Fluid-structure Interaction Problems Research Articles

The existence of a weak solution for a compressible multicomponent fluid structure interaction problem

We analyze a system of PDEs governing the interaction between two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time dependent 3D domain filled by the fluids. The dynamics of the fluids is modeled by a system resembling compressible Navier-Stokes equations with a physically realistic pressure depending on densities of both the fluids. The shell possesses a non-linear, non-convex Koiter energy. Considering that the densities are comparable initially we prove the existence of a weak solution until the degeneracy of the energy or the self-intersection of the structure occurs for two cases. In the first case the adiabatic exponents are assumed to satisfy max⁡{γ,β}>2, min⁡{γ,β}>0, and the structure involved is assumed to be non-dissipative. For the second case we assume the critical case max⁡{γ,β}≥2 and min⁡{γ,β}>0 and the dissipativity of the structure. The result is achieved in several steps involving, extension of the physical domain, penalization of the interface condition, artificial regularization of the shell energy and the pressure, the almost compactness argument, added structural dissipation and suitable limit passages depending on uniform estimates.

A direct multimode method for the reduction of vibration induced oscillations on force signals during “pseudo-rigid” water impact experiments

A new experimental method is proposed to improve the force measurements during water impact experiments (e.g. water entry or wave impact tests) carried out with “pseudo-rigid” mock-ups. Despite the efforts of making the mock-up as stiff as possible, the impulsive nature of water impact loads may induce a transient response of the mock-up with a broad frequency content and a perturbation of the force measurements. Using the principles of momentum conservation, it can be shown that the load cell signal is the sum of the hydrodynamic forcing term and of an additional inertial term directly related to the vibrations of the structure. In the present paper, we suggest to estimate the inertial term using several accelerometers which record the response of the structure at different locations. Assuming that the structure response can be approximated by a set of natural modes, we show that it is possible to estimate the inertial term by a linear combination of the acceleration signals. The coefficients of the linear combination may be identified a priori by performing hammer tests, but in certain cases they can also be identified a posteriori using a segment of the signal time series. The performance of the method is demonstrated by considering two experimental test cases of increasing complexity. The first test case is a hydrofoil of constant section impacting water at constant speed which exhibits two-dimensional beam-like vibrations. The second test case is a segmented model of a vertical cylinder impacted by a breaking wave whose segments exhibit three-dimensional vibrations. The proposed method is efficient, conceptually simple and very simple to implement from a signal processing point of view, which makes it promising not only for water impact problems but also for other unstationary fluid–structure interaction problems.

Numerical Simulation of wind load on Inflated Membrane Structure

The fluid-structure interaction (FSI) program were used to simulate the condition that inflated membrane structure transport process in incoming flow. A comparison between the results from numerical simulation and from the ground simulation test was used to validate the computational method. Due to the analysis of flow field and membrane structure’s deformation, the law of force variation of inflated membrane structure during FSI was discussed, and the causes of deformation instability in FSI problems were preliminary discussed. Possible ways to reduce the sensitivity of envelope deformation caused by constraint position were explored, and the effect of this improved method on the surface stress of the envelope was investigated.

Topology optimization of stationary fluid–structure interaction problems considering a natural frequency constraint for vortex-induced vibrations attenuation

Topology optimization applied to fluid–structure interaction problems is challenging because the physical phenomenon in real engineering applications is usually transient and strongly coupled. This leads to costly solutions for the forward and adjoint problems, the computational bottleneck of the topology optimization method. Thus, this paper proposes a topology optimization problem formulated in the steady state with post-processing and verification in the transient state. The objective is to design a stiff structure with lower effects of vibrations induced by the transient fluid vortices. For that, the compliance minimization problem is solved subject to a natural frequency constraint (without any volume constraint). The TOBS-GT (Topology Optimization of Binary Structures with geometry trimming) method is used to solve the problem. To observe the vortex-shedding around the structure, a transient simulation is performed considering an incompressible fluid flow under a laminar regime and the structure subject to large displacements. For topology optimization, the fluid flow is at a steady state and the structure is modeled considering small displacements, i.e., a one-way coupled analysis. The finite element method is used to solve the governing equations and obtain the direct/adjoint sensitivities for the compliance and natural frequency functions. In this approach, the natural frequency of the structure is shifted away from the fluid flow vortex-shedding frequency, avoiding resonance. Numerical examples show that the proposed method can be effectively applied to design 2D structures in FSI problems with lower effects of Flow-Induced Vibration, attenuating the levels of displacement at the analyzed points of the structure.

