Fluid-structure Interaction System Research Articles

Initialization Algorithms of a Rigid–Flexible Coupling Fluid–Structure Interaction System by Considering Length-and-Area Constraints

Rigid–flexible coupling fluid–structure interaction systems are expected to be future solutions for reducing energy lost in water. The dynamics of these systems is usually investigated via numerical simulations. However, in existing numerical works there is no accurate algorithm for the initialization of the flexible filament, which ensures both the length and area constraints, leading to inaccurate results or even severe numerical instabilities. We propose two alternative initialization algorithms, respectively, the “Trapezoidal arrangement” and the “Quartic curve arrangement”. The performances of both of these two algorithms are investigated in numerical simulations by using the immersed boundary method. The motion responses and force characteristics of the flexible filament are analyzed carefully, verifying the capability of the proposed algorithms. Specifically, “Quartic curve arrangement” is further recommended due to its good property of convergence.

Advanced piezoelectric fluid energy harvesters by monolithic fluid–structure–piezoelectric coupling: A full-scale finite element model

A full-scale finite element model is presented for monolithic fluid–structure interaction (FSI) simulations of thin-walled piezoelectric fluid energy harvesters (PFEHs). Unlike widely used beam/plate-based models, our model employs a solid finite element discretization to precisely represent the complex PFEH designs involving microstructured transducers and non-uniform cantilevers. These features, plus the local FSI effects, are often ignored by simplified models. We applied the Galerkin method to formulate the weak form of the mixed equation system, integrating the flow dynamics, the geometrically nonlinear cantilever, the piezoelectric components, the electrode, and the output circuit within a closed-circuit electro-mechanical coupled system. The coupling of the multiple domains is achieved through boundary-fitted discretization within a monolithic scheme, using shifted-Crank–Nicolson temporal integration. This work explored implementing piezoelectric FSI systems within the FEniCS-based TurtleFSI library, and experimented techniques such as employing penalty functions for achieving electrode components with uniform electric potentials. We investigated various advanced PFEH features, including the baseplate design, the arrangement and microstructure of the piezoelectric components, and their influence on the system's dynamic and energy output behavior. The results confirmed the model's key advantages: full-scale modeling allows the integration of complex base structures and transducer microstructures in PFEH design. Combined with monolithic FSI coupling, it offers greater versatility, supporting a wider range of fluid environments and configurations in both wind and hydropower harvesting. Additionally, the modeling strategy can be intended not only to enhance power output, but also to minimize material usage, reduce mechanical fatigue, and extend the operational lifespan of PFEH systems.

Investigating resonance frequency in advanced composite structures as the main part of bridge construction: a multi-physics simulation approach

This paper investigates the nonlinear vibration characteristics and resonance frequencies of a graphene oxide powders (GOP) reinforced beam structure, which is in contact with fluid, serving as a crucial component in bridge construction. Utilizing a multi-physics simulation approach, this study integrates both mathematical modeling and COMSOL simulations to analyze the behavior of the GOP-reinforced beam. The fluid in the analysis is modeled as incompressible, non-viscous, and irrotational, contributing to the interaction with the beam structure. The isogeometric approach, coupled with the harmonic balance method and the arc-length technique, is employed to solve the complex nonlinear partial differential equations (PDEs). This coupled method ensures the accurate capture of the nonlinear response and resonance frequencies of the beam, which are critical for the safe design and performance of bridge structures. The findings reveal the significant influence of GOP reinforcement on the vibration and stability characteristics of the beam, highlighting its potential to enhance structural performance under dynamic loading conditions. The study also emphasizes the importance of considering fluid-structure interactions in the design process, as the fluid’s presence substantially affects the vibration behavior. This research contributes to the understanding of the dynamic behavior of advanced composite structures in fluid environments, offering valuable insights for the design and analysis of bridge components. The results demonstrate the efficacy of the proposed simulation approach in addressing the complexities of nonlinear vibrations in fluid-structure interaction systems, paving the way for future developments in civil engineering applications.

