Keynote Talks

Microfluidics: Electric fields, Fluids & Particles
Nadine Aubry, Raymond J. Lane Distinguished Professor and Head
Mechanical Engineering Department, Carnegie Mellon University

The manipulation of particles and enhancement of fluid mixing are often two crucial steps in microfluidic devices.  This talk will focus on these issues by using the effect of electric fields on dielectric particles and/or liquids.    Particular emphasis will be on the manipulation of electrically neutral particles in bulk liquids and at electrified fluid-fluid interfaces for the directed assembly of monolayers or ultra-thin membranes, as well as the enhancement of mixing in simple geometries via chaotic advection or by using an electrohydrodynamic interfacial instability of a two-fluid layer.

Particle Entrainment Under Turbulent Flow Conditions
Panayiotis Diplas, Virginia Tech, Department of Civil and Enviromental Engineering.

(Invited presentation at the 62nd Annual Meeting of the American Physical Society Division of Fluid Dynamics.)

Erosion, transportation and deposition of sediments and pollutants influence the hydrosphere, pedosphere, biosphere and atmosphere in profound ways. The global amount of sediment eroded annually over the continental surface of the earth via the action of water and wind is estimated to be around 80 billion metric tons, with 20 of them delivered by rivers to the oceans. This redistribution of material over the surface of the earth affects most of its physical, chemical and biological processes in ways that are exceedingly difficult to comprehend. The criterion currently in use for predicting particle entrainment, originally proposed by Shields in 1936, emphasizes the time-averaged boundary shear stress and therefore is incapable of accounting for the fluctuating forces encountered in turbulent flows. A new criterion that was developed recently in an effort to overcome the limitations of the previous approach will be presented. It is hypothesized that not only the magnitude, but also the duration of energetic near bed turbulent events is relevant in predicting grain removal from the bed surface. It is therefore proposed that the product of force and its duration, or impulse, is a more appropriate and universal criterion for identifying conditions suitable for particle dislodgement. Analytical formulation of the problem and experimental data are used to examine the validity of the new criterion.

Session I

The Stochastic and Driven Dynamics of Microscopic Elastic Objects Coupled by a Viscous Fluid

Matthew Clark Mark Paul (Virginia Tech)

We investigate analytically and numerically the coupled motion of microscopic objects in a viscous fluid. Fluid-coupled structures are encountered across a broad range of fields, including spheres and cantilevers in microscopic instruments and fluid motion sensing in biological systems. Many small scale systems undergo high frequency oscillations with small magnitude resulting in a flow field with significant local inertia contributions that must be described using the unsteady Stokes equation. We study the fluid coupled motion of two infinite cylinders that are each attached to a spring. This geometry is chosen due to its wide use in modeling cantilevers and beams in fluid. We show that the stochastic and driven correlated motion of the two cylinders can be found from a single deterministic calculation -- the response of the cylinders to an impulse in force. The stochastic dynamics are found using the fluctuation-dissipation theorem and the driven dynamics are found using transfer function theory. We derive analytical expressions for the cylinder dynamics that neglects effects of back-action. We compare our analytical expressions with finite element numerical simulations and find our analysis is valid over a range of larger separations. For small separations, with overlapping Stokes layers, we find interesting variations in both the amplitude and phase of the cylinders.

Characterizing the Chaotic Degrees of Freedom of High-Dimensional Fluid Convection

Alireza Karimi (Virginia Tech) Mark Paul (Virginia Tech)

The variation of the Lyapunov exponent spectra and fractal dimension with system parameters can yield fundamental insights into the nature of spatiotemporal chaos. We explore this numerically for two systems: the Lorenz 96 model and Rayleigh-Benard convection. The Lorenz 96 model is a phenomenological model that captures important features of atmosphere dynamics. We compute the fractal dimension as a function of system size and external forcing for very long times and over many initial conditions. When varying system size we find extensive chaos with significant deviations from extensivity for small changes in system size and also the power-law growth of the dimension with increasing forcing. We use large-scale parallel numerical simulations to study chaotic Rayleigh-Benard convection for experimentally accessible conditions. We compute the variation of the fractal dimension with system size, Prandtl number, and Rayleigh number. Using statistical properties of the Lyapunov exponents and Lyapunov vectors we connect these features with the dynamics of the flow field pattern.

