Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session H33: Flow Instability: Nonlinear Dynamics |
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Chair: Thomas Ward, Iowa State University Room: 615 |
Monday, November 25, 2019 8:00AM - 8:13AM |
H33.00001: Linear stability analysis of a miscible two-layer power-law fluid in Couette flow Thomas Ward, Tejaswi Soori We examine the stability of a miscible two-layer power-law fluid in a 2D shear flow. The problem is motivated by recent experiments showing that miscible displacement of shear-thinning fluids yields an instability. To study fluid stability we analyze the mass, momentum and species conservation equations in a Couette flow geometry. Layer depth, consistency and power-law index are varied for zero wall slip conditions. We also examine the interface by treating the two-layer problem as a two-fluid one with zero surface tension. The governing equations are linearized about base states to estimate growth rates for dependent variables in the limit of infinitesimally small disturbances. We integrate the resulting ODE equations using a standard Chebyshev collocation method. We also compare results with prior ones for two-fluid layer and miscible two-layer problems, along with critical values observed in experiments. [Preview Abstract] |
Monday, November 25, 2019 8:13AM - 8:26AM |
H33.00002: Exploiting noise-induced dynamics for system identification near a Hopf bifurcation Minwoo Lee, Yuanhang Zhu, Yu Guan, Larry K.B. Li, Vikrant Gupta We propose a system identification framework that exploits the noise-induced dynamics inherent to nonlinear systems near a supercritical or subcritical Hopf bifurcation. The key assumption made is that the system response can be modeled with a Stuart--Landau equation and its corresponding Fokker--Planck equation. We demonstrate the framework on two different flow systems: a hydrodynamic system (a low-density jet) undergoing a subcritical Hopf bifurcation, and a thermoacoustic system (a Rijke tube) undergoing a supercritical Hopf bifurcation. For both systems, we extract the model coefficients using experimental measurements of the noise-induced dynamics in only the unconditionally stable regime, prior to both the Hopf and saddle-node points. We show that the framework can accurately predict (i) the order of nonlinearity, (ii) the types and locations of the bifurcation points, and (iii) the limit-cycle characteristics beyond such points. As the noise-induced dynamics of nonlinear systems are expected to be universal in the vicinity of a Hopf bifurcation (Ushakov et al. 2005, Phys. Rev. Lett., vol. 95, 123903), the proposed framework should be applicable to a variety of flow systems in nature and engineering. [Preview Abstract] |
Monday, November 25, 2019 8:26AM - 8:39AM |
H33.00003: The Role of Cubic Nonlinearity in Limit Cycle Oscillations of Variable-Density Shear Flows Christopher Douglas, Benjamin Emerson, Timothy Lieuwen This work is directed toward understanding the limit cycle features of globally unstable flows with variable density. Analysis of limit cycles in constant-density shear flows have revealed that oscillation characteristics are controlled by two key effects: mean flow distortions and harmonic interactions. Both of these effects are manifestations of the quadratic nonlinearity of the incompressible Navier-Stokes equations, and their respective roles vary in different flow configurations. However, in flows such as bluff body wakes, surprisingly accurate predictions of important limit cycle features such as frequency and amplitude are possible by neglecting the latter effect and performing a linear analysis about the mean flow. Crucially, even when its amplitude is not small, the quadratic nonlinearity does not allow the limit cycle fundamental to directly modify itself. Conversely, when the fluid density is not constant, a cubic nonlinearity arises and enables self-interactions which are independent from the other effects. This calls into question the validity of linear approaches in such contexts and motivates an investigation of the role of these triadic self-interactions in variable-density shear flows. [Preview Abstract] |
Monday, November 25, 2019 8:39AM - 8:52AM |
H33.00004: Nonlinear Fluid Flow Analysis Using Integral Quadratic Constraints Aniketh Kalur, Peter J. Seiler, Maziar S. Hemati The exact mechanism for sub-critical transition to turbulence in shear flows is complicated and not fully understood due to the interaction between the linear and nonlinear terms in the Navier-Stokes equations (NSE). The linear operator in NSE causes a transient amplification of perturbation energy -- a necessary condition for sub-critical transition. The nonlinearity in NSE acts in feedback with the linear system and mixes energy between modes. This static lossless nonlinearity is responsible for triggering transition and sustaining turbulence. In this talk, we will show that the nonlinearity in NSE can be replaced by a set of integral quadratic constraints (IQCs), which effectively represent correlations between the inputs and outputs of the nonlinearity. Thus, analysis of nonlinear flows can be cast as problems in the analysis of linear dynamics -- coupling energy-based methods with corresponding IQCs. We perform our investigations on the Waleffe-Kim-Hamilton (WKH) model, which is a low-dimensional mechanistic model developed to capture the physics of transition. IQC-based stability and performance analysis of the WKH model will be presented. [Preview Abstract] |
Monday, November 25, 2019 8:52AM - 9:05AM |
