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Research Papers: Flows in Complex Systems

Numerical and Experimental Analysis of the Fluid-Structure Interaction in Presence of a Hyperelastic Body

[+] Author and Article Information
H. Esmailzadeh

Mechanical Engineering Department,
Ferdowsi University of Mashhad,
Mashhad 91775-1111, Iran
e-mail: esmailzadeh_hamed@yahoo.com

M. Passandideh-Fard

Associate Professor
Mechanical Engineering Department,
Ferdowsi University of Mashhad,
Mashhad 91775-1111, Iran
e-mail: mpfard@um.ac.ir

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 28, 2013; final manuscript received June 18, 2014; published online September 4, 2014. Assoc. Editor: Zhongquan Charlie Zheng.

J. Fluids Eng 136(11), 111107 (Sep 04, 2014) (12 pages) Paper No: FE-13-1457; doi: 10.1115/1.4027893 History: Received July 28, 2013; Revised June 18, 2014

In this study, a numerical algorithm is developed for simulating the interaction between a fluid and a 2D/axisymmetric hyperelastic body based on a full Eulerian fluid-structure interaction (FSI) method. In this method, the solid volume fraction is used for describing the multicomponent material and the deformation tensor for describing the deformation of the hyperelastic body. The core elements of the simulation method are the constitutive law in the Cauchy stress form and an equation for the transport of the deformation tensor field. A semi-implicit formulation is used for the elastic stress to avoid instability especially for solid with high stiffness. The strain rate has a discontinuity across the fluid/solid interface. For improving the accuracy in capturing the interface, solid is treated as a highly viscous fluid. The viscosity term has the effect of smoothing the velocity and keeping the simulation stable. An experimental setup is used to validate the numerical results. The movement of a sphere made of silicone in air and its impact on a rigid substrate are investigated. The images are captured using a high speed CCD camera and the image processing technique is employed to obtain the required data from the images. For all cases considered, the results are in good agreement with those of the experiment performed in this study and other numerical results reported in the literature.

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Figures

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Fig. 1

Flowchart of the sequence of the computational cycle for velocity, deformation tensor, and solid volume fraction

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Fig. 2

Schematic of the experimental setup for the motion and impact of a hyperelastic sphere onto a rigid substrate

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Fig. 3

Iamge processing technique using the Matlab software to obtain the position of the center of sphere volume: (a) image of sphere and a certain piece with known dimension for calibration, (b) the image after being processed using a threshold to reveal the sphere and the calibration piece by reducing the color values into black and white, (c) the top and bottom pixels of the sphere to obtain the position of its center while moving in air, and (d) the detection of the fluid/solid and solid/substrate interfaces to obtain the center during the impact

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Fig. 4

Schematic of a sphere during its motion in air and the initial and boundary conditions for the simulation

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Fig. 5

The result of mesh refinement study for (a) the position of the center of the sphere volume versus time and (b) the axial velocity versus time. The mesh size is characterized based on the number of CPR of the solid.

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Fig. 6

The evolution of the motion and impact of a hyperelastic sphere with a radius 19.2 mm and a density 1106 kg/m3 in air onto a rigid substrate from the present model for (a) cross-sectional images, (b) 3D views, and (c) experimental results performed in this study

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Fig. 7

Comparison of the numerical results with those of the experiments for (a) the position of the center of sphere volume and (b) the axial velocity

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Fig. 8

Comparison of the numerical results with those of the experiments for various initial positions and velocities of the sphere: (a) the position of center of the sphere volume and (b) the axial velocity

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Fig. 9

The simulation results for a soft wall in a lid-driven cavity flow from (a) present study and (b) those of Wang et al. [34]. (Reprinted with permission from Springer Science and Business Media.)

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Fig. 10

The simulation results for a deformable solid motion in a lid-driven cavity flow from (a) present study and (b) those of Zhao et al. [35]. (Reprinted with permission from Elsevier.)

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Fig. 11

The simulation results for an oscillating disk in fluid from (a) present study and (b) those of Robinson et al. [36]. (Reprinted with permission from Elsevier.)

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Fig. 12

The hyperelastic rectangle in a time-varying shear flow: (a) present study and (b) those of Sugiyama et al. [19]. (Reprinted with permission from Elsevier.)

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