Simulation of Orientation in Injection Molding of Short Fiber Thermoplastic Composites

GM Vélez-García (Macromolecules and Interfaces Institute), P Wapperom (Mathematics Department) and DG Baird (Chemical Engineering Department)

A 2D coupled Hele-Shaw approximation for predicting the flow-induced orientation of glass fibers in injection molded composite parts is presented. For a highly concentrated short glass fiber PBT suspension, the impact of particle interactions and the orientation at the gate is investigated for a center-gated disk using material parameters determined from rheometry. Experimental orientation is determined using a modified version of the method of ellipses. The constitutive equations are discretized using discontinuous Galerkin Finite Elements. Flow simulations were performed using a measured orientation profile at the gate instead of random assumed in previous studies. The fiber orientation in the entry region and the core layer structure at the end of fill region can now be reproduced qualitatively.

Reduced-Order Models for Fluids with Parameter Dependent Domains

Jeff Borggaard, Imran Akhtar, Alexander Hay, Traian Iliescu, Zhu Wang (Virginia Tech)

One of the main drawbacks to using reduced-order models in optimization (and for parametric studies) is that they are typically defined using a set of baseline values of the parameter set. The resulting models can often reproduce the reference dynamics very accurately but generally lack of robustness away from the reference parameter set. This limitation is even more serious when the parameters of the system modify the geometry of the problem at hand. As reported in the literature, it is therefore crucial to enlarge the range of validity for these models. This talk considers presents two strategies based on Shape Sensitivity Analysis to partially address this limitation of the POD. We first detail the methodology to compute both the POD modes and their Lagrangian sensitivities with respect to shape parameters. From them, we derive reduced-order bases to approximate a class of solutions over a range of parameter values. Secondly, we demonstrate the efficiency and limitation of these approaches on three typical flow problems : (1) the one-dimensional Burgers’ equation, (2) the two-dimensional flows past a square cylinder over a range of incidence angles, and (3) flow past an ellipse with varying aspect ratios.

Modeling in Large Eddy Simulation and Proper Orthogonal Decomposition

Traian Iliescu, Zhu Wang , Imran Akhtar, and Jeff Borggaard (Interdisciplinary Center for Applied Mathematics, Virginia Tech)

Large eddy simulation (LES) and proper orthogonal decomposition (POD) have been put forth independently as distinct approaches for the numerical simulation of turbulent flows around the same time (in the sixties). The closure modeling strategies for these two approaches, however, have taken completely different paths. Indeed, the closure modeling in LES has experienced an explosive development in the last four decades, whereas in POD, the closure modeling has been limited to relatively simple approaches. In this talk, we will present the main similarities and differences between LES and POD and argue that the main hurdle in the development of more sophisticated closure models in POD of turbulent flows has been the lack of efficient computational strategies for the discretization of the nonlinear closure models.

Two-Level Strategies for Large Eddy Simulation Proper Orthogonal Decomposition Models

Zhu Wang, Imran Akhtar, Jeff Borggaard, and Traian Iliescu (Interdisciplinary Center for Applied Mathematics, Virginia Tech)

This paper proposes a two-level method to overcome the major computational hurdle in the development of LES inspired closure models in POD of turbulent flows. The two-level method computes the nonlinear terms of the reduced-order model on a coarse mesh. Compared with a brute force computational approach in which the nonlinear terms are evaluated on the fine mesh at each time step, the two-level method attains the same level of accuracy while reducing dramatically the computational cost. We illustrate numerically these improvements in the two-level method by using it in three settings: the one-dimensional Burgers equation with a small diffusion parameter u = 10^{-5}, the two-dimensional flow past a cylinder at Reynolds number Re = 200, and the three-dimensional flow past a cylinder at Reynolds number Re = 1000.

