On the interaction of a planar shock with a light polygonal interface

Zhigang Zhai,Ting Si,Minghu Wang,Xisheng Luo

doi:10.1017/jfm.2014.516

Zhigang Zhai, Ting Si + Show 2 more

Open Access

https://doi.org/10.1017/jfm.2014.516

Copy DOI

Abstract

AbstractThe interaction of a planar shock wave with a polygonal $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathrm{N}}_2$ volume surrounded by ${\mathrm{SF}}_6$ is investigated experimentally and numerically. Three polygonal interfaces (square, triangle and diamond) are formed by the soap film technique developed in our previous work, in which thin pins are introduced as angular vertexes to connect adjacent sides of polygonal soap films. The evolutions of the shock-accelerated polygonal interfaces are then visualized by a high-speed schlieren system. Wave systems and interface structures can be clearly identified in experimental schlieren images, and agree well with the numerical ones. Quantitatively, the movement of the distorted interface, and the length and height of the interface structures are further compared and good agreements are achieved between experimental and numerical results. It is found that the evolution of these polygonal interfaces is closely related to their initial shapes. In the square interface, two vortices are generated shortly after the shock impact around the left corner and dominate the flow field at late stages. In the triangular and diamond cases, the most remarkable feature is the small ‘${\mathrm{SF}}_6$ jet’ which grows constantly with time and penetrates the downstream boundary of the interface, forming two independent vortices. These distinct morphologies of the three polygonal interfaces also lead to the different behaviours of the interface features including the length and height. It is also found that the velocities of the vortex pair predicted from the theory of Rudinger and Somers (J. Fluid Mech., vol. 7, 1960, pp. 161–176) agree with the experimental ones, especially for the square case. Typical free precursor irregular refraction phenomena and the transitions among them are observed and analysed, which gives direct experimental evidence for wave patterns and their transitions at a slow/fast interface. The velocities of triple points and shocks are experimentally measured. It is found that the transmitted shock near the interface boundary has weakened into an evanescent wave.

Highlights

When a shock wave passes through a density inhomogeneity, the strong coupling of several types of fluid dynamics phenomena, including shock–wave refraction and reflection, vorticity production and transport, and turbulence, is involved
It is found that the evolution of these polygonal interfaces is closely related to their initial shapes
In the triangular and diamond cases, the most remarkable feature is the small ‘SF6 jet’ which grows constantly with time and penetrates the downstream boundary of the interface, forming two independent vortices. These distinct morphologies of the three polygonal interfaces lead to the different behaviours of the interface features including the length and height

Summary

Introduction

When a shock wave passes through a density inhomogeneity, the strong coupling of several types of fluid dynamics phenomena, including shock–wave refraction and reflection, vorticity production and transport, and turbulence, is involved. The shapes of the gas interface in previous studies mainly include the single-mode interface (Meshkov 1969; Brouillette 2002; Jacobs & Krivets 2005; Mariani et al 2008; Long et al 2009; Balakumar et al 2012; Luo, Wang & Si 2013), the spherical or cylindrical bubble formed by a soap film (Haas & Sturtevant 1987; Hosseini & Takayama 2005; Layes, Jourdan & Houas 2009; Haehn et al 2011, 2012; Ranjan, Oakley & Bonazza 2011; Zhai et al 2011; Si et al 2012), the membrane-less gas cylinder (Jacobs 1992, 1993; Tomkins et al 2008; Zhai et al 2014; Zou et al 2010) or gas curtain (Jacobs et al 1993; Orlicz et al 2009; Balakumar et al 2012; Balasubramanian et al 2012; Tomkins et al 2013) formed by the jet technique and the inclined planar interface (Wang et al 2012; McFarland et al 2014) Besides these classical interface shapes, Mikaelian (2005) theoretically and numerically studied the RMI on an initial interface with a discontinuous change in its first derivative.

Concave mirror

Initial interface ts fps is

Xl H

Conclusions