Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session R8: Non-Newtonian Flows III |
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Chair: Michael Shelley, New York University Room: 311 |
Tuesday, November 22, 2011 12:50PM - 1:03PM |
R8.00001: The effects of long-chain polymers on tip vortex flow and cavitation inception Quan Zhang, Chao-Tsung Hsiao, Georges L. Chahine Experiments have shown that propeller/hydrofoil tip vortex cavitation can be suppressed by properly injecting dilute polymer solutions at the tip. However, the mechanisms for this phenomenon are not well understood yet. To understand better the underlying flow physics the tip vortex flow generated by a rotating propeller in water and a dilute polymer solution (FENE-P model) was numerically simulated. It is found that the vortex flow structure is changed by the non-Newtonian features of polymers. Phenomenally the vortical rotation in a polymer solution is slower and the vortex center pressure is higher than in water. The non-Newtonian stress is much stronger than the Newtonian stresses in water. To further understand the non-Newtonian stresses contribution, the FENE-P model is also applied to a simplified quasi-cylindrical vortex. It is found analytically that in addition to the three normal stresses that are expected to be quadratic in the shear rate, one of the shear components is also quadratic. We also studied polymer effects on the dynamics of a bubble nucleus in the tip vortex. The bubble was found to grow to an elongated large cavity in water while it collapses in the polymer solution for the same cavitation number. This work was supported by the Office of Naval Research, Contract N00014-04-C-0110, monitored by Dr. Ki-Han Kim. [Preview Abstract] |
Tuesday, November 22, 2011 1:03PM - 1:16PM |
R8.00002: Modeling Vortex Cavitation Inception Delay in a Swirl Chamber by Polymer Injection J. Ma, Q. Zhang, C.T. Hsiao, G.L. Chahine Experimental studies have shown tip vortex cavitation can be delayed with injection of drag reducing dilute polymer solutions. We present here numerical simulations conducted to understand the mechanisms responsible for cavitation suppression with local polymer injection. A canonical flow in a linear vortex chamber was simulated by using the NS solver, \textsc{3DynaFS-Vis}$^{\copyright }$, equipped with a FENE-P viscoelastic model for the polymer solution and a transport equation to track its concentration. The simulation showed that injection of dilute polymer can delay cavitation inception at a much lower injection flow rate than needed with massive injection of water or a higher viscosity liquid. Injection of polymer increases the pressure along the vortex axis and a much earlier vortex breakdown created by the elasticity of the polymers appears to be responsible for the strong modification of the flow character. This results in a fast reduction of the rotational velocity, increase of the pressure, and delay of cavitation inception. The dependency of polymer effects on the injection flow rate and polymer concentration was also investigated, finding good consistency with experimental observations. [Preview Abstract] |
Tuesday, November 22, 2011 1:16PM - 1:29PM |
R8.00003: Viscoelastic instabilities in a 3D Stokes-Oldroyd-B fluid Becca Thomases, Michael Shelley The consequences of three-dimensional viscoelastic instabilities are examined numerically using the Oldroyd-B model in the low Reynolds number (Stokes) regime. The fluid is driven by a simple time-independent forcing that, in the absence of viscoelastic stresses, creates a four-roll mill in (x,y) which is constant in z. It is now known that such forcing will force the 2d version of this system into symmetry breaking and flow mixing. Here we find that at sufficiently large, but O(1), Weissenberg number, 3d perturbations grow exponentially and lead to complex three-dimensional flow dynamics which can differ markedly from the 2d case. [Preview Abstract] |
Tuesday, November 22, 2011 1:29PM - 1:42PM |
R8.00004: ABSTRACT WITHDRAWN |
Tuesday, November 22, 2011 1:42PM - 1:55PM |
R8.00005: Study of the behavior of rising bubbles in a Boger-type fluid J.R. Velez-Cordero, D. Samano, R. Zenit Particle aggregation is a common phenomenon observed in viscoelastic multiphase flows. In this work a new effect has been observed to occur in monodispersed bubbly flows in a Boger-type fluid. It was found that the dispersion of bubble changes dramatically depending on the bubble size: if the diameter of the bubbles is small, large vertical clusters are formed; on the other hand, the bubble assembly rises in a dispersed manner if the bubble size is increased. To understand the condition for which agglomeration occurs two additional experiments were conducted: the interaction of two side-by-side bubble chains was analyzed; and, the unsteady behavior of the first normal stress difference was studied in a rheometric flow. These analyses suggest that there is a process of accumulation of elastic stress; when the accumulated elastic stress surpasses the viscous repulsive stress, aggregation can occur even at supercritical speeds. Interestingly, the two bubble diameters tested in the bubbly flow experiments are above and below the critical diameter for which the velocity of an isolated bubble becomes discontinuous, the so-called bubble velocity discontinuity. This suggests that the bubble dispersion improvement could result from the modification of the gas-liquid interface. [Preview Abstract] |
