Atwood Number Effects Research Articles

Exploring the Atwood number impact on shock-driven hydrodynamic instability at pentagonal interface using discontinuous Galerkin simulations

Investigation of Atwood number impact is crucial for comprehending the flow dynamics of the evolving hydrodynamic instability. In this paper, the Atwood number impacts on the shock-driven hydrodynamic instability at a backward-facing pentagonal interface in its early stages are explored numerically. The shock-driven pentagonal interface has a unique property in which the incident angle of the shock wave is constant along the interface edge. This property provides the ideal environment for the shock-refraction process. To examine the Atwood number impact, we consider five distinct gases, including sulfur hexafluoride, krypton, argon, neon, and helium, which are filled inside the pentagonal interface and surrounded by nitrogen gas. A mixed modal discontinuous Galerkin method is used to solve the two-dimensional Navier–Stokes–Fourier equations for two-component gas flows for numerical simulations. The simulation results illustrate that the Atwood number plays a crucial role in the flow fields of the shocked-pentagonal gas interface, which have not been reported in the literature. The flow fields are greatly impacted by the Atwood number, leading to complex wave patterns, shock focusing, jet formation, interface deformation, and vorticity generation. Further, the Atwood number effects on the flow fields are also thoroughly examined by a quantitative study based on the integral quantities and the interface features. Finally, a quantitative analysis is performed to examine the intrinsic differences between the evolution of the flow fields at the square and pentagonal interfaces.

Linear analysis of Atwood number effects on shear instability in the elastic\u2013plastic solids

The evolution of shear instability between elastic–plastic solid and ideal fluid which is concerned in oblique impact is studied by developing an approximate linear theoretical model. With the velocities expressed by the velocity potentials from the incompressible and irrotational continuity equations and the pressures obtained by integrating momentum equations with arbitrary densities, the motion equations of the interface amplitude are deduced by considering the continuity of normal velocities and the force equilibrium with the perfectly elastic–plastic properties of solid at interface. The completely analytical formulas of the growth rate and the amplitude evolution are achieved by solving the motion equations. Consistent results are performed by the model and 2D Lagrange simulations. The characteristics of the amplitude development and Atwood number effects on the growth are discussed. The growth of the amplitude is suppressed by elastic–plastic properties of solids in purely elastic stage or after elastic–plastic transition, and the amplitude oscillates if the interface is stable. The system varies from stable to unstable state as Atwood number decreasing. For large Atwood number, elastic–plastic properties play a dominant role on the interface evolution which may influence the formation of the wavy morphology of the interface while metallic plates are suffering obliquely impact.

Atwood number effects on the instability of a uniform interface driven by a perturbed shock wave.

The evolution of a uniform interface subjected to a perturbed shock wave has been experimentally studied over a range of Atwood numbers 0.22≤A≤0.68 and Mach numbers 1.2≤M≤1.8 using a vertical shock tube. The perturbed shock wave is produced by diffracting a planar incident shock over a rigid cylinder. The wave patterns of the perturbed shock are captured by high-speed shadowgraphy, while the evolution of the shocked interface is captured by planar Mie scattering. Besides the formations of a cavity and two steps, an apparent counter-rotating vortex pair emerges on the shocked interface due to the baroclinic vorticity deposition, as both the Atwood number and Mach number increase. Quantitatively, it is interesting to note that the amplitude growth rate of the shocked interface decreases with increasing the Atwood number, which is fundamentally different from the results related to the classical RM instability. This notable feature is explained by the approximation of an oblique shock hitting a uniform interface. For weak shock, a suitable time scaling is employed to collapse experimental data irrespective of the Atwood number difference.

Large eddy simulation of high atwood number rayleigh-taylor mixing

Large eddy simulation of Rayleigh-Taylor instability at high Atwood numbers is performed using recently developed, kinetic energy-conserving, non-dissipative, fully-implicit, finite volume algorithm. The algorithm does not rely on the Boussinesq assumption. It also allows density and viscosity to vary. No interface capturing mechanism is requried. Because of its advanced features, unlike the pure incompressible ones, it does not suffer from the loss of physical accuracy at high Atwood numbers. Many diagnostics including local mole fractions, bubble and spike growth rates, mixing efficiencies, Taylor micro-scales, Reynolds stresses and their anisotropies are computed to analyze the high Atwood number effects. The density ratio dependence for the ratio of spike to bubble heights is also studied. Results show that higher Atwood numbers are characterized by increasing ratio of spike to bubble growth rates, higher speeds of bubble and especially spike fronts, faster development in instability, similarity in late time mixing values, and mixing asymmetry.

