Fully-coupled Fluid-structure Interaction Research Articles

A monolithic one-velocity-field optimal control formulation for fluid–structure interaction problems with large solid deformation

In this article, we formulate a monolithic optimal control method for general time-dependent Fluid–Structure Interaction (FSI) systems with large solid deformation: we consider a displacement-tracking type of objective with a constraint of the solid velocity, and tackle the time-dependent control problems by a piecewise-in-time control method; we cope with the large solid displacement using a one-velocity fictitious domain method, and solve the fully-coupled FSI and the corresponding adjoint equations in a monolithic manner. The proposed method is implemented in open-source software package FreeFEM++ and assessed by three numerical experiments, in the aspects of stability of the numerical scheme for different regularisation parameters, and efficiency of reducing the objective function with control of the solid velocity.

Passive concentration dynamics incorporated into the library IB2d, a two-dimensional implementation of the immersed boundary method

In this paper, we present an open-source software library that can be used to numerically simulate the advection and diffusion of a chemical concentration or heat density in a viscous fluid where a moving, elastic boundary drives the fluid and acts as a source or sink. The fully-coupled fluid-structure interaction problem of an elastic boundary in a viscous fluid is solved using Peskin’s immersed boundary method. The addition or removal of the concentration or heat density from the boundary is solved using an immersed boundary-like approach in which the concentration is spread from the immersed boundary to the fluid using a regularized delta function. The concentration or density over time is then described by the advection-diffusion equation and numerically solved. This functionality has been added to our software library, IB2d, which provides an easy-to-use immersed boundary method in two dimensions with full implementations in MATLAB and Python. We provide four examples that illustrate the usefulness of the method. A simple rubber band that resists stretching and absorbs and releases a chemical concentration is simulated as a first example. Complete convergence results are presented for this benchmark case. Three more biological examples are presented: (1) an oscillating row of cylinders, representative of an idealized appendage used for filter-feeding or sniffing, (2) an oscillating plate in a background flow is considered to study the case of heat dissipation in a vibrating leaf, and (3) a simplified model of a pulsing soft coral where carbon dioxide is taken up and oxygen is released as a byproduct from the moving tentacles. This method is applicable to a broad range of problems in the life sciences, including chemical sensing by antennae, heat dissipation in plants and other structures, the advection-diffusion of morphogens during development, filter-feeding by marine organisms, and the release of waste products from organisms in flows.

Linear vs non-linear analysis on self-induced vibration of OTEC cold water pipe due to internal flow

This paper presents analytical and numerical analyses on self-induced vibration of Ocean Thermal Energy Conversion (OTEC) Cold Water Pipe (CWP) for a 100 MW-net OTEC power plant. The CWP is described as a vertically-hanged, top-tensioned riser subjected to internal flow effect (IFE) and ambient fluid effects (added mass and drag force). In the analytical analysis, two definitions of the drag force equation in the frequency-domain term and time-domain term are considered yielding a linear differential equation and a non-linear differential equation. The stability is assessed by discretizing the equations using Frobenius method and Galerkin Method and then plotting its eigenfrequencies or its eigenvalues in an Argand diagram. Separately, a fully-coupled fluid-structure interaction is carried out in a numerical simulation for particular cases. The scantlings of the riser are chosen from the available size of Fiber Reinforced Plastic (FRP) pipe in a manufacturer and varied accordingly for future production capacity development. The riser is pinned at the top and mounted at the bottom. Results indicate that the predicted critical velocity in the time domain is averagely 20% higher compared to the frequency domain. The effect of the clump weight on the critical velocity is more significant for light material compared with relatively high-density material.

3D design and numerical simulation of a check-valve micropump for lab-on-a-chip applications

In this paper, we concentrated on designing and simulation of check-valve micropump for on-chip applications. A series of simulations were carried out by using 3D two-way fully-coupled fluid structure interaction analysis in combination with Arbitrary Lagrangian-Eulerian (ALE) method to understand pumping chamber and inlet/outlet micro check-valves. After extraction of characteristic equations of each component, micropump main equation is solved to find time-domain pumping chamber pressure. Then, Effects of actuation amplitude and frequency on micropump’s flow rate were studied for different chamber sizes from 2 mm to 4 mm. In addition, the effect of backpressure on micropumps’ flow rate was evaluated. Using this method of simulation helps the researchers to estimate performance of micropump before initiating fabrication process.