Stability of Time-Dependent Motions for Fluid–Rigid Ball Interaction

We aim at the stability of time-dependent motions, such as time-periodic ones, of a rigid body in a viscous fluid filling the exterior to it in 3D. The fluid motion obeys the incompressible Navier–Stokes system, whereas the motion of the body is governed by the balance for linear and angular momentum. Both motions are affected by each other at the boundary. Assuming that the rigid body is a ball, we adopt a monolithic approach to deduce Lq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^q$$\\end{document}–Lr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^r$$\\end{document} decay estimates of solutions to a non-autonomous linearized system. We then apply those estimates to the full nonlinear initial value problem to find temporal decay properties of the disturbance. Although the shape of the body is not allowed to be arbitrary, the present contribution is the first attempt at analysis of the large time behavior of solutions around nontrivial basic states, that can be time-dependent, for the fluid–structure interaction problem and provides us with a stability theorem which is indeed new even for steady motions under the self-propelling condition or with wake structure.

A multi-resolution smoothed particle hydrodynamics with multi-GPUs acceleration for three-dimensional fluid-structure interaction problems

This paper presents a parallel SPH of high efficiency to tackle fluid-structure interaction (FSI) problems involving large aspect ratio structures. A unified updated Lagrangian SPH algorithm is developed for modelling both the fluid and solid simultaneously, which involves employment of the Lagrangian kernel for modelling solids to avoid the tension instability problem. Considering the high computational cost of large-scale problems, we develop an adaptive multi-resolution SPH with multi-GPUs acceleration. Specifically, coupling CUDA and MPI acceleration modes are proposed, which exploit the high computational capacity of GPU devices and the cross-device parallelism properties in multi-GPUs. To enhance the occupancy of each GPU, an efficient message-passing pattern and load balancing algorithm are of interest. To address the data race in multi-resolution SPH, a combination hybrid competition mode is proposed. Through a series of optimization algorithms, the numerical efficiency of the multi-resolution SPH approach in multi-GPUs parallel computing is further promoted. After verifying the parallel efficiency of these proposed algorithms in some typical free-surface flows, the proposed model is applied to solve the FSI problem including under-water explosion problem. The results have demonstrated the effectiveness and applicability of the proposed accelerated algorithm for SPH modeling of large-scale FSI problems.

Topology optimization for stationary fluid–structure interaction problems with turbulent flow via sequential integer linear programming and smooth explicit boundaries

Topology optimization methods face serious challenges when applied to structural design with fluid–structure interaction (FSI) loads, especially for high Reynolds fluid flow, i.e., considering turbulence. In this problem, the information at the fluid–structure interface is crucial for the modeling and convergence of the turbulent fluid flow analysis. This paper devises a new explicit boundary method that generates two- and three-dimensional smooth surfaces to be used in topology optimization with binary {0,1} design variables. A phase-field function is obtained after nodal spatial filtering of the design variables. The 0.5 isoline defines a smooth surface to construct the topology. The FSI problem can then be modeled with accurate physics and explicitly defined regions. The Finite Element Method is used to solve the fluid and structural domains. This is the first work to consider a turbulent flow in the fluid–structure topology optimization framework. The fluid flow is solved considering the k−ɛ turbulence model including standard wall functions at the fluid and fluid–structure boundaries. The structure is considered to be linearly elastic. Semi-automatic differentiation is employed to compute sensitivities and the optimization problem is solved via sequential integer linear programming. Results show that the proposed methodology is able to provide structural designs with smooth boundaries considering loads from low and high Reynolds flow.

