Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session JN: General Fluid Dynamics I |
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Chair: Patrick Weidman, University of Colorado Room: Salt Palace Convention Center 251 B |
Monday, November 19, 2007 3:35PM - 3:48PM |
JN.00001: Bi-velocity fluid mechanics Howard Brenner Four physically-different velocities appear in the mass, momentum, and energy equations governing single-component fluid mechanics prior to making any constitutive assumptions regarding the stress tensor and heat flux vector appearing therein: (i) the ``mass velocity'' ${\bf{v}}_m$ appearing in the continuity equation; (i) the ``momentum velocity'' ${\bf{\hat m}}$ representing the fluid's specific momentum density (momentum per unit mass) appearing in the linear momentum equation; (iii) the ``kinetic-energy velocity'' ${\bf{v}}_k$ embedded in the fluid’s scalar specific kinetic-energy density $\hat e_k = (1/2){\bf{v}}_k \bullet {\bf{v}}_k$ appearing in the energy equation; and (iv) the ``work velocity'' ${\bf{v}}_w$ whose scalar product ${\bf{P}} \bullet {\bf{v}}_w$ with the pressure tensor ${\bf{P}}$ constitutes the power vector (related to the rate working) appearing in the energy equation. Contrary to the current tenets of fluid mechanics, which arbitrarily assumes (without proof) all four velocities to be the same, it is theoretically demonstrated in the case of non-isothermal fluids that the mass velocity ${\bf{v}}_m$ is different from the other three velocities (whose members prove to be identical to one another), with the disparity in velocities being proportional to the temperature gradient. The concomitant need for two independent velocities is noted to have major theoretical consequences, not only for fluid mechanics per se but also for peripheral subjects such as irreversible thermodynamics. [Preview Abstract] |
Monday, November 19, 2007 3:48PM - 4:01PM |
JN.00002: Generation of velocity distribution functions in a coupled microscopic-continuum-level approach for gas flows David Kessler, Elaine Oran, Carolyn Kaplan Gas flows can be treated as either a collection of discrete molecules or as a continuum. In the continuum treatment, using linear relations for the energy flux and deviatoric stress tensor produced the Navier-Stokes equations. These linear relations lose their validity at moderate Knudsen numbers. The molecular-level description, however, has no such limitation and molecular velocities are described statistically by a velocity distribution function. Particle-based solution algorithms, such as the DSMC method, describe gas flows for a very broad range of Knudsen numbers, but are expensive. Here we describe a coupled microscopic-continuum-level method in which the molecular kinetic description replaces the linear constitutive relations in the continuum equations. One step in the process is to reconstruct the molecular velocity distribution from the continuum-level flow field. We discuss limitations of using the Maxwellian and Chapman-Enskog distribution functions and compute the temporal evolution of these functions in a steady channel flow using DSMC. [Preview Abstract] |
Monday, November 19, 2007 4:01PM - 4:14PM |
JN.00003: Experimental Measurements of Pressure Structure Functions and Acceleration Correlations in High Reynolds number Turbulence Dario Vincenzi, Haitao Xu, Nicholas T. Ouellette, Eberhard Bodenschatz We present measurements of fluid particle accelerations in turbulent water flows between counter-rotating disks using three-dimensional Lagrangian particle tracking. By simultaneously following multiple particles with sub-Kolmogorov-time-scale temporal resolution, we measured the spatial correlation of fluid particle acceleration at Taylor microscale Reynolds numbers between 200 and 690. We also obtained indirect, non-intrusive measurements of the Eulerian pressure structure functions by integrating the acceleration correlations. Our experimental data provide strong support to the theoretical predictions of the acceleration correlations and the pressure structure function in isotropic high Reynolds number turbulence by Obukhov and Yaglom in 1951. The measured pressure structure functions display K41 scaling in the inertial range. [Preview Abstract] |