Towards Accurate Model Reduction Through Closure Approach

Imran Akhtar, Jeff Borggaard, Traian Iliescu, Zhu Wang (Interdisciplinary Center for Applied Mathematics, Virginia Tech)

Reduced-order models based on the proper orthogonal decomposition (POD) are often used to represent a complex dynamical system in fluid flows. These models give insight to the flow physics, reproduce the data, and may be used for control purposes. However, for Navier-Stokes equations, these models have been successfully developed mainly for 2-D flows. For 3-D flows, one would require a large number of POD modes to accurately represent the flow field. Large dimension of the model contradicts the essence of model reduction. Furthermore, the resulting reduced-order model is numerically unstable. In this study, we suggest an LES-type closure model within the POD-based reduced-order modeling framework. We simulate the flow past a 3-D cylinder at Re=1000 and collect a large set of snapshots to capture turbulent structures in the wake. We develop a reduced-order model using a small number of POD modes and introduce an additional term within the model to capture the effects of high frequencies in the system. We compare the results of the model with the DNS data to establish accuracy of the modified reduced-order model.

Strategies for PIV Outlier Replacement using Gappy POD

Sam Raben, John Charonko Pavlos Vlachos (Virginia Tech)

This work presents methodologies for reconstructing erroneous measurements in gappy DPIV data using Proper Orthogonal Decomposition (POD). Current methods for data reconstruction using POD require a priori knowledge of the true solution [Venturi and Karniadakis, J. Fluid Mech. 2004]. This limitation renders the method ineffective for reconstructing experimental data. Here, strategies for optimizing Gappy POD reconstruction using different criteria for modal convergence as well as an iteratively reducing point selection algorithm are shown. Gappy flow fields were created using wall turbulence DNS data. Gappyness levels of 5%, 10%, 20%, 50% and, 80% were created with gap sizes of 1x1, 3x3, 5x5, and arbitrary NxM vector spacing. Noise, equivalent to that of DPIV error, was also added. Data reconstruction accuracy was compared against other currently used methodologies, including bootstrapping, kriging, and the universal outlier detection. The gappy POD method presented here is shown to accurately predict the optimum reconstruction with errors on the order of the error associated with basic DPIV velocity measurements.

Session II

Identifying atmospheric transport barriers using Lagrangian coherent structures

Phanindra Tallapragada Shane D. Ross (Virginia Tech)

Geophysical fluid flows exhibit complex dynamics and transport structures that govern passive advection and enable long range transport. Many microbes use the atmosphere to flow from one habitat to another. The movement of these microbes in the atmosphere is characterized by the processes of liberation(take off and ascent), drift (transport in the atmosphere) and deposition (descent and landing). This motivates the study of passive transport in the atmosphere. Despite the seeming complexity of geophysical flows, one can discern transport barriers that geometrically organize the motion over large scales. Preliminary evidence suggests that atmospheric transport barriers(ATBs), that separate air masses could play a significant role in the transport of microbes. We identified these ATBs using the concept of Lagrangian coherent structures(LCS). We discuss the application of LCS to atmospheric flows and how they organize long range passive transport.

On the role of topological chaos and ghost rods in fluid mixing

Mohsen Gheisarieha Mark A. Stremler (Department of Engineering Science and Mechanics, Virginia Tech)

We consider stirring and mixing of two-dimensional Stokes flow in a circular domain due to the motion of three rods. Two similar protocols are discussed that are expected to give significantly different results based on the predictions of the Thurston-Nielsen (TN) theorem. Somewhat surprisingly, under many conditions the topologically ‘trivial’ finite order protocol produces a larger stretch rate than does the pseudo-Anosov protocol, which is guaranteed to be chaotic by the TN theorem. We show that, in these cases, periodic points in the flow act as ‘ghost rods’ that can be considered responsible for the large stretch rates produced by the finite order protocol. However, the existence and importance of these ghost rods is dependent on the specific system geometry, and perturbations can lead to very low stretch rates when using the finite order protocol. In contrast, selection of a pseudo-Anosov protocol leads to a robust minimum for the stretch rates as predicted by the TN theorem. In order to associate the stretch rate results to fluid mixing, we also discuss the homogenization of a passive scalar advected by the flow.

