1. Hydrodynamics in ICF: The Rayleigh-Taylor Instability 2005 HEDP Summer School W. Kraft Phd, Msc, A. Banerjee Phd, N. Mueschke Phd, Msc, P. Ramaprabhu Phd, P. Wilson Phd, L. DeChant Phd, K. Leicht Msc, D. Snider Phd And Professor M.J. Andrews Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123 ( mandrews@mengr.tamu.edu ) This research is sponsored by the National Nuclear Security Administration under the Stewardship Science Academic Alliances program through DOE Research Grant # DE-FG03-99DP00276/A000 and DE-FG03-02NA00060. Rayleigh-Taylor Instability: Background Rayleigh-Taylor instability (R-T) occurs when a density gradient is accelerated by a pressure gradient such that. When a heavy fluid rests above a light fluid under the influence of gravity, the density interface is unstable to infinitesimal perturbations. The resulting flow evolves in three stages: Exponential growth of infinitesimal perturbations Nonlinear saturation of perturbations Transition to turbulence and self-similar growth RT flows occur in the ejecta of supernovae, in atmospheric flows, and in the ablation interface of Inertial Confinement Fusion capsules. Hot Cold Water Camera 640H x 480V Pixels 1200 Image Capacity on Board Lasers Two 120 mJ 15 Hz pulse Sample rate: 30/sec. PIV/PLIF Image field 8 cm Hort. x 6 cm Vert. 0.0125 cm/pix 0.3 m 0.2 m 1.0 m PIV particle concentration: 3mL/2000 L E-type thermocouples Nickel-Chromium and Constantan Junction diameter of 0.01-0.02 cm Response time 0.001 s/ o C Acquisition rate 100 Hz. Low Atwood number water channel ( A t ~ 10 -3 ) 10 cm A t = 10 -3   C U 0 = 4.4 cm/s Flow direction Cold water Warm water Figure shows a snapshot of the experiment, with nigrosene dye added to the cold water stream. The evolution of the mix is quadratic in x (downstream coordinate), with the mix width depending on the Atwood number (A t ), and the acceleration due to gravity. In this experiment,the distance downstream can be related to time through the Taylor hypothesis. High Atwood number He/Air gas channel, ( A t ≤ 0.75 ) Flow straightener Inlet ducting Air/Helium Facility as of December 8, 2003. UG Research Asst. (6ft tall) Exit plenum Flow channel Splitter plate Meshes Fans Air He 0.6 m Air in He in Exit Plenum 1.0 m 2.0 m Side View Vents Splitter Plate Meshes Flow Straighteners Vents 1.0 m 0.4 m Exit Plenum 2.0 m Top View Rayleigh-Taylor mixing layer with Atwood #, A t = 0.035 Volume fraction ( f 1 ) profiles from the mixing layer shown on the right using 400 images, where f 1 + f 2 = 100 % Fluid 2, f 1 = 0 % Fluid 1, f 1 = 100 % Downstream evolution of the mixture fraction (i.e. density) profile across the mixing layer  = 0.07 Determination of the growth constant, , for self-similar growth of the Rayleigh-Taylor instability where the half mix width, h =  A t g t 2 PIV-S : Visualization and measurement using seed particles (x = 35 cm) (a) (b) (c) Image Analysis: Volume fraction, mixing layer width measurement Velocity power spectra at x = 35 cm (obtained from PIV) show the vertical velocity component dominating over horizontal velocity fluctuations. A developing inertial range (k -5/3 ) and a dissipative range (k -3 ) at the high-wavenumber end is visible. Consecutive grayscale images (a), separated by  t = 0.033 s, of seed particles are cross-correlated to yield a velocity vector field (b). The corresponding out-of-plane component of vorticity (c) shows regions of positive and negative vorticity concentrated within the R-T rollup. Density information may be obtained from (a) through local window averages of particle concentration. PIV-Scalar (PIV-S), a variant of conventional PIV, was developed to simultaneously measure density and velocity fields in a R-T mix. Velocity – density correlations inside the Rayleigh-Taylor mixing layer (a) At x ~ 2.5 cm, and (b) at x ~ 35 cm. is strongly correlated at both locations while is only weakly correlated near the splitter plate Evolution of mixing layer centerline velocity fluctuations. Vertical velocity fluctuations (in the direction of the density gradient ) are significantly larger the stream wise fluctuations. Late time velocity fluctuations grow linearly once the flow is self-similar PIV: Velocity measurements Statistically steady experiment with long run times Evolution of velocity fluctuation profiles across the mix width as the mixing layer grows Background image is an experimentally captured PLIF image ~ 35 cm downstream. Cold and warm water enter through separate inlet plenums. As they pass through flow straighteners and wire meshes, they are kept separated by a splitter plate. As the different-density streams leave the edge of the splitter plate, they form an unstable interface resulting in a statistically-steady R-T mix.