Tuesday, November 22, 2011 1:55PM - 2:08PM |
R8.00006: Pertrurbation theory for dynamic behavior of a sphere settling in a viscoelastic fluid Matthew Nick Moore, Bin Liu, Jun Zhang, Michael J. Shelley We present a new perturbation theory for the motion of a rigid sphere settling in a viscoelastic Oldroyd-B fluid that can be generalized to other scenarios of viscoelastic fluid-structure interaction. In contrast to previous perturbation theories, the perturbative expansion variable is not the Weissenberg number, but instead it is a parameter measuring the feedback of the viscoelastic stress into the fluid momentum. This allows for accurate calculations at large Weissenberg numbers. Previous experiments, including our own, have documented that a sphere overshoots its terminal velocity on a transient timescale comparable to the fluid relaxation time. Our theory predicts this behavior as well as a non-trivial dependence of the drag on the Weissenberg number. I will also discuss experiments in which periodic forcing is applied to a body moving through a viscoelastic fluid, and the perturbation theory is used as a predictive tool. [Preview Abstract] |
Tuesday, November 22, 2011 2:08PM - 2:21PM |
R8.00007: Phase syncronization of swimming infinite sheets in viscoelastic fluids John Chrispell, Michael Shelley, Lisa Fauci A Navier-Stokes/Oldroyd-B immersed boundary algorithm is used to examine the interaction of swimming infinite sheets with a viscoelastic fluid. In particular, we examine the spatial and temporal evolution of the polymer stress field. The effects of the bulk viscoelasticity on hydrodynamic synchronization of swimming sheets and sheets swimming next to solid walls is analyzed. [Preview Abstract] |
Tuesday, November 22, 2011 2:21PM - 2:34PM |
R8.00008: Effects of viscoelasticity on the migration of a viscous drop in a shear flow near a wall Swarnajay Mukherjee, Kausik Sarkar Dynamics of a drop migrating in a shear flow of a viscoelastic liquid (FENE-CR) near a wall is numerically investigated. Viscoelasticity hinders migration, and it is explained by investigating the viscoelastic forces around the drop. The orientation angle and the lateral migration velocities both decrease linearly with increasing viscoelasticity (Deborah number and amount of polymer viscosity). The enhanced curvature of the streamlines above the drop adds to this effect, it being more prominent for smaller deformation at lower capillary numbers. The slip velocity of the drop decreases with increasing Deborah number. For viscosity matched systems, the initial position does not influence the migration for the low values of Deborah number considered. However, at higher viscosity ratios, initial position plays a role. Increasing the viscosity ratio lowers the migration velocity and addition of viscoelasticity decreases it further. For very high viscosity ratio, viscoelasticity can induce drop migration towards the wall. [Preview Abstract] |
Tuesday, November 22, 2011 2:34PM - 2:47PM |
R8.00009: Significance of viscoelastic effects on the rising of a bubble and bubble-to-bubble interaction Arturo Fernandez Numerical results for the rising of a bubble and the interaction between two bubbles in non-Newtonian fluids will be discussed. The computations are carried out using a multiscale method combining front-tracking with Brownian dynamics simulations. The evaluation of the material properties for the non-Newtonian fluid will be discussed firstly. The results from the computations of a single bubble show how elastic effects modify the deformation and rising of the bubble by pulling the tail of it. The relationship between the strength of the elastic forces and the discontinuity in the bubble terminal velocity, when plotted versus bubble volume, is also observed in the computations. The bubble-to-bubble interaction is dominated not only by elastic effects but also by the shear-thinning caused by the leading bubble, which leads the trailing bubble to accelerate faster and coalesce with the leading bubble. [Preview Abstract] |
Tuesday, November 22, 2011 2:47PM - 3:00PM |
R8.00010: Viscoelastic droplet deformation in complex flow: application of the extended finite element Arash Sarhangi Fard, Martien Hulsen, Patrick Anderson Deformation of a viscoelastic drop in a Newtonian matrix under Stokes flow is simulated using a eXtended finite element method (XFEM). We consider the matrix inside a continuous mixer (like twin screw extruder), where shear and elongational flows are presents. Surface tension is included in the traction vector across the interface between the droplet and the matrix. The governing balance equations~ are solved once over entire domain (droplet and matrix). The surface of droplet is described by a discretized mesh and its position is updated by tracking the nodal positions in time. For XFEM integration, the position of the surface is determined explicitly by a numerical level set. To couple the velocity between droplet and matrix, a constrain is applied on balance equations. Constraints are enforced using a Lagrangian multiplier and also using weak interface conditions. Results are discussed for different viscosity ratio's and different Weissenberg numbers. [Preview Abstract] |
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