Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Volume 67, Number 19
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session T19: Non-Newtonian Flows: Instability and Turbulence II |
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Chair: Anubhab Roy, Indian Institute of Technology Madras Room: 205 |
Monday, November 21, 2022 4:10PM - 4:23PM |
T19.00001: Inertio-elastic instability of a vortex column Anubhab Roy, Piyush Garg, Ganesh Subramanian We analyse the instability of a vortex column in a dilute polymer solution at large Re and De with El = De/Re, the elasticity number being finite. The stability of small-amplitude two-dimensional perturbations in this distinguished limit is governed by the elastic Rayleigh equation whose spectrum is parameterized by E = El(1-β), β being the ratio of the solvent to the solution viscosity. In the said limit, neglecting the relaxation terms implies that the polymer solution supports undamped elastic shear waves propagating relative to the base-state flow, leading to a pair of elastic continuous spectra besides the familiar inviscid one. Further, unlike the neutrally stable inviscid case, an instability of the vortex column arises for finite E due to a pair of elastic shear waves being driven into a resonant interaction under the differential convection by the irrotational shearing flow outside the core. An asymptotic analysis for the Rankine profile shows the absence of an elastic threshold for this instability. The growth rate is O(Ω0) for order unity E, although it becomes transcendentally small for E«1, being O(Ω0E2e-1/√E). An accompanying numerical investigation shows that the instability persists for smooth monotonically decreasing vorticity profiles, provided the radial extent of the transition region (from the rotational core to the irrotational exterior) is less than a certain E-dependent threshold. |
Monday, November 21, 2022 4:23PM - 4:36PM |
T19.00002: Forced oscillations of a rigid cylinder in viscoelastic fluid flow Umang Patel, Jonathan P Rothstein, Yahya Modarres-Sadeghi We investigate the effects of fluid elasticity on the flow forces and the wake structure when a rigid cylinder is forced to oscillate sinusoidally in a viscoelastic fluid flow. A two-dimensional, uniform, incompressible flow of viscoelastic fluid is considered at Re=100. The FENE-P model is used to model the viscoelastic fluid. We study how the flow forces and the wake patterns change as the reduced velocity, U*, Weissenberg number, Wi, oscillation amplitude, A*, and the maximum polymer extensibility, L2, change. We analyze the flow forces in the frequency domain to determine the lock-in range in terms of Wi at a constant U*. The average power is calculated to determine the range of Wi, where self-excited oscillations might occur if the cylinder is allowed to oscillate. We also investigate the effect of fluid elasticity on the added mass coefficient at a constant reduced velocity. For a constant Wi, the strength of the elastic stresses increases, and the strength of vortices reduces with increasing reduced velocity. |
Monday, November 21, 2022 4:36PM - 4:49PM |
T19.00003: An Experimental Study of Vortex-Induced Vibrations of a Cylinder in Shear- and Extensional-Thinning Flows Pieter R Boersma, Jonathan P Rothstein, Yahya Modarres-Sadeghi We present experimental results of the response of a one-degree-of-freedom cylinder placed in shear- and extensional flows. A flexibility-mounted rigid cylinder is subjected to flow generated in a water channel. The thinning of the fluids is increased by increasing the concentration of Xanthan gum in water. For the low concentration fluids, the VIV response follows the response of a Newtonian fluid. As the concentration is increased, the lock-in range and the maximum amplitude of oscillations decrease until VIV is completely suppressed for the maximum concentration tested here within the range of Reynolds numbers considered in these experiments (Re<100). We discuss differences between these experiments and our previous numerical results on VIV of a cylinder in purely shear thinning fluids |
Monday, November 21, 2022 4:49PM - 5:02PM |
T19.00004: Time-dependent elastic instabilities in a shear flow: spanning the entire Wi—Re phase plane Rishabh V More, Gareth H McKinley It is well known that the simple shear flow of a viscoelastic fluid, such as the torsional flow between a cone and plate in the low Reynolds number (Re) regime becomes unstable to a three-dimensional time-dependent instability. This elastically-driven instability emerges from the onset of a secondary motion resulting in a Bernoulli spiral-like flow at conditions just above critical. Here we present the effects of increasing Re on the critical conditions for the onset of elastic instabilities in a torsional shear flow between a cone and plate, thus, spanning the entire Weissenberg (Wi)-Reynolds (Re) number phase plane. Flow visualizations reveal the combined effects of varying Wi and Re on the secondary recirculation at the onset of instability. The results provide insight into non-Newtonian fluid mechanics and elevate our fundamental physical understanding of inertia-elastic coupling and the role of shear-thinning and second normal stresses on elastic instabilities. |
