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 M30: Flow Instability: Rayleigh-Taylor |
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Chair: Daniel Attinger, Iowa State University Room: F151 |
Tuesday, November 22, 2016 8:00AM - 8:13AM |
M30.00001: Self-similarity of a Rayleigh-Taylor mixing layer at low Atwood number with a multimode initial perturbation Brandon Morgan, Britton Olson, Justin White, Jacob McFarland High-fidelity large eddy simulation (LES) of a low-Atwood number ($A$ = 0.05) Rayleigh-Taylor mixing layer is performed using the tenth-order compact difference code Miranda. An initial multimode perturbation spectrum is specified in Fourier space as a function of mesh resolution such that a database of results is obtained in which each successive level of increased grid resolution corresponds approximately to one additional doubling of the mixing layer width, or \emph{generation}. The database is then analyzed to determine approximate requirements for self-similarity, and a new metric is proposed to quantify how far a given simulation is from the limit of self-similarity. It is determined that the present database reaches a high degree of self-similarity after approximately 4.5 generations. Finally, self-similar turbulence profiles from the LES database are compared with one-dimensional simulations using the $k$-$L$-$a$ and BHR-2 Reynolds-averaged Navier-Stokes (RANS) models. The $k$-$L$-$a$ model, which is calibrated to reproduce a quadratic turbulence kinetic energy profile for a self-similar mixing layer, is found to be in better agreement with the LES than BHR-2 results. [Preview Abstract] |
Tuesday, November 22, 2016 8:13AM - 8:26AM |
M30.00002: Viscous effects on the Rayleigh-Taylor instability with background temperature gradient Daniel Livescu, Sergiy Gerashchenko The growth rate of the compressible Rayleigh-Taylor instability is studied in the presence of a background temperature gradient, $\Theta$, using a normal mode analysis. The effect of $\Theta$ variation is examined for three interface types corresponding to combinations of the viscous properties of the fluids (inviscid-inviscid, viscous-viscous and viscous-inviscid) at different Atwood numbers, At, and, when at least one of the fluids' viscosity is non-zero, as a function of the Grashof number. Compared to the $\Theta=0$ case, the role of $\Theta<0$ (hotter light fluid) is destabilizing and becomes stabilizing when $\Theta>0$ (colder light fluid). The most pronounced effect of $\Theta\neq 0$ is found at low At and/or at large perturbation wavelengths relative to the domain size for all interface types. The results are applied to two practical examples, using sets of parameters relevant to Inertial Confinement Fusion coasting stage and solar corona plumes. The role of viscosity on the growth rate reduction is discussed together with highlighting the range of wavenumbers most affected by viscosity. The viscous effects further increase in the presence of a background temperature gradient, when the viscosity is temperature dependent. [Preview Abstract] |
Tuesday, November 22, 2016 8:26AM - 8:39AM |
M30.00003: Predictions and Measurements of Blood Backspatter from a Gunshot in Bloodstain Pattern Analysis Patrick Comiskey, Alexander Yarin, Sungu Kim, Daniel Attinger A theoretical model for predicting and interpreting blood spatter patterns resulting from a gunshot wound is proposed. The physical process generating a backward spatter of blood is linked to the Rayleigh-Taylor instability of blood accelerated toward the surrounding air allowing the determination of initial distribution of drop sizes and velocities. Then, the motion of many drops in air is considered with governing equations accounting for gravity and air drag. The model predicts the atomization process, the trajectories of the back spatter drops of blood from the wound to the ground, the impact angle and the impact Weber number on the ground, as well as the number of, distribution, and location of blood stains and their shapes and sizes. The drop cloud originating from a wound entrains a significant mass of air due to the action of viscous forces. As a result of this collective effect, air drag acting on individual drops in the cloud is significantly reduced and fully accounted for in the model. The results of the model are compared to experimental data on back spatter generated by a gunshot impacting a blood-impregnated sponge. The model proposed in this work is in reasonable agreement with the results from the experimental data. [Preview Abstract] |
Tuesday, November 22, 2016 8:39AM - 8:52AM |
