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 C34: Flow Instability: Rayleigh-Taylor I |
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Chair: Irmgard Bischofberger, MIT Room: 616 |
Sunday, November 24, 2019 8:00AM - 8:13AM |
C34.00001: Pattern formation of a thin film flowing under an inclined plane Pier Giuseppe Ledda, Gaetan Lerisson, Gioele Balestra, Francois Gallaire We discuss the pattern formation of a thin film flowing under an inclined planar substrate, combining theoretical, experimental and numerical results. The phenomenon is related to the Rayleigh-Taylor instability, in which one heavier fluid is placed above a lighter one. When an upper wall and the substrate inclination are considered, a variety of patterns are observed. The natural and forced dynamics of the flat film to spanwise perturbations and the resulting non-linear structures are studied; in both cases, spanwise-periodic, streamwise-aligned structures, called rivulets, arise. The impulse response of a flat film is numerically and experimentally studied. We analyze the linear response, which does not show any preferential direction; a weakly non-linear model highlights however the selection of the streamwise structures. The fully non-linear evolution leads to a steady pattern characterized by fully saturated rivulets, the profile of which is analyzed in detail. A secondary stability analysis reveals the presence of a range of parameters in which only rivulets are observed, in agreement with the experimental observations. Outside of this range, lenses appear on the rivulets, which may eventually drip. [Preview Abstract] |
Sunday, November 24, 2019 8:13AM - 8:26AM |
C34.00002: A Buoyancy--Shear--Drag-Based Turbulence Model for Rayleigh--Taylor, Reshocked Richtmyer--Meshkov, and Kelvin--Helmholtz Mixing Oleg Schilling A phenomenological turbulence model for Rayleigh--Taylor, reshocked Richtmyer--Meshkov, and Kelvin--Helmholtz instability-induced mixing is developed using a general buoyancy–shear–drag model. Analytical solutions are used to calibrate the coefficients to predict specific values of the mixing growth parameters and exponents. The model is applied to the three instability cases to demonstrate its utility. It is shown that the numerical solutions of the model calibrated using specific values of the instability growth parameters and exponents: (1) produces mixing layer widths in agreement with the expected self-similar growth power laws; (2) gives spatiotemporal profiles of turbulent fields that are expected and consistent with previous results; (3) predicts the expected power-law growths and decays of the spatially-integrated turbulent fields, and; (4) gives spatiotemporal profiles of the mean fields that are expected and consistent with previous results. [Preview Abstract] |
Sunday, November 24, 2019 8:26AM - 8:39AM |
C34.00003: Combined effects of finite plate thickness and acceleration rates on Rayleigh-Taylor instability in elastic-plastic materials. Arindam Banerjee, Rinosh Polavarapu, Aren Boyaci Majority of theoretical and computational studies of Rayleigh-Taylor instability (RTI) in solid-fluid interfaces assume the materials to be incompressible with infinite/semi-infinite thickness subjected to a constant driving acceleration. A recent theoretical study by Piriz et al. (PRE $\backslash $textbf\textbraceleft 95\textbraceright , 053108, 2017) has explored finite thickness effects using an impulsive acceleration profile where the initial rate of increase in the driving pressure is nearly infinite. In previous studies, our group has addressed the independent effects of the finite plate/slab thickness and finite rate of increase in driving acceleration (pressure). In this talk, we will address the combined effects of both the aforementioned parameters on RTI by employing the soft solid (mayonnaise)-air interface using our rotating wheel experimental setup. A set of experiments was run at four different acceleration rates in combination with three test-section container halves of varying depths using initial conditions with different wavelengths and amplitudes. The aggregate effects of these parameters on interface growth were quantified in terms of instability acceleration, which signifies the material transition from elastic-plastic regime to the viscous regime. In addition, the growth rates for each experiment are determined and compared to the existing theoretical models which tackle the RTI problem in solids. [Preview Abstract] |
