Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session M11: Instability: General |
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Chair: Malcolm Andrews, Texas A&M University Room: 3007 |
Tuesday, November 25, 2014 8:00AM - 8:13AM |
M11.00001: Encapsulated formulation of the selective frequency damping method Bastien Jordi, Colin Cotter, Spencer Sherwin We present an alternative ``encapsulated'' formulation of the selective frequency damping (SFD) method. This (time-discrete) formulation makes use of splitting methods, which means that it can be wrapped around an existing time-stepping code as a ``black box.'' Hence the implementation of a steady-state solver is very easy because the existing unsteady solver does not need to be modified. It is simply called each time-step and a linear operator (modelling a feedback control and a low-pass time filter) is applied to its outcome. The method is first applied to a scalar problem in order to analyse its stability and highlight the roles of the control coefficient and the filter width in the convergence (or not) towards the steady-state. Then we show that by knowing the most unstable eigenmode of a fluid flow, we can guarantee convergence of the SFD method towards the steady-state solution. Finally, we discuss the possibility of coupling the SFD method with an Arnoldi method. The goal is to approximate the eigenmodes of an unstable flow and then to adjust the parameters of the SFD method to ensure convergence towards the steady-state. We are currently using this approach to obtain a steady-state solution of co-rotating Batchelor vortices and we present our latest results. [Preview Abstract] |
Tuesday, November 25, 2014 8:13AM - 8:26AM |
M11.00002: Stability Results on Multi-Layer Radial Hele-Shaw Flows with Variable Viscosity Craig Gin, Prabir Daripa Saffman-Taylor instability, which occurs when a less viscous fluid drives a more viscous fluid, has been studied for many years and has a wide range of applications. In particular, an understanding of this phenomenon is helpful in the attempt to maximize the effectiveness of chemically enhanced oil recovery techniques. We study this instability through linear stability analysis of three-layer radial Hele-Shaw flows of immiscible fluids in which the middle layer consists of a variable viscosity fluid. We study the growth rate of instabilities both numerically and analytically, including the derivation of upper bounds. We also connect this problem to the related cases of variable viscosity rectilinear flows and constant viscosity radial flows. We attempt to extend this work to an arbitrary number of fluid layers. [Preview Abstract] |
Tuesday, November 25, 2014 8:26AM - 8:39AM |
M11.00003: Unsteady regimes in a T-mixer Maria Vittoria Salvetti, Simone Camarri, Andrea Fani Micro T-mixers are devices aimed at providing efficient mixing. Most of the studies in the literature focused on the steady engulfment regime, characterized by a loss of the flow symmetries in the outflow channel which leads to a considerable increase of the mixing efficiency. Unsteady regimes were recently observed for Reynolds numbers (Re) larger than the steady engulfment critical value. We investigated these regimes for a given T-mixer configuration through direct numerical simulations. A first unsteady regime appears, in which the flow remains asymmetric in the mean but becomes periodic in time. As Re is further increased, the flow remains time-periodic but it continuously switches between a symmetric configuration and an asymmetric one. Three-dimensional linear stability and sensitivity analyses are also used to characterize the instability leading to the unsteady asymmetric regime (UAR), which is interesting for applications due to its high mixing efficiency. The largest sensitivity was observed to base-flow modifications introduced close to the 3D vortical structures forming at the confluence between the inlet channels. Finally, it is found that for a flat inlet velocity profile the UAR onset is delayed at larger Re than for a fully developed profile. [Preview Abstract] |
Tuesday, November 25, 2014 8:39AM - 8:52AM |
M11.00004: Stability theory for the synchronized waving of marine grass Ravi Singh, Amala Mahadevan, Shreyas Mandre, L.M. Mahadevan Synchronized waving of grass blades in the presence of fluid flow has been observed in cases such as wheat field in wind, marine grass in tidal currents. The synchronous motion can have important environmental and ecological impact via mixing of fluid due to waving. When the hydrodynamic and elastic time scales are well separated, this waving is thought to be due to Kelvin-Helmholtz instability resulting from an inflection point in the flow profile. We find that the inflection point is located near the tip of grass canopy. We extend the Orr-Sommerfeld equation for the stability of a shear flow to include a continuum mean-field approximation for the vegetation, thus capturing the essential ingredients for flow instability leading to coherent waving. Our linear stability analysis shows that the flow in presence of grass become unstable not only through a mechanism of Kelvin-Helmholtz instability but also through shear instability of flow above grass. We also find that flow with low submergence ratio of grass becomes unstable due to Kelvin-Helmholtz instability whereas flow high submergence ratio becomes unstable due to shear instability of flow above the grass. Numerical results demonstrating these instability mechanism will also be presented. [Preview Abstract] |
Tuesday, November 25, 2014 8:52AM - 9:05AM |