Monday, November 21, 2022 5:02PM - 5:15PM |
T19.00005: Viscoelastic 'narwhals': two-dimensional coherent states in pressure-driven channel flow at vanishing inertia Alexander Morozov, Martin Lellep, Moritz Linkmann In this talk we present the first coherent state in purely elastic parallel shear flows [1]. We perform direct numerical simulations of a model viscoelastic fluid driven by an applied pressure gradient through a two-dimensional channel. While the flow is linearly stable, we find that a sufficiently strong finite-amplitude perturbation leads to the appearance of sub-critical travelling-wave solutions, in line with previous theoretical [2] and experimental [3] studies. We refer to these solutions as ‘narwhals’ for their visual resemblance. We explore the region of their existence and discuss how ‘narwhals’ are sustained. |
Monday, November 21, 2022 5:15PM - 5:28PM |
T19.00006: A phase diagram for viscoelastic wavy-channel flow Jacob Page, Tamer A Zaki Viscoelastic channel flow exhibits a wealth of interesting dynamics in areas of parameter space where the corresponding Newtonian flow would be laminar. The most significant regimes – inertialess elastic turbulence and elasto-inertial turbulence – are known to be subcritical, and there is a need to identify the mechanisms by which vortical perturbations can be established in the bulk of the flow. In this work, we study the flow response to surface waviness at the lower wall, specifically the penetration depth of the vorticity perturbation. We construct a phase diagram in terms of the dimensionless roughness lengthscale and an elastic critical-layer height. The strongest vortical response is observed over long-wave distortions. For inertialess flows, the vanishing streamwise normal stress at the channel centreline creates a blocking effect whereby the rolls created by the surface waves are confined to the lower half of the channel and a large vorticity perturbation is established in a central boundary layer. In elasto-inertial flows, a resonance generates a strong vorticity response at critical layers in both halves of the channel. |
Monday, November 21, 2022 5:28PM - 5:41PM |
T19.00007: Turbulence and intermittency in homogeneous isotropic flows of elastoviscoplastic fluids Ianto Cannon, Mohamed S Abdelgawad, Marco Edoardo Rosti Elastoviscoplastic (EVP) fluids behave as a viscoelastic solid when the applied stress is low, and as a viscous liquid when the applied stress is above a critical value known as the yield stress. Examples include mud, lava, and toothpaste. We make direct numerical simulations of a number of EVP fluids in homogeneous isotropic turbulence with microscale Reynolds number~435. Spectral and scale-by-scale analyses reveal a new apparent scaling of the kinetic energy E~k^(-2.3) beyond the inertial range. In addition, we define a "non-Newtonian dissipation" term arising from viscoelastic forces in the Navier-Stokes equation. This non-Newtonian dissipation takes more extreme values as plasticity increases, leading to an increase in intermittency, as observed in plots of the structure functions. |
Monday, November 21, 2022 5:41PM - 5:54PM |
T19.00008: Elastic turbulence enhances solute mixing in 3D porous media Sujit S Datta, Christopher A Browne Polymer solutions are often injected in porous media for applications such as groundwater remediation, column chromatography, or packed bed reactions. In these settings, it is often important to mix solutes in initially separated streams. For Newtonian fluids, the flow is typically laminar, limiting mixing to the dispersion inherent to the disordered pore space. However, it remains unknown how polymer solutions modify this mixing. Here, we directly visualize the mixing of two fluorescently dyed streams within a transparent 3D porous medium. We find that, above a threshold flow rate, the mixing rate increases above the expected laminar dispersion. By imaging the pore-scale velocity field, we demonstrate that the increase in solute mixing rate is concomitant with the onset of an elastic instability in which the flow exhibits strong spatio-temporal fluctuations reminiscent of inertial turbulence, despite the vanishingly small Reynolds number. This "elastic turbulence'' produces a spectrum of solute concentration fluctuations that follow power-law scalings consistent with Batchelor mixing. Thus, by linking macro-scale mixing to the pore-scale unstable flow, our work provides generally-applicable guidelines to control mixing of passive scalars in disordered porous media. |
Monday, November 21, 2022 5:54PM - 6:07PM |