H33.00005: Effects of entry shapes on evolution and transition mechanisms of internal swirling flows Xingjian Wang, Yanxing Wang Previous works have investigated the characteristics of the central recirculation zone and intrinsic instability waves of a swirling flow injected through a tangential slit entry. In practice, orifice entry is frequently used to generate the swirling motion in a cylindrical chamber, but is much less documented. In this study, we numerically explore flow evolution and transition mechanisms of internal swirling flow with orifice entry using Galerkin finite element method. A grid convergence study is conducted to ensure the appropriate grid resolution at the orifice entry and in regions with complex flow structures. The effects of Reynolds number and swirl level controlled by the orifice angle are examined in detail. The numerical results of tangential slit and orifice entries will be compared systematically in terms of flow topologies and underlying instability mechanisms. A unified theory connecting different flow states of swirling flow will be established. [Preview Abstract] |
Monday, November 25, 2019 9:05AM - 9:18AM |
H33.00006: On slow--fast generalized quasilinear dynamical systems Greg Chini, Alessia Ferraro, Guillaume Michel, Colm-cille Caulfield The quasilinear (QL) reduction has proved surprisingly useful in the analysis and modeling of anisotropic turbulent flows. As first introduced in the context of fluid turbulence by Stuart (1958), the QL approximation involves parsing flow variables into suitable (e.g., streamwise) mean and fluctuation fields and then retaining fluctuation-fluctuation nonlinearities only where they feed back onto the mean fields through Reynolds stress divergences. Although increasingly invoked as a useful albeit \emph{ad hoc} approximation, the QL reduction can be formally justified in the asymptotic limit of temporal scale separation between the mean and fluctuation dynamics, as arises, e.g., in the asymptotic description of strongly stratified shear turbulence and of certain exact coherent states in wall-bounded shear flows. A fundamental and vexing feature of such systems, however, is that when the slow mean fields are locally frozen in time, the fast linearized dynamics can admit exponential fluctuation growth. In this work, a new multiscale formalism is introduced that obviates the need to co-evolve the mean and fluctuation dynamics on the fast time scale (i.e., the usual fix) by exploiting the necessity of slow--fast QL systems to self-tune toward a marginal-stability manifold. [Preview Abstract] |
Monday, November 25, 2019 9:18AM - 9:31AM |
H33.00007: Stability of Flow past a Freely-Rotatable Sprung Cylinder. Ke Ding, Arne Pearlstein Recent work (Tumkur \textit{et al.}, \textit{J. Fluid }Mech. \textbf{828}, 196-235, 2017; Blanchard \textit{et al.}, \textit{Phys. Rev. Fluids}, \textbf{4}, 054401, 2019) considers flow past a linearly-sprung circular cylinder whose transverse rectilinear motion is inertially coupled to linearly-damped rotational motion of an attached mass about the cylinder axis. (The rotating mass is either inside the cylinder or beyond the span of the flow, thus having no contact with the fluid.) That work reveals chaotic response at Reynolds numbers (\textit{Re}) well below the fixed-cylinder critical value \textit{Re}$_{fixed,c}$, and multiple unsteady long-time solutions for many combinations of the parameters. Here, we consider flow past a linearly-sprung circular cylinder with a nonaxisymmetric density distribution, which is free to rotate, and whose rotational motion is linearly damped. As for the case where the cylinder cannot rotate, a steady, symmetric, motionless-cylinder (SSMC) solution exists for all values of the parameters and all density distributions and orientations. We use a spectral-element technique to investigate the stability boundary in the space of \textit{Re} and spring stiffness, and find that over a limited stiffness range, rotatability renders the SSMC solution stable for \textit{Re }\textgreater \textit{Re}$_{fixed,c}$. We also show that stability boundaries for different (initial) orientations of the density distribution are very similar to those for different (initial) orientations of an attached mass, suggesting that much of the complex dynamical behavior in the attached-mass case can be realized using a cylinder with nonuniform density, with no attached mass. [Preview Abstract] |
Monday, November 25, 2019 9:31AM - 9:44AM |
H33.00008: Effect of electric field on the linear stability characteristics of two-layer channel of Newtonian and Herschel-Bulkley fluids Gautam Kumar, Puranam Ananth L Narayana, Kirti Sahu We investigate the effect of electric field on the linear stability characteristics of pressure-driven flow in a channel, wherein a Newtonian fluid layer superposed on a layer of Herschel-Bulkley fluid. Both fluids are assumed to be incompressible and leaky dielectric media. The modified Orr-Sommerfeld eigenvalue equations are derived and solved using an efficient spectral collocation method. An asymptotic analysis is also performed in the long-wave limit. The effects of electric field, Bingham number, flow index and the ratios of density, viscosity, electrical conductivity and permittivity between the fluids are studied. We observed that the electric field can stabilize or destabilize the systems in different regimes. [Preview Abstract] |
Monday, November 25, 2019 9:44AM - 9:57AM |
