In-Plane Parametric Vibrations of Curved Bellows Subjected to Oscillating Internal Fluid Pressure Excitation

This paper deals with the theoretical stability analysis of in-plane parametric vibrations of a curved bellows subjected to periodic internal fluid pressure excitation. The curved bellows studied in this paper are fixed at both ends rigidly, and are excited by the periodic internal fluid pressure. In the theoretical stability analysis, the governing equation of the curved bellows subjected to periodic internal fluid pressure excitation is derived as a Mathieu’s equation by using finite element method (FEM). Natural frequencies of the curved bellows are examined and stability maps are presented for in-plane parametric instability. It is found that the natural frequencies of the curved bellows decrease with increasing the static internal fluid pressure and buckling occurs due to high internal fluid pressure. It is also found that two types of parametric vibrations, longitudinal and transverse vibrations, occur to the curved bellows in-plane direction due to the periodic internal fluid pressure excitation. Moreover, effects of axis curvature on the parametric instability regions are examined theoretically.

Fully Three Dimensional Modeling of Fluid-Structure Interaction Problems Using High Order Finite Elements for the Structural Simulation

Our approach is to use fully three-dimensional models for both the fluid and the structure. For thin-walled structures, which are typically sensitive to loads resulting from the surrounding fluid, it will be shown that the use of high-order hexahedral elements with high aspect ratios is feasible. Furthermore, it will be demonstrated that three-dimensional elements of high order can be used very efficiently by choosing a high polynomial degree in in-plane direction and a low polynomial degree in thickness direction. By varying the polynomial degrees in the local directions of the elements, the choice of an appropriate structural model can be achieved in an adaptive way. This will be demonstrated by means of a numerical example.

Micro Fluidics Using Novel Materials

We report two novel microfluidic devices fabricated from PDMS (polydimethylsiloxane). Such devices are indicative of the increasing migration of microfluidics to materials distinct from those of the mainstream Silicon MEMS industry. Specifically, plastics fabrication techniques and materials such as SU8 photostructurable epoxy and microcasting, which are employed in these examples, are proving particularly topical and are discussed here. The devices reported consist of PDMS-glass-piezoelectric hybrids exploiting the compliant nature of elastomer substrates to yield valuable functionality. The first device is a micropump employing novel, non-sealing valves and pumping 300 microlitres per minute and developing a maximum pressure of 6kPa. The second reported device is a micromixer employing temporal interleaving of samples via PDMS-glass microvalves in order to mix effectively within the laminar, microfluidic flow regime.

Fluid Structure Interaction Modelling

Numerical modeling of fluid/structure interaction (FSI) falls into the multi-physics domain and has significant importance in many engineering problems. It is an active research area in the field of computational mechanics and examples are found in diverse applications such as aeronautics, biomechanics and the offshore industries. As such, Computational Fluid Dynamics (CFD) and Finite Element (FE) analysis techniques have continuously evolved into this field. This paper presents one such technique and focuses on the further developments of a displacement based finite volume method previously presented by the author, in particular, its ability to now predict fixed displacement, normal, shear and thermal stresses and strains within a single CFD program. An advantage of this method is that a single solution procedure has the potential to be employed to predict both fluid, structural and fluid/structure interaction effects simultaneously.

Shock Analysis of Underwater Explosion Using Smoothed Particle Hydrodynamics

A blasting process includes large deformations and inhomogeneities caused by shock waves as well as the detonation gases generated by explosives. Smoothed Particle Hydrodynamics (SPH) is a meshless and complete Lagrangian method. The properties of SPH method can overcome the difficulty of a simulation in a blasting process. In this study, the simulation of an underwater explosion using SEP (Safety Explosives) as a cylindrical high explosive is carried out to confirm the advantage of SPH method for the analysis in a blasting process. The Euler equations are used for the governing equations of both water and the detonation products of the explosive. The Jones-Wilkins-Lee (JWL) equation and the Mie-Gru¨neisen equation are used as the equation of states for the detonation products and water, respectively. The two-dimensional and axisymmetrical simulation in cylindrical coordinate system is adopted to analyze the underwater explosion. The simulation result is compared with the experimental result and shows that SPH method can well simulate the underwater explosion.

