Nonlinear Fluid-structure Interaction Research Articles

Fluid–structure interaction between pulsatile blood flow and a curved stented coronary artery on a beating heart: A four stent computational study

This work focuses on fluid–structure interaction (FSI) between a curved (tortuous) coronary artery with an implanted stent, pulsatile blood flow, and heart contractions. The goal is to understand which geometric distribution of stent struts, given by four different, commercially available stent geometries, is least likely to be associated with parameters correlated with pathobiologic responses leading to restenosis, in the case of curved coronary arteries, whose curvature changes significantly with each heart contraction. The stent geometries considered in this study correspond to a Palmaz-like stent, an Express-like stent, a Cypher-like stent, and a Xience-like stent. The biomechanical environment induced by each implanted stent is evaluated in terms of displacement magnitude, Von Mises stress, normal stress experienced by the intimal layer with implanted stent, and wall shear stress. Arterial walls are modeled as multi-layered structures: the intimal layer with the internal elastic laminae is modeled as a nonlinearly elastic membrane, while the media–adventitia complex is modeled as a 3D linearly elastic material. The Navier–Stokes equations for an incompressible, viscous fluid, are used to model the blood flow. Full, two-way coupling between the fluid and the structure, and between the thin and thick structure, is considered. To include the effects of the force exerted by the pericardium and heart muscle contractions, external force is applied to the coronary artery walls. Pulsatile boundary conditions were imposed at the inlet and outlet of the coronary segment, approximating measured diastolic coronary flow. The presence of an implanted stent was modeled by its impact on the mass and elasticity properties of the intimal layer where the stent is located. The stent material is modeled as a 316L stainless steel. A novel, loosely coupled partitioned scheme combined with an ALE approach was used to solve this nonlinear FSI problem. It was found that the Cypher-like stent geometry outperforms the other three stent geometries. The ranking from best to worst is as follows: Cypher-like stent, Express-like stent, Xience-like stent, Palmaz-like stent. It is conjectured that the sinusoidal horizontal stent struts and large cells associated with open-cell design, give rise to a stent geometry that conforms best to the native curved coronary artery, with smallest deviations in Von Mises stress and displacement from the nonstented curved coronary artery both during systole and diastole. To the best of our knowledge, this is the first computational study in which the behavior of different stent geometries implanted in curved coronary arteries is studied using full FSI capturing the behavior of multi-layered, curved, stented coronary arteries contracting on a beating heart.

Nonlinear sloshing response of liquid-filled rectangular concrete tanks under seismic excitation

The current study is mainly focused on nonlinear sloshing analysis of rectangular liquid storage tanks. The main response quantity of interest is free surface sloshing height. There are some key factors to be investigated in order to make a better understanding of the performance of liquid tanks under seismic loading. These include three-dimensional geometry, corner sloshing, tank aspect ratio, bidirectional loading, and earthquake frequency content. The main focus of this work is to investigate these important parameters through a comprehensive parametric study using a rigorous finite element technique capable of accounting for nonlinear fluid-structure interaction effects. The validity of current code provisions in seismic analysis of such structures is then investigated by comparing the obtained numerical results with those recommended by current practice and important conclusions are drawn. The present paper suggests that the sloshing nonlinearity could have a significant effect on the seismic performance of liquid containing structures and failing to account for it properly could introduce a major concern with respect to their satisfactory performance for a certain group of tanks in particular shallow tanks.

Unconditionally Stable Pressure-Correction Schemes for a Nonlinear Fluid-Structure Interaction Model

We consider in this paper numerical approximation of a nonlinear fluid-structure interaction (FSI) model with a fixed interface. We construct a new class of pressure-correction schemes for the FSI problem, and prove rigorously that they are unconditionally stable. These schemes are computationally very efficient, as they lead to, at each time step, a coupled linear elliptic system for the velocity and displacement in the whole region and a discrete Poisson equation in the fluid region.