Prediction of aeroelastic response of bridge decks using artificial neural networks

The assessment of wind-induced vibrations is considered vital for the design of long-span bridges. The aim of this research is to develop a methodological framework for robust and efficient prediction strategies for complex aerodynamic phenomena using hybrid models that employ numerical analyses as well as meta-models. Here, an approach to predict motion-induced aerodynamic forces is developed using artificial neural network (ANN). The ANN is implemented in the classical formulation and trained with a comprehensive dataset which is obtained from computational fluid dynamics forced vibration simulations. The input to the ANN is the response time histories of a bridge section, whereas the output is the motion-induced forces. The developed ANN has been tested for training and test data of different cross section geometries which provide promising predictions. The prediction is also performed for an ambient response input with multiple frequencies. Moreover, the trained ANN for aerodynamic forcing is coupled with the structural model to perform fully-coupled fluid–structure interaction analysis to determine the aeroelastic instability limit. The sensitivity of the ANN parameters to the model prediction quality and the efficiency has also been highlighted. The proposed methodology has wide application in the analysis and design of long-span bridges.

Simultaneous vortex- and wake-induced vibration suppression of tandem-arranged circular cylinders using active feedback control system

This paper deals with the active flow-induced vibration (FIV) suppression of two identical tandem-arranged circular cylinders at a low Reynolds number of Re=100. The adopted control system employs fuzzy PID controller in which the desired control force is computed based on the cylinder displacement amplitude, and applied transversely for effective attenuation of flow-induced instabilities in both transverse and streamwise directions. Moreover, the effect of FIV suppression of each cylinder on the response amplitude of other one, and the simultaneous vibration reduction of both cylinders are investigated based on fully-coupled fluid-structure interaction (FSI) simulations. The rigid body motion equations in streamwise and transverse directions are incorporated into the computational fluid dynamics solver to treat the coupling which exists between the fluid flow and cylinders movement. Next, in the utilized co-simulations, the active fuzzy PID controller implemented in Matlab/Simulink is coupled with the FSI oscillator model constructed in computational fluid dynamics solver package. It was shown that, the sudden suppression of the upstream cylinder vibration causes quick distortion in the flow field around the rear cylinder, and consequently, its steady-state response amplitude is destabilized and experiences transient fluctuations once again. On the contrary, the decrease in the transverse oscillation of the downstream cylinder leaves no sensible effect on the vibration of upstream cylinder. In particular, the active control system effectively reduces the transverse displacement amplitudes of upstream and downstream cylinders by as much as 99.9% and 98.7%, respectively, for Vr=5.5, while the corresponding values are 99.8% and 99.7% for Vr=7.5. This superb performance of active FIV control systems is mainly due to de-synchronization-type action in which the vortex shedding frequency is deviated from the oscillator natural frequency. Lastly, it is demonstrated that the vortex shedding patterns for uncontrolled cylinders, which primarily depend on reduced velocity, are turned very similar to that of the stationary cylinders after adopting the fully active control systems.

Dynamics of a squid-inspired swimmer in free swimming

The untethered swimming performance of a two-dimensional squid-inspired swimmer is studied. Our model includes fully-coupled fluid-structure interaction and an idealized activation algorithm that drives periodic shape change of the body. We present results of both escape jetting via a single deflation-coasting motion and long-distance swimming via repeated inflation-deflation cycles. In both cases added-mass-related force is found to contribute significantly to thrust generation. Moreover, we find that the increase of the jet speed and oscillation frequency leads to higher swimming velocity. This, however, is achieved at the cost of reduced propulsion efficiency (i.e. higher cost of transport). During long-distance swimming, the system experiences three successive stages, acceleration, steady-state swimming, and off-track swimming caused by symmetry-breaking instability in the wake. Associated with these stages, three wake patterns are observed, nozzle-vortex-dominated wake, transit wake, and asymmetrical wake.

