Arbitrary Lagrangian-Eulerian Description Research Articles

A Partitioned Implicit Coupling Strategy for Incompressible Flow Past an Oscillating Cylinder

A partitioned implicit coupling strategy is proposed for fluid–structure interaction (FSI) problems in this paper. The incompressible Navier–Stokes equations under arbitrary Lagrangian–Eulerian description are solved by the characteristic-based split scheme while the structural equation is evaluated by the composite implicit time integration method. Moving submesh approach is performed for the mesh deformation and a mass source term (MST) is introduced into the pressure Poisson equation for respecting geometric conservation law. Fluid-structure coupling is achieved by the combined interface boundary condition (CIBC) method. The iterative loops are realized by fixed-point iterations with Aitken's Δ2 method. A structural force predictor is employed within the present algorithm, ensuring that the latest quantities belonging to different subdomains are adopted for the CIBC method. The proposed methodology is validated by flow-induced oscillations of a bluff body. The obtained results agree with the well-documented data. Some well-known flow phenomena have been detected successfully.

Flow-induced vibrations of four circular cylinders with square arrangement at low Reynolds numbers

Flow-induced vibrations (FIV) of four identical circular cylinders placed in a square arrangement are numerically investigated. Modeled as a spring-damping system subjected to uniform flows, each cylinder is allowed to freely oscillate with equal natural frequencies in the inline and transverse directions. The spacing ratio, L/D, remains 5, where L is the central distance of any two adjacent cylinders and D the cylinder diameter. The Reynolds numbers are chosen as Re=80 and 160. The incidence angle of the incoming uniform flow is α=0°. The mass ratio for each cylinder is Mr=6.0 and the reduce velocity, Ur, varies from 3 to 14. The coupled system is numerically resolved by a semi-implicit characteristics-based split (CBS) finite element algorithm under the arbitrary Lagrangian–Eulerian description. The calculated results are analyzed in detail. In particular, some intrinsic mechanisms are interpreted on the cylinder responses and the wake patterns. The unsymmetrical figures of “8” and “O”, and other irregular figures are observed in the cylinders’ X–Y trajectories. Besides the “4S” wake pattern, the “2P+2S” pattern is discovered herein. The “dual-resonance” phenomenon, which indicates the cylinders’ synchronizations occurring in both the inline and transverse directions, is detected in this work.

Integrated Fluid–Structure Simulation for Full Burning of a Solid-Propellant Rocket Interior

Fully integrated computational simulations inside solid-propellant rockets are carried out to examine the nonlinear feedback interaction between fluid, structure, and burning module. The arbitrary Lagrangian Eulerian description is employed to efficiently track the burning process along the grain surface. An automatic remeshing algorithm is added to the fluid, structure, and burning process to accurately analyze unsteady fluid–structure coupling phenomena with deforming solid grain during the simulation. The developed solver is then applied to the full-burning simulation of a solid-propellant grain, which is a highly coupled unsteady phenomenon between the gas flow and propellant structure. Based on the integrated computed results, the detailed burning mechanism and flame propagation process along the propellant grain surface are investigated. In particular, flame propagation delay and secondary burning phenomena are explained from the physical and numerical perspectives. Furthermore, the virtual contact line method is introduced to overcome the boots contact problem occurring in the gas flow–propellant interaction, and the deforming behavior of the full-burning solid propellant is examined.

Modeling of heat and moisture transfers with stress–strain formation during convective air drying of deformable media

A mathematical formulation of heat, mass and momentum transfers’ phenomena during drying of saturated deformable porous media was developed. The effect of the fluid pressure gradient on the fluid transfer is described by using the Darcy law. An elastic comportment has been used to close the mechanical problem. The model is solved numerically by using finite elements method based on Arbitrary Lagrangian–Eulerian description. The evolutions of moisture content, liquid pressure and stresses within a clay sample were discussed. A large tensional stress, which could induce a crack, was observed at the product surface exposed to the drying air.

