Leading Edge Vortex Shedding Research Articles

Experimental and numerical investigation of the fluid-structure interaction on a flexible composite hydrofoil under viscous flows

This research investigates the fluid-structure interaction and hydroelastic response of a composite hydrofoil using an innovative joint experimental and numerical method. The main novelties are, first, the use of a state-of-the-art strain measurement technique, via a fully-distributed-optical fiber sensor directly embedded within the composite plies. This method allows for a finer representation of the structural deformations under hydrodynamic loading. Second, a tightly-coupled high-fidelity fluid-structure interaction numerical model taking into account the turbulent effects in the flow and the ply-by-ply modelling of the composite, is compared to the experimental results. A composite profile is specifically designed as a trapezoidal hydrofoil and is tested for moderate Reynolds number and pre-stall and post-stall incidences. High-speed imaging of the hydrofoil tip and vibrometer measurements are carried out to determine the experimental tip displacements and hydrofoil's vibrations. The numerical and experimental results show a very strong hydroelastic response, with a structural resonance even for low Reynolds numbers due to the high flexibility of the structure. Strong coupling of the fluid and the structure, with lock-in of the von Kármán vortex-shedding to the structure for small incidences, and an excitation of the structure by leading-edge vortex-shedding for higher incidences, are also observed.

Large-Amplitude Intermittent Swimming in Viscous and Inviscid Flows

Recently, it was demonstrated in an inviscid flow that burst-and-coast or intermittent swimming can save energy when compared with continuous swimming and that the energy savings are maximized for large-amplitude pitching motions where flow separation is likely to occur. This paper examines the effects of flow separation on altering inviscid flow predictions. As such, viscous and inviscid flow simulations are presented of a hydrofoil pitching intermittently with large-amplitude motions. It is observed that leading-edge vortex formation and shedding in a viscous flow significantly alter the wake dynamics from the inviscid flow solutions where only trailing-edge shedding is modeled. Moreover, the inviscid flow solutions predict higher peak force production, lower cost of transport, and lower optimal duty cycles than the viscous flow solutions. Despite these differences, the trends in the force production and energetics seen in a viscous flow are well captured by the inviscid flow simulations. Importantly, both predict energy savings on the order of 10–30% for intermittent swimming, and the energy savings increase when the amplitude of motion is increased even when significant leading-edge separation occurs.

Aerodynamic characteristics of flexible wings with leading-edge veins in pitch motions

To demonstrate the effects of wing deformations on aerodynamic performances during the wing reversal, aerodynamic force/torque and flow vector-fields were measured. Wing models consisted of wing planes with various thicknesses and two leading-edge veins, which obstructed spanwise deformations (Case 1 as a rigid wing and Cases 2 to 4 as flexible wings). They also underwent three different pitching periods (t/TR,α=0.1,0.2, and 0.4) to determine the distinct changes in vortical structures and corresponding aerodynamic characteristics. Flexible wings generally showed a negative camber in the stroke motion, causing poor aerodynamic performance relative to a rigid wing. This was also related to the positive camber and camber change to the negative during the pitch motions. After the start of the stroke, the positive camber caused separated and weakened tip vortex (TV) structures, hindering leading-edge vortex (LEV) formations around the wingtip. Depending on the LEV shedding, the flexible wings generated less aerodynamic forces than the rigid wing in stroke motion. During the pitch motions, on the other hand, the dynamic cambers influenced rotational mechanisms such as the wing–wake interaction and rotational force, causing higher or less initial lift increment. As the t/TR,α increased, the amount of the lift augmentation decreased due to the weakened wing–wake interaction, instead showing a downwash. At t/TR,α=0.4, however, the higher initial lift peak was occurred due to the absence of distinct trailing-edge vortex (TEV) generation during the wing-reversal. This lack of the U_TEV2 led to the decline of the downwash. Thus, the delayed U_LEV1 dispersal and the U_TEV2 traces generated similar induced flows to the wing–wake interaction, resulting in higher lift augmentation. Furthermore, Case 2 achieved higher lift augmentations than the other cases in all pitching periods. The slight wing deformations not only reduced the distance between the vortices and the wing surface, but also caused the delayed vortex dispersals. These induced the stronger rapid flows toward the wing surface, causing the higher initial lift peaks. Case 2 also had the highest C¯L/C¯P,t at t/TR,α=0.1 than the other cases. These results suggest that the flexible wing with leading-edge veins can have higher aerodynamic efficiency in its specific chordwise flexibility range.

