Numerical Investigation Of Planar Shock Wave Impinging On The Inert Elliptical Bubble

Richtmyer-meshkov?RM?instability,as a physical phenomenon widely existing in nature and practical engineering applications,has been one of the research hotspots in the field of fluid mechanics for a long time.For the past few years,under the background of supersonic combustion propulsion and Inertial Confinement Fusion?ICF?,the study of RM instability has received extensive attention.Because the sphere itself is a special ellipse,and the bubbles with different densities tend to be ellipses under the influence of gravity,buoyancy and other factors in the actual experiment,it is of great research significance to study the RM instability process of elliptic bubbles under the impinging of shock wave.In this paper,a high-precision computational scheme and two-dimensional N-S equation is used to conduct a detailed numerical study on the process of RM instability caused by incident and reflected shock waves impacting elliptical inert bubbles.Furthermore,the effects of different shock wave Ma number and Atwood number on the wave system and bubble evolution have been investigated.The main research contents and consequences follow from this:?1?With the increase of Ma number,whether a single elliptical SF₆ bubble is placed vertically or horizontally,the focusing position of the shock wave inside the bubble is closer to the downstream pole.When Ma=2.1,the reflected shock waves in the flow field interact with the boundary layer on the upper and lower walls and form a bifurcation.Meanwhile,a supersonic vortex ring is formed outside the interface on the right side of the vertical and horizontal SF₆ bubble,moving continuously downstream and gradually increasing.In addition,when At>0,as the Atwood number decreases,within the vertical and horizontal bubbles,the focusing position of the shock wave is closer to the downstream pole of the bubble.When At<0,an air jet impelling from the outside to the inside is formed on the left interface of the bubble.In particular,it is worth pointing out that the He bubble is divided into upper and lower parts by the inward air jet divides.?2?No matter what the bubble is vertical or horizontal,with the increase of the shock Mach number,the bubble volume and effective bubble volume gradually decrease,while the average vorticity strength and the mixing degree of air and SF₆gas gradually increase.The difference is that the baroclinic effect is more obvious when the bubble is placed horizontally,leading to a larger average vorticity intensity in the flow field than when the bubble is placed vertically.Moreover,as the Atwood number decreases,the effective bubble volume gradually decreases.When At>0,the mixing degree of the gas inside and outside the bubble,the intensity of the average vorticity and the absolute value of the net ring all decrease with the decrease of the Atwood number.When At<0,the changes of the above physical quantities are opposite to that when At>0.The difference is that the interaction time between horizontal bubble and shock wave is longer and the degree of bubble compression is greater than that of vertical bubble.When the bubble is placed horizontally and vertically,the largest absolute values of net ring of the four kinds of bubbles are He and SF₆,respectively.?3?When the shock wave interacts with the double elliptical bubble,under the impacting of the incident and reflected shock wave,the double elliptical bubble in the flow field under three different arrangements and combinations all merge into a whole in the end.When the double elliptical bubble is placed side by side and perpendicular to each other,the incident shock waves in both cases sequentially impact the bubbles in the flow field;and under the action of high pressure generated by the shock wave focusing,the jet structure is formed at the left and right interfaces of each bubble.When the double elliptical bubble is placed horizontally,the incident shock wave simultaneously impacts the two elliptical bubbles above and below the axis of symmetry;the jet in the downstream of the flow field is developed from the vortex,while the jet in the upstream is formed by the collision and squeeze of bubbles.Besides,compared with the former two circumstances,the speed of bubble volume reduction and vortex growth in the flow field are also faster when two bubbles are placed horizontally.