Slipper Surface Geometry Optimization of the Slipper/Swashplate Interface of Swashplate-Type Axial Piston Machines

The slipper/swashplate interface, as one of the three main lubricating interfaces in swashplate type axial piston machine, serves both a sealing function and a bearing function while dissipating energy into heat due to viscous friction. The sealing function prevents the fluid in the displacement chamber from leaking out through the gap to the case, and the bearing function prevents the slipper from contacting to the swashplate. The challenge of the conventional slipper/swashplate lubricating interface design is to rely on the tribological pairing self-adaptive wearing process to find a slipper surface profile that fulfills the bearing function. However, the resulted slipper surface profile from uncontrollable wearing process is not necessarily able to achieve good energy efficiency. This article proposes a novel slipper design approach that overcomes this challenge by adding a quadratic spline curvature to the slipper running surface which eliminates the wear while keeping good efficiency. A fully-coupled fluid-structure and thermal interaction model is used to simulate the performance of the slipper/swashplate interface. A computationally inexpensive optimization scheme is used to find the desired slipper design. This article presents the simulation methodology, the optimization scheme, the full factorial simulation study results, and the optimized slipper running surface.

Efficient FSI solvers for multiple-degrees-of-freedom flow-induced vibration of a rigid body

Flow-induced vibration (FIV) of a bluff body is a complex fluid-structure interaction (FSI) problem, for which analytical solutions generally don’t exist. Therefore, such problems generally need to be examined with experimental methods or computational simulations. Researchers have developed various numerical methodologies to solve FSI problems using either conforming or non-conforming grid methods. However, these methods are not always ideal for flow-induced vibration problems, as they can be computationally expensive or generate low accuracy solutions, especially for the cases with large body displacements. FIV problems often require long simulation times because, for a given parameter set, the transient flow solution time can be long and generally at least 10 oscillation cycles are required to simulate the representative long term behaviour. Thus, to gain a clear understanding and enhance knowledge of FIV of a bluff body, it is advantageous to have an efficient numerical methodology. We have developed two efficient fully-coupled FSI solvers to accurately predict the FIV of an elastically mounted bluff body and a tethered bluff body. These FSI solvers were developed based on the widely used open-source CFD package OpenFOAM. In these solvers, the fluid flow was modelled in a reference frame attached to the centre of mass of the solid body, so that a non-deforming grid can be employed. A predictor-corrector iterative method was used to enable strong coupling between the solid motion and the fluid flow. Each of the FSI solvers was validated against previously reported investigations. While efficient, the limitation of these FSI solvers is that they can only be used to examine the nature of FIV of a single, rigid bluff body.

Numerical study of a membrane-type micro check-valve for microfluidic applications

In this paper, we present a method to simulate membrane-type micro check-valve using finite element method with fluid structure interaction formulation. The designed micro check-valve which is analogue of semiconductor device, diode, allows the fluid to pass in forward-mode and blocks it in reverse mode. To have a better understanding on the valve design we also studied the effect of design dimensions on the valve performance. Our study shows the valve flow rate-pressure curve is similar to diode current–voltage characterization curve. A series of simulations were carried out by using two-way fully-coupled Fluid Structure Interaction (FSI) analysis. Using Arbitrary Lagrangian–Eulerian (ALE) method in combination with high viscosity region instead of solid valve-seat enables the designer to overcome simulations difficulties and reduces the amount of calculation time by not considering the contact phenomenon of the membrane and the valve seat. The results show the valve can withstand pressures of up to 11 kPa in reverse-mode regardless of membrane’s hole-size and length of chamber-inlet. Also, chamber-inlet size has high effect on valve opening threshold point in a way that increment of chamber-inlet area will reduce opening threshold point and vice versa.