Monday, November 19, 2007 4:14PM - 4:27PM |
JN.00004: Contraction of an inviscid swirling liquid jet: Comparison with results for a rotating granular jet. P.D. Weidman, J.P. Kubitschek In honor of the tercentenary of Leonhard Euler, we report a new solution of the Euler equations for the shape of an inviscid rotating liquid jet emanating from a tube of inner radius R$_{0}$ aligned with gravity. Jet contraction is dependent on the exit swirl parameter $\chi_{0}$ = R$_{0}$ $\Omega_{0}$/U$_{0}$ where $\Omega_{0}$ and U$_{0}$ are the uniform rotation rate and axial velocity of the liquid at the exit. The results reveal that rotation reduces the rate of jet contraction. In the limit $\chi_{0} \to$ 0 one recovers the contraction profile for a non-rotating jet and the limit $\chi_{0} \to \infty $ gives a jet of constant radius. In contrast, experiments and a kinematic model for a rotating non-cohesive granular jet show that it expands rather than contracts when a certain small angular velocity is exceeded. The blossoming profiles are parabolic in nature. The model predicts a jet of uniform radius for $\chi_{0} \to$ 0 and a jet with an initially horizontal trajectory in the limit $\chi_{0} \to \infty$. [Preview Abstract] |
Monday, November 19, 2007 4:27PM - 4:40PM |
JN.00005: Exact pressure evolution equation for incompressible fluids Massimo Tessarotto, Marco Ellero, Necdet Aslan, Michael Mond, Piero Nicolini Several issues concerning the foundations of hydrodynamics still remain unanswered. A significant aspect is the determination of the fluid pressure in isothermal incompressible fluids and the construction of algorithms with permit to time-advance the same fluid pressure. In fact, the incompressible Navier-Stokes equations represent a mixture of hyperbolic and elliptic pde's, which are extremely hard to study both analytically and numerically. However, the interesting question arises whether there exists actually an evolution equation for the fluid pressure which is exactly equivalent to the Poisson equation (i.e., is a Poisson solver). The search of an exact pressure-evolution equation, besides being a still unsolved mathematical problem, is potentially relevant in fluid dynamics. In this note we intend to show that, based on an inverse kinetic theory (IKT) recently proposed for the incompressible Navier-Stokes equations [M. Ellero and M. Tessarotto, Physica A 355, 233 (2005)], a solution to this problem can actually be reached. Basic consequences of the result are presented. [Preview Abstract] |
Monday, November 19, 2007 4:40PM - 4:53PM |
JN.00006: IKT for quantum hydrodynamic equations Massimo Tessarotto, Marco Ellero, Piero Nicolini A striking feature of standard quantum mechanics (SQM) is its analogy with classical fluid dynamics. In fact, it is well-known that the Schr\"odinger equation is equivalent to a closed set of partial differential equations for suitable real-valued functions of position and time (denoted as quantum fluid fields) [Madelung, 1928]. In particular, the corresponding quantum hydrodynamic equations (QHE) can be viewed as the equations of a classical compressible and non-viscous fluid, endowed with potential velocity and quantized velocity circulation. In this reference, an interesting theoretical problem, in its own right, is the construction of an inverse kinetic theory (IKT) for such a type of fluids. In this note we intend to investigate consequences of the IKT recently formulated for QHE [M.Tessarotto et al., Phys. Rev. A 75, 012105 (2007)]. In particular a basic issue is related to the definition of the quantum fluid fields. [Preview Abstract] |
Monday, November 19, 2007 4:53PM - 5:06PM |
