Session NT: Rayleigh-Taylor Instability II

Experiments on the Rayleigh-Taylor and Richtmyer-Meshkov instabilities utilizing a large Atwood number miscible liquid combination.

Experiments are presented in which an incompressible system of two miscible liquids having a relatively large density difference is accelerated to produce the Richtmyer-Meshkov (RM) or Rayleigh-Taylor (RT) Instabilities. The fluid combination (having an Atwood number of approximately 0.5) is contained within a rectangular tank and initially orientated in the stably stratified configuration. The tank is oscillated in the horizontal direction producing a standing wave two-dimensional initial perturbation on the interface. In the RM experiments the system is released from the top of the rail system, and bounces off a spring to produce the impulsive acceleration. In the RT experiments, the same rail system is used. However, in this case the system is accelerated downward at constant rate using a weight and pulley system. The resulting fluid flows are visualized using a backlit photography. Amplitude measurements taken from the images are compared with existing models and solutions.   

Experimental study of the Rayleigh-Taylor instability initiated with a complex, short-wavelength initial perturbation.

Experiments exploring the Rayleigh-Taylor (RT) instability initiated with a short-wavelength near single-mode initial perturbation have been performed. The experiments were conducted using a square Plexiglass tank mounted to a vertical rail system. The tank is filled with a stably stratified combination of two miscible liquids having an Atwood number of approximately 0.15. The instability is initiated with an imposed initial perturbation in the form of internal Faraday waves at the interface of the two fluids. RT instability is then generated by accelerating the tank down the rails through a pulley-weight system. Net accelerations ranging from 0.4 to 1.4 g's are achieved. The Faraday waves are created by oscillating the tank vertically. The current configuration is capable of creating Faraday waves with a three-dimensional nearly single-mode pattern with wavelengths ranging from 7 to 10 mm. PLIF images of the instability developing from these perturbations reveal what appears to be the beginnings of the development of a turbulent self-similar flow.   

Progress With the Velocity and Density Measurements in High Atwood Number Rayleigh-Taylor Mixing

A statistically steady gas channel experiment is used to study the non-equilibrium development of high Atwood number Rayleigh-Taylor mixing. Two gas streams, one containing air-helium mixture and the other air, flow parallel to each other separated by a thin splitter plate. The streams meet at the end of a splitter plate leading to the formation of an unstable interface and initiation of buoyancy driven mixing. This set up is statistically steady in space and allows for long data collection times. Here, we describe initial validation work to measure the self similar evolution of mixing at density differences (At $\sim $ 0.05). In addition we also present velocity and density measurements at density differences of At $\sim $ 0.25. The facility is being currently used for studying the evolution of the mix at large density differences up to At $\sim $ 0.75. Diagnostics include a Constant Temperature (CT) as well as a Constant current (CC) Hot Wire anemometer and a high resolution digital image analysis. Analysis of measured data is used to explain the structure of mixing as it develops to a self-similar regime. The purpose of this paper is to describe the progress made in the High Atwood number facility and present the initial validation results as well as density and velocity measurements using the diagnostics described above.   

Magneto-rotational instability and turbulent angular momentum transport

We present numerical simulations of magnetized-Couette flow between concentric rotating cylinders in axisymmetric and fully three-dimensional geometry. This work complements the Princeton liquid gallium experiment by Goodman and Ji to study the nonlinear development of the Magneto-Rotational Instability (MRI). The simulations are carried out with a spectral element code incorporating realistic hydro boundary conditions at the upper and lower boundaries and consisting of differentially rotating rings. These conditions were chosen in the experimental setup so as to minimize the effects of Ekman circulations thereby exposing the MRI in its cleanest form. Changes in the flow structure and in the mechanism for angular momentum transport in the magnetic and non-magnetic cases will be discussed as well as the impact of upper and lower boundary conditions (periodic vs. finite container).   

Experimental study of Rayleigh-Taylor instability using magnetic liquids.

Novel experiments are presented that utilize the properties of paramagnetic fluids to study Rayleigh-Taylor instability. The fluids, a miscible combination of paramagnetic salt solution and one of three nonmagnetic solutions, are contained in a tank placed between the poles of a large electromagnet. The magnetic field generated is capable of suspending the heavy paramagnetic fluid over the lighter non-magnetic fluid utilizing the gradient field principle. Rayleigh-Taylor instability is initiated by rapidly removing power to the electromagnet which results in the heavy fluid falling under the gravitational influence. The resulting instability is visualized using back-lit photography. Experiments initiated with an apparently flat initial interface develop into a random surface pattern with dominant length scale well approximated by the fastest growing wavelength given by viscous linear stability theory. Measurements of the mean mixing zone width posses an $\alpha {\kern 1pt}A{\kern 1pt}g{\kern 1pt}t^2$ dependence with a value of \textit{$\alpha $ }in agreement with previous experiments.   

