For Fluid-structure Interaction Research Articles

Anisotropic adaptive meshing and monolithic Variational Multiscale method for fluid–structure interaction

This paper presents a monolithic formulation framework combined with an anisotropic mesh adaptation for fluid–structure interaction (FSI) applications with complex geometry. The fluid–solid interfaces are captured using a level-set method. A new a posteriori error estimate, based on the length distribution tensor approach and the associated edge based error analysis, is then used to ensure an accurate capturing of the discontinuities at the fluid–solid interface. It enables to calculate a stretching factor providing a new edge length distribution, its associated tensor and the corresponding metric. The optimal stretching factor field is obtained by solving an optimization problem under the constraint of a fixed number of edges in the mesh. The presence of the structure will be taken into account by means of an extra stress tensor in the Navier–Stokes equations. The system is solved using a stabilized three-field, stress, velocity and pressure finite element (FE) formulation. It consists in the decomposition for both the velocity and the pressure fields into coarse/resolved scales and fine/unresolved scales and also in the efficient enrichment of the extra constraint. We assess the accuracy of the proposed formulation by simulating 2D and 3D time-dependent numerical examples such as: falling disk in a channel, turbulent flows behind an airfoil profile and flow behind an immersed vehicle.

Numerical Stability of Partitioned Approach in Fluid-Structure Interaction for a Deformable Thin-Walled Vessel

Added-mass instability is known to be an important issue in the partitioned approach for fluid-structure interaction (FSI) solvers. Despite the implementation of the implicit approach, convergence of solution can be difficult to achieve. Relaxation may be applied to improve this implicitness of the partitioned algorithm, but this commonly leads to a significant increase in computational time. This is because the critical relaxation factor that allows stability of the coupling tends to be impractically small. In this study, a mathematical analysis for optimizing numerical performance based on different time integration schemes that pertain to both the fluid and solid accelerations is presented. The aim is to determine the most efficient configuration for the FSI architecture. Both theoretical and numerical results suggest that the choice of time integration schemes has a significant influence on the stability of FSI coupling. This concludes that, in addition to material and its geometric properties, the choice of time integration schemes is important in determining the stability of the numerical computation. A proper selection of the associated parameters can improve performance considerably by influencing the condition of coupling stability.

Fluid–Structure Interaction Using a Modal Approach

A new method for fluid‐structure interaction (FSI) predictions is here introduced, based on a reduced-order model (ROM) for the structure, described by its mode shapes and natural frequencies. A linear structure is assumed as well as Rayleigh damping. A two-way coupling between the fluid and the structure is ensured by a loosely coupling staggered approach: the aerodynamic loads computed by the flow solver are used to determine the deformations from the modal equations, which are sent back to the flow solver. The method is first applied to a clamped beam oscillating under the effect of von Karman vortices. The results are compared to a full-order model. Then a flutter application is considered on the AGARD wing 445.6. Finally, the modal approach is applied to the aeroelastic behavior of an axial compressor stage. The influence of passing rotor blade wakes on the downstream stator blades is investigated.

Some manufactured solutions for verification of fluid-structure interaction codes

This paper presents manufactured solutions (MS) for verification of a fluid-structure interactions code. MS provide benchmark solutions for direct evaluation of the solution errors. The method of manufactured solutions (MMS) is a straight forward and general procedure for generating exact analytical solutions with a sufficiently rich structure to ensure that all terms of the differential equations are exercised in the simulations. When used with systematic grid refinement studies, the MMS provides strong code verification with a theorem-like quality. Manufactured solutions for fluid-structure interaction (FSI) problems with large displacements are presented with sample results from grid convergence studies.

Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines

In this paper we develop a framework for fluid–structure interaction (FSI) modeling and simulation with emphasis on isogeometric analysis (IGA) and non-matching fluid–structure interface discretizations. We take the augmented Lagrangian approach to FSI as a point of departure. Here the Lagrange multiplier field is defined on the fluid–structure interface and is responsible for coupling of the two subsystems. Thus the FSI formulation does not rely on the continuity of the underlying function spaces across the fluid–structure interface in order to produce the correct coupling conditions between the fluid and structural subdomains. However, in deriving the final FSI formulation the interface Lagrange multiplier is formally eliminated and the formulation is written purely in terms of primal variables. Avoiding the use of Lagrange multipliers adds efficiency to the proposed formulation. As an added benefit, the ability to employ non-matching grids for multi-physics simulations leads to significantly relaxed requirements that are placed on the geometry modeling and meshing tools for IGA.We show an application of the proposed FSI formulation to the simulation of the NREL 5MW offshore wind turbine rotor, where the aerodynamics domain is modeled using volumetric quadratic NURBS, while the rotor structure is modeled using a cubic T-spline-based discretization of a rotation-free Kirchhoff–Love shell. We conclude the article by showing FSI coupling of a T-spline shell with a low-order finite element method (FEM) discretization of the aerodynamics equations. This combined use of IGA and FEM is felt to be a good balance between speed, robustness, and accuracy of FSI simulations for this class of problems.

