Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session GH: General Fluid Dynamics* |
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Chair: Howard Brenner, Massachusetts Institute of Technology Room: Tampa Marriott Waterside Hotel and Marina Florida Salon 6 |
Monday, November 20, 2006 10:30AM - 10:43AM |
GH.00001: Fluid Mechanics Revisited Howard Brenner The ``velocities'' appearing in the respective Eulerian forms of the continuity and linear momentum equations are those of mass and momentum. Despite possessing the units of velocity, neither is really a velocity, the latter notion being reserved exclusively for quantifying the movement of a single immutable material object through space. Rather, the mass velocity appearing in the continuity equation is really the fluid's mass flux divided by its density, whereas the momentum velocity is really the fluid's specific (i.e., per unit mass) momentum density. When founding the subject of rational fluid mechanics in 1755, Euler implicitly assumed these two quantities to be the same by assigning to each the same symbol, namely \textbf{v}, symbolically suggesting (without proof) the notion of velocity. In this talk the standard pre-constitutive equations of irreversible thermodynamics are combined with the Chapman-Enskog-Burnett equations of single-component monatomic gas-kinetic theory jointly with Onsager's reciprocal theorem to negate the general applicability of Euler's 250-year old implicit \textit{constitutive hypothesis}, at least in circumstances where temperature gradients exist. [Preview Abstract] |
Monday, November 20, 2006 10:43AM - 10:56AM |
GH.00002: Collisionless Closure P.J. Morrison, C.S. Jones In practice, various fluid equations are derived from kinetic theories by various procedures involving the taking of velocity moments and then expanding in terms of small parameters such as the Knudsen number. Usually such expansions, like the Hilbert and Chapman-Enskog procedures for the Boltzmann equation, assume the collision term of the kinetic theory is dominant. We describe what appears to be a novel closure procedure in the opposite limit where collisions are negligible. Sets of closed fluid equations are obtained in this limit. The procedure is general and the equations obtained can be generalized to include electromagnetic forces, which are necessary for e.g. a fluid description of a plasma. [Preview Abstract] |
Monday, November 20, 2006 10:56AM - 11:09AM |
GH.00003: A Bayesian approach to inverse problems in scalar transport Youssef M. Marzouk, Habib N. Najm Estimating the initial conditions or source term of a scalar transport equation from a sparse set of noisy measurements has practical relevance to the environmental dispersion of contaminants, as well as more fundamental connections to fluid mixing. We present a Bayesian approach to this {\em inverse problem}, in which the posterior distribution provides a quantitative assessement of uncertainty in the inverse solution, conditioned on the available data. Features that are underdetermined by the prior and the data are endowed with broad posterior variability, reflecting ill-posedness of the inversion. We also present new algorithmic developments for Bayesian inference in this context, showing connections between the Bayesian solution of the inverse problem and the forward propagation of uncertainty through the corresponding advection-diffusion equations. These connections underlie a stochastic spectral formulation that substantially accelerates the Bayesian solution of certain inverse problems. [Preview Abstract] |
Monday, November 20, 2006 11:09AM - 11:22AM |
GH.00004: General solutions of the unsteady Navier-Stokes equations in one, two and three dimensions Victor A. Miroshnikov General solutions of the unsteady Navier-Stokes equations in 1D, 2D, and 3D are derived symbolically as the Boussinesq-Rayleigh series in a coordinate and continued numerically by parallel computing. The main results of this presentation are sorted in three groups. First, several exact theorems are proved for the Navier-Stokes equations and the Stokes equations since the differential and tensor recurrent relations may be written in the closed form. For instance, it is shown that flows away from boundaries may be decomposed into the following basic flows: the Couette flow, the Poiseuille flow, the Bernoulli flow and the Stokes flow. Second, symbolic existence theorems are obtained since computation, validation, and convergence of the free and forced general solutions of the Navier-Stokes equations is treated symbolically. Third, new numerical algorithms of evaluation, continuation, and visualization of multi-scale flow structures are developed. In 3D, the flow structures are visualized by stream surfaces and stream tubes formed by streamlines with constant integration times, which continue two-dimensional isocurves of the streamfunction. [Preview Abstract] |
