Session T25: Aerodynamics: Fluid Structure Interactions, Membranes, Flutter II

Development and validation of a fully analytical model for designing pressure-compensating flow devices for drip irrigation and other applications

Design of pressure-compensating (PC) devices can be a time-consuming, expensive process. PC devices often use a flexible diaphragm whose deformation under increasing pressure proportionally raises the flow resistance, resulting in a constant flow rate. This 'Fluid-Structure Interaction' (FSI) is governed by coupled, nonlinear differential equations, which raises the computational cost of the simulating PC action. The most common alternative to this is to run time-consuming iterative design experiments. To enable rapid design-space exploration, we propose a novel 1D analytical model to simulate the entire flow-pressure response of a PC device, focusing initially on drip emitters. Each emitter feature is treated as a flow resistance depending on device geometry, material properties, pressure, and flow rate. Resistances are evaluated in series using suitable analytical expressions, before being wrapped into an iterative scheme to resolve the inherent nonlinearity of the problem. This approach's main benefit is to avoid the overhead of fully simulating the FSI by instead modeling multiple, simple features inside the emitter. We demonstrate the utility of the model by designing a new PC emitter capable of regulating flow from 40-50% lower pressures than comparable commercial products. This allows for reduced energy consumption, lowering the overall operating costs of drip irrigation.   

Piezoelectric energy harvesting from cantilevered-rectangular bluff bodies using fluid-structure interaction

Rigid rectangular bluff bodies of varying B/D ratios attached to two piezoelectric cantilevers are subjected to vortex-induced vibrations (VIV) and flutter in a suction-type wind tunnel to study the influence of different flow-induced vibrations. The cantilevered-rectangular bluff bodies were arranged in a parallel configuration to aid in vibration frequency control. Images of the vibrating cylinders were captured at high speeds and compared with the voltage levels generated as a function of incident wind speed. The ratio of natural frequency to vibration frequency proved to be an indicator of operating efficiency. The energy harvesting efficiency of the bluff bodies was also calculated and was shown to be dependent on the frequency ratio. The maximum power harvested was found to be 1.8μW. An operating limit for each bluff body of a given B/D ratio was established in terms of non-dimensional parameters such as Reynolds number (Re)-(1500-5500), Strouhal number (St)-(0.06-0.16), Dimensionless frequency (0.1-0.7), Scruton number (Sc) and reduced velocity (4-14).  Beyond the operating limit, no positive effect on the resultant voltage was observed. These results will further aid the design and development of vibration-based ambient energy harvesters.   

Bayesian Calibration for Large-Scale Fluid Structure Interaction Problems Under Embedded/Immersed Boundary Framework

Seamless integration of observation data with computational models starts to play a significant role in improving the prediction for Fluid‐Structure Interaction (FSI) problems (e.g., patient-specific hemodynamic modeling). The integration can be formulated as a Bayesian calibration problem, which has been widely applied in inverse analysis and uncertainty analysis. In this talk, we focus on Bayesian calibration for large-scale fluid-structure interaction systems that feature large structural deformations. We aim to address three major challenges: 1) observation data are noisy; 2) the FSI solvers are given as a black box, or the associated numerical methods are not differentiable (e.g., immersed/embedded boundary methods and fracture mechanics models); 3) each forward FSI evaluation is computationally expensive for real-world applications. In this regard, a new Bayesian framework built on unscented Kalman filter/inversion is developed. The approach is derivative-free and non-intrusive, and it can efficiently calibrate and provide uncertainty estimations of FSI models with noisy observation data. We demonstrate and validate the framework by successfully calibrating the model parameters of a piston problem and identifying the damage field of an airfoil under transonic buffeting.   

Dynamics of tethered membranes in inviscid flow

We study the dynamics of membranes (with stretching stiffness but zero bending stiffness) that shed vortex wakes in inviscid flows. Previous studies have focused on membranes with fixed ends, where only static deflection occurs. Here we consider instead membranes held by tethers with hinged ends, and find that a variety of unsteady large-amplitude motions, both periodic and chaotic, may occur. We characterize the dynamics over ranges of the key parameters: membrane mass density, stretching stiffness, pretension, and tether length. We find the region of instability and the small-amplitude behavior in a linearized model by solving a nonlinear eigenvalue problem. We also derive asymptotic scaling laws by considering a simplified model: an infinite periodic membrane. We find qualitative similarities among all three models in terms of the oscillation frequencies and membrane shapes at small and large values of the parameters.   