Leading-Edge Vortices: Mechanics and Modeling

The leading-edge vortex (LEV) is known to produce transient high lift in a wide variety of circumstances. The underlying physics of LEV formation, growth, and shedding are explored for a set of canonical wing motions including wing translation, rotation, and pitching. A review of the literature reveals that, while there are many similarities in the LEV physics of these motions, the resulting force histories can be dramatically different. In two-dimensional motions (translation and pitch), the LEV sheds soon after its formation; lift drops as the LEV moves away from the wing. Wing rotation, in contrast, incites a spanwise flow that, through Coriolis tilting, balances the streamwise vorticity fluxes to produce an LEV that remains attached to much of the wing and thus sustains high lift. The state of the art of vortex-based modeling to capture both the flow field and corresponding forces of these motions is reviewed, including closure conditions at the leading edge and approaches for data-driven strategies.

Experimental Studies on a Mesoscale Cycloidal Rotor in Hover

This paper details the performance and flowfield measurements on a mesoscale cycloidal rotor (rotor radius of 1 in.), which operates at ultralow Reynolds numbers () and uses a design different from previous cycloidal rotor studies. The mesoscale rotor uses a cantilevered blade with a flat-plate airfoil and low-aspect-ratio elliptical blade planform. A three-component balance was developed to measure the vertical and sideward thrust, torque, and rotation frequency as the number of blades, pitch amplitude, and blade aspect ratio were varied. The studies showed that the highest efficiency was achieved with higher number of blades (4–6), high pitch amplitude (40–45 deg), and moderate aspect ratios. Phase-locked flowfield measurements were conducted using a particle image velocimetry (PIV) technique in two different orientations: chordwise and spanwise. PIV measurements show that the flowfield on the present mesoscale cycloidal rotor is highly three-dimensional and unsteady, characterized by the growth and shedding of leading-edge vortices and a trailing-edge vortex sheet similar to that seen on flapping wings; strong root and tip vortices that interact with each other to create an undulating wake; skewed inflow; and the strong interaction of the slip stream from the upper blade on the lower blade.

On the nonlinear dynamics of self-sustained limit-cycle oscillations in a flapping-foil energy harvester

The nonlinear dynamics of an airfoil at Reynolds number Re=10,000 constrained by two springs and subject to a uniform oncoming flow is studied numerically. The studies are carried out using open source computational fluid dynamics toolbox OpenFOAM. Under certain conditions related to aerodynamic flutter, this two-degree-of-freedom system undergoes self-sustained limit-cycle oscillations (LCOs) with potential application as an energy harvester. When the system is given a small initial perturbation, it is seen that the response of the system decays to zero at flow velocities below the flutter velocity, or oscillates in a limit cycle at velocities greater than the flutter velocity. The flutter velocity at Re=10,000 is shown to deviate significantly from the theoretical prediction (which is derived with an assumption of infinite Reynolds number) owing to the effect of viscosity. The LCOs at freestream velocities higher than the flutter velocity result in unsteady flows that are heavily influenced by leading-edge vortex shedding as well as trailing-edge flow separation. The influence of different system parameters on the onset of flutter and on the limit-cycle response characteristics is investigated in this research. This is done by defining a baseline case and examining the effects of varying aerodynamic parameters such as freestream velocity, and structural parameters such as the pitch-to-plunge frequency ratio and the type of spring stiffnesses. The conditions corresponding to the lowest flutter velocities (and consequently the lowest “cut-in” speeds for power extraction) and the parameter space that provide single-period, single-amplitude and harmonic LCOs (ideal for power extraction) are identified. Calculation of instantaneous and time-averaged power is presented by modeling the extraction of energy through a viscous damper. The highest power coefficients and efficiencies are obtained at velocities just higher than the flutter velocity. Introduction of positive cubic stiffening in the system springs is seen to make the system more stable, LCOs more harmonic and single-period, and to potentially increase power extraction efficiency of the system.

