Time-averaged Lift Research Articles

Lift Enhancement of a Stationary Wing in a Wake

A stationary wing placed in the wake of a bluff body experiences lift enhancement. The quasi-periodic flow in the wake causes excitation of the separated flow in the poststall conditions. The increase in the time-averaged lift force is associated with the flow separation, leading-edge vortex formation, and subsequent reattachment in a process similar to the dynamic stall of oscillating wings. The lift enhancement is maximum for an optimal offset distance from the wake centerline. At the optimal location, potential flow oscillations, rather than the direct impingement of large vortices in the wake, provide the excitation. The smaller amplitude flow oscillations lead to a large separation bubble in the time-averaged sense in the poststall regime. The delayed flow separation in the wake has a similar mechanism and frequency to those of the active flow control methods for separation. The degree of the lift enhancement is remarkable, given that the wake at a Reynolds number of 50,000 is expected to be highly three-dimensional.

Jet deflection by two side-by-side arranged hydrofoils pitching in a quiescent fluid

The present work reports a computational study on the pitching of two identical NACA 0012 airfoils arranged in a side-by-side (parallel) configuration in a still medium. Pitching of airfoils arranged in a side-by-side (parallel) configuration in a still medium leads to the formation of a deflected jet. The angle at which the jet is deflected depends on the oscillation phase difference between the airfoils and the frequency of oscillation. The deflection angle is high at a lower frequency of oscillation for a given phase difference between the foils. The time-averaged jet deflection angle, thrust, and lift on airfoils are quantified for a range of frequencies (0.5 Hz–2 Hz) and phase differences (0°–180°) between the airfoils. The thrust force increases gradually with an increase in the phase difference between the foils until 120°, and beyond this, it decreases. The maximum jet deflection angle is found to be 28° when the phase difference is 45° for a frequency of 0.5 Hz. It is observed that the initially deflected jet switches toward the centerline position after specific periods of pitching. This switching of the jet from a deflected position toward the centerline initiates once the vortices from the lower foil interact completely with the upper foil. Some of these findings are relatively new in the domain of bio locomotion, which is useful for various related engineering applications.

Pulsed Jet Characteristics of Circulation Control Airfoil

Compared with the steady jet, the mass flow consumed by the pulsed jet is lower, which is of great significance for solving the jet source in the circulation control technology. In order to further study the effects of different parameters on energy consumption and aerodynamic coefficient pulse in pulsed jet, based on the Reynolds average N-S equation, the aerodynamic characteristic calculation and flow field analysis of the circulation control airfoil under the action of pulsed jet are carried out, and the aerodynamic benefit is evaluated with the combination of energy consumption and aerodynamic coefficient fluctuation. The results show that: Pulsed jet is more suitable for use at high angle of attack. By using the combination of pulsed jet and steady jet, good results can be obtained in three aspects: time-averaged lift coefficient, lift coefficient fluctuation and energy consumption. The research results can be used as a reference for guiding the use of pulsed jet in circulation control technology.

Aerodynamic-force production mechanisms in hovering mosquitoes

For many insects in hovering flight, the stroke amplitude is relatively large (above ) and the lift is mainly produced by the leading-edge vortex (LEV) attaching to the wing (the delayed-stall mechanism). Mosquitoes have a very small stroke amplitude ( ) and the LEV does not have enough time to form before a stroke ends; thus, the delayed-stall mechanism can not be used. In the present study, we show that their lift is produced by different aerodynamic mechanisms from those of insects with a large stroke amplitude: in a downstroke and upstroke, two large lift peaks and a relatively small one are generated. The first large lift peak (at the beginning of the stroke) mainly comes from the added-mass force caused by the large acceleration of the wing. The second large lift peak (in the mid-portion of the stroke) is produced by the ‘fast-pitching-up rotation’ mechanism: the wing fast pitches up while moving forward, generating a large-magnitude, opposite-sign vorticity at the trailing edge of the wing and near the leading edge of the wing; the rapid generation of opposite-sign vorticity at different locations of the wing results in a large time rate of change in the first moment of vorticity, hence a large aerodynamic force. The third lift peak, which is near the end of the stroke and is small, is a result of the fast-pitching-up rotation of a rapidly decelerating wing. Note that although the added-mass force contributes positive lift in the beginning part of the stroke when the wing is in acceleration, it gives negative lift in the next part of the stroke when the wing is in deceleration; i.e. the added-mass force has no effect on the time-average lift, but it greatly changes the time distribution of the lift.