Data-driven aeroelastic modeling for control

From insect wings to wind turbines, flows over flexible structures encounter broad operating regimes that may include viscous separated flow and dynamic stall. Effective real-time control of these structures relies on accurate and efficient estimates of unsteady aeroelastic forces. Traditional models, such as Theodorsen's model, typically involve quasi-steady or idealized unsteady aerodynamic forces and do not describe transients. For rigid wings, reduced order unsteady aerodynamic models have recently been extended to include viscous effects at low Reynolds numbers. Here we further extend this modeling procedure to include the effects of a flexible wing, incorporating wing deformation in addition to the quasi-steady forces, added mass forces, and large unsteady transients due to viscous effects. We develop low order linear models based on data from direct numerical simulations of flow past a flexible wing at low Reynolds number. We demonstrate the effectiveness of these models to track an aggressive reference lift maneuver with model predictive control while constraining maximum wing deformation. This modeling procedure could enable agile control for aerodynamic systems with deforming surfaces.   

Unsteady aerodynamics of membrane wings

The ability of membrane wings to adapt their shape passively in unsteady flow conditions enables several aerodynamic advantages over rigid wings. In pursuit of a theoretical model for evaluating these benefits, a theoretical framework is developed to predict the two-dimensional membrane wing response to unsteady flow conditions in an inviscid flow. An extensible membrane of small camber is assumed, with a constant tension along its length, encountered by a vertical gust. The aerodynamic load on the airfoil is obtained using unsteady thin airfoil theory, where special consideration is given to the modeling of the wake vortices. The dynamic response and unsteady lift of the membrane wing due to arbitrarily-shaped gusts are analyzed for various values of membrane mass and tension to highlight their role in the membrane wing aeroelastic performance. The indicial lift responses are compared with known analytical functions available for rigid airfoils (e.g., Sears and Küssner functions) to assess the effect of membrane flexibility on the unsteady lift response.    

Investigating the Effect of Chord-wise Flexibility to Control Aperiodicity in the Flow-field around a Flapping Foil

Bio-inspired Flapping-wing Micro Air Vehicle (FMAV) has received significant attention in recent times due to its multi-fold applications. The present work investigates the nonlinear Fluid-Structure Interaction (FSI) of a chord-wise flexible flapping foil with surrounding unsteady flow-field at a low Reynolds number (Re = 300). The foil is modeled as an inextensible flexible filament, and heaving motion is prescribed at the leading edge. The aerodynamic loads on the foil are computed using a discrete forcing Immersed Boundary Method (IBM) based in-house FSI solver. Numerical simulations have been performed at different heave amplitudes for various flexibility values $(\gamma)$ of the foil. It is observed that the system transitions from periodicity to chaos at the heaving amplitude of $0.475$ for the rigid foil. However, when flexibility is introduced, the foil with bending rigidity, $\gamma=1.0$  shows periodic dynamics up to the heaving amplitude of $0.575$. Surprisingly, higher flexibility ($\gamma < 1.0$) advances the onset to a chaotic regime. Therefore, the proper choice of flexibility can be effective in delaying aperiodicity in the flow field. Time series analysis tools have been employed to characterize various dynamical states of the coupled FSI system.   

Self-excited aeroelastic instability of a flexible cantilever cylinder at laminar subcritical Reynolds number

Fluid-structure interaction of a flexible cantilever cylinder with the surrounding flow is ubiquitous in nature and present in many engineering systems. In particular, the FSI of a rat's whisker with low-speed airflow has gained importance in recent years due to its implications for the development of novel flow-measurement sensors. A rat's whisker interacting with airflow at laminar subcritical Reynolds numbers, (i.e., no periodic vortex shedding) has been shown to undergo sustained large-amplitude oscillations (i.e., self-excited aeroelastic instability) that carry information about the direction and magnitude of the airflow. In this work, we use high-fidelity numerical simulations to examine the aeroelastic instability of a flexible cantilever cylinder with a constant circular cross-section, as a canonical model of a whisker. Through a parametric investigation, we assess the self-excited instability of the cylinder and highlight the key aspects of the fluid-structure system. We show that the cylinder could undergo sustained oscillations when certain conditions are satisfied. The amplitude of the oscillations is found to be a function of flow velocity and the frequency of the perturbation in the flow field.   