JN.00007: A finite-time thermodynamics of unsteady shear flows Bernd R. Noack, Michael Schlegel, Boye Ahlborn, Gerd Mutschke, Marek Morzy\'nski, Pierre Comte, Gilead Tadmor A finite-time thermodynamics (FTT) formalism (Andresen, Salamon \& Berry 1977) is proposed to compute the mean flow and fluctuation levels of unsteady, incompressible, shear flows. That formalism yields a definition for a thermodynamic degree of freedom of the velocity fluctuation as well as conditions for local thermal equilibrium. In general, the dynamics of unsteady flow is shown to be in partial thermal equilibrium, a state governed by finite time scales of energy transfer. The FTT model has been successfully applied to shear flows with simple to complex dynamics, e.g. vortex shedding and homogenous shear turbulence. [Preview Abstract] |
Monday, November 19, 2007 5:06PM - 5:19PM |
JN.00008: Lattice-gas flow of flexible long clusters Takashi Mashiko, Takashi Nagatani We propose a new type of random-walk model, where each walker consists of serially-connected particles and behaves like a snake. This is an extended version of conventional single-particle random-walk model, and expected to have a potential for application in engineering fields like mobile robotics. Results of simulations on square lattice will be presented and discussed, especially for channel flows with a bias toward one direction, in comparison with the case of conventional random-walkers. [Preview Abstract] |
Monday, November 19, 2007 5:19PM - 5:32PM |
JN.00009: ABSTRACT WITHDRAWN |
Monday, November 19, 2007 5:32PM - 5:45PM |
JN.00010: The turbulence dissipation constant is not universal because of its universal dependence on large-scale flow topography John Christos Vassilicos, Nicolas Mazellier The dimensionless dissipation rate constant $C_{\epsilon}$ of homogeneous isotropic turbulence is such that $C_{\epsilon} = f(\log Re_{\lambda}) {C'}_s^3$ where $f(\log Re_{\lambda})$ is a dimensionless function of $\log Re_{\lambda}$ which tends to 0.26 (by extrapolation) in the limit where $\log Re_{\lambda} \gg 1$ (as opposed to just $Re_{\lambda} \gg 1$) if the assumption is made that a finite such limit exists. The dimensionless number $C'_{s}$ reflects the number of large-scale eddies and is therefore non-universal. The non-universal asymptotic values of $C_{\epsilon}$ stem, therefore, from its universal dependence on $C'_{s}$. The Reynolds number dependence of $C_{\epsilon}$ at values of $\log Re_{\lambda}$ close to and not much larger than 1 is primarily governed by the slow growth (with Reynolds number) of the range of viscous scales of the turbulence. An eventual Reynolds number independence of $C_{\epsilon}$ can be achieved, in principle, by an eventual balance between this slow growth and the increasing non-gaussianity of the small-scales. The turbulence is characterised by five length-scales in the following order of increasing magnitude: the Kolmogorov microscale $\eta$, the inner cutoff scale $\eta_{*} \approx \eta (7.8 + 9.1\log Re_{\lambda})$, the Taylor microscale $\lambda \sim {Re_{\lambda}}^{1/2} \eta$, the voids length-scale $\lambda_{v} \sim {Re_{\lambda}}^{1/3} \lambda$ and the integral length scale $L\sim {Re_{\lambda}}^{2/3} \lambda_{v}$. [Preview Abstract] |
Monday, November 19, 2007 5:45PM - 5:58PM |
JN.00011: Near-bed particle motion due to turbulent flow using image-processing techniques Anindita Bhattacharya, B.S. Mazumder, Satya P. Ojha This study investigates the behavior of particle motion over the rough bed surface due to near-bed turbulence in an open channel flow using image processing techniques. The instantaneous fluid velocity components are measured by 16MHz 3D-Micro acoustic Doppler velocimeter (\textbf{ADV}). High-speed Motion-Scope (\textbf{HSMS}) system has been used to record the motion-picture photography of the particles movement on the surface of the rough bed at the rate of 250 frames/sec. The recorded images are analyzed in the light of particle motions, trajectories, saltation heights and lengths of individual particles, angles of orientation and their interactions with the boundary using digital image processing techniques with the help of the software Image Pro-Plus (IPP). [Preview Abstract] |
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