Experimental Study On Converging Shock Wave Generation And Its Interaction With Polygonal Interfaces

Richtmyer-Meshkov (RM) instability occurs when an initially perturbed interface separating two different fluids is impulsively accelerated by a shock wave. The perturbation of the interface will grow because of the misalignment between density gradient and pressure gradient. Spikes and bubbles appear in the flow field, enhancing the interpenetration and mixing between two fluids. Recent years, studies on RM instability have received much attention due to the extensive applications in scientific and industrial fields. However, it is still a challenge for us to generate a converging shock wave and to apply in the RM instability study in laboratory, which motivates this study.In this work, based on the work of Takayama, a vertical annular diaphragmless shock tube is constructed to generate cylindrical shock waves. Although smaller in size than the one by Takayama, our facility has two important features:accessibility of laser sheet and controllable interface formation. Through the experimental and numerical methods, the shock tube is tuned and the feasibility and reliability of this shock tube is verified to generate the annular coaxial cylindrical converging shock wave. A parametric study is then carried out to explore the characteristics of the annular coaxial cylindrical converging shock wave under the condition of incident shock Ms=1.17. Pressure variations with time at different positions in the test section are acquired from both the experiment and numerical simulation, and the converging effect of the shock wave is emphasized. A high speed schlieren system is set up to visualize the converging shock wave. The images show that the shock front matches well with a circular arc whose center is located at the axis of the test section, which indicates that the cylindrical shock waves are uniformly formed in perfectly two-dimensional circular shapes. There is a self-similar solution for the cylindrical converging shock wave. A similarity constant a=0.836±0.005is obtained in air from the experimental data points using the method of least squares, which agrees well with previous experimental and analytical results in the literature.Three kinds of polygonal interfaces including octagon, square and triangle are formed by using thin wires to restrict soap films. The influence of the thin wires and chamfers on the interface evolution is also assessed by numerical simulation. The results indicate that the thin wires and chamfers have limited effect on the interface development. The evolutions of polygonal Air/SF6interfaces induced by a cylindrical shock wave are recorded by a high speed camera under the illumination of a continuous laser sheet. Corresponding numerical simulations are also performed for comparing with the experiments, and good agreements are found qualitatively and quantitatively. During the evolution, the interface is first compressed after the incident converging shock wave and then the "spike" and "bubble" configurations are generated due to the deposition of the baroclinic vorticity on the interface. Phase reversal occurs on the interfaces after the interaction with the reflected shock wave, which creates an opposite pressure gradient compared with the initial incident shock. The secondary "spike" configuration is generated at the original "bubble" position while the secondary "bubble" configuration is generated at the original "spike" position and they grow gradually with time. From the observation, it can be found that the interface evolution is quite symmetric which once again verifies the reliabilities of the converging shock wave generated and the interface formation method. However, the pollution of the test gas in the square interface leads to some differences between experimental and numerical result.In order to analyze the vorticity of the flow field, we calculate the circulation between the three polygonal interfaces. Results indicate that in early stage of the evolution more baroclinic vorticity is deposited on the interface which has less edges after interacting with the incident shock wave, due to the longer time in interaction. Different from incident shock wave, more baroclinic vorticity is deposited on the interface during the reshock stage, and the vorticity is in opposite direction. After reshock, more vorticity is deposited on the octagon interface.