Monday, November 20, 2006 11:22AM - 11:35AM |
GH.00005: Traffic flow equations coming from the Grad's method. Rosa M. Velasco, Alma R. M\'endez The usual Grad's method in kinetic theory of gases is developed to construct a new model in traffic flow problems. This is applied to the kinetic equation called as the Paveri-Fontana equation which tells us how the distribution function evolves in time [1]. We assume a special model for the desired velocity of drivers [2] and the Grad's method provides us with a closure relation in the macroscopic equations. The simulation results for this model allow us to find the behavior of density, mean velocity and the velocity variance in the system. All the results are consistent with the validity region of the kinetic equation and with the qualitative behavior proper to traffic models. We show some comparisons with other models in the literature [3]. \newline [1] S.L Paveri-Fontana; Transp. Res. 9 (1975), 225. \newline [2] R.M. Velasco, W. Marques Jr.; Phys. Rev. E72 (2005), 046102. \newline [3] D. Helbing; Phys. Rev. E51 (1995), 3164. [Preview Abstract] |
Monday, November 20, 2006 11:35AM - 11:48AM |
GH.00006: Turbulent-like laminar flows sustained and controlled by multiscale electromagnetic forces Erwan Hascoet, Lionel Rossi, John Christos Vassilicos We perform DNS of electromagnetically fractal-forced and Rayleigh-damped 2D flows and compare the results with a recent laboratory experiment of a similarly forced quais-2D thin layer of brine (JFM (2006) vol. 558 p. 207). We determine a range of DNS parameters where the multiscale streamline topology is the same as in the laboratory. It is possible to vary flow intensity whilst keeping multiscale flow topology constant. Our simulations show broad band power law energy spectra $E(k)\sim k^{-p}$. When the fractal distribution of magnets is as in the laboratory experiment then $p\approx 2.5$ in agreement with the experiment. When the fractal distribution of magnets is changed, then $p$ is found to vary linearly with $D_f$, the fractal dimension of the magnet set up. Hence, fractal control of the energy spectrum is possible. The multiscale flow imposed by the fractal electromagnetic forcing resembles a deterministic $\beta$-model of turbulence which also predicts a linear relation between $p$ and the fractal dimension of the multiscale flow. In both cases, $p$ increases as the fractal dimension decreases. In the power-law range the Rayleigh damping balances the fractal forcing's energy input rate scale by scale. The small difference between the two equals the interscale energy transfer function which is severely depleted. The energy flux oscillates between positive and negative values and the wavenumbers where it cancels are a direct reflection of the multiscale stagnation point structure of the flow. [Preview Abstract] |
Monday, November 20, 2006 11:48AM - 12:01PM |
GH.00007: Particle removal from smooth and rough surfaces by turbulent jet impingement Thomas Liebner, Gary Settles Recent experiments, e.g. Phares, Smedley {\&} Flagan, J. Aerosol Sci. 31(11) 1335, 2000, have characterized monodisperse particle removal as a function of the theoretical wall shear stress induced by a free turbulent jet impinging upon a smooth surface. These experiments were done with variable jet impingement angle, duration, pressure, standoff distance, etc. The current research expands upon this theme through the experimental investigation of particle removal at larger standoff distances and correspondingly lower wall shear stress levels. We determine particle removal efficiency ratings as a function of the induced wall shear stress for particles of varying size and composition. Finally, we address the complications that arise in particle removal by turbulent jets if the impingement surface is no longer smooth (e.g. a fabric surface). This work has application to such problems as contamination control and the sampling of chemical traces from common surfaces. [Preview Abstract] |
Monday, November 20, 2006 12:01PM - 12:14PM |