Variational implementation of immersed finite element methods

Dirac-δ distributions are often crucial components of the solid–fluid coupling operators in immersed solution methods for fluid–structure interaction (FSI) problems. This is certainly so for methods like the immersed boundary method (IBM) or the immersed finite element method (IFEM), where Dirac-δ distributions are approximated via smooth functions. By contrast, a truly variational formulation of immersed methods does not require the use of Dirac-δ distributions, either formally or practically. This has been shown in the finite element immersed boundary method (FEIBM), where the variational structure of the problem is exploited to avoid Dirac-δ distributions at both the continuous and the discrete level.In this paper, we generalize the FEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid. Specifically, we allow (i) the mass density to be different in the solid and the fluid, (ii) the solid to be either viscoelastic of differential type or purely elastic, and (iii) the solid to be either compressible or incompressible. At the continuous level, our variational formulation combines the natural stability estimates of the fluid and elasticity problems. In immersed methods, such stability estimates do not transfer to the discrete level automatically due to the non-matching nature of the finite dimensional spaces involved in the discretization. After presenting our general mathematical framework for the solution of FSI problems, we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces, which guarantee semi-discrete stability estimates and strong consistency of our spatial discretization.

Combined interface boundary condition method for fluid–rigid body interaction

This research is motivated by the recent work which has presented a new loosely-coupled partitioned algorithm for fluid–structure interaction (FSI) [R. Jaiman, P. Geubelle, E. Loth, X. Jiao, Combined interface boundary condition method for unsteady fluid–structure interaction, Comput. Methods Appl. Mech. Engrg. 200 (2011) 27–39]. The loosely-coupled partitioned algorithm is intrinsically exposed to the notorious time lag effect whose remedy promotes the combined interface boundary condition (CIBC) method. In this method, correction terms for velocity and traction are introduced at two sequential time steps with a coupling parameter ω that plays an important part in the stability and accuracy of the coupled system. The structural traction ratio that appears explicitly in the traction correction is estimated based on the solution of the structural subsystem. This handling asks for the structural traction before it is corrected by the CIBC method. In this paper, a new formulation for the CIBC method is developed to repair the aforementioned inconvenience. After simple manipulation, the structural traction ratio is removed in constructing the traction correction. Therefore the structural traction is no more needed in CIBC correction terms. Meantime the ratio ω/Δt is employed to tune the interfacial corrections instead of the coupling parameter ω. An arbitrary Lagrangian–Eulerian finite element method is used to analyze FSI. The characteristic-based split (CBS) scheme is employed to solve incompressible Navier–Stokes equations while the equation for rigid-body dynamics is solved by Newmark-β method. A numerical technique called moving submesh approach is performed for the mesh deformation. For respecting geometric conservation law, a mass source term is implanted into the CBS scheme on the moving mesh. Several numerical examples are tested to validate the proposed methodology for fluid–rigid body interaction. The obtained results are in agreement with the existing data and some famous features of flow phenomena have been detected successfully.

Fluid-Structure Interaction Modeling of Spacecraft Parachutes for Simulation-Based Design

Even though computer modeling of spacecraft parachutes involves a number of numerical challenges, advanced techniques developed in recent years for fluid-structure interaction (FSI) modeling in general and for parachute FSI modeling specifically have made simulation-based design studies possible. In this paper we focus on such studies for a single main parachute to be used with the Orion spacecraft. Although these large parachutes are typically used in clusters of two or three parachutes, studies for a single parachute can still provide valuable information for performance analysis and design and can be rather extensive. The major challenges in computer modeling of a single spacecraft parachute are the FSI between the air and the parachute canopy and the geometric complexities created by the construction of the parachute from “rings” and “sails” with hundreds of gaps and slits. The Team for Advanced Flow Simulation and Modeling has successfully addressed the computational challenges related to the FSI and geometric complexities, and has also been devising special procedures as needed for specific design parameter studies. In this paper we present parametric studies based on the suspension line length, canopy loading, and the length of the overinflation control line.

