Coupled Fluid Structure System Research Articles

Fluid-structure coupling analysis in liquid-filled containers using scaled boundary finite element method

In this study, a semi-analytical model is developed to investigate the fluid-structure coupling characteristics of liquid sloshing in an elastic rectangular container subjected to horizontal external excitation based on the scaled boundary finite element method (SBFEM) for the first time. The fluid inside the container is assumed to be incompressible, inviscid and irrotational, with the hydrodynamic pressure chosen as independent nodal variable in the governing equations. The container walls are considered as cantilever beams. The coupled fluid-structure system is initially divided into the structural domain and fluid domain, after which the SBFEM is employed to obtain the governing equations for each sub-domain. In the framework of the SBFEM, only the boundary of each sub-domain, rather than the entire computational domain, needs to be meshed and discretized. This method reduces the spatial dimension of the problem by one and offers an efficient approach to model the computational domain, while allowing for analytical formulations to be derived for the internal of the domain, resulting in an accurate description of the field variables. The fundamental equation of the entire coupled fluid-structure system is then assembled by performing the equilibrium condition and compatibility condition to ensure the balance of interaction forces at the interface between container walls and the liquid. The free vibrations analysis of the fluid-structure coupling system is solved by utilizing the generalized eigenvalue problem, and the transient dynamic response is determined using the synchronous solution algorithm in conjunction with the implicit-implicit scheme of the Newmark method. To validate the excellent accuracy and stability of the proposed formulation, several numerical examples are presented to investigate the free vibration and transient dynamic characteristics for the fluid-structure coupling problem. The obtained results show good agreement with reference solutions available in the literature. Additionally, the effects of geometrical and material parameters on the system responses are examined and discussed.

Shape optimization to enhance energy harvesting from vortex-induced vibration of a circular cylinder

In previous research on energy harvesting from vortex-induced vibrations (VIVs), the cross section of the structure commonly utilizes basic geometric shapes like circular, ellipse, square, and semicircle. Nevertheless, exploring optimized shapes for energy harvesting from VIV remains an understudied area. To address this gap, this paper employs adjoint-based unsteady shape optimization to increase the efficiency of energy harvesting from VIV of a circular cylinder at low Reynolds numbers. The goal of the optimization is to maximize the plunge-damping derivative of a single-degree-of-freedom transversely vibrating cylinder, which represents the rate of energy injected into the structure by the flow. To facilitate this process, an efficient method to evaluate the gradient of the objective function with respect to shape parameters is provided via the proposed unsteady discrete adjoint method. Results show that, through optimization, the low-pressure region behind the cylinder is significantly enlarged and the separation points move forward, resulting in the faster development of separation vortex and reduced stability of the fluid–structure coupling system. As a consequence, the intensity of VIV as well as the corresponding power generation efficiency is remarkably enhanced, accompanied by a notable expansion in the energy harvesting region.

Investigation of offshore landslides impact on bucket foundations using a coupled SPH–FEM method

BackgroundAs the exploitation of marine resources intensifies, the impact of submarine landslides on underwater structures has become a significant issue. Existing research primarily focuses on the impact on pipelines, often neglecting the actual deformation and mechanical response of underwater structures under impact loads in numerical simulations, thus complicating the evaluation of the reliability of these engineering structures in extreme conditions. Moreover, the dynamic response of bucket foundations, a common form of underwater base, under the effect of submarine landslide impacts remains unclear.MethodsTo address this knowledge gap, we have developed a fluid-structure coupling system that employs the coupled Smoothed Particle Hydrodynamics (SPH)-Finite Element Method (FEM) to investigate a single impact process and analyze the displacement response of bucket foundations within a water-offshore landslide-bucket foundationsubgrade context. The accuracy of this developed method has been systematically verified through comparisons with previous experimental and numerical results.ResultsDuring a submarine landslide impact event, the impact force demonstrates a distinct decrease followed by stabilization, and the displacement response of the bucket foundation exhibits a rebound effect after reaching its maximum value. Furthermore, we conducted an extensive analysis of different impact angles for underwater data centers equipped with multi-bucket foundations. Our study revealed that group-bucket foundations experience a combined translation-turnover failure when subjected to submarine landslide impacts, and the most unfavorable scenario for such impact is identified. The research introduces a novel numerical simulation approach for investigating the impact of submarine landslides on complex underwater structures.