A second-order time accurate semi-implicit method for fluid–structure interaction problems

This paper is concerned with numerical solution of fluid–structure interaction (FSI) problems involving an incompressible viscous flow and an elastic structure. A semi-implicit partitioned method with second-order temporal accuracy is proposed. The method separates the pressure term of the fluid equations and strongly couples it to the structure, while the remaining fluid terms and the geometrical nonlinearities are treated explicitly. A second-order projection method is used to solve the fluid equations and also as a framework for the FSI coupling. Particular attention is paid to the boundary conditions for fluid equations and the accuracy of the fluid pressure on the common interface. The proposed coupling method retains the second-order accuracy for fully-coupled nonlinear FSI problems. Extensive numerical tests are carried out on a number of benchmark FSI problems and the second-order temporal accuracy for all the variables of interest (fluid velocity and pressure, and structural displacement) is demonstrated.

Nonlinear fluid-structure interaction of bridge deck: CFD analysis and semi-analytical modeling

Nonlinear behavior in fluid-structure interaction (FSI) of bridge decks becomes increasingly significant for modern bridges with increasing spans, larger flexibility and new aerodynamic deck configurations. Better understanding of the nonlinear aeroelasticity of bridge decks and further development of reduced-order nonlinear models for the aeroelastic forces become necessary. In this paper, the amplitude-dependent and neutral angle dependent nonlinearities of the motion-induced loads are further highlighted by series of computational fluid dynamics (CFD) simulations. An effort has been made to investigate a semi-analytical time-domain model of the nonlinear motion induced loads on the deck, which enables nonlinear time domain simulations of the aeroelastic responses of the bridge deck. First, the computational schemes used here are validated through theoretically well-known cases. Then, static aerodynamic coefficients of the Great Belt East Bridge (GBEB) cross section are evaluated at various angles of attack, leading to the so-called nonlinear backbone curves. Flutter derivatives of the bridge are identified by CFD simulations using forced harmonic motion of the cross-section with various frequencies. By varying the amplitude of the forced motion, it is observed that the identified flutter derivatives are amplitude-dependent, especially for A_2* and H_2* parameters. Another nonlinear feature is observed from the change of hysteresis loop (between angle of attack and lift/moment) when the neutral angles of the cross-section are changed. Based on the CFD results, a semi-analytical time-domain model for describing the nonlinear motion-induced loads is proposed and calibrated. This model is based on accounting for the delay effect with respect to the nonlinear backbone curve and is established in the state-space form. Reasonable agreement between the results from the semi-analytical model and CFD demonstrates the potential application of the proposed model for nonlinear aeroelastic analysis of bridge decks.

Vibration investigation on fluid-structure interaction of AP1000 shield building subjected to multi earthquake excitations

Fluid-structure interaction (FSI) between water and water tank of AP1000 nuclear power plant has always been a hot topic because the gravity water tank plays a key role in protecting structural safety in an emergency such as an earthquake. The main target of this study is to investigate the FSI effect on structural dynamic responses of AP1000 shield building with filled and empty water tanks and to explore the most reasonable height of water level for reducing seismic response under inputs of multi three-direction earthquake excitations. For this purpose, method of nonlinear FSI algorithm of finite element is employed based on ANSYS platform. The numerical procedure is validated by comparison with theoretical calculation and existing experimental results of fluid free vibration and structural seismic responses in the situation of El Centro wave. Based on the validated numerical model, a series of numerical simulations on seven partially-filled models in six natural and one artificial earthquake are carried out and corresponding results, such as peak acceleration & displacement, floor response spectrum and structural base shear, are studied comparatively in details. Discussions of this study show that the partially-filled shield building appears significant FSI effect, which generates great influence on structural dynamic characteristics and responses. Reasonable design of the water level can contribute to reducing structural responses and improving seismic safety.

Chaotic motion analysis of fluid-conveying viscoelastic nanotubes

In the current analysis, an attempt is made to develop a nonlinear size-dependent fluid-structure interaction model for the chaotic motion of nanofluid-conveying nanotubes subject to an external excitation. The material properties of the nanotube are assumed to be viscoelastic. Size effects in both solid and fluid nanoscale parts are taken into consideration. In addition, the effects of both centripetal and Coriolis accelerations are incorporated in the model. Using Hamilton's principle, the nonlocal strain gradient elasticity and the Beskok-Karniadaki theory, the nonlinear size-dependent governing equation is derived. For developing a precise solution approach, Galerkin's procedure and a direct-time-integration method are eventually used. Different parameters of the nanosystem are taken into consideration to study the size-dependent chaotic motion of the viscoelastic nanotube conveying nanofluid subject to a harmonic excitation.

