Shock cavity implosion morphologies and vortical projectile generation in axisymmetric shock–spherical fast/slow bubble interactions
Shock cavity implosion morphologies and vortical projectile generation in axisymmetric shock–spherical fast/slow bubble interactions
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DOI：
10.1017/s0022112097008045
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发表时间：
1998-05
影响因子：
3.7
通讯作者：
N. Zabusky;S. Zeng
中科院分区：
文献类型：
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作者：
N. Zabusky;S. Zeng
快/慢(F/S)球形和近球形构型中的激波边界空泡的塌缩会产生喷流和涡环。本文用欧拉方程模拟了平面激波与R12轴对称球形气泡的相互作用。我们将显示上游和下游复杂波型演变的结果可视化和量化，并强调涡环的出现。我们研究了这些结构的大小如何随马赫数的变化而变化。气泡内的激波空穴坍塌导致界面上的二次激波折射，并在低马赫数时产生弱喷流。在较高的马赫数(如M=2.5)下，气泡下游出现“旋涡抛射体”(Vp)。初级Vp产生于马赫圆盘上产生的延迟锥形涡旋层，它是在气泡下游发生碰撞的弯曲入射激波相互作用的结果。这些环以一种自相似的方式增长，它们的循环是到来的激波马赫数的函数。当M=5.0时，它与沉积在气泡界面上的初级负循环具有相同的数量级。同样，在M=2.5和5.0时，在气泡顶端附近出现双涡层并移出界面。它演化成一个VP，一个不对称的扩散双环，并径向移动到气泡的顶点之外。数值模拟采用二阶精度的Harten-Yee迎风TVD格式，网格分辨率为803×123，气泡半径为55个区域。
Collapsing shock-bounded cavities in fast/slow (F/S) spherical and near-spherical configurations give rise to expelled jets and vortex rings. In this paper, we simulate with the Euler equations planar shocks interacting with an R12 axisymmetric spherical bubble. We visualize and quantify results that show evolving upstream and downstream complex wave patterns and emphasize the appearance of vortex rings. We examine how the magnitude of these structures scales with Mach number. The collapsing shock cavity within the bubble causes secondary shock refractions on the interface and an expelled weak jet at low Mach number. At higher Mach numbers (e.g. M=2.5) ‘vortical projectiles’ (VP) appear on the downstream side of the bubble. The primary VP arises from the delayed conical vortex layer generated at the Mach disk which forms as a result of the interaction of the curved incoming shock waves that collide on the downstream side of the bubble. These rings grow in a self-similar manner and their circulation is a function of the incoming shock Mach number. At M=5.0, it is of the same order of magnitude as the primary negative circulation deposited on the bubble interface. Also at M=2.5 and 5.0 a double vortex layer arises near the apex of the bubble and moves off the interface. It evolves into a VP, an asymmetric diffuse double ring, and moves radially beyond the apex of the bubble. Our simulations of the Euler equations were done with a second-order-accurate Harten–Yee-type upwind TVD scheme with an approximate Riemann Solver on mesh resolution of 803×123 with a bubble of radius 55 zones.