Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session T9: Flow Instabilities, Turbulence and CFD |
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Sponsoring Units: DFD Chair: Prabir Daripa, Texas A&M University Room: D220 |
Wednesday, March 23, 2011 2:30PM - 2:42PM |
T9.00001: ABSTRACT WITHDRAWN |
Wednesday, March 23, 2011 2:42PM - 2:54PM |
T9.00002: Modal decomposition of free and forced circular jets at low and high Reynolds numbers Muralidhar Krishnamurthy, Trushar Gohil, Arun Saha Free and forced jets are important in applications such as combustion, propulsion, mixing, and aero-acoustics. Jet control for noise reduction and mixing efficiency can be achieved by manipulating the flow structures. The most energetic structures of a flow field can be objectively recovered by proper orthogonal decomposition. POD extracts a basis for modal decomposition as eigenfunctions from an ensemble of signals. In the present work, the snapshot POD method is applied to data recorded from direct numerical simulation as well as large eddy simulation in three dimensions. Free jets are reported at a Reynolds number of 1000 and 10000 and 4300 for forced jets. Results show that all of the kinetic energy of laminar flow is stored in large-scale structures while for the turbulent jet, a broader distribution of kinetic energy is obtained. At Re = 1000, 40 snapshots of the flow field are adequate to resolve the major flow structures. For Re=10000, at least 100 snapshots are required for a good spectral representation. Blooming jets arising from dual mode forcing show the formation of odd-even pairs. The first pair contains the details of branching. In addition, the higher order modes capture the inherent jet instability mechanisms. [Preview Abstract] |
Wednesday, March 23, 2011 2:54PM - 3:06PM |
T9.00003: Generalized Saffman-Taylor formula for multi-layer Hele-Shaw flows Prabir Daripa Stability theory plays a major role from fundamental science to applied sciences. It is useful in the design of many processes and engineering instruments as well as in explaining many phenomena. In this paper we review some of the author's and his collaborator's recent works on the extension of Saffman-Taylor instability which occurs at an interface between two immiscible fluids in porous media and Hele-Shaw cells when displacing fluid is less viscous than the displaced one. The growth rate of interfacial disturbances is given by a formula called Saffman-Taylor formula which plays a very important role in many areas including flows in porous media and oil recovery among many others. In this talk, we will present our results on the generalization of this formula to multi-layer flows involving many interfaces. As an application of the generalized Saffman-Taylor formula, we will derive necessary conditions for suppressing instability of two-layer flows by introducing arbitrary number of constant viscosity fluid layers in between. The important role that these conditions play in stabilization of hydrodynamic instabilities in Hele-Shaw flows will be discussed. [Preview Abstract] |
Wednesday, March 23, 2011 3:06PM - 3:18PM |
T9.00004: The stability of a droplet suspended in a straight micro-channel Haider Hekiri, Takumi Hawa CFD simulations of the dynamics of a two-dimensional, incompressible, and two coupled spherical-cap water droplets suspended in a straight micro-channel, whose channel height is D, have been conducted to investigate the stability of the droplet. FLUENT with a 2-D pressure based solver is utilized in this simulation. The suspended droplet states are measured by the location of the central of mass of the droplet. We find that there is a critical volume, Vc(D), where asymmetric droplet states appear in addition to the basic symmetric states when V $>$ Vc(D). Using the CFD it is demonstrated that when V $<$ Vc(D) the symmetric droplet states have a stable mode. However, when V $>$ Vc(D) the symmetric states become unstable and asymmetric states have a stable mode. The bifurcation of asymmetric states at Vc(D) has a pitchfork nature. The simulations clarify the relationship between the linear stability results and the experimental results of the droplet behavior. [Preview Abstract] |
Wednesday, March 23, 2011 3:18PM - 3:30PM |
T9.00005: Liquid-air interface instability due to an in-plane electric field Mikhail Pevnyi, Jake Fontana, Peter Palffy-Muhoray We report observations of an instability at the free surface of a liquid due to an in-plane electric field. The horizontal air-liquid interface in a partially filled sample cell between vertical electrodes exhibited first oscillations, then increasingly turbulent fluctuations as the strength of the horizontal electric field was increased. This behavior was observed in toluene and choloroform; the applied AC field was sinusoidal with f= 60Hz. The dynamics of the interface was probed via dynamic light scattering. We present our experimental observations, as well as a simple model and numerical simulations of the interface dynamics under the influence of the applied electric field. [Preview Abstract] |
Wednesday, March 23, 2011 3:30PM - 3:42PM |
