Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session LT: Rayleigh-Taylor Instability I |
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Chair: Oleg Schilling, Lawrence Livermore National Laboratory Room: Hilton Chicago Stevens 5 |
Tuesday, November 22, 2005 8:00AM - 8:13AM |
LT.00001: Direct numerical simulation of a small Atwood number Rayleigh-Taylor instability-driven mixing layer Nicholas Mueschke, Oleg Schilling, Malcolm Andrews A direct numerical simulation (DNS) of a small Atwood number Rayleigh-Taylor mixing layer was performed using a spectral/compact-difference scheme. The initial conditions were parameterized from interfacial and velocity perturbations measured from water channel experiments at Texas A\&M University. Turbulence and mixing statistics, as well as energy spectra, obtained from experimental measurements are compared with those from the DNS to validate the use of experimental measurements as computational initial conditions. The experimental and numerical data are used to examine the transitional dynamics of the mixing layer. The DNS results indicate that initial conditions including both interfacial and velocity perturbations are required to accurately simulate the flow. This research was sponsored by the U.S. DOE National Nuclear Security Administration under the Stewardship Science Academic Alliances program through DOE Research Grant \#DE-FG03- 02NA00060. This work was also performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under Contract No. W- 7405-Eng-48. UCRL-ABS-214352. [Preview Abstract] |
Tuesday, November 22, 2005 8:13AM - 8:26AM |
LT.00002: Buoyancy-driven variable density turbulence Daniel Livescu, J.R. Ristorcelli Buoyancy generated motions in an unstably stratified field composed of two incompressible miscible fluids with different densities, as occurs in the Rayleigh-Taylor instability, are examined. The statistically homogeneous case is considered as a unit problem for variable density turbulence and no Boussinesq approximation is made so that high Atwood numbers are allowed. The flow starts with zero solenoidal velocity in a non-premixed state and turbulence is generated due to the baroclinic production of vorticity and eventually dies as the two fluids become molecularly mixed. Results from Direct Numerical Simulations are used to follow the turbulence birth-life-death process and examine the influence of various parameters, Atwood, Reynolds and Schmidt numbers, and initial length scale of the density field on the mixing. [Preview Abstract] |
Tuesday, November 22, 2005 8:26AM - 8:39AM |
LT.00003: On the late-time behavior of the single-mode Rayleigh-Taylor problem Praveen Ramaprabhu, Guy Dimonte We report on the behavior of a single-mode Rayleigh-Taylor flow at late-times. Numerical simulations in a long square duct of size $\lambda$x$\lambda$x8$\lambda$ exhibit four distinct stages of evolution: exponential growth, transition to nonlinear saturation, terminal velocity,\footnote{P. Ramaprabhu and Guy Dimonte, Phys. Rev. E 71, 036314 (2005) } and acceleration. In the terminal velocity phase, the bubble has a rounded tip consistent with potential flow calculations. Later in time, the bubble tip becomes more streamlined and the bubble accelerates. Such acceleration has been observed in other simulations, where the flow was allowed to develop to such late-times. We will survey these results, and put forth a possible explanation for our observations. [Preview Abstract] |
Tuesday, November 22, 2005 8:39AM - 8:52AM |
LT.00004: Tracking the front of the Rayleigh-Taylor Unstable Interface Xiaolin Li We describe our recent renovation of the Front Tracking package, especially in the 3D handling of topological bifurcations. We also assess the performance of the package, in comparison with publicly distributed interface codes(the level set method), with published performance results (VOF and other methods) and with previous versions of front tracking. The major new algorithm presented here is Locally Grid Based tracking(LGB), which combines the best features of two previous 3D tracking algorithms. It combines the robustness of grid based tracking with the accuracy of grid free tracking, and thus it is a significant improvement to both of these algorithms. We also discuss the surface curvature and normal algorithms and a higher order propagation algorithm,used for the comparison studies presented here. This new front tracking code has now been used for more detailed study of the Rayleigh-Taylor instability with controlled experiments on physical surface tension and mass diffusion. We have found significant improvement on the accuracy of the fluid mixing rate with the experiment. [Preview Abstract] |
Tuesday, November 22, 2005 8:52AM - 9:05AM |
LT.00005: Rayleigh-Taylor turbulent mixing of immiscible, miscible and stratified fluids Andrei E. Gorobets, Snezhana I. Abarzhi, Katepalli R. Sreenivasan We propose a simple phenomenological model to describe the Rayleigh-Taylor turbulent mixing of immiscible, miscible, and stratified fluids. The model accounts for the multi-scale character of the interface dynamics and distinguishes between the evolution of horizontal and vertical scales. The results obtained indicate two distinct mechanisms for the mixing development. The first is the traditional “merge” associated with the growth of horizontal scales. The second is associated with the production of small-scale structures and with the growth of the vertical scale, which plays the role of the integral scale for energy dissipation. For immiscible fluids, the rate of momentum loss is the flow invariant, whereas the energy dissipation rate is not, and the fundamental scaling properties of the accelerated flow differ from those of the classical Kolmogorov turbulence. The turbulent diffusion calculated through the temperature fluctuations does not stop mixing, but decreases its growth-rate significantly, makes it time-dependent and sensitive to the initial conditions. A stratified density distribution can terminate the mixing process. [Preview Abstract] |
Tuesday, November 22, 2005 9:05AM - 9:18AM |
LT.00006: Asymptotic behavior of the Rayleigh--Taylor instability Laurent Duchemin, Christophe Josserand, Paul Clavin We investigate long time numerical simulations of the inviscid Rayleigh-Taylor instability at Atwood number one using a boundary integral method. We are able to attain the asymptotic behavior for the spikes predicted by Clavin \& Williams for which we give a simplified demonstration. In particular we observe that the spike's curvature evolves like $t^3$ while the overshoot in acceleration shows a good agreement with the suggested $1/t^5$ law. Moreover, we obtain consistent results for the prefactor coefficients of the asymptotic laws. Eventually we exhibit the self-similar behavior of the interface profile near the spike. [Preview Abstract] |
Tuesday, November 22, 2005 9:18AM - 9:31AM |
LT.00007: Linear and Weakly Nonlinear Analysis of Shear-Induced Stabilization of Rayleigh-Taylor Problem Abdullah Kerem Uguz, Ranga Narayanan Shear induced Rayleigh-Taylor instability in an open-channel flow and in a closed container is studied in this paper. It is known that when a liquid is sheared with constant stress, the interface is not flat and the stability limit is decreased. In this study, for both cases, i.e., open channel flow and closed flow, at the base state, a flat interface between the two liquids is satisfied and the stability of this base state to small disturbances is studied via linear stability analysis. In the open channel flow, the critical point remains unchanged compared to the classical Rayleigh-Taylor instability, but the critical point exhibits oscillations and the frequency of these oscillations depends on the wall speed. On the other hand, in a closed geometry, moving the wall stabilizes an otherwise unstable configuration. This result shows the importance of taking the second fluid layer as active, provided a flat interface is an allowable base solution. The physics of the stabilization is explained. A weakly nonlinear analysis is used to study the nature of the bifurcation via dominant balance method and it is concluded that the problem shows a backward pitchfork bifurcation just like the classical Rayleigh-Taylor instability problem. [Preview Abstract] |
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