Numerical investigation on suppression effect of movable part with spring system

Liquid sloshing in the tank not only affects the movement of the carrier, but also easily causes structural fatigue, or even structural damage. How to effectively suppress sloshing is one of the most important issues in naval architecture and ocean engineering. In this paper, an anti-sloshing method with a movable vertical part and spring system is presented. Based on CFD and FEM, sloshing states and displacements of the movable part at different spring stiffness are numerically studied, in order to investigate dynamic response characteristics of the fluid-structure coupling system formed by the tank-fluid-part. The results illustrate that the movable part with appropriate spring stiffness can suppress the sloshing more effectively than fixed part. By analysis of the relationship between sloshing liquid movement and the part displacement, phase difference between the part displacement and the wave elevation is found to be suitable to estimate the appropriate spring stiffness of the movable part under different conditions. In addition, numerical results of free decay tests and sine sweep tests illustrate that the movable part with appropriate spring stiffness can also shift the natural frequency of the tank-fluid-part system.

Finite Element Analysis of Fluid–Structure Interaction in a Model of an L-Type Mg Alloy Stent-Stenosed Coronary Artery System

The coronary stent deployment and subsequent service process is a complex geometric/physical nonlinear and fluid–structure coupling system. Analyzing the distribution of stress–strain on the stent is of great significance in studying the deformation and failure behavior. A coupled system dynamics model comprising stenotic coronary artery vessels and L-type Mg alloy stents was established by applying the polynomial hyperelastic constitutive theory. The nonlinear, significant deformation behavior of the stent was systematically studied. The stress–strain distribution of the coupling system during stent deployment was analyzed. The simulation results show that the edges of the supporting body fixed without a bridge are the weakest zone. The stress changes on the inside of the wave of the supporting body are very large, and the residual stress accumulated in this area is the highest. The peak stress of the plaque and the arterial wall was lower than the damage threshold. The velocity of the blood between the wave crest of the supporting body is large and the streamline distribution is concentrated. In addition, the inner surface pressure on the stent is evenly distributed along its axial dimension. The maximum arterial wall shear stress always appears on the inside of the wave crest of the supporting body fixed with a bridge, and, as such, the largest obstacle to the blood flow is in this zone.

Failure and deformation characteristics of shale subject to true triaxial stress loading and unloading under water retention and seepage.

A multi-functional true triaxial fluid-structure coupling system was used to conduct water retention and seepage tests of shale under true triaxial loading and unloading stress paths. The stress–strain evolution of shale specimens under different experimental conditions was obtained, and the corresponding deformation and strength were analysed. The evolution and failure characteristics of cracks in shale were obtained by CT scanning images before and after the experiment. The results show that the volumetric strain of shale specimen increases first, then decreases and finally continues to increase with an increase in deviatoric stress under water retention, indicating that the volumetric change has experienced a compaction-expansion-compacting. The σ-ε1 curve of the sample increases first and then decreases, while the deformation in the σ2 direction shows the repeated compression and expansion. In the seepage test, the permeability–strain curve can be divided into two parts before and after fracture according to the σ-ε1 curve. Before fracture, the compression velocity of the specimen in the loading direction exceeds the expansion velocity in the unloading direction, resulting in a decrease in volume and a decrease in permeability. With an increase in deviatoric stress, fractures occur inside the particles and continue to spread from the tip until the fractures break through the shale specimen. The pore fissure area increases and the permeability of the sample increases rapidly. In terms of fracture evolution, for the water retention test, dense tensile and shear cracks appear on the failure plane perpendicular to the σ1 and σ3 directions, and complex shear fracture network appears on the failure plane perpendicular to the σ2 direction. For the seepage test, heavy shear failure occurs throughout the original fracture of the sample. With an increase in the penetration depth, the fracture shape on the failure surface perpendicular to the σ2 direction gradually changes from single to complex.