Suppressing tip-leakage vortex cavitation by overhanging grooves

In the present paper, a new control method for tip-leakage vortex (TLV) cavitation is proposed. This method, which combines the effects of grooves and winglets, is made of overhanging grooves (OHGs) fitted at the tip of a hydrofoil. Experimental and numerical investigations are conducted to evaluate the performances of OHGs in terms of TLV cavitation suppression. The results are systematically compared with the baseline, conventional grooves (CGs) and anti-cavitation lip (ACL) and a significant improvement of TLV cavitation suppression is obtained with the OHGs. We also carried out a primary optimization design of the OHGs and a more effective suppression on TLV cavitation is obtained for small gaps and TLV cavitation is almost suppressed for middle and large gaps. The underlying reasons for TLV cavitation mitigation are discussed in detail with the help of numerical simulations. It indicates that for small gap sizes, OHGs can effectively weaken the strength of both TLV and tip-separation vortex (TSV) and mitigate TLV cavitation. For middle and large gap sizes, it is found that OHGs will induce an increase in the TLV core size, which further increases local minimum pressure. The influence of OHGs on the performance of hydrofoil is also examined, which indicates that the fluctuation of TLV cavitation can be effectively suppressed by OHGs and no significant alteration of time-averaged drag and lift is induced by OHGs. Our work shows that the OHGs can effectively suppress TLV cavitation with limited influence on the performances of hydrofoil in a large range of the gap sizes, which is a promising method for the control of TLV cavitation in hydraulic machinery.

Influences of marshalling length on the flow structure of a maglev train

In this paper, transient numerical simulations of maglev trains of different marshalling lengths (2, 4, and 8-car group trains) were conducted in the open air and without wind. This was done by solving the three-dimensional incompressible Navier-Stokes equations using an SST K-ω double-equation IDDES turbulence model. The results were compared with the results of wind tunnel experiments to verify the feasibility of numerical simulation. The results show an increase in the marshalling lengths of the train affects the flow above and below the train. With the increase of the marshalling length, the position of the flow separation in the tail car is advanced. The turbulence generated by the average shear on the x, y-plane and the x, z-plane as a component of the turbulence of the wake region increases. The region that produces non-vorticial vorticity in the main vortex becomes narrow and moves towards tail car. The structural analysis of the wake indicates that the wake structure of the 8-car group train is quite different from the other two groups. Both the time-averaged slipstream and the gust analysis show that the maximum expected slipstream velocity at the track-side increases as the train marshalling length increases. At the platform height, the change in vertical position of the wake vortex structure of the 2, 4, and 8-car group trains caused the difference of the shear flow regions. This is why the maximum expected slipstream velocity generated by the 4-car group train at this position is largest. As the marshalling length of the train increases, the time-average drag and lift force coefficient of the tail car have a significant negative correlation.

Numerical study on characteristics of flow and thermal fields around rotating cylinder

In this paper, a numerical simulation has been performed to study the fluid flow and heat transfer around a rotating circular cylinder over low Reynolds numbers. Here, the Reynolds number is 200, and the values of rotation rates (α) are varied within the range of 0 < α < 6. Two-dimensional and unsteady mass continuity, momentum, and energy equations have been discretized using the finite volume method. SIMPLE algorithm has been applied for solving the pressure linked equations. The effect of rotation rates (α) on fluid flow and heat transfer were investigated numerically. Also, time-averaged (lift and drag coefficients and Nusselt number) results were obtained and compared with the literature data. A good agreement was obtained for both the local and averaged values.

