. It is seen that the leading-order description of the jet in the limit $\varepsilon \rightarrow 0$ exhibits a front-like structure, including a neatly defined separating boundary at which heat conduction and viscous shear stresses vanish in the first approximation. Separate analyses are given for the jet discharging into a stagnant atmosphere, when the jet boundary is a conductive front, and for the jet discharging into a coflowing stream, when the jet boundary appears as a contact surface. We provide in particular the numerical description of the jet development region corresponding to axial distances of order $R_j a$ for buoyant and non-buoyant jets, as well as the self-similar solutions that emerge both in the near field and in the far field. In all cases considered, the comparisons with the numerical integrations of the boundary-layer problem for moderately small values of $\varepsilon$ indicate that these front descriptions give excellent predictions for the temperature and velocity fields in the near-axis region. [Preview Abstract] |
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