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 D22: Instability: Rayleigh-Taylor II |
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Chair: Jeff Jacobs, University of Arizona Room: 2012 |
Sunday, November 23, 2014 2:15PM - 2:28PM |
D22.00001: 2D Rayleigh-Taylor instability: Interfacial arc-length vs. deformation amplitude Marie-Charlotte Renoult, Pierre Carles, Sameh Ferjani, Charles Rosenblatt Fluid interface instabilities are usually studied through the time evolution of the amplitude of deformation of the interface. While this approach is convenient, it often fails to fully describe the evolution of a deforming interface, especially when the interface cannot be represented as a single-valued function of a space coordinate. Here, we present experimental data on the Rayleigh-Taylor 2D instability for immiscible fluids having a single-mode sinusoidal initial perturbation, which is obtained through the use of magnetic levitation. We observe that new information can be retrieved by using an alternate metric to the amplitude, viz., the total arc-length of the interface (in 2D), or equivalently its total surface area (in 3D). In particular, we identify a master curve for the evolution of the arc-length over time, following three different regimes and on which all our data points fall. We conjecture that the exploration of such alternate metrics will yield interesting results on a broad range of interface instabilities. [Preview Abstract] |
Sunday, November 23, 2014 2:28PM - 2:41PM |
D22.00002: Interface node behavior due to nonlinearities in a 2D Rayleigh-Taylor instability Marie-Charlotte Renoult, Charles Rosenblatt, Pierre Carles We report a quantitative study on the symmetry effect of nonlinearities in a typical Rayleigh-Taylor (RT) instability for a single-mode sinusoidal initial perturbation. We use the interface zero-crossings (nodes) to monitor the asymmetrical deformation of the interface due to the growth of nonlinear odd harmonics. A weakly nonlinear model is developed and compared to measurements of node positions in fourteen RT experiments performed using the magnetic levitation technique. Our results suggest that monitoring the nodes' spatial displacement over time is a powerful technique for detecting the first nonlinear harmonic, and more broadly, exploring the transitional regime between linearity and fully-developed nonlinearity. The nodes approach provides a metric complementary to the deformation amplitude, which is widely used to measure the amplitude effect of nonlinearities in most interface instabilities. [Preview Abstract] |
Sunday, November 23, 2014 2:41PM - 2:54PM |
D22.00003: Generalized Cahn-Hilliard Navier-Stokes equations for numerical simulations of multicomponent immiscible flows Zhaorui Li, Daniel Livescu By using the second-law of thermodynamics and the Onsager reciprocal method for irreversible processes, we have developed a set of physically consistent multicomponent compressible generalized Cahn-Hilliard Navier-Stokes (CGCHNS) equations from basic thermodynamics. The new equations can describe not only flows with pure miscible and pure immiscible materials but also complex flows in which mass diffusion and surface tension or Korteweg stresses effects may coexist. Furthermore, for the first time, the incompressible generalized Cahn-Hilliard Navier-Stokes (IGCHNS) equations are rigorously derived from the incompressible limit of the CGCHNS equations (as the infinite sound speed limit) and applied to the immiscible Rayleigh-Taylor instability problem. Extensive good agreements between numerical results and the linear stability theory (LST) predictions for the Rayleigh-Taylor instability are achieved for a wide range of wavenumber, surface tension, and viscosity values. The late-time results indicate that the IGCHNS equations can naturally capture complex interface topological changes including merging and breaking-up and are free of singularity problems. [Preview Abstract] |
Sunday, November 23, 2014 2:54PM - 3:07PM |
