Numerical Investigation of Freely Falling Objects Using Direct-Forcing Immersed Boundary Method

Cheng-Shu You, Ming-Jyh Chern, Dedy Zulhidayat Noor and Tzyy-Leng Horng
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Cheng-Shu You: Department of Applied Mathematics, Feng Chia University, Taichung 40724, Taiwan
Ming-Jyh Chern: Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan
Dedy Zulhidayat Noor: Department of Mechanical Engineering, Institute Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia
Tzyy-Leng Horng: Department of Applied Mathematics, Feng Chia University, Taichung 40724, Taiwan

Mathematics, 2020, vol. 8, issue 9, 1-20

Abstract: The fluid-structure interaction of solid objects freely falling in a Newtonian fluid was investigated numerically by direct-forcing immersed boundary (DFIB) method. The Navier–Stokes equations are coupled with equations of motion through virtual force to describe the motion of solid objects. Here, we rigorously derived the equations of motion by taking control-volume integration of momentum equation. The method was validated by a popular numerical test example describing the 2D flow caused by the free fall of a circular disk inside a tank of fluid, as well as 3D experimental measurements in the sedimentation of a sphere. Then, we demonstrated the method by a few more 2D sedimentation examples: (1) free fall of two tandem circular disks showing drafting, kissing and tumbling phenomena; (2) sedimentation of multiple circular disks; (3) free fall of a regular triangle, in which the rotation of solid object is significant; (4) free fall of a dropping ellipse to mimic the falling of a leaf. In the last example, we found rich falling patterns exhibiting fluttering, tumbling, and chaotic falling.

Keywords: fluid-structure interaction; direct-forcing immersed boundary method; equation of motion; circular disk sedimentation; tandem circular disks sedimentation; multiple circular disks sedimentation; falling triangle; falling ellipse (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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