Pitching Plate Research Articles

Analyses of aerodynamic forces on a three-dimensional pitching plate above surface waves

Analyses of aerodynamic forces on a three-dimensional pitching plate above surface waves

Small-amplitude waves in a floating poroelastic plate forcing by vertical pitching plate

The linear two-dimensional problem of flexural-gravity waves generated by an oscillating rigid plate build-in a floating poroelastic plate is studied. The problem is coupled. The plate deflections and the hydrodynamics loads are determined at the same time. The liquid under the poroelastic plate is inviscid and incompressible. Dynamics of the floating plate is described by a thin elastic plate equation. Porosity of the floating plate is taken into account only through the liquid flux into the plate. The velocity of the inflow is assumed to be governed by Darcy's law being proportional to the hydrodynamic pressure at the plate/liquid interface. Two cases of the oscillating rigid plate with and without its part in the liquid are considered. The problems are solved by the Fourier transform method for non-zero porosity and by the vertical mode method for elastic plates with zero porosity. The deflection and strain distributions are analyzed depending on the excitation frequency and the porosity. Two models of floating plate porosity, where the hydrostatic pressure is included into Darcy's law (Zavyalova's model) and excluded (Meylan's model), are compared. Plate porosity induces damping to the system. It is shown that the damping rate is non-monotonic with respect to the plate porosity.

Lift generation mechanism of the leading-edge vortex for an unsteady plate

The lift generation mechanism of leading-edge vortex (LEV) in the case of a pitching and plunging plate is studied using an experimental approach and the improved discrete vortex method in this research. A formation condition of the secondary structure is introduced into the traditional discrete vortex method to compensate for the shortcomings in the simulation of the viscous effect between LEV and plate. The simulation of the secondary structure helps the improved method perform better in flow-field reconstruction and lift prediction. Accordingly, the lift generation mechanism of the LEV and influence of the secondary structure are studied. The lift contribution of the vortex structure is isolated and linearly decomposed into two parts according to sources of flow field: the quasi-potential flow part and the vortex-induced flow part. The vortex lift is defined as the lift contribution of the vortex structure in vortex-induced flow, which gives a new insight into the production of lift of the LEV. The lift generation mechanism through the discrete vortex method is verified and extended in viscous flow through experimental measurement. In addition, a vortex lift indicator based on the reverse flow of the LEV is proposed to examine the change of vortex lift in experimental measurement. The flow mechanism for the decline of vortex lift for different maximum effective angles of attack is revealed based on the vortex lift indicator. Furthermore, for the LEV-dominating flow, the indicator can also be applied in estimating the maximum value and corresponding critical time of overall lift in experiments.

Experimental study on passive plate pitching and coherent structures in a square channel by TR-PIV

The interaction of plate pitching and vortex may damage the accumulator isolation passive valve in nuclear power plant. The plate pitching and turbulent flow in a square channel were studied by high-speed camera (HSC) and time-resolved particle image velocimetry (TR-PIV) at Reynolds numbers (Re) from 1474 to 58952.The plate angle captured by HSC were analyzed by edge detection algorithm. The plate is inclined in hydraulic equilibrium without oscillation when Re is less than 14738. The plate pitching start to be periodic at Re = 22107, and then the periodicity weakens with Re increasing from 22,107 to 51583. The time-averaged pitching angle increases from 0.08467 rad to 1.454 rad with Re increasing from Re = 1474 to Re = 51583. The standard deviation of pitching angle increases from zero with Re less than 14,738 to 0.1294 rad at Re = 22107, and then it decreases to 0.006536 rad at Re = 51583. The peak frequency of plate pitching is the same as that of turbulent flow extracted from the power spectral density of instantaneous velocity downstream of the pitching plate, indicating the passive plate pitching is determined by turbulence. The plate pitching is driven by lift force torque due to the leading-edge-vortex shedding from the pitching plate.The interaction between passive plate pitching and fluid generates complicated turbulence. The time-averaged flow structures are typical shear-flow due to small plate inclination angle without oscillation when Re is less than 14738. The Reynolds stresses are highly enhanced in the shear flow. At Re = 22107, the time-averaged flow structures behave as vortex bubble over the plate and shear flow surrounding the plate, and the Reynolds stresses downstream of the plate are obviously enhanced by shedding vortices from the plate. With Re increasing from 22,107 to 58952, the time-averaged vortex bubble becomes smaller and shifts downwards to the plate trailing end, while the Reynolds stresses with similar distribution patterns decrease fast. The peak frequency of vortex shedding increases with Re increasing. The large spatial and temporal length scales are induced by shear flow at low Re less than 14738. The large length scales are dominated by von Kármán street shedding from the plate at Re from 22,107 to 58952, which are identified by proper orthogonal decomposition (POD) analysis, because the first two modes are the same mode of von Kármán street with a phase difference.The experimental work improves understandings of plate-fluid-interaction of the isolation passive valve and supports validations of numerical simulations.

