Unsteady fluid–structure interactions of membrane airfoils at low Reynolds numbers

Membrane wings are used both in nature and small aircraft as lifting surfaces. Separated flows are common at low Reynolds numbers and are the main sources of unsteadiness. Yet, the unsteady aspects of the fluid–structure interactions of membrane airfoils are largely unknown. An experimental study of unsteady aerodynamics of two-dimensional membrane airfoils at low Reynolds numbers has been conducted. Measurements of membrane shape with a high-speed camera were complemented with the simultaneous measurements of unsteady velocity field with a high frame-rate particle image velocimetry system and flow visualization. Vibrations of the membrane and mode shapes were investigated as a function of angle of attack and free stream velocity. While the mean membrane shape is not very sensitive to angle of attack, the amplitude and mode of the vibrations of the membrane depend on the relative location and the magnitude of the unsteadiness of the separated shear layer. The results indicate strong coupling of unsteady flow with the membrane oscillations. There is evidence of coupling of membrane oscillations with the vortex shedding in the wake, in particular, for the post-stall incidences. Comparison of rigid (but cambered) and flexible membrane airfoils shows that the flexibility might delay the stall. Hence this is a potential passive flow control method using flexibility in nature and engineering applications.     

Measurement of parallel blade–vortex interaction at low Reynolds numbers

In this study parallel blade–vortex interaction for a Schmidt-propeller configuration has been examined using particle image velocimetry (PIV). This tandem configuration consists of a leading airfoil (forefoil), used to generate a vortical wake of leading-edge vortices (LEVs) and trailing-edge vortices (TEVs) through a pitching or plunging motion, and a trailing airfoil (hindfoil), held fixed with a specified angle of attack and vertical spacing in its wake. The hindfoil incidence (loading) and not the vertical spacing to the incoming vortical wake has been found to dictate the nature of the interaction (inviscid vs. viscous). For cases where the vortex–blade offset is small and the hindfoil is loaded, vortex distortion and vortex-induced separations are observed. By tracking the circulation of the LEV and TEV, it has been found that the vortices are strengthened for the tandem arrangement and in certain cases dissipate quicker in the wake when interacting with the hindfoil. Time-averaged forces obtained using a standard control-volume analysis are then obtained and used to evaluate these vortex-interaction cases. A subsequent analysis of the varying pressure distribution over the suction side of the hindfoil is performed by integrating the Navier–Stokes equations through the velocity field. This allows for a direct comparison of the vortex-induced loading for the various configurations.     

Numerical modeling of current loads on a net cage considering fluid–structure interaction

In this paper we propose and discuss a numerical method to model the current loads on a net cage. In our numerical model, the fluid–structure interaction is taken into consideration. The net cage is modeled on the mass-spring model; the flow field is modeled by the finite volume method (FVM). A novel hybrid volume approach is used to add the resistance force of the net cage into the flow field for coupling the fluid and net. The net resistance to the flow is calculated directly by the net’s current load using Newton’s Third Law. The resistance force is discretized in the hybrid volume and represented in the source term of the Navier–Stokes equation. By using the hybrid volume method, the mesh grid is separated from the net shape, and sparse grid (0.1 m) can be used to calculate the flow field for computational efficiency. Based on the detailed flow field, we can predict the net’s current load more accurately. The final results are derived by the segregated iterative calculation of net shape and flow field. Current forces acting on both rigid and flexible net cages are simulated at water velocity from 0 to 1 m/s; the simulation results of proposed numerical method are compared with the existing experiments, good agreements are shown in both flow field and current force, the mean normalized absolute error of the current force between simulations and measurements is about 5%.     

