Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session M23: Flow Instability: GeneralInstabilities
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Chair: Anirban Guha, Indian Institute of Technology Kanpur Room: 710 |
Tuesday, November 21, 2017 8:00AM - 8:13AM |
M23.00001: Identification of spatially-localized initial conditions via sparse PCA Anubhav Dwivedi, Mihailo Jovanovic Principal Component Analysis involves maximization of a quadratic form subject to a quadratic constraint on the initial flow perturbations and it is routinely used to identify the most energetic flow structures. For general flow configurations, principal components can be efficiently computed via power iteration of the forward and adjoint governing equations. However, the resulting flow structures typically have a large spatial support leading to a question of physical realizability. To obtain spatially-localized structures, we modify the quadratic constraint on the initial condition to include a convex combination with an additional regularization term which promotes sparsity in the physical domain. We formulate this constrained optimization problem as a nonlinear eigenvalue problem and employ an inverse power-iteration-based method to solve it. The resulting solution is guaranteed to converge to a nonlinear eigenvector which becomes increasingly localized as our emphasis on sparsity increases. We use several fluids examples to demonstrate that our method indeed identifies the most energetic initial perturbations that are spatially compact. [Preview Abstract] |
Tuesday, November 21, 2017 8:13AM - 8:26AM |
M23.00002: Finite amplitude instability in two layer viscosity-stratified plane Poiseuille flow Priyanka Shukla, Geetanjali Chattopadhyay, Usha R The weakly nonlinear analysis of two-layer viscosity stratified plane-Poiseuille flow (PPF) is examined using Stuart-Landau type order parameter equation. The amplitude expansion method is used to derive weakly nonlinear equations upto cubic order in amplitude. The resulting set of equations is then solved numerically using Chebyshev spectral collocation method and the results are validated from the limiting case of single layer PPF. We show that while in the case of single layer PPF subcritical region spans larger range in $({\rm Re},\alpha)$-plane with ${\rm Re}$ and $\alpha$ being the Reynolds number and wave number, respectively, the subcritical region is confined only to a narrow region around the neutral stability curve in the case of two-layer viscosity stratified PPF. Owing to this, there is a region below ${\rm Re}_c^{nl}$ where the flow is always nonlinealy stable. The linear stability of two-layer PPF predicts stability of the base flow for ${\rm Re}<{\rm Re}_c$, however, the weakly nonlinear analysis reveals the subcritical instability for ${\rm Re}^{nl}_c < {\rm Re}< {\rm Re}_c$ and the existence of supercritical region for ${\rm Re}> {\rm Re}_c$. It is found that there is a significant reduction in the critical Reynolds number. [Preview Abstract] |
Tuesday, November 21, 2017 8:26AM - 8:39AM |
M23.00003: Instability of dilute suspensions in a channel coated with porous media Parisa Mirbod, Zhenxing Wu We present the linear instability analysis of plane Poiseuille flow of low concentrated suspensions in a channel coated with random soft porous media. The system consists of low concentrated suspensions over soft random porous media at low Reynolds numbers. We used the linear stability analysis, carried out via spectral methods to model perturbations from the coupled Brinkman and suspension models. To calibrate our code and our calculation procedure, we compared our data to the classical plane Poiseuille flow of previous works. Our results are in good agreement with Orszag's result to solve the Orr-Sommerfeld instability equation. In the limit when Reynolds number is very low and there is no porous media in the channel, we found stability in the system, i.e., the characteristics of incompressible Newtonian flows in a smooth Poiseuille flow. However, we found the depth ratio between free fluid and porous medium, the porosity, and permeability of porous medium have critical effect on instability. Depending on these parameters, the instability occurs in the so-called fluid mode or porous mode. [Preview Abstract] |
Tuesday, November 21, 2017 8:39AM - 8:52AM |
M23.00004: Viscoelastic instabilities generate filamentous flows and enhance dispersion in porous media Jeffrey S. Guasto, Derek Walkama, Nicolas Waisbord Viscoelastic porous media flows are ubiquitous in both nature and industry, where their unique transport properties can dominate the function and performance of relevant systems. Utilizing a microfluidic model porous medium, we map the flow topology of a viscoelastic fluid (400ppm PAA in 87{\%} aqueous glycerol) via micro-PIV for a range of Weissenberg numbers (Wi) and pore geometries. We demonstrate that steady filamentous flow patterns are present in viscoelastic flows at moderate Wi, which dominate longitudinal transport and increase dispersion relative to Newtonian flows. As Wi increases in flow through disordered porous media, existing high velocity filaments grow, while flow through low velocity regions is further suppressed. We directly demonstrate that the resulting increase in the spatial correlation length of the flow topology is linked to the dispersive properties of the flow field, in line with recent theory. With precise control over the geometrical order/disorder of the porous medium through lithography, we also demonstrate that in the limiting case of a ordered, hexagonal microstructure, the flow topology undergoes a bifurcation at a critical Wi representative of mirror symmetry breaking. [Preview Abstract] |
