Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session W39: Computational Fluid Dynamics 
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Sponsoring Units: DFD Chair: Gorges L. Chahine, Dynaflo, Inc Room: 348 
Thursday, March 21, 2013 2:30PM  2:42PM 
W39.00001: Transient NonNewtonian Screw Flow Nariman Ashrafi The influence of axial flow on the transient response of the pseudoplastic rotating flow is carried out. The fluid is assumed to follow the CarreauBird model and mixed boundary conditions are imposed. The fourdimensional loworder dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional nonlinear terms in the velocity components originated from the sheardependent viscosity. In absence of axial flow the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the pseudoplasticity increases. The emergence of the vortices corresponds to the onset of a supercritical bifurcation which is also seen in the flow of a linear fluid. However, unlike the Newtonian case, pseudoplastic Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Existence of an axial flow, manifested by a pressure gradient appears to further advance each critical point on the bifurcation diagram. In addition to the simulation of spiral flow, the proposed formulation allows the axial flow to be independent of the main rotating flow. Complete transient flow field together with viscosity maps are also presented. [Preview Abstract] 
Thursday, March 21, 2013 2:42PM  2:54PM 
W39.00002: Indeterminism in Classical Dynamics of Particle Motion Gregory Eyink, Ethan Vishniac, Cristian Lalescu, Hussein Aluie, Kalin Kanov, Randal Burns, Charles Meneveau, Alex Szalay We show that ``God plays dice'' not only in quantum mechanics but also in the classical dynamics of particles advected by turbulent fluids. With a fixed deterministic flow velocity and an exactly known initial position, the particle motion is nevertheless completely unpredictable! In analogy with spontaneous magnetization in ferromagnets which persists as external field is taken to zero, the particle trajectories in turbulent flow remain random as external noise vanishes. The necessary ingredient is a rough advecting field with a powerlaw energy spectrum extending to smaller scales as noise is taken to zero. The physical mechanism of ``spontaneous stochasticity'' is the explosive dispersion of particle pairs proposed by L. F. Richardson in 1926, so the phenomenon should be observable in laboratory and natural turbulent flows. We present here the first empirical corroboration of these effects in high Reynoldsnumber numerical simulations of hydrodynamic and magnetohydrodynamic fluid turbulence. Since powerlaw spectra are seen in many other systems in condensed matter, geophysics and astrophysics, the phenomenon should occur rather widely. Fast reconnection in solar flares and other astrophysical systems can be explained by spontaneous stochasticity of magnetic fieldline motion [Preview Abstract] 
Thursday, March 21, 2013 2:54PM  3:06PM 
W39.00003: Higher Order Thermal Lattice Boltzmann Model Shahajhan Sorathiya, Santosh Ansumali Lattice Boltzmann method (LBM) modelling of thermal flows, compressible and micro flows requires an accurate velocity space discretization. The sub optimality of GaussHermite quadrature in this regard is well known [1]. Most of the thermal LBM in the past have suffered from instability due to lack of proper Htheorem and accuracy [2]. Motivated from these issues, the present work develops along the two works [3] and [4] and imposes an eighth higher order moment to get correct thermal physics. We show that this can be done by adding just 6 more velocities to D3Q27 model and obtain a ``multispeed on lattice thermal LBM'' with 33 velocities in 3D and ${\cal{O}}(u^4)$ and ${\cal{O}}(T^4)$ accurate $f_{i}^{\rm eq}$ with a consistent Htheorem and inherent numerical stability. Simulations for RayleighBernard as well as velocity and temperature slip in micro flows matches with analytical results. Lid driven cavity set up for grid convergence is studied. Finally, a novel data structure is developed for HPC.\\[4pt] [1] X. Shan and X. He, Phys. Rev. Lett. 80, 65 (1998).\\[0pt] [2] G. McNamara, A. Garcia, and B. Alder, J. Stat. Phys. 81, 395 (1995).\\[0pt] [3] S. Chikatamarla and I. Karlin, Phys. Rev. E 79, 046701 (2009).\\[0pt] [4] W. Yudistiawan et al. Phys. Rev. E 82, 046701 (2010) [Preview Abstract] 
Thursday, March 21, 2013 3:06PM  3:18PM 