M30.00004: Effect of noise on Rayleigh-Taylor mixing with space-dependent acceleration Arun Pandian, Snezhana Abarzhi We analyze, for the first time by our knowledge, the effect of noise on Rayleigh-Taylor (RT) mixing with space-dependent acceleration by applying the stochastic model. In these conditions, the RT mixing is a statistically unsteady process where the means values of the flow quantities vary in space and time, and there are also the space and time dependent fluctuations around these mean values. The stochastic model is derived from the momentum model and is represented by a set of nonlinear differential equations with multiplicative noise. The models equations are solved theoretically and numerically. Investigating a broad range of values of acceleration, self-similar asymptotic solutions are found in the mixing regime. There are two types of mixing sub-regimes (acceleration-driven and dissipation-driven respectively), each of which has its own types of solutions and characteristic values with the latter saturating to a value on the order of one. It is also observed that the representation of the dynamics in an implicit form is noisier as compared to the case of an explicit time-dependent form. [Preview Abstract] |
Tuesday, November 22, 2016 8:52AM - 9:05AM |
M30.00005: Highly symmetric interfacial coherent structures in Rayleigh Taylor instability with time-dependent acceleration Aklant K. Bhowmick, Snezhana Abarzhi Rayleigh Taylor instability in a power-law time dependent acceleration field is investigated theoretically for a flow with the symmetry group p6mm (hexagon) in the plane normal to acceleration. In the nonlinear regime, regular asymptotic solutions form a one-parameter family. The physically significant solution is identified with the one having the fastest growth and being stable (bubble tip velocity). Two distinct regimes are identified depending on the acceleration exponent. Particularly, the RM-type regime, where the dynamics is identical to conventional RM instability and is dominated by initial conditions, and the RT-type regime where the dynamics is dominated by the acceleration term. For the latter, the time dependence has profound effects on the dynamics. In the RT non-linear regime, the time dependence has no consequence on the morphology of the bubbles; the growth rate (bubble tip velocity) evolves as power law with the exponent set by the acceleration. The solutions for a one-parameter family, and are convergent with exponential decay of Fourier amplitudes. The solutions are stable at maximum tip velocity, whereas flat bubbles are unstable, and the growth/decay of perturbations is no longer purely exponential and depends on the acceleration exponent. [Preview Abstract] |
Tuesday, November 22, 2016 9:05AM - 9:18AM |
M30.00006: Low-symmetric coherent structures and dimensional crossover in Rayleigh Taylor flows driven by time dependent accelerations Aklant Bhowmick, Snezhana Abarzhi We investigate the nature of the dimensional crossover i.e. transition between the nearly isotropic 3D periodic flows with group p4mm (square) to highly anisotropic 2D periodic flows with group p2m1 in Rayleigh Taylor (RT) instability. Power law time dependence of the acceleration is considered with the emphasis on sub-regime, where the behavior is the RT type. We consider flow with group p2mm (rectangle) and obtain the 3D square and 2D limits with leading order rectangular corrections. Regular asymptotic solutions evolve as power law and form a two parameter family parametrized by the principal curvatures of the bubble. The bubbles with “near circular contour” separate the 2-dimensional solution space into two sub-regimes having distinct properties under the dimensional crossover. In one sub-regime, the elongated bubbles transform to 2D solutions, whereas in the other they flatten. 3D square bubbles are universally stable whereas 2D bubbles are unstable with respect to 3D modulations, implying that the dimensional crossover is discontinuous. We find that the time dependence affects the growth/decay of perturbations and has no consequence on the overall stability properties of the solution. [Preview Abstract] |
Tuesday, November 22, 2016 9:18AM - 9:31AM |
