Numerical study on the interaction of a weak shock wave with an elliptic gas cylinder
Numerical study on the interaction of a weak shock wave with an elliptic gas cylinder
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弱冲击波与椭圆气缸相互作用的数值研究
DOI：
10.1007/s00193-018-0828-y
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发表时间：
2019
期刊：
影响因子：
2.2
通讯作者：
Wang B
中科院分区：
文献类型：
--
作者：
Zhang W;Zou L;Zheng X;Wang B
通过求解二维直角坐标系下的欧拉方程，研究了弱激波与重椭圆形气柱的相互作用。基于该模型和有限体积加权本质无振荡格式，采用界面捕捉算法追踪非连续界面的运动。考虑了三种不同Atwood数的气体对，包括空气中的二氧化碳柱（空气-），空气中的六氟化硫柱（空气-）和氦气中的氪柱（He-Kr）。对于每个气体对，椭圆柱展弦比范围从1/4到4被定义为流向轴长度与展向轴长度之比。特别注意的是纵横比的波型和环流的影响。随着纵横比的减小，相互作用中的波型可归纳为透射激波反射、规则相互作用和透射激波分裂。基于Samtaney和Zabusky（J Fluid Mech 269：45-78，1994）的标度律模型，开发了一种理论方法，用于预测当最快冲击波到达气缸的背风极点时的循环（即，第一次沉积循环）。对于两个扁长（即，椭圆的短轴是沿着流向）和扁圆（即，椭圆的短轴沿着展向）情况下，发现所提出的方法可以很好地估计一次沉积环流。
The interaction of a weak shock wave with a heavy elliptic gas cylinder is investigated by solving the Eulerian equations in two-dimensional Cartesian coordinates. An interface-capturing algorithm based on the-model and the finite volume weighed essential non-oscillatory scheme is employed to trace the motion of the discontinuous interface. Three gas pairs with different Atwood numbers ranging from 0.21 to 0.91 are considered, including carbon dioxide cylinder in air (air–), sulfur hexafluoride cylinder in air (air–), and krypton cylinder in helium (He–Kr). For each gas pair, the elliptic cylinder aspect ratio ranging from 1/4 to 4 is defined as the ratio of streamwise axis length to spanwise axis length. Special attention is given to the aspect ratio effects on wave patterns and circulation. With decreasing aspect ratio, the wave patterns in the interaction are summarized as transmitted shock reflection, regular interaction, and transmitted shock splitting. Based on the scaling law model of Samtaney and Zabusky (J Fluid Mech 269:45–78, 1994), a theoretical approach is developed for predicting the circulation at the time when the fastest shock wave reaches the leeward pole of the gas cylinder (i.e., the primary deposited circulation). For both prolate (i.e., the minor axis of the ellipse is along the streamwise direction) and oblate (i.e., the minor axis of the ellipse is along the spanwise direction) cases, the proposed approach is found to estimate the primary deposited circulation favorably.