Numerical simulation of the fluid–structure interaction in a tube array under cross flow at moderate and high Reynolds number

The unsteady loads in a tube bundle are studied at moderate and high Reynolds number by means of URANS and hybrid (DDES) modelling. The onset of fluid-elastic instability is analysed for different structural parameters, Scruton number and reduced velocity. The simulations have been carried out with the code NSMB (Navier–Stokes Multi Block) by using turbulence modelling methods URANS and DDES (Delayed Detached Eddy Simulation). The CEA-DIVA configuration is considered for the cylinders array for an inter-tube Reynolds number 60 000. The study is carried out for a configuration of (4×5) cylinders in static conditions as well as for the vertical free motion of one of the central cylinders in one DOF (Degree Of Freedom).The inter-tube Reynolds number is 60 000. It is found that this cylinder spontaneously displays an oscillatory motion which first corresponds to Vortex Induced Vibration (VIV), associated to a lock-in mechanism for low values of the reduced velocity and secondly develops Movement Induced Vibration, MIV, for higher values of the reduced velocity. The variation of the cylinder׳s oscillations frequency, of the unsteady loads and the structure׳s displacement are studied as a function of the reduced velocity for low and high values of the Scruton number. The increase of the phase-lag between the forces and the displacement is predicted and discussed for different Scruton number values and reduced velocities.     

A computational framework for fluid–porous structure interaction with large structural deformation

We study the effect of poroelasticity on fluid–structure interaction. More precisely, we analyze the role of fluid flow through a deformable porous matrix in the energy dissipation behavior of a poroelastic structure. For this purpose, we develop and use a nonlinear poroelastic computational model and apply it to the fluid–structure interaction simulations. We discretize the problem by means of the finite element method for the spatial approximation and using finite differences in time. The numerical discretization leads to a system of non-linear equations that are solved by Newton’s method. We adopt a moving mesh algorithm, based on the Arbitrary Lagrangian–Eulerian method to handle large deformations of the structure. To reduce the computational cost, the coupled problem of free fluid, porous media flow and solid mechanics is split among its components and solved using a partitioned approach. Numerical results show that the flow through the porous matrix is responsible for generating a hysteresis loop in the stress versus displacement diagrams of the poroelastic structure. The sensitivity of this effect with respect to the parameters of the problem is also analyzed.

     

Two forms of continuum shape sensitivity method for fluid–structure interaction problems

Continuum Sensitivity Equation (CSE) methods for deriving and computing derivatives with respect to shape design variables are developed in two forms and compared in their application to fluid–structure interaction (FSI) problems. The local derivative form poses the CSEs in terms of the partial derivatives of the state variables with respect to shape parameters, while the CSEs in total derivative form are posed in terms of the total derivative, also known as the material or substantial derivative. In the literature CSEs are often posed in local form for fluids and total form for solids. The two forms are compared here for the purpose of applying a single form to both fluid and structure domains. The local form, also known as the boundary velocity method, requires design velocity only at the boundaries and interfaces of the domains to pose the CSEs. In contrast, the total form, also known as the domain velocity method, requires the design velocity in the whole domain. The local form requires higher-order spatial derivatives of the analysis solution than the total form, which affects the accuracy of its results. Higher order p-elements are shown to be a remedy to the inaccuracy of local form CSE seen in the literature for finite element solutions. The practicality, accuracy, and efficiency of these two CSE forms are compared based on the implementation and computed derivatives for three examples: a linear Timoshenko beam subject to a tip force, fluid flow around an airfoil, and an airfoil attached to a nonlinear joined beam subject to a gust load.     

Bi-directional fluid–structure interaction for large deformation of layered composite propeller blades

Bi-directional fluid–structure interaction becomes important when viscous flow changes the geometry of the domain significantly because of the pressure load. Large deformation in domain causes numerical convergence problems, which are solved by mesh smoothing, re-meshing and a time discrete iterative solver algorithm using industrial computational fluid dynamics and finite element analysis code. In this paper, this approach is used for laminated composite propellers considered as mixers. It experiences heavy thrust, which causes large deformations. Each layer of laminate is modeled as a solid element with anisotropic material data. Comparative study is presented between uni-directional and bi-directional fluid–structure interaction for mixer blades. Change in pressure distribution, stress distribution, thrust, torque and pitch angle of the blade are presented in later parts of the paper.     

