Nonlinear Fluid-structure Interaction Problem Research Articles

A particle refinement technique with dynamic splitting and coalescing pattern for fluid-structure interaction problem

With the increasing demand of large scale computation, multi-resolution particle methods have been paid much attention by many researchers. In multi-resolution method, high resolution is applied in local area to reduce the whole computational costs and maintain the local accuracy. However, there are still many challenges in the stability and accuracy of multi-resolution particle methods. In this research, an efficient variable particle size (VSP) multi-resolution method, using particle splitting and coalescing techniques, is developed in moving semi-implicit particle (MPS) method. Particles split or coalesce in dynamic five steps to avoid particle overlap and clustering. The mixed splitting mechanism by combining hexagonal splitting pattern and pair splitting pattern are proposed in the five-step splitting algorithm. Pair splitting and coalescing techniques with variable particle size are proposed to strictly ensure the conservation of mass and momentum and avoid particle clustering. To solve the non-linear fluid-structure interaction problem, the VSP algorithm is introduced in MPS-DEM method. The numerical results are compared with the analytical solutions and experimental results. It shows that the proposed VSP algorithm cannot only maintain the local accuracy, but also improve the computational efficiency by avoiding unnecessary chain operations between particle splitting and coalescing.

The loading on a vertical cylinder in steep and breaking waves on sheared currents using smoothed particle hydrodynamics

Waves and currents coexist in a wide range of natural locations for the deployment of offshore structures and devices. This combined wave–current environment largely determines the loading of vertical surface piercing cylinders, which are the foundations typically used for offshore wind turbines along with many other offshore structures. The smoothed particle hydrodynamics (SPH) code DualSPHysics is used to simulate focused waves on sheared currents and assess subsequent loading on a vertical cylinder. Outputs from another numerical model are used to define the SPH inlet–outlet boundary conditions to generate the wave–current combinations. A modified damping zone is used to damp the waves, but allow the currents to exit the domain. Numerical results are validated against experimental measurements for surface elevation and associated loading on the cylinder. Four phase repeats are used in the SPH model to understand the harmonic structure of the surface elevation at the front face of the cylinder and associated loading. It is shown that the SPH model provides agreement with experimental measurements of harmonic components for both force and elevations. Taking advantage of the SPH method, wave amplitudes were increased up to, and beyond, the breaking threshold highlighting a complex relationship between peak force and wave phase, requiring detailed investigation. The numerical modeling of interactions of steep and breaking waves on sheared currents with the cylinder demonstrates the SPH model's capability for modeling highly nonlinear fluid–structure interaction problems.

Numerical study of the splashing wave induced by a seaplane using mesh-based and particle-based methods

In recent years, forest fires and maritime accidents have occurred frequently, which have had a bad impact on human production and life. Thus, the development of seaplanes is an increasingly urgent demand. It is important to study the taxiing process of seaplanes for the development of seaplanes, which is a strong nonlinear fluid-structure interaction problem. In this paper, the smoothed particle hydrodynamics (SPH) method based on the Lagrangian framework is utilized to simulate the taxiing process of seaplanes, and the SPH results are compared with those of the finite volume method (FVM) based on the Eulerian method. The results show that the SPH method can not only give the same accuracy as the FVM but also have a strong ability to capture the splashing waves in the taxiing process, which is quite meaningful for the subsequent study of the effect of a splash on other parts of the seaplane.

Fluid-structure interaction analysis of nonlinear flapping dynamic behaviors of variable stiffness composite laminated plates in viscous flows

This paper is concerned with the development of a numerical model for the analysis of nonlinear fluid–structure interaction problems of large-deformable curvilinear fiber-reinforced composite laminated plates in viscous flows. A higher-order shear deformation zig-zag theory in conjunction with nonlinear von Kármán strains is employed to accommodate the large deformations of variable stiffness composite laminated plates. An implicit partitioned fluid–structure interaction method based on an arbitrary Lagrangian-Eulerian framework is adopted for dealing with the coupling of the large-deformable plate and the viscous flow. The validity of the proposed model and method is confirmed by comparing the computed results of a two-layered plate with those available solutions in the literature. Effects of material properties and fiber paths of composite plates on the periodic limit cycle oscillation and the wake-flow vortices are examined. It is found that symmetrical lay-ups of the constant stiffness composite laminated plates can produce asymmetrical flapping shapes, resulting in asymmetrical hairpin vortex structures in the wake flow. For a variable stiffness composite laminated plate, the flexibility of the leading or trailing sections can be adjusted by the curved fiber path, which in turn leads to changes in the plate flapping shapes.

Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange

In this paper, we study a nonlinear interaction problem between a thermoelastic shell and a heat-conducting fluid. The shell is governed by linear thermoelasticity equations and encompasses a time-dependent domain which is filled with a fluid governed by the full Navier-Stokes-Fourier system. The fluid and the shell are fully coupled, giving rise to a novel nonlinear moving boundary fluid-structure interaction problem involving heat exchange. The existence of a weak solution is obtained by combining three approximation techniques – decoupling, penalization and domain extension. In particular, the penalization and the domain extension allow us to use the methods already developed for compressible fluids on moving domains. In such a way, the proof is more elegant and the analysis is drastically simplified. Let us stress that this is the first time the heat exchange in the context of fluid-structure interaction problems is considered.

Nonlinear Aeroelastic Analysis for Highly Flexible Flapping Wing in Hover

Aeromechanics of highly flexible flapping wings is a complex nonlinear fluid–structure interaction problem and, therefore, cannot be analyzed using conventional linear aeroelasticity methods. This paper presents a standalone coupled aeroelastic framework for highly flexible flapping wings in hover for micro air vehicle (MAV) applications. The MAV-scale flapping wing structure is modeled using fully nonlinear beam and shell finite elements. A potential-flow-based unsteady aerodynamic model is then coupled with the structural model to generate the coupled aeroelastic framework. Both the structural and aerodynamic models are validated independently before coupling. Instantaneous lift force and wing deflection predictions from the coupled aeroelastic simulations are compared with the force and deflection measurements (using digital image correlation) obtained from in-house flapping wing experiments at both moderate (13 Hz) and high (20 Hz) flapping frequencies. Coupled trim analysis is then performed by simultaneously solving wing response equations and vehicle trim equations until trim controls, wing elastic response, inflow and circulation converge all together. The dependence of control inputs on weight and center of gravity (cg) location of the vehicle is studied for the hovering flight case.

Numerical simulation of fluid–structure interaction with SPH method

Smoothed particle hydrodynamics (SPH) is a meshfree, Lagrangian, particle method, which combines the advantages of Euler and Lagrangian method and has special advantages in simulating violent non-linear fluid–structure interaction problems. In this study, an improved SPH method is used to simulate four fluid–structure interaction cases. Firstly, the violent flow in the mould filling process is simulated to validate that the SPH model can obtain accurate flow patterns with any complex solid boundaries. Secondly, the dam-break flow against a vertical wall is simulated, and the pressure curves are compared with the experiment. Then liquid sloshing problems under different external excitations are simulated, and the complex coupling characteristics can be captured. Finally, the interactions between fluid and floating bodies are researched. The obtained numerical results show good agreement with the results from other sources, and clearly demonstrate the effectiveness of the presented SPH method in modelling fluid–structure interaction problems.

Convergence analysis and error estimate of finite element method of a nonlinear fluid-structure interaction problem

In this paper, a semi-discrete finite element method for the nonlinear fluid-structure interaction problem interacts between the Navier-Stokes fluids and linear elastic solids, is studied and developed. A classical mixed variational principle of the weak formulation is given, and the corresponding finite element method is defined. As for the nonlinearity arising from the nonlinear interaction problem, we consider in time of a solution for suitably small data, and uniqueness hypothesis. This approach is fairly robust and adapts to the important case of interface with fractures or cracks. Convergence and estimate of the finite element method are also obtained for the nonlinear fluid-structure interaction problem. Finally, numerical experiments are presented to show the performance of the proposed method.

A generalized minimal residual method-based immersed boundary-lattice Boltzmann flux solver coupled with finite element method for non-linear fluid-structure interaction problems

A generalized minimal residual method (GMRES) based immersed boundary-lattice Boltzmann flux solver (IB-LBFS) coupled with the finite element method (FEM) is presented in this paper for nonlinear fluid-structure interaction (FSI) problems. This approach effectively combines LBFS for the simulation of the flow field, the total Lagrangian FEM for the evaluation of nonlinear structural deformations, and the immersed boundary method (IBM) for the exchange of information on the fluid-solid interface and implementation of boundary conditions. Both the multidirect forcing and the implicit IBM are considered to examine their effects on numerical accuracy and efficiency. Through numerical simulations on flow past a cylinder, it is shown that the implicit IBM with the GMRES for the linear equation system is more efficient and accurate, which justify the conventional misunderstanding that implicit IBM is always less efficient than explicit methods. Numerical simulations on the lid-driven cavity flow in an inclined cavity, incompressible flows of a uniformly accelerated vertical plate, and the flow induced vibrations of a beam attached behind a cylinder in a channel are also successfully carried out and the obtained results are in good agreement with the published data, which verify the reliability and flexibility of the proposed solver for simulating nonlinear FSI problems. After that, the external flows past two hyperelastic cylinder-beam structures at the Reynolds number of 40–300 are studied and three different modes of static, linear, and nonlinear deformations of the beam are obtained, demonstrating its capability of simulating flows with nonlinear FSI problems with multiple deformable objects.