Wing–wake interaction: comparison of 2D and 3D flapping wings in hover flight

The wing–wake interaction of flapping wings while hovering has been investigated, with the focus on the difference in wing–wake interaction between 2D and 3D flapping wings. Numerical simulations are conducted at a Reynolds number of 100, and the flapping configurations are divided into the 2D, quasi-3D and 3D categories. Variations of the aspect ratio and Rossby number allow the flapping configuration to morph gradually between categories. The wing–wake interaction mechanisms are identified and the effect of three-dimensionality on these mechanisms is discussed. Three-dimensionality affects wing–wake interaction through four primary aerodynamic mechanisms, namely, induced jet, downwash/upwash, leading-edge vortex (LEV) shedding due to vortex pairing, and the formation of a closely attached LEV. The first two mechanisms are well-established in the literature. With regard to the LEV shedding mechanism, it is revealed that the interaction between the LEV and the residue vortex from the previous stroke plays an important role in the early vortex shedding of 2D flapping wings. This effect diminishes with increasing three-dimensionality. With regard to the mechanism of the closely attached LEV, the wake encourages the formation of an LEV that is closely attached to the wing’s top surface, which is beneficial to lift generation. This closely attached LEV mechanism accounts for most of the lift enhancement that arises from wake effects. Three-dimensionality alters the efficacy of the different aerodynamic mechanisms. Consequently, the dual peak lift coefficient pattern typically seen on 2D flapping wings transforms into the single peak lift coefficient pattern of the 3D flapping wing. It is also demonstrated that the mean lift enhancement due to wing–wake interaction diminishes rapidly when three-dimensionality is introduced. Results suggest that, for wings with parameters close to those of natural flyers, wing–wake interaction yields marginal lift enhancement and a small increase in energy consumption.

Force-motion phase relations and aerodynamic performance of a plunging plate

Due to the unsteady motion of a plunging plate, forces acting on the body experience a phase difference with respect to the motion. These phase relations are investigated experimentally for a harmonically plunging plate within an amplitude range of $$0.05\le {a/c}\le 0.6$$ , reduced frequency range of $$0.78<{k}<7.06$$ , and at a constant Reynolds number of 10,000. Both streamwise and cross-stream force components are found to have a phase lag following the motion; however, their variations are different. The phase lag of the force on the cross-stream direction increases as the amplitude increases. Drag–thrust transition has an influence on the streamwise force phase lags, which starts to increase when the thrust starts to be produced. Particle image velocimetry measurements are also performed to reveal the relations between vortex structures and force measurements. Leading edge vortex shedding characteristics are observed to be changing from drag occurring cases to thrust producing cases in parallel with the increment in phase lags.

Effects of geometrical parameters on the aerodynamic characteristics of a streamlined flat box girder

The effects of aspect ratio (B/D, width to height ratio), wind fairing angle (θ) and relative height of wind nose (H/h, h and H are the distances from the wind nose to the upper and lower surfaces of the girder, respectively) on the aerodynamic characteristics of a streamlined flat box girder were systematically investigated through wind tunnel experiments. A total of 21 cases were tested with B/D = 6, 9 and 12, θ = 45°, 55°, 65° and 75°, and H/h = 1, 2, 3 and 4, which covered most of the typical large span bridges in use. The Reynolds number based on the freestream oncoming velocity U∞ and model height D was 3.3 × 104. The experimental results show that the effects of B/D, θ and H/h are negligible at small wind attack angle (α) with |α| < 4°. The aerodynamic performance of the girder is very sensitive to these geometric parameters at |α| > 4°, which is associated with the states of the flow around the girder. With the increases of |α|, the flow around the girder may transfer from trailing edge vortex shedding (TEVS) to impinging leading edge vortex (ILEV) and leading edge vortex shedding (LEVS). Generally, the girder with H/h = 2–3 and larger B/D and θ corresponds to larger range of α with TEVS, which is favorable to the wind resistance stabilization of the girder.

