Interaction Effect of Two Ellipse Richtmyer-Meshkov Flows
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摘要: 实验研究了在马赫数为1.18的平面激波冲击作用下，双椭圆界面Richtmyer-Meshkov不稳定性演化的动力学过程。椭圆短轴b与入射激波方向垂直，通过改变双椭圆的中心间距d，采用片光高速摄影和PIV(粒子图像测速)技术，观测了4种不同情形的演化模态，获得了界面演化多幅像和700 μs时刻的速度场，分析了双椭圆气柱之间的相互干扰效应。当d/b为4.0或3.0时，相互干扰效应较弱，双椭圆气柱演化为两个反向旋转的对涡，速度极大值接近30 m/s，出现在2个位置，速度最小值几乎为零，出现在4个位置。当d/b为2.0或1.2时，相互干扰效应很强，两个内涡完全消失，双椭圆气柱演化为一个反向旋转的涡对结构, 速度极大值出现在4个位置，速度极小值出现在两个位置。d/b =2.0时，界面演化图像与圆形气柱演化过程类似。相比d/b =2.0的情形，d/b =1.2时产生更大的斜压涡量，界面演化发展更快，后期出现二次涡现象和分叉结构，整体结构类似于单椭圆气柱演化过程。当d/b在2.0~3.0之间变化时，存在一个是否形成两个内涡的非线性临界值。针对双气柱界面演化明显的内涡弱化现象，分析了4种可能的机制。
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关键词:
- 双椭圆界面 /
- Richtmyer-Meshkov不稳定性 /
- 高速摄影 /
- 粒子图像测速技术
Abstract: The dynamic evolution process and velocity field of two elliptic heavy-gas (SF6) cylinders accelerated by a planar shock wave are studied by laser-sheet high-speed photograph and PIV (particle image velocimetry) diagnostics techniques, respectively.The minor axes (b) of the elliptic cross-sections are aligned perpendicular to the shock direction.While the cylinder dimensions are fixed, we adjust the center-to-center separation (d) between the cylinders.The flow morphologies are visualized and the interaction effect between cylinders is analyzed.When d/b equals 4.0 or 3.0, the two elliptical cylinders roll up into 2 counter-rotating vortex pairs and the interaction is weak.The maximal velocity appears at 2 positions and its magnitude is close to 30 m/s, while the minimal velocity is close to zero and arises at 4 positions.Whend/b decreases to 2.0 or 1.2, due to the strong interaction of the two inner vortices, the inner structure completely disappears and the flow morphology evolves into a counter-vortex pair.The maximal velocity occurs at 4 locations, while the minimal velocity only appears at 2 positions.For the d/b =2.0 case, the evolving images assemble those of the single circular cylinder except for the small gap in the middle.Compared with the d/b =2.0 case, larger amount of baroclinic vorticity is produced in the d/b =1.2 case, and the morphology is similar to the single elliptic cylinder case, with a second vortex phenomenon and bifurcation structure occurring at later times.Actually, we observe a nonlinear, threshold-type behavior of inner vortex formation when d/b varies from 2.0 to 3.0.Finally, we outline and discuss 4 possible mechanisms which may lead to the obvious weakening phenomenon of inner vortices. -
图 1 激波管装置、光测系统和初始气柱示意图
Figure 1. Schematic of the shock tube, optical diagnostic system and initial elliptic cylinders
图 2 激波管波系图(横轴0处为破膜位置，虚线表示观测窗位置，箭头所指为采集数据的时-空区域)
Figure 2. Wave diagram of the shock tube (Position 0 is the location of the diaphram, and the dotted line represents the viewing window, the arrow shows the region in space-time domain where data are taken)
图 3 双椭圆气柱示意图(Ma=1.18)
Figure 3. Schematic of two elliptic cylinders and the incident shock (Ma=1.18)
图 4 双椭圆气柱界面的涡量分布示意图
Figure 4. Vorticity distributions due to the interaction of a shock wave with two elliptic gas cylinders
图 5 弱干扰情形双椭圆气柱演化图像(从左到右依次为t=0, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 ms)
Figure 5. Weak interaction image sequences at t=0 (initial) and t=0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0 ms (dynamic) after shock passage
图 6 强干扰情形双椭圆气柱演化图像(从左到右依次为t=0, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 ms)
Figure 6. Strong interaction image sequences at t=0 (initial) and t=0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 ms (dynamic) after shock passage
图 7(a) 情形2中，700 μs时刻PIV图像(左)及速度场(右)
Figure 7(a). PIV image (left) and velocity field (right) at 700 μs for case 2 (d/b =3.0)
图 7(b) 情形3中，700 μs时刻PIV图像(左)及速度场(右)
Figure 7(b). PIV image (left) and velocity field (right) at 700 μs for case 3 (d/b =2.0)
表 1 双椭圆气柱的初始尺寸
Table 1. Initial gas cylinder geometry sizes
Case a/
(mm)b/
(mm)d/
(mm)d/b 1 10.0 2.5 10.0 4.0 2 10.0 2.5 7.5 3.0 3 10.0 2.5 5.0 2.0 4 10.0 2.5 3.0 1.2 
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