Fluid-structure Interaction Solver Research Articles

Numerical Simulation of a Submerged Floating Tunnel: Validation and Analysis

The dynamic response analysis of submerged floating tunnels (SFTs) under seismic action is a complex two-way fluid–structure coupling problem that requires expertise in structural dynamics, fluid mechanics, and advanced computational methods. The coupled Eulerian–Lagrangian (CEL) method is a promising method for solving fluid–structure interaction problems, but its application to SFTs is not well established. Therefore, it is crucial to verify the accuracy and reliability of the CEL method in fluid–structure coupling simulations. This study verified the applicability of the CEL method for simulating one-way and two-way fluid–structure coupling cylindrical flow problems, and then applied the CEL method for the analysis of a shaking table test of a model SFT. A comparison of results obtained with the CEL method with those obtained in a previous indoor model test of an SFT demonstrates the agreement between the results of the CEL method and the overall trend of the experimental results, indicating the reliability of the method for the seismic analysis of SFTs. Moreover, the analysis of the dynamic response characteristics of SFTs under seismic conditions provides data support and a technological means for the seismic design of SFTs.

A reduced smoothed integration scheme of the cell‐based smoothed finite element method for solving fluid–structure interaction on severely distorted meshes

AbstractThis article describes an inexpensive partitioned coupling strategy for computational fluid–structure interaction (FSI) admitting negative‐Jacobian elements. The emphasis is very much on a reduced smoothed integration (RSI) scheme of the cell‐based smoothed finite element method (CSFEM) using four‐node quadrilateral (Q4) elements for a cost‐effective solution to the Navier–Stokes (NS) equations. In the discrete fluid field, each Q4 element is considered as one single smoothing cell so as to diminish the smoothed integration loops substantially. However, the RSI scheme does not respect the stability condition of smoothed Galerkin weak‐form integral in the CSFEM. To tackle this issue, a simple hourglass control is introduced to the under‐integrated formulation of the NS solver. Importantly, the stabilized RSI scheme has an inbuilt advantage of its enormous tolerance towards negative‐Jacobian elements. The developed technique is easy‐to‐implement and has been tested in various FSI examples adopting both fine and distorted meshes.

Coupling of the immersed boundary and Fourier pseudo-spectral methods applied to solve fluid–structure interaction problems

The current manuscript addresses fluid–structure interaction (FSI) problems to the analysis of vortex-induced vibration (VIV), employing the methodology designated as IMERSPEC2D. The approach seamlessly integrates the Fourier pseudo-spectral method (FPSM) and the immersed boundary method (IBM) to solve the Navier–Stokes (NS) and continuity equations. Simultaneously, the effects of cylindrical structure, involving 1 and 2 degrees of freedom (d.o.f.) are simulated, by incorporating structural motion equations into NS via the IBM source term and implementing a two-way FSI algorithm. In the paper are presented the comparison of low and high-order temporal integration methods applied to solve the dynamic behavior of the structure and the dimensionless of the cylinder’s structural motion equations, resulting in an increase in computational time step from 1E(-9\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-9$$\\end{document}) to 1E(-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-3$$\\end{document}). Validation results to refined mesh simulations include the accurate representation of the lock-in phenomenon to simulations of 1 d.o.f. obtaining the range between reduced velocity 5.456 and 5.568 and the maximal amplitude is 0.352. Notably, the eight-shape pattern of the 2 d.o.f. cylinder displacement is obtained and the formation of C2S wake patterns is achieved, as presented by other authors. In conclusion, the dimensionless approach reduces computational time, while the high-order both of IMERSPEC methodology and time advancement integration to FSI improve the results of the cylinder’s motion and alters distinct vortex shedding patterns in fluid dynamics.

Efficient control of the fully passive oscillating foil in 2D confined flows with adjustment of the heave damping

A foil that is free to pitch and heave in an upstream flow can oscillate very regularly and with large amplitudes given that its inertial properties and support stiffness in pitch and heave are well adapted to the flow velocity. Useful energy can be extracted from these oscillations via an appropriate damping in heave that models the presence of an electric generator. In recent years, the structural parameters of such a fully passive oscillating-foil turbine (OFT) have been optimized, yielding a maximum energy extraction efficiency of 51.0% under the assumptions of 2D and unconfined flow. However, the turbine is normally deployed in channels with finite cross-sectional area, thus impacting the flow rate passing through the turbine via the blockage effect. In this work, we extend the applicability of the 2D optimized structural parameters to 2D confined scenarios with a simple tuning of the viscous heave damping coefficient. Performance is determined via a fluid-structure interaction solver based on an unsteady Reynolds-averaged Navier–Stokes approach. As expected, confining the turbine increases the heave amplitude and the power, up to a point where the motions become chaotic, and thus require an increase in the heave damping coefficient. This study shows that in all confined 2D scenarios, reasonably good performances of the fully passive OFT can be maintained when using its optimal structural parameters obtained in 2D unconfined conditions, given that the generator is adjusted accordingly.