Existence of local strong solutions to fluid–beam and fluid–rod interaction systems

We study an unsteady nonlinear fluid–structure interaction problem. We consider a Newtonian incompressible two-dimensional flow described by the Navier–Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear wave equation or a linear beam equation. The fluid and the structure systems are coupled via interface conditions prescribing the continuity of the velocities at the fluid–structure interface and the action-reaction principle. Considering three different structure models, we prove existence of a unique local-in-time strong solution, for which there is no gap between the regularity of the initial data and the regularity of the solution enabling to obtain a blow up alternative. In the case of a damped beam this is an alternative proof (and a generalization to non zero initial displacement) of the result that can be found in [20]. In the case of the wave equation or a beam equation with inertia of rotation, this is, to our knowledge the first result of existence of strong solutions for which no viscosity is added. The key points consist in studying the coupled system without decoupling the fluid from the structure and to use the fluid dissipation to control, in appropriate function spaces, the structure velocity.

Error estimates for projection-based dynamic augmented Lagrangian boundary condition enforcement, with application to fluid–structure interaction

In this work, we analyze the convergence of the recent numerical method for enforcing fluid–structure interaction (FSI) kinematic constraints in the immersogeometric framework for cardiovascular FSI. In the immersogeometric framework, the structure is modeled as a thin shell, and its influence on the fluid subproblem is imposed as a forcing term. This force has the interpretation of a Lagrange multiplier field supplemented by penalty forces, in an augmented Lagrangian formulation of the FSI kinematic constraints. Because of the non-matching fluid and structure discretizations used, no discrete inf-sup condition can be assumed. To avoid solving (potentially unstable) discrete saddle point problems, the penalty forces are treated implicitly and the multiplier field is updated explicitly. In the present contribution, we introduce the term dynamic augmented Lagrangian (DAL) to describe this time integration scheme. Moreover, to improve the stability and conservation of the DAL method, in a recently-proposed extension we projected the multiplier onto a coarser space and introduced the projection-based DAL method. In this paper, we formulate this projection-based DAL algorithm for a linearized parabolic model problem in a domain with an immersed Lipschitz surface, analyze the regularity of solutions to this problem, and provide error estimates for the projection-based DAL method in both the [Formula: see text] and [Formula: see text] norms. Numerical experiments indicate that the derived estimates are sharp and that the results of the model problem analysis can be extrapolated to the setting of nonlinear FSI, for which the numerical method was originally proposed.

Solving 2-D highly nonlinear free-surface problems with an improved smoothed particle hydrodynamics method

A numerical program based on the smoothed particle hydrodynamics (SPH) method has been developed to solve the nonlinear fluid–structure interaction problems. The numerical method simulates the breaking free-surface flows and evaluates hydrodynamic loads on structures. A kernel function was employed to interpolate the flow field and solve the Euler equations. The solid boundaries were modelled using a fixed ghost particle method. A particle shifting technique was adopted and improved to minimize the interpolation error caused by the non-uniform particle configuration on the free surface. Validation studies were carried out for three cases, including the dam-break flow impacting a vertical wall, water entry of a free-fall wedge and the sloshing flow in a rectangular container excited by roll motions. The numerical results were compared with the experimental data and other published numerical solutions.

Finite Element Analysis of Flexible Structure and Cavitating Nonlinear Acoustic Fluid Interaction under Shock Wave Loading