Comparative turbulent three-dimensional Navier–Stokes hydrodynamic analysis and performance assessment of oscillating wings for renewable energy applications

Oscillating wings can extract energy from an oncoming water or air stream, and first large-scale marine demonstrators are being tested. Oscillating wing hydrodynamics is highly unsteady, may feature dynamic stall and leading edge vortex shedding, and is significantly three-dimensional due to finite-wing effects. Understanding the interaction of these phenomena is essential for maximizing power generation efficiency. Much of the knowledge on oscillating wing hydrodynamics stemmed from two-dimensional low-Reynolds number computational fluid dynamics studies and laboratory testing; real installations, however, will feature Reynolds numbers higher than 1 million and unavoidable finite-wing-induced losses. This study investigates the impact of flow three-dimensionality on the hydrodynamics and the efficiency of a realistic aspect ratio 10 device in a stream with Reynolds number of 1.5 million. The improvements achievable by using endplates to reduce finite-wing-induced losses are also analyzed. Three-dimensional time-dependent Navier–Stokes simulations using the shear stress transport turbulence model and a 30-million-cell grid are performed. Detailed comparative hydrodynamic analyses of the finite and the infinite wings reveal that flow three-dimensionality reduces the power generation efficiency of the finite wing with sharp tips and that with endplates by about 17% and 12% respectively. Presented analyses suggest approaches to further reducing these power losses.

Aerodynamic Effects of Elevating Motion on Hovering Rigid Hawkmothlike Wings

Flapping of an insect wing can be broadly separated into sweeping, elevating, and rotational motions. The sweeping motion generates forward velocity, and the rotational motion imposes an appropriate angle of attack; both are vital to lift generation. However, the purpose of elevating motion in insect flight remains unclear. In this paper, the aim is to better understand the effects of elevating motion to lift generation and vortex structure development when rigid wings are subjected to three-dimensional simple harmonic motion and hovering hawkmoth flapping motion. Both experimental and numerical techniques are used, and results show that, among the different types of simple harmonic motions considered here, only figure-of-eight motions at a relatively low midstroke angle of attack (25 deg) outperform flapping motions without elevating motion. In this case, lift is enhanced by approximately 11% with insignificant cost to hovering efficiency. The lift enhancement could be attributed to rapid growth of the leading-edge vortex, due to an increase in instantaneous angle of attack when the wing elevates downward during midstroke. For the hawkmoth motion, a small elevating motion has minimal aerodynamic effects, whereas a large one causes reduction in lift due to detachment of the leading-edge vortex from the wing surface. Generally, elevating motion affects lift and power coefficients via four mechanisms: alteration of instantaneous angle of attack, introduction of radial force component, wake capture, and early shedding of leading-edge vortex. Although elevating motion confers a significant lift enhancement to specific sets of flapping-wing kinematics, it is generally detrimental to flight performance.

Unsteady flow over flexible wings at different low Reynolds numbers

In this study, unsteady flow around flexible membrane wing which had aspect ratio of 1 (AR=1) was investigated experimentally at various Reynolds numbers (Re = 25000 and Re = 50000). Smoke-wire technique for flow visualization over the flexible membrane wing was utilized in the experiments. Digital Image Correlation system (DIC) was used for measuring deformation of AR = 1 flexible membrane wing. Instantaneous deformation measurements of membrane wing were combined with the flow field measurements. In low aspect ratio flexible membrane wings, unsteadiness includes tip vortices and vortex shedding, and the combination of tip vortices. In these types of wings, complex unsteady deformations occurred due to vortex shedding. The results showed that the increasing angle of attack results in increase of membrane deformation. Moreover, it was concluded that analysis of the instantaneous deformation revealed chordwise and spanwise, modes which were due to the shedding of leading-edge vortices as well as tip vortices. Consequently, vibrational mode decreased and maximum standard deviation location approached to the trailing edge by reason of increasing angle of attack.