Influences of flapping modes and wing kinematics on aerodynamic performance of insect hovering flight

A numerical investigation into the effects of flapping modes on the aerodynamic performance of insect hovering flight is carried out through the solution of the two-dimensional unsteady Navier-Stokes equations. Four types of idealized flapping modes with the identical quasi-steady lift force are compared, and the influences of the Reynolds number (Re), the translational duration and the rotational duration on the aerodynamic characteristics of the hovering are systematically analyzed flight. It is found that the instantaneous aerodynamic forces of the wing differ significantly in each flapping mode. The mode with harmonic translation and harmonic rotation leading the highest lifting efficiency is suitable for long-time flight while the mode with harmonic translation and trapezoid rotation giving the largest instantaneous forces is suitable for maneuvering flight. When Re increases from 100 to 1000, the lift force and lifting efficiency of the wing are increased significantly with the increasing Re first, and then slow down with the further increase in Re. In addition, the fast-translational mode with short translational duration will reduce the time-averaged lift force and the efficiency, whereas the fastrotational mode with short rotational duration can enhance the time-averaged lift force with the sustained efficiency.

Kinematic parameter optimization of a flapping ellipsoid wing based on the data-informed self-adaptive quasi-steady model

This paper constructs an optimization framework based on the data-informed self-adaptive quasi-steady model. The framework aims at achieving a specific aerodynamic force coefficient by optimizing the kinematic parameters of the flapping motion of an ellipsoid wing. All the model coefficients of this quasi-steady model are calibrated empirically by the data-informed training. At each optimization iteration, the data-informed training is implemented by the local ridge regression, where the initial training samples are extracted from simulation examples, and the weight coefficients are calculated by the compactly supported radial basis function with the previous optimal solution as the center point. Furthermore, a numerical simulation is conducted to evaluate the accurate aerodynamic force coefficient corresponding to the current optimal solution. The relative error between the accurate simulation result and optimization objective is calculated as the convergence criteria of the optimization. Then, the effects of the kinematic parameters on the time-averaged lift coefficient are first investigated, which indicate that the in-phase flapping with high flapping angle amplitude and medium geometric angle of attack amplitude is beneficial to the lift coefficient. Moreover, the kinematic optimization is conducted for a three-dimensional flapping ellipsoid wing in the hovering mode. The results demonstrate that the leading-edge vortex is crucial for the force generation. Moreover, in one flapping period, the asymmetrical wake and two unequal lift coefficient peaks emerge under the figure-O motion pattern while the vortex structures are highly symmetrical under the figure-8 motion pattern.

Flow Interactions Between Low Aspect Ratio Hydrofoils in In-line and Staggered Arrangements.

Many species of fish gather in dense collectives or schools where there are significant flow interactions from their shed wakes. Commonly, these swimmers shed a classic reverse von Kármán wake, however, schooling eels produce a bifurcated wake topology with two vortex rings shed per oscillation cycle. To examine the schooling interactions of a hydrofoil with a bifurcated wake topology, we present tomographic particle image velocimetry (tomo PIV) measurements of the flow interactions and direct force measurements of the performance of two low-aspect-ratio hydrofoils () in an in-line and a staggered arrangement. Surprisingly, when the leader and follower are interacting in either arrangement there are only minor alterations to the flowfields beyond the superposition of the flowfields produced by the isolated leader and follower. Motivated by this finding, Garrick’s linear theory, a linear unsteady hydrofoil theory based on a potential flow assumption, was adapted to predict the lift and thrust performance of the follower. Here, the follower hydrofoil interacting with the leader’s wake is considered as the superposition of an isolated pitching foil with a time-varying cross-stream velocity derived from the wake flow measurements of the isolated leader. Linear theory predictions accurately capture the time-averaged lift force and some of the major peaks in thrust derived from the follower interacting with the leader’s wake in a staggered arrangement. The thrust peaks that are not predicted by linear theory are likely driven by spatial variations in the flowfield acting on the follower or nonlinear flow interactions; neither of which are accounted for in the simple theory. This suggests that unsteady potential flow theory that does account for spatial variations in the flowfield acting on a hydrofoil can provide a relatively simple framework to understand and model the flow interactions that occur in schooling fish. Additionally, schooling eels can derive thrust and efficiency increases of 63-80% in either a in-line or a staggered arrangement where the follower is between two branched momentum jets or with one momentum jet branch directly impinging on it, respectively.