Surrogate-based optimization for the worst-case prediction regarding a flexible structure impacted by wind gusts

The paper is a follow-up of the recent study on the assessment of discrete wind gust parameters impacting a flexible lightweight structure as a first step towards the evaluation of the worst-case scenario caused by strong wind gusts (JWEIA 231, 105207, 2022). The present study goes beyond by suggesting an optimization framework which allows to determine the worst-case scenario automatically. For this purpose, a stochastic response surface algorithm with a surrogate model based on radial basis functions is chosen. The algorithm relies on costly evaluations of the objective function, which consist of CPU-time intensive fully coupled fluid–structure interaction (FSI) high-fidelity simulations including the pre- and post-processing of the results. Besides the parallelization of the coupled FSI solver, a parallel version of the optimization algorithm allows to carry out several costly evaluations simultaneously. The Metric Stochastic Response Surface algorithm determines the worst case fast. Then, it continues to explore the optimization space to ensure that the global extremum is reached. A sensitivity study on relevant parameters of the optimization algorithm is conducted. Typically, for the present FSI setup, an optimization run takes one week with 6 evaluations in parallel to compute 100 different configurations. The worst case is found after about one third of the evaluations. The increase of parallel evaluations drastically reduces the wall-clock time, but the worst case is found later after half of the evaluations. This later finding is due to the parallel nature of the algorithm. Finally, the various sources of uncertainties that arise throughout the entire procedure are assessed and discussed.

A predictive surrogate model for hemodynamics and structural prediction in abdominal aorta for different physiological conditions

Background and objectiveThis study investigates the application of a Predictive Surrogate Model (PSM) for the prediction of the fluid and solid variables in the abdominal aorta by integrating Proper Orthogonal Decomposition (POD) and Long Short-Term Memory (LSTM) techniques. MethodsThe Fluid-Structure Interaction (FSI) solver, which serves as the Full-Order Model (FOM), can capture the blood hemodynamics and structural mechanics precisely for a variety of physiological states, namely the rest and exercise conditions. ResultsDetailed analyses have been conducted on velocity components, pressure, Wall Shear Stress (WSS), and Oscillatory Shear Index (OSI) variables. Firstly, the reconstruction error has been derived based on a specific number of POD bases to assess the Reduced Order Model (ROM). Notably, the reconstruction error for velocity components in the rest condition is one order of magnitude higher than that in the exercise condition, yet both remained below 10%. This error for pressure is even more minimal, being less than 1%. ConclusionsThe PSM is evaluated against rest and exercise conditions, exhibiting promising results despite the inherent complexities of the physiological conditions. Despite the inherent complexities of phenomena in the aorta, the predictive model demonstrates consistent error magnitudes for velocity components and wall-related indices, while solid variables show slightly higher errors.

Power synchronisations determine the hovering flight efficiency of passively pitching flapping wings

The power exchange between fluid and structure plays a significant role in the force production and flight efficiency of flapping wings in insects and artificial flyers. This work numerically investigates the performance of flapping wings by using a high-fidelity fluid–structure interaction solver. Simulations are conducted by varying the hinge flexibility (measured by the Cauchy number, $Ch$ , i.e. the ratio between aerodynamic and torsional elastic forces) and the wing shape (quantified by the radius of the first moment of area, $\bar {r}_1$ ). Results show that the lift production is optimal at $0.05 < Ch \leq 0.2$ and larger $\bar {r}_1$ where the minimum angle of attack is around $45^\circ$ at midstroke. The power economy is maximised for wings with lower $\bar {r}_1$ near $Ch=0.2$ . Power analysis indicates that the optimal performance measured by the power economy is obtained for those cases where two important power synchronisations occur: anti-synchronisation of the pitching elastic power and the pitching aerodynamic and inertial powers and nearly in-phase synchronisation of the flapping aerodynamic power and the total input power of the system. While analysis of the kinematics for the different wing shapes and hinge stiffnesses reveals that the optimal performance occurs when the timing of pitch and stroke reversals are matched, thus supporting the effective transfer of input power from flapping to passive pitching and into the fluid. These results suggest that careful optimisation between wing shapes and hinge properties can allow insects and robots to exploit the passive dynamics to improve flight performance.

