Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session D28: Flow Instability: General |
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Chair: Bruno Welfert, Arizona State University Room: Georgia World Congress Center B316 |
Sunday, November 18, 2018 2:30PM - 2:43PM |
D28.00001: Double-diffusive salt-particle systems: The role of settling-driven collective instabilities on the growth of γ-instabilities Raphael Ouillon, Philip Edel, Eckart Heinz Meiburg High Prandtl number, double-diffusive systems such as salt and particles in water can be, in theory and in the absence of settling, unstable to the γ-instability but stable to collective instabilities. We show through numerical simulations that such systems can remain in a fingering regime for much longer times than suggested by the growth rate of γ-modes. We extend previous work on generalized mean-field theory of double-diffusive systems to incorporate settling and find a generalized expression for the growth rate of instabilities. We find the collective instability condition in the presence of settling, and recover known results in the limit of purely vertical γ-modes in a unifying framework. We estimate fluxes using small-scale numerical simulations and show that there is a critical settling velocity beyond which collective instabilities grow from the fingering regime. Visualization of the energy spectrum of the system reveals the transfer of energy from the inclined-wave driven collective instability to the γ-modes. We propose that the generalized mean-field theory with settling can fully characterize the stability of such systems. |
Sunday, November 18, 2018 2:43PM - 2:56PM |
D28.00002: Dendritic growth in the viscous fingering instability Qing Zhang, Irmgard Bischofberger The displacement of a more viscous fluid by a less viscous one in a quasi-two dimensional geometry leads to the formation of complex fingering patterns. In isotropic system the pattern forms by dense branching growth characterized by repeated tip-splitting of the evolving finger. When anisotropy is introduced into the system, the growth morphology changes dramatically to a highly ordered dendritic growth characterized by stable needle-like protrusions decorated with regular side-branches. We investigate dendritic structure in anisotropic environments by engraving six-fold symmetric lattice on the Hele-Shaw cell. The morphology transition from dense-branching growth to dendritic growth is controlled by two parameters: the degree of anisotropy and the viscosity ratio between the less-viscous inner fluid and the more-viscous outer one. Remarkably, the imposed six-fold symmetry only leads to six-fold symmetric dendrites at low viscosity ratio. At higher viscosity ratio, the pattern instead adopts a twelve-fold symmetry. In addition to the six main branches evolving in the imposed direction, an additional six sub-branches emerge, at a 30° angle to the preferred growth direction. We discuss how this transition is related to an intrinsic length scale that depends on the viscosity ratio. |
Sunday, November 18, 2018 2:56PM - 3:09PM |
D28.00003: Fingering Instabilities in Oxidizing Liquid Metal Keith Hillaire, Michael Dickey, Karen Daniels Eutectic gallium-indium (eGaIn), a room-temperature liquid metal alloy, has the largest tension of any liquid at room temperature, and yet we are remarkably able to induce the spreading of liquid metal fingers. It has been shown that under an applied voltage an oxide builds up on the surface of the metal, which acts like a surfactant, lowering the surface tension and allowing spreading under gravity. In the experiments described here, we place the eGaIn in an electrolyte bath of sodium hydroxide; by fabricating our own copper electrodes, which eGaIn readily wets, we are able to impose a fingering wavelength on the spreading. We find there to be a critical current for which the liquid metal fingers will begin to spread, which we associate with a Marangoni instability. We have found that increasing the imposed wavelength of the fingers decreases the critical current, and that increasing the current for a given wavelength increases the rate of spreading. Since fingering instabilities are well understood, we have provided a new route for quantifying which forces are at play in oxidizing liquid metals. |
Sunday, November 18, 2018 3:09PM - 3:22PM |
D28.00004: Electrohydrodynamic instability between a newtonian and a non-newtonian fluid in a microchannel Seymen İlke Kaykanat, Abdullah Kerem Uğuz When two immiscible liquids flow in a microchannel, the challenge is to generate droplets. Applying an electric field is an effective method which enables to generate droplets. The focus of this study is the linear stability analysis between a Newtonian and a non-Newtonian fluid in a microchannel in the presence of an electric field. The effects of the dimensionless groups, the electric number, the ratio of the fluid to electric time scales, the Reynolds number, the ratios of the physical properties and the direction of the electric field are analyzed. The maximum growth rates versus the power-law index and the neutral stability curves, i.e. the plot of the power-law indexes versus the critical dimensionless wavenumbers are examined for different thickness ratios which change the effect of the power-law index on the stability. Moreover, the practical ways to destabilize the stable system are investigated, i.e. the electric number related to the applied voltage, the thickness ratio related to the flow rate ratio and the viscosity ratio. The electric number versus the critical dimensionless wavenumbers are plotted to observe the effect of the length of the electrode on the critical electric number. |
Sunday, November 18, 2018 3:22PM - 3:35PM |
D28.00005: Compound convection patterns in a layer of volatile fluid driven by a horizontal temperature gradient Tongran Qin, Roman Grigoriev Stability of, and pattern formation in, liquid layers driven by a horizontal temperature gradient have been studied extensively in various limiting cases. In particular, in very thin liquid layers, thermocapillary stresses dominate and the instability typically leads to hydrothermal waves traveling in the direction of thermal gradient. In thicker layers, when the effect of buoyancy becomes comparable (i.e., for dynamic Bond numbers of order unity), one tends to find stationary patterns of co-rotating convection cells instead. However, what happens in the intermediate range has not been studied well. Our linear stability analysis predicted that the emerging convection pattern should be composed of hydrothermal waves on the cold side and stationary convection cells on the hot side. We confirmed the analytical predictions using numerical simulations based on a comprehensive two-sided transport model which describes a confined layer of volatile liquid in local equilibrium with its vapor at ambient conditions. |