Modeling Molten-Fuel-Moderator Interactions

CANDU reactors are pressurized heavy-water moderated and cooled nuclear reactor designs. During commissioning of nuclear power plants a range of possible accidents must be considered to assure the plants' robust design. One must consider a complete channel blockage in the CANDU reactor. Such an extreme flow blockage event would result in fuel overheating, pressure tube failure, partial melting of fuel rods and possible molten fuel-moderator interactions (MFMI). The MFMI phenomenon would occur immediately following tube rupture, and involves a mixture of steam, hydrogen and molten fuel being ejected into the surrounding moderator water in the form of a high-pressure vapor bubble mixture. This bubble mixture would accelerate the surrounding denser water, causing interfacial mixing due to hydrodynamic instabilities at the interface. As a result of these interfacial instabilities, water is entrained into the growing two-phase bubble mixture with the attendant mass and heat transfer; e.g., water vaporization, fuel oxidation. A comprehensive model has been developed to investigate the complex phenomena resulting from a postulated complete flow blockage and pressure tube failure. This dynamic model will serve as a baseline to characterize the pressure response due to a pressure tube rupture and the associated MFMI phenomena.   

Study of the Rayleigh-Taylor instability at a hemispherical interface using a magnetorheological fluid

The behavior of a single Rayleigh-Taylor spike is studied starting with a hemispherical interface between water and a magnetorheological (MR) fluid. Experiments are performed with two different MR fluids, one consisting of carbonyl iron particles suspended in mineral oil with a small amount of surfactant, the other of carbonyl iron particles suspended in water with a small amount of a suspension agent. This allows for the study of two different pairs of Atwood and Reynolds numbers. A sharp, membrane-less interface is created by freezing water in a mold containing the desired perturbation, and then freezing the MR fluid on top of the ice using a magnetic field. Once the ice melts, the magnetic field is released, and the development of the Rayleigh-Taylor instability is observed using back-lighting and a high speed digital camera framing at 262 frames per second. The growth rates are compared with linear and non-linear theories, and the scaled spike velocities are compared with the results of recent potential flow theories as well as numerical results.   

Interaction of a planar shock wave with a spherical gas inhomogeneity. Part I: experiments.

Experiments are performed in a vertical shock tube of square internal cross section to study the interaction of a planar shock wave with a spherical soap bubble. The argon-filled bubble is prepared at the tip of an injector and released to fall freely under the action of gravity inside the shock tube (filled with nitrogen) while the injector is retracted into the shock tube wall. Shock waves of strength in the range 1.3 $\le M \le $ 3.4 are used to accelerate the bubble. The bubble is initially compressed into a near-disk; a vortex ring then develops at the periphery of the bubble and leads to the entrainment of nitrogen into the argon and, in certain cases, to the development of a secondary vortex ring and an upward jet at the center of the ring. A high-speed digital motion picture of the free-falling bubble is recorded prior to the interaction with the shock wave, using front illumination with diffuse white light. Five post-shock images are recorded, four based on planar Mie scattering obtained illuminating the bubble with a laser sheet and one based on the shadowgraph technique. Numerical simulations of the experiments are performed using the \textit{Raptor }code (LLNL) and the time evolution of the bubble height and width, measured from the experiments, is compared to the corresponding numerical predictions. Good agreement is obtained between experiments and calculations, especially at the earlier post-shock times.   

Interaction of a planar shock wave with a spherical gas inhomogeneity. Part II: calculations.

Results are presented from a series of 3-D simulations studying the compression and unstable growth of a spherical argon bubble accelerated by a planar shock wave of variable strength in a nitrogen environment. These include Mach numbers up to 3.38 and times up to 80 cloud-crushing times. Direct comparison is made between large- and small-scale flow features observed in experiments and obtained in simulations. Integral length scales of the mixing region are investigated, and their time evolution is characterized. Some of the properties of the turbulent velocity field are also investigated using the simulation results. The results indicate a high sensitivity of the calculations to the initial conditions and a significant difference in the post-shock time histories for shock Mach numbers smaller and larger than about 2, suggesting the importance of compressibility effects. These efforts are carried out in continuation of previous experimental and computational investigations performed at the University of Wisconsin Shock Tube Laboratory over the past two years.