M11.00005: Hydrodynamic Stability Analysis on Sheared Stratified Flow in a Convective Flow Environment Yuan Xiao, Wenxian Lin, Steven Armfiled, Michael Kirkpatrick, Yinghe He A hydrodynamic stability analysis on the convective sheared boundary layer (SCBL) flow, where a sheared stratified flow and a thermally convective flow coexist, is carried out in this study. The linear unstable stratifications representing the convective flow are included in the TaylorGoldstein equations as an unstable factor Jb. A new unstable region corresponding to the convective instability, which is not present in pure sheared stratified flows, is found with the analysis. It is also found that the boundaries of the convective instability regions expand with increasing Jb and interact with the sheared stratified instability region. More results will be presented at the conference [Preview Abstract] |
Tuesday, November 25, 2014 9:05AM - 9:18AM |
M11.00006: Study of spatial growth of disturbances in an Incompressible Double Shear Layer flow configuration Hareshram Natarajan, Gustaaf Jacobs The spatial growth of disturbance within the linear instability regime in an incompressible 2D double shear layer flow configuration is studied by performing a Direct Numerical Simulation. The motivation of this study is to characterize the effect of the presence of an additional shear layer on the spatial growth of a shear layer instability. Initially, a DNS of an incompressible single shear layer is performed and the spatial growth rate of various disturbance frequency modes are validated with Linear Stability Analysis. The addtional shear layer is found to impact the spatial growth rates of the different disturbances and the frequency of the mode with the maximum growth rate is found to be shifted. [Preview Abstract] |
Tuesday, November 25, 2014 9:18AM - 9:31AM |
M11.00007: Stability of a rolling fluid filled cylinder Rohit Supekar, Mahesh Panchagnula We present an analytical solution to the problem of a fluid filled hollow cylindrical shell rolling on an inclined plane and then investigate the temporal stability of the system using linear stability analysis. We study the motion in two dimensions by analyzing the interaction between the fluid and the hollow cylinder. We show that the terminal state is associated with a constant acceleration, similar to a rigid body motion. Surprisingly, it is independent of the liquid viscosity and only depends on the ratio of the mass of the shell to the mass of the fluid contained (say, $\pi _{\mathrm{m}})$. We analyze this base flow for its stability behavior using the frozen-time approximation. In this approach, we treat time as a parameter, the evolution of which causes the flow to transition from a stable to an unstable state. The point of neutral stability is noted and the spatial modes that show the maximum growth rate are analyzed. It was observed that instability sets in due to long wavelength axial waves, which are transverse to the flow direction. We find a critical Reynolds number based on the time to instability, above which the flow becomes unstable. Again, this Reynolds number appears to be only a function of $\pi _{\mathrm{m}}$. [Preview Abstract] |
Tuesday, November 25, 2014 9:31AM - 9:44AM |
M11.00008: Stability study of flows around an airfoil based on energy gradient method Jade Junqua, Hua-Shu Dou Numerical simulation is carried out to study the turbulent flow around an airfoil and the energy gradient theory is used to analyze the stability of the flow. The governing equations are the Reynolds averaged Navier-Stokes equations for compressible flow and the k-epsilon turbulent model is used to close the system. The finite volume method and the time marching scheme are used to solve the unsteady governing equations. The simulation and calculation have been completed for various attack angle of the airfoil, from 0 and 8 degree. The Reynolds number is about 3.5X10**6 for all situations, and the Mach number is about 0.15. The flow is considered as shear driven flow and the distribution of the energy gradient function K around the airfoil is calculated with the simulation data. The results shows good agreement between the distribution of the energy gradient function and the experimental observations in regard of the turbulent intensity, while there is little relation between the distribution of the vorticity and the turbulent intensity. It is concluded that energy gradient function dominates the flow stability and the sustenance of turbulence rather than the magnitude of vorticity. [Preview Abstract] |
Tuesday, November 25, 2014 9:44AM - 9:57AM |
M11.00009: A straightforward characterization of non-modal effects from the evolution of linear dynamical systems Cristobal Arratia A simple construction will be shown, which reveals a general property satisfied by the evolution in time of a state vector composed by a superposition of orthogonal eigenmodes of a linear dynamical system. This property results from the conservation of the inner product between such state vectors evolving forward and backwards in time, and it can be simply evaluated from the state vector and its first and second time derivatives. This provides an efficient way to characterize, instantaneously along any specific phase-space trajectory of the linear system, the relevance of the non-normality of the linearized Navier-Stokes operator on the energy (or any other norm) gain or decay of small perturbations. Examples of this characterization applied to stationary or time dependent base flows will be shown. [Preview Abstract] |
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