Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session M20: Instability: General IV |
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Chair: John Cressman, George Mason University Room: 315 |
Tuesday, November 26, 2013 8:00AM - 8:13AM |
M20.00001: Localized convection in a rotating system Cedric Beaume, Hsien-Ching Kao, Edgar Knobloch, Alain Bergeon We study two-dimensional spatially localized convection in a horizontal fluid layer rotating around the vertical and heated from below [1]. With stress-free boundary conditions stationary spatially localized convection is present [2]. These states are embedded in a background shear layer and lie on a pair of intertwined solution branches exhibiting ``slanted snaking'' [3]. Similar solutions with no-slip boundary conditions are no longer embedded in a background shear and exhibit standard snaking, i.e. snaking without a slant. These solutions may be stable [4]. Homotopic continuation from free-slip to no-slip boundary conditions is used to track the changes in the properties of the solutions and the associated bifurcation diagrams. An explanation of the results is given.\\[4pt] [1] Veronis, J. Fluid Mech. 5, 401--435 (1959)\\[0pt] [2] Beaume et al., J. Fluid Mech. 717, 417--448 (2013)\\[0pt] [3] Dawes, SIAM J. Appl. Dyn. Syst. 7, 186--206 (2008)\\[0pt] [4] Beaume et al., submitted [Preview Abstract] |
Tuesday, November 26, 2013 8:13AM - 8:26AM |
M20.00002: Electro-convective instability at an ion-selective membrane Mathias B. Andersen, Clara L. Druzgalski, Joseph W. Nichols, Ali Mani In electrochemical engineering processes a major unresolved problem is the theoretical understanding of transport above the nominal diffusion limitation. When an electric current is passed from an aqueous electrolyte into an ion-selective membrane, ionic depletion next to the surface leads to transport limitation for a stagnant electrolyte. However, it has been shown that electrolytes under such conditions are hydrodynamically unstable when biased above a critical voltage. Mixing by the resulting flow can lead to enhanced transport. In this presentation we touch upon different elements of two studies of electro-convective instability at an ion-selective membrane: (1) the linear spatiotemporal stability when subject to a plane-Poiseuille cross flow, and (2) the chaotic transport characteristics at high voltages (cross flow absent). In (1) we identify absolutely and convectively unstable regimes and show that the imposed shear acts as a stabilization mechanism. [Preview Abstract] |
Tuesday, November 26, 2013 8:26AM - 8:39AM |
M20.00003: One-way Euler equations: a novel spatial marching technique for convective instabilities Aaron Towne, Tim Colonius The parabolized stability equations (PSE) are a tool for rapid computation of convectively unstable flows. The efficiency of the method is achieved by solving the equations in frequency space using a spatial marching technique in the downstream direction. Unfortunately, the PSE operator contains upstream propagating acoustic modes that cause instability in this march unless these waves are numerically damped. Existing damping techniques introduce additional error into the solution and in particular contaminate the acoustic mid- and far-field. We have developed a method that removes the upstream acoustic modes from the linearized Euler equations without damaging the downstream modes. The upstream and downstream dynamics are decoupled using a recursive filtering technique that was originally developed for generating non-reflecting boundary conditions. The decoupled downstream modes are then evolved in the downstream direction. Our talk will focus on the validation of this method through comparison with PSE and direct solutions of the linearized Euler equations. [Preview Abstract] |
Tuesday, November 26, 2013 8:39AM - 8:52AM |
M20.00004: Doubly-shocked Richtmyer-Meshkov Instability Varad Karkhanis, Praveen Ramaprabhu We report on detailed numerical simulations of a doubly-shocked Richtmyer-Meshkov Instability where two successive incident shock waves interact with a sinusoidally perturbed material interface. The problem is relevant to Inertial Confinement Fusion, type IA supernovae, and the design of mix experiments where multiple incident shocks have been proposed to potentially achieve freeze-out. In our simulations, the timing of the second incident shock was varied to realize a finite-amplitude initialization of the RM instability. The simulations were performed at two Atwood numbers, A $=$ 0.15 and A $=$ -0.99, where the latter condition is relevant to ejecta formation. For A $=$ -0.99, the shock-interface interactions result in two successive phase inversions corresponding to the passage of the shocks from heavy to light media in each instance. We have investigated initial interface perturbations of different forms including sinusoidal, triangular and sawtooth waveforms and compare the growth rates from each interaction with linear and nonlinear models [1,2]. \\[4pt] [1] Guy Dimonte and P. Ramaprabhu, Phys. Fluids 22, 014104 (2010).\\[0pt] [2] Guy Dimonte, Guillermo Terrones, F.J. Cherne and P. Ramaprabhu, J. Appl. Phys. 113, 024905 (2013). [Preview Abstract] |
Tuesday, November 26, 2013 8:52AM - 9:05AM |
