ALBERT

Description: Experiments are conducted to study the longitudinal vortices that develop in the boundary layer on the upper surface of an inclined, heated plate. An isothermal plate in water is inclined at angles ranging from 20 to 60 degrees (from the vertical) while the temperature difference is varied from 2 to 23°C. A double-pass Schlieren system is used to visualize the vortices and particle image velocimetry (PIV) is used to measure velocities. In addition, a unique method is developed such that both the Schlieren visualization and PIV can be performed simultaneously. The wavelengths of the vortices and the critical modified Reynolds numbers (R̃) for the onset, merging, and breakup of the vortices are determined from Schlieren images for Pr = 5.8. The critical values for R̃ and the critical wavelengths are compared to results of previous experiments and stability analyses. The spatial growth rates of vortices are determined by using the PIV measurements to determine how the circulation in the vortices grows with distance from the leading edge. This is the first time that the growth rate of the vortices have been found using velocity measurements. These spatial growth rates are compared to the results of Iyer & Kelly (1974) and found to be in general agreement. By defining a suitable circulation threshold, the critical R̃ for the onset of the vortices can be found from the growth curves.

Description: Investigations of the Richtmyer-Meshkov instability carried out in shock tubes have traditionally used membranes to separate the two gases. The use of membranes, in addition to introducing other experimental difficulties, impedes the use of advanced visualization techniques such as planar laser-induced fluorescence (PLIF). Jones and Jacobs (1997) recently developed a new technique by which a perturbed, membrane-free gas-gas interface can be created in a shock tube. The gases enter the shock tube from opposite ends and exit through two small slots on opposite sides of the test section, forming a stagnation point flow at the interface location. A gentle rocking motion of the shock tube then provides the initial perturbation in the form of a standing wave. The original investigation using this technique utilized dense for seeding for visualization, which allowed large-scale effects to be observed, but was incapable of resolving smaller-scale features. PLIF visualization is used in the present study to investigate the instability generated by two incident shock strengths (Ms = 1.11 and 1.21), yielding very clear digital images of the flow. Early-time growth rate measurements obtained from these experiments are found to be in excellent agreement with incompressible linear stability theory (appropriately adjusted for a diffuse interface). Very good agreement is also found between the late-time amplitude measurements and the nonlinear models of Zhang and Sohn (1997) and Sadot et al. (1998). Comparison of images from the Ms = 1.11 and 1.21 sequences reveals a significant increase in the amount of turbulent mixing in the higher-Mach-number experiments, suggesting that a mixing transition has occurred.

Description: The Rayleigh-Taylor instability of a system of three fluids separated by one unstable and one stable interface has been investigated experimentally. The experiments were gravitationally driven and conducted with miscible liquids consisting of salt solutions and fresh water. The lower two layers are initially gravitationally stable and are formed by depositing the lighter fluid on top of a thicker layer of the heavier one. The relatively thick top layer is initially separated from the two lower layers by a rigid barrier that is removed at the start of an experiment. In situations where the density of the bottom-layer fluid equals that of the top-layer fluid, the resulting turbulent flow is found to be self-similar as demonstrated by the collapse of the mean concentration distributions as well as the behaviour of the decay of the peak of the mean concentration profiles. In this configuration, the erosion of the bottom layer by the turbulence generated by the upper unstable interface is found to be small. When the density of the bottom-layer fluid is increased above that of the top-layer fluid, the degree of erosion is further decreased. In the cases where the lower interface is stably stratified at late-time, the entrainment rate E at the lower (statically stable) interface is found to follow a power law of the Richardson number, i.e. E ∝ Ri-n, with n ≈ 1.3, a result in agreement with studies of mixing induced by oscillating grids. When the density of the bottom-layer fluid is decreased below that of the top-layer fluid, the erosion increases as expected. However, in this case, the overall density distribution is such that it is globally Rayleigh-Taylor unstable at late time. In this situation, the turbulent mixing region at late times grows similarly to that of single-interface Rayleigh-Taylor instability with approximately the same value of the growth constant. In these late-time unstable experiments the density profile approaches that of an equivalent two-layer Rayleigh-Taylor unstable system. © 2005 Cambridge University Press.

Description: Richtmyer-Meshkov instability causes spatially periodic perturbations initially imposed on a shock-accelerated, thin gas layer to develop into one of three distinct flow patterns. Planar laser-induced fluorescence imaging of the evolving layer, produced by a perturbed SF6 planar jet in air, shows an apparent flow bifurcation that is observed as mushroom-shaped or sinuous-shaped interfacial patterns. Analysis of this nonlinear instability growth, accomplished by modelling the flow field as a row of line vortices, predicts that the layer thickness grows logarithmically at later times and compares well with our measurements. Because the row of vortices is unstable, the model also provides an explanation for the appearance of the three observed interfacial patterns. © 1995, Cambridge University Press. All rights reserved.