Tuesday, November 21, 2017 8:52AM - 9:05AM |
M23.00005: Amplification of disturbances generated by localized body forces in channel flows of viscoelastic fluids Gokul Hariharan, Mihailo Jovanovic, Satish Kumar The study of non-modal amplification of distributed body forces in channel flows of viscoelastic fluids has provided useful insight into the mechanisms that may govern the initial stages of transition to elastic turbulence. However, distributed body forces are not easy to implement in experiments and there is a need to examine amplification of localized body forces. In this work, we use the linearized governing equations to examine such amplification in plane Poiseuille flow of FENE-CR fluids. We first identify the location at which the impulsive excitations experience the largest amplification and then analyze the energy of the fluctuations and resulting flow structures. For both a Newtonian fluid at high Reynolds number and a viscoelastic fluid at low Reynolds number, the largest amplification occurs for disturbances that are located near the channel wall. Analysis of the energy evolution shows that the localized point force directed in the spanwise direction has the largest impact and that the streamwise velocity is most affected. For viscoelastic fluids we observe the development of vortical structures away from the source of impulsive excitation, a feature absent in Newtonian fluids that may provide a mechanism for the initial stages of transition to elastic turbulence. [Preview Abstract] |
Tuesday, November 21, 2017 9:05AM - 9:18AM |
M23.00006: ABSTRACT WITHDRAWN |
Tuesday, November 21, 2017 9:18AM - 9:31AM |
M23.00007: On the Linear Global Instability of a Rotating Disk Flow Yu Nishio, Keunseob Lee, Seiichiro Izawa, Yu Fukunishi Linear global instability in a rotating disk flow is investigated by a direct numerical simulation for 2$\pi $/68 section of the disk. A sponge region, in which the velocity fluctuations inside a boundary layer are forced to damp, is used in the outer end. A short-duration disturbance of azimuthal mode 68 is introduced into the flow field at a high Reynolds number region, \textit{Re} $=$930 or 1030, and the growth of the fluctuations is observed. The disturbances start to grow immediately after they are introduced and converge to a certain positive value, regardless of the location where the sponge region starts. The results suggest that the flow over an infinite rotating disk is globally unstable in the linear regime, which is inconsistent with the previous studies. [Preview Abstract] |
Tuesday, November 21, 2017 9:31AM - 9:44AM |
M23.00008: Fluctuations of wormlike micelle fluids in capillary flow Paul Salipante, Stephen Meek, Steven Hudson We investigate the effect of entrance geometry on the flow stability of wormlike micelles solutions in capillary flow. These solutions exhibit strong shear thinning behavior resulting from micelle breakage and have been observed to undergo large flow rate fluctuations. We investigate these fluctuations using simultaneous measurements of flow rate and pressure drop across a capillary, and we adjust entrance geometry. With a tapered constriction, we observe large persistent fluctuations above a critical flow rate, characterized by rapid decreases in the pressure drop with corresponding increase in flow rate followed by a period of recovery where pressure increases and flow rate decreases. Flow field observations in the tapered entrance show large flow circulations. An abrupt contraction produces smaller transient fluidized jets forming upstream of the constriction and the magnitude of the fluctuations are significantly diminished. The effect of fluid properties is studied by comparing the magnitude and timescales of the fluctuations for surfactant systems with different relaxation times. The onset of fluctuations is compared to a criterion for the onset of elastic instabilities and the magnitude is compared to estimates for changes in channel resistance. [Preview Abstract] |
Tuesday, November 21, 2017 9:44AM - 9:57AM |
M23.00009: Three-dimensionality of one- and two-layer electromagnetically driven thin-layer flows Benjamin Martell, Jeffrey Tithof, Douglas Kelley We measure and compare the out-of-plane motion in a variety of experimental models for approximating two-dimensional chaotic and turbulent flow. It was previously found that out-of-plane motion grows suddenly when the viscous Reynolds number $Re$ exceeds a critical value $Re_c$ in a two-layer miscible electromagnetically driven flow model. Here, our goal is to determine whether similar onsets occur in two-layer immiscible models and in single-layer models, and how the critical values depend on thickness. We use particle tracking to measure the flow velocity and use a least-squares projection onto stream function modes, boundary modes, and potential modes to quantify out-of-plane motion. We also consider how the magnitude of out-of-plane motion depends on the Rayleigh friction Reynolds number $Rh$. We find that immiscible and single-layer models approximate two-dimensional flow better than miscible models in most situations. [Preview Abstract] |
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