Research on Numerical Method for Fluid-Structure Interaction in Engine Blades

A numerical analysis method for fluid-structure interaction (FSI) to analyze engine blades dynamic response was presented. Fluid-structure interaction is an important research field. It is mostly studies the interaction between the influence upon the fluid by the deformation of the solids, the important characteristic of fluid-solid interaction mechanics is the fluid-solid interaction between the both phase mediums. The solutions of strongly coupling and weakly coupling were discussed firstly in this paper. We compared the advantages and disadvantages of the strongly coupling and weakly coupling. And using numerical analysis method based on weakly coupling, we established a fluid-solid interaction control equation taking solid and fluid as a unified mathematical model. And we study about blades deformation and displacement under the action of air loading in engine. Using computational structural dynamics (CSD) calculate the displacements of blades, and using computational fluidic dynamics (CFD) calculate the pressures of blades, completing the fluid-structure interaction analysis in engine blades by iterating this two values(the displacements and the pressures) until the computational convergence solution is obtained. At the end of this paper, the model of fluid-structure interaction and the simulate procession of the numerical analysis method were presented. Based on the analysis, the simulation result is qualitatively discussed referring to the factual conditions of the engine for validating the feasibility of analysis method.

공탄성 변형효과를 고려한 5MW급 풍력발전 블레이드의 피치각에 따른 성능해석

In this study, performance analyses have been conducted for a 5㎿ class wind turbine blade model. Advanced computational analysis system based on computational fluid dynamics(CFD) and computational structural dynamics(CSD) has been developed in order to investigate detailed dynamic responsed of wind turbine blade. Reynolds-averaged Navier-Stokes (RANS) equations with K- turbulence model are solved for unsteady flow problems of the rotating turbine blade model. A fully implicit time marching scheme based on the Newmark direct integration method is used for computing the coupled aeroelastic governing equations of the 3D turbine blade for fluid-structure interaction (FSI) problems. Predicted aerodynamic performance considering structural deformation effect of the blade show different results compared to the case of rigid blade model.

On the similarity between Dirichlet–Neumann with interface artificial compressibility and Robin–Neumann schemes for the solution of fluid-structure interaction problems

In this note, the similarity between two implicit, partitioned solution techniques for fluidstructure interaction (FSI) problems is analyzed using finite volume discretization of the flow equations. Fluid-structure interaction refers to the mutual interaction between a fluid flow and a flexible structure. Partitioned solution techniques solve the flow equations and the structural equations separately. These techniques are classified as implicit (or strongly coupled) if they satisfy the interaction conditions on the fluid-structure interface in each time step and as explicit (or loosely coupled) if they do not. Both techniques analyzed in this note use block Gauss-Seidel (GS) iterations, meaning that the flow equations and the structural equations are solved consecutively within a time step until some convergence tolerance is reached. As the flow and structural equations are solved separately, the interaction conditions on the fluid-structure interface have to be converted into boundary conditions on the common boundary of the fluid and structure subdomains. Several types of boundary conditions can be applied, resulting in different decompositions. In the case of Dirichlet-Neumann (DN) decomposition, the flow equations are solved with a Dirichlet boundary condition (given velocity) on the fluid-structure interface, while the structural equations are solved with a Neumann boundary condition (given stress) on the interface. Conversely, RobinNeumann (RN) decomposition, introduced in [1], denotes a Robin boundary condition on the fluid side of the interface and a Neumann boundary condition on the structure side. The first technique in this comparison is block Gauss-Seidel iterations applied to the monolithic system previously multiplied by a suitable permutation matrix, leading to a Robin-Neumann decomposition (GS-RN). This first technique includes a simplified version of the structural model in the flow equations by means of a Robin boundary condition to accelerate the convergence of the GS iterations [1, 2]. The second technique is block Gauss-Seidel iterations with DirichletNeumann decomposition and Interface Artificial Compressibility (GS-DN-IAC). This second