W39.00004: ODTLES: Simulations of wallbounded turbulent flows with smallscale resolution Esteban Gonzalez, Alan Kerstein, Rod Schmidt The numerical simulation of turbulent flows is difficult because of their broad range of scales of motion and because they include a large variety of smallscale processes, such as friction near a wall, diffusion at an interface, multiphase couplings, and chemical reactions. Traditional approaches to model these flows are limited in breadth and accuracy because they filter out information from smallscale processes. An alternative method that circumvents this problem is ODTLES. This method resolves, not models, smallscale phenomena in a computationally affordable way, in comparison with full threedimensional resolution, through the use of a latticework of onedimensional (1D) domains, where flow properties are timeadvanced with 1D stochastic simulations. This talk will discuss the methodology behind ODTLES and results for incompressible wallbounded turbulence. [Preview Abstract] 
Thursday, March 21, 2013 3:18PM  3:30PM 
W39.00005: Shock Formation and Disintegration in Fluids with NonConvex Equations of State Fatemeh Bahmani, Mark Cramer We consider the steady, twodimensional, inviscid, highspeed, flow around thin turbine blade profiles with special attention given to fluids having a nonconvex equation of state; such fluids are commonly known as BetheZel'dovichThompson (BZT) fluids. We show that the essential flow physics can be described by an inviscid Burgers equation having quartic nonlinearity rather than the quadratic nonlinearity of perfect gases. In order to illustrate the flow behavior, a fifthorder WENO (weighted essentially nonoscillatory) numerical scheme is employed. New results of interest include the formation of oblique expansion shocks, shocksplitting induced by the interaction of a single shock with Mach waves, the capture of shockfan combinations, and the collision of oblique compression and expansion shocks. [Preview Abstract] 
Thursday, March 21, 2013 3:30PM  3:42PM 
W39.00006: Polarized Turbulence on the 3sphere Owen Dix, Rena Zieve We have simulated He II superfluid turbulence on a 3sphere, using the Hopf vector field $(y,x,w,z)$ as the driving velocity. This vector field lies along parallel great circles of the 3sphere. It has a uniform magnitude, is divergencefree, and is analogous to a uniform driving velocity in periodic boundaries (a flat 3torus), with the important exception that it has a nonzero curl tangent to the field itself. The resultant system is an interesting modification of rotating counterflow turbulence, which produces a state of polarized turbulence for driving velocities above a critical velocity $V_{DG}$. The average polarization of the vortex tangent field on the 3sphere is 0.80.95, significantly higher than rotating counterflow. We also found a vortex reconnection rate proportional to $L^{1.6}$, in contrast to homogeneous turbulence, which yields exponents of 5/2 or 2, depending on the importance of the local velocity term and on the turbulence state. A reduced exponent is consistent with predictions and previous simulations of polarized turbulence, but the degree of reduction is remarkable. Development of this polarized turbulence state is still under investigation. [Preview Abstract] 
Thursday, March 21, 2013 3:42PM  3:54PM 
W39.00007: A Spectral Adaptive Mesh Refinement Method for the Burgers equation Leila Nasr Azadani, Anne Staples Adaptive mesh refinement (AMR) is a powerful technique in computational fluid dynamics (CFD). Many CFD problems have a wide range of scales which vary with time and space. In order to resolve all the scales numerically, high grid resolutions are required. The smaller the scales the higher the resolutions should be. However, small scales are usually formed in a small portion of the domain or in a special period of time. AMR is an efficient method to solve these types of problems, allowing high grid resolutions where and when they are needed and minimizing memory and CPU time. Here we formulate a spectral version of AMR in order to accelerate simulations of a 1D model for isotropic homogenous turbulence, the Burgers equation, as a first test of this method. Using pseudo spectral methods, we applied AMR in Fourier space. The spectral AMR (SAMR) method we present here is applied to the Burgers equation and the results are compared with the results obtained using standard solution methods performed using a fine mesh. [Preview Abstract] 
Thursday, March 21, 2013 3:54PM  4:06PM 