A mathematical model of a ‘2P mode’ vortex wake

Alireza Salmanzadeh-Dozdabi Mark A. Stremler (Virginia Tech)

The standard von Karman vortex street, also known as the ‘2S’ mode, is the most common vortex configuration to appear in the wake of a bluff body. The next most common configuration is the ‘2P’ mode, in which two pairs of vortices are shed per cycle. We consider a simple model of the ‘2P’ mode consisting of a singly-periodic Hamiltonian system of four point vortices with identical strength magnitudes and zero net strength. An imposed spatial symmetry results in integrable dynamics that depend only on the relative vortex positions. Comparison of our model with a recent experimental result (Schnipper, Andersen, and Bohr, JFM 2009) suggests that this model approach can be used to characterize the experimental vortex motion and estimate the experimental vortex strengths.

Stability of four point vortices in a periodic strip, the “Domm system”

Vasileios Vlachakis (Engineering Science & Mechanics, Virginia-Tech)
Hassan Aref (Engineering Science & Mechanics, Virginia-Tech & Center for Fluid Dynamics, Fluid•DTU, Technical University of Denmark)

We approach the modeling of vortex wakes and their stability by considering a system of four vortices, two of circulation +Γ, two of circulation −Γ, in a periodic strip, a system first considered by Domm in 1956. The four-degree-of-freedom “Domm system” can be reduced to a system with two degrees of freedom by canonical transformations (Eckhardt & Aref,1988). The reduced representation allows us to construct perturbations that preserve linear impulse (momentum) and kinetic energy (Hamiltonian) of the system improving upon earlier work by Dolaptschiev and Schmieden from the 1930’s. We show that the only translating relative equilibria of the Domm system are the vortex streets that one already finds for two opposite vortices in a periodic strip. We also find by numerical experiments that the vortex street will dissolve into vortex pairs that escape to infinity, a mode of vortex street breakdown observed numerically by Aref & Siggia (1981) and in soap film experiments by Couder & Basdevant (1986). The dissolution process is extremely sensitive to the initial perturbation, suggesting that a form of chaos is involved.

Boundary Layer/Shock Interaction with Wall Slip

George R.Inger (Virginia Tech)

Shock/Boundary layer interaction is an important feature of hypersonic vehicle flow fields,especially under high altitude laminar flow flight conditions. This paper supplements experimental and CFD studies of the problem by offering an analytical treatment for the case of small Knudsen Numbers,the results provide basic insight to the interactive pressure and skin friction behavior. We address the specific paradigm problem of the viscous/inviscid interaction field generated by laminar supersonic flow past a slender compression corner.A fundamental analysis of first-order wall slip effects in this problem is given based on Triple-Deck Theory.It is found that these effects along the small scale interaction region are governed by a new "interactive Knudsen Number" Kn* that is much larger than that of the incoming boundary layer,consequently,the interactive slip effects are considerably more significant than usual.For example, slip is found to cause a first order reduction in skin friction(proportional to Kn#) in the free-interaction region uptream of the shock,which in turn delays the onset of local separation.

Reynolds number effects on the dynamics of the turbulent horseshoe vortex

Nikolaos Apsilidis, Sam Raben, Panayiotis Diplas, Clinton Dancey, Pavlos Vlachos,(Virginia Tech),
Ali Khosronejad, Fotis Sotiropoulos (University Of Minnesota)

High resolution experiments and numerical simulations Turbulent flows past wall-mounted obstacles are dominated by dynamically rich, slowly evolving coherent structures producing most of the turbulence in the junction region. Numerical simulations [Paik et al., Phys. of Fluids 2007] elucidated the large-scale instabilities but important questions still remain unexplored. One such question is with regard to the effect of the Reynolds number on the dynamics of the turbulent horseshoe vortex (THV). We carry out high-resolution laboratory experiments for the flow past a wall mounted cylinder in a laboratory water tunnel for ReD= 26000, 48000 and 117000. We employ the Time-Resolved Particle Image Velocimetry technique to resolve the dynamics of the flow at the symmetry plane of the cylinder and analyze the instantaneous velocity fields using the Proper Orthogonal Decomposition technique. The experimental study is integrated with coherent-structure-resolving numerical simulations providing the first comprehensive investigation of Reynolds number effects on the dynamics of the THV.