M20.00005: Numerical Simulations of the Single-mode, Reacting Richtmyer-Meshkov Instability Using Detailed Chemistry Nitesh Attal, Praveen Ramaprabhu The interaction of a shock wave with a chemically reacting front is of importance to the design of supersonic combustors and scramjets where mixing from the Richtmyer-Meshkov Instability (RMI) could be tapped to increase combustion efficiency. We will describe results of shock-driven, reacting RMI of a sinusoidally perturbed, single-mode interface separating Hydrogen (fuel) and Oxygen at 300K and 1625K respectively. The non-premixed interface was accelerated by a Mach 1.2 shock traversing from the light (H$_{2})$ to heavy (O$_{2})$ fluid (Atwood number $=$ 0.5) in a numerical shock tube of aspect ratio 12. The 2D simulations were performed using the compressible flow code FLASH [1], with modifications [2] to handle detailed chemistry and temperature-dependent material properties. The initial thickness of the material interface was systematically varied to study the effect of the diffusion thickness on the flame and instability dynamics. Product formation and heat release as a result of chemical reactions were described according to the 9-species, 19-steps detailed reaction mechanism [3].\\[4pt] [1] B. Fryxell et al., Astrophys. J., Suppl. Ser. 131, 273 (2000)\\[0pt] [2] N. Attal et al., Comput. Fluids (submitted for review)\\[0pt] [3] G. Billet, J. Comput. Phys. 204, 319 (2005) [Preview Abstract] |
Tuesday, November 26, 2013 9:05AM - 9:18AM |
M20.00006: Behavior of embedded phase in shock-driven two-phase flow Garrett Kuehner, Patrick Wayne, Dell Olmstead, Clint Corbin, Tennille Bernard, Peter Vorobieff, C. Randall Truman We present an experimental study of droplet acceleration in a shock-driven two-phase flow (air with embedded liquid droplets). The droplets (propylene glycol, diameter 0.5-3~$\mu$m) were pre-mixed with the air in the test section of a shock tube, then impulsively accelerated with planar shock wave with a Mach number of 1.7. A cross-section of the flow is illuminated with multiple pulses from Nd:YAG lasers, producing time-resolved visualizations of the seeded volume. The images are then analyzed to quantify droplet velocity and acceleration from the shock passage to about 1.5 ms after the shock. Based on the velocity measurements, we can resolve the droplet lag after the shock, when the massive droplets ``catch up'' with the flow of the surrounding air, as well as validate our earlier estimates of boundary layer growth. [Preview Abstract] |
Tuesday, November 26, 2013 9:18AM - 9:31AM |
M20.00007: Multicomponent Reynolds-Averaged Navier--Stokes Simulations of Reshocked Richtmyer--Meshkov Instability and Turbulent Mixing: Reshock Time and Atwood Number Effects Tiberius Moran-Lopez, Oleg Schilling Reshocked Richtmyer--Meshkov turbulent mixing of gases with various Atwood numbers and shock Mach numbers is simulated using a third-order weighted essentially nonoscillatory implementation of a $K$--$\epsilon$ multicomponent Reynolds-averaged Navier--Stokes model. First, mixing layer widths from simulations with Mach number $Ma = 1.20$, Atwood number $At = 0.67$ (air/SF$_6$), and different times of reshock are shown to be in very good agreement with the experimental data of Leinov et al. [J. Fluid Mech. \textbf{626}, 449 (2009)]. Second, widths from simulations with $Ma = 1.50$ and $At = \pm 0.21$, $\pm 0.67$ and $\pm 0.87$ (corresponding to air/CO$_2$, air/SF$_6$ and H$_2$/air) are compared to the large-eddy simulation data of Lombardini et al. [J. Fluid Mech. \textbf{670}, 439 (2011)] and discussed. Budgets of the turbulent transport equations are considered to elucidate the mechanisms contributing to turbulent mixing in reshocked Richtmyer--Meshkov instability. Convergence of the mixing layer widths, mean fields, and turbulent fields under grid refinement is also assessed. [Preview Abstract] |
Tuesday, November 26, 2013 9:31AM - 9:44AM |
M20.00008: Linear and Nonlinear Simulations of the Richtmyer- Meshkov Instability in Magnetohydrodynamics Ravi Samtaney, Abeer Baksh, Song Gao, Vincent Wheatley Nonlinear ideal magnetohydrodynamics (MHD) simulations and analysis indicate that the Richtmyer-Meshkov instability (RMI) is suppressed in the presence of a magnetic field in Cartesian slab geometry. We present results of linear and nonlinear MHD simulations of RMI in cylindrical geometry. The linear simulations are performed with a numerical method that is an extension of the method proposed by Samtaney (J. Comput. Phys. 2009). In the absence of a magnetic field, linear analysis indicates that RMI growth rate during the early time period is similar to that observed in Cartesian geometry. However, this RMI phase is short-lived and followed by a Rayleigh-Taylor growth phase with an accompanied exponential increase in the perturbation amplitude. We examine several strengths of the magnetic field (characterized by $\beta={2p}/{B^2} $). For the strongest field case studied ($\beta\approx 2$) we see a significant suppression of the instability. We will present a description of the numerical methods, a complete characterization of the RMI linear stability in cylindrical geometry, and comparisons between linear and nonlinear MHD simulations for field strengths, and azimuthal and axial wavenumbers. [Preview Abstract] |
Tuesday, November 26, 2013 9:44AM - 9:57AM |
M20.00009: ABSTRACT WITHDRAWN |
Tuesday, November 26, 2013 9:57AM - 10:10AM |
M20.00010: Instability of laterally heated cylindrical convection De-Jun Sun, Bo-Fu Wang The three dimensional instabilities of axisymmetric flow in a vertical cylinder partially heated from the sidewall are explored. The cylindrical wall is heated in a central zone and is insulated above and below this zone, while both ends of the cylinder are cooled. The length of the heated zone equals to the cylinder radius. The dependence of the critical Rayleigh number on the Prandtl number is obtained for three fixed values of aspect ratio, A$=$1.92, 2, 2.1 (A$=$height/radius). The Prandtl number ranges from 0.02 to 6.7. The instability curve for A$=$1.92 is monotonous. The instability curves for A$=$2 and A$=$2.1 are non-monotonous and contain hysteresis, particularly, an instability island is found for A$=$2. The flow is oscillatory unstable at small Prandtl number due to hydrodynamic instability. At medium Prandtl number, the interaction of buoyancy and shear of base flow lead to the instability results. The Rayleigh-Benard instability is dominant at large Prandtl number, and the flow loses stability through a steady bifurcation. [Preview Abstract] |
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