T19.00009: Mixing of passive scalar and polymer concentration in turbulent viscoelastic planar jets and wakes analysed by direct numerical simulations Mateus C Guimãraes, Fernando T Pinho, Carlos B da Silva Direct numerical simulations (DNS) of spatially evolving turbulent planar jets and wakes of FENE-P viscoelastic fluids is performed in order to study the small scale mixing and large scale stirring of passive and active scalars in free turbulent viscoelastic flows. The DNS are based on a highly accurate numerical algorithm employing pseudo-spectral and 6th order compact finite differences, and the shock-capturing Kurganov-Tadmor scheme. The details of the numerical methods and code validation can be found in our previous works (Guimarães et al., J. Fluid Mech., vol. 899, 2020, p. A11; Guimarães et al., J. Fluid Mech., 2022, in press). For the non-uniform polymer concentration cases, a viscoelastic fluid issues into a Newtonian environment, while for the uniform cases the fluid is viscoelastic everywhere. We show that viscoelasticity suppresses small scale mixing, but large and intermediate scale stirring can be suppressed or enhanced depending on the fluid rheological parameters and flow region in consideration. |
Monday, November 21, 2022 6:07PM - 6:20PM |
T19.00010: Linear stability analysis of a shear-imposed Oldroyd-B liquid flowing down a slippery inclined plane Subham Pal, Arghya Samanta A linear stability analysis is performed by using the Orr-Sommerfeld type boundary value problem (OS BVP) for an Oldroyd-B liquid flowing down a slippery plane in the presence of an imposed shear stress. The OS BVP is solved analytically and numerically by using the long-wave asymptotic expansion at low Reynolds number and the Chebyshev spectral collocation technique for low to high values of the Reynolds number, respectively. The long-wave approach shows the existence of surface mode, while the finite wavelength shear mode appears in the high Reynolds number regime. Expression of critical Reynolds number for the surface mode indicates a destabilizing nature of slip and imposed shear stress (co-flow direction). But when the imposed shear stress acts in the counter-flow direction, the critical Reynolds number for the surface mode increases, thus a stabilizing effect is seen. While using the numerical approach in the moderate Reynolds number regime, the Weissenberg number and the viscosity ratio have a dual nature on the primary instability. Finally, at the high Reynolds number, the shear mode is stabilized by the viscosity ratio, slip length, and imposed shear stress (counter-flow direction), and destabilized by the Weissenberg number and imposed shear stress (co-flow direction). |
Monday, November 21, 2022 6:20PM - 6:33PM |
T19.00011: Transient of flow restart in a gas void embedded gelled pipeline and voids deformation Lomesh Tikariha, Aniruddha Sanyal, Lalit Kumar The multiphase flow of complex fluids has a wide range of applications due to its influence on modification in the physical properties of the medium. Some examples are waxy gel, aerated concrete, and food products, which present a complex fluid-gas interface during processing and pipeline transportation. For instance, the pressure applied to dislodge the waxy gel structure confronts the high compressibility of the gas voids. The interaction of the pressure front with gas voids leads to localized deformation, causing extensive structural evolution of the gelled medium. Such interaction during initial pressure propagation significantly impairs the crystal network. An understanding of the pressure propagation mechanism is imperative to demonstrate the role of void space during the transient of a start-up operation. The simulation results for the pressure profile indicate a considerable delay in its propagation owing to the difference in compressibility of the two phases. Further propagation of pressure depends on compressive deformation of the gas void as a result of degraded upstream gel movement. A detailed examination of the 2-D circular gas void's motion and corresponding topological changes illustrates the localized gel degradation in the vicinity of the gel-gas interface. |
Monday, November 21, 2022 6:33PM - 6:46PM |
T19.00012: Regulation of Viscoelastic Instability by Crystallization of Particle Suspension Sijie Sun, Nan Xue, Stefano Aime, Hyoungsoo Kim, Gareth H McKinley, Howard A Stone, David A Weitz The viscoelasticity of a polymer solution can destabilize the shear flow and convert such flow into a steady primary flow plus an unsteady secondary flow, where the fully-developed secondary flow contains hierarchical flow structures. These flow structures typically have a power-law distribution in frequency. Here we report that adding particle suspension into a viscoelastic polymer solution regulates the secondary flow and disturbs the power-law distribution by introducing an unexpected rotational motion while suppressing other flow structures. |
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