A Fully Explicit Lattice Spring Elastoplastic Solid Model for Fluid Structure Interaction Applications

The Fluid Structure Interaction (FSI) solver based on mesh-less methods developed at University of Nottingham Malaysia has been proven to be successful in solving hydroelastic problems involving elastic body. In this paper, the possibility of modelling elastocplastic material behaviour using mesh-less method is further explored. Elastoplastic material bahaviour is essential for modelling ductile fracture in a wide range of engineering problems. The use of a type of nonlocal lattice spring model (LSM) based on fully explicit integration scheme in modelling elastoplastic material behaviour is presented in this work. Specifically, the return mapping algorithm is incorporated in the solid solver for modelling J2 plasticity. The effect of time step size and particle spacing on the accuracy of the solver are investigated by checking the predicted strain against theoretical solution. It is found out that the strain results obtained by varying the time step size are somewhat consistent with the theoretical solution. The predicted strain also converges to the theoretical result as the particle spacing is refined.

Airflow Field and Shelter Effect Around Flexible Plants Using Fluid‐Structure Interaction (FSI)‐Large‐Eddy‐Simulation (LES) Simulations

AbstractVegetative windbreaks have a significant advantage in regulating microclimates and improving soil conditions. Some studies highlight the importance of turbulence and plant flexibility, but few has investigated the relationship between flexibility and the shelter effect of windbreaks. Therefore, we perform a series of 3D fluid‐structure interaction (FSI)‐large‐eddy‐simulation (LES) simulations to study the airflow passing through flexible single‐plant windbreaks. We first model the plants with branches according to their geometric features in the field, present a FSI solver to strongly couple the airflow velocity field and windbreak vibration, and then use a LES turbulent model to resolve the turbulent flows. Based on the simulations, the airflow fields around the plants (Plant #1 and Plant #2) with different flexibilities, evaluated by Young's modulus, were analyzed and compared. Afterward, the shelter effect of flexible plants is analyzed based on three indices, including turbulence intensity, surface shear stress and plant swing displacement. The peak turbulence intensity of the three plants follows the order Plant #1 > Plant #2 > rigid plant. Regardless of wind speed, the surface shear stress around the plants follows the order Plant #1 < Plant #2 < rigid plant. The swing displacement increases as the velocity and flexibility increase. It is concluded that the flexible plant has a better shelter effect than the rigid plant, and within a certain range, the stronger the flexibility of the plant is, the better its shelter effect. This study not only investigates the interaction mechanism between flexible plants and airflow, but also provides a theoretical reference for the application of flexible plants in wind protection engineering.

Design of a high fidelity Fluid–Structure Interaction solver using LES on unstructured grid

Despite promising experimental works, high fidelity numerical simulations of chordwise flexible blade are useful to better understanding. However, such simulation remains a challenging problem as it requires a Fluid–Structure Interaction (FSI) solver capable of accurately predicting the stall dynamics, while computing the deformation of a solid with complex geometry. In this paper, the authors propose a LES-based FSI solver using 3D solid elements for the solid and unstructured grid for fluid and solid solvers. This approach aims at being universal and is based on a partitioned coupling scheme, allowing low density ratios of the structure to the fluid. It uses an original pseudo-solid method for the mesh movement solving, specifically developed for this work. Besides, this solver is suited for massively parallel computing and can perform Dynamic Mesh Adaptation to be able to take into account any solid movement. Both fluid and solid solvers are validated independently before validation of the FSI solver against a 2D laminar benchmark, including mesh convergence study. The entire methodology is then successfully applied to experimental 3D complex case with high Reynolds number, confirming the potential of the FSI solver for its intended use, without geometry restriction. This is finally illustrated with a simulation of an experiment involving a chordwise flexible blade with large deformation, which has never been reproduced with a 3D LES approach in literature so far.