Numerical Investigation on Flapping Aerodynamic Performance of Dragonfly Wings in Crosswind

Numerical simulations are performed to investigate the influence of crosswind on the aerodynamic characteristics of rigid dragonfly-like flapping wings through the solution of the three-dimensional unsteady Navier-Stokes equations. The aerodynamic forces, the moments, and the flow structures of four dragonfly wings are examined when the sideslip angleϑbetween the crosswind and the flight direction varied from 0oto 90o. The stability of the dragonfly model in crosswind is analyzed. The results show that the sideslip angleϑhas a little effect on the total time-average lift force but significant influence on the total time-average thrust force, lateral force, and three-direction torques. An increase in the sideslip angle gives rise to a larger total time-average lateral force and yaw moment. These may accelerate the lateral skewing of the dragonfly, and the increased rolling and pitching moments will further aggravate the instability of the dragonfly model. The vorticities and reattached flow on the wings move laterally to one side due to the crosswind, and the pressure on wing surfaces is no longer symmetrical and hence, the balance between the aerodynamic forces of the wings on two sides is broken. The effects of the sideslip angleϑon each dragonfly wing are different, e.g.,ϑhas a greater effect on the aerodynamic forces of the hind wings than those of the fore wings. When sensing a crosswind, it is optimal to control the two hind wings of the bionic dragonfly-like micro aerial vehicles.

Effect of Turbulence and Sinusoidal Pitching on Low-Reynolds-Number Lift

Small fixed-wing unmanned aerial vehicles (UAVs) are becoming increasingly popular in civil and military use. However, their ability to fly in adverse weather and turbulent flows is hindered by their low-Reynolds-number wings. It is shown that turbulence produces a significant pitching flow, as observed by the wing, which raises the possibility of intermittent dynamic stall comparable to a pitching airfoil situation. Two airfoils (one symmetrical and the other cambered) were tested in the wind tunnel at Reynolds numbers relevant to small UAVs: between 50,000 and 200,000. Two turbulence intensities of 5 and 15% were compared to sinusoidal pitching of the airfoils at equivalent amplitudes and three frequencies. It is shown that an increase in either the pitch amplitude or the onset turbulence intensity produces comparable changes in the time-averaged lift coefficient, and both experience forms of dynamic stall. The transient behavior is, however, significantly different; and the airfoil form has greater influence on the response to pitching motion than to turbulent flow.

Rudimentary Emulation of Covert Feathers on Low-AR Wings for Poststall Lift Enhancement

Covert feathers, a group of feathers on the upper surface of bird wings, are one of birds’ features that aid them in flight at high angles of attack, making them more maneuverable. In a previous study, the authors found that a rudimentary emulation of this feature (termed a self-adaptive flap) enhances the poststall lift characteristics of low-aspect-ratio flat-plate wings at . This enhancement, however, was found to vary with the different chordwise locations of the flap and across different planforms. In a continued effort to understand this further, two-dimensional particle image velocimetry investigation was carried out in the midspan plane of the low-aspect-ratio wings. For the varying-span elliptical wings, the results reveal that the flap/shear layer interaction promotes reattachment of the separated shear layer via increased entrainment. This reattachment location varies for the different chordwise location of the flap, resulting in a different extent of the separation bubble and bubble-induced camber, which in turn is responsible for different poststall lift enhancement. On the other hand, for the rectangular wing, the flap promotes large-scale vortex formation. The formation and shedding cycle of large-scale vortices has a significant impact on the mean-body forces because of which the time-averaged poststall lift is enhanced.

Maximum propulsive efficiency of two pitching and plunging plates in tandem at low Reynolds number

PurposeThis paper aims to consider the thrust force generated by two plunging and pitching plates in a tandem configuration in forward flight to find out the configuration that maximizes the propulsive efficiency with high-enough time-averaged lift force.Design/methodology/approachTo that end, the Navier–Stokes equations for the incompressible and two-dimensional flow at Reynolds number $500 are solved. As the number of parameters is quite large, the case of constant separation between the plates (half their chord length), varying seven non-dimensional parameters related to the phase shift between the heaving motion of the foils, the phase lag between pitch and heave of each plate independently and the frequency and amplitude of the heaving and pitching motions are considered. This analysis complements some other recent studies where the separation between the foils has been used as one of the main control parameters.FindingsIt is found that the propulsive efficiency is maximized for a phase shift of 180° (counterstroking), when the reduced frequency is 2.2 and the Strouhal number based on half the plunging amplitude is 0.17, the pitching amplitude is 25° and when pitch leads heave by 135° in both the fore -plate and the hind plate. The propulsive efficiency is about 20 per cent, just a bit larger than that of an isolate plate with the same motion as the fore-plate, but the corresponding lift force is negligible for a single plate. The paper discusses this vortical flow structure in relation to other less efficient ones. Finally, the effect of the separation between the plates and the Reynolds number is also briefly discussed.Originality/valueThe kinematics of two flapping plates in tandem configuration that maximizes the propulsive efficiency are characterized discussing physically the associated vortical flow structures in comparison with less efficient kinematic configurations. A much larger number of parameters in the optimization procedure than in previous related works is considered.