Numerical modeling and analysis of heat transfer for floatation nozzle with a flexible substrate

Floatation nozzle is employed to guide the flexible substrate without contact in simultaneous double-sided coating. The deformation of the flexible substrate is significant to the flow and thermal fields. The heat transfer for floatation nozzle with a flexible substrate is studied in this paper. A fully-coupled fluid-structure interaction numerical model is developed to investigate the heat transfer characteristics and deformation for floatation nozzle with a flexible substrate. The fluid domain is updated by diffusion-based smoothing dynamic mesh formulation that is fully coupled to the deformation of the flexible substrate. The deformation profile of flexible substrate coupled to fluid domain is approximated by cosine series, and the coefficients in cosine series are calculated by Galerkin least square method. The steady state solutions of floatation nozzle with a flexible substrate can be obtained by a pseudo transient approach. The numerical results show that the deformation of flexible substrate changes the relative magnitude of potential core length and nozzle-to-plate distance. The size increase, position move and disappear of recirculation bubbles of flexible substrate change the streamline, turbulence intensity, temperature distributions. Three peaks of heat transfer coefficient for rigid substrate are observed and the mechanisms are elucidated. The average heat transfer coefficient of flexible substrate is larger than that of rigid substrate, although the maximum heat transfer coefficient of flexible substrate is smaller. Furthermore, a significant decrease of centerline pressure of flexible substrate is observed. Reynolds number and inlet width are the most significant parameters influencing the flow and thermal fields.

The Perfectly Matched Layer absorbing boundary for fluid–structure interactions using the Immersed Finite Element Method

In this work, a non-reflective boundary condition, the Perfectly Matched Layer (PML) technique, is adapted and implemented in a fluid–structure interaction numerical framework to demonstrate that proper boundary conditions are not only necessary to capture correct wave propagations in a flow field, but also its interacted solid behavior and responses. While most research on the topics of the non-reflective boundary conditions are focused on fluids, little effort has been done in a fluid–structure interaction setting. In this study, the effectiveness of the PML is closely examined in both pure fluid and fluid–structure interaction settings upon incorporating the PML algorithm in a fully-coupled fluid–structure interaction framework, the Immersed Finite Element Method. The performance of the PML boundary condition is evaluated and compared to reference solutions with a variety of benchmark test cases including known and expected solutions of aeroacoustic wave propagation as well as vortex shedding and advection. The application of the PML in numerical simulations of fluid–structure interaction is then investigated to demonstrate the efficacy and necessity of such boundary treatment in order to capture the correct solid deformation and flow field without the requirement of a significantly large computational domain.

Fully-coupled fluid-structure interaction simulation of the aortic and mitral valves in a realistic 3D left ventricle model.

In this study, we present a fully-coupled fluid-structure interaction (FSI) framework that combines smoothed particle hydrodynamics (SPH) and nonlinear finite element (FE) method to investigate the coupled aortic and mitral valves structural response and the bulk intraventricular hemodynamics in a realistic left ventricle (LV) model during the entire cardiac cycle. The FSI model incorporates valve structures that consider native asymmetric leaflet geometries, anisotropic hyperelastic material models and human material properties. Comparison of FSI results with subject-specific echocardiography data demonstrates that the SPH-FE approach is able to quantitatively predict the opening and closing times of the valves, the mitral leaflet opening and closing angles, and the large-scale intraventricular flow phenomena with a reasonable agreement. Moreover, comparison of FSI results with a LV model without valves reveals substantial differences in the flow field. Peak systolic velocities obtained from the FSI model and the LV model without valves are 2.56 m/s and 1.16 m/s, respectively, compared to the Doppler echo data of 2.17 m/s. The proposed SPH-FE FSI framework represents a further step towards modeling patient-specific coupled LV-valve dynamics, and has the potential to improve our understanding of cardiovascular physiology and to support professionals in clinical decision-making.

Comprehensive Evaluation of Fast-Response, Reynolds-Averaged Navier–Stokes, and Large-Eddy Simulation Methods Against High-Spatial-Resolution Wind-Tunnel Data in Step-Down Street Canyons