Multiscale space–time fluid–structure interaction techniques

We present the multiscale space---time techniques we have developed for fluid---structure interaction (FSI) computations. Some of these techniques are multiscale in the way the time integration is performed (i.e. temporally multiscale), some are multiscale in the way the spatial discretization is done (i.e. spatially multiscale), and some are in the context of the sequentially-coupled FSI (SCFSI) techniques developed by the Team for Advanced Flow Simulation and Modeling $${({\rm T} \bigstar {\rm AFSM})}$$ . In the multiscale SCFSI technique, the FSI computational effort is reduced at the stage we do not need it and the accuracy of the fluid mechanics (or structural mechanics) computation is increased at the stage we need accurate, detailed flow (or structure) computation. As ways of increasing the computational accuracy when or where needed, and beyond just increasing the mesh refinement or decreasing the time-step size, we propose switching to more accurate versions of the Deforming-Spatial-Domain/Stabilized Space---Time (DSD/SST) formulation, using more polynomial power for the basis functions of the spatial discretization or time integration, and using an advanced turbulence model. Specifically, for more polynomial power in time integration, we propose to use NURBS, and as an advanced turbulence model to be used with the DSD/SST formulation, we introduce a space---time version of the residual-based variational multiscale method. We present a number of test computations showing the performance of the multiscale space---time techniques we are proposing. We also present a stability and accuracy analysis for the higher-accuracy versions of the DSD/SST formulation.

A Simulation Method for Fluid-Structure Interaction Problems with Free Surface based on the Finite Cover Method

This paper presents a new Eulerian type numerical method for Fluid-Structure Interaction (FSI) problems with free surface based on the finite cover method (FCM). Since the physical domain is defined independently of the mathematical domain in the FCM, which is known as a generalized version of the FEM, the physical boundaries of the structure are represented explicitly in a spatially fixed mesh so that the continuity condition can be imposed directly on the actual interface within the framework of Eulerian approach. The VOF and Level Set method are employed to represent interfaces, and the stabilized method based on the streamline-upwind/Petrov-Galerkin (SUPG) and pressure-stabilizing/Petrov-Galerkin (PSPG) methods are employed for flow analysis. The weak coupling scheme is employed for the interaction between fluid and structure. The proposed method is applied to several numerical examples to show the validity and efficiency of the method.

Partitioned iterative solution methods for fluid–structure interaction

AbstractThe basic subiteration method for fluid–structure interaction (FSI) problems is based on a partitioning of the fluid–structure system into a fluidic part and a structural part. The effect of the fluid on the structure can be represented by an added mass to the structural operator. This added mass can be identified as an upper bound on the norm or spectral radius of the Poincar'e–Steklov operator of the fluid. The convergence behavior of the subiteration method depends sensitively on the ratio of the added mass to the actual structural mass. For FSI problems with large added‐mass effects, the subiteration method is either unstable or its convergence behavior is prohibitively inefficient. In recent years, several more advanced partitioned iterative solution methods have been proposed for this class of problems, which use subiteration as a component. The rudimentary characterization of the Poincaré–Steklov operator provided by the added mass is, however, inadequate to analyze these methods. Moreover, this characterization is inappropriate for compressible flows. In this paper, we investigate the fine properties of the Poincaré–Steklov operators and of the corresponding subiteration operators for incompressible‐ and compressible flow models and for two distinct structural operators. Based on the characteristic properties of the subiteration operators, we subsequently examine the convergence behavior of several partitioned iterative solution methods for FSI, viz. subiteration, subiteration in conjunction with underrelaxation, the modified‐mass method, Aitken's method, and interface‐GMRES and interface‐Newton–Krylov methods. Copyright © 2010 John Wiley & Sons, Ltd.

Coupling impedance boundary conditions for absorptive structures with spectral finite elements in room acoustical simulations

Models for Fluid Structure Interaction (FSI) in room acoustical calculations are used in many different fields of engineering like automotive industry or civil engineering. In order to obtain the sound field within an acoustic cavity, which is covered by absorptive boundary structures, with its spatial distribution, very often techniques based on Finite Element formulations are used instead of energy methods. In order to reduce the number of degrees of freedom and therefore the numerical effort, a model reduction method, based on a Component Mode Synthesis (CMS), is presented in this article. Macrostructures are assembled out of single substructures applying shape functions at the interfaces. These substructures contain acoustical design elements, like absorbers or resonators. They are calculated separately in the frame of the CMS approach. The acoustic fluid is modeled with the Spectral Finite Element Method (SEM) and coupled with plate-like compound absorbers at interfaces via impedances using Hamilton’s Principle and a Ritz approach. The porous foam in the absorber is modeled with the Theory of Porous Media (TPM) and the impedances are calculated with the help of the Integral Transform Method (ITM). The method for coupling two macrostructures is compared with an analytical solution and the model for the porous absorber is validated via measurements. Finally an example for the coupled system is presented.