Optimization of vibration and sound insulation in GPLRC honeycomb structures based on circle chaos mapping and Levy flight-enhanced YDSE with constraints

Utilizing the first-order shear deformation theory (FSDT) and Hamilton's principle, dynamic equations for tunable Poisson's ratio metamaterial honeycomb sandwich panels have been derived. These panels include petal-shaped, star-shaped, and butterfly-shaped designs. The acoustic response of these panels when subjected to plane harmonic sound waves has been formulated, treating them as fluid-structure interaction systems. To enhance the structural vibration and sound propagation attributes, traditional metallic aluminum has been replaced with graphene platelet-reinforced composites (GPLRC). Through computational analysis and finite element simulation data, the natural frequencies and sound transmission loss (STL) characteristics of the panels have been determined. An improved heuristic algorithm called the circle chaos mapping and levy flight enhanced Young's double-slit experiment optimizer (CLYDSE) has been introduced to optimize their vibrational and acoustic properties. This algorithm builds upon Young's double-slit experiment optimizer (YDSE) by incorporating circle chaos mapping for initializing a monochromatic light source and utilizing the levy flight principle for more accurate search results. These enhancements allow the CLYDSE algorithm to avoid local optima and improve convergence velocity. A penalty function method was employed to establish mass and equivalent elastic modulus as optimization constraints, aiming to achieve superior specific stiffness. Finally, structural optimization using the proposed CLYDSE method was conducted to enhance the vibrational and acoustic performance of the three types of honeycomb sandwich panels. The results validate the effectiveness of the theoretical model in predicting vibration and acoustic response, as well as the improved performance of the CLYDSE algorithm in terms of convergence velocity and optimization accuracy. This demonstrates the algorithm's efficacy in refining the acoustic and vibrational qualities of these advanced honeycomb structures.

A novel method for predicting fluid–structure interaction with large deformation based on masked deep neural network

Traditional fluid–structure interaction (FSI) simulation is computationally demanding, especially for bi-directional FSI problems. To address this, a masked deep neural network (MDNN) is developed to quickly and accurately predict the unsteady flow field. By integrating the MDNN with a structural dynamic solver, an FSI system is proposed to perform simulation of a flexible vertical plate oscillation in fluid with large deformation. The results show that both the flow field prediction and structure response are consistent with the traditional FSI system. Furthermore, the masked method is highly effective in mitigating error accumulation during temporal flow field predictions, making it applicable to various deformation problems. Notably, the proposed model reduces the computational time to a millisecond scale for each step regarding the fluid part, resulting in an increase in nearly two orders of magnitude in computational speed, which greatly enhances the computational speed of the FSI system.

Flow field interference effect on energy harvesting enhancement of a combined fluid–structure interaction system in channel flow

In this paper, the flow field between two vibrating systems and the potential to increase the harvested energy by the interference of flow fields was numerically evaluated. A combined configuration of a cylinder-splitter hyperelastic plate placed at the wake of a vortex-induced oscillating cylinder was studied in a laminar channel flow at a Reynolds number of 200. A finite-volume method was adopted for solving the flow field over polyhedral cells. Overset grid and mesh morpher algorithms were employed to handle different mesh motions. On the other hand, a finite element method was exploited to solve the structural displacement of the hyperelastic plate. Having validated two individual similar systems, the effects of different spacing values and the reduced frequency of the vibrating cylinder on the amount of harvested energy were investigated in the combined configuration. According to results, no flow unsteadiness took place for the small spacing values at low reduced velocity. Increasing the natural frequency, the oscillation of the vibrating cylinder excited its boundary layer, causing it to separate. Moreover, the presence of such oscillations at downstream of the vibrating cylinder altered its response yielding higher energy production. Results showed that at some specific reduced velocities of the oscillating cylinder, the vortex shedding phenomenon did not occur if the spacing between the cylinders was small. However in other cases, the relative power efficiency of the oscillating cylinder in the combined system was increased from 29% to more than five times of the isolated oscillating cylinder depending on the parameters.