Three computational fluid dynamics (CFD) methods with different levels of flow-physics modelling are comprehensively evaluated against high-spatial-resolution wind-tunnel velocity data from step-down street canyons (i.e., a short building downwind of a tall building). The first method is a semi-empirical fast-response approach using the Quick Urban Industrial Complex (QUIC-URB) model. The second method solves the Reynolds-averaged Navier–Stokes (RANS) equations, and the third one utilizes a fully-coupled fluid-structure interaction large-eddy simulation (LES) model with a grid-turbulence inflow generator. Unlike typical point-by-point evaluation comparisons, here the entire two-dimensional wind-tunnel dataset is used to evaluate the dynamics of dominant flow topological features in the street canyon. Each CFD method is scrutinized for several geometric configurations by varying the downwind-to-upwind building-height ratio ( $$H_\mathrm{d}/H_\mathrm{u}$$ ) and street canyon-width to building-width aspect ratio (S / W) for inflow winds perpendicular to the upwind building front face. Disparities between the numerical results and experimental data are quantified in terms of their ability to capture flow topological features for different geometric configurations. Overall, all three methods qualitatively predict the primary flow topological features, including a saddle point and a primary vortex. However, the secondary flow topological features, namely an in-canyon separation point and secondary vortices, are only well represented by the LES method despite its failure for taller downwind building cases. Misrepresentation of flow-regime transitions, exaggeration of the coherence of recirculation zones and wake fields, and overestimation of downwards vertical velocity into the canyon are the main defects in QUIC-URB, RANS and LES results, respectively. All three methods underestimate the updrafts and, surprisingly, QUIC-URB outperforms RANS for the streamwise velocity component, while RANS is superior to QUIC-URB for the vertical velocity component in the street canyon.

Sharp interface immersed boundary methods and their application to vortex-induced vibration of a cylinder

The sharp interface immersed boundary method is assessed for suitability and accuracy in simulating flow-induced vibration, specifically the phenomenon of vortex-induced vibration (VIV) in the two-dimensional flow past an elastically-mounted cylinder. Inherent to immersed boundary methods are the spurious force oscillations observed when the immersed boundary moves across the underlying grid. This deficiency in immersed boundary methods is acute in flows featuring fully-coupled fluid–structure interaction, where these oscillations are fed directly back into the coupled system and have the potential to significantly affect the solution. Here, the immersed boundary method is tested and compared directly and in detail to an accurate and validated spectral-element method. The immersed boundary method performs well for the given problem, excepting a few cases, such as those featuring disordered vortex-shedding. A heuristic model is developed to analyze the frequency content of the observed spurious force oscillations and their potential to affect the global solution. A guide to the resolution required for spatial accuracy is proposed, that around 40 points should span the peak-to-peak distance of any significant oscillation.

Numerical study of rogue wave overtopping with a fully-coupled fluid-structure interaction model

For decades, researchers have been devoting efforts to revealing the physical mechanisms of rogue waves. However, research works on the interaction between rogue waves and marine structures, especially those which take into account hydroelastic effects are still not adequate (due to the fact that the wave-breaking, overturning and slamming phenomena are complex especially when hydroelasticity is considered as well as the nonlinearity of rogue waves). In this paper, the nonlinear rogue-wave overtopping phenomenon is simulated in a numerical wave tank. The simulation results are compared against the theoretical solution predicted by the dam-breaking model. Hydroelastic effects are considered by applying a fully-coupled fluid-structure interaction model. The vibration of the elastic deck is analyzed and compared against the one obtained without considering hydroelasticity. Green water events, caused by a rogue wave and a regular wave respectively, are compared to reveal the special features of rogue-wave-induced overtopping. It is found that hydroelastic effects lead to the local vibration of the deck, lower vibration frequencies through introducing the added mass effect, and make the deck deformation larger at certain moments. It is also found that green water induced by rogue waves shows asymmetry and unregularity in comparison with that induced by regular waves.

Evaluation of aerodynamic characteristics of a coupled fluid-structure system using generalized Bernoulli's principle: An application to vocal folds vibration.

In this work we explore the aerodynamics flow characteristics of a coupled fluid-structure interaction system using a generalized Bernoulli equation derived directly from the Cauchy momentum equations. Unlike the conventional Bernoulli equation where incompressible, inviscid, and steady flow conditions are assumed, this generalized Bernoulli equation includes the contributions from compressibility, viscous, and unsteadiness, which could be essential in defining aerodynamic characteristics. The application of the derived Bernoulli's principle is on a fully-coupled fluid-structure interaction simulation of the vocal folds vibration. The coupled system is simulated using the immersed finite element method where compressible Navier-Stokes equations are used to describe the air and an elastic pliable structure to describe the vocal fold. The vibration of the vocal fold works to open and close the glottal flow. The aerodynamics flow characteristics are evaluated using the derived Bernoulli's principles for a vibration cycle in a carefully partitioned control volume based on the moving structure. The results agree very well to experimental observations, which validate the strategy and its use in other types of flow characteristics that involve coupled fluid-structure interactions.