T9.00006: Stretch-induced wrinkles in reinforced membranes Atsushi Takei, Fabian Brau, Beno\^It Roman, Jos\'e Bico We study through model experiments the buckling of a rigid stripe (or fiber) embedded in a soft membrane under compression. The compression is induced through Poisson effect when the membrane is stretched perpendicularly to the stripe. The wavelength of the wrinkles is found to depend on the material properties and the stretching strain. A balance between the bending and stretching energies of both the membrane and the stripes dictates this wavelength: \textit{$\lambda $} $\sim $ (\textit{Bd }/$E_{S}H_{S}$\textit{$\delta $ })$^{1/3}$, where $B$ is the bending stiffness, $d$ the width of the rigid band, \textit{$\delta $} the strain, and $E_{S}$ and$ H_{S}$ the Young modulus and the thickness of the membrane, respectively. The characteristic extension of the wrinkled zone is set by the wavelength. This result also applies to fibers imbedded in a thin membrane. However, in-plane buckling is observed when the thickness of the membrane is large compared with the radius of the fiber. In this last regime, we find \textit{$\lambda $} $\sim R (E_{F}$ /$E_{S}$ )$^{1/4}$, where $E_{F }$and $R$ are the Young modulus and the radius of the fiber, respectively. [Preview Abstract] |
Wednesday, March 23, 2011 3:42PM - 3:54PM |
T9.00007: Computational Parametric Study of R-M Instability Growth for an Inclined Interface Jacob McFarland, Devesh Ranjan, Jeff Greenough An inclined interface perturbation is studied for an RM instability to model upcoming experiments in the Texas A{\&}M inclined shock tube facility. Simulations were created using the ARES code developed at Lawrence Livermore National Lab. A parametric study was performed for inclination angles from 30 to 60 degrees, incident Mach numbers of 1.5 to 2.5, and high Atwood number gas pairs air-SF6 and helium/SF6. Qualitative results are examined to show the relative effects of these parameters. Interface growth rates are calculated and compared to the existing linear growth regime models. A new model is proposed based on the interface geometry and compared to the simulation results. [Preview Abstract] |
Wednesday, March 23, 2011 3:54PM - 4:06PM |
T9.00008: Drop Splashing on a Smooth Surface at Low Velocities Cacey Stevens, Sidney Nagel When a low viscosity liquid drop impacts on a smooth, dry surface, a thin fluid sheet is emitted which subsequently breaks up into a distribution of secondary droplets. Ambient gas pressure is crucial in creating this splash: splashing is completely suppressed below a threshold pressure [1]. There are several regimes that occur as the velocity and liquid viscosity are varied [2]. Here, we discuss splashing in the low velocity, low viscosity regime. We explore how the threshold pressure scales with drop size, as well as liquid viscosity. We also characterize the dependence of threshold pressure with molecular weight of the surrounding gas. \\[4pt] [1] L. Xu, S. Nagel, and W. Zhang. Phys. Rev. Lett. 94, 184505 (2005).\\[0pt] [2] L. Xu. Phys. Rev. E 75, 056316 (2007). [Preview Abstract] |
Wednesday, March 23, 2011 4:06PM - 4:18PM |
T9.00009: Elastic effects on the shear flow instabilities in viscoelastic fluids Ahmed Kaffel A linear stability analysis was applied and the stability equation is derived and solved numerically using the spectral Chebyshev collocation method. The objective is to study the elastic effects on the instability of inviscid parallel shear flows. We focus on the upper convected Maxwell model in the limit of infinite Weissenberg and Reynolds numbers. Specifically, we study the effects of elasticity on the instability of a few classes of simple parallel flows, specifically plane Poiseuille and Couette flows, the hyperbolic-tangent shear layer and the Bickley jet. The algorithm is computationally efficient and accurate in reproducing the discrete eigenvalues. We consider flows bounded by walls as well as flows bounded by free surfaces. In the inviscid, nonelastic case all the flows we study are unstable for free surfaces. In the case of wall bounded flow, there are instabilities in the shear layer and Bickley jet flows. In all cases, the effect of elasticity is to reduce and ultimately suppress the inviscid instability. The numerical solutions are compared with the analysis of the long wave limit and excellent agreement is shown. We found flows which are long wave stable, but nevertheless unstable to wave numbers in a certain finite range. While elasticity is ultimately stabilizing, this effect is not monotone; there are instances where a small amount of elasticity actually destabilizes the flow. [Preview Abstract] |
Wednesday, March 23, 2011 4:18PM - 4:30PM |
T9.00010: Thermal convection in multiphase systems Luca Biferale, Prasad Perlekar, Mauro Sbragaglia, Andrea Scagliarini, Federico Toschi We present preliminary results of a numerical study of two dimensional and three dimensional multiphase thermal convection close to the phase transition and in presence of phase coexistence. The numerical algorithm is based on a suitable implementation of multiphase Lattice Boltzmann scheme with non-ideal pressure tensor. We discuss the effects of droplets and bubbles formation on the global heat flux from bottom to top boundaries. [Preview Abstract] |
Wednesday, March 23, 2011 4:30PM - 4:42PM |