Sunday, November 18, 2018 3:35PM - 3:48PM |
D28.00006: Aspect ratio and capillary ratio dependence of thermal-solutal capillary-buoyancy flow of a binary mixture in an annular pool Jiajia Yu, Yourong Li, Chuanyin Tang, Chunmei Wu 3D simulations are carried out to understand the aspect ratio and capillary ratio dependence of the thermal-solutal capillary-buoyancy flow in an annular pool. The annular pool was filled with silicon-germanium melt (C_{0}=1.99%). Results show that the axisymmetric stable flow occurs when the thermal capillary Reynolds number is small. The evolution of the flow pattern undergoes two and three stages with the aspect ratio and capillary ratio. Besides the special case of R_{σ}=-1, the critical thermal Reynolds number for the flow bifurcations into a 3D flow rises with the increase of the capillary ratio and decrease of the aspect ratio. Various three-dimensional flow patterns, including the lotus-like pattern, spoke pattern, hydrosolutal waves, ear-like pattern, growth-ring-like pattern and petal-like pattern, are observed, which are related to the capillary ratio, aspect ratio and thermal capillary Reynolds number. The wave number of the spoke pattern, hydrosolutal waves and petal-like pattern decreases with the aspect ratio, but rises up with the capillary ratio. |
Sunday, November 18, 2018 3:48PM - 4:01PM |
D28.00007: Dynamics and Transport of a Solute in Taylor-Couette Flow Bounded by Permeable Walls Rouae Ben Dhia, Denis Martinand, Nils Tilton In this work, linear stability analysis and Direct numerical simulations (DNS) are used to investigate the coupling between hydrodynamic instabilities, membrane transfer and osmotic pressure in Taylor-Couette configuration. The emphasis is on characterizing the effect of the osmotic pressure related to the concentration boundary layer forming near the membrane on the structure and dynamics of Taylor vortices. We consider a Taylor-Couette cell with two semi-permeable membranes totally rejecting the solute transported by a newtonian fluid filling the gap. For fixed operating conditions, linear stability analysis shows that the osmotic pressure tends to alter centrifugal instabilities as a result of an original self-sustained mechanism coupling the advection of the concentration boundary layer by the vortices, molecular diffusion and osmotic pressure driving a transmembrane flow fostering the vortices. This mechanism can induce a substantial reduction of the critical rotation rate above which vortices are observed. Furthermore, stability analysis shows that critical conditions are also impacted by the radius ratio. These analytical results are compared to recent DNS. |
Sunday, November 18, 2018 4:01PM - 4:14PM |
D28.00008: Comparing free surface and interface motion in electromagnetically driven thin-layer flows Benjamin C Martell, Jeffrey R Tithof, Douglas H Kelley Two-dimensional fluid dynamics is often approximated experimentally using a thin fluid layer which is driven by electromagnetic forces. That approximation is most accurate when both the direction and magnitude of the flow are nearly uniform over the depth of the layer. In this study we test uniformity by measuring fluid motion at two depths simultaneously. We use a two-layer configuration with immiscible fluids and track particles at the free surface and the interface of the two layers for Reynolds numbers Re ≤ 400. We find that the flow direction is almost entirely independent of depth, though its slight misalignment grows as the Reynolds number increases. Similarly, we find that the ratio of speeds at the free surface and interface nearly matches a recent theoretical prediction, even for complex flows, but deviates systematically as Re increases. We find that flows with thinner fluid layers are better aligned and more nearly match the predicted speed ratio than flows with thicker layers. Finally, we observe that in time-dependent flows, flow structures at the interface tend to follow flow structures at the free surface via complicated dynamics, moving along similar paths with a short time delay. |
Sunday, November 18, 2018 4:14PM - 4:27PM |
D28.00009: Maximum initial growth-rate of strong-shock-driven Richtmyer-Meshkov instability Aklant Bhowmick, Zachary R Dell, Arun Pandian, R. F. Stellingwerf, Snezhana Abarzhi We focus on the classical problem of the dependence on the initial conditions of the initial growth-rate of strong shock driven Richtmyer-Meshkov instability (RMI) by developing a novel empirical model and by employing rigorous theories and Smoothed Particle Hydrodynamics simulations to describe the simulation data with statistical confidence in a broad parameter regime. For the given values of the shock strength, fluid density ratio, and wavelength of the initial perturbation of the fluid interface, |
Sunday, November 18, 2018 4:27PM - 4:40PM |
D28.00010: How a wing-tip vortex escapes the streamwise impingement onto a downstream-located obstacle Pasche Simon, Francois Gallaire, François Avellan Impingement of vortices on surfaces can take place with the vortex axis aligned either normal or parallel to the obstacle. The latter case is considered, which could be encountered in turbomachinery blade cascade or in formation flight, possibly affecting the efficiency or the flight performance. More precisely, the focus is on the dynamics governing the escape of the vortex from a downstream-located obstacle, which is slightly displaced from the vortex centreline. To this end, a Batchelor vortex impinging a downstream sphere is numerically investigated. Above a specific swirl number, defined as the ratio between the maximum tangential velocity and the centreline axial velocity, the vortex impinging the sphere breaks down with the development of a self-sustained instability. However, the breakdown disappears when a sufficient lateral displacement of the sphere is introduced, resulting in a fixed and steady deflection of the vortex circumventing the sphere. The interactions of the instability and the sphere lateral displacement are investigated by a weakly nonlinear analysis coupled to a domain perturbation method. |
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