A 1D model for the dynamic instability of magnetized beams in leakage flow energy harvesters

This paper presents a one-dimensional fluid–structure interaction model for investigating the dynamic stability of elastic mounted beams under the influence of magnetic forces in a leakage flow energy harvesting environment. The interaction between the beam and external magnetic fields is represented by a nonlinear long range force distribution that is non linearly dependent on the beam displacement. The formulation results in a two way coupled fluid–structure interaction system that is one way coupled with the electromagnetic system. A perturbation technique is utilized to linearize the second order equilibrium equations of the coupled system, which are then transformed into a set of first-order ordinary differential equations in the state space. The effect of the linearized magnetic force coefficient on the eigenvalues and dynamic stability of the system is analyzed through a parametric study. The results indicate the onset of oscillatory dynamics in the coupled magneto-fluid-structural system is a non monotonic function of the magnetic force.

Adaptive control of transonic buffet and buffeting flow with deep reinforcement learning

The optimal control of flow and fluid–structure interaction (FSI) systems often requires an accurate model of the controlled system. However, for strongly nonlinear systems, acquiring an accurate dynamic model is a significant challenge. In this study, we employ the deep reinforcement learning (DRL) method, which does not rely on an accurate model of the controlled system, to address the control of transonic buffet (unstable flow) and transonic buffeting (structural vibration). DRL uses a deep neural network to describe the control law and optimizes it based on data obtained from interaction between control law and flow or FSI system. This study analyzes the mechanism of transonic buffet and transonic buffeting to guide the design of control system. Aiming at the control of transonic buffet, which is an unstable flow system, the control law optimized by DRL can quickly suppress fluctuating load of buffet by taking the lift coefficient as feedback signal. For the frequency lock-in phenomenon in transonic buffeting flow, which is an unstable FSI system, we add the moment coefficient and pitching displacement to feedback signal to observe pitching vibration mode. The control law optimized by DRL can also effectively eliminate or reduce pitching vibration displacement of airfoil and buffet load. The simulation results in this study show that DRL can adapt to the control of two different dynamic modes: typical forced response and FSI instability under transonic buffet, so it has a wide application prospect in the design of control laws for complex flow or FSI systems.

Predicting fluid–structure interaction with graph neural networks

We present a rotation equivariant, quasi-monolithic graph neural network framework for the reduced-order modeling (ROM) of fluid–structure interaction systems. With the aid of an arbitrary Lagrangian–Eulerian (ALE) formulation, the system states are evolved temporally with two sub-networks. The movement of the mesh is reduced to the evolution of several coefficients via complex-valued proper orthogonal decomposition (POD), and the prediction of these coefficients over time is handled by a single multi-layer perceptron (MLP). A finite element-inspired hypergraph neural network is employed to predict the evolution of the fluid state based on the state of the whole system. The structural state is implicitly modeled by the movement of the mesh on the solid–fluid interface; hence, it makes the proposed framework quasi-monolithic. The effectiveness of the proposed framework is assessed on two prototypical fluid–structure systems, namely, the flow around an elastically mounted cylinder and the flow around a hyperelastic plate attached to a fixed cylinder. The proposed framework tracks the interface description and provides stable and accurate system state predictions during roll-out for at least 2000 time steps and even demonstrates some capability in self-correcting erroneous predictions. The proposed framework also enables direct calculation of the lift and drag forces using the predicted fluid and mesh states, in contrast to existing convolution-based architectures. The proposed reduced-order model via the graph neural network has implications for the development of physics-based digital twins concerning moving boundaries and fluid–structure interactions.

