Richtmyer–Meshkov instability of an unperturbed interface subjected to a diffracted convergent shock

Abstract

The Richtmyer–Meshkov (RM) instability is numerically investigated on an unperturbed interface subjected to a diffracted convergent shock created by diffracting an initially cylindrical shock over a rigid cylinder. Four gas interfaces are considered with Atwood number ranging from $-0.18$ to 0.67. Results indicate that the diffracted convergent shock increases its strength gradually and reduces its amplitude quickly when it propagates towards the convergence centre. After the strike of the diffracted convergent shock, the initially unperturbed interface deforms with a bulge structure at the centre and two interface steps at both sides, which can be ascribed to the non-uniformity of the pressure distribution behind the diffracted convergent shock. With the decrease of Atwood number, the bulge structure becomes more pronounced. Quantitatively, the interface amplitude experiences a fast but short growing stage and then enters a linear stage. A good collapse of the dimensionless amplitude is found for all cases, which indicates a weak dependence of the growth rate on Atwood number in the deformed shock-induced RM instability. Then the impulsive theory is modified by eliminating the Atwood number and considering the geometry convergence, which well predicts the amplitude growth for the deformed shock-induced RM instability. Finally, the underlying mechanism is decoupled into three parts, and it is found that both the impulsive pressure perturbation and the geometry convergence promote the growth of interface perturbation while the continuous pressure perturbation inhibits the growth. As the Atwood number decreases, the impulsive perturbation plays an increasingly important role, which suggests that the impulsive perturbation dominates the deformed shock-induced RM instability at the linear stage.

Convergent Richtmyer–Meshkov instability of heavy gas layer with perturbed inner surface

“…Firstly, the interaction between the TS 3 and the outer interface is an instance of the non-standard RMI (Ishizaki et al 1996), in which a distorted shock interacts with a uniform interface. As reported by Zhai et al (2018a) and Zou et al (2019), the driving mechanisms of such a non-standard RMI are different from those of its standard counterpart (in which a uniform shock impacts a distorted interface), and the instability growth is much slower than for the latter. Secondly, due to geometric expansion, the instability growth induced by a diverging shock TS 3 is inherently slower than that of the planar or convergent setting.…”

“…Recently, a novel semiannular shock tube was designed by Luo et al (2015), and its semistructure was demonstrated to bring great conveniences for interface formation and flow diagnostics. For instance, an advanced soap film technique which is able to generate controllable gas interfaces free of three-dimensionality, short-wavelength perturbations and diffusion layers (Luo, Wang & Si 2013; Liu et al 2018), developed in a planar geometry, can be readily extended to the convergent test section of this facility, which has enabled the successful execution of a series of convergent RMI experiments (Ding et al 2017; Liang et al 2017; Ding et al 2019; Zou et al 2019). Experimental results showed that geometric convergence (Bell 1951; Plesset 1954) and the Rayleigh–Taylor (RT) effect (Rayleigh 1883; Taylor 1950) significantly influence the growth of convergent RMI.…”

Statistical characteristics of turbulent mixing in spherical and cylindrical converging Richtmyer–Meshkov instabilities

“…Experimental investigations of cylindrical converging RMI in shock tubes had been conducted by several researchers, such as Hosseini & Takayama (2005), Biamino et al (2015), Luo et al (2015Luo et al ( , 2018Luo et al ( , 2019a, Zhai et al (2017), Rodriguez et al (2017), Ding et al (2017Ding et al ( , 2019, Lei et al (2017), Li et al (2020), Vandenboomgaerde et al (2018, Courtiaud et al (2019), Sun et al (2020b) and Zou et al (2019). These experimental results are particularly helpful for the development of theory and numerical simulation.…”

Effects of velocity shear layer on detonation propagation in a supersonic expanding combustor

“…59 In two-dimensional problems, the vorticity caused by stretching and twisting as well as the influence of the initial viscosity terms can be ignored. 60 The initial vorticity of the interface is not considered. 61 Thus, the baroclinic vorticity equation is expressed as Eq.…”