Vibro-acoustic analysis of a circumferentially coupled composite laminated annular plate backed by double cylindrical acoustic cavities

The current work focuses on the vibro-acoustic analysis of fluid-structure coupling system composed of a circumferentially coupled composite laminated annular plate and two cylindrical acoustic cavities considering arbitrary acoustic impedance. By employing the unified Ritz energy scheme in conjunction with the first-order shear lamination scheme, the acoustic and structural models in the studied physical system are reasonably established, where the required structural and plate-cavity continuity conditions are taken into account by means of the coupled spring technology and work, respectively. One-dimensional and two-dimensional orthogonal polynomials with the aid of the Fourier harmonic functions are separately applied to construct the variables functions of structural and acoustic domains without meshing requirements. The convergence and correctness of the developed prediction model including various physical parameters are carefully investigated through several comparative examples as well as vibro-acoustic experiment analysis, which illustrates the good insight in the vibro-acoustic mechanism of the studied physical system. Some parametric analysis respecting the effect of structural/acoustic boundaries, cavity depth, coupling radius and material parameter etc. on the coupled vibro-acoustic performance is implemented in detail, which may give some guidance for the low-noise pre-design of circumferentially coupled laminated annular plate.

Data-driven modeling of transonic unsteady flows and efficient analysis of fluid–structure stability

The reduced-order aerodynamic models constructed via the linear/nonlinear system identification methodologies cannot reveal the flow characteristics of the fluid–structure coupling system because the state variables of the reduced-order model do not explicitly represent fluidic properties. In this study, a data-driven modeling procedure is proposed to reconstruct a physics-based, reduced-order aerodynamic model. In the procedure, the transonic unsteady flows of concern are projected onto low-dimensional base vectors first via the proper orthogonal decomposition of pressure snapshots subject to a specific structural excitation. Then a state-space representation of the temporal coefficients of proper orthogonal decomposition modes subject to the structural excitation is established by using the dynamic mode decomposition with control. Finally, for the fluid–structure stability analysis, pressure snapshots are recovered from the coefficients of proper orthogonal decomposition, and aerodynamic forces are derived by integrating the pressure coefficients around the wing surface. The state vector in above-mentioned data-driven model has a clear sense in physics with regard to pressure distribution. To demonstrate the accuracy of the proposed procedure, a two-dimensional, transonic aeroelastic wing with an NACA0012 profile is studied. The unsteady aerodynamic forces, frequency responses of the reduced-order aerodynamic model, transonic flutter boundary, and flow characteristics at the flutter condition are predicted and compared with direct computational fluid dynamic simulations. The results show that the modeling procedure can accurately predict the transonic flutter boundary and flow characteristics.

Aeroelastic stability analysis of a pyrotechnic separation plate in subsonic airflow

Pyrotechnic separation devices are widely used in aerospace engineering. In separation process, the pyrotechnic separation device breaks into several parts, and the velocity of the separated structure changes intricately, which make the pyrotechnic separation device and the external airflow a complex fluid-structure coupling system. Since the stability of the structure is crucial for the safety, it is necessary to investigate the aerodynamic stability of the pyrotechnic separation device interacting with surrounding airflow. In the present study, the aeroelastic stability of a pyrotechnic separation plate in axial subsonic airflow is studied. The velocity of the residual plate is derived from the momentum theorem. The dynamic model of the pyrotechnic separation plate in subsonic airflow is established based on the linear potential flow theory and the von Kármán plate theory. The effects of the residual length, the pyrotechnic explosion strength and the separation velocity on the stability of the plate are investigated, and the vibration properties of the plate are discussed. From the results, the plate loses stability rapidly when it subjects to the explosion, and restores stability under the negative pressure. The displacement jumping phenomenon is observed. The amplitude of the plate in unstable period increases rapidly, which may cause damage to the structure.

Stability and drag reduction in turbulent flow of skin with quasi-periodic elastic supports

In order to reduce the flow resistance on the surface of ships, the skin with quasi-periodic elastic supports is designed based on the flexible skin drag reduction technology inspired by dolphin skin. In this paper, the stability characteristic equation of fluid-structure coupling system is established based on small perturbation theory and solved by MATLAB. The results indicate that the skin with quasi-periodic elastic supports has the ability of maintaining stability of turbulent boundary layer when the structural parameters are reasonable. In addition, the drag reduction performance of the skin with quasi-periodic elastic supports is studied by immersion boundary method. The analysis results demonstrate that the skin with quasi-periodic elastic supports can show better drag reduction performance than the skin with periodic elastic supports when the structural parameters q and the support spacing L are rationally set. In a certain speed range, the relative drag reduction rate is up to 72.16%. These optimal distribution parameter data of the skin under certain speed conditions obtained in this paper provide a reference for the practical application and intelligent optimization design of the skin with quasi-periodic elastic supports.

