Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session G38: Flow Instability: Nonlinear Dynamics |
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Chair: Qiqi Wang, Massachusetts Institute of Technology Room: Portland Ballroom 255 |
Monday, November 21, 2016 8:00AM - 8:13AM |
G38.00001: Lyapunov Exponents and Covariant Vectors for Turbulent Flow Simulations Patrick Blonigan, Scott Murman, Pablo Fernandez, Qiqi Wang As computational power increases, engineers are beginning to use scale-resolving turbulent flow simulations for applications in which jets, wakes, and separation dominate. However, the chaotic dynamics exhibited by scale-resolving simulations poses problems for the conventional sensitivity analysis and stability analysis approaches that are vital for design and control. Lyapunov analysis is used to study the chaotic behavior of dynamical systems, including flow simulations. Lyapunov exponents are the growth or a decay rate of specific flow field perturbations called the Lyapunov covariant vectors. Recently, the authors have used Lyapunov analysis to study the breakdown in conventional sensitivity analysis and the cost of new shadowing-based sensitivity analysis [1]. The current work reviews Lyapunov analysis and presents new results for a DNS of turbulent channel flow, wall-modeled channel flow, and a DNS of a low pressure turbine blade. Additionally, the implications of these Lyapunov analyses for computing sensitivities of these flow simulations will be discussed. \\ \noindent [1] Q. Wang, R. Hui, and P. Blonigan. Least squares shadowing sensitivity analysis of chaotic limit cycle oscillations. Journal of Computational Physics, 267:210–224, June 2014. [Preview Abstract] |
Monday, November 21, 2016 8:13AM - 8:26AM |
G38.00002: Stability of Couette flow past a viscoelastic solid Andrew Hess, Tong Gao Soft materials such as polymer gels have been widely used in engineering applications such as microfluidics, micro-optics, and active surfaces. It is important to obtain fundamental understandings of the dynamics of various soft materials when interacting with fluid. Here we investigate the material behavior of a viscoelastic solid film immersed in a simple Newtonian Couette flow. An Eulerian formulation of the Zener model is used to model the solid phase with the surface tension effect. A linear stability analysis is first performed to predict the material instabilities induced by the shear flow field, and provide an analytical basis to the numerical results. The nonlinear fluid/elastic structure interactions are further explored by using the direct numerical simulations. Phase tracking is accomplished through the use of a generalized Cahn-Hilliard model for the surface tension between the gel-like material and the ambient fluid. The coupled Cahn-Hilliard/Navier-Stokes/Zener equations are then solved on a staggered grid through a finite difference method. The results are compared with previous studies for both the hyperelastic and viscoelastic materials. [Preview Abstract] |
Monday, November 21, 2016 8:26AM - 8:39AM |
G38.00003: Lyapunov exponents, covariant vectors and shadowing sensitivity analysis of 3D wakes: from laminar to chaotic regimes Qiqi Wang, Georgios Rigas, Lucas Esclapez, Luca Magri, Patrick Blonigan Bluff body flows are of fundamental importance to many engineering applications involving massive flow separation and in particular the transport industry. Coherent flow structures emanating in the wake of three-dimensional bluff bodies, such as cars, trucks and lorries, are directly linked to increased aerodynamic drag, noise and structural fatigue.?For low Reynolds laminar and transitional regimes, hydrodynamic stability theory~has aided the understanding and prediction of the unstable dynamics.~In the same framework, sensitivity analysis provides the means for efficient and optimal control, provided the unstable modes can be accurately~predicted. ?However, these methodologies are limited to laminar regimes where only a few unstable modes manifest. Here we extend the stability analysis to low-dimensional chaotic regimes by computing the Lyapunov covariant vectors and their associated Lyapunov exponents. We compare them to eigenvectors and eigenvalues computed in traditional hydrodynamic stability analysis. Computing Lyapunov covariant vectors and Lyapunov exponents also enables the extension of sensitivity analysis to chaotic flows via the shadowing method. We compare the computed shadowing sensitivities to traditional sensitivity analysis. These~Lyapunov~based methodologies do not rely on mean flow assumptions, and are mathematically rigorous for calculating sensitivities of fully unsteady flow simulations. [Preview Abstract] |
Monday, November 21, 2016 8:39AM - 8:52AM |