Sunday, November 24, 2019 8:39AM - 8:52AM |
C34.00004: Suppression of the Rayleigh-Taylor instability in a confined geometry Samar Alqatari, Thomas Videbaek, Peko Hosoi, Irmgard Bischofberger We study the Rayleigh-Taylor instability of two miscible fluids in a Hele-Shaw geometry; confined in a thin gap, of size $b$, between two large flat plates. Using this geometry, we inject a fluid into another with a different density as to produce an unstable situation in which a heavy fluid initially resides above a layer of lighter fluid. Below a critical gap spacing, $b_c$, we find that no Rayleigh-Taylor fingers form despite the fluid density gradient that typically instigates the instability. We use simulations, validated by comparison with experiments, to determine $b_c$ as a function of the difference of fluid densities $\Delta\rho$, the viscosities $\eta$, and diffusivities $D$. We argue that this critical confinement scale is set by a competition between destabilizing buoyancy forces and stabilizing effects of viscosity and diffusion. An argument based on dimensional analysis gives scaling exponents consistent with the observed results, $b_c \sim (D\eta / g \Delta\rho)^{1/3}$. In addition to the critical gap, we measure the characteristic wavelength and onset time in this confined geometry and compare it to the theoretical predictions for the Rayleigh-Taylor instability in open space. [Preview Abstract] |
Sunday, November 24, 2019 8:52AM - 9:05AM |
C34.00005: Group theory analysis of early-time scale-dependent dynamics of the Rayleigh-Taylor instability with time varying acceleration Desmond L. Hill, Aklant K. Bhowmick, Dan V. Ilyin, Snezhana I. Abarzhi We consider the long-standing problem of Rayleigh-Taylor instability with variable acceleration, and focus on the early-time scale-dependent dynamics of an interface separating in-compressible ideal fluids of different densities subject to an acceleration being a power-law function of time for a spatially extended three-dimensional flow periodic in the plane normal to the acceleration with symmetry group p6mm. By employing group theory and scaling analysis, we discover two distinct sub-regimes of the early-time dynamics depending on the exponent of the acceleration power-law. The time scale and the early-time dynamics are set by the acceleration for exponents greater than (-2), and by the initial growth-rate (due to, e.g., initial conditions) for exponents smaller than (-2). At the exponent value (-2) a transition occurs from one sub-regime to the other with varying acceleration strength. For a broad range of the acceleration parameters, the instability growth rate is explicitly found, the dependence of the dynamics on the initial conditions is investigated, and theory benchmarks are elaborated. [Preview Abstract] |
Sunday, November 24, 2019 9:05AM - 9:18AM |
C34.00006: Rayleigh-Taylor Instability Between Unequally Stratified Layers Stuart Dalziel, Valentin Mouet While the classical Rayleigh-Taylor instability between two homogeneous incompressible layers continues to accelerate until the influence of boundaries become dominant, when the instability grows between two otherwise stably stratified layers, the initial growth is limited by the stratification and can be arrested before the instability reaches the boundaries. Here we study the intermediate case where one of the two layers is stably stratified and the other homogeneous, thus introducing an asymmetry where the instability grows into one layer without restriction, but is eventually arrested by the stratification in the other layer. Experimental measurements of the density and velocity fields show both similarities and differences compared with the two limiting cases in terms of both the evolution of the height of the mixing zone and the final stratification achieved. [Preview Abstract] |
Sunday, November 24, 2019 9:18AM - 9:31AM |
C34.00007: Optimal perturbations for linear stability of two fluid columns of different densities subject to gravity Aditya Prathama, Carlos Pantano We study the linear stability of a vertical interface separating two fluid columns of different densities under the influence of gravity. Initially, we assume quasi-steady state (QSSA) of the base flow and pose the problem as an eigenvalue problem. Subsequently, we carry out adjoint-based optimization of the most amplified eigenmode. This results in an initial condition that leads to the maximum growth of disturbances at a finite time. Preliminary results indicate that the perturbation energy of wave modes with small wave numbers may experience substantial transient growth prior to decaying asymptotically in time, despite infinitesimal assumption of the linearized problem. It is also found that the maximum growth rate is about one order of magnitude higher than that of the non-optimized case. The sensitivity of perturbation growth with respect to initial time, density, and viscosity ratios will be investigated. [Preview Abstract] |