Injection and Escape: A new model on the thrust generated by a thin pitching plate

We have proposed a physical model to describe the underlying physics behind the drag or thrust produced by a pitching panel in a uniform stream. Over the clockwise and counterclockwise pitching motions, the model categorizes Injection and Escape kinematic phases. The former estimates the total fluid volume gathered at the trailing edge, and the latter amount to the fluid volume fenced by the plate reaching the trailing edge. To verify our proposed model, we have performed three-dimensional simulations using an immersed boundary-based numerical code for the flow past a thin pitching plate at a Reynolds number of Re = 1000 for the aspect range of 0.54≤AR≤16 at maximum pitching angle of θmax=5°,15° with pitching frequency St=0.5,1. Our model reveals that the plate generates a net thrust in a pitching cycle when Injection dominates Escape and conversely for the drag cases.

Effect of aspect ratio on the wake transition behind a thin pitching plate

We study the influence of Aspect Ratio (AR) on three-dimensional wake transition past a thin pitching plate at Reynolds number of 1000 by performing computations for the range 0.54≤AR≤16 at pitching frequencies St=0.5,1 and maximum pitching angles θmax=5°,15°. For all AR, larger θmax and St promote thrust generation. However, higher AR imparts a stabilizing influence in the wake of the drag regime. For the ranges of AR, the drag-producing wake consisting of horseshoe vortices and bridgelets-type vortex structures, whereas twin-jet type bifurcated wakes with entangled vortices are observed for thrust-generating wakes. At higher AR, the wakes show a two-dimensional signature in the drag regime, whereas a spatial wake transition is observed in the thurst regime. The spanwise wake width shows the effect of wake compression for larger St even at θmax=5°, which is also substantiated by particle tracking showing wake compression for the thrust cases up to AR≤12. The near wake oscillations are prevalent for higher AR, although the core region remains unaffected by the aiding influence of spanwise instability for larger AR. The time average streamwise velocity for both drag and thrust regimes resembles an apparent feature of the reverse von Kármán vortex street.

Spatial wake transition past a thin pitching plate.

The spatial transition of the wake behind a thin pitching plate in the thrust regime is studied. The drag-to-thrust transition is seen to occur at a threshold pitching frequency which becomes smaller for higher pitching angle and aspect ratio. The reverse von Kármán wake shows deflected asymmetric vortex pairing in two dimensions, while a bifurcated wake with a swirling ring is the signature in three dimensions, both resulting in nearly the same scaling for the power coefficient. The wake transition in the thrust regime occurs through three spatial regions comprising the reverse von Kármán vortex street, transitional zone, and twin jet region. Near the trailing edge, reverse von Kármán shedding is marked by linear decay of the spanwise wake width and growth of secondary instability. A large volume of fluid resulting from inward horizontal acceleration renders a weak form drag in the subsequent transition zone which is followed by vertical bifurcation into twin jet formation in the far wake. The spanwise pressure gradient is seen to guide the wake compression, with a streamwise adverse pressure gradient aiding it in the near wake.

A variational flexible multibody formulation for partitioned fluid–structure interaction: Application to bat-inspired drones and unmanned air-vehicles

We present a three-dimensional (3D) partitioned aeroelastic formulation for a flexible multibody system interacting with incompressible turbulent fluid flow. While the incompressible Navier–Stokes system is discretized using a stabilized Petrov–Galerkin procedure, the multibody structural system consists of a generic interaction of multiple components such as rigid body, beams and flexible thin shells along with various types of joints and connections among them. A co-rotational framework is utilized for the category of small strain problems where the displacement of the body is decomposed into a rigid body rotation and a small strain component. This assumption simplifies the structural equations and allows for the incorporation of multiple bodies (rigid as well as flexible) in the system. The displacement and rotation constraints at the joints are imposed by a Lagrange multiplier method. The equilibrium conditions at the fluid–structure interface are satisfied by the transfer of tractions and structural displacements via the radial basis function approach, a scattered data interpolation technique, which is globally conservative. For the coupled stability in low structure-to-fluid mass ratio regimes, a nonlinear iterative force correction scheme is employed in the partitioned staggered predictor–corrector scheme. The convergence and generality of the radial basis function mapping are analyzed by carrying out systematic error analysis of the transfer of fluid traction across the non-matching fluid–structure interface where a third-order of convergence is observed. The proposed aeroelastic framework is then validated by considering a flow across a flexible pitching plate configuration with serration at the trailing edge. Finally, we demonstrate the flow across a flexible flapping wing of a bat modeling the bone fingers as beams and the flexible membrane as thin shells in the multibody system along with the joints.