The Mechanism of Heat Transfer Augmentation in Stagnation Flow Subject to Freestream Turbulence

David O. Hubble Tom E. Diller Pavlos P. Vlachos (Virginia Tech)

A physical model is presented which predicts the time-resolved heat transfer coefficient based on the properties of the coherent structures present. Water tunnel experiments have been performed to investigate the mechanism of heat transfer augmentation in stagnation flow subject to freestream turbulence. The experiment combined Time-Resolved Digital Particle Image Velocimetry with an array of simultaneous time-resolved heat transfer measurements. Passive grids produced freestream turbulence with an intensity of 5% at length scales of 1cm, 2cm, and 3cm. The measurements reveal flow fields dominated by coherent structures whose number and strength strongly correlate with the length scale of the freestream turbulence. By examining the transient circulation and location of the identified structures, we observe that stretching and vorticity amplification significantly affects the near-wall flow. The transient heat transfer correlates well with the flow field induced by these structures. The time-resolved model developed represents a large advance over previous time-average predictors.

Session III

Thermo-chemical energy storage in a flow of hydrated magnesium sulfate

Ganesh Balasubramanian(Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University)
Sohail Murad(Department of Chemical Engineering, University of Illinois at Chicago)
Ishwar K. Puri(Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University)

Salt hydrates undergo desorption on being heated above certain charging temperatures, releasing water and forming anhydrous salts which have a higher energy content. Since these salts are hygroscopic, energy is easily retrieved back by passing water vapor over the anhydrous form. Such a technique of energy conversion, storage and retrieval enables these salts to be impregnated into porous media for thermo-chemical energy application. However, to investigate the thermal transport at the interface of the porous material and the salt, atomistic simulations are necessary. We employ molecular dynamics to simulate the heat transfer mechanism in a flow of hydrated magnesium sulfate impregnated into mesoporous silica and understand the role of interfacial thermal resistance on the charging temperature and total heat storage capacity of such salts.

Wall energy relaxation in Cahn-Hilliard model for moving contact lines

Pengtao Yue (Department of Mathematics, Virginia Tech)
James J. Feng (Department of Chemical and Biological Engineering, University of British Columbia)

Contact angle in the Cahn-Hilliard model is determined by wall energy. The finite-rate relaxation of this wall energy results in a dynamic contact angle which differs from the static one. According to our numerical simulation, the wall energy relaxation is crucial to the successful fitting of experimental data with a numerically manageable slip length, which could be two orders of magnitude larger than the physical one. Through a simple analysis, we establish a relationship between the dynamic contact angle and the capillary number, which is verified by our numerical simulation. We further show that this relationship is consistent with Cox's hydrodynamic model. In a sense, the wall energy relaxation coarse-grains an area surrounding the contact line into a ``slip region'' while keeping the apparent contact angle outside the region unchanged. In the end, we show some new results on drop spreading.

Lubrication forces in air measured by oscillatory modes using an atomic force microscope

William Ducker, Chris Honig, Adam Bowles, Rattaporn Chatchaidech, John Sader (Virginia Tech)

Recent work in our group has established that the no-slip boundary condition is accurately obeyed at solid–liquid boundary conditions, even for very narrow channels ( ~ 100 nm) and high shear rates (100, 000 s-1). This talk describes measurements of lubrication in narrow air channels between solid surfaces, where slip is theoretically predicted. By analysis of thermally- or mechanically-driven oscillation of an atomic force microscope (AFM) cantilever, we have measured both the damping and static forces acting on a sphere near a flat plate immersed in gas. By varying the proximity of the sphere to the plate, we can continuously vary the Knudsen number (Kn) at constant pressure, thereby accessing the slip flow, transition, and molecular regimes at a single pressure. We use measurements in the slip-flow regime to determine the combined slip length (on both sphere and plate) and the tangential momentum accommodation coefficient, σ. For ambient air at 1 atm between two methylated glass solids, the inverse damping is linear with separation and the combined slip length on both surfaces is 250 nm ± 105 nm, which corresponds to σ = 0.75 ± 0.25.