Modeling of a micro auto-electrolytic cell for hydrogen production

This paper numerically investigates a portable fuel processor, i.e., micro-scale auto-electrolytic cell (AEC), for on-site hydrogen production in an economical, spontaneous and controllable manner. The AEC in this study consists of a galvanic couple of magnesium and steel in sodium chloride solution. A single Laplace's equation with boundary conditions determined from electrode reaction kinetics is solved for the potential inside the AEC. A dynamic mesh model based on arbitrary Lagrangian–Eulerian description is applied to track the moving boundary of the dissolving magnesium anode. Based on the model, the spatio-temporal distributions of potential, current density, hydrogen generation rate and other important parameters associated with the AEC are obtained. A great enhancement of hydrogen generation rate is found achievable by miniaturizing the AEC. In addition, parametric analyses are also performed focusing on important geometric factors. The study suggests that it would be better to arrange a number of micro-scale AEC units together to attain a desired total hydrogen output. The present study contributes to a better understanding of the hydrogen generation characteristics of AECs, hence facilitates their future development. The developed model can also serve as a useful tool to study other similar electrochemical systems.

Numerical simulation of three dimensional non-Newtonian free surface flows in injection molding using ALE finite element method

This paper presents a scheme for numerical simulation of non-Newtonian fluid flows in three-dimensional injection molding process using arbitrary Lagrangian–Eulerian (ALE) finite element method. The proposed scheme is based on the pressure-stabilized fractional step algorithm for incompressible Navier–Stokes equations. In light of the ALE description, the moving free surface is accurately tracked in a self-adaptive manner by introduction of the moving least square (MLS) surface fitting method to fully determine the movement of the nodes on the moving free surface, meanwhile the mesh distortions are effectively alleviated. By virtue of the ALE method, a local remeshing strategy is developed for the mesh regeneration frequently required in moving free surface flow problems, so that the interpolation errors due to the mesh regeneration process are minimized and occur only limited to some local regions, and the computational cost for the remeshing process is reduced decisively. The numerical examples of three dimensional injection molding flows are presented to demonstrate the capabilities of the proposed numerical scheme.

An arbitrary Lagrangian–Eulerian discontinuous Galerkin method for simulations of flows over variable geometries

A numerical method for simulations of flow over variable geometries including deformable domains or moving boundaries is presented in the context of high-order discontinuous Galerkin (DG) methods in the framework of an arbitrary Lagrangian Eulerian (ALE) description to take into account the deformable domains where boundaries are moving with prescribed motions or deformed under external forces. The ALE DG approach is shown to satisfy the geometric conservation law while preserving high-order accuracy. For variable geometries, we develop a simple and effective mesh smoothing technique based on element size functions to handle deformable grids due to moving boundaries. The current approach is applied to simulations of moving domain problems including laminar flows over oscillating cylinders and a flapping foil to show the ability of handling variable geometries with large deformation and high accuracy. The simulation results are compared with earlier experimental and numerical studies.

Application of nonlinear fluid–structure interaction methods to seismic analysis of anchored and unanchored tanks