Experimental investigation on the leading-edge vortex formation and detachment mechanism of a pitching and plunging plate

Abstract

Numerical exploration of the pitching plate parameter space with application to thrust scaling

The thrust performance of a two-dimensional plate pitching harmonically in a uniform flow is assessed numerically using the OpenFOAM toolbox [1]. The mesh displacement vector associated with the rigid body motion is computed as the solution of a Laplace equation with variable diffusivity, using the appropriate mesh manipulation class of the toolbox. For a Reynolds number of 2000, the accuracy of the pressure and viscous stress distributions is assessed by comparison with reference data available for an equivalent fluid configuration. The efficiency and flexibility of the solver allows exploring large ranges of the pitching parameter space, that is the pitching frequency, amplitude and pivot-point location of the pitching plate. The forces induced by the pitching motion are computed for pitching amplitudes up to 15∘, for Strouhal numbers varying between 0.2 and 0.5 and for different pitch pivot points. Performing a thrust scaling analysis, a classical theoretical model for the swimming of a waving plate is reliably fitted to the numerical pressure force data. The dependence of the time averaged thrust with the pitching axis is shown to be predicted accurately by a classical potential flow formula (known as Garrick’s theory) for pivot points within the front quarter of the plate. The viscous drag is computed as well for the Reynolds number 2000. The time-averaged values are shown to depend on the pitching amplitude and frequency and for instance a Blasius-type scaling, sometimes used to model the viscous drag correction for oscillating two-dimensional foils in this Reynolds number range, is not reliable.

Thrust generation by pitching and heaving of an elastic plate at low Reynolds number

We computationally study thrust generation and propulsive characteristics of an elastic plate pitching and/or heaving in free stream laminar flow. The pitching is considered about the leading edge, and the Reynolds number based on the plate length and free stream velocity is 150. An in-house fluid–structure interaction (FSI) solver is employed to simulate the large-scale flow-induced deformation of the structure along with active pitching and heaving in two-dimensional coordinates. The FSI solver utilizes a partitioned approach to strongly couple a sharp-interface immersed boundary method based flow solver with an open-source finite-element structural dynamics solver. We elucidate the mechanism of the thrust generation in the rigid and elastic plate by comparing the time-variation of thrust and work done by the plate, together with the wake signatures in the downstream. The time variation of the thrust is explained using first-order scaling arguments. The computed thrust as a function of pitching frequency for the rigid pitching plate shows a similar trend as compared to the published data of rigid foils, while the elastic plate exhibits a strong influence of the flow-induced deformation of the plate. They both exhibit reverse von Kármán-like vortex shedding in the downstream. We quantify the differences in propulsive characteristics of these two plate types as a function of pitching frequency. We found that there lies an optimum pitching frequency for the elastic plate for efficient propulsion, while the rigid one outperforms the elastic plate at larger pitching frequency. This is due to the fact that the elastic plate locks in to a higher mode of vibration at a larger pitching frequency. Furthermore, the influence of mass ratio, flexural rigidity, pitching amplitude, and Reynolds number on the performance of the elastic plate is also investigated. Finally, we study the combined effect of pitching and heaving on the propulsive performance. The pitching frequency for the maximum efficiency is lesser for the combined heaving and pitching plate as compared to only heaving or only pitching. Our results provide fundamental insights into the propulsive characteristics of the elastic pitching and/or heaving plates, which could help design autonomous underwater vehicles.

Locomotion of a self-propulsive pitching plate in a quiescent viscous fluid

The locomotion of a flexible plate pitching in a quiescent viscous fluid is numerically studied by using the lattice Boltzmann method (LBM) for the fluid and a finite element method (FEM) for the plate, with an immersed boundary (IB) method for the fluid–structure interaction (FSI). In the simulation, the leading edge of the plate undergoes a prescribed pitching motion, and the entire plate moves freely due to the fluid–plate interaction. The effects of the pitching amplitude, bending rigidity, plate-to-fluid mass ratio and Reynolds number on the propulsive performance of the flexible plate are examined in a range of parameters. The numerical results show that a certain flexibility can remarkably improve the propulsive speed and efficiency. The optimal parameters for the pitching plate are obtained, i.e. [Formula: see text] ([Formula: see text] is a non-dimensional frequency, with [Formula: see text] means rigid plate and larger [Formula: see text] means more flexible) and 20° ≤ α0 ≤ 25° ( α0 is the pitching amplitude). The comparisons of three plate-to-fluid mass ratios (1.0, 2.5 and 5.0) show that the mass of the plate decreases the propulsive speed, but contrarily increases the efficiency. The results obtained in the present study provide an insight into the understanding of the performance of self-propulsive plate in pitching motion and can further guide the engineering design of micro aerial vehicles.