Two-dimensional numerical simulations of solitary wave interaction with a vertical elastic plate

In this study, we numerically investigated the interaction between a solitary wave and a bottom-mounted, submerged elastic plate. The fluid structure interaction (FSI) solver (solids4Foam), the stabilized k-ω SST turbulence closure model, and the geometric volume of fluid approach (isoAdvector) were combined to simulate the dynamic process, including the plate movement and the flow field. The model package was first validated by using experimental data, and the effects of plate height, plate thickness, and the Young's modulus of plate material on the hydrodynamics were further investigated. Moreover, the Euler-Bernoulli beam theory was used to calculate the plate displacement. Lengthening the plate height, reducing the plate thicknesses, or reducing Young's modulus can all increase the plate displacement. Among them, lengthening the plate height has the greatest impact. Finally, the effects of the wave nonlinearity and plate material property on wave reflection, transmission, and dissipation were also analyzed. The results show that while the height of the plate has the most significant effect on the reflection coefficient, the plate thickness and the plate material have little influence on the reflection coefficient. The more flexible the plate is, the smaller the transmitted coefficient, and the larger the dissipation coefficient are.

A monolithic, finite element-based strategy for solving fluid structure interaction problems coupled with electrostatics

In this work, we present a monolithic finite-element-based strategy for problems involving the deformation of a hyperelastic solid, an incompressible fluid and electrostatics. We use a two-field hybrid Lagrangian formulation for the structure, and a velocity-based ALE mixed formulation for the fluid with appropriately chosen interpolations for the various field variables to ensure stability of the resulting numerical procedure. The equations of electrostatics are solved on the reference configuration over both the solid and fluid domains, with voltage and electric displacement continuity imposed at the interface. Keeping in view that the thickness of typical MEMS structures is small, a stress-based hybrid formulation is used to prevent locking. The use of a monolithic strategy provides a robust and stable algorithm, and allows the user to take large time steps. The consistent linearization ensures a quadratic rate of convergence of the non-linear iterations at each time step. Detailed expressions for the tangent stiffness and associated matrices for the three-way coupled problem are provided. The robustness and accuracy of the proposed method are demonstrated by solving several benchmark problems from the literature.

Fully Coupled Analysis of Flutter Induced Limit Cycles: Frequency Versus Time Domain Methods

Abstract To save resources and reduce emissions, it is crucial to reduce weight of aircraft engines and further increase aerodynamic efficiency of gas and steam turbines. For turbine blades, these goals often lead to flutter. Thus, innovative flutter-tolerant designs are explored, where flutter induces limit cycle oscillations (LCOs) of tolerable yet nonzero levels. Flutter represents a self-excitation mechanism and, in the linear case, would lead to exponential divergence. Flutter-induced LCOs are therefore an inherently nonlinear phenomenon. The saturation of flutter-induced vibrations can be caused by nonlinear frictional contact interactions, e.g., in tip shroud interfaces. To develop flutter-tolerant designs, efficient methods are required which compute LCOs based on an appropriate modeling of elastic, inertia, aerodynamic, and contact forces. We recently developed a Frequency Domain Fluid-Structure Interaction (FD-FSI) solver for flutter-induced LCOs. The solver relies on the Harmonic Balance method applied to the structure as well as the fluid domain. It was shown that especially for long and slender blades with friction in shroud interfaces and strong aerodynamic influence, a coupled analysis can significantly increase the accuracy of predicted LCOs compared to the current state-of-the-art methods. Conventional methods do not properly account for the nonlinear change of frequency and deflection shape, and the effect of these changes on the aerodynamic damping, and thus fail in predicting certain LCOs at all. In the current work, the FD-FSI solver is numerically validated against Time Domain Fluid-Structure Interaction (TD-FSI) simulations. As a test case, a shrouded low-pressure turbine with friction in the shroud interfaces is considered. The point of operation is highly loaded and transonic in order to make the test case challenging. Apart from a successful validation of the FD-FSI solver, we shed light on important advantages and disadvantages of both solvers. Due to the lack of robust phase-lag boundary conditions for time domain solvers, a full blade row must be simulated. Thus, the FD-FSI solver typically requires only a fraction of the computational costs. Moreover, the FD-FSI solver contributes to an increased physical understanding of the coupled vibrations: By analyzing the contribution of individual harmonics, we analyze why unexpected even harmonics appear in a certain LCO. On the other hand, the FD-FSI solver does not provide information on the asymptotic stability of the LCOs and is strictly limited to periodic oscillations. Indeed, quasi-periodic limit torus oscillations (LTOs) appear in our test case. Using the TD-FSI solver, we confirm the internal combination resonance, postulated recently as necessary condition for LTOs, for the first time, in a fully coupled analysis.