Seismic response of liquid storage tanks is quite different from conventional structures not only due to hydrodynamic effects acting on the tank shell but also owing to many sources of nonlinear behavior mechanisms of tanks such as buckling of the tank shell, large amplitude nonlinear sloshing, nonlinear tank–soil interaction, material yielding, plastic rotation of base plate and successive contact and separation between tank base and soil. For the assessment of earthquake response of such structures, numerical methods are indispensable tools since they offer a concise way of accurately considering all these nonlinearities in the same model. Yet, before using numerical techniques for design purposes for the evaluation of different configurations of the fluid–tank systems when subjected to several earthquake ground motions, they should be validated by experimental results. For this purpose, in this study, a fully nonlinear fluid–structure interaction algorithm of finite element method is employed for the seismic analysis of anchored and unanchored steel liquid storage tanks. An existing experimental study carried out on anchored and unanchored tanks is utilized for the verification of the numerical procedure. In the numerical models, Arbitrary Lagrangian Eulerian (ALE) description of the liquid–structure interface which is described by the mesh nodes at the boundary is employed. Fluid motion is governed by compressible Navier–Stokes equations. Both material and geometric nonlinearities are considered in order to accurately determine stress, strain and strain rate distributions throughout the tank. Successive contact and separation between base plate and foundation along with friction effects are taken into account by contact modeling algorithm. Response parameters of tanks, such as free surface sloshing wave height, pressure time histories, base plate uplifting and shell stresses obtained by numerical simulations are correlated with those of experimentally observed. By means of experimental and numerical results, the principal effects of base uplifting on the seismic response of unanchored cylindrical steel tank are highlighted with comparing that of rigidly restrained tank. Moreover, the provisions given in the current tank seismic design codes for metal cylindrical tanks are discussed and the response parameters of tanks are computed per minimum requirements of these codes. The results are compared with findings of numerical and experimental studies and the comments on the consistency of these results are explained in detail. Strong correlation between the experimental and numerical results is obtained for investigated response parameters although code requirements present deviations from the reference experimental study especially for uplift displacement and free surface wave height.

A new coupling strategy for fluid–solid interaction problems by using the interface element method

AbstractThis paper presents a new approach to simulate fluid–solid interaction (FSI) problems involving non‐matching meshes. The coupling between the fluid and solid domains with dissimilar finite element meshes consisting of 4‐node quadrilateral elements is achieved by using the interface element method. Continuity and compatibility conditions across the interface between fluid and solid meshes are satisfied exactly by introducing the interface elements defined on an interfacing region. Importantly, a consistent transfer of loads through the interface elements guarantees the present method to be an efficient approach of the solution strategy to FSI problems. An arbitrary Lagrangian–Eulerian description is adopted for the fluid domain, while for the solid domain an updated Lagrangian formulation is considered to accommodate finite deformations of an elastic structure. The fluid equations for velocity and pressure and the solid equations for velocity are strongly coupled in a single computational domain by means of the interface elements. Numerical results are presented for FSI problems involving non‐matching meshes to demonstrate the effectiveness of the methodology. Copyright © 2009 John Wiley & Sons, Ltd.

Rate-dependent dynamic ALE analysis of finite deformation of elasto-viscoplastic solids

In this paper, formulation and implementation of finite element analysis within an Arbitrary Lagrangian Eulerian (ALE) description is presented for large deformation analysis of elasto-viscoplastic materials. The rate effects are included using a consistent procedure. An implicit algorithm with backward Euler integration scheme is used to integrate the elasto-viscoplastic constitutive equations. Also, the closed form of the consistent tangent operator is derived using the momentum balance equation to reduce the computation time. A fully coupled ALE procedure is used which includes dynamic effects. The proposed algorithm is implemented in an ALE code and its effectiveness and efficiency is verified through several numerical simulation problems and comparison with available experimental results.

Isogeometric fluid-structure interaction: theory, algorithms, and computations

We present a fully-coupled monolithic formulation of the fluid-structure interaction of an incompressible fluid on a moving domain with a nonlinear hyperelastic solid. The arbitrary Lagrangian–Eulerian description is utilized for the fluid subdomain and the Lagrangian description is utilized for the solid subdomain. Particular attention is paid to the derivation of various forms of the conservation equations; the conservation properties of the semi-discrete and fully discretized systems; a unified presentation of the generalized-α time integration method for fluid-structure interaction; and the derivation of the tangent matrix, including the calculation of shape derivatives. A NURBS-based isogeometric analysis methodology is used for the spatial discretization and three numerical examples are presented which demonstrate the good behavior of the methodology.