Abstract This paper describes a numerical model and its finite element implementation that used to compute the cavitation effects on nonlinear acoustic fluid and adjacent flexible structure interaction. The system is composed of two sub-systems, namely, the fluid and the flexible flat plate. A fully coupled approach using iterative implicit partitioned scheme was implemented in the present work which can account for the effects associated whit a mutual interaction. This approach included a compressible nonlinear acoustic fluid Eulerian solver and a Lagrangian solver for the flexible structure both in finite element formulation. A novel implementation of acoustic cavitation was made possible with the introduction of a simplified one-fluid cavitation model. The element-by-element PCG (Preconditioned Conjugate Gradient) solver together with diagonal preconditioning is used to solve the large equation system resulting from the finite element discretization of the governing equation of fluid domain. The capability of three different cavitation model, as the cut-off model, Modified Schmidt model and developed model are compared with each other in the evaluation of plate vibration response. Simulation results are presented on a large size shock tube, in which planar shock waves were impacting in “face on” configuration flat plates mounted at tube's end. Results are presented to demonstrate the capability of proposed solver in simulating cavitating nonlinear acoustic fluid. Obtained results show that impact forces caused impinging shock wave and reloading by cavitating region collapse have a considerable effect on the dynamic response of flexible plate.

Nonlinear Dynamics of Three-Dimensional Prediction Model for a Flexible Riser Under Linearly Sheared Currents

This paper presents a three-dimensional vortex-induced vibration prediction model for a long flexible riser under linearly sheared currents. Two distributed and coupled van der Pol wake oscillators are utilized to characterize the fluctuating lift and drag coefficients, respectively. It should be noted that geometric and hydrodynamic nonlinearities are also considered in our model. Numerical simulations by finite element method are carried out to solve the highly coupled nonlinear fluid–structure interaction equations. Firstly, modal analysis is performed to obtain the foremost ten natural frequencies of the flexible riser under top-end tension by theoretical and numerical methods, and the results agree very well. Then, nonlinear dynamic analyses are carried out to investigate the effects of linear shear flow on displacements, stresses, modal variations and phase portraits. The results obtained in uniform and linear shear currents are compared in detail. The results indicate that the asymmetric phenomenon along the riser span is more obvious with increasing linear shear velocity and the lock-in phenomenon of IL (in-line) response frequencies with multi-frequency is also observed along riser span. Moreover, it is also revealed that the dynamic responses simultaneously exhibit the standing and travelling wave patterns under linearly sheared currents, and the dynamic responses become more irregular than uniform flow.

A classification approach to efficient global optimization in presence of non-computable domains

Gaussian-Process based optimization methods have become very popular in recent years for the global optimization of complex systems with high computational costs. These methods rely on the sequential construction of a statistical surrogate model, using a training set of computed objective function values, which is refined according to a prescribed infilling strategy. However, this sequential optimization procedure can stop prematurely if the objective function cannot be computed at a proposed point. Such a situation can occur when the search space encompasses design points corresponding to an unphysical configuration, an ill-posed problem, or a non-computable problem due to the limitation of numerical solvers. To avoid such a premature stop in the optimization procedure, we propose to use a classification model to learn non-computable areas and to adapt the infilling strategy accordingly. Specifically, the proposed method splits the training set into two subsets composed of computable and non-computable points. A surrogate model for the objective function is built using the training set of computable points, only, whereas a probabilistic classification model is built using the union of the computable and non-computable training sets. The classifier is then incorporated in the surrogate-based optimization procedure to avoid proposing new points in the non-computable domain while improving the classification uncertainty if needed. The method has the advantage to automatically adapt both the surrogate of the objective function and the classifier during the iterative optimization process. Therefore, non-computable areas do not need to be a priori known. The proposed method is applied to several analytical problems presenting different types of difficulty, and to the optimization of a fully nonlinear fluid-structure interaction system. The latter problem concerns the drag minimization of a flexible hydrofoil with cavitation constraints. The efficiency of the proposed method compared favorably to a reference evolutionary algorithm, except for situations where the feasible domain is a small portion of the design space.

Flexible hydrofoil optimization for the 35th America's Cup with constrained EGO method

