Sergey G. Chefranov
The condition of linear instability for a converging cylindrical shock wave in an arbitrary inviscid medium is obtained. The shape of resulting shock wave front is not changed significantly, but the restriction of energy cumulation can be caused by exponential grows of the medium rotation behind the front. The correspondence with experimental and simulation data is considered.
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The condition of linear instability for a converging cylindrical strong shock wave (SW) in an arbitrary viscous medium is obtained in the limit of a large stationary SW radius, when it is possible to consider the same Rankine-Hugoniot jump relations as for the plane SW. This condition of instability is substantially different from the condition of instability for the plane SW because a cylindrical SW does not have chiral symmetry in the direction of the SW velocity (from left to right or vice versa) as in the case of a plane SW. The exponential growth rate of perturbations for the converging c…
In the present paper, an efficient method to generate "pure" cylindrically converging shock wave without a following contact surface is proposed firstly. Then, the Richtmyer-Meshkov instabilities of two interfaces driven by the generated cylindrically converging shock wave and the associated fluids' mixing behaviors are numerically studied. The results show that the instability of the interface is characterized by the growth of perturbation amplitude before re-shock. However, the mixing of fluids is enhanced dramatically after re-shock, which is manifested not only by the evolutions of flow st…
The Richtmyer-Meshkov instability (RMI) refers to the baroclinic generation of vorticity at a perturbed density interface when impacted by a shock wave. It is often thought of as the impulsive limit of the Rayleigh-Taylor instability (RTI). The fluid dynamics video "large-eddy simulations (LES) of RMI in a converging geometry" shows the mixing of materials resulting from the interaction of an imploding cylindrical shock wave with a concentric perturbed interface that separates outside light gas from heavy gas (initially 5 times denser) inside a wedge. At the initial impact, the incident shock …
The commonly applied self-similar solution of the problem of the converging shock wave (shock) evolution with constant compression of the medium behind the shock front results in an unlimited increase of the medium velocity in the vicinity of the implosion. In this paper, the convergence of cylindrical shocks in water is analyzed using the mass conservation law, when the water compression behind the shock front is a variable. The model predicts a finite range of radii, which depends on the adiabatic index of water and where the increase in pressure exceeds the sum of the change of the kinetic …
Molecular Dynamic (MD) approach is applied to study the converging cylindrical shock waves in a dense Lennard-Jones (LJ) fluid. MD method is based on tracking of the atom motions and hence it has an fundamental advantages over hydrodynamic methods which assumes shocks as a structureless discontinuity and requires an equation of state. Due to the small thickness of shock fronts in liquid the two million particles is enough to simulate propagation of a cylindrical shocks in close detail. We investigate stability of converging shocks with different perturbation modes and its mixture. It was shown…
Self-similar solutions to converging (implosions) and diverging (explosions) shocks have been studied before, in planar, cylindrical or spherical symmetry. Here we offer a unified treatment of these apparently disconnected problems . We study the flow of an ideal gas with adiabatic index $γ$ with initial density $ρ\sim r^{-ω}$, containing a strong shock wave. We characterize the self-similar solutions in the entirety of the parameter space $γ,ω$, and draw the connections between the different geometries. We find that only type II self-similar solutions are valid in converging shocks, and that …
The focusing of a secondary shock wave was experimentally recorded during the implementation of an extended nanosecond high-current discharge of a cylindrical configuration in air. Using high-speed shadowgraph recording (up to 300 000 frames/s) of the emerging unsteady flow, cylindrically symmetric gas-dynamic discontinuities were visualized: a diverging shock wave moving from the discharge plasma boundary, a diverging contact discontinuity separating the shock-heated gas from the nonequilibrium region excited by the discharge plasma, and also a converging compression wave (secondary shock wav…
Two converging and superimposing shock and Rayleigh waves are generated on a glass substrate by focusing laser pulses on two concentric rings in a bullseye configuration (67\mm~and 96\mm~radii). We study experimentally the threshold for substrate damage as a function of the number of repetitions and the delay (0-20\,ns). The bullseye focusing experiments are compared to a single focusing ring. Additionally, fluid-structure interaction simulations using a Volume-of-Fluid framework are utilized to estimate the stresses. The lowest number of repetitions to attain surface damage is found for const…
Solutions of the converging and diverging shock problem in a medium with varying density
本文研究变密度介质中Guderley问题的汇聚与发散激波自相似解，重点分析反射激波系数，并通过与拉格朗日模拟对比验证了解析解的准确性，可用于代码验证。
We extend Guderley's problem of finding a self-similar scaling solution for a converging cylindrical or spherical shock wave from the ideal gas case to the case of flows with an arbitrary equation of state closure model, giving necessary conditions for the existence of a solution. The necessary condition is a thermodynamic one, namely that the adiabatic bulk modulus, $K_S$, of the fluid be of the form $pf(ρ)$ where $p$ is pressure, $ρ$ is mass density, and $f$ is an arbitrary function. Although this condition has appeared in the literature before, here we give a more rigorous and extensive tre…
The compression of a cylindrical gas bubble by an imploding molten lead (Pb) shell may be accompanied by the development of the Richtmyer-Meshkov (RM) instability at the liquid-gas interface due to the initial imperfection of the interface. A converging pressure wave impinging upon the interface causes a shell of liquid to detach and continue to travel inwards, compressing the gas bubble. The efficiency of compression and collapse evolution can be affected by development of the RM instability. Investigations have been performed in the regime of extreme Atwood number $A=-1$ with the additional …
Nonlinear asymptotic bubble growth in single-mode spherical Rayleigh-Taylor instability
针对球形几何中单模态瑞利-泰勒不稳定性气泡的非线性增长，构建了适用于任意阿特伍德数及会聚、发散重力构型的解析模型，揭示了球形几何对气泡增长的不同影响，其预测与数值模拟吻合良好。
We show that converging spherical and cylindrical shock waves may ignite a detonation wave in a combustible medium, provided the radius at which the shocks become strong exceeds a critical radius, R_c. An approximate analytic expression for R_c is derived for an ideal gas equation of state and a simple (power-law-Arrhenius) reaction law, and shown to reproduce the results of numerical solutions. For typical acetylene-air experiments we find R_c~0.1 mm (spherical) and R_c~1 mm (cylindrical). We suggest that the deflagration to detonation transition (DDT) observed in these systems may be due to …
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