Jason Oakley

A computational parameter study for the three-dimensional shock-bubble interaction

The morphology and time-dependent integral properties of the multifluid compressible flow resulting from the shock–bubble interaction in a gas environment are investigated using a series of three-dimensional multifluid-Eulerian simulations. The bubble consists of a spherical gas volume of radius 2.54 cm (128 grid points), which is accelerated by a planar shock wave. Fourteen scenarios are considered: four gas pairings, including Atwood numbers −0.8 A M ≤ 5.0. The data are queried at closely spaced time intervals to obtain the time-dependent volumetric compression, mean bubble fluid velocity, circulation and extent of mixing in the shocked-bubble flow. Scaling arguments based on various properties computed from one-dimensional gasdynamics are found to collapse the trends in these quantities successfully for fixed A . However, complex changes in the shock-wave refraction pattern introduce effects that do not scale across differing gas pairings, and for some scenarios with A > 0.2, three-dimensional (non-axisymmetric) effects become particularly significant in the total enstrophy at late times. A new model for the total velocity circulation is proposed, also based on properties derived from one-dimensional gasdynamics, which compares favourably with circulation data obtained from calculations, relative to existing models. The action of nonlinear-acoustic effects and primary and secondary vorticity production is depicted in sequenced visualizations of the density and vorticity fields, which indicate the significance of both secondary vorticity generation and turbulent effects, particularly for M > 2 and A > 0.2. Movies are available with the online version of the paper.

Experimental validation of a Richtmyer-Meshkov scaling law over large density ratio and shock strength ranges

A universal scaling law for the Richtmyer–Meshkov instability is validated with experimental results covering a wide range of density ratios and shock strengths. These results include the first membraneless, gas-phase, interface experiments for A>0.5 and M>1.5. The shock-accelerated, sinusoidal interface experiments are conducted in a vertical shock tube with a large square cross section and cover the experimental parameter space: 0.29<A<0.95, 1.1<M<3, and 3.1×104<Re<1.4×107. Results provide growth-rate data for comparison with computational fluid dynamics simulation codes and verify the nondimensional time and amplitude parameters chosen for scaling are the correct ones. Correct scaling is obtained by including a growth-reduction factor that accounts for diffusion at the interface. Planar imaging techniques are used to diagnose the instability development for a nearly single-mode interface, and results are reported for eight scenarios (including three distinct gas pairs) that span the linear and nonlinea...

Structural network models for molten plastics evaluated in large amplitude oscillatory shear

The kinetic rate equation proposed by Mewis and Denn (1983) for their structural network model is found to predict accurately the large amplitude oscillatory shear behavior of molten low density polyethylene IUPAC X. Spectral analysis is used to compare the predictions of several kinetic rate equations. Frequency versus strain amplitude maps are constructed to examine each harmonic of the shear stress response predicted by the Mewis–Denn model. A Pipkin diagram is calculated for this model using contours for the amplitude of the third harmonic.

Turbulent mixing measurements in the Richtmyer-Meshkov instability

The Richtmyer-Meshkov instability is experimentally investigated in a vertical shock tube using a new type of broadband initial condition imposed on an interface between a helium-acetone mixture and argon (A = 0.7). The initial condition is created by first setting up a gravitationally stable stagnation plane between the gases and then injecting the same two gases horizontally at the interface to create a shear layer. The perturbations along the shear layer create a statistically repeatable broadband initial condition. The interface is accelerated by a M = 1.6 planar shock wave, and the development of the ensuing turbulent mixing layer is investigated using planar laser induced fluorescence. By the latest experimental time, 2.1 ms after shock acceleration, the layer is shown to be fully turbulent, surpassing both turbulent transition criteria based on the Reynolds number and shear layer scale. Mixing structures are nearly isotropic by the latest time, as seen by the probability density function of gradien...