Input-output analysis of fluid–structure interaction to optimize stone breakage in burst-wave lithotripsy

Burst-wave lithotripsy is a non-invasive treatment of kidney stones using short pulses of focused ultrasound. In this talk, we present the use of input-output analysis to optimize the design and control of a multi-element array transducer to achieve optimal stone breakage. The analysis is based on a linear fluid-structure coupled system that maps the acoustic forcing from individual elements to the stress in a stone of assumed shape, size, and composition. We determine the optimal frequency and optimal distribution of the phase and amplitude across the aperture by maximizing a cost function that represents the strain energy in stone. The optimal parameters are obtained by applying a state-of-the-art, randomized singular value decomposition (SVD) to the discrete linear operator. The results show that carefully controlling the relative phase and amplitude between elements can increase the strain energy (by 2-3 times in certain cases) compared to a uniform distribution under the same input energy. This suggests that the stone fragmentation can be accelerated or performed with lower energy for safer treatment. The improvement is interpreted and validated by combining high-fidelity simulations with high-speed camera images of crack formation in model stones from in vitro- experiments. [Work supported by NIH, Grant No. P01-DK043881.]

A strong coupling prediction-correction immersed boundary method

In the traditional immersed boundary methods for solving compressible fluid-structure interaction problems, conservation is one of the problems that must be considered. When the coupling boundary moves on the fixed grid, the structure coverage will change, resulting in many dead elements and emerging elements on the fluid grid. In the ghost-cell immersed boundary method, the reconstructed grid can not maintain the strict mass conservation when the dead elements and emerging elements appear. In order to overcome the shortcomings of traditional methods, a strong coupling prediction-correction immersed boundary method for compressible fluid-structure interaction problems was proposed. Firstly, the matrix representation of a general fluid-structure coupling system was described, and a strong coupling Gauss-Seidel iterative scheme of fluid-structure coupling system was derived. Furthermore, a prediction-correction scheme was derived, and a prediction-correction immersed boundary method was proposed. The fluid-structure coupling boundary was regarded as a free surface, and the space originally occupied by the solid was initialized as zero mass elements, allowing the fluid to pass through the coupling boundary freely. For the calculation of fluid, the second-order MUSCL finite volume scheme with the minmod limiter and the AUSM+-up flux based on Zha-Bilgen splitting were used to advance the time step with the third-order Runge-Kutta scheme. In the correction step, the transport process was realized by a set of mass conservation transport rules. The transport algorithm could be summarized as marking the fluid inside the boundary, dividing and moving the fluid in a uniform way according to the marking order, generating a flow pointing to the outside of the boundary, and finally applying a velocity correction near the boundary to ensure the no-slip condition. The marking and transport algorithm avoided the tedious geometric treatment of the cut-cells, and ensured the easy implementation of the algorithm. For the calculation of solids, the first-order difference scheme and the implicit dynamic finite element scheme were used to solve the rigid body and linear elastic body respectively, and the Gauss quadrature was used to obtain the coupling force on the solid surface. The one-dimensional and two-dimensional problems were calculated by the prediction-correction immersed boundary method. In the one-dimensional piston problem, the accuracy, conservation and convergence of the method were investigated by comparing the results with those in the literature. In the two-dimensional shock wave impact problem, the experimental optical schlieren images were compared with those obtained by the numerical simulation, and the deflection history of the plate structure was investigated. The study shows that this method can accurately maintain the mass conservation of the flow field and has the advantage of easy implementation, which is different from the traditional ghost-cell method and the cut-cell method. This method has the first-order convergence accuracy, and can accurately predict the flow field after shock diffraction and the deflection of plate under shock waves. It provides a new idea for the development of fluid-structure coupling algorithms.