H33.00009: Genesis of Taylor--Couette Flow Instabilities H. Oualli, M. Mekadem, M. Khirennas, Y. Rezga, S. Tebtab, T. Azzam, A. Bouabdallah, M. Gad-El-Hak Numerical simulations are conducted of a Taylor--Couette flow from early structuring stages to completion of the Taylor’s axial stationary waves. We seek to elucidate the underlying mechanisms responsible for the genesis of this flow type and to identify the intermediate embryonic stages up to the birth and completion of the Taylor’s axial stationary vortices. A 3D numerical simulations of liquid benzene are implemented on FLUENT. The calculations are based on the finite-volume method with a mesh size of 32$\times$28$\times$256 in, respectively, the radial, azimuthal, and axial directions. The simulations are validated using prior experimental results. The calculations span Taylor numbers from $Ta = 10^9$ to $Ta = 43.8$. The results show that the incipient pressure variations are of the order of $10^{12}$ Pa, detected at $Ta = 10^9$, on four symmetrically separated cardinal points within the system. When $Ta > 10^9$, a progressive propagation of alternating overpressure and depression zones operate in both azimuthal directions. This is the first step in the chain of mechanisms responsible for the Taylor’s wave building process. The study reports, for the first time, all the details to explain the instability mechanisms’ evolution. [Preview Abstract] |
Monday, November 25, 2019 9:57AM - 10:10AM |
H33.00010: Linear and nonlinear thermosolutal instabilities in an inclined porous layer Puranam Ananth L Narayana, Gautam Kumar, Kirti Sahu We investigate the double-diffusive instability in an inclined porous layer with a concentration based internal heat source by conducting linear instability and nonlinear energy analyses. The effects of various dimensionless parameters, such as the thermal $(Ra_T)$ and solutal $(Ra_S)$ Rayleigh numbers, the angle of inclination ($\phi$), the Lewis number $(Le)$, and the concentration based internal heat source $(Q)$ have been investigated. A comparison between the linear and nonlinear thresholds for the longitudinal and transverse rolls provides the region of the subcritical instability. We found that the system becomes more unstable when the diffusivity of the temperature is larger than that of the solute and with an increase in the internal heat source strength. It is observed that increasing inclination angle stabilises the system. Although the longitudinal roll remains stationary without the region of subcritical instability, the transverse roll transforms changes from stationary-oscillatory-stationary mode with the increase in the inclination angle. [Preview Abstract] |
Monday, November 25, 2019 10:10AM - 10:23AM |
H33.00011: Stability of the interface of an isotropic active fluid Wan Luo, Harsh Soni, Robert Pelcovits, Thomas Powers We study the linear stability of an isotropic active fluid in three geometries: a film of active fluid on a rigid substrate, a cylindrical thread of fluid, and a spherical fluid droplet. The active fluid is modeled by the hydrodynamic theory of an active nematic liquid crystal in the isotropic phase. In each geometry, we calculate the growth rate of sinusoidal modes of deformation of the interface. There are two distinct branches of growth rates; at long wavelength, one corresponds to the deformation of the interface, and one corresponds to the evolution of the liquid crystalline degrees of freedom. The passive cases of the film and the spherical droplet are always stable. For these geometries, a sufficiently large activity leads to instability. Activity also leads to propagating damped or growing modes. The passive cylindrical thread is unstable for perturbations with wavelength longer than the circumference. A sufficiently large activity can make any wavelength unstable, and again leads to propagating damped or growing modes. Our calculations are carried out for the case of zero Frank elasticity. While Frank elasticity is a stabilizing mechanism as it penalizes distortions of the order parameter tensor, we show that it has a small effect on the instabilities considered here. [Preview Abstract] |
Monday, November 25, 2019 10:23AM - 10:36AM |
H33.00012: The stability of evaporating binary liquid film heated from below Robson Nazareth, George Karapetsas, Pedro Saenz, Omar Matar, Khellil Sefiane, Prashant Valluri In this work we consider the evaporation of a thin liquid layer which consists of a binary mixture of volatile liquids on top of a heated horizontal substrate and in contact with the gas phase that consists of the same vapour of the binary mixtures. The effect of vapour recoil, thermo- and soluto-capillarity and the van der Waals interactions are considered. We derive the long-wave evolution equations for the free interface and the concentration that govern the two-dimensional stability of the layer subject to the above coupled mechanisms and perform a linear stability analysis. The developed linear theory highlight the dominants effects that drive the instabilities and describes two modes of instabilities, a monotonic instability mode and an oscillatory instability mode. A map is presented with the regions of monotonic and oscillatory instabilities in the volatility vs ratio of thermal- and solutal- Marangoni numbers. By means of transient simulations we analyse how these instabilities develop and its dependence on the destabilising effects are considered. More precisely we discuss how the solutal Marangoni effect defines the mode of instability that develops during the evaporation of the liquid layer due to preferential evaporation of one of the components. [Preview Abstract] |
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