Experimental Study of Reynolds Number and Gust Influence on Transient Force and Flow Generated by a Robotic Hummingbird

A two-degree-of-freedom, up-scaled, robotic hummingbird model with rigid wings was used to simulate the hovering, flapping kinematics of a hummingbird to understand the flow structure around the wing and the underlying mechanism for dynamic force generation. Digital Particle Image Velocimetry (DPIV) method was applied to visualize the flow field at the mid-section of the wing over a range of Reynolds numbers (850 &lt; Re &lt; 13,000). It was observed that in the major duration of the stroke the leading edge vortex (LEV) was kept attached to the wing's suction side over the entire range of Reynolds numbers. It was also found that the rapid change of angle of attack at the beginning of each half stroke generated shedding of LEV. Time history of the lift and drag forces were measured to relate the dynamic response with the flow field development. The magnitudes of lift and drag forces increased with Reynolds number, however, the overall lift coefficient decreased for Re &lt; 6,000. Beyond this limitation, influence of Reynolds number on the mean lift coefficients was indiscernible. Additionally, it was verified that the effects of horizontal gust on both flow field and dynamic forces were equivalent to that of effective Reynolds numbers, e.g., the effect of the head-on gust during the down-stroke increased the lift and drag forces, similar to the influence of increased Reynolds number.

Aerodynamics of dynamic wing flexion in translating wings

We conducted a systematic experimental study to investigate the aerodynamic effects of active trailing-edge flexion on a high-aspect-ratio wing translating from rest at a high angle of attack. We varied the timing and speed of the trailing-edge flexion and measured the resulting aerodynamic effects using a combination of direct force measurements and two-dimensional PIV flow measurements. The results indicated that the force and flow characteristics depend strongly on the timing of flexion, but relatively weakly on its speed. This is because the force and vortical flow structure are more sensitive to the timing of flexion relative to the shedding of starting vortex and leading-edge vortex. When the trailing-edge flexion occurred slightly before the starting vortex was shed, the lift production was greatly improved with the instantaneous peak lift increased by 54 % and averaged lift increased by 21 % compared with the pre-flexed case where the trailing-edge flexed before wing translation. However, when the trailing-edge flexed during or slightly after the leading-edge vortex shedding, the lift was significantly reduced by the disturbed development of leading-edge vortex. The force measurement results also imply that the trailing-edge flexion prior to wing translation does not augment lift but increases drag, thus resulting in a lower lift–drag ratio as compared to the case of flat wing.

Limit-cycle oscillations in unsteady flows dominated by intermittent leading-edge vortex shedding

High-frequency limit-cycle oscillations of an airfoil at low Reynolds number are studied numerically. This regime is characterized by large apparent-mass effects and intermittent shedding of leading-edge vortices. Under these conditions, leading-edge vortex shedding has been shown to result in favorable consequences such as high lift and efficiencies in propulsion/power extraction, thus motivating this study. The aerodynamic model used in the aeroelastic framework is a potential-flow-based discrete-vortex method, augmented with intermittent leading-edge vortex shedding based on a leading-edge suction parameter reaching a critical value. This model has been validated extensively in the regime under consideration and is computationally cheap in comparison with Navier–Stokes solvers. The structural model used has degrees of freedom in pitch and plunge, and allows for large amplitudes and cubic stiffening. The aeroelastic framework developed in this paper is employed to undertake parametric studies which evaluate the impact of different types of nonlinearity. Structural configurations with pitch-to-plunge frequency ratios close to unity are considered, where the flutter speeds are lowest (ideal for power generation) and reduced frequencies are highest. The range of reduced frequencies studied is two to three times higher than most airfoil studies, a virtually unexplored regime. Aerodynamic nonlinearity resulting from intermittent leading-edge vortex shedding always causes a supercritical Hopf bifurcation, where limit-cycle oscillations occur at freestream velocities greater than the linear flutter speed. The variations in amplitude and frequency of limit-cycle oscillations as functions of aerodynamic and structural parameters are presented through the parametric studies. The excellent accuracy/cost balance offered by the methodology presented in this paper suggests that it could be successfully employed to investigate optimum setups for power harvesting in the low-Reynolds-number regime.

Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding

AbstractUnsteady aerofoil flows are often characterized by leading-edge vortex (LEV) shedding. While experiments and high-order computations have contributed to our understanding of these flows, fast low-order methods are needed for engineering tasks. Classical unsteady aerofoil theories are limited to small amplitudes and attached leading-edge flows. Discrete-vortex methods that model vortex shedding from leading edges assume continuous shedding, valid only for sharp leading edges, or shedding governed by ad-hoc criteria such as a critical angle of attack, valid only for a restricted set of kinematics. We present a criterion for intermittent vortex shedding from rounded leading edges that is governed by a maximum allowable leading-edge suction. We show that, when using unsteady thin aerofoil theory, this leading-edge suction parameter (LESP) is related to the $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}A_0$ term in the Fourier series representing the chordwise variation of bound vorticity. Furthermore, for any aerofoil and Reynolds number, there is a critical value of the LESP, which is independent of the motion kinematics. When the instantaneous LESP value exceeds the critical value, vortex shedding occurs at the leading edge. We have augmented a discrete-time, arbitrary-motion, unsteady thin aerofoil theory with discrete-vortex shedding from the leading edge governed by the instantaneous LESP. Thus, the use of a single empirical parameter, the critical-LESP value, allows us to determine the onset, growth, and termination of LEVs. We show, by comparison with experimental and computational results for several aerofoils, motions and Reynolds numbers, that this computationally inexpensive method is successful in predicting the complex flows and forces resulting from intermittent LEV shedding, thus validating the LESP concept.

Optimal Operating Parameters for an Oscillating Foil Turbine at Reynolds Number 500,000

The use of oscillating foils to develop turbines to extract energy from an oncoming flow has recently been found competitive with rotor blade designs. Moreover, the rectangular extraction plane of the oscillating-foil turbine presents clear advantages in the field of hydrokinetic turbines. The present study, based on two-dimensional unsteady Reynolds-averaged Navier–Stokes numerical simulations, focuses on the range of operating parameters maximizing power extracted by a single oscillating foil for small-scale application Reynolds number. The power-extraction efficiency is mapped in parametric spaces associated with different motion amplitudes. Efficiency maxima reach about 43% in all the parametric spaces considered, but for different values of pitching amplitude and frequency. It is found that the best parametric zones in all cases exhibit similar characteristics with regards to the effective angle of attack. Indeed, they are all associated with a maximum effective angle of attack of about 33 deg and a maximum (normalized) rate of change of the latter of 0.55. It is further observed that, contrary to laminar results previously published, the occurrence of leading-edge vortex shedding is not necessarily observed in optimal cases at these higher Reynolds number conditions.

Low-Flow-Coefficient Centrifugal Compressor Design for Supercritical CO2

This paper presents a design strategy for very low flow coefficient multistage compressors operating with supercritical CO2 for carbon capture and sequestration (CCS) and enhanced oil recovery (EOR). At flow coefficients less than 0.01, the stage efficiency is much reduced due to dissipation in the gas-path and more prominent leakage and windage losses. Instead of using a vaneless diffuser as is standard design practice in such applications, the current design employs a vaned diffuser to decrease the meridional velocity and to widen the gas path. The aim is to achieve a step change in performance. The impeller exit width is increased in a systematic parameter study to explore the limitations of this design strategy and to define the upper limit in efficiency gain. The design strategy is applied to a full-scale reinjection compressor currently in service. Three-dimensional, steady, supercritical CO2 computational fluid dynamics (CFD) simulations of the full stage with leakage flows are carried out with the National Institute of Standards and Technology (NIST) real gas model. The design study suggests that a nondimensional impeller exit width parameter b2* = (b2/R)ϕ of six yields a 3.5 point increase in adiabatic efficiency relative to that of a conventional compressor design with vaneless diffuser. Furthermore, it is shown that in such stages the vaned diffuser limits the overall stability and that the onset of rotating stall is likely caused by vortex shedding near the diffuser leading edge. The inverse of the nondimensional impeller exit width parameter b2* can be interpreted as the Rossby number. The investigation shows that, for very low flow coefficient designs, the Coriolis accelerations dominate the relative flow accelerations, which leads to inverted swirl angle distributions at impeller exit. Combined with the two-orders-of-magnitude higher Reynolds number for supercritical CO2, the leading edge vortex shedding occurs at lower flow coefficients than in air suggesting an improved stall margin.

