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 G25: Flow Instability: KelvinHelmholtz, Wakes & Pulsatile Flow 
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Chair: Yuji Tasaka, Hokkaido University Room: Georgia World Congress Center B313 
Monday, November 19, 2018 10:35AM  10:48AM 
G25.00001: Optimal perturbations in a timedependent round jet Gabriele Nastro, Jérôme Fontane, Laurent Joly We analyse the influence of the specific features of a timedependent round jet undergoing the KelvinHelmholtz instability on the development of threedimensional secondary instabilities. We proceed to a nonmodal linear stability analysis based on a directadjoint approach in order to determine the fastest growing perturbation over a single period of the timeevolving twodimensional base flow during a given time interval, [t_{0},T]. An optimisation loop allows to adapt the control criteria depending on the quantity to maximise. In particular, it enables to explore the sensitivity of the optimal perturbation to the azimuthal periodicity of the mode, m, as well as the Reynolds number, Re. We focus on the influence of the azimuthal wavenumber, m, on the optimal energy gain as a function of the horizon time, T. We also consider the impact of the injection time, t_{0}, on the transient dynamics of the optimal perturbation and, in particular, on the contribution of the Orr mechanism. Through a detailed analysis of the kinetic energy budget, we identify the different types of instability (elliptical, hyperbolic) and their coexistence associated with the threedimensionalisation process of the round jet. 
Monday, November 19, 2018 10:48AM  11:01AM 
G25.00002: Viscous waves in microchannels Xiaoyi Hu, Thomas Cubaud Rapid layering of viscous materials in microsystems encompasses a range of hydrodynamic instabilities that facilitate mixing and emulsification processes of fluids having large differences in viscosity. We experimentally study viscous waves arising at the interfaces between viscous stratifications made of miscible and immiscible fluid pairs with large viscosity ratios in microchannels and systematically investigate the effects of fluid handling, flow rates, viscosity ratios, diffusion coefficients and interfacial tension between model fluid pairs. We demonstrate that key features of interfacial viscous waves, including emission frequency, propagating celerity, wavelength and amplitude can be readily described by functional relationships to delineate effects of inertia, viscosity and interfacial tension. We also shed light on wave crest breaking process, which produces viscous ligaments that continuously transport thick material into the fast coflowing lowviscosity stream. Finally, we examine the transition from droplet to wave regime to provide a comprehensive scenario of interfacial instabilities in microfluidic viscosity stratifications. 
Monday, November 19, 2018 11:01AM  11:14AM 
G25.00003: Finite amplitude KelvinHelmholtz billows at high Richardson number Jeremy Parker, Colmcille Caulfield, Rich Kerswell We study the dynamical system of a stratified mixing layer at finite Reynolds number and unity Prandtl number with hyperbolic tangent profiles in streamwise background velocity and density, forced in such a way that these background profiles are a steady solution of the governing equations.
As is wellknown, if the minimum Richardson number $Ri_m$ is less than a certain critical value $Ri_c$, the flow is linearly unstable to KelvinHelmholtz instability. We show that unstable, steady, twodimensional, finite amplitude elliptical vortex structures , i.e. `KelvinHelmholtz billows', exist above $Ri_c$. Bifurcation diagrams are produced using branch continuation, and we explore how these diagrams change with varying Reynolds number. In particular, we examine whether such finite amplitude KelvinHelmholtz billows can exist at $Ri_m>1/4$, where the flow is linearly stable by the MilesHoward theorem.

Monday, November 19, 2018 11:14AM  11:27AM 
G25.00004: Frequency predictions from global stability in the Benard vortex street Jose Eduardo Wesfreid, Yacine Bengana In 1908, Henri Bénard published the results of his experiments performed in LyonFrance on the discovery of an alternate vortex street when a body of prismatic shape is displaced in a fluid at rest. Using optical methods and cinematography, Bénard obtained the value of the frequency of the vortex shedding for this bluff body, with different sizes, velocities of the body and viscosities of the fluid. The comparison of this results (in modern terms, the variation of the Strouhal number with the Reynolds number) with similar ones obtained after, with a cylinder, by Karman and Rubach (1912), Kruger (1914), Relf (1921) and Camichel (1927), provided, in the 30’s, discussions. In this talk, we are presenting for the first time, more than a century later, quantitative predictions of the Strouhal number evolution for the geometry used in the pioneering experiments of Bénard. Global linear stability study is applied using the time averaged or mean base flow behind this prismatic body. We are comparing these predictions with the original experimental results. Similar comparisons are presented for the case of the vortex shedding from cylinders observed in many historical experiments beginning with Strouhal’ ones in 1878. 
Monday, November 19, 2018 11:27AM  11:40AM 
G25.00005: Spatiotemporal Linear Stability Analysis of Reacting Wake Systems Jacob Sebastian, Benjamin Emerson, Timothy C Lieuwen Large scale coherent flow structures, ensuing from the hydrodynamic stability characteristics, play a controlling role in several combustion phenomena, such as combustion instability, mixing and entrainment and blowoff. Hydrodynamic stability characteristics of multibluff body systems is significantly different in comparison with that of single bluff body systems. The confined wake system, through the method of images, represents an infinite wake system with an imposed symmetry (sinuous or varicose) at the wakewake interface. The objective of the work is to compare the stability characteristics of the infinitewake system with the confined wake system. Presence of an additional element destabilizes the system. The stability characteristics of the multiwake system converge onto the behavior of the confined wake system in the asymptotic limit of infinite wake system. Further, the study utilizes the resonant wave interaction[Juniper, J. Fluid Mech., 565, 171195 (2006)] as a theoretical model to predict the behavior of the multiwake systems. The model predicts the critical L/D, which correspond to the maximum destabilization of the multiwake system, accurately for parametric ranges when the system is absolutely stable. 