T9.00011: Vortex Sheet Model for a Turbulent Mixing Layer Ujjayan Paul, Roddam Narasimha, Meheboob Alam The primary aim of this work is to study instability induced roll up of a slightly perturbed vortex sheet in an Euler fluid. A point vortex model tends to evolve into a chaotic cloud of point vortices instead of smooth double branched spirals. The present model uses linear splines to interpolate the vortex sheet. Computer simulation of this vortex sheet is numerically prohibitive. However, the evolution of the vortex sheet can be performed conveniently using a closed form equation of motion which derived from the basic equations of vortex dynamics. The vortex sheet rolls up into a smooth double branched spiral. A vortex core is formed by regular windings of the vortex sheet and irrotational fluid in between the layers. Various statistical quantities like the growth rate and mean velocity profiles are computed along with the evolution of the vortex sheet. The problem of spontaneous appearance of singularity in an evolving vortex sheet is treated in detail. The critical time for the present vortex sheet model is calculated analytically and compared to the numerical value. [Preview Abstract] |
Wednesday, March 23, 2011 4:42PM - 4:54PM |
T9.00012: Nonlinear Deformation in Weak Turbulence Nicholas Ouellette, Douglas Kelley, Yang Liao Turbulent and chaotic flows are well known to mix efficiently: by repeatedly stretching and folding material volumes, material lines stretch exponentially quickly and gradients of an advected scalar field can become very large. By adapting a technique originally introduced to study plasticity in glassy solids, we explicitly separate stretching (a linear transformation) from folding (a nonlinear transformation) in a quasi-two-dimensional experimental flow and study them independently. We compare results from two forcing schemes: one that is dominated by rotation, and another that is dominated by shear. [Preview Abstract] |
Wednesday, March 23, 2011 4:54PM - 5:06PM |
T9.00013: Principal Direction of Scalar Transport in Wall Turbulence Chiranth Srinivasan, Dimitrios Papavassiliou Lagrangian scalar tracking in conjunction with direct numerical simulation is utilized in an infinitely long channel to study the principal direction of scalar transfer for both forwards and backwards single particle dispersion. Four regions are of interest: the viscous sub-layer, the transition region (between the viscous sub-layer and the logarithmic region), the logarithmic region and the center of channel. Fluctuating velocities of scalar markers released in the flow field are correlated forwards and backwards in time to find the components of the correlation coefficient tensor. Eigenvalues and eigenvectors are obtained for both the forwards and backwards dispersion and for fluids with Prandtl number between 0.1 and 1000. The largest eigenvalues are higher in the case of backwards dispersion compared to the case of forwards dispersion. The eigenvector inclinations relative to the yz plane are different for forwards and backwards dispersion (at times comparable to the Lagrangian timescale). [Preview Abstract] |
Wednesday, March 23, 2011 5:06PM - 5:18PM |
T9.00014: Molecular origins of continuum fluid mechanics: Atomic migrations of single-phase fluid and slip boundary conditions Alan Graham, Shihai Feng, Tony Redondo We report the results of molecular dynamics simulations of pressure-driven flows of liquid argon in circular and planar conduits. We find that in inhomogeneous shear flows the molecules migrate to the center of the conduits and establish large radial density gradients under conditions that were previously assumed to be incompressible. These are the first predictions of shear-induced migration in pure fluids subjected to inhomogeneous shear flows. These density gradients increase monotonically with P\'{e}clet number. They result in a blunted velocity profile that deviates from the parabolic profile predicted by the Navier-Stokes equations for an incompressible fluid. Comparisons with simulations where the flow exhibits zero or linear shear indicate that this phenomenon is the result of the nonlinear shear flows and the finite size of the molecules. [Preview Abstract] |
Wednesday, March 23, 2011 5:18PM - 5:30PM |
T9.00015: Search for Euler Singularity using Vortex Filaments Sahand Hormoz, Michael Brenner A promising mechanism for generating a finite-time singularity in the incompressible Euler equations is stretching of vortex filaments. An exhaustive search of all possible initial conditions involving filaments, however, is not practically feasible. In this talk, I will show that two interacting vortex filaments can not generate a singularity for any initial conditions, by analyzing the asymptotic self-similar limit of their collapse. Essentially, our approach entails a separation of the dynamics of the filament shape, from the shrinking of its core. We solve for the dynamics using a self-similar ansatz and show that the core does not shrink fast enough for a self-consistent collapse. The similarity solution allows for many different collapse geometries, consistent with the tireless effort in the past of investigating new initial conditions. Potential for a singularity at higher number of filaments is also discussed. [Preview Abstract] |
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