M30.00007: Rayleigh-Taylor mixing with space-dependent acceleration Snezhana Abarzhi We extend the momentum model to describe Rayleigh-Taylor (RT) mixing driven by a space-dependent acceleration. The acceleration is a power-law function of space coordinate, similarly to astrophysical and plasma fusion applications. In RT flow the dynamics of a fluid parcel is driven by a balance per unit mass of the rates of momentum gain and loss. We find analytical solutions in the cases of balanced and imbalanced gains and losses, and identify their dependence on the acceleration exponent. The existence is shown of two typical sub-regimes of self-similar RT mixing – the acceleration-driven Rayleigh-Taylor-type mixing and dissipation-driven Richtymer-Meshkov-type mixing with the latter being in general non-universal. Possible scenarios are proposed for transitions from the balanced dynamics to the imbalanced self-similar dynamics. Scaling and correlations properties of RT mixing are studied on the basis of dimensional analysis. Departures are outlined of RT dynamics with space-dependent acceleration from canonical cases of homogeneous turbulence as well as blast waves with first and second kind self-similarity. [Preview Abstract] |
Tuesday, November 22, 2016 9:31AM - 9:44AM |
M30.00008: Long-wave analysis and control of the viscous Rayleigh-Taylor instability with electric fields Radu Cimpeanu, Thomas Anderson, Peter Petropoulos, Demetrios Papageorgiou We investigate the electrostatic stabilization of a viscous thin film wetting the underside of a solid surface in the presence of a horizontally acting electric field. The competition between gravity, surface tension and the nonlocal effect of the applied electric field is captured analytically in the form of a nonlinear evolution equation. A semi-spectral solution strategy is employed to resolve the dynamics of the resulting partial differential equation. Furthermore, we conduct direct numerical simulations (DNS) of the Navier-Stokes equations and assess the accuracy of the obtained solutions when varying the electric field strength from zero up to the point when complete stabilization at the target finite wavelengths occurs. We employ DNS to examine the limitations of the asymptotically derived behavior in the context of increasing liquid film heights, with agreement found to be excellent even beyond the target lengthscales. Regimes in which the thin film assumption is no longer valid and droplet pinch-off occurs are then analyzed. Finally, the asymptotic and computational approaches are used in conjunction to identify efficient active control mechanisms allowing the manipulation of the fluid interface in light of engineering applications at small scales, such as mixing. [Preview Abstract] |
Tuesday, November 22, 2016 9:44AM - 9:57AM |
M30.00009: Experimental investigation of late time Rayleigh---Taylor mixing at high Atwood number Prasoon Suchandra, Mark Mikhaeil, Devesh Ranjan Dynamics of late time, high Reynolds number (Re \textgreater 20000) Rayleigh--Taylor (RT) mixing is studied using statistically steady experiments performed in a multi-layer gas tunnel. The density ratio of air and air-Helium mixture used in the present experiment results in an Atwood number \textasciitilde 0.73. Three types of diagnostics --- back-lit visualization, hot-wire anemometry and stereo particle image velocimetry (S-PIV) --- are employed to obtain mixing width, velocity and density fields, with S-PIV employed for the first time for such experimental conditions. Velocity and density statistics, and their correlations (\textit{u', v', w', }$\rho ', \rho 'v')$ are presented. Calculations of probability density functions (p.d.f.s) and energy spectra are made to provide further insight into the flow physics. Energy budget of the flow is also discussed. \underline {Reference:} AKULA, B. {\&} RANJAN, D. 2016 Dynamics of buoyancy-driven flows at moderately high Atwood numbers. \textit{Journal of Fluid Mechanics 795, 313--355.} [Preview Abstract] |
Tuesday, November 22, 2016 9:57AM - 10:10AM |
M30.00010: Effects of acceleration rate on Rayleigh-Taylor instability in elastic-plastic materials. Arindam Banerjee, Rinosh Polavarapu The effect of acceleration rate in the elastic-plastic transition stage of Rayleigh-Taylor instability in an accelerated non-Newtonian material is investigated experimentally using a rotating wheel experiment. A non-Newtonian material (mayonnaise) was accelerated at different rates by varying the angular acceleration of a rotating wheel and growth patterns of single mode perturbations with different combinations of amplitude and wavelength were analyzed. Experiments were run at two different acceleration rates to compare with experiments presented in prior years at APS DFD meetings and the peak amplitude responses are captured using a high-speed camera. Similar to the instability acceleration, the elastic-plastic transition acceleration is found to be increasing with increase in acceleration rate for a given amplitude and wavelength. The experimental results will be compared to various analytical strength models and prior experimental studies using Newtonian fluids. [Preview Abstract] |
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