A Rigid-Flexible Coupling Dynamic Model for Robotic Manta with Flexible Pectoral Fins

The manta ray, exemplifying an agile swimming mode identified as the median and paired fin (MPF) mode, inspired the development of underwater robots. Robotic manta typically comprises a central rigid body and flexible pectoral fins. Flexible fins provide excellent maneuverability. However, due to the complexity of material mechanics and hydrodynamics, its dynamics are rarely studied, which is crucial for the advanced control of robotic manta (such as trajectory tracking, obstacle avoidance, etc.). In this paper, we develop a multibody dynamic model for our novel manta robot by introducing a pseudo-rigid body (PRB) model to consider passive deformation in the spanwise direction of the pectoral fins while avoiding intricate modeling. In addressing the rigid-flexible coupling dynamics between flexible fins and the actuation mechanism, we employ a sequential coupling technique commonly used in fluid-structure interaction (FSI) problems. Numerical examples are provided to validate the MPF mode and demonstrate the effectiveness of the dynamic model. We show that our model performs well in the rigid-flexible coupling analysis of the manta robot. In addition to the straight-swimming scenario, we elucidate the viability of tailoring turning gaits through systematic variations in input parameters. Moreover, compared with finite element and CFD methods, the PRB method has high computational efficiency in rigid-flexible coupling problems. Its potential for real-time computation opens up possibilities for future model-based control.

A parallel solver for fluid–structure interaction problems with Lagrange multiplier

The aim of this work is to present a parallel solver for a formulation of fluid–structure interaction (FSI) problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method. The fluid subproblem, consisting of the non-stationary Stokes equations, is discretized in space by Q2–P1 finite elements, whereas the structure subproblem, consisting of the linear or finite incompressible elasticity equations, is discretized in space by Q1 finite elements. A first order semi-implicit finite difference scheme is employed for time discretization. The resulting linear system at each time step is solved by a parallel GMRES solver, accelerated by block diagonal or triangular preconditioners. The parallel implementation is based on the PETSc library. Several numerical tests have been performed on Linux clusters to investigate the effectiveness of the proposed FSI solver.

Sedimentation of two circular particles with different sizes in a vertical channel at low Reynolds numbers

In this study, the generalized finite-difference with singular value decomposition method for fluid–structure interaction problems is used to simulate the sedimentation of the two circular particles with different sizes in a vertical channel. The effects of the Reynolds number (8 ≤ Re ≤ 70) and the size difference (0 ≤ β ≤ 0.1) on the final motions of the two particles are analyzed. Over the ranges of the parameters investigated, three modes in the final state of the two-particle system are identified, i.e., the steady state, the periodic oscillation state, and the period-doubling bifurcation (PDB) state. Depending on the importance of the inertial force, the steady state can be classified as the steady state I and the steady state II. Similarly, the periodic oscillation state can be categorized into the periodic motion I (PMI) and the periodic motion II (PMII) based on the influence of the wake between the two particles. The directions of the limit cycles corresponding to PMI and PMII are counterclockwise and clockwise, respectively. In PMI, the limit cycle at 8 ≤ Re ≤ 9 decreases in size with increasing β, while the limit cycle at 12 ≤ Re < 70 behaves oppositely. The limit cycle in PMII always increases in size with β. PDB, characterized by the limit cycle with two branches, mainly appears at 14 ≤ Re ≤ 30.

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.

Hemodynamics in arterial bypass graft anastomoses with varying cuff sizes and proximal flow paths: a fluid–structure interaction study

This article investigates the effect of the cuff size of arterial bypass grafts and the flow conditions on the hemodynamics in the anastomosis (connection) to the artery, using numerical simulations. We consider a fluid-structure interaction problem which is solved based on a partitioned scheme. Additionally, we employ computational fluid dynamics to investigate the effect of a rigid wall assumption. The work focuses on clinically relevant hemodynamic quantities associated with the development of intimal hyperplasia. We also include a model for the prediction of hemolysis into the simulation. The results show that even minor changes of the cuff size can result into significant differences in the corresponding quantities of interest. The importance of the inflow path is shown to be lower than that of the cuff size. The usually employed rigid wall assumption is found to be adequate to address wall shear stress oscillations but falls short on predicting maximum and minimum wall shear stress-related quantities of interest.