The effect of the tower’s modeling on the aero-elastic response of the NREL 5 MW wind turbine

In this work, we aim at evaluating the aeroelastic response of the blades of a standalone NREL 5MW wind turbine by means of a high-fidelity fluid-structure interaction solver based on large-eddy simulation, and compare the results with those of engineering-fidelity methods based on the Blade Element Momentum (BEM) theory. For the latter, we use the software OpenFAST [1], which couples an aerodynamic solver based on the BEM theory with a solver of the blades’ structural dynamics. Concerning the computational fluid dynamics (CFD) solver, the tower and nacelle are modeled by means of an immersed boundary method, whereas the aeroelastic rotor is modeled by an actuator line model coupled with a Computational Structural Dynamics (CSD) solver representing the blades as rotating cantilever beams. A comparison of the CFD-CSD results with the corresponding ones obtained by OpenFAST shows that the predicted displacements at the blade tip remarkably differ between the two approaches in correspondence of the passages of the blades in front of the tower. Indeed, the interaction between the blades and the tower introduces a significant perturbation in the local aerodynamics that leads to a drop of the displacement at the tip of the blade and of the root reaction magnitude, which appear to be not accurately described by OpenFAST.

Coupling an SPH-based solver with an FEA structural solver to simulate free surface flows interacting with flexible structures

This work proposes a two-way coupling between a Smoothed Particle Hydrodynamics (SPH) model-based named DualSPHysics and a Finite Element Analysis (FEA) method to solve fluid–structure interaction (FSI). Aiming at having a computationally efficient solution via spatial adjustable resolutions for the two phases, the SPH-FEA coupling herein presented implements the Euler–Bernoulli beam model, based on a simplified model that incorporates axial and flexural deformations, to introduce a solid solver in the DualSPHysics framework. This approach is particularly functional and very precise for slender beam elements undergoing large displacements, and large deformations can also be experienced by the structural elements due to the non-linear FEA implementation via a co-rotational formulation. In this two-way coupling, the structure is discretised in the SPH domain using boundary particles on which the forces exerted by fluid phases are computed. Such forces are passed over to the FEA structural solver that updates the beam shape and, finally, the particle positions are subsequently reshuffled to represent the deformed shape at each time step. The SPH-FEA coupling is validated against four reference cases, which prove the model to be as accurate as other approaches presented in literature.

Fast Aero-Structural Model of a Leading-Edge Inflatable Kite

Soft-wing kites for airborne wind-energy harvesting function as flying tensile membrane structures, each of whose shape depends on the aerodynamic load distribution and vice versa. The strong two-way coupling between shape and loading poses a complex fluid-structure interaction problem. Since computational models for such problems do not yet meet the requirements of being accurate and at the same time fast, kite designers usually work on the basis of intuition and experience, combined with extensive iterative flight testing. This paper presents a fast aero-structural model of leading-edge inflatable kites for the design phase of airborne wind-energy systems. The fluid-structure interaction solver couples two fast and modular models: a particle system model to capture the deformation of the wing and bridle-line system and a 3D nonlinear vortex step method coupled with viscous 2D airfoil polars to describe the aerodynamics. The flow solver was validated with several wing geometries and proved to be accurate and computationally inexpensive for pre-stall angles of attack. The coupled aero-structural model was validated using experimental data, showing good agreement in the deformations and aerodynamic forces. Therefore, the speed and accuracy of this model make it an excellent foundation for a kite design tool.

Neural-network-based fluid–structure interaction applied to vortex-induced vibration

In this paper, a fluid–structure interaction (FSI) solver with neural-network-based fluid-flow prediction is proposed. This concept is applied to the problem of vortex-induced vibration of a cylinder. The majority of studies that are concerned with fluid-flow prediction using neural networks solve problems with fixed boundary. In this paper, a convolutional neural network (CNN) is used to predict unsteady incompressible laminar flow with moving boundary. A deformable non-Cartesian grid, which traces the boundary of the fluid domain, is used in this paper. The CNN is trained for oscillating cylinder with various frequencies and amplitudes. The dynamics of the elastically-mounted cylinder is modelled using a linear spring–mass–damper model and solved by an implicit differential scheme. The results show that the CNN-based FSI solver is capable of capturing the so-called lock-in phenomenon for the problem of vortex-induced vibration of a cylinder and the quantitative behaviour is similar to the results of the CFD-based FSI solver. Moreover, the CNN-based FSI solver is two orders of magnitude faster than the CFD-based FSI solver and the speedup is expected to be even greater on larger problems.