A meshless rheological model for blood-vessel interaction in endovascular simulation

A meshless rheological model is proposed for medical simulation of vascular procedures. Due to the complexity of rheologic models involved in endovascular simulations, delivering a high level of interactivity with realistic biomechanical feedback is still a challenge. In this paper, we propose a particle-based rheologic modeling method for virtual catheterisation training applications. The effect of blood rheology has been simulated through a smoothed particle hydrodynamics (SPH) formulation of non-Newtonian flow. By modeling vessel wall structure as virtual particles, a pure Lagrange particle formulation for fluid-structure interaction (FSI) is purposed for modeling the blood-vessel interaction. We further propose a flow-related thrombus (clot) formation-dissolution model based on our fluid–solid interaction framework. A physics processing API (PhysX) friendly implementation is proposed for incorporating the rheological properties of blood and vessel wall into our framework. Results have demonstrated the feasibility of employing our proposed meshfree framework in simulating blood-vessel interaction and clotting behaviors which are essential to endovascular simulations. Having benefited from the elegant formulation of Lagrangian particle interaction, interactive framerates of the simulation can be maintained under hardware-acceleration.

Analysis of some partitioned algorithms for fluid‐structure interaction

PurposeThe purpose of this paper is to analyse algorithms for fluid‐structure interaction (FSI) from a purely algorithmic point of view.Design/methodology/approachFirst of all a 1D model problem is selected, for which both the fluid and structural behavior are represented through a minimum number of parameters. Different coupling algorithm and time integration schemes are then applied to the simplified model problem and their properties are discussed depending on the values assumed by the parameters. Both exact and approximate time integration schemes are considered in the same framework so to allow an assessment of the different sources of error.FindingsThe properties of staggered coupling schemes are confirmed. An insight on the convergence behavior of iterative coupling schemes is provided. A technique to improve such convergence is then discussed.Research limitations/implicationsAll the results are proved for a given family of time integration schemes. The technique proposed can be applied to other families of time integration techniques, but some of the analytical results need to be reworked under this assumption.Practical implicationsThe problems that are commonly encountered in FSI can be justified by simple arguments. It can also be shown that the limit at which trivial iterative schemes experience convergence difficulties is very close to that at which staggered schemes become unstable.Originality/valueAll the results shown are based on simple mathematics. The problems are presented so to be independent of the particular choice for the solution of the fluid flow.

스테이터-로터 상호간섭 효과를 고려한 3차원 터빈 블레이드의 유체/구조 연계해석

ABSTRACT In this study, fluid/structure coupled analyses have been conducted for 3-D stator and rotor configuration. Advanced computational analysis system based on computational fluid dynamics(CFD) and computational structural dynamics(CSD) has been developed in order to investigate fluid/structure responses of general stator-rotor configurations. To solve the fluid/structure coupled problems, fluid domains are modeled using the structural grid system with dynamic moving and local deforming techniques. Reynolds-averaged Navier-Stokes equations with Spalart-Allmaras(S-A) and SST  turbulence models are solved for unsteady flow problems. A fully implicit time marching scheme based on the Newmark direct integration method is used for computing the coupled aeroelastic governing equations of the 3-D turbine blades for fluid-structure interaction(FSI) problems. Detailed fluid/structure analysis responses for stator-rotor interaction flow conditions are presented to show the physical performance and flow characteristics.

3차원 축류압축기 블레이드의 유체유발진동 해석

In this study, flow-induced vibration(FIV) analyses have been conducted for a 3D compressor blade model. Advanced computational analysis system based on computational fluid dynamics(CFD) and computational structural dynamics(CSD) has been developed in order to investigate detailed dynamic responses of designed compressor blades. Fluid domains are modeled using the computational grid system with local grid deforming and remeshing techniques. Reynolds-averaged Navier-Stokes equations with <TEX>$\kappa-\epsilon$</TEX> turbulence model are solved for unsteady flow problems of the rotating compressor model. A fully implicit time marching scheme based on the Newmark direct integration method is used for computing the coupled aeroelastic governing equations of the 3D compressor blade for fluid-structure interaction(FSI) problems. Detailed dynamic responses and instantaneous pressure contours on the blade surfaces considering flow-separation effects are presented to show the multi-physical phenomenon of the rotating compressor blade.

Neuro-control of fixed offshore structures under earthquake

An intelligent control technique using a neural network is proposed for seismic protection of offshore structures. Fluid-structure interaction was considered in developing controller and a training algorithm for the neuron-controller is presented. In the numerical example, the performance of the proposed neuron-controller was evaluated. Moreover, a neuron-controller is tested even when it is trained by using a linearized equation of motion for fluid structure interaction (FSI). Based on the examples, it can be concluded that the proposed neuro-control scheme can be used for offshore structures which have intrinsic nonlinearity due to FSI.