Numerical investigation of liquid sloshing in 2D flexible tanks subjected to complex external loading

Due to the complexity of fluid–structure interactions (FSI), the majority of studies in the literature dealing with the sloshing problem are restricted to rigid tanks. This paper is devoted to a numerical investigation of the liquid sloshing behavior in a flexible tank subjected to external loading. A numerical methodology is proposed, taking into account the FSI problem by coupling two open-source codes: OpenFOAM for the fluid and FEniCS for the solid, using the preCICE library, a free library for fluid–structure interaction. The Arbitrary Lagrangian–Eulerian formulation is used for the two-phase flow system to solve the Navier–Stokes equations in the fluid domain using the finite volume method. Simultaneously, the linear-elastic equation of the structure is solved using the finite element method. An implicit coupling scheme is considered at the fluid–structure interface. The numerical methodology is validated by the results given in literature for harmonic excitation at different frequencies. Subsequently, an analysis of complex external loading, such as Gabor wavelets and earthquake ground motion, is conducted to highlight the significant impact of the wall flexibility on sloshing, as well as the influence of hydrodynamic forces on the structure’s deformation. The proposed coupling methodology is robust and effective, it can be applied to all types of liquids and materials. A dataset of one of the studied cases is given as a supplement to the paper (Kha et al., 2024).

On the use of the spectral element method for the modeling of fluid–structure interaction problems

This study addresses a fluid–structure interaction problem that models flow in a channel. Simulations were conducted to investigate the method's effectiveness when applied to real obstacle scenarios, where the obstacle is explicitly represented within the channel. To tackle the Navier–Stokes equations, we utilized the spectral–Fourier–asymptotic approach, which is a mesh-free method that combines Chebyshev polynomials and Fourier series with the asymptotic method based on power series.

Numerical modeling of cutting force and chip formation during water Jet Assisted Machining of Ti17 based on SPH/FEM method

In this paper, we conduct a numerical simulation of a water jet-assisted machining process for a titanium alloy Ti17, with a focus on addressing the Fluid-Structure Interaction (FSI) problem arising during lubricated machining. The proposed coupling strategy employs the Smoothed Particle Hydrodynamics (SPH) free mesh method, coupled with an ordinary Lagrangian mesh. The SPH method is utilized to model the water jet, while the Lagrangian Finite Element Method (FEM) is employed to represent the workpiece and the tool. The hydrodynamic behavior of water is captured using the linear Huguenot form of the Mie-Greisen equation of state. Additionally, the Johnson-Cook constitutive law is applied to describe the thermoviscoplastic behavior of the titanium alloy. It is essential to note that thermal and mechanical effects were decoupled in this study. The investigation focuses on cutting force and chip morphology under two distinct cutting regimes: Dry Machining (DM) and Water Jet Assisted Machining, specifically with conventional lubrication (CL). The numerical simulations are compared with experimental results found in the literature, with an emphasis on cutting force and chip morphology. The obtained simulation results exhibit a favorable correlation with the experimental data. All numerical simulations were conducted using ABAQUS version 6.14.

Fluid-Solid Interaction Analysis of a Flow Passing Cylinder Based on Variational Mode Decomposition

The fluid-structure interaction problem of cylindrical flow around the cylinder is a classic problem, especially in many fields such as energy engineering, fluid dynamics, engineering structure, energy utilization and development, and environmental protection. In this article, we have heard about the simplified model and analyzed it with the help of the classical cylindrical flow model. In this paper, the flow field was pre-processed on the Workbench software platform, and the pressure distribution and eddy current phenomenon were observed by post-processing given the velocity of the flow field of 1m/s. There is a large number of thunder (2.799552×106) and the Carmen Vortex appears around the cylinder. The vortex falls off periodically, and the wake structure is relatively irregular. The maximum pressure appears at the bottom of the cylinder and the maximum deformation at the top. Then, the pressure term of the simulation results was transferred to the Ansys solver for finite element structural analysis to observe the stresses and strains of the structure under the action of fluids. Finally, the response signal is based on Variational Mode Decomposition (VMD). Its periodic signal corresponded to the flow field, and its components were analyzed in detail. The application of VMD in this area provides innovative inspiration for related fields.