Nonlinear shock-induced flutter of a compliant panel using a fully coupled fluid-thermal-structure interaction model

A comprehensive study has been conducted on the fully coupled aero-thermo-elastic interaction between a shock wave and a laminar boundary layer over a flexible surface with different thermal conditions. In this investigation, the flow is characterized by an oblique impinging shock on a laminar boundary layer over a compliant panel with a cavity pressure and temperature. To model the fluid–structure interaction (FSI), we have combined a finite element model of the structure with a high-order sharp interface immersed boundary method implemented in a finite-difference flow solver. We have analyzed the behavior of the FSI coupling over a wide range of parameters and various boundary conditions while the panel undergoes relaxation to its unexcited state or exhibits limit cycle oscillations. Notably, the panel oscillation and the fluctuations in the shear layer exhibit strong coupling and demonstrate a lock-in resonance frequency response. The colder wall conditions result in a reduced separation bubble and a raised aerodynamic pressure difference between the maximum and minimum instantaneous dynamic pressures, consequently amplifying the amplitude of panel oscillation. For the cases with thermal coupling, the behavior of panel oscillation is notably influenced by specific heat and thermal expansion coefficients. In these scenarios, the thermal state of the solid material emerges as the pivotal factor governing the sustained oscillation of the panel. The non-linear impact of the thermal dependency of the structural properties plays a crucial role in determining the stability of the coupled FSI system. The study revealed that the stable decaying sinusoidal oscillation undergoes a transformation into a limit-cycle oscillation when panel stiffness is affected by reduced temperature. During the sustained oscillation, a mode switch is observed between the first and second modes of deformation of the panel.

Simplified earthquake response analysis of rectangular liquid storage tanks considering fluid-structure interactions

A simplified model of a rectangular liquid storage tank is proposed to estimate the earthquake responses of the system while considering the effects of fluid-structure interactions. The complicated three-dimensional structural behavior of a rectangular tank is represented by the simple combination of the fundamental modes of a rectangular-ring-shaped frame structure and a cantilever beam. The governing equation for the system is derived from Lagrange’s equation. The earthquake responses of deflection, hydrodynamic pressure and its resultant force and moment, base shear and overturning moment due to the structural deformation are obtained from the solution of the governing equation. The effective masses of the system and their heights are presented with the effective added masses and their heights from the hydrodynamic effects. The total earthquake responses are obtained with the convective earthquake responses taken into consideration. The proposed simplified model is applied to example rectangular liquid storage tanks with various aspect ratios, and the accuracy of the model is demonstrated. The proposed simplified model can be employed for the seismic design of a rectangular liquid storage tank, and reliable estimations for earthquake responses of the considered fluid-structure interaction system are obtained without sophisticated and/or complicated dynamic analysis.

Flow sensing method for fluid-structure interaction systems via multilayer proper orthogonal decomposition

Flow sensing is widely used to forecast flow field in fluid-structure interaction (FSI) systems. The FSI system with multiple flexible structures usually involves complex unsteady flow and large number of sensors, which makes it difficult to perform flow sensing. In this study, a flow sensing method for FSI systems via multilayer proper orthogonal decomposition (POD) is proposed to achieve real-time forecast of flow field using structural deformation. First, we establish the POD model of structural deformation. To improve model accuracy for flow field, we propose the multilayer POD model, which mainly focus on the local modeling accuracy in the region with complex flow structures. Then, we establish the multilayer model of flow field. Furthermore, the deep neural network model is employed to map the mode coefficients of the structure to all the mode coefficients of the multilayer POD. The proposed method is applied in two FSI systems, including the flow past a flexible filament clamped behind a cylinder and the flow past flexible filament set. Both constant inflow and transient flow conditions are considered. The results indicate that the proposed flow sensing method exhibits excellent spatial-temporal performance, performs accurately in flow properties forecasting, and is suitable for FSI systems with complex flow structures such as coherent vortices.

Controllability of a fluid-structure interaction system coupling the Navier–Stokes system and a damped beam equation

Controllability of a fluid-structure interaction system coupling the Navier–Stokes system and a damped beam equation

Feedback boundary stabilization for a viscous incompressible fluid with Navier slip boundary conditions in interaction with a damped beam

We show the stabilization by a finite number of controllers of a fluid–structure interaction system where the fluid is modeled by the Navier–Stokes system into a periodical canal and where the structure is an elastic wall localized on top of the fluid domain. The elastic deformation of the structure follows a damped beam equation. We also assume that the fluid can slip on its boundaries and we model this by using the Navier slip boundary conditions. Our result states the local exponential stabilization around a stationary state of strong solutions by using dynamical controllers in order to handle the compatibility conditions at initial time. The proof is based on a change of variables to write the fluid–structure interaction system in a fixed domain and on the stabilization of the linearization of the corresponding system around the stationary state. One of the main difficulties consists in handling the nonlinear terms coming from the change of variables in the boundary conditions.