Shock-bubble interactions : Features of divergent shock-refraction geometry observed in experiments and simulations

The interaction of a planar shock wave with a spherical bubble in divergent shock-refraction geometry is studied here using shock tube experiments and numerical simulations. The particular case of a helium bubble in ambient air or nitrogen (A≈−0.8) is considered, for 1.4<M<3.0. Experimental planar laser diagnostics and three-dimensional multifluid Eulerian simulations clearly resolve features arising as a consequence of divergent shock refraction, including the formation of a long-lived primary vortex ring, as well as counter-rotating secondary and tertiary upstream vortex rings that appear at late times for M⩾2. Remarkable correspondence between experimental and numerical results is observed, which improves with increasing M, and three-dimensional effects are found to be relatively insignificant. Shocked-bubble velocities, length scales, and circulations extracted from simulations and experiments are used successfully to evaluate the usefulness of various analytical models, and characteristic dimensionle...

Experimental and numerical investigation of shock-induced distortion of a spherical gas inhomogeneity

Results are presented from a series of experiments and simulations, studying the interaction of a planar shock wave (2.0≤M≤5.0) with a discrete gas inhomogeneity. Experiments and computations confirm that the phenomenology of shock–bubble interactions is fundamentally altered by the changes in the Atwood number. In the case of a low Atwood number, the late time flow field is dominated by coherent vortical structures, whereas in the case of a high Atwood number, the shocked bubble is effectively reduced to a small core of compressed fluid, which trails behind a plume-like structure indicative of a well-developed mixing region.

Molecular origins of nonlinear viscoelasticity

Polymer melts are discussed in terms of relationships between their nonlinear viscoelasticity and molecular structure. The challenges of making nonlinear measurements and the rheometers available for studying nonlinear viscoelasticity are presented. Theories and constitutive models are reviewed and compared with one another and experimental data. Future studies of the molecular origins of nonlinear viscoelasticity are discussed especially in terms of rheometer development and future prospects for nonlinear viscoelastic models.

Obtaining Fourier series graphically from large amplitude oscillatory shear loops

Large amplitude oscillatory shear (LAOS) flow has been used to characterize the nonlinear viscoelasticity of polymer melts and solutions. Results are frequently reported with shear stress versus strain loops, or with shear stress versus shear rate loops. A Fourier analysis of the stress response to LAOS is often desired for comparison with theory, or for quantitative comparison between resins. A method is presented which employs the discrete Fourier transform to obtain the Fourier series coefficients from LAOS loops.

Experimental investigation of a twice-shocked spherical density inhomogeneity

Results are presented from a series of experiments investigating the behavior of a twice-shocked spherical density inhomogeneity. The experiments are performed at the Wisconsin Shock Tube Laboratorys (WiSTL) 9?m long vertical shock tube with a square internal cross section, 0.254?m on a side, equipped with a pneumatically retracting bubble injector. Baroclinic vorticity deposition occurs during the interaction of the shock wave with the spherical density inhomogeneity, leading to the formation of a vortex ring. The incident shock wave reflects from the tube end wall and interacts with the translating vortex ring (reshock), resulting in additional vorticity deposition. After reshock, the ambient particle velocity is zero and the subsequent translational motion of the vortex ring is due entirely to the net circulation present. Circulation models are investigated for the reshock scenario and a new model is developed and applied to both once-shocked and reshocked scenarios. Two Atwood numbers (A=0.17,?0.68) and three initial Mach numbers (M=1.35,?2.00,?2.33) are investigated. High-speed cameras at 10?000?fps are used to observe the development of the vortex ring after reshock. An understanding of the shock-induced compression and vortex generation is vital to the future study of turbulent combustion initiated by the shock focusing phenomenon.

Richtmyer-Meshkov Parameter Study

The growth of an interfacial perturbation after acceleration by a shock wave, known as the Richtmyer-Meshkov instability (RMI), plays an important role in the compression of an ICF target. Experiments studying the RMI are performed in a vertical shock tube by observing the growth of the interface between a pair of gases after acceleration by a planar shock wave. A near 2D, sinusoidal, membraneless interface is created in a shock tube by oscillating rectangular pistons at the stagnation plane between the two gases. The interface is visualized by seeding one of the gases with acetone, smoke, or atomized oil and observing the fluorescence or Mie scattering from a planar laser sheet. The results presented here span a range of Atwood numbers, 0.30<A<0.95, and shock wave strengths, 1.1<M<3. Numerical simulations of the experimental conditions are performed and compared with the experiments using the 2D hydrodynamics code Raptor (LLNL).