G38.00004: Tangent double Hopf bifurcation in a counter-rotating split cylinder Paloma Gutierrez-Castillo, Juna M. Lopez A tangent double Hopf bifurcation has been found in the flow in a counter-rotating cylinder split at its mid-plane. The cylinder of radius $a$ and length $h$ is completely filled with fluid of kinematic viscosity $\nu$. Both halves rotate with the same angular speed $\omega$, but in opposite directions. The flow, which is solved numerically via spectral methods, is dominated by the shear layer between both halves of the cylinder. For sufficiently small $\textit{Re}=\omega a^2/\nu$, the basic state, which is axisymmetry, reflection symmetric and steady, is stable. A range of aspect ratios $\Gamma=h/a$ were studied, with $\Gamma\in[0.5,2]$. The basic state loses stability via a number of different Hopf bifurcations breaking axisymmetry, leading to waves with different azimuthal wavenumbers. For $\Gamma\in[1.3,1.76]$, there is a double Hopf bifurcation of waves with $m=2$ and $m=3$. This bifurcation divides $(\Gamma,\textit{Re})$ space into 6 different regions, some of which include multiple stable states due to the nonlinearities of the problem. The states in the various regions are very well described by the normal form dynamics of the bifurcation, which we use to gain deeper insights into the complicated dynamics created by the nonlinear competition between the various states. [Preview Abstract] |
Monday, November 21, 2016 8:52AM - 9:05AM |
G38.00005: Extension to nonlinear stability theory of the circular Couette flow pun wong yau, Shixiao Wang, Zvi Rusak A nonlinear stability analysis of the viscous circular Couette flow to axisymmetric perturbations under axial periodic boundary conditions is developed. The analysis is based on investigating the properties of a reduced Arnol'd energy-Casimir function $\mathscr{A}_{rd}$ of Wang (2009). We show that all the inviscid flow effects as well as all the viscous-dependent terms related to the flow boundaries vanish. The evolution of $\Delta \mathscr{A}_{rd}$ depends solely on the viscous effects of the perturbation's dynamics inside the flow domain. The requirement for the temporal decay of $\Delta \mathscr{A}_{rd}$ leads to novel sufficient conditions for the nonlinear stability of the circular Couette flow in response to axisymmetric perturbations. Comparisons with historical studies show that our results shed light on the experimental measurements of Wendt (1933) and significantly extend the classical nonlinear stability results of Serrin (1959) and Joseph \& Hung (1971). When the flow is nonlinearly stable and evolves axisymmetrically for all time, then it always decays asymptotically in time to the circular Couette flow determined uniquely by the setup of the rotating cylinders. This study provides new physical insights into a classical flow problem that was studied for decades. [Preview Abstract] |
Monday, November 21, 2016 9:05AM - 9:18AM |
G38.00006: Nonlinear Pattern Selection in Bi-Modal Interfacial Instabilities Jason Picardo, Ranga Narayanan We study the evolution of two interacting unstable interfaces, with the aim of understanding the role of non-linearity in pattern selection. Specifically, we consider two superposed thin films on a heated surface, that are susceptible to thermocapillary and Rayleigh-Taylor instabilities. Due to the presence of two unstable interfaces, the dispersion curve (linear growth rate plotted as a function of the perturbation wavelength) exhibits two peaks. If these peaks have equal heights, then the two corresponding disturbance patterns will grow with the same linear growth rate. Therefore, any selection between the two must occur via nonlinear effects. The two-interface problem under consideration provides a variety of such bi-modal situations, in which the role of nonlinearity in pattern selection is unveiled. We use a combination of long wave asymptotics, numerical simulations and amplitude expansions to understand the subtle nonlinear interactions between the two peak modes. Our results offer a counter-example to Rayleigh’s principle of pattern formation, that the fastest growing linear mode will dominate the final pattern. Far from being governed by any such general dogma, the final selected pattern varies considerably from case to case. [Preview Abstract] |
Monday, November 21, 2016 9:18AM - 9:31AM |
G38.00007: A recurrence network approach to analyzing forced synchronization in hydrodynamic systems Meenatchidevi Murugesan, Yuanhang Zhu, Larry K.B. Li Hydrodynamically self-excited systems can lock into external forcing, but their lock-in boundaries and the specific bifurcations through which they lock in can be difficult to detect. We propose using recurrence networks to analyze forced synchronization in a hydrodynamic system: a low-density jet. We find that as the jet bifurcates from periodicity (unforced) to quasiperiodicity (weak forcing) and then to lock-in (strong forcing), its recurrence network changes from a regular distribution of links between nodes (unforced) to a disordered topology (weak forcing) and then to a regular distribution again at lock-in (strong forcing). The emergence of order at lock-in can be either smooth or abrupt depending on the specific lock-in route taken. Furthermore, we find that before lock-in, the probability distribution of links in the network is a function of the characteristic scales of the system, which can be quantified with network measures and used to estimate the proximity to the lock-in boundaries. This study shows that recurrence networks can be used (i) to detect lock-in, (ii) to distinguish between different routes to lock-in, and (iii) as an early warning indicator of the proximity of a system to its lock-in boundaries. [Preview Abstract] |