Validation of a 2-D semi-coupled numerical model for fluid–structure–seabed interaction

A 2-D semi-coupled model PORO-WSSI 2D (also be referred as FSSI-CAS 2D) for the Fluid-Structure-Seabed Interaction (FSSI) has been developed by employing RANS equations for wave motion in fluid domain, VARANS equations for porous flow in porous structures; and taking the dynamic Biot's equations (known as "u − p" approximation) for soil as the governing equations. The finite difference two-step projection method and the forward time difference method are adopted to solve the RANS, VARANS equations; and the finite element method is adopted to solve the "u − p" approximation. A data exchange port is developed to couple the RANS, VARANS equations and the dynamic Biot's equations together. The analytical solution proposed by Hsu and Jeng (1994) and some experiments conducted in wave flume or geotechnical centrifuge in which various waves involved are used to validate the developed semi-coupled numerical model. The sandy bed involved in these experiments is poro-elastic or poro-elastoplastic. The inclusion of the interaction between fluid, marine structures and poro-elastoplastic seabed foundation is a special point and highlight in this paper, which is essentially different with other previous coupled models The excellent agreement between the numerical results and the experiment data indicates that the developed coupled model is highly reliablefor the FSSI problem.     

Numerical modeling and investigation of viscoelastic fluid–structure interaction applying an implicit partitioned coupling algorithm

We investigate the interaction between a viscoelastic Oldroyd-B fluid and an elastic structure via simulations applying an implicit partitioned coupling algorithm. Simulations are done for a flow through a channel with a flexible wall and a lid-driven cavity flow with flexible bottom. In addition, we make use of a mass–spring–dashpot prototype model to study the dynamic interaction problem. Both the simulation results and the analysis of the prototype model show that there are obvious differences in the fluid–structure interaction if the fluids are viscoelastic instead of purely viscous. These differences appear in the deformation of the solid at stationary state and in the equilibrium position, amplitude, frequency as well as phase shift of the oscillation. Moreover, we investigate the influence of numerical and physical parameters on the implicit partitioned coupling algorithm for simulation of viscoelastic fluid–structure interaction problems.     

Validation of a fluid–structure interaction model for a bileaflet mechanical heart valve

A fluid-structure interaction (FSI) model for heart valve simulation is presented. In a partitioned framework, separate fluid and structure solvers are weakly coupled, which in combination with the use of artificial compressibility in the fluid solver, leads to a stable and efficient approach. An Arbitrary Lagrangian Eulerian formulation is employed in the fluid solver to permit the accurate calculation of shear stresses next to the valve boundary. The mesh quality is maintained through a combination of smoothing and local remeshing in 3D. The FSI algorithm is validated on experiments of an idealised quasi-2D mechanical heart valve, and the efficiency of the remeshing approach is demonstrated on a realistic 3D heart-valve geometry.     

A fluid–structure interaction analysis of anisotropic Dacron fabric used for aortic replacement

We present the results of a computational study aimed at capturing the behavior over time of Dacron fabric used for surgical correction of aortic aneurysms. The study concerns the problem of compliance mismatch between the graft and the native aorta and is very important to clinicians. The aorta is represented by a sophisticated anisotropic hyperelastic model (GOH), which takes into account the orientation of the collagen fibers. The corrugations present on the Dacron fabric are modeled geometrically using experimental data retrieved from the literature. The viscoelastic behavior of the Dacron graft reported by clinicians is also taken into account. Mechanical quantities experienced by the graft sewn to an aortic segment are obtained using fluid–structure interaction (FSI) simulations assuming realistic blood flow conditions. Both ascending and descending aorta with two curvatures are considered. Results of this study indicate that (i) the strains on the Dacron-aorta structure increase with increasing curvature and over time (ii) the simulations are capable of capturing stress concentrations at the junction of the graft and the aorta and (iii) the wall shear stresses (WSS) are substantially higher on the aortic segment than on the Dacron graft.     

