21 st Annual International Conference on Mechanical Engineering-ISME2013 7-9 May, 2013, School of Mechanical Eng., K.N.Toosi University, Tehran, Iran ISME2013-735 Numerical and Experimental Analysis of the Motion of a Hyperelastic Body in a Fluid Hamed Esmailzadeh 1 , Mohammad Passandideh-Fard 2 1 Graduate Student, Ferdowsi University of Mashhad; esmailzadeh_hamed@yahoo.com 2 Associate Professor, Ferdowsi University of Mashhad; mpfard@um.ac.ir Abstract 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 multi component material and the deformation tensor for describing the deformation of the hyperelastic body. The constitutive law in the Cauchy stress form and an equation are used for the transport of the deformation tensor field which are the core elements of the simulation method. For materials with a low stiffness, an explicit formulation is used for the elastic stress. In some cases, however, due to high stiffness a semi implicit formulation is used for the elastic stress to avoid instability. The strain rate has a discontinuity across the fluid-body interface. For improving accuracy in capturing the interface, solid is treated as a highly viscous fluid. 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 surface are investigated. A high speed Charge-Coupled Device (CCD) camera is used to capture images and image processing techniques are employed to obtain the required data from 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. Keywords: Fluid Solid Interaction, Hyperelastic Material, Implicit Elastic Term, Image Processing Introduction Numerical methods for solving the fluid-structure interaction are classified in three major methods: Lagrangian-Lagrangian, Eulerian-Lagrangian and Eulerian-Eulerian. In the Lagrangian-Lagrangian method, a structured grid for the fluid and an unstructured grid for the solid are used. The computation is done with a moving mesh updated based on a method known as ALE (Arbitrary Lagrangian- Eulerian) [1-2]. In the Eulerian-Lagrangian method, however, an Eulerian background mesh is used for the fluid and a Lagrangian moving mesh for the solid. A number of these methods have been proposed by many researchers such as Gilmanov et al. [3] who introduced the hybrid immersed boundary method; Huang et al. [4] and Wang et al. [5-6] who proposed the immersed boundary method; and Glowinski et al. [7] who introduced the fictitious domain method. In the Eulerian-Eulerian method, a fixed mesh grid is used for both fluid and solid. Recently, Sugiyama et al. [8] used a FSI model based on an Eulerian framework for an incompressible fluid and a hyperelastic solid. They used this model to simulate biconcave neo-Hookean particles in a Poiseuille flow. They improved the model in later publications [9-14]. In the present study, a numerical method is developed based on the FSI model of Sugiyama et al. [9]. This method is capable of handling unprescribed motion of the solid. The method of Ii et al. [10] is used for elastic stress in order to simulate materials with high stiffness. They used a fourth-order Jacobian tensor to overcome the difficulty associated with the difference between the constitutive laws of solid and fluid. For improving the dynamic condition of the interface, high viscosity method is used for the solid. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. In the method of Sugiyama et al. [9], the fifth-order Weighted Essentially Non- Oscillatory (WENO) method is used to advect the solid volume fraction field, which temporally makes the interface numerically diffusive. In this paper, however, the Youngs Piecewise Linear Interface Calculation (PLIC) algorithm [15] is used that suppresses the numerical diffusion; this algorithm is frequently used in the multiphase flow simulations [16]. The present study also deals with the experimental characterization of silicone as a hyperelastic body. The neo-Hookean constitutive equation for this purpose is used based on the Marckmann et al. [17]. The neo- Hookean model is used for small deformation that involves only one material parameter and is able to predict the material response for different types of loading conditions. Numerical Method The following equations over the entire domain including both fluid and solid are solved: 0 V   (1)     1 T V P V V V V t e g                         (2) where V is the velocity vector, ρ the density, P the pressure, μ the dynamic viscosity and g the acceleration due to gravity. The solid body is treated as a fluid with high viscosity. The solid volume fraction is advected using the VOF method by means of a scalar field ϕ, defined as: 1163