Combination Resonances of Traveling Unidirectional Plates Partially Immersed in Fluid With Time-Dependent Axial Velocity and Axially Varying Tension

Abstract Nonlinear vibrations of axially moving plates partially immersed in fluid are investigated in this paper. The system has time dependency in velocity and tension in axial direction. The Galerkin method is used to solve the nonlinear vibration differential equation. The method of multiple scales and Runge–Kutta method are applied to solve the nonlinear vibration response of the system. Additionally, the stability conditions of trivial and nontrivial solutions are analyzed using the Routh–Hurwitz criterion. The effects of mean velocity, amplitude of pulsating velocity, mean tension, amplitude of pulsating tension, and pulsating frequency on the complex dynamics of the system are obtained. The study results reveal rich dynamic behaviors of fluid–structure coupling system.

Performance analysis of thermoelectric generation system with controlled heat distribution

The number of automobiles is rising, but much of the fuel energy is wasted through exhaust gas. Thermoelectric power generation (TEG) technology can be used to recover waste energy from automobile exhaust, but its effective application is limited for low conversion rate of thermoelectric generation. Considering the continuous operating temperature limit of thermoelectric generation materials and its influence on the exhaust system, the model of a new type of thermoelectric power generation system with double collectors was proposed. The three-dimensional steady-state model of the fluid structure coupling system between exhaust gas and thermoelectric device was established, and the test bench was carried out. The influence of controlled heat distribution on the voltage and output power was analyzed by simulation and experiment. The results show the optimal opening ratio (ωopt) of thermoelectric power generation system increases with the rise of temperature, which is a linear function. The optimal opening ratio was close to 1 at high input temperature (predicted to be 984 K). With the input temperature of 673 K, heat energy distributed to each thermoelectric module was about 0.5 W and 0.3 W when opening ratio was set to 0.1 and 1 respectively, and the output power could be increased from 86.1 W to 95.2 W by controlling the heat distribution (the optimal opening ratio = 0.5). However, the optimal opening ratio was still less than 1 when the input temperature was as high as 723 K, which indicates that uneven distribution may be a better choice for most gas conditions.

Parametric Resonance of Axially Accelerating Unidirectional Plates Partially Immersed in Fluid

Abstract This paper investigates the nonlinear vibration of an axially accelerating moving plate considering fluid-structure interaction. Nonlinear coupled equations of motion are derived by means of Kármán plate theory, the Galerkin method is then applied to transform the nonlinear partial differential equations into nonlinear ordinary differential equations. The steady-state response, various bifurcations and chaotic behavior of the system are studied by the multiple scales method and Runge-Kutta method. The dynamical characteristics of the system are examined via response curves and bifurcation diagrams of Poincaré maps. By three-dimension bifurcation diagrams, change of motion state can be easily observed along with the variation of system parameters during the whole parametric space, meanwhile, it is found that fluctuation amplitude plays a most significant role in the change of motion state for the fluid-structure coupling system.

Aeroelastic analysis of rectangular plates coupled to sloshing fluid

In this study, an aeroelastic model that accounts for the fluid–structure interaction is developed to investigate vibration and stability of rectangular plates in contact with sloshing fluid on one side and under supersonic aeroelastic load on the other side. The fifth-order shear deformation theory, which is capable of considering rotary inertia and transverse shear stress, is employed to model the structure. Bulging and sloshing modes of the incompressible, inviscid and irrotational fluid are obtained with satisfying Laplace’s equation and fluid boundary conditions. The first-order piston theory is applied to consider the supersonic aeroelastic load. On the basis of Hamilton’s principle, the governing equations of the coupled fluid–structure system are derived and discretized using the Galerkin method. Numerical results for specific cases are compared with available results in the literature and an excellent agreement is observed. In the discussion section, influences of various parameters such as the dimensions of the fluid domain, plate dimensions and aerodynamic parameters on the natural frequencies and flutter behavior are studied.

Fluid–structure system with boundary conditions involving the pressure

We study a coupled fluid–structure system involving boundary conditions on the pressure. The fluid is described by the incompressible Navier–Stokes equations in a 2D rectangular type domain where the upper part of the domain is described by a damped Euler–Bernoulli beam equation. Existence and uniqueness of local strong solutions without assumptions of smallness on the initial data is proved.