This paper investigates the use of constrained surrogate models to solve the multi-design optimization problem of a flexible hydrofoil. The surrogate-based optimization (EGO) substitutes the complex objective function of the problem by an easily evaluable model, constructed from a limited number of computations at carefully selected design points. Associated with ad-hoc statistical strategies to propose optimum candidates within the estimated feasible domain, EGO enables the resolution of complex optimization problems. In this work, we rely on Gaussian processes (GP) to model the objective function and adopt a probabilistic classification method to treat non-explicit inequality constraints and non-explicit representation of the feasible domain. This procedure is applied to the design of the shape and the elastic characteristics of a hydrofoil equipped with deformable elements providing flexibility to the trailing edge. The optimization concerns the minimization of the hydrofoil drag while ensuring a non-cavitating flow, at selected sailing conditions (boat speed and lifting force). The drag value and cavitation criterion are determined by solving a two-dimensional nonlinear fluid-structure interaction problem, based on a static vortex lattice method with viscous boundary layer equations, for the flow, and a nonlinear elasticity solver for the deformations of the elastic components of the foil. We compare the optimized flexible hydrofoil with a rigid foil geometrically optimized for the same sailing conditions. This comparison highlights the hydrodynamical advantages brought by the flexibility: a reduction of the drag over a large range of boat speeds, less susceptibility to cavitation and a smaller angle of attack tuning range.

A family of position- and orientation-independent embedded boundary methods for viscous flow and fluid–structure interaction problems

The Finite Volume method with Exact two-material Riemann Problems (FIVER) is both a computational framework for multi-material flows characterized by large density jumps, and an Embedded Boundary Method (EBM) for computational fluid dynamics and highly nonlinear Fluid–Structure Interaction (FSI) problems. This paper deals with the EBM aspect of FIVER. For FSI problems, this EBM has already demonstrated the ability to address viscous effects along wall boundaries, and large deformations and topological changes of such boundaries. However, like for most EBMs – also known as immersed boundary methods – the performance of FIVER in the vicinity of a wall boundary can be sensitive with respect to the position and orientation of this boundary relative to the embedding mesh. This is mainly due to ill-conditioning issues that arise when an embedded interface becomes too close to a node of the embedding mesh, which may lead to spurious oscillations in the computed solution gradients at the wall boundary. This paper resolves these issues by introducing an alternative definition of the active/inactive status of a mesh node that leads to the removal of all sources of potential ill-conditioning from all spatial approximations performed by FIVER in the vicinity of a fluid–structure interface. It also makes two additional contributions. The first one is a new procedure for constructing the fluid–structure half Riemann problem underlying the semi-discretization by FIVER of the convective fluxes. This procedure eliminates one extrapolation from the conventional treatment of the wall boundary conditions and replaces it by an interpolation, which improves robustness. The second contribution is a post-processing algorithm for computing quantities of interest at the wall that achieves smoothness in the computed solution and its gradients. Lessons learned from these enhancements and contributions that are triggered by the new definition of the status of a mesh node are then generalized and exploited to eliminate from the original version of the FIVER method its sensitivities with respect to both of the position and orientation of the wall boundary relative to the embedding mesh, while maintaining the original definition of the status of a mesh node. This leads to a family of second-generation FIVER methods whose performance is illustrated in this paper for several flow and FSI problems. These include a challenging flow problem over a bird wing characterized by a feather-induced surface roughness, and a complex flexible flapping wing problem for which experimental data is available.

A harmonic balance method for nonlinear fluid structure interaction problems

Over the past decade the Harmonic-Balance technique has been established as a viable alternative to direct time integration methods to predict periodic aeroelastic instabilities. This article reports the progress made in using a frequency updating procedure, based on a coupled fluid-structural solver using the Harmonic-Balance formulation. In particular, this paper presents an efficient implicit time-integrator that accelerates the convergence of the structural equations of motion to the final solution. To demonstrate the proposed approached, the paper includes a detailed investigation of the impact of input parameters and exercises the method for two types of fluid-structural nonlinear instabilities: transonic limit-cycle oscillations and vortex-induced vibrations.

Nonlinear dynamics of three-dimensional vortex-induced vibration prediction model for a flexible fluid-conveying pipe

In this article, a three-dimensional nonlinear dynamic model, which takes into account both the geometric and hydrodynamic nonlinearities, is presented to characterize the behavior of a flexible fluid-conveying pipe under vortex-induced vibration by extended Hamilton's principle. It should be noted that the pipe conveying fluids is placed in a uniform cross flow. Two distributed and coupled van der Pol wake oscillators are utilized to model the fluctuating lift and drag coefficients, respectively. The finite element method is adopted to directly solve the highly coupled nonlinear fluid-structure interaction equations. Model validations are firstly performed through comparisons with published experimental data and numerical simulation results. The results show that the natural frequency will rapidly decrease with the increase of internal flow velocity. Parametric studies highlight that the maximum displacements and stresses of the riser can be increased or decreased depending on the internal flow velocity, and the critical internal flow velocities result in the increase of mode order for different cross-flow velocities. The opposite variation between axial and in-line or cross-flow displacement amplitude and maximum stress within the modal transition region is revealed. Moreover, the discontinuous jumping phenomenon of in-line response modal is discovered.