Description: The Richtmyer-Meshkov instability of a low-Atwood-number miscible two-liquid system is investigated experimentally. The initially stratified fluids are contained within a rectangular tank mounted on a sled that rides on a vertical set of rails. The instability is generated by dropping the sled onto a coil spring, producing a nearly impulsive upward acceleration. The subsequent free-fall that occurs as the container travels upward and then downward on the rails allows the instability to evolve in the absence of gravity. The interface separating the two liquids initially has a well-defined sinusoidal perturbation that quickly inverts and then grows in amplitude after undergoing the impulsive acceleration. Disturbance amplitudes are measured and compared to theoretical predictions. Linear stability theory gives excellent agreement with the measured initial growth rate, ao, for single-mode perturbations with the predicted amplitudes differing by less than 10% from experimental measurements up to a non-dimensional time kaot = 0.7, where k is the wavenumber. Linear stability theory also provides excellent agreement for the individual mode amplitudes of multimode initial perturbations until the interface becomes multi-valued. Comparison with previously published weakly nonlinear single-mode models shows good agreement up to kaot = 3, whereas published nonlinear single-mode models provide good agreement up to kaot = 30. The effects of Reynolds number on the vortex core evolution and overall growth rate of the interface are also investigated. Measurements of the overall amplitude are found to be unaffected by the Reynolds number for the range of values studied here. However, experiments carried out at lower values of Reynolds numbers were found to have decreased vortex core rotation rates. In addition, an instability in the vortex cores is observed. The time of appearance of this instability was found to increase when the Reynolds number is decreased.

Description: Rayleigh-Taylor instability experiments are performed using both immiscible and miscible incompressible liquid combinations having a relatively large Atwood number of A ≡ (ρ2-ρ1)/(ρ2 + ρ1) = 0.48. The liquid-filled tank is attached to a test sled that is accelerated downwards along a vertical rail system using a system of weights and pulleys producing approximately 1g net acceleration. The tank is backlit and images are digitally recorded using a high-speed video camera. The experiments are either initiated with forced initial perturbations or are left unforced. The forced experiments have an initial perturbation imposed by vertically oscillating the liquid-filled tank to produce Faraday waves at the interface. The unforced experiments rely on random interfacial fluctuations, resulting from background noise, to seed the instability. The main focus of this study is to determine the effects of forced initial perturbations and the effects of miscibility on the growth parameter, α. Measurements of the mixing-layer width, h, are acquired, from which α is determined. It is found that initial perturbations of the form used in this study do not affect measured α values. However, miscibility is observed to strongly affect α, resulting in a factor of two reduction in its value, a finding not previously observed in past experiments. In addition, all measured α values are found to be smaller than those obtained in previous experimental studies. © 2015 Cambridge University Press.

Description: Theory and experiments are reported that explore the behaviour of the Rayleigh-Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order of , where is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duff et al. (Phys. Fluids, vol. 5, 1962, pp. 417-425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh-Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162-178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duff et al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a decay in growth rates as for large-wavenumber perturbations. © 2016 Cambridge University Press.

Description: In the present study, shock tube experiments are used to study the very late-time development of the Richtmyer-Meshkov instability from a diffuse, nearly sinusoidal, initial perturbation into a fully turbulent flow. The interface is generated by two opposing gas flows and a perturbation is formed on the interface by transversely oscillating the shock tube to create a standing wave. The puncturing of a diaphragm generates a Mach 1.2 shock wave that then impacts a density gradient composed of air and SF6, causing the Richtmyer-Meshkov instability to develop in the 2.0 m long test section. The instability is visualized with planar Mie scattering in which smoke particles in the air are illuminated by a Nd:YLF laser sheet, and images are recorded using four high-speed video cameras operating at 6 kHz that allow the recording of the time history of the instability. In addition, particle image velocimetry (PIV) is implemented using a double-pulsed Nd:YAG laser with images recorded using a single CCD camera. Initial modal content, amplitude, and growth rates are reported from the Mie scattering experiments while vorticity and circulation measurements are made using PIV. Amplitude measurements show good early-time agreement but relatively poor late-time agreement with existing nonlinear models. The model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502) agrees with growth rate measurements at intermediate times but fails at late experimental times. Measured background acceleration present in the experiment suggests that the late-time growth rate may be influenced by Rayleigh-Taylor instability induced by the interfacial acceleration. Numerical simulations conducted using the LLNL codes Ares and Miranda show that this acceleration may be caused by the growth of boundary layers, and must be accounted for to produce good agreement with models and simulations. Adding acceleration to the Richtmyer-Meshkov buoyancy-drag model produces improved agreement. It is found that the growth rate and amplitude trends are also modelled well by the Likhachev-Jacobs vortex model (Likhachev & Jacobs, Phys. Fluids, vol. 17, 2005, 031704). Circulation measurements also show good agreement with the circulation value extracted by fitting the vortex model to the experimental data. © 2012 Cambridge University Press.

Description: Experiments and large eddy simulation (LES) were performed to study the development of the Rayleigh-Taylor instability into the saturated, nonlinear regime, produced between two gases accelerated by a rarefaction wave. Single-mode two-dimensional, and single-mode three-dimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a non-constant acceleration, and a time decreasing Atwood number, A=(p2-p1)/(p2+p1)p2 and p1 where are the densities of the heavy and light gas, respectively. Experiments and simulations are presented for initial Atwood numbers of A = 0:49, A = 0:63, A = 0:82 and A = 0:94. Nominally two-dimensional (2-D) experiments (initiated with nearly 2-D perturbations) and 2-D simulations are observed to approach an intermediate-time velocity plateau that is in disagreement with the late-time velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2-D bubbles in large wavenumber, k=2/=0:247 mm-1, experiments and simulations, where is the wavelength of the initial perturbation. At moderate Atwood numbers, the bubble and spike velocities approach larger values than those predicted by Goncharov's model. These late-time velocity trends are predicted well by numerical simulations using the LLNL Miranda code, and by the 2009 model of Mikaelian (Phys. Fluids., vol. 21, 2009, 024103) that extends Layzer type models to variable acceleration and density. Large Atwood number experiments show a delayed roll up, and exhibit a free-fall like behaviour. Finally, experiments initiated with three-dimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry. © 2018 Cambridge University Press.