Analysis of the blade aeroelastic effect on the floating offshore wind turbine wake in a focusing wave with a hybrid model

With the recent trend toward larger floating offshore wind turbines (FOWT), the influence of blade deformation becomes more obvious. Modelling this fully coupled fluid-structure interaction (FSI) system, especially at extreme sea level with large-scale motion of the entire system, is an essential challenge. A hybrid numerical model integrating the potential-viscous flow model (qaleFOAM), the unstable actuator line method (UALM), the Legendre spectral finite element model (BeamDyn), and the Lumped Mass Mooring Model (MoorDyn) is employed in the current research. This model is capable of effortlessly and accurately reflecting the blade aeroelastic effect on the dynamics of a FOWT system under the circumstances of a focused wave and uniform wind. The result reveals that the aeroelastic impacts have been identified to not only increase the fatigue damage on the turbine blades but also affect the wake field distribution. Based on the temporal and spatial distribution of the velocity fields, it is found that the coupled effects of the large wave elevation and the FOWT high-frequency motions will disturb the velocity in the wake region. The slight variation of the wind speed in the wake region will be exacerbated by about 0.21% to 18.6%, and it transforms the shape of the wake region when the blade aeroelastic effect participates in the coupled effect. This phenomenon may further affect the downstream FOWT system features through the upstream FOWT wake field.

Simulating the mechanical stimulation of cells on a porous hydrogel scaffold using an FSI model to predict cell differentiation.

3D-structured hydrogel scaffolds are frequently used in tissue engineering applications as they can provide a supportive and biocompatible environment for the growth and regeneration of new tissue. Hydrogel scaffolds seeded with human mesenchymal stem cells (MSCs) can be mechanically stimulated in bioreactors to promote the formation of cartilage or bone tissue. Although in vitro and in vivo experiments are necessary to understand the biological response of cells and tissues to mechanical stimulation, in silico methods are cost-effective and powerful approaches that can support these experimental investigations. In this study, we simulated the fluid-structure interaction (FSI) to predict cell differentiation on the entire surface of a 3D-structured hydrogel scaffold seeded with cells due to dynamic compressive load stimulation. The computational FSI model made it possible to simultaneously investigate the influence of both mechanical deformation and flow of the culture medium on the cells on the scaffold surface during stimulation. The transient one-way FSI model thus opens up significantly more possibilities for predicting cell differentiation in mechanically stimulated scaffolds than previous static microscale computational approaches used in mechanobiology. In a first parameter study, the impact of the amplitude of a sinusoidal compression ranging from 1% to 10% on the phenotype of cells seeded on a porous hydrogel scaffold was analyzed. The simulation results show that the number of cells differentiating into bone tissue gradually decreases with increasing compression amplitude, while differentiation into cartilage cells initially multiplied with increasing compression amplitude in the range of 2% up to 7% and then decreased. Fibrous cell differentiation was predicted from a compression of 5% and increased moderately up to a compression of 10%. At high compression amplitudes of 9% and 10%, negligible areas on the scaffold surface experienced high stimuli where no cell differentiation could occur. In summary, this study shows that simulation of the FSI system is a versatile approach in computational mechanobiology that can be used to study the effects of, for example, different scaffold designs and stimulation parameters on cell differentiation in mechanically stimulated 3D-structured scaffolds.