A 3D Variational BEM Formulation for Fluid-Structure Interaction in Viscous Compressible Flow

This paper is aimed at presenting recent advances in modeling and simulation of vibrating structures in presence of external as well as of internal fluid flows using methods based on symmetric variational BEM formulation coupled with the FE. The structural weak form is coupled with a novel boundary element variational formulation of a compressible viscous fluid. The proposed formulation has distinct advantages: (i) over the classical FE, it avoids the discretisation of the fluid domain; (ii) over the collocation BEM formulation, it avoids the explicit calculation of the finite part of hypersingular integrals. Also, the discretisation, by the boundary finite element procedure, of the resulting mixed variational functional leads to a symmetric algebraic system. A computer code based on these concepts has been developed and applied to calculate 3D vibroacoustic behavior of various coupled mechanical systems.

A Priori Analysis of Explicit Algebraic Stress Models for a Turbulent Flow Through a Straight Square Duct

The ability of two explicit algebraic Reynolds stress models (EARSMs) to accurately predict the problem of fully turbulent flow in a straight square duct is studied. The first model is devised by Gatski and Rumsey (2001) and the second is the one derived by Wallin and Johansson (2000). These models are studied using a priori procedure based on data resulting from direct numerical simulation (DNS) of the Navier-Stokes equations, which is available for this problem. For this case, we show that the equilibrium assumption for the anisotropy tensor is found to be correct. The analysis leans on the maps of the second and third invariants of the Reynolds stress tensor. In order to handle wall-proximity effects in the near-wall region, damping functions are implemented in the two models. The predictions and DNS obtained for a Reynolds number of 4800 both agree well and show that these models are able to predict such flows.

Eulerian-Lagrangian Coupling in Finite Element Calculations With Applications to Machining

Multi-material Eulerian finite element methods are attractive for problems in solid mechanics where new free surfaces are created, e.g., the formation of chips in machining. One weakness associated with the Eulerian finite element formulation, however, is the interaction of materials at the contact interface. The standard mixture theories effectively bond the materials together, and prohibit the relative slip between the materials that is crucial for an accurate machining simulation. In this paper, we compare the results of a machining calculation performed using an Eulerian formulation with a contact mixture theory and a coupled Eulerian-Lagrangian calculation, where the workpiece is Eulerian, and the tool is Lagrangian.

Numerical Simulation of Bird Strike Damage on Jet Engine Fan Blade

Aircraft jet engine should be designed to keep the required performance against for the event of foreign object ingestion, such as bird-strike. For the purpose to realize highly efficient and more advanced design of fan blade of jet engine, a numerical simulation technique for bird-strike problem has developed. Good agreement was obtained between simulation results and the soft body impact tests described in this paper. It was also shown that bird-strike problem has to be recognized as a fluid-structure interaction problem, because the impacted bird behaves like fluid and the impact force is highly influenced by the deformation of fan blade.

ALE and Fluid/Structure Interaction in LS-DYNA

Fluid-structure interactions play an important role in many different types of real-world situations and industrial applications involving large structural deformation and material or geometric nonlinearities. Numerical problems due to element distortions limit the applicability of a Lagrangian description of motion when modeling large deformation processes. An alternative technique is the multi-material Eulerian formulation for which the material flows through a mesh, fixed in space and each element is allowed to contain a mixture of different materials. The method completely avoids element distortions and it can, through an Eulerian-Lagrangian coupling algorithm, be combined with a Lagrangian description of motion for parts of the model. The Eulerian formulation is not free from numerical problems. There are dissipation and dispersion problems associated with the flux of mass between elements. In addition, many elements might be needed for the Eulerian mesh to enclose the whole space where the material will be located during the simulated event. This is where the multi-material arbitrary Lagrangian-Eulerian (ALE) formulation has its advantages. By translating, rotating and deforming the multi-material mesh in a controlled way, the mass flux between elements can be minimized and the mesh size can be kept smaller than in an Eulerian model. A new Fluid Structure coupling algorithms based on the penalty method is presented in this paper. The coupling algorithm and improved multi-material ALE-capabilities have made LS-DYNA an efficient tool for analyzing large deformation processes, such as bird strike events, forging operations and penetration problems and airbag simulations. This paper contains five example problems that illustrate the current features of the code.