Large Eddy Simulations of convergent–divergent channel flows at moderate Reynolds numbers

The paper is focused on the study of fully turbulent channel flows, using Large Eddy Simulations (LES), in order to address the effects of adverse pressure gradient regions. Analyses of the effects of streak instabilities, which have been shown to be relevant in such regions, are extended to moderate Reynolds numbers. The work considers two different channel geometries in order to further separate influences from wall curvature, flow separation and adverse pressure gradients. Turbulent kinetic energy and Reynolds stress budgets are investigated at separation and re-attachment points. The numerical approach used in the present work is based on the incompressible Navier–Stokes equations, which are solved by a pseudo-spectral methodology for structured grids. Wall-resolved LES calculations are performed using the WALE subgrid scale model. The study shows that the streak instability mechanism persists at higher Reynolds numbers with and without wall curvature in the adverse pressure gradient regions. Moreover, the observed effects are also present regardless of the existence of flow separation regions. Finally, the study of turbulent kinetic energy budgets indicates that, independently of the flow condition, there are well-defined patterns for such turbulent properties at separation and re-attachment points.     

Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier–Stokes: Applications to fluid–structure interaction

Stabilised mixed velocity–pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier–Stokes. In these formulations, the Newton–Raphson scheme is employed to solve the nonlinearity in the convection term. One fundamental issue with this approach is the computational cost incurred in the Newton–Raphson iterations at every load/time step. In this paper, we present an iteration-free mixed finite element formulation for incompressible Navier–Stokes that preserves second-order temporal accuracy of the generalised-alpha and related schemes for both velocity and pressure fields. First, we demonstrate the second-order temporal accuracy using numerical convergence studies for an example with a manufactured solution. Later, we assess the accuracy and the computational benefits of the proposed scheme by studying the benchmark example of flow past a fixed circular cylinder. Towards showcasing the applicability of the proposed technique in a wider context, the inf–sup stable P2–P1 pair for the formulation without stabilisation is also considered. Finally, the resulting benefits of using the proposed scheme for fluid–structure interaction problems are illustrated using two benchmark examples in fluid-flexible structure interaction.     

A new approach for computing the steady state fluid–structure interaction response of periodic problems

A special type of fluid–structure interaction (FSI) problems are problems with periodic boundary conditions like in turbomachinery. The steady state FSI response of these problems is usually calculated with similar techniques as used for transient FSI analyses. This means that, when the fluid and structure problem are not simultaneously solved with a monolithic approach, the problem is partitioned into a fluid and structural part and that each time step coupling iterations are performed to account for strong interactions between the two sub-domains. This paper shows that a time-partitioned FSI computation can be very inefficient to compute the steady state FSI response of periodic problems. A new approach is introduced in which coupling iterations are performed on periodic level instead of per time step. The convergence behaviour can be significantly improved by implementing existing partitioned solution methods as used for time step coupling (TSC) algorithms in the time periodic coupling (TPC) framework. The new algorithm has been evaluated by comparing the convergence behaviour to TSC algorithms. It is shown that the number of fluid–structure evaluations can be considerably reduced when a TPC algorithm is applied instead of a TSC. One of the most appealing advantages of the TPC approach is that the structural problem can be solved in the frequency domain resulting in a very efficient algorithm for computing steady state FSI responses.     

Development of a fully Lagrangian MPS-based coupled method for simulation of fluid–structure interaction problems

A fully Lagrangian particle-based method is developed for simulating the FSI (Fluid–Structure Interaction) problems corresponding to incompressible fluid flows and elastic structures. First, the developed elastic structure model is verified by static and dynamic tests corresponding to a simple cantilever beam. The simulation results are compared with analytical and other researchers׳ numerical solutions. Then, the structure model is carefully coupled with a fluid model comprising of the so-called PNU-MPS (Pusan-National-University-modified Moving Particle Simulation) method and several recently developed enhanced schemes. The coupled fluid–structure method is applied to a dam break with an elastic gate and a violent sloshing flow with a hanging rubber baffle. The results of simulations are compared with those of the experiments by Antoci et al. (2007) and Idelsohn et al. (2008).     