Empirical tuning of the van der Pol wake oscillator model coupled with a 1DOF cylinder undergoing

Experimental vortex induced vibration data collected for 3 < U* < 11, m*zeta = 0.04, and Re = 4000, is used for tuning a coupled van der Pol wake oscillator and mass-spring-damper system. In the past, the coupled model is often evaluated in comparison to a small set of experimental data and fixed values for the tuning parameters are chosen for a range of reduced velocities. Rather than tuning each equation to a data set, in this study we explore the behavior of the coupled equation and its tuning parameters, including the selected stationary lift coefficient (Clo). The coupled model is evaluated over a parameter space of the nonlinear damping parameter, ε, and coupling parameter, β. Each calculated response is compared to experimental data to generate an error surface. The results show that the selected lift coefficient together with the tuning parameters enables manipulation of the maximum amplitude and range of synchronization. The error surfaces show large ranges where tuning parameters may be used to obtain a reasonable fit to experimental data. Furthermore, for each reduced velocity, there is unique set of ε and β that provide a best fit to the experimental displacement, indicating a dependance on the reduced velocity.   

Keeping the nose to the wind: key to aerodynamic stability of suspension bridges

For the past three decades significant amount of research has been conducted on aerodynamic stability of bridge girders. Current wind tunnel measurements and numerical fluid-structure-interaction computational fluid dynamics (FSI-CFD) simulations have revealed that a twin-box bridge deck obtains a higher aerodynamic stability when the bridge deck assumes a "nose-up" twist relative to horizontal when exposed to high wind speeds. From the investigations it is found that a moment coefficient having a positive value at 0° of rotation angle and a positive slope, decreasing with increasing mean angle of rotation, leads to a decrease in the reduction of aerodynamic stiffness through the Α^*₃ coefficient. This in turn ensures an increase in aerodynamic stability. Thus, a positive moment coefficient at 0° with a positive slope, decreasing with increasing mean angels of rotation, is desirable for achieving higher critical wind speeds for onset of flutter than predicted for the deck cross section being horizontal. Through this study, a flutter model is developed for a twin-box bridge deck which allows prediction of the increase of the critical wind speed for onset of flutter as function of the deck section rotation angle.   

Shape reconfiguration through origami folding boosts drag reduction

Being flexible is an effective self-protection strategy for objects exposed to strong winds; it reduces their drag through shape streamlining and reduction of their frontal area. Slender objects like sheets deform primarily through bending, but introducing a network of folds expands the accessible deformation modes. Such origami folding notably allows for large shape changes, which would drastically alter fluid loading on the system when placed in a flow. Here, we study how articulated kinematics impact reconfiguration processes in an airflow and subsequent drag reduction, starting with a single waterbomb origami unit. We show that its ability to fold into a very compact object exacerbates drag reduction, to the point that fluid loading saturates in strong flows and no longer depends on flow speed. We investigate the underlying fluid/structure mechanisms through a combination of experiments and theoretical modeling, to evaluate in particular the influence of the crease pattern and the origami mechanical properties. Results pave the way to understand the impact of creases on fluid-elastic processes. Such creases are ubiquitous in nature (as in leaves and insect wings) and synthetic thin-walled structures, which are systems brought to interact with a fluid environment.   

Can sheet cuttings (kirigami) control flow-induced deformation?

Kirigami, which is the Japanese art of paper cutting, has emerged as a promising design tool to produce surfaces morphing into sophisticated shapes and with programmable mechanical properties. Those features can be tuned through the network of cuts, offering levers to control the way the object deforms in a fluid flow. Here, we study the deformation a kirigami sheet in a water cross-flow. Under fluid loading, the structure expands through the opening of pores that let fluid through, thus acting as a poro-elastic surface. We characterize experimentally and theoretically the relation between the cuts geometry and the resulting shape transformation. We show that the macroscopic morphing is dictated by interactions with fluid at the local scale of the pores, whose geometry changes in turns with the sheet elongation. Understanding those multi-scale couplings provides a novel control strategy for shape-shifting in flows through the reverse-engineering of cut motifs.