Global weak solutions to a 3D/3D fluid-structure interaction problem including possible contacts

In this paper, we study an interaction problem between a 3D compressible viscous fluid and a 3D nonlinear viscoelastic solid fully immersed in the fluid, coupled together on the interface surface. The solid is allowed to have self-contact or contact with the rigid boundary of the fluid container. For this problem, a global weak solution with defect measure is constructed by using a multi-layered approximation scheme which decouples the body and the fluid by penalizing the fluid velocity and allowing the fluid to pass through the body, while the body is supplemented with a contact-penalization term. The resulting defect measure is a consequence of pressure concentrations that can appear where the fluid meets the (generally irregular) points of self-contact of the solid. Moreover, we study some geometrical properties of the fluid-structure interface and the contact surface. In particular, we prove a lower bound on area of the interface.

Numerical investigations on water entry and/or exit problems using a multi-resolution Delta-plus-SPH model with TIC

As a classical Fluid-Structure Interaction (FSI) problem, water entry and/or exit of marine structures involve large deformations of free-surface and splashing, which have long been a great challenge for numerical modeling. Smoothed Particle Hydrodynamics (SPH) is a meshless Lagrangian particle method that has natural advantages in dealing with the non-linear variation of free-surface and moving interfaces. However, the characteristics of weakly-compressible SPH itself may lead to deficiencies such as pressure noise, tensile instability, heterogeneous particle distributions and computational inefficiency. Therefore, in this work, an acoustic damper term is formulated in the momentum equation to eliminate the amount of acoustic pressure waves induced by liquid impacts. Meanwhile, the Adaptive Particle Refinement (APR) is applied to obtain sufficiently fine particle resolution and reduce the computational cost. For the tensile instability issues induced by negative pressures, especially at the water exit stage, the Tensile Instability Control (TIC) is adopted into the SPH simulations to suppress its adverse impact. Furthermore, the Particle Shifting Technique (PST) is beneficial to the two schemes above, and it is also employed in this study. That is to say, PST can effectively solve the problem of particle disorder, which increases the accuracy and robustness of APR and reduces the momentum conservation error caused by TIC. Finally, we propose an improved Free-Surface Detection Method (FSDM) to allow the flow separation from the structure surface at the water entry stage that is impacted by PST. The fairly good agreements between the numerical results and the experimental data indicate the present SPH model can be treated as a reliable numerical tool for accurately solving such problems of structures penetrating fluid interfaces.

Error analysis of an effective numerical scheme for a temporal multiscale plaque growth problem

In this work, we propose a simple numerical scheme based on a fast front-tracking approach for solving a fluid-structure interaction (FSI) problem of plaque growth in blood vessels. A rigorous error analysis is carried out for the temporal semi-discrete scheme to show that it is first-order accurate for all macro time step ΔT, micro time step Δt and scale parameter ϵ. A numerical example is presented to verify the theoretical results and demonstrate the excellent performance of the proposed multiscale algorithm.

A localized subdomain smoothing MMALE particle method for efficient modeling FSI problems

Fluid–structure-interaction (FSI) phenomena with multi-phase flow dynamics and structural damage commonly exist in engineering practice, which however bring great challenges to nowadays numerical FSI algorithms. A novel localized subdomain smoothing MMALE particle method (ls-ALEPM) is proposed in this paper for efficient and accurate simulations of large scale FSI problems. The MMALE method and the MPM are strongly coupled by immersing the MPM particles into the MMALE grid. In order to avoid the spurious strain induced by the mixed FSI velocity field, a decoupled stress updating scheme is proposed to update the stress of solid particles by introducing a virtual velocity field in the vicinity of FSI interface. And specifically, the highly accurate polyhedron intersection based method is employed for its remapping phase, which however is time-consuming. Thus, the localized subdomain smoothing method (LSSM) is put forward to accelerate the remapping phase which only involves the distorted regions of computational grid. The LSSM is composed of a distorted subdomain determination step and a combinated mesh smoothing step. Each iteration of the combinated mesh smoothing step consists of the modified GETMe and the weighted average method, and the transfinite interpolation method is adopted if the quality criteria is still not satisfied after prescribed maximum number of iterations. The validity and efficiency of ls-ALEPM is verified by several benchmark numerical examples and practical engineering simulations.