Hydrodynamics in ICF: The Rayleigh-Taylor Instability

1. Hot Cold Water Water Hydrodynamics in ICF: The Rayleigh-Taylor Instability Splitter plate Exit plenum Meshes 1.0 m Flow straightener 2005 HEDP Summer School W. KraftPhd,Msc, A. BanerjeePhd, N. MueschkePhd, Msc, P. RamaprabhuPhd, P. WilsonPhd, L. DeChantPhd, K. LeichtMsc, D. SniderPhd 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. 0.2 m UG Research Asst. (6ft tall) PIV/PLIF Image field 8 cm Hort. x 6 cm Vert. 0.0125 cm/pix 0.3 m Air Inlet ducting He 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/oC Acquisition rate 100 Hz. Flow channel Fans Camera 640H x 480V Pixels 1200 Image Capacity on Board • 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. Lasers Two 120 mJ 15 Hz pulse Sample rate: 30/sec. Air/Helium Facility as of December 8, 2003. Flow direction Cold water At = 10-3 DT = 5oC U0 = 4.4 cm/s Warm water Side View 10 cm 2.0 m 1.0 m 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 (At), and the acceleration due to gravity. In this experiment,the distance downstream can be related to time through the Taylor hypothesis. Airin Exit Plenum Vents 0.6 m Hein Splitter Plate Meshes Flow Straighteners Exit Plenum Vents 0.4 m (a) 2.0 m 1.0 m 1.0 m Top View Fluid 1, f1 = 100 % (b) Fluid 2, f1 = 0 % (c) Background image is an experimentally captured PLIF image ~ 35 cm downstream. Low Atwood number water channel ( At ~ 10-3 ) Statistically steady experiment with long run times 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. High Atwood number He/Air gas channel, ( At ≤ 0.75 ) PIV: Velocity measurements PIV-S : Visualization and measurement using seed particles (x = 35 cm) PIV-Scalar (PIV-S), a variant of conventional PIV, was developed to simultaneously measure density and velocity fields in a R-T mix. 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 Image Analysis: Volume fraction, mixing layer width measurement 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. Volume fraction ( f1 ) profiles from the mixing layer shown on the right using 400 images , where f1+ f2 = 100 % Evolution of velocity fluctuation profiles across the mix width as the mixing layer grows Rayleigh-Taylor mixing layer with Atwood #, At = 0.035 Velocity – density correlations inside the Rayleigh-Taylor mixing layer (a) At x ~ 2.5 cm, and (b) at x ~ 35 cm. < ’v’> is strongly correlated at both locations while < ’u’> is only weakly correlated near the splitter plate  = 0.07 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. Downstream evolution of the mixture fraction (i.e. density) profile across the mixing layer Determination of the growth constant, , for self-similar growth of the Rayleigh-Taylor instability where the half mix width, h =  At g t 2