Session Z03: Aerodynamics: Fluid-Structure Interactions, Membranes, Flutter III

Fluid-structure interaction of a phononic bi-layer flat plate with an aerodynamic flow

Passive, adaptive flow control strategies offer significant promise in overcoming the challenges associated with active flow control. We explore the fluid structure interaction (FSI) of flexible phononic materials towards this aim. Phononic materials are architected materials with frequency-dependent characteristics that arise from their periodic structure. In this study, we investigate the FSI between an aerodynamic flow and a phononic material defined by a bi-layer flat plate. The flat plate is modeled as a clamped-clamped linear Euler-Bernoulli beam with a periodic mass and stiffness distribution throughout the entire length of the beam. We perform high-fidelity 2D numerical FSI simulations of unsteady flow past the bi-layer flat plate at Re=500 and an angle of attack of 15 degrees. The nonlinear simulations are initiated from a formal base state of the FSI system. The analysis will focus on the ensuing limit cycle interplay between the plate vibrations and the vortex-shedding process. The effect of various phononic material parameters (equivalent mass, equivalent stiffness, periodicity) on the nature of the limit cycle will be characterized. A global stability analysis will then be employed to mechanistically explain the system's departure from the base state, with a detailed analysis of the nonlinear simulation data used to investigate the long-time nonlinearly saturated dynamics. In this process, we will also identify the relevant structural parameters that lead to performance benefits/detriments (lift,drag) of the phononic flat plate as compared to the baseline rigid flat plate flow configuration.   

Reconfiguring it out: how flexible structures withstand high fluid forces

Plants and other flexible structures reduce the drag they experience when subject to high velocity flows. Plants streamline their bodies and reduce their projected area to the flow, in a process known as reconfiguration. The drag reduction results from changes in the topology of the vortex ring that forms behind the reconfiguring object. Here, we study the evolution of the vortex ring and its effects on the transient drag force behind flexible disks. Radial incisions are made to the disks to allow them to reconfigure symmetrically without buckling. We quantify the reduction in the projected area of the disks from deformation measurements and analyse the vortical structures behind the disks using time-resolved particle image velocimetry. We relate these quantities to the transient drag force measured with a high-resolution load cell. We also provide a prediction of the drag coefficient for disks with different flexibilities based on the projected area and vortex topology. These findings enable us to better understand the behavior of reconfiguring plants and design structures that withstand high fluid loading.

    

Aerodynamic stability of a wind turbine section including dynamic stall and dynamic inflow

The dynamics of a rigid airfoil section under aerodynamic forces is a classic aero-elastic problem, where: 1) the effects of unsteady aerodynamics and induced velocities are often neglected; and, 2) the dynamics of the section is simplified by neglecting effects related to offsets of the center of mass, elastic center, shear center and principal axes.

In this work, we include a dynamic stall model and a dynamic inflow model in state-space form. The dynamic inflow model accounts for slow variation of induced velocities in wind energy applications. The airfoil section is modeled as a rigid body, but the location of the center of mass, shear center, elastic axis, and aerodynamic center are parameters of the model, and the direction of the principal axes of inertia and elasticity are not assumed to coincide with the chord axis. 

We present the equations of the aero-elastic state space model and linearize them. We analyse the problem in time and frequency domain and study the parameters affecting the stability of the airfoil section. In particular, we study the influence of the locations of the different structural points and the point where the angle of attack is defined. The stiffnening and damping contributions from the aerodynamics are assessed. 

    

Spiral dynamics of a freely falling sphere with flexible filaments

The passive structures located behind a bluff body change the wake characteristics and fluid-dynamic forces of the bluff body. For example, a splitter plate or hairy filaments attached to the rear of a circular cylinder reduce the drag force by suppressing wake instability. In this study, we investigate the effects of flexible filaments attached to the rear of a freely falling sphere by changing the length and number of filaments. According to our experiments, the filaments reduce the vertical falling speed of the sphere, compared with the sphere without filaments. The flexible filaments of a freely falling body induce the increase in net drag along the vertical direction, which is in contrast to the passive structures behind a fixed body that reduce drag. The trajectory of the falling sphere becomes more spiral because of the wavy deformation of the flexible filaments, thereby increasing the total length of the falling trajectory.   