W39.00008: Multiscale simulation of electroosmotic flows Lin Guo, Mark Robbins, Shiyi Chen, Jin Liu We develop an efficient hybrid multiscale method for simulating nanoscale electroosmotic flow based on spatial ``domain decomposition'' [1]. Molecular dynamics (MD) is used in the near wall region where atomistic details are important. A multigrid ParticleParticle ParticleMesh (PPPM) method [2] is used to calculate the longrange Coulombic interaction between charged ions. Continuum (incompressible NavierStokes) equations for the solvent are solved in the bulk region, reducing the computational cost substantially. A discrete description of ions is retained in the continuum region because of the low density of ions and the longrange of electrostatic interactions. Langevin dynamics is used to model the Brownian motion of these ions in the implicit solvent. The fully atomistic and continuum descriptions are coupled through ``constrained dynamics'' [1] in an overlap region. Continuity of flux of both charged and solvent particles is ensured. The scheme is implemented in channel flow simulations with and without wall roughness. Results are compared with pure MD simulations. \\[4pt] [1] X. Nie, S. Chen, W. E, and M. O. Robbins, J. Fluid Mech., 500:5564, 2004.\\[0pt] [2] J. Liu, M. Wang, S. Chen, and M. O. Robbins, J. Comput. Phys., 229:78347847, 2010. [Preview Abstract] 
Thursday, March 21, 2013 4:06PM  4:18PM 
W39.00009: Chaos Synchronization in NavierStokes Turbulence Cristian Lalescu, Charles Meneveau, Gregory Eyink Chaos synchronization (CS) has been studied for some time now (Pecora \& Carroll 1990), for systems with only a few degrees of freedom as well as for systems described by partial differential equations (Boccaletti et al 2002). CS in general is said to be present in coupled dynamical systems when a specific property of each system has the same time evolution for all, even though the evolution itself is chaotic. The NavierStokes (NS) equations describe the velocity for a wide range of fluids, and their solutions are usually called turbulent if fluctuation amplitudes decrease as a power of their wavenumber. There have been some studies of CS for continuous systems (Kocarev et al 1997), but CS for NS turbulence seems not to have been investigated so far. We focus on the synchronization of the small scales of a turbulent flow for which the time history of large scales is prescribed. Our DNS results show that highwavenumbers in turbulence are fully slaved to modes with wavenumbers up to a critical fraction of the Kolmogorov dissipation wavenumber. The motivation for our work is to study deeply subKolmogorov scales in fully developed turbulence (Schumacher 2007), which we found to be recoverable even at very high Reynolds number from simulations with moderate resolutions. [Preview Abstract] 
Thursday, March 21, 2013 4:18PM  4:30PM 
W39.00010: Multiscale Modeling of Cavitating Bubbly Flows J. Ma, C.T. Hsiao, G.L. Chahine Modeling of cavitating bubbly flows is challenging due to the wide range of characteristic lengths of the physics at play: from micrometers (e.g., bubble nuclei radius) to meters (e.g., propeller diameter or sheet cavity length). To address this, we present here a multiscale approach which integrates a Discrete Bubble Model for dispersed microbubbles and a level set NS solver for macro cavities, along with a mesoscale transition model to bridge the two. This approach was implemented in 3DYNAFS$^{\copyright}$ and used to simulate sheettocloud cavitation over a hydrofoil. The hybrid model captures well the full cavitation process starting from free field nuclei and nucleation from solid surfaces. In low pressure region of the foil small nuclei are seen to grow large and eventually merge to form a large scale sheet cavity. A reentrant jet forms under the cavity, travels upstream, and breaks it, resulting in a bubble cloud of a large amount of microbubbles as the broken pockets shrink and travel downstream. This is in good agreement with experimental observations based of sheet lengths and frequency of lift force oscillation. [Preview Abstract] 

W39.00011: ABSTRACT WITHDRAWN 
Thursday, March 21, 2013 4:42PM  4:54PM 
W39.00012: Surface cooling mechanism of fire suppression by aqueous foam Michael Conroy, Ramagopal Ananth We investigate the ability of roomtemperature foam to directly cool the surface of a liquid fuel pool at burning conditions and to reduce the fuel vapor pressure. We solve an unsteady, onedimensional heat conduction equation using the finite element method to predict the temperature within an aqueous foam layer above a liquid fuel (heptane) layer. The sharp gradients in temperature and thermal properties at the foamfuel interface are treated approximately inside of a thin interfacial layer above the fuel surface. We predict a rapid, significant reduction in the fuel surface temperature due to the large initial temperature gradient and the foam thermal diffusivity. The predicted surface cooling leads to a significant decrease in the fuel vapor pressure in less than a second. The mechanisms of fire suppression by aqueous foams are not well understood and the model predictions show that direct surface cooling could provide an important contribution to fire suppression. Experiments are in progress to quantify the surface cooling effect on heptane pool fire suppression. [Preview Abstract] 
