Eulerian method for multiphase interactions of soft solid bodies in fluids

We introduce an Eulerian approach for problems involving one or more soft solids immersed in a fluid, which permits mechanical interactions between all phases. The reference map variable is exploited to simulate finite-deformation constitutive relations in the solid(s) on the same fixed grid as the fluid phase, which greatly simplifies the coupling between phases. Our coupling procedure, a key contribution in the current work, is shown to be computationally faster and more stable than an earlier approach, and admits the ability to simulate both fluid--solid and solid--solid interaction between submerged bodies. The interface treatment is demonstrated with multiple examples involving a weakly compressible Navier--Stokes fluid interacting with a neo-Hookean solid, and we verify the method's convergence. The solid contact method, which exploits distance-measures already existing on the grid, is demonstrated with two examples. A new, general routine for cross-interface extrapolation is introduced and used as part of the new interfacial treatment

Fluid-structure interaction simulation of prosthetic aortic valves : comparison between immersed boundary and arbitrary Lagrangian-Eulerian techniques for the mesh representation

In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary Lagrangian-Eulerian) or an Eulerian formulation. The majority of the reported 3D heart valve FSI simulations are performed with the Eulerian formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an Eulerian-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations' outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results

Modelling the effectiveness of oil lubrication in reducing both friction and wear in a fretting contact

Lubrication is often employed in fretting contacts to reduce wear and stresses associated with high friction. Owing to the very small displacements associated with fretting, penetration of lubricating oils into the contact may not be effective. The efficacy of the penetration of the lubricant into the contact is very difficult to observe experimentally, and accordingly, this paper presents a numerical simulation of a lubricated fretting contact using a Coupled–Eulerian–Lagrangian (CEL) finite element method. Meso-scale CEL finite element models are developed to simulate the cylinder–on–flat arrangement used experimentally at the University of Nottingham in which the roughness of contact surfaces is characterized as fractal geometry by the Weierstrass-Mandelbrot (W-M) function. The fluid–solid and solid–solid contact in the lubricated fretting contact are simulated, and from these, wear and friction coefficients are determined. The effects of contact geometry on lubricated fretting contacts and lubricant on fretting wear are modelled and compared with experimental observations. Results indicate that oil lubrication reduces fretting wear and friction effectively in the less–conforming contacts but has little effect in the more–conforming contacts

Computational Eulerian Hydrodynamics and Galilean Invariance

Eulerian hydrodynamical simulations are a powerful and popular tool for modeling fluids in astrophysical systems. In this work, we critically examine recent claims that these methods violate Galilean invariance of the Euler equations. We demonstrate that Eulerian hydrodynamics methods do converge to a Galilean-invariant solution, provided a well-defined convergent solution exists. Specifically, we show that numerical diffusion, resulting from diffusion-like terms in the discretized hydrodynamical equations solved by Eulerian methods, accounts for the effects previously identified as evidence for the Galilean non-invariance of these methods. These velocity-dependent diffusive terms lead to different results for different bulk velocities when the spatial resolution of the simulation is kept fixed, but their effect becomes negligible as the resolution of the simulation is increased to obtain a converged solution. In particular, we find that Kelvin-Helmholtz instabilities develop properly in realistic Eulerian calculations regardless of the bulk velocity provided the problem is simulated with sufficient resolution (a factor of 2-4 increase compared to the case without bulk flows for realistic velocities). Our results reiterate that high-resolution Eulerian methods can perform well and obtain a convergent solution, even in the presence of highly supersonic bulk flows.Comment: Version accepted by MNRAS Oct 2, 2009. Figures degraded. For high-resolution color figures and movies of the numerical simulations, please visit http://www.astro.caltech.edu/~brant/Site/Computational_Eulerian_Hydrodynamics_and_Galilean_Invariance.htm

Direct Numerical Simulation of Complex Multi-Fluid Flows Using a Combined Volume of Fluid and Immersed Boundary Method