Computational fluid dynamic analysis of flutter characteristics for self-anchored suspension bridges

This paper outlines the essentials and procedures of computational fluid dynamics (CFD) simulation applicable to evaluating flutter derivatives of bridge decks. An arbitrary Lagrangian-Eulerian (ALE) description of the flow around the moving rigid box girder combined with the finite volume discretization and multi-grid algorithm is presented. The proposed methods are employed to identify flutter derivatives of the bridge deck of the Sanchaji Selfanchored Suspension Bridge. The results agree well with ones from wind tunnel tests. It demonstrates accuracy and efficiency of the present method.

Parallel numerical simulation with domain decomposition for the fluid-filled drum crash

Fluid—structure interaction (FSI) problems simultaneously bring together some of the critical aspects associated with both fluid dynamics and structural dynamics. In this research, the simulation of the three-dimensional flexible fluid-filled drum in the crash is achieved through multi-material arbitrary Lagrangian-Eulerian (ALE) finite-element method because of its ability to control mesh geometry independently from geometry. The ALE description is adopted for the fluid domain, whereas for the structural domain the Lagrangian formulation is adopted. The computation of the FSI and the crash contact between the drum and the ground is realized by the penalty-based coupling method. Then the dynamic behaviour of the drum in the crash is analysed and the parallelism is discussed because the computation of the FSI and the crash contact is quite time-consuming. Based on domain decomposition, the recursive coordinate bisection (RCB) is improved according to the time-consuming characteristics of the fluid-filled container in the crash. The results indicate, in comparison with RCB method, the improved recursive coordinate bisection method has improved the speedup and the parallel efficiency.

Wind Tunnel and CFD Study on Identification of Flutter Derivatives of a Long‐Span Self‐Anchored Suspension Bridge

Abstract: The Sanchaji Bridge with a main span of 328 m, located in Changsha City across Xiangjiang River, is one of the longest self‐anchored suspension bridges completed in China. This article presents the results from a combined wind tunnel and CFD (computational fluid dynamics) study on identification of flutter derivatives of the bridge deck. Based on the Covariance Block Hankel Matrix (CBHM) algorithm in time domain, sectional model wind tunnel tests are conducted in smooth flow to recover modal parameters and to further identify flutter derivatives from free‐decay vibration records. On the other hand, based on the ALE (Arbitrary Lagrangian Eulerian) description and a second‐order projection algorithm, the CFD study uses the FVM (Finite Volume Method) on staggered grids and a forced vibration manner of the bridge deck to evaluate the flow field around the bridge deck. With the obtained aerodynamic forces acting on the bridge deck, flutter derivatives can be evaluated based on system identification. Finally, both of the suggested methods are applied to identification of flutter derivatives of the bridge deck of the Sanchaji Bridge. The results of the present methods have the same trends with Theodorsen analytical solutions, while the results from the CFD study compare well with those from the wind tunnel test. The agreement on the present results suggests that the aeroelastic phenomenon of bridge decks with sharp edges does not appear sensitive to the Re number and turbulence modeling.

The Simulation of Dual Layer Fuel Tank During the Impact With the Ground Based on Parallel Computing

The crashworthiness of a dual layer fuel tank, with the outer layer made of metal and the inner layer made of woven fabric composite material, is fundamental for the survivability of an impact with the ground in emergency. In this research, the simulation of a three-dimensional dual layer fuel tank in the impact with the ground is achieved through the multimaterial arbitrary Lagrangian-Eulerian (ALE) finite element method because of its ability to control mesh geometry independently of geometry. At the same time, the naked flexible tank in the impact with the ground is simulated for the evaluation of the outer metal tank. The ALE description is adopted for the fluid domain, while for the structural domain the Lagrangian formulation is considered. The computation of the fluid-structure interaction and the impact contact between the tank and the ground are realized by the penalty-based coupling method. Then, the dynamic behaviors of the dual layer fuel tank and the naked flexible tank in the impact are analyzed. In the meantime, the parallelism of the dual layer fuel tank is discussed because the computation of the fluid-structure interaction and the impact contact is quite time consuming. Based on domain decomposition, the recursive coordinate bisection (RCB) is improved according to the time-consuming characteristics of fluid-filled tank in the impact. The result indicates, comparing with the RCB algorithm, that the improved recursive coordinate bisection algorithm has improved the speedup and parallel efficiency.