Thursday, March 21, 2013 4:54PM  5:06PM 
W39.00013: Formation of Kinneyia via shearinduced instabilities in microbial mats Katherine Thomas, Stephan Herminghaus, Hubertus Porada, Lucas Goehring Kinneyia are a class of microbially mediated sedimentary fossils. Characterised by clearly defined ripple structures, Kinneyia are generally found in areas that were formally littoral habitats and covered by microbial mats. To date there has been no conclusive explanation as to the processes involved in the formation of these fossils. Microbial mats behave like viscoelastic fluids. We propose that the key mechanism involved in the formation of Kinneyia is a KelvinHelmholtz instability induced in a viscoelastic film under flowing water. A ripple corrugation is spontaneously induced in the film and grows in amplitude over time. Theoretical predictions show that the ripple instability has a wavelength proportional to the thickness of the film. Experiments carried out using viscoelastic films confirm this prediction. The ripple pattern that forms has a wavelength roughly three times the thickness of the film. This behaviour is independent of the viscosity of the film and the flow conditions. Wellordered patterns form, with both honeycomblike and parallel ridges being observed, depending on the flow speed. These patterns correspond well with those found in Kinneyia fossils, with similar morphologies, wavelengths and amplitudes being observed. [Preview Abstract] 
Thursday, March 21, 2013 5:06PM  5:18PM 
W39.00014: Optimal Concentrations in Transport Networks Kaare Jensen, Jessica Savage, Wonjung Kim, John Bush, N. Michele Holbrook Biological and manmade systems rely on effective transport networks for distribution of material and energy. Mass flow in these networks is determined by the flow rate and the concentration of material. While the most concentrated solution offers the greatest potential for mass flow, impedance grows with concentration and thus makes it the most difficult to transport. The concentration at which mass flow is optimal depends on specific physical and physiological properties of the system. We derive a simple model which is able to predict optimal concentrations observed in blood flows, sugar transport in plants, and nectar feeding animals. Our model predicts that the viscosity at the optimal concentration $\mu_{\mathrm{opt}}=2^{n}\mu_0$ is an integer power of two times the viscosity of the pure carrier medium $\mu_0$. We show how the observed powers $1\leq n\leq 6$ agree well with theory and discuss how $n$ depends on biological constraints imposed on the transport process. The model provides a universal framework for studying flows impeded by concentration and provides hints of how to optimize engineered flow systems, such as congestion in traffic flows. [Preview Abstract] 
Thursday, March 21, 2013 5:18PM  5:30PM 
W39.00015: Resonating Vector Strength: How to Find Periodicity in a Time Sequence J. Leo van Hemmen For a given periodic stimulus with angular frequency $\omega_{\circ} = 2\pi/T_{\circ}$ we find responses as events at times $\{t_{1}, t_{2},\ldots, t_{n} \}$ located on the real axis $R$. How periodic are they? And do they repeat in ``some'' sense in accordance with the stimulus period $T_{\circ}$? The question and the answer are at least as old as a classical paper of von Mises dating back to 1918. The key idea is simply this. We map the events $t_{j}$ onto the unit circle or torus through $t_{j} \mapsto \exp (i \omega t_{j})$ and consider their center of gravity, $\rho(\omega)$, a complex number in the unit disk. Its absolute value $\rho(\omega_{\circ})$ with $\omega := \omega_{\circ}$ is what von Mises studied and is now called the vector strength. We prove that the nearer $\rho(\omega_{\circ})$ is to $1$ the more periodic the events $t_{j}$ are w.r.t. $T_{\circ}$. Furthermore, we also show why it is useful to study $\rho(\omega)$ as a function of $\omega$ so as to obtain a `resonating' vector strength, an idea strongly deviating from the classical characteristic function. [Preview Abstract] 
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