D22.00004: Combined Rayleigh-Taylor and Kelvin-Helmholtz instabilities on cylindrical interfaces Vadivukkarasan M, Mahesh V Panchagnula Hydrodynamic instabilities that occur on a fluid interface are of interest to a wide range of applications. We study the combined effect of Rayleigh-Taylor (R-T) and Kelvin-Helmholtz (K-H) mechanisms of instability simultaneously attempting to destabilize a cylindrical interface. Linear stability analysis is used to study the process by which relative velocity (characterized by a Weber number) and acceleration (characterized by a Bond number) induced effects distort the interface. We investigate the effect of three dimensional disturbances and study the effect of varying Bo and We. From the dispersion relation obtained in this study, we are able to recover the R-T and K-H mechanism dispersion relations as special cases. From this study, we observe the occurrence of two-dimensional Taylor and flute modes as well as three-dimensional helical modes. A regime chart is presented in the (Bo,We) space to demonstrate the energy budget in the acceleration and shear induced instability mechanisms. In addition, we show that the length scale associated with the distorted interface is minimum in the helical mode. Finally, we show that an optimal Weber number exists above which it is not beneficial to increase relative velocity based kinetic energy. [Preview Abstract] |
Sunday, November 23, 2014 3:07PM - 3:20PM |
D22.00005: Hydrodynamic Instabilities in Blast-Driven Systems Marc Henry de Frahan, Eric Johnsen Mixing from hydrodynamics instabilities such as Richtmyer-Meshkov, Rayleigh-Taylor, and Kelvin-Helmholtz, occurs in a wide range of engineering applications such as inertial confinement fusion, supernova collapse, and scramjet combustion. The success of these applications depends on an accurate understanding of these phenomena. Following previous work investigating hydrodynamic mixing from the interaction of a perturbed interface with a planar blast wave, we model the perturbation growth by analyzing the different acceleration phases of a blast wave: an instantaneous acceleration (a pressure increase) followed by a gradual, time-dependent deceleration (a pressure decrease). Depending on the characteristics of these phases, the instability will be dominated by Richtmyer-Meshkov or Rayleigh-Taylor growth. We use a high-order accurate Discontinuous Galerkin method that prevents pressure errors at interfaces with variable specific heats ratios to simulate these systems and understand the different growth regimes. [Preview Abstract] |
Sunday, November 23, 2014 3:20PM - 3:33PM |
D22.00006: On the treatment of material interfaces in the presence of finite mass physical diffusion Pooya Movahed, Eric Johnsen In incompressible miscible variable-density flows, density is a function of composition and temperature (but not pressure), and velocity does not remain divergence-free in mixing regions. In numerical simulations of diffuse interfaces, it was previously shown that a specific form of the velocity, based on the density profile, should be prescribed initially, for consistency. In this work, we are interested in extending these ideas to compressible miscible flows, where the density and pressure are coupled through an equation of state. We study the temporal evolution of an isolated material interface in the presence of diffusion processes (mass, momentum and energy). ~We show that a velocity profile similar to that introduced in the incompressible case should be prescribed initially to avoid generating spurious waves at the interface. A new form of the initial velocity profile is suggested for an isothermal problem in the presence of gravity. The single-mode Richtmyer-Meshkov instability is used to illustrate the importance of this prescribed velocity on large-scale flow dynamics after re-shock. [Preview Abstract] |
Sunday, November 23, 2014 3:33PM - 3:46PM |
D22.00007: Immiscible experiments on the Rayleigh-Taylor instability using simultaneous particle image velocimetry and planar laser induced fluorescence concentration measurements Matthew Mokler, Jeffrey Jacobs Incompressible Rayleigh-Taylor instability experiments are presented in which two stratified liquids having Atwood number of 0.2 are accelerated in a vertical linear induction motor driven drop tower. A test sled having only vertical freedom of motion contains the experiment tank and visualization equipment. The sled is positioned at the top of the tower within the linear induction motors and accelerated downward causing the initially stable interface to be unstable and allowing the Rayleigh-Taylor instability to develop. Forced and unforced experiments are conducted using an immiscible liquid combination. Forced initial perturbations are produced by vertically oscillating the test sled prior to the start of acceleration. The interface is visualized using a 445nm laser light source that illuminates a fluorescent dye mixed in one of the fluids and aluminum oxide particles dispersed in both fluids. The laser beam is synchronously swept across the fluorescent fluid, at the frame rate of the camera, exposing a single plane of the interface. The resulting images are recorded using a monochromatic high speed video camera. Time dependent velocity and density fields are obtained from the recorded images allowing for 2D full field measurements of turbulent kinetic energy and turbulent mass transport. [Preview Abstract] |