The numerical simulation of local scour in front of a vertical-wall breakwater

A two-dimensional numerical wave flume was established based on an arbitrary Lagrangian-Eulerian (ALE) description of the Navier-Stokes equations for incompressible and viscous fluid, which is spatially discretized by finite element method (FEM) and marching in time with a fractional step algorithm. The second-order nonlinear Stokes waves were generated numerically and the standing waves were formed in front of a vertical-wall breakwater. The transports of uniformly noncoherent sediment bed load were modeled to simulate the local scour process at the toe of the breakwater. The scouring patterns at the earlier stage of scouring agree with that obtained in Xie's experiment (1983).

A NEW MESH RE-GENERATION METHOD FOR FREE SURFACE FLOW ANALYSIS BASED ON INTERFACE-TRACKING METHOD

This paper presents a new mesh re-generation technique for free surface flow analysis based on the interface-tracking method. The incompressible Navier-Stokes equation based on the arbitrary Lagrangian-Eulerian description is used as the governing equation. The SUPG/PSPG formulation is employed for the finite element discretization. The coupled non-linear finite elemente quation systems are linearlized by the Newton-Raphson method. As numerical examples, the present method is applied to the sloshing problem, the broken-dam problem and the fountain flow problem in a rectangular tank. The efficiency of the present method is shown by these numerical results.

ALE finite element method for FSI problems with free surface using mesh re-generation method based on background mesh

This paper presents an arbitrary Lagrangian–Eulerian (ALE) finite element method for fluid-structure interaction (FSI) problems with a free-surface using the mesh re-generation method. The mesh re-generation method using the background mesh is introduced to improve the applicability to the complicated FSI problem with large deformed interface. The incompressible Navier–Stokes equation based on ALE description is used as the governing equation of fluid. The stabilization method based on the SUPG/PSPG method is employed. The presented method is applied to several numerical examples to show the validity and efficiency of the method.

バックグラウンドメッシュに基づくメッシュ再構築手法を用いた自由表面を有する流体―構造連成問題のためのＡＬＥ有限要素法

This paper presents an ALE (Arbitrary Lagrangian-Eulerian) finite element methodfor fluidstructure interaction (FSI) problems with free surface. The mesh re-generation method based on background mesh is introduced to improve the applicability to the complicated FSI problems. The incompressible Navier-Stokes equation based on ALE description is used as the governing equation of fluid. The SUPG/PSPG formulation is employed for the finite element discretization. The structure is assumed to be a rigid body. As numerical examples, the present method is applied to the floating problem of a circular object, the water entry problem ofa wedge object and the falling problem of a circular object. The efficiency of the present method is shown by numerical results.

Numerical Simulations and Design of Shearing Process for Aluminum Alloys

This work combines experimental studies with finite element simulations to develop a reliable numerical model for the simulation of shearing process in aluminum alloys. The critical concern with respect to product quality in this important process is burr formation. Numerical simulations are aimed at understanding the role of process variables on burr formation and for recommending process design parameters. The commercial code ABAQUS-Explicit with the arbitrary Lagrangian-Eulerian kinematic description is used in this study for numerical simulations. An elastic-plastic constitutive model with experimentally validated damage models are incorporated through the user subroutine VUMAT in ABAQUS, for modeling deformation and ductile fracture in the material. Macroscopic experiments with microscopic observations are conducted to characterize the material and to calibrate the constitutive and damage models. Parametric study is done to probe the effect of process parameters and finally, a genetic algorithm (GA) based design method is used to determine process parameters for minimum burr formation.