Monday, November 19, 2018 11:40AM  11:53AM 
G25.00006: On the critical spacing of stationary tandem circular cylinders Wenchao Yang, Mark A. Stremler For steady flow past two stationary circular cylinders that are aligned in tandem with their axes perpendicular to the flow direction, the wake pattern, vortex shedding frequency, and forces on the cylinders typically show an abrupt change as a function of the dimensionless centertocenter cylinder spacing over a range of critical spacing values. This fundamental problem has been studied for over a century, but knowledge gaps remain and published results are inconsistent. For Re<190, the flow is expected to be laminar and two dimensional, and hence well behaved, yet prior experimental and computational results do not agree regarding the value of the critical spacing. Using flow visualization techniques in a flowing soap film system with Re=100, we have obtained, apparently for the first time, experimental results that are consistent with published computational results. We will discuss the physical characteristics of this flow, particularly the hysteresis that occurs in the value of the critical spacing as a function of the initial conditions. 
Monday, November 19, 2018 11:53AM  12:06PM 
G25.00007: Effect of Reynolds number on the separatedreattached flow upstream of a fence Supun Pieris, Burak Ahmet Tuna, Serhiy Yarusevych, Sean D. Peterson The flow development upstream of a rigid fence is investigated experimentally for three Reynolds numbers 18 000, 36 000, and 54 000. Timeresolved, planar particle image velocimetry is used to capture the instantaneous velocity fields with high spatiotemporal resolution in key areas, while smoke wire flow visualization is used to obtain a global description of the flow. The results reveal a complex separatingreattaching flow region two to three fence heights upstream of the fence. In addition to a local flow separation in the immediate vicinity of the fence, a laminar separation bubble is formed upstream and its mean extent decreases with increasing Reynolds number. Coherent structures are shed from the upstream separation region significantly affecting flow development downstream and exhibiting a strong dependence on the Reynolds number. 
Monday, November 19, 2018 12:06PM  12:19PM 
G25.00008: The effect of wall motion on the velocity field inside a flexible tube with a pulsatile flow. Oleg Goushcha, Daniel Saporito, Frank J Raguso Internal pulsatile flows exhibit a cyclic behavior of the mean axial velocity. These flows appear in many industrial and natural applications. Of particular interest is a pulsatile flow inside a cardiovascular system where fluid is driven by periodic cardiac pressure. To mimic this flow in an elastic aorta, an experimental setup has been assembled consisting of a pistoncylinder assembly connected to a flexible silicone tube. The amplitude of cyclic pressure was varied by adjusting piston’s maximum speed. The wall of the tube expanded and contracted under the force exerted by the fluid. TimeResolved Particle Image Velocimetry (TRPIV) technique was used to acquire velocity data on the plane of a CW laser illumination sheet to observe the effect of wall motion on the flow. In the case of lowpressure amplitude, walls were nearly stationary, resulting in a velocity field similar to that observed in rigid tubes. For larger pressure amplitude, resulting in a noticeable wall motion, the formation vortical structures were observed in the velocity field. These vortical structures were responsible for large instantaneous velocity fluctuations even for relatively small wall motion. 
Monday, November 19, 2018 12:19PM  12:32PM 
G25.00009: Transition in Pulsatile Flows: The Role of Pressure Field Joan Gomez, Oleg Goushcha, Yiannis Andreopoulos Pulsatile flows are of interest because for certain range of characteristic nondimensional parameters, they display laminar and turbulent behavior at different times of the pulsating cycle. Addressing how turbulence appears, decays and is suppressed is challenging due to the flow unsteadiness and flowwall interactions. An experiment was setup to replicate pulsatile motion of water in a clear, rigid pipe. The flow is driven by a pistonmotor assembly controlled by a computer to induce cyclic motion of the mean flow. TimeResolved Particle Image Velocimetry (TRPIV) techniques are used to acquire velocity data on the plane of a CW laser illumination sheet. Pressure sensors were installed along the length of the pipe to monitor the flow and its variation during the transition process. Depending on the Reynolds number the hydrostatic pressure difference along the vertical diameter of the pipe causes the velocity profile to become asymmetric. Timedependent activities related to transition and turbulence in the near wall are highly asymmetric. 
Monday, November 19, 2018 12:32PM  12:45PM 
G25.00010: Transition mechanisms of pulsatile flow in a constricted channel João Anderson Isler, Rafael S Gioria, Bruno Souza Carmo Physical mechanisms based on the energy variation of twodimensional modes are proposed for a pulsatile flow in a constricted channel with 50% occlusion. Floquet stability analysis and direct numerical simulations are carried out to explain the transition mechanisms observed in this system. This system is characterized by two distinct states; the first state lies in a twodimensional space and the second in a threedimensional space. When a threedimensional nonlinear simulation is seeded with a twodimensional base flow and an infinitesimal perturbation, there is energy transfer from the threedimensional modes to the twodimensional mode, such that the energy of the latter slightly increases and the threedimensional modes go to zero, leading the system to its unconstrained state. In addition, the base flow behaviour follows the energy variation of the twodimensional modes with Reynolds number. Thus, base flow changes occur when the Reynolds number is increased, even after the primary instability. Besides that, the twodimensional modes go through an energy minimum in this process which lead the system to a different dynamic. 
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