Droplet and multiphase effects in a shock-driven hydrodynamic instability with reshock

Shock-driven multiphase instabilities (SDMI) are unique physical phenomena that have far-reaching applications in engineering and science such as high energy explosions, scramjet combustors, and supernovae events. The SDMI arises when a multiphase field is impulsively accelerated by a shock wave and evolves as a result of gradients in particle-gas momentum transfer. A new shock tube facility has been constructed to study the SDMI. Experiments were conducted to investigate liquid particle and multiphase effects in the SDMI. A multiphase cylindrical interface was created with water droplet laden air in our horizontal shock tube facility. The interface was accelerated by a Mach 1.66 shock wave, and its reflection from the end wall. The interface development was captured using laser illumination and a high-resolution CCD camera. Laser interferometry was used to determine the droplet size distribution. A particle filtration technique was used to determine mass loading within an interface and verify particle size distribution. The effects of particle number density, particle size, and a secondary acceleration (reshock) of the interface were noted. Particle number density effects were found comparable to Atwood number effects in the Richtmyer–Meshkov instability for small ( $$\sim 1.7~{\upmu }$$ m) droplets. Evaporation was observed to alter droplet sizes and number density, markedly after reshock. For large diameter droplets ( $$\sim 10.7~{\upmu }$$ m), diminished development was observed with larger droplets lagging far behind the interface. These lagging droplets were also observed to breakup after reshock into structured clusters of smaller droplets. Mixing width values were reported to quantify mixing effects seen in images.

Effects of Atwood number on shock focusing in shock–cylinder interaction

The evolution of shock-accelerated heavy-gas cylinder surrounded by the air with different Atwood numbers ( $$A_t=0.28, 0.50, 0.63$$ ) is investigated, concentrating on shock focusing and jet formation. Experimentally, a soap film technique is used to generate an ideal two-dimensional discontinuous gas cylinder with a clear surface, which can guarantee the observation of shock wave movements inside the cylinder. Different Atwood numbers are realized by different mixing ratios of $$\hbox {SF}_6$$ and air inside the cylinder. A high-speed schlieren system is adopted to capture the shock motions and jet morphology. Numerical simulations are also performed to provide more information. The results indicate that an inward jet is formed for low Atwood numbers, while an outward jet is generated for high Atwood numbers. Different Atwood numbers will lead to the differences in the relative velocities between the incident shock and the refraction shock, which ultimately results in the differences in shock competition near the downstream pole. The morphology and feature of the jet are closely associated with the position and intensity of shock focusing. The pressure and vorticity contours indicate that the jet formation should be attributed to the pressure pulsation caused by shock focusing, and the jet development is ascribed to the vorticity induction. Finally, a time ratio proposed in the previous work for determining the shock-focusing type is verified by experiments.

Direct Numerical Simulations of Rayleigh-Taylor instability

The development of the Rayleigh-Taylor mixing layer is studied using data from an extensive new set of Direct Numerical Simulations (DNS), performed on the 0.5 Petaflops, 150k compute cores BG/L Dawn supercomputer at Lawrence Livermore National Laboratory. This includes a suite of simulations with grid size of 10242 × 4608 and Atwood number ranging from 0.04 to 0.9, in order to examine small departures from the Boussinesq approximation as well as large Atwood number effects, and a high resolution simulation of grid size 40962 × 4032 and Atwood number of 0.75. After the layer width had developed substantially, additional branched simulations have been run under reversed and zero gravity conditions. While the bulk of the results will be published elsewhere, here we present preliminary results on: 1) the long-standing open question regarding the discrepancy between the numerically and experimentally measured mixing layer growth rates and 2) mixing characteristics.