A Methodology for Time-Resolved microDPIV

Jaime Schmieg, Adric Eckstein, John Charonko, Pavlos Vlachos (Virginia Tech)

Micro Digital Particle Image Velocimetry (µDPIV) measurements are often limited to time averaged analyses due to low signal to noise ratios, high background illumination, and low particle seeding. As a result, the measurement of transient, microscale flows is difficult to achieve through conventional DPIV correlation methods. Eckstein and Vlachos (2009), presented the Robust Phase Correlation (RPC) method which utilizes a spectral filter and advanced windowing techniques resulting in a method immune to background noise1. This study further explores the potential of RPC using experimentally derived, time-resolved µPIV images taken within three different microchannels of various geometries. Performance comparisons were based on RMS error, as well as percent of erroneous vectors, as determined by the mode-ratio bootstrapping method (Pun et. al. 2007)2. Results displayed a significant reduction of RMS error and erroneous vectors for the RPC method in comparison to standard techniques. 1. Eckstein and Vlachos. Meas. Sci. Technol. (2009). 2. Pun et al. Meas. Sci. Technol. (2007).

Closure of a 2D Saint Venant model for free surface flows on rough bottoms

Ahmed Kaffel (Department of Mathematics Virginia Tech)

The effects of secondary flows on the momentum dispersion were analyzed in this study, for the case of free surface flows above non-uniform bottom roughness. In a first step, 3D-simulations were achieved using an anisotropic Reynolds stress model to determine the wall friction and the dispersion terms present in the depth averaged momentum equation. In a second step closure assumption of these terms were tested to define a 2D-Saint Venant model which is solved to calculate the transverse profile of the depth-averaged velocity. This approach was applied, to experiments achieved in a free surface flows above non-homogeneous rough bottom in a rectangular channel (realized at the ‘Institut de Mécanique des Fluides de Toulouse –IMFT-‘), and also to experimental results available in literature, and witch are achieved in open channels with periodic transverse variation of the bottom roughness Keywords: 2D-Saint Venant equations, wall friction, Secondary flows , Roughness, free surface flows, Dispersion , Turbulence

Numerical Simulation of the Free Surface Impact of a Sphere

Andrew Bloxom Dr. Wayne Neu (Virginia Tech, AOE)

Numerical simulations of the free surface impact of a sphere were performed in a Volume of Fluid (VOF) framework using the commercial code STAR-CCM+. The importance of surface contact angle was discovered in literature and applied successfully to achieve the proper flow characteristics of the impact of a sphere. The force data and flow visualization from the numerical work agreed reasonably with experiments of Truscott and Techet, 2007, for both hydrophobic and hydrophilic surface conditions. Numerical smearing of the cavity walls occurs where the volume fraction becomes extremely mixed as a result of both timestep and the movement of the contact line. The forces on the sphere in the region of the initial impact are under predicted when compared to the work of Moghisi and Squire, 1981. Further comparison of the initial impact force peak with more experimental data is desired, as this was the original focus of the work before the complexity of the splash behavior became apparent. Future work aims to solve these issues with the development of a dynamic contact angle model to account for the effect of a moving contact line.

Dynamic Characteristics at the Interface of Underwater Round Gas Jets

Chris Weiland Pavlos Vlachos (Virginia Tech)

The gas-liquid interface characteristics of round gas-jets submerged in water was studied across a wide range of Mach numbers (0.4-1.9). High speed shadowphotography was used to image the gas jet and the interface was tracked from the digital images for all points in space and time. The results show how the interface characteristics are governed by buoyancy to momentum driven flow as the Mach number increases. The jet penetration, defined as the maximum length a continuous gas jet occupies 98 percent of the time, increases with the injection Mach number. The penetration is related to the compressible jetting length, defined as the distance from the orifice where the momentum and buoyancy forces are balanced, and signifies a change in the jet behavior spatially from a momentum to buoyancy driven flow. The interface motion is computed as a function of the Mach number and the distance downstream from the orifice. These results indicate the most unsteady jetting process near the orifice occurs at Mach 1, presumably due to the formation of a shock cell structures.