Computational framework for efficient high-fidelity optimization of bio-inspired propulsion and its application to accelerating swimmers

A new computational framework for high-fidelity optimization of kinematic gaits during self-propelled undulatory swimming is developed. A computational framework utilizes a spectral-element method on moving body-fitted grids for a simulation of self-propelled swimming, and a surrogate-based optimization (SBO) procedure. A new volume-conservation method for reconstruction of a swimmer's geometry during the undulatory motion is proposed to ensure numerical stability of the fluid-structure interaction solver in an incompressible flow framework. A surrogate-based optimization algorithm that utilizes a Kriging response surface method is adopted and further developed in this work to manage the optimization process in the presence of physiological constraints on the fish body motion. A grid convergence of the optimization results is established, and the influence of the polynomial refinement on the results of optimization procedure is assessed. The increase in polynomial order does not change the optimum gaits of locomotion or relative efficiency rankings between the modes, but it results in slightly lower predicted efficiency for all the modes. The optimum solution is characterized by a kinematic gait that generates the reverse Karman vortex street associated with high propulsive efficiency. Efficiency of sub-optimum modes is found to increase with both the tail amplitude and the effective flapping length of the swimmer, and a new scaling law is proposed to capture these trends. Lastly, the SBO algorithm converged to an optimized gate with significantly less function evaluations than typically observed for evolutionary algorithms. This suggests that the SBO framework is a well suited alternative for high-fidelity optimization of fluid and structure problems.

An interface and geometry preserving phase-field method for fully Eulerian fluid-structure interaction

We present an interface and geometry preserving (IGP) method for modeling fully Eulerian fluid-structure interaction via phase-field formulation. While the time-dependent mobility model preserves the hyperbolic tangent interface profile, the proposed method maintains the geometry of the solid-fluid interface by minimizing the volume-conserved mean curvature flow. To reduce the curvature flow, we construct a gradient-minimizing velocity field (GMV) for the convection of the order parameter. The constructed velocity field retains the solid velocity in the solid domain while extending the velocity in the normal direction throughout the diffuse interface region. With this treatment, the GMV reduces the normal velocity difference of the isosurfaces of the order parameter, alleviating the undesired thickening or thinning of the diffuse interface region due to the convection. As a result, the time-dependent mobility coefficient is substantially reduced and there is a lesser volume-conserved mean curvature flow. Furthermore, the GMV ensures that the diffuse interface region moves with the solid bulk despite the fluid flow, such that the fluid-solid interface conforms to the geometry of the solid. Using the unified momentum and mass conservation equations via the phase-dependent interpolation, we integrate the IGP method into a fully Eulerian fluid-structure interaction solver based on the incompressible viscous fluid and the neo-Hookean solid models. The kinematics of the solid in an Eulerian frame of reference is resolved by evolving the left Cauchy-Green tensor. We first demonstrate the ability of the phase-field-based IGP method for the convection of circular and square interfaces in a prescribed velocity field. The variational fluid-structure interaction framework with the IGP method is then examined on the deformation of a solid block under cavity flow. We next explore the geometry-preserving effect of the proposed framework when the fluid flow passes over a fixed deformable block in a channel. Finally, the vibration of a flexible plate attached behind a stationary cylinder is considered to demonstrate the ability of the framework in solving unsteady fluid-structure interaction problems.

Development of analytical method of estimation of drag coefficient for flexible structures

Flexible structures used in devices, such as micro/nano resonators, sensors, etc. are subjected to fluid forces. Estimation of damping coefficient due to the fluid forces in flexible structures is of utmost importance for the designs of these structures. In existing literatures, empirical correlation for the estimation of damping coefficient are available for the non-flexible structures only. Therefore, development of, preferably simple, analytical method of estimation of damping coefficient in flexible structures subjected to various mode shapes. In this work we attempt to develop such a model from the first principle. The results of the model are validated with the data available for non-flexible structure. Analysis of three mode shapes is performed using the analytical model and the results are compared with the numerical data. Computations are conducted using the finite difference method-based IB2d fluid–structure interaction solver, which solves Navier-Stokes equation for fluid-region using the Eulerian and an equation of motion for solid-region using the Lagrangian approach. A connectivity between fluid and structure is made through a forcing function which is a source term in the momentum equation. From the numerical simulations the average damping coefficients respectively, for first, second and third mode shape are found to be 0.79×10-3, 1.49×10-3, and 2.01×10-3. It is concluded that, with the given flow velocity (low Re), reasonable predictions of damping coefficients can be made using the proposed analytical model for the flexible structures.