Existence of a weak solution to the fluid-structure interaction problem in 3D

We study a nonlinear fluid-structure interaction problem in which the fluid is described by the three-dimensional incompressible Navier-Stokes equations, and the elastic structure is modeled by the nonlinear plate equation which includes a generalization of Kirchhoff, von Kármán and Berger plate models. The fluid and the structure are fully coupled via kinematic and dynamic boundary conditions. The existence of a weak solution is obtained by designing a hybrid approximation scheme that successfully deals with the nonlinearities of the system. We combine time-discretization and operator splitting to create two sub-problems, one piece-wise stationary for the fluid and one in the Galerkin basis for the plate. To guarantee the convergence of approximate solutions to a weak solution, a sufficient condition is given on the number of time discretization sub-intervals in every step in a form of dependence with number of the Galerkin basis functions and nonlinearity order of the plate equation.

Numerical investigation of the skip characteristics of a disk based on the coupled FEM-SPH method

The skip phenomenon that may occur when a disk impacts water is a subject of perennial fascination for children as well as adults alike; it is also a fairly complex and highly nonlinear fluid-structure interaction problem. In this paper, the coupled FEM-SPH algorithm is used to numerically study the skip characteristics of disk impacting water. The critical conditions of the skip and the relationship between the initial velocity and the maximum skipping times are obtained. Moreover, the dissipation role of energy during the skipping process is discussed. Our conclusions can provide references for other similar issues, such as aircraft ditching, trans-medium vehicles, bouncing projectiles and so on.

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.

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.

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.

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.

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 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.

A pseudo-coupled analytic fluid-structure interaction method for underwater implosion of cylindrical shells

Underwater implosion, the rapid collapse of a structure caused by hydrostatic pressure, is a fully coupled, highly dynamic and nonlinear fluid-structure interaction (FSI) problem. The primary motivation behind studying implosion is the short-duration, high-pressure pulse generated in the surrounding water. This paper presents a simplified analytic method to estimate the energy in the pressure pulse, based on potential flow theory. The method accounts for the varying fluid pressure and accompanying FSI. The focus is on long, thin, unstiffened metallic cylindrical shells that collapse in mode 2. The implosion pulse energy is shown to be equal to the maximum system kinetic energy developed during collapse. The kinetic energy is calculated using an energy balance approach and analytic solutions for plastic energy dissipation and energy required to compress the internal air. The time-varying fluid pressure, and subsequently the work done by the fluid on the cylinder, is found using a novel explicit time-stepping methodology. The result is a pseudo-coupled analytic solution for the fluid pressure time history and implosion pulse energy. Solutions for pulse energy agree with RANS numerical simulations within 5%.

Efficient optimization procedure in non-linear fluid-structure interaction problem: Application to mainsail trimming in upwind conditions

This paper investigates the use of Gaussian processes to solve sail trimming optimization problems. The Gaussian process, used to model the dependence of the performance with the trimming parameters, is constructed from a limited number of performance estimations at carefully selected trimming points, potentially enabling the optimization of complex sail systems with multiple trimming parameters. The proposed approach is tested on a two-parameter trimming for a scaled IMOCA mainsail in upwind sailing conditions. We focus on the robustness of the proposed approach and study especially the sensitivity of the results to noise and model error in the point estimations of the performance. In particular, we contrast the optimization performed on a real physical model set in a wind tunnel with a fully non-linear numerical fluid-structure interaction model of the same experiments. For this problem with a limited number of trimming parameters, the numerical optimization was affordable and found to require a comparable amount of performance estimation as for the experimental case. The results reveal a satisfactory agreement for the numerical and experimental optimal trimming parameters, considering the inherent sources of errors and uncertainties in both numerical and experimental approaches. Sensitivity analyses have been eventually performed in the numerical optimization problem to determine the dominant source of uncertainties and characterize the robustness of the optima.

A Nonlinear Fluid-Structure Interaction Problem in Compliant Arteries Treated with Vascular Stents

We study a nonlinear fluid-structure interaction problem between an incompressible, viscous fluid in 3D and an elastic structure whose Lame elastic parameters, thickness and density are all functio...