GH.00008: Cavity dynamics of spinning spheres impacting the air-water interface at high velocity T.T. Truscott, A.H. Techet Impact of a sphere, spinning at a high rate, on the free surface of a quiescent tank of water generates an air-side splash curtain and subsurface air cavity which initially resembles the features generated by the impact of a non- spinning sphere. However after only milliseconds, it is clear that this problem is quite unique. The splash curtain forms and collapses asymmetrically and the ball moves through the water in a curved path, bending the air cavity along its trajectory. The hydrodynamics of a billiard ball (diameter 5.7 cm) impacting the free surface with a downward vertical velocity of 7.5 m/s and a clockwise angular velocity of 232 rad/s, at impact, are revealed using high speed video imaging. Initially, at impact, the momentum transfer forms a radial jet just above the free surface, until vertical growth outpaces radial expansion forming the splash curtain which eventually collapses inward, forming a dome. This dome continues to collapse, doing so asymmetrically due to the spinning motion of the sphere. A clockwise spinning sphere draws fluid from the left side of the cavity forming a vertical wedge of fluid that travels towards the right side of the cavity. The fluid eventually impacts the opposite wall, forcing air to be ejected from the cavity. As the ball travels along its curved trajectory, the cavity continues to elongate but no longer grows radially, eventually resulting in cavity pinch-off. [Preview Abstract] |
Monday, November 20, 2006 12:14PM - 12:27PM |
GH.00009: Numerical Study of Turbulent Mass Transfer around a Rotating Stepped Cylinder Dong-Hyeog Yoon, Kyung-Soo Yang, Klaus Bremhorst DNS was carried out to predict mass transfer in turbulent flow around a rotating stepped cylinder. This investigation is a follow-up study of Nesic et al, [Corrosion, Vol. 56, No. 10, pp. 1005 - 1014]. The original motivation of this work stemmed from the efforts to design a simple device which can generate flows of high turbulence intensity at low cost for corrosion researchers. We attempt to provide more detail of the flow structure and its interrelationship with the scalar field to assist with the understanding of this backward facing stepped flow of a rotating geometry. We consider \textit{Sc}=1 and 10 both at \textit{Re}=168. Here, \textit{Sc} and \textit{Re} stand for Schmidt number and Reynolds number, respectively, based on the step height and the surface speed of the cylinder upstream the step. Main focus was placed on the correlation between turbulent fluctuation and concentration field with particular reference to the wall layer. The spatio-temporal evolution of concentration field is discussed. Budgets for turbulent kinetic energy, scalar fluctuations and their respective dissipation rates at the locations of interest are also presented. The numerical results are qualitatively compared with those of the experiment conducted with the same flow configuration. This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2005-041- D00122). [Preview Abstract] |
Monday, November 20, 2006 12:27PM - 12:40PM |
GH.00010: Characterization of Flow Generated by Dielectric Barrier Discharges (DBD). Roger Kimmel, Jordi Estevadeordal, Sivaram Gogineni The use of dielectric barrier discharges (DBD) for flow control has received increasing attention over the past several years.~ Despite numerous applications for DBD's, the fundamental mechanism of their operation is still unknown.~ For this reason, experiments were conducted to characterize the plasma flow actuation mechanisms. The DBD discharges were created in a quiescent environment and experiments were performed for various DBD driving signal characteristics such as frequency, amplitude, phase, and waveform.~ The effects of buoyancy and large-scale background air movement around the test device were explored.~Particle image velocimetry (PIV) was used to characterize the flow field induced by the discharge for various conditions including the ones phase-locked to the DBD driving frequency. Effects of seeding material on the plasma discharge were evaluated. Flow field characteristics including wall jet formation and thickness, entrainment of ambient fluid, recirculation behind the discharge and flow unsteadiness were analyzed and the results are being used for validation and development of CFD models. [Preview Abstract] |
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