Monday, November 21, 2016 9:31AM - 9:44AM |
G38.00008: Unravelling the mechanism behind Swirl-Switching in turbulent bent pipes Philipp Schlatter, Lorenz Hufnagel, Jacopo Canton, Ramis \"{O}rl\"{u}, Oana Marin, Elia Merzari Turbulent flow through pipe bends has been extensively studied, but several phenomena still miss an exhaustive explanation. Due to centrifugal forces, the fluid flowing through a curved pipe forms two symmetric, counter-rotating Dean vortices. It has been observed, experimentally and numerically, that these vortices change their size, intensity and axis in a periodic, oscillatory fashion, a phenomenon known as swirl-switching. These oscillations are responsible for failure due to fatigue in pipes, and their origin has been attributed to a recirculation bubble, disturbances coming from the upstream straight section and others. The present study tackles the problem by direct numerical simulations (DNS) analysed, for the first time, with three-dimensional proper orthogonal decomposition (POD) as to distinguish between the spatial and temporal contributions. The simulations are performed at a friction Reynolds number of about 360 with a divergence-free synthetic turbulence inflow, as to avoid the interference of low-frequency oscillations generated by a standard recycling method. Results indicate that a single low-frequency, three-dimensional POD mode, representing a travelling wave, and previously mistaken by 2D POD for two different modes, is responsible for the swirl-switching. [Preview Abstract] |
Monday, November 21, 2016 9:44AM - 9:57AM |
G38.00009: Homoclinic snaking in plane Couette flow: bending, skewing, and finite-size effects John Gibson, Tobias Schneider Invariant solutions of shear flows have recently been extended from spatially periodic solutions in minimal flow units to spatially localized solutions on extended domains. One set of spanwise-localized solutions of plane Couette flow exhibits homoclinic snaking, a process by which steady-state solutions grow additional structure smoothly at their fronts when continued parametrically. In this talk, we present a numerical study of the snaking solutions, generalizing beyond the fixed streamwise wavelength of previous studies. We find a number of new solution features, including bending, skewing, and finite-size effects. We establish the parameter regions over which snaking occurs and show that the finite-size effects of the traveling-wave solution are due to a coupling between its fronts and interior that results from its shift-reflect symmetry. A new winding solution of plane Couette flow is derived from a strongly-skewed localized equilibrium. [Preview Abstract] |
Monday, November 21, 2016 9:57AM - 10:10AM |
G38.00010: Dampening the asymmetric instability in pipe flow of shear thinning fluids using elasticity David Dennis, Chaofan Wen, Robert Poole Recent experimental results have shown that the asymmetric flow of shear-thinning fluid through a cylindrical pipe, which was previously associated with the laminar-turbulent transition process, is actually a non-hysteretic and reversible, supercritical instability of the laminar base state. These experiments were performed using largely inelastic shear-thinning fluids (aqueous solutions of xanthan gum) and it was found that the greater the degree of shear-thinning the larger the magnitude of the asymmetry. In this talk we show that a viscoelastic fluid (an aqueous solution of high molecular weight polyacrylamide), with approximately the same shear-thinning characteristics as the inelastic fluid, does not exhibit the asymmetry when freshly mixed. However, once the elasticity of this fluid is degraded (by prolonged shearing) the asymmetry reappears. This suggests that the shear-thinning nature of the fluid causes the instability and the viscoelastic nature works to dampen the asymmetry. To test this hypothesis we add varyingly small amounts of polyacrylamide to xanthan gum solutions and find an inverse relationship between viscoelasticity and the magnitude of the asymmetry, although the Reynolds number at which the instability is first observed stays approximately constant. [Preview Abstract] |
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