Three-dimensional characteristics of the jet flows induced by a pitching plate in a quiescent fluid

Jet flows induced by pitching cantilever plates provide a power-efficient solution for fluid acceleration and cooling enhancement. In such applications, the time-averaged (mean) properties of the induced jet flows are of great importance. We report a combined experimental and numerical study on the three-dimensional (3-D) characteristics of the mean jet downstream of a harmonically pitching cantilever plate in a quiescent fluid. These characteristics are then correlated with the transient 3-D vortex structures emanated from the trailing and side edges. Our particle image velocimetry and 3-D numerical simulations reveal that the mean induced jet has two distinct regions – a shrinking region immediately downstream of the trailing edge followed by an abrupt expansion region – separated by a necking point. We investigate the transient 3-D wake vortex evolution downstream of the plate to help elucidate the physics underlying the geometry of the mean jet. Our observations suggest that the breakdown of the shed vortex structure and reorientation of the consequent substructures are the primary factors governing the shape of the jet. These factors in turn are controlled primarily by the plate width and the amplitude of the oscillations. The results presented in this study improve our understanding of the complicated 3-D geometry of the induced mean jet in oscillating plates and facilitate optimal design of devices that operate based on this principle, such as piezoelectric fans.

An image-guided computational approach to inversely determine in vivo material properties and model flow-structure interactions of fish fins

We present an image-guided computational approach for inversely determining in vivo material properties of fish fins and simulating flow-structure interactions (FSI) of fin deformations based on a highly realistic hybrid membrane-beam structure. This approach is established by coupling an imaged-based reconstruction, a genetic-algorithm (GA)-based optimization, a finite-element-method (FEM)-based computational structural dynamics model and an immersed-boundary-method (IBM)-based computational fluid dynamics (CFD) solver. An inverse-problem procedure is developed to determine material properties from prescribed kinematic motions obtained from high-speed images. The procedure is validated through two tests including a flexible pitching plate and a shell-beam structured flexible plate in heaving motion. The FSI model (forward problem) is validated through two benchmark tests including flow-induced vibration of a flexible beam attached to a fixed cylinder and a flexible pitching plate in a uniform flow. This integrated method is then applied to the FSI analysis of propulsion of a rainbow trout caudal fin with a specific focus on the fin material properties, fin deformations, hydrodynamic performances and flow structures. We demonstrate that, by using reconstructed kinematics and deformation obtained from the high-speed videos, the non-uniform material properties of the fin can be determined through the inverse problem procedure. A fully-coupled FSI simulation is then carried out based on the outcome of the inverse problem. The results have shown the feasibility of the present integrated approach in accurately modeling and quantitatively evaluating flexible-fin kinematics and hydrodynamics in swimming in terms of both chordwise and spanwise deformations, thrust and lateral forces, and vortex dynamics.

Thrust and drag scaling of a rigid low-aspect-ratio pitching plate

The flow around a rigid rectangular pitching plate immersed in a free stream is numerically investigated, addressing the force and drag generated by the oscillatory motion. Several aspect ratios (plate’s span to plate’s length) lower than 0.5 are considered, for a Reynolds number based on the plate’s length and the incoming flow velocity of 2000. The validity of the scaling law for viscous drag production, previously established for finite-span plates in uniform flapping motion, is investigated for the pitching motion, which is more representative in the context of propulsion modeling. The time averaged pressure force is shown to decompose into a propulsive part, scaling linearly with the aspect ratio and induced by the plate’s movement, and an opposite pressure force deficit, often interpreted as vortex induced drag and generally associated with the pair of longitudinal vortices at the plate’s lateral edges. A scaling for the time averaged pressure deficit is proposed, by analyzing the pressure drop along the span in terms of a Bernoulli-type effect induced by the transverse flow velocity. It is shown, that the pressure thrust is reduced, compared to what would be predicted by the elongated body theory, by more than 30% for the aspect ratios considered.