Flow-induced reconfiguration and cross-flow vibrations of an elastic plate and implications to energy harvesting

We numerically study flow-induced vibrations (FIV) of an elastic cantilevered plate in a cross-flow configuration. The plate is kept upright in an open domain with a fixed bottom end. Such a configuration eliminates energy losses in the wall boundary. Due to allowed vortex shedding from its bottom end, the resulting novel dynamics of the fluid-structure interaction (FSI) system is explored. An in-house sharp-interface immersed boundary method-based flow solver, coupled with a Saint-Venant Kirchhoff material model-based open-source finite element solver, is employed. Two sets of simulations were carried out in two-dimensional Cartesian coordinates at Reynolds number of 100 for a wide range of reduced velocity (UR), by performing a parametric sweep of dimensionless Young’s modulus (E) and mass ratio (M). In general, FIV characteristics of the plate are similar to the transverse vortex-induced vibration of an elastically-mounted cylinder. The plate deforms to a curved mean position depending on E and M and exhibits angular oscillations. In particular, the following FIV regimes are obtained with increasing UR: initial excitation, lock-in with the first mode, desynchronization after the first lock-in, lock-in with the second mode, and desynchronization after the second lock-in. During lock-in, the plate oscillation and vortex shedding frequency are closer to the first or second mode natural frequency of plate. A larger angular amplitude and increased energy exchange between the structure and fluid characterize the lock-in. We quantify the modal contributions of Euler-Bernoulli modes in the plate’s vibration response with a curved mean position. The spatiotemporal variation of energy exchange between the fluid and plate is analyzed to understand the observed plate dynamics. The flow physics of the wake is discussed using wake patterns, vortex formation length, and vortex strength. Drag over the plate reduces due to flow-induced reconfiguration and strongly correlates with these parameters. Lastly, based on the spatial distribution of strain energy density over the plate, we present a potential design for an ambient fluid energy harvester to harness the plate’s vibration energy with optimized piezoelectric patching. The optimum location and height of a piezoelectric patch on the plate for different cases are reported.

Investigation of dynamic characteristics in the hydraulic shock absorber based on different FSI FEA methods

Two three-dimensional fluid-structure interaction (FSI) finite element analysis (FEA) models with different fluid cells and coupling solution methods of a gas-pressured hydraulic shock absorber is constructed, and the results are partially verified experimentally. Models with FCBI fluid cell and direct FSI solution method or FCBI-C fluid cell and iterative FSI solution method provide good simulation results of the FSI system of the hydraulic damper.

Definition and calculation method of modal effective mass of asymmetric fluid-structure interaction system for seismic analysis

In this paper, modal effective mass for asymmetric fluid-structure interaction system is defined and equations for its calculation is derived. To establish consistency, modal effective mass in symmetric structure only system is briefly reviewed, followed by a definition of the modal effective mass in asymmetric system. The equations for calculating modal effective mass in asymmetric system are derived by utilizing the properties of left and right eigenvectors. To simplify the equations, the assumption is made that the mass matrix is only affected by the fluid. The simplified equation is then compared to the equation already used in ANSYS. Finally, the validity of the modal effective mass definition and derivation in this paper is demonstrated through a simple example.

Stability and nonlinear vibration of a fuel rod in axial flow with geometric nonlinearity and thermal expansion

The vibration of fuel rods in axial flow is a universally recognized issue within both engineering and academic communities due to its significant importance in ensuring structural safety. This paper aims to thoroughly investigate the stability and nonlinear vibration of a fuel rod subjected to axial flow in a newly designed high temperature gas cooled reactor. Considering the possible presence of thermal expansion and large deformation in practical scenarios, the thermal effect and geometric nonlinearity are modeled using the von Karman equation. By applying Hamilton's principle, we derive the comprehensive governing equation for this fluid-structure interaction system, which incorporates the quadratic nonlinear stiffness. To establish a connection between the fluid and structure aspects, we utilize the Galerkin method to solve the perturbation potential function, while employing mode expansion techniques associated with the structural analysis. Following convergence and validation analyses, we examine the stability of the structure under various conditions in detail, and also investigate the bifurcation behavior concerning the buckling amplitude and flow velocity. The findings from this research enhance the understanding of the underlying physics governing fuel rod behavior in axial flow under severe yet practical conditions, while providing valuable guidance for reactor design.