Fluid-structure Interaction System Research Articles

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.

On the stability of viscoelastic tapered rotors with internal flow

In this paper, the stability of viscoelastic tapered rotors with internal flow is investigated. The constitutive equation of the viscoelastic material is described on the basis of the Kelvin–Voigt model. Using Hamilton's principle, the governing equation of motion for the rotor system is formulated. The Galerkin discretization technique is then employed to discrete the partial differential equations. Thus, the complex frequencies in the first two modes of the simply supported rotor system are calculated, which are utilized to discriminate the stability of the system. Then, the stability evolution process of the system is analyzed. Also, the divergence flow velocity and spinning speed are computed numerically. Finally, a comprehensive parametric discussion is carried out to evaluate the effect of parameters such as hollowness ratio, mass ratio, taper ratio, and viscosity coefficient on the stability and critical spinning speed of the fluid–structure interaction system. The results show that for a viscoelastic tapered rotor with the internal flow, the rotor experiences a stability evolution of “stable-first mode divergence-stable-first mode flutter-first mode divergence-first mode flutter.” The dynamic behavior of the rotor system depends strongly on the mass ratio, hollowness ratio, taper ratio, flow velocity, and viscoelasticity of the material.

Nonlinear planar and non-planar vibrations of viscoelastic fluid-conveying pipes with external and internal resonances

In this study, nonlinear vibrations of a viscoelastic fluid-conveying pipe under in-plane and out-of-plane transverse excitations are investigated, with emphasis on external and internal resonances. For this purpose, a three-dimensional pipe model that couples the in-plane and out-of-plane vibrations is developed based on the Euler–Bernoulli beam theory together with the Kelvin–Voigt viscoelasticity. The Galerkin method is performed on the nonlinear governing equations, and the resultant discretized equations are solved via the pseudo-arclength continuation method and a direct integration method. The dynamical responses of the pipe are examined in both sub- and super-critical regions and presented by plotting the frequency–amplitude curves, force–amplitude curves, basins of the attraction, time histories, and phase portraits. A comparison between the simplified two-dimensional model and the present three-dimensional model is presented to showcase the possibility of the in-plane and out-of-plane vibrations in regions of primary and principal parametric resonances, highlighting the modal interaction between the in-plane and out-of-plane transverse modes. In the presence of a two-to-one internal resonance, in addition to typical jumping and hysteresis, the two-peak resonance behavior is observed. The numerical results not only show complex nonlinear dynamics of the fluid–structure interaction system, but also provide hints for safe design and novel application of such structures.

Deep learning for predicting frequency lock-in of a freely vibrating sphere

In this paper, we present a deep learning-based reduced-order model (DL-ROM) for the stability prediction of unsteady three-dimensional fluid–structure interaction systems. The proposed DL-ROM has the format of a nonlinear state-space model and employs a recurrent neural network with long short-term memory (LSTM) cells. We consider a canonical fluid–structure system of an elastically mounted sphere coupled with the incompressible fluid flow in a state-space format. Specifically, we develop a nonlinear data-driven coupling for predicting the unsteady forces and the vortex-induced vibration (VIV) lock-in of the freely vibrating sphere in a transverse direction. We design an input–output relationship as a temporal sequence of force and displacement datasets for a low-dimensional approximation of the fluid–structure system. Based on the prior knowledge of the VIV lock-in process, the input function contains a range of frequencies and amplitudes, which significantly affects the system realization ability and enables an efficient DL-ROM without the need for a massive training dataset for the low-dimensional modeling. Once trained, the network provides a nonlinear mapping of input–output dynamics that can predict the coupled fluid–structure dynamics for a longer horizon via the feedback process. By integrating the LSTM network with the eigensystem realization algorithm (ERA), we construct a data-driven state-space model for the reduced-order stability analysis. We investigate the underlying mechanism and stability characteristics of VIV of a freely vibrating sphere via an eigenvalue selection process. Using the reduced-order eigenvalue analysis, we characterize the vibrating sphere-wake lock-in phenomenon and demonstrate that the lock-in responds at preferred vibration frequencies. To understand the frequency lock-in mechanism, we study the eigenvalue trajectories for a range of the reduced oscillation frequencies and the mass ratios. Consistent with the full-order simulations, the frequency lock-in branches are accurately captured by the combined LSTM-ERA procedure. The proposed DL-ROM aligns with the development of physics-based digital twin of engineering systems involving moving boundaries and fluid–structure interactions.

A new monolithic design approach for topology optimization for transient fluid–structure interaction system

This study presents a new topology optimization method for transient coupled fluid–structure interaction (FSI) problems. The transient FSI problem is formulated using the monolithic design approach combining the design variables and the governing equations. This new approach allows for the possibility of considering the effect of transient FSI on topologically optimized layouts. Throughout this work, the analysis domain for the fluid and structure is modeled using the unified monolithic approach, in which the structure equation and the Navier–Stokes equation are coupled. With a fixed mesh and design variables assigned to each finite element, the governing equations as well as the involved material properties are interpolated. This modeling and analysis approach provides accurate solutions to the strongly coupled FSI system. An adjoint approach for calculating the transient sensitivity information and a gradient-based optimizer are used. Several numerical examples are solved to reveal the importance of considering the transient FSI. In addition, these examples demonstrate that the present approach can control transient FSI phenomena.