An adaptive multi-moment FVM approach for incompressible flows

In this study, a multi-moment finite volume method (FVM) based on block-structured adaptive Cartesian mesh is proposed for simulating incompressible flows. A conservative interpolation scheme following the idea of the constrained interpolation profile (CIP) method is proposed for the prolongation operation of the newly created mesh. A sharp immersed boundary (IB) method is used to model the immersed rigid body. A moving least squares (MLS) interpolation approach is applied for reconstruction of the velocity field around the solid surface. An efficient method for discretization of Laplacian operators on adaptive meshes is proposed. Numerical simulations on several test cases are carried out for validation of the proposed method. For the case of viscous flow past an impulsively started cylinder (Re=3000,9500), the computed surface vorticity coincides with the result of the body-fitted method. For the case of a fast pitching NACA 0015 airfoil at moderate Reynolds numbers (Re=10000,45000), the predicted drag coefficient (CD) and lift coefficient (CL) agree well with other numerical or experimental results. For 2D and 3D simulations of viscous flow past a pitching plate with prescribed motions (Re=5000,40000), the predicted CD, CL and CM (moment coefficient) are in good agreement with those obtained by other numerical methods.

Wave Motion Control Over Submerged Horizontal Plates

The interaction of surface gravity waves with horizontal pitching plate for actively control waves is investigated based on the linearized theory of water waves. The three-dimensional (3D) problem is formulated for the submerged plate pitching about its middle point and the other plate is considered to be floating above the submerged plate. The submerged plate's thickness is considered negligible in comparison with the water depth and wavelength of the incident wave. The study is carried out using the matched eigenfunction expansion method and the analytical solution is developed for the interaction of the surface gravity waves with horizontal submerged structure. The performance is analyzed for both impermeable and porous submerged pitching plate. The numerical results for the reflection coefficient, transmission coefficient, and free-surface deflection are computed and analyzed. The study is carried to find the optimal value of the length and depth of the submerged plate at which the dissipation of the incident wave energy is observed. The reduction the wave transformation due to the pitching of the plate with the change in angle of incidence is also analyzed. The present study will be helpful in the analysis of proper functioning of submerged pitching plate to control wave motion for the protection of offshore structures.

Linear and Nonlinear Decomposition of Aerodynamic Force Acting on an Oscillating Plate

An exact Lamb vector-based theory for the computation and decomposition of the aerodynamic force in unsteady viscous flows is presented and analyzed. This decomposition allows for a correct and straightforward computation of the dynamic force derivatives even in strongly nonlinear flows. Theory has been applied to numerical solutions around a pitching and plunging plate at low (300) and high () Reynolds numbers. A breakdown between thrust and drag contributions is also obtained, evidencing the flow regions where the thrust force is generated. The obtained decomposition is compared with the classical analytical linear inviscid theories. In addition, a new mixed inertial–non-inertial formula is proposed for the computation of the aerodynamic force, which is more accurate when dealing with high Reynolds numbers flows.

Stability and three-dimensional evolution of a transitional dynamic stall vortex

This paper describes a series of experiments using particle image velocimetry to investigate the dynamic stall resulting due to a rapid pitching motion of a flat plate. There exist in such unsteady separated flows multiple time-dependent coherent structures, whose interaction and evolution are complex and nonlinear. The experiments presented here are aimed at determining the behaviour of a dynamic stall vortex system in the Reynolds number range $10^{3}<Re<10^{4}$. Evidence is presented for the development of the three-dimensional structure associated with the dynamic stall vortex and its interaction with the no-slip boundary condition at the surface of the pitching plate. The analysis presented suggests that a centrifugal instability exists, and that the form of the three-dimensional structure is consistent with that expected of a centrifugal instability. The structure and scale dependence of the flow are explored using wavelet and Fourier methods, with the dependence of the flow on Reynolds number examined, as well as the influence of spanwise end boundary conditions.

To flap or not to flap: comparison between flapping and clapping propulsions

A comparison between swimming by flapping and by periodic contractions is conducted. Swimming by flapping is approximated as a pitching plate while swimming by periodic contractions is approximated as clapping plates. A direct comparison is made between the two propulsion mechanisms by utilizing a machine that can operate in either a flapping or a clapping mode between Reynolds numbers of 1880 and 11 260 based on the average plate tip velocity and span. The average thrust generated and the average input power required per cycle are compared between cases where the total sweep angle and the total sweep time are identical. Variation of the kinematics results in a similar thrust between the two mechanisms, but a greater power is required for clapping. Variation of the flexibility results in a consistent decrease in the required power for clapping and a decrease in thrust at high flexibility. Variation of the duty cycle for clapping rigid plates results in a significant increase in thrust and a significant decrease in the required power. Overall, the results suggest that flapping propulsion is the more effective propulsion mechanism within the range of Reynolds numbers tested.