Bubble merger in initial Richtmyer-Meshkov instability on inverse-chevron interface

We report the shock tube experiments on Richtmyer-Meshkov instability to evaluate the bubble merger effect in initial stages. The initial interface is specially designed by alternatively arranging the major and minor inverse-chevron shapes with different amplitudes and wavelengths such that the bubble merger effect is highlighted. The results show that the major and minor shapes develop independently at very early stages, and after a short transient the bubble merger occurs. The bubble merger promotes the width growth of the major shape while it inhibits the width growth of the minor one. However, the bubble merger has a greater effect on the development of the minor shape than the major one. As the initial size difference between two shapes increases, the bubble merger occurs earlier, and the minor shape is affected more heavily. The developments of bubble front difference seem to experience two different linear stages before it enters a nonlinear stage, and collapse well in dimensionless form for different cases. As a result, the initial size difference has a limited effect on the bubble merger in the streamwise direction. The ratio of the major bubble diameter in spanwise direction to the bubble width increases with time, and does not reach a stable phase because the flow is far from the turbulent mixing region.

Figure 1

Schematics of the interface arrangement of the major and minor inverse-chevron shapes with a different wavelength ratio $\kappa =1$ (a), 1.5 (b), 2 (c), and 3 (d). ${\lambda }_l$ and ${\lambda }_s$ are the initial wavelengths of the major and minor inverse-chevron shapes, respectively; $h_{l0}$ and $h_{s0}$ are the corresponding initial widths, respectively. The unit of numbers is millimeters.

Figure 2

The arrangement of the wires at the vertex for $\kappa =1.5$ (a) and the interface formation device (b).

Figure 3

Schlieren images of the $\mathrm{air}/{\mathrm{SF}}_6$ interfaces impacted by a planar shock with $\kappa =1$ (a), 1.5 (b), 2 (c), and 3 (d). $h_l$ and $h_s$ are mixing widths of major and minor shapes, respectively; $D_b$ is diameter of major shape, $a_b$ is bubble width, $a_s$ is spike width, and $\mathrm{\Delta }h$ is bubble front difference. Numbers denote time with a unit of microseconds.

Figure 4

Time variation of the mixing width of the major and minor shapes in dimensionless form.

Figure 5

Time variation of the spike width (a) and bubble width (b). $a_{s0}$ and $a_{b0}$ are spike and bubble widths at time $t_0$, respectively; $v_s$ and $v_b$ are linear velocities of the spike and bubble widths obtained from experiments, respectively.

Figure 6

Time variation of the bubble front difference in dimensional form (a) and dimensionless form (b).

Figure 7

Time variation of $\beta$ and $\overline{\beta }$ for three cases.