Sunday, November 23, 2014 3:46PM - 3:59PM |
D22.00008: Numerical study of the single-mode Rayleigh-Taylor instability with non-unity Schmidt number Maxwell Hutchinson, Robert Rosner Recent experiments[1] and simulations[2,3] of the single mode Rayleigh-Taylor instability question the assumed existence of a bubble terminal velocity regime[4], particularly for low Atwood numbers. We present numerical results using the spectral element method and Boussinesq approximation with purely physical viscosity and diffusivity. The Schmidt number is chosen away from unity and boundary conditions are no-slip in an effort to bring the simulations closer to physically realizable conditions. \\[4pt] [1] J. P. Wilkinson and J. W. Jacobs, Phys. Fluids 19, 124102 (2007).\\[0pt] [2] P. Ramaprabhu et al., Phys. Fluids 24, 074107 (2012).\\[0pt] [3] T. Wei and D. Livescu, Phys. Rev. E 86, 046405 (2012).\\[0pt] [4] R. M. Davies and G. Taylor, Proc. R. Soc. A Math. Phys. Eng. Sci. 200, 375 (1950). [Preview Abstract] |
Sunday, November 23, 2014 3:59PM - 4:12PM |
D22.00009: Buoyancy Driven Mixing with Continuous Volumetric Energy Deposition Adam J. Wachtor, Farzaneh F. Jebrail, Nicholas A. Dennisen, Malcolm J. Andrews, Robert A. Gore An experiment involving a miscible fluid pair is presented which transitioned from a Rayleigh-Taylor (RT) stable to RT unstable configuration through continuous volumetric energy deposition (VED) by microwave radiation. Initially a light, low microwave absorbing fluid rested above a heavier, more absorbing fluid. The alignment of the density gradient with gravity made the system stable, and the Atwood number (\textit{At}) for the initial setup was approximately -0.12. Exposing the fluid pair to microwave radiation preferentially heated the bottom fluid, and caused its density to drop due to thermal expansion. As heating of the bottom fluid continued, the \textit{At} varied from negative to positive, and after the system passed through the neutral stability point, \textit{At} $=$ 0, buoyancy driven mixing ensued. Continuous VED caused the \textit{At} to continue increasing and further drive the mixing process. Successful VED mixing required careful design of the fluid pair used in the experiment. Therefore, fluid selection is discussed, along with challenges and limitations of data collection using the experimental microwave facility. Experimental and model predictions of the neutral stability point, and onset of buoyancy driven mixing, are compared, and differences with classical, constant \textit{At} RT driven turbulence are discussed. [Preview Abstract] |
Sunday, November 23, 2014 4:12PM - 4:25PM |
D22.00010: Experiments on the rarefaction wave driven Rayleigh-Taylor instability initiated with a random initial perturbation Robert Morgan, Jeffrey Jacobs Experiments are presented in which a diffuse interface between two gases is accelerated to become Rayleigh-Taylor unstable. The initially flat interface is generated by the opposing flow of two test gases at matched volumetric flow rates exiting through small holes in the test section. A random, three-dimensional interface perturbation is forced using a loudspeaker. The interface is then accelerated by an expansion wave which is generated by the rupturing of a diaphragm separating the heavy gas from a vacuum tank evacuated to $\sim$ 0.01atm. The expansion wave generates a large (of order 1000 g), non-constant acceleration acting on the interface causing the Rayleigh-Taylor instability to develop. Planar Mie scattering is employed to visualize the flow using a planar laser sheet generated at the top of the apparatus, which illuminates smoke particles seeded in the heavy gas. The scattered light is then recorded using a CMOS camera operating at 12kHz. The mixing layer width is obtained from an ensemble of experiments and the turbulent growth parameter $\alpha $ is extracted and compared with previous experiments and simulations. [Preview Abstract] |
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