Computational modeling and analysis of flow-induced vibration of an elastic splitter plate using a sharp-interface immersed boundary method

We present the development and benchmarking of an in-house fluid–structure interaction (FSI) solver. An implicit partitioned approach is utilized to couple a sharp-interface immersed boundary method-based flow solver and a finite-element method-based structural solver. In the present work, the coupling is accelerated using a dynamic under-relaxation scheme. The revised coupling is around two to three times faster and numerically stable, as compared to the one that uses a constant under-relaxation parameter. The solver is validated against two FSI benchmarks in which a thin, finite thickness, elastic splitter plate is attached to the lee side of a circular or square rigid cylinder, subjected to laminar flow. In these two-dimensional benchmarks, the flow induces a wave-like deformation in the plate, and it attains a periodic self-sustained oscillation. We employ the FSI solver to analyze the flow-induced vibration (FIV) of the plate in a uniform laminar free-stream flow for a wide range of mass ratio and bending stiffness at Reynolds number (Re) of 100, based on the diameter of the cylinder. At the given Re, two-dimensional numerical simulations show that the FIV of the plate effectively depends only on the mass ratio and bending stiffness. The largest displacement of the plate vibration is found to occur in the lock-in region, where the vortex shedding frequency of the coupled fluid–structure system is close to the natural frequency of the splitter plate. We briefly discuss wake structures and phase plots for different cases of mass ratio and bending stiffness.

Frequency analysis and control of sloshing coupled by elastic walls and foundation with smoothed particle hydrodynamics method

Broadband stochastic excitations from environment such as seismic activities, sea waves, wind gusts, and tremors can lead to the terrible damages of tall structures and buildings which usually have a low amount of vibration damping. Tuned liquid dampers (TLD) have been considered for around thirty years regarding their ability for passive suppression and absorb the vibration energy in such structures. In this paper, the fluid-structure interaction of a two-dimensional rectangular tank with elastic side walls and foundation is investigated by the smoothed particle hydrodynamics (SPH) method. First, the implementation of SPH for the frequency analysis of a rectangular container with flexible boundaries, partially filled with liquid, is described. The governing equations of the sloshing of an inviscid liquid in a two-dimensional Cartesian coordinate system coupled with the thin plate vibration on sides are linearized and solved by the SPH method. The sloshing and bulging modes of the system are derived and discussed in this paper. The results of the frequency spectrum of the sloshing tank coupled with the spring-damper system are analyzed and compared with the mechanical equivalent system. Results are validated by analytical benchmark and show the applicability as well as the simplicity of the SPH method for analytical vibration analysis of a fluid-structure coupled system. Then various control method including: Active mass damping (AMD) control designed based on proportional feedback control, the tuned liquid damper (TLD) control based on the analytical model, and a hybrid method of active tuned liquid damper (ATLD) are modeled and compared in a one-story structure. Results demonstrated that although the AMD is more efficient and stable in a specific range of feedback coefficient, the proposed ATLD is reliable in a wider range of control parameters.

Uncertainty quantification for dynamics of geometrically nonlinear structures coupled with internal acoustic fluids in presence of sloshing and capillarity

In this paper, we propose an uncertainty quantification analysis, which is the continuation of a recent work performed in a deterministic framework. The fluid–structure system under consideration is the one experimentally studied in the sixties by Abramson, Kana, and Lindholm from the Southwest Research Institute under NASA contract. This coupled system is constituted of a linear acoustic liquid contained in an elastic tank that undergoes finite dynamical displacements, inducing geometrical nonlinear effects in the structure. The liquid has a free surface on which sloshing and capillarity effects are taken into account. The problem is expressed in terms of the acoustic pressure field in the fluid, of the displacement field of the elastic structure, and of the normal elevation field of the free surface. The nonlinear reduced-order model constructed in the recent work evoked above is reused for implementing the nonparametric probabilistic approach of uncertainties. The objective of this paper is to present a sensitivity analysis of this coupled fluid–structure system with respect to uncertainties and to use a classical statistical inverse problem for carrying out the experimental identification of the hyperparameter of the stochastic model. The analysis show a significant sensitivity of the displacement of the structure, of the acoustic pressure in the liquid, and of the free-surface elevation to uncertainties in both linear and geometrically nonlinear simulations.