Sunday, November 24, 2019 9:31AM - 9:44AM |
C34.00008: Experimental investigation of Rayleigh---Taylor mixing in gases using simultaneous PIV-PLIF Prasoon Suchandra, Mark Mikhaeil, Gokul Pathikonda, Devesh Ranjan Dynamics of Rayleigh--Taylor (RT) mixing is studied using statistically stationary experiments performed in a multi-layer gas tunnel. The density ratio of air and air-helium-nitrogen mixture used results in an Atwood number ($A)$ \textasciitilde 0.13. Two types of diagnostics --- particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF) --- are employed to obtain mixing width and simultaneous velocity-density data. PLIF using acetone is implemented for the first time for convective-type (flowing) statistically stationary RT experiments with gases. Velocity and density statistics, and their correlations ($u', v', \rho ', \rho 'v')$ are presented. As Atwood number for current experiments exceeds the widely accepted $A$ \textasciitilde 0.1 limit for Boussinesq approximation, non-Boussinesq-ness and anisotropy effects at this Atwood number are evaluated using metrics like higher-order moments (skewness, kurtosis) and anisotropy tensor. Results from current experiments are compared with existing turbulent RT mixing models (like BHR models). \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] |
Sunday, November 24, 2019 9:44AM - 9:57AM |
C34.00009: The adjoint Rayleigh criterion in compressible reacting flow instabilities Luca Magri, Matthew P. Juniper, Jonas P. Moeck Thermoacoustic oscillations are one of the most challenging flow instabilities faced by the gas turbine and rocket motor industry. The instability mechanism is described in the time domain by the Rayleigh criterion. In this contribution, the Rayleigh criterion is interpreted in the frequency domain by deriving functional formulae for the eigenvalue. The first variation of the Rayleigh criterion is calculated both in the time and frequency domain, both with and without Lagrange multipliers (adjoint variables). The Lagrange multipliers are physically interpreted with the system's observables, e.g., pressure, velocity, temperature. Finally, the adjoint Rayleigh criterion is proposed. The relations and criteria proposed can enable the calculation of adjoint sensitivities from measurable quantities in experiments. The methodology proposed is versatile and can be applied to other problems in flow instability that are tackled by adjoint analysis. [Preview Abstract] |
Sunday, November 24, 2019 9:57AM - 10:10AM |
C34.00010: On the Rayleigh-Taylor unstable dynamics of three-dimensional interfacial coherent structures with time-dependent acceleration Snezhana Abarzhi, Desmond L. Hill Rayleigh-Taylor instability (RTI) occurs in a range of natural and industrial processes. Whereas the majority of existing studies have considered constant acceleration, RTI is in many instances driven by variable acceleration. Here we focus on RTI driven by acceleration with a power-law time-dependence, and, by applying a group theoretic method, find solutions to this classical nonlinear boundary value problem. We deduce that the dynamics is dominated by the acceleration and that the solutions depend critically on the acceleration parameters for values of the acceleration exponent greater than (-2). We find that in the early-time dynamics, the RTI growth-rate is defined by modified Bessel functions. For the late-time dynamics, we link the interface dynamics with an interfacial shear function, find a continuous family of regular asymptotic solutions and identify invariant properties of nonlinear RTI. The essentially interfacial and multi-scale character of the dynamics is also demonstrated. The velocity field is potential in the bulk, and vortical structures may appear at the interface due to interfacial shear. The multi-scale character becomes clear from the invariance properties of the dynamics. We agree with existing observations and elaborate new benchmarks for the future. [Preview Abstract] |
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