In this paper a simulation model is presented for the Direct Numerical Simulation (DNS) of complex multi-fluid flows in which simultaneously (moving) deformable (drops or bubbles) and non-deformable (moving) elements (particles) are present, possibly with the additional presence of free surfaces. Our model combines the VOF model developed by van Sint Annaland et al. (2005) and the Immersed Boundary (IB) model developed by van der Hoef et al. (2006). The Volume of Fluid (VOF) part features i) an interface reconstruction technique based on piecewise linear interface representation ii) a three-dimensional version of the CSF model of Brackbill et al. (1992). The Immersed Boundary (IB) part incorporates both particle-fluid and particle-particle interaction via a Direct Forcing Method (DFM) and a hard sphere Discrete Particle (DP) approach. In our model a fixed (Eulerian) grid is utilized to solve the Navier-Stokes equations for the entire computational domain. The no-slip condition at the surface of the moving particles is enforced via a momentum source term which only acts in the vicinity of the particle surface. For the enforcement of the no-slip condition Lagrangian force points are used which are distributed evenly over the surface of the particle. Dissipative particle-particle and/or particle-wall collisions are accounted via a hard sphere DP approach (Hoomans et al., 1996) using a three-parameter particle-particle interaction model accounting for normal and tangential restitution and tangential friction. The capabilities of the hybrid VOF-IB model are demonstrated with a number of examples in which complex topological changes in the interface are encountered

An integrated approach to modelling the fluid-structure interaction of a collapsible tube

The well known collapsible tube experiment was conducted to obtain flow, pressure and materials property data for steady state conditions. These were then used as the boundary conditions for a fully coupled fluid-structure interaction (FSI) model using a propriety computer code, LS-DYNA. The shape profiles for the tube were also recorded. In order to obtain similar collapse modes to the experiment, it was necessary to model the tube flat, and then inflate it into a circular profile, leaving residual stresses in the walls. The profile shape then agreed well with the experimental ones. Two departures from the physical properties were required to reduce computer time to an acceptable level. One of these was the lowering of the speed of sound by two orders of magnitude which, due to the low velocities involved, still left the mach number below 0.2. The other was to increase the thickness of the tube to prevent the numerical collapse of elements. A compensation for this was made by lowering the Young's modulus for the tube material. Overall the results are qualitatively good. They give an indication of the power of the current FSI algorithms and the need to combine experiment and computer models in order to maximise the information that can be extracted both in terms of quantity and quality

The 1999 Center for Simulation of Dynamic Response in Materials Annual Technical Report

Introduction: This annual report describes research accomplishments for FY 99 of the Center for Simulation of Dynamic Response of Materials. The Center is constructing a virtual shock physics facility in which the full three dimensional response of a variety of target materials can be computed for a wide range of compressive, ten- sional, and shear loadings, including those produced by detonation of energetic materials. The goals are to facilitate computation of a variety of experiments in which strong shock and detonation waves are made to impinge on targets consisting of various combinations of materials, compute the subsequent dy- namic response of the target materials, and validate these computations against experimental data

Multifluid Eulerian modeling of dense gas–solids fluidized bed hydrodynamics: Influence of the dissipation parameters

Computational fluid dynamic (CFD) models must be thoroughly validated before they can be used with confidence for designing fluidized bed reactors. In this study, validation data were collected from a fluidized bed of (Geldart's group B) alumina particles operated at different gas velocities involving two fluidization hydrodynamic regimes (bubbling and slugging). The bed expansion, height of bed fluctuations and frequency of fluctuations were measured from videos of the fluidized bed. The Eulerian–Eulerian two fluid model MFIX was used to simulate the experiments. Two different models for the particle stresses—Schaeffer [Syamlal, M., Rogers, W., O’Brien, T.J., 1993. MFIX documentation: theory guide. Technical Report DOE/METC-94/1004 (DE9400087), Morgantown Energy Technology Centre, Morgantown, West Virginia (can be downloaded from Multiphase Flow with Interphase eXchanges (MFIX) website left angle brackethttp://www.mfix.orgright-pointing angle bracket); Schaeffer, D.G., 1987. Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations 66, 61–74.] and Princeton [Srivastava, A., Sundaresan, S., 2003. Analysis of a frictional–kinetic model for gas–particle flow. Powder Technology 129(1–3), 72–85.] models—and different values of the restitution coefficient and internal angle of friction were evaluated. 3-D simulations are required for getting quantitative and qualitative agreement with experimental data. The results from the Princeton model are in better agreement with data than that from the Schaeffer model. Both free slip and Johnson–Jackson boundary conditions give nearly identical results. An increase in coefficient of restitution (e) from 0.8 to 1 leads to larger bed expansions and lower heights of fluctuations in the bubbling regime, whereas it leads to unchanged bed expansion and to a massive reduction in the height of fluctuations in the slugging regime. The angle of internal friction (φ) in the range 10–40ring operator does not affect the bed expansion, but its reduction significantly reduces the height of fluctuations