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Lagrangian analysis of the formation and mass transport of compressible vortex rings generated by a shock tube |
| Haiyan Lin(林海燕), Yang Xiang(向阳)†, Hong Liu(刘洪), and Bin Zhang(张斌) |
| 1 School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China |
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Abstract In order to understand the mass transport and the dynamic genesis associated with a compressible vortex formation, a dynamic analysis of compressible vortex rings (CVRs) generated by shock tubes by using the framework of Lagrangian coherent structures (LCSs) and finite-time Lyapunov exponents field (FTLE) is performed. Numerical calculation is performed to simulate the evolution of CVRs generated by shock tubes with 70 mm, 100 mm, and 165 mm of the driver section at the circumstances of pressure ratio=3. The formation of CVRs is studied according to FTLE fields. The mass transport during the formation is obviously seen by the material manifold reveled by FTLE fields. A non-universal formation number for the three CVRs is obtained. Then the elliptic LCSs is implemented on three CVRs. Fluid particles separated by elliptic LCSs and ridges of FTLE are traced back to t=0 to identify the fluid that eventually forms the CVRs. The elliptic LCSs encompass around 60% fluid material of the advected bulk but contain the majority of the circulation of the ring. The other parts of the ring carrying almost zero circulation advect along with the ring. Combining the ridges of FTLE and the elliptic LCS, the whole CVR can be divided into three distinct dynamic parts: vortex part, entrainment part, and advected part. In addition, a criterion based on the vortex part formation is suggested to identify the formation number of CVRs.
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Received: 03 July 2020
Revised: 16 October 2020
Accepted manuscript online: 31 October 2020
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PACS:
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05.60.-k
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(Transport processes)
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07.05.Tp
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(Computer modeling and simulation)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 91441205 and 91941301) and China Postdoctoral Science Foundation (Grant No. 2018M642007). |
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Corresponding Authors:
†Corresponding author. E-mail: xiangyang@sjtu.edu.cn
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Cite this article:
Haiyan Lin(林海燕), Yang Xiang(向阳, Hong Liu(刘洪), and Bin Zhang(张斌) Lagrangian analysis of the formation and mass transport of compressible vortex rings generated by a shock tube 2021 Chin. Phys. B 30 030501
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