Data-Driven Modeling of Unsteady Aerodynamics for Fluid-Structure Interaction

Compliant structures are prominent in aerodynamic design and require quick and accurate unsteady aerodynamic models to predict their behavior. The state of the art consists of coupled fluid-structural simulation methods that are too numerically expensive for rapid structural stability assessment. Piston theory presents a simple, inexpensive aerodynamic model to predict the pressure fluctuations arising on a deforming surface, but is accurate only for high-speed flow regimes. This work investigates the use of dynamic mode decomposition (DMD) to develop unsteady aerodynamic models that remain numerically inexpensive yet offer accurate predictions in subsonic and low-supersonic flow regimes. DMD is used to develop a low-rank approximation to the difference between piston theory predicted pressure fluctuations and full-model predictions. Elements of aeroacoustic theory are used to inform the model. A canonical panel flutter scenario is considered as the motivating example. An improved unsteady aerodynamic model of the flow over a deforming panel is developed from a subset of the learned modes from DMD. The ability of the improved model to predict the stability of the panel configuration is presented, and the framework to develop models for alternate flow configurations is discussed.   

Vortex dynamics and aerodynamic performance of highly deformable flapping wings

Flexible wings show great potential to increase the flight performance of nature's fliers and human-engineered flying vehicles. However, the performance gain is only achieved if the proper aeroelastic conditions are met. If the flexibility is either too high or too low the aeroelasticity can impact the lift production negatively.

In this study, we present a flapping membrane wing platform and identify optimal aeroelastic parameters to achieve the highest lift production or most efficient hovering flight experimentally. Additional deformation and flow field measurements are conducted, to relate the fluid-structure interaction of the passively deforming membrane with the force production on the wing. At high wing deformations, the flow separates over the high membrane curvature instead of the wing's leading edge. At lower angles of attack, the local angle at the leading edge becomes negative and we observe the formation of a vortex on the pressure side of the wing. These two vortical structures are unique to the membrane wings. Their position relative to the wing is unfavourable which leads to dramatic losses in lift production and hovering efficiency.   

Elastically mounted cylinder undergoing 1DOF vortex induced vibrations near profiled walls

Vortex-induced vibrations near planar and curved solid walls are investigated for a 1DOF elastically mounted rigid cylinder of diameter D. The experimental system parameters are m*ζ = 3.08, 2.5 ≤ U* ≤ 11.5, and 0.0 ≤ e/D ≤ 1.0, 1600 < Re_D  < 7500,  with m*ζ  the non-dimensional mass damping of the system, U* the reduced velocity, Re_D the Reynolds number based on D, and e the neutral cylinder-wall gap. Considered are baseline (no wall), planar wall, and scour wall profiles mimicking riverbeds. The presence of a wall has a major impact on the structural response.  The extent of the lock-in region, 4.8 < U* < 8.5, the peak amplitude, A* = 0.7, and peak C_L = 0.87 for the baseline increases by more than 20% (4.5 < U* < 10; A* = 0.85; C_L = 1.0). Within the initial branch, the vortex shedding frequency is undetectable in the force and position response spectra, indicating fundamental changes in the vortex formation dynamics compared to the baseline.  The excitation of inter-harmonic and subharmonic frequencies in the response spectra suggest that the wall and its shape reinforce nonlinear interactions with the wake flow.    

Forcing categorization and identification for fluid-structure interaction

Flow-induced structural vibration is a complicated and often undesirable phenomena. There are a variety of physical mechanisms that lead to vibration, which often makes cause and effect relationships difficult to determine. Here we identify three main categories of aerodynamic forcing mechanisms. The first is external forcing related to upstream disturbances, such as wind gusts or wakes of upstream objects. The second mechanism is termed ``self forcing'', and is related to unsteady aerodynamics caused by the flow over the object itself. Examples include vortex shedding, separated flow, and turbulence. The third mechanism is motion-dependent forcing, in which the unsteady forces are caused specifically by the motion of the structure. The latter mechanism is often termed ``flutter'' and is characterized by negative aerodynamic damping. Example experimental measurements from an axial compressor will be used to demonstrate forcing identification: the temporal response characteristics of blade vibration inform characterization of the causal forcing mechanism.   

Aerodynamics of porous airfoils with nonlinear Forchheimer boundary condition

Owls have aero-acoustic advantages to fly silently due to the flexibility and porosity of their feathers. Researchers have shown that modeling the trailing edge with bio-inspired features is very effective for noise suppression. However, noise reduction and aerodynamic performance are in competition.

This study investigates the pressure distribution over porous airfoils in an incompressible flow. A Darcy-type porosity condition on the airfoil surface provides a Fredholm integral equation that can be solved exactly for Hölder-continuous porosity distributions. However, the generated lift predicted by the model diverges from the experimental data for highly-porous airfoils. To improve the mathematical model, we replace the linear Darcy porosity condition with the nonlinear Forchheimer boundary condition. The result indicates that the Forchheimer boundary condition performs better than the Darcy condition; the theoretical lift prediction for a porous SD7003 airfoil demonstrates better agreement with the available experimental data. The methodology will be combined with previous work on the aeroacoustics of a porous airfoil with a Forchheimer boundary condition to address the conflicting aims of improving aerodynamic performance but reducing unwanted aeroacoustic emissions.