Nonlinear sound and structure interaction in a fluid–filled flexible waveguide

In this study, a 2-D infinite flexible waveguide is considered. The waveguide carries a weakly nonlinear acoustic fluid. It is bounded on one side by a weakly nonlinear flexible membrane and the other side is rigid. The infinite waveguide is driven at the origin by a piston oscillating at a single frequency. However, we focus only on the positive side of the piston. As the coupled waves propagate in the membrane and the fluid, the modal interactions lead to resonances and beats which form the main focus of this work. A regular perturbation method is used to derive the linear and the quasilinear order equations which are then solved. At the linear order, the primary wavenumbers are solved for and the modes are found to be non-orthogonal because of the flexible membrane. Only the propagating waves are included in the analysis. Both self-mode and cross-mode interactions of the planar and the non-planar modes are considered. The novelty of this work lies in obtaining conditions and the closed form solutions for the resonances and beats along the spatial coordinate. It is found that the self-mode interactions lead to beats only. And in the self-mode interactions, the coupled planar mode plays an important role. On the other hand, the cross-mode interactions can lead to either resonances or beats.     

Development of a hybrid model based on mesh and meshfree methods and its application to fluid–elastic structure interaction for free surface waves

In this paper, a hybrid scheme, Fluid–Fluid–Elastic Structure (FFES) model was developed in the time domain to address the wave breaking impact on the structure. The model is developed based on the partitioned approach with different governing equations that describe various regions of the model domain. The fluid–fluid model denotes that two different fluid models were used to describe fluid in the actual physical domain. The method is a physics-based approximation to reduce the computational time, i.e. in the far-field inviscid fluid (fully nonlinear potential flow theory model), and near to the structure, viscous fluid (Navier Stokes model) is used. The coupled model then interacts with the elastic structure (based on Euler–Bernoulli beam theory). The system of equations is strongly coupled both in space and time. The Fluid–Fluid coupling uses an implicit predictor–corrector scheme, and the fluid–structure coupling works based on an iterative scheme. This approach makes the method more robust and for future extension. Three different possibilities for introducing the coupling was identified and implemented. The model was validated against results from the analytical solution and literature. The method proposed is a reliable, robust, and efficient alternative for simulating fluid–structure interaction problems.     

Phase dynamics of effective drag and lift components in vortex-induced vibration at low mass–damping

In this work, we investigate the dynamics of vortex-induced vibration of an elastically mounted cylinder with very low values of mass and damping. We use two methods to investigate this canonical problem: first we calculate the instantaneous phase between the cylinder motion and the fluid forcing; second we decompose the total hydrodynamic force into drag and lift components that act along and normal to, respectively, the instantaneous effective angle of attack. We focus on the phase dynamics in the large-amplitude–response range, consisting of the initial, upper and lower “branches” of response. The instantaneous phase between the transverse force and displacement shows repeated phase slips separating periods of constant, or continuous-drifting, phase in the second half of the upper branch. The phase between the lift component and displacement shows strong phase locking throughout the large-amplitude range – the average phase varies linearly with the primary frequency – however the modulation of this phase is largest in the second half of the upper branch. These observations suggest that the large-amplitude–response dynamics is driven by two distinct limit cycles – one that is stable over a very small range of reduced velocity at the beginning of the upper branch, and another that consists of the lower branch. The chaotic oscillation between them – the majority of the upper branch – occurs when neither limit cycle is stable. The transition between the upper and lower branches is marked by intermittent switching with epochs of time where different states exist at a constant reduced velocity. These different states are clearly apparent in the phase between the lift and displacement, illustrating the utility of the force decomposition employed. The decomposed force measurements also show that the drag component acts as a damping factor whereas the lift component provides the necessary fluid excitation for free vibration to be sustained.