Transient and Stable Chaos in Dipteran Flight Inspired Flapping Motion

This paper deals with the nonlinear fluid structure interaction (FSI) dynamics of a Dipteran flight motor inspired flapping system in an inviscid fluid. In the present study, the FSI effects are incorporated to an existing forced Duffing oscillator model to gain a clear understanding of the nonlinear dynamical behavior of the system in the presence of aerodynamic loads. The present FSI framework employs a potential flow solver to determine the aerodynamic loads and an explicit fourth-order Runge–Kutta scheme to solve the structural governing equations. A bifurcation analysis has been carried out considering the amplitude of the wing actuation force as the control parameter to investigate different complex states of the system. Interesting dynamical behavior including period doubling, chaotic transients, periodic windows, and finally an intermittent transition to stable chaotic attractor have been observed in the response with an increase in the bifurcation parameter. Similar dynamics is also reflected in the aerodynamic loads as well as in the trailing edge wake patterns.

Nonlinear three-dimensional dynamics of a marine viscoelastic riser subjected to uniform flow

The three-dimensional nonlinear dynamic model of a long marine riser with Kelvin-Voigt viscoelasticity properties under vortex-induced vibration is proposed and investigated. The objective is to find the appropriate viscoelastic coefficients to suppress the nonlinear dynamic response of a marine riser. The pipe is placed in a uniform cross flow and geometric nonlinearities are considered. Two distributed and coupled Van der Pol wake oscillators are applied to characterize the fluctuating lift and drag coefficients, respectively. The highly nonlinear fluid-structure interaction equations are directly coupled and solved by the finite element method. Firstly, the model is validated by comparing with published experimental data and numerical simulation results. Then, modal analysis is performed to determine the impact of viscoelastic coefficients on the natural frequency for different damping values. A nonlinear dynamic analysis is carried out to determine the impacts of the viscoelastic coefficients on displacements, stresses, modal variation and phase portraits. The results show that the viscoelastic coefficients have a significant effect on the natural frequency of the studied marine riser. It is also demonstrated that appropriate viscoelastic coefficients are very important to effectively suppress the maximum displacements and stresses.

Feedback control of unstable flow and vortex-induced vibration using the eigensystem realization algorithm

We present an active feedback blowing and suction (AFBS) procedure via model reduction for unsteady wake flow and the vortex-induced vibration (VIV) of circular cylinders. The reduced-order model (ROM) for the AFBS procedure is developed by the eigensystem realization algorithm (ERA), which provides a low-order representation of the unsteady flow dynamics in the neighbourhood of the equilibrium steady state. The actuation is considered via vertical suction and a blowing jet at the porous surface of a circular cylinder with a body-mounted force sensor. While the optimal gain is obtained using a linear quadratic regulator (LQR), Kalman filtering is employed to estimate the approximate state vector. The feedback control system shifts the unstable eigenvalues of the wake flow and the VIV system to the left half-complex-plane, and subsequently results in suppression of the vortex street and the VIV in elastically mounted structures. The resulting controller designed by a linear low-order approximation is able to suppress the nonlinear saturated state of wake vortex shedding from the circular cylinder. A systematic linear ROM-based stability analysis is performed to understand the eigenvalue distribution for the flow past stationary and elastically mounted circular cylinders. The results from the ROM analysis are consistent with those obtained from full nonlinear fluid–structure interaction simulations, thereby confirming the validity of the proposed ROM-based AFBS procedure. A sensitivity study on the number of suction/blowing actuators, the angular arrangement of actuators and the combined versus independent control architectures has been performed for the flow past a stationary circular cylinder. Overall, the proposed control concept based on the ERA-based ROM and the LQR algorithm is found to be effective in suppressing the vortex street and the VIV for a range of reduced velocities and mass ratios.