Fluid-Structure Interaction Study of Transcatheter Aortic Valve Dynamics Using Smoothed Particle Hydrodynamics.

Computational modeling of heart valve dynamics incorporating both fluid dynamics and valve structural responses has been challenging. In this study, we developed a novel fully-coupled fluid-structure interaction (FSI) model using smoothed particle hydrodynamics (SPH). A previously developed nonlinear finite element (FE) model of transcatheter aortic valves (TAV) was utilized to couple with SPH to simulate valve leaflet dynamics throughout the entire cardiac cycle. Comparative simulations were performed to investigate the impact of using FE-only models vs. FSI models, as well as an isotropic vs. an anisotropic leaflet material model in TAV simulations. From the results, substantial differences in leaflet kinematics between FE-only and FSI models were observed, and the FSI model could capture the realistic leaflet dynamic deformation due to its more accurate spatial and temporal loading conditions imposed on the leaflets. The stress and the strain distributions were similar between the FE and FSI simulations. However, the peak stresses were different due to the water hammer effect induced by the fluid inertia in the FSI model during the closing phase, which led to 13-28% lower peak stresses in the FE-only model compared to that of the FSI model. The simulation results also indicated that tissue anisotropy had a minor impact on hemodynamics of the valve. However, a lower tissue stiffness in the radial direction of the leaflets could reduce the leaflet peak stress caused by the water hammer effect. It is hoped that the developed FSI models can serve as an effective tool to better assess valve dynamics and optimize next generation TAV designs.

Neuromechanical pumping: boundary flexibility and traveling depolarization waves drive flow within valveless, tubular hearts

In this paper, we develop a neuromechanical model of pumping in a valveless, tubular heart inspired by the tunicate, Ciona savignyi. Valveless, tubular hearts are common throughout the animal kingdom. The vertebrate embryonic heart first forms as a valveless, tubular pump. The embryonic, juvenile, and adult hearts of many invertebrates are also valveless, tubular pumps. Several different pumping mechanisms have been propsed for tubular hearts, and it is not clear if all animals employ the same mechanism. We compare the flows generated by this pumping mechanisms to those produced by peristalsis using a prescribed contraction wave and to those produced by impedance pumping across a parameter space relevant to Ciona savignyi. The immersed boundary method is used to solve the fully-coupled fluid-structure interaction problem of an elastic tubular heart immersed in a viscous fluid. The FitzHugh–Nagumo equations are used to model the propagation of the action potential which initiates the contraction. We find that for the scales relevant to Ciona, both the neuromechanical pumping mechanism and peristalsis produce the strong flows observed in the tunicate heart. Only the neuromechanical model produces flow patterns with all of the characteristics reported for valveless, tubular hearts. Namely, the neuromechanical pump generates a bidirectional wave of contraction and peristalsis does not.

Lift vs. drag based mechanisms for vertical force production in the smallest flying insects

We used computational fluid dynamics to determine whether lift- or drag-based mechanisms generate the most vertical force in the flight of the smallest insects. These insects fly at Re on the order of 4–60 where viscous effects are significant. Detailed quantitative data on the wing kinematics of the smallest insects is not available, and as a result both drag- and lift-based strategies have been suggested as the mechanisms by which these insects stay aloft. We used the immersed boundary method to solve the fully-coupled fluid-structure interaction problem of a flexible wing immersed in a two-dimensional viscous fluid to compare three idealized hovering kinematics: a drag-based stroke in the vertical plane, a lift-based stroke in the horizontal plane, and a hybrid stroke on a tilted plane. Our results suggest that at higher Re, a lift-based strategy produces more vertical force than a drag-based strategy. At the Re pertinent to small insect hovering, however, there is little difference in performance between the two strategies. A drag-based mechanism of flight could produce more vertical force than a lift-based mechanism for insects at Re<5; however, we are unaware of active fliers at this scale.