Numerical simulation of unsteady cavitating flows around a transient pitching hydrofoil

The objective of this paper is to improve the understanding of the influence of multiphase flow on the turbulent closure model, the interplay between vorticity fields and cavity dynamics around a pitching hydrofoil. The effects of pitching rate on the subcavitating and cavitating response of the pitching hydrofoil are also investigated. In particular, we focus on the interactions between cavity inception, growth, and shedding and the vortex flow structures, and their impacts on the hydrofoil performance. The calculations are 2-D and performed by solving the incompressible, multiphase Unsteady Reynolds Averaged Navier Stokes (URANS) equations via the commercial CFD code CFX. The k-ω SST (Shear Stress Transport) turbulence model is used along with the transport equation-based cavitation models. The density correction function is considered to reduce the eddy viscosity according to the computed local fluid mixture density. The calculation results are validated with experiments conducted by Ducoin et al. (see Computational and experimental investigation of flow over a transient pitching hydrofoil, Eur J Mech/B Fluids, 2009, 28: 728–743 and An experimental analysis of fluid structure interaction of a flexible hydrofoil in various flow regimes including cavitating flow, Eur J Mech B/fluids, 2012, 36: 63–74). Results are shown for a NACA66 hydrofoil subject to slow (quasi static, \(\dot \alpha = {{6^ \circ } \mathord{\left/ {\vphantom {{6^ \circ } s}} \right. \kern-\nulldelimiterspace} s}\), \(\dot \alpha ^ * = 0.18\)) and fast (dynamic, \(\dot \alpha = {{63^ \circ } \mathord{\left/ {\vphantom {{63^ \circ } s}} \right. \kern-\nulldelimiterspace} s}\), \(\dot \alpha ^ * = 1.89\)) pitching motions from α = 0° to α = 15°. Both subcavitaing (σ=8.0) and cavitating (σ=3.0) flows are considered. For subcavitating flow (σ=8.0), low frequency fluctuations have been observed when the leading edge vortex shedding occurs during stall, and delay of stall is observed with increasing pitching velocity. For cavitating flow (σ=3.0), small leading edge cavities are observed with the slow pitching case, which significantly modified the vortex dynamics at high angles of attack, leading to high frequency fluctuations of the hydrodynamic coefficients and different stall behaviors compared to the subcavitating flow at the same pitching rate. On the other hand, for the fast pitching case at σ=3.0, large-scale sheet/cloud cavitation is observed, the cavity behavior is unsteady and has a strong impact on the hydrodynamic response, which leads to high amplitude fluctuations of the hydrodynamic coefficients, as well as significant changes in the stall and post-stall behavior. The numerical results also show that the local density modification helps to reduce turbulent eddy viscosity in the cavitating region, which significantly modifies the cavity lengths and shedding frequencies, particularly for the fast pitching case. In general, compared with the experimental visualizations, the numerical results with local density correction have been found to agree well with experimental measurements and observations for both slow and fast transient pitching cases.

Lift evaluation of a two-dimensional pitching flat plate

Several previous experimental and theoretical studies have shown that a leading edge vortex (LEV) on an airfoil or wing can provide lift enhancement. In this paper, unsteady two-dimensional (2D) potential flow theory is employed to model the flow field of a pitching flat plate wing. A multi-vortices model is developed to model both the leading edge and trailing edge vortices (TEVs), which offers improved accuracy compared with using only single vortex at each separation location. The lift is obtained by integrating the unsteady Blasius equation. It is found that the motion of vortices contributes significantly to the overall aerodynamic force on the flat plate. A Kutta-like condition is used to determine the vortex intensity and location at the leading edge for large angle of attack cases; however, it is proposed to relax this condition for small angle of attack cases and apply a 2D shear layer model to calculate the circulation of the new added vortex. The results of the simulation are then compared with classical numerical, theoretical, and experimental data for canonical unsteady flat plat problems. Good agreement with these data is observed. Moreover, these results suggested that the leading edge vortex shedding for small angles of attack should be modeled differently than that for large angles of attack. Finally, the results of vortex motion vs. lift indicate that the slow convection of the LEV creates less negative lift while the rapid shedding of the TEV creates more positive lift. The difference between these two contributions of lift results in a total positive lift that lasts for about two chord-length travel of the plate. It is therefore concluded that the lift enhancement during the LEV “stabilization” above the wing is a combined effect of both the LEV and TEV motion. This also provides the insights for future active flow control of micro aerial vehicles (MAVs) that the formation and shedding process of LEVs and TEVs can be manipulated to provide lift enhancement.