Swimming freely near the ground leads to flow-mediated equilibrium altitudes

Experiments and computations are presented for a foil pitching about its leading edge near a planar, solid boundary. The foil is examined when it is constrained in space and when it is unconstrained or freely swimming in the cross-stream direction. It was found that the foil has stable equilibrium altitudes: the time-averaged lift is zero at certain altitudes and acts to return the foil to these equilibria. These stable equilibrium altitudes exist for both constrained and freely swimming foils and are independent of the initial conditions of the foil. In all cases, the equilibrium altitudes move farther from the ground when the Strouhal number is increased or the reduced frequency is decreased. Potential flow simulations predict the equilibrium altitudes to within 3 %–11 %, indicating that the equilibrium altitudes are primarily due to inviscid mechanisms. In fact, it is determined that stable equilibrium altitudes arise from an interplay among three time-averaged forces: a negative jet deflection circulatory force, a positive quasistatic circulatory force and a negative added mass force. At equilibrium, the foil exhibits a deflected wake and experiences a thrust enhancement of 4 %–17 % with no penalty in efficiency as compared to a pitching foil far from the ground. These newfound lateral stability characteristics suggest that unsteady ground effect may play a role in the control strategies of near-boundary fish and fish-inspired robots.

Effect of chordwise wing flexibility on flapping flight of a butterfly model using immersed-boundary lattice Boltzmann simulations.

Wing flexibility is one of the important factors not only for lift and thrust generation and enhancement in flapping flight but also for development of micro-air vehicles with flapping wings. In this study, we construct a flexible wing with chordwise flexibility by connecting two rigid plates with a torsion spring, and investigate the effect of chordwise wing flexibility on the flapping flight of a simple butterfly model by using an immersed boundary-lattice Boltzmann method. First, we investigate the effects of the spring stiffness on the aerodynamic performance when the body of the model is fixed. We find that the time-averaged lift and thrust forces and the required power increase with the spring stiffness. In addition, we find an appropriate range of the spring stiffness where the time-averaged lift and thrust forces are larger than those of the rigid wings. The mechanism of the lift and thrust enhancements is as follows: in the downstroke the flexible wings can generate not only the lift force but also the thrust force due to the deformation of wings; in the upstroke the flexible wings can generate not only the thrust force but also the lift force due to the deformation of wings. Second, we simulate free flights when the body of the model can only move translationally. We find that the model with the flexible wings at an appropriate value of the spring stiffness can fly more effectively than the model with the rigid wings, which is consistent with the results when the body of the model is fixed. Finally, we simulate free flights with pitching rotation. We find that the model gets off balance for any value of the spring stiffness. Therefore, the passive control of the pitching motion by the chordwise wing flexibility cannot be expected for the present butterfly model.

Aerodynamic interaction of collective plates in side-by-side arrangement

In the tip-reversal upstroke of avian flight, individual feathers twist so as to create gaps between them. Although this behavior allows the feathers to function as individual lift-generating bodies, the lift generation mechanism of these multiple bodies remains unclear. This paper reports a numerical investigation of multiple stationary plates arranged side by side in a uniform flow. The aim is to elucidate the collective mechanism of the flow generated by the plates and the lift contribution of each plate. The angle of attack of each plate and the gap between the plates are varied to determine their influence on the flow and lift of the collection of plates. The time-averaged lift increases from the lowermost to the uppermost plate, and, at a high angle of attack, the total lift coefficient of the plates becomes greater than that of a single plate solely placed in a uniform flow. At a high angle of attack, vortex shedding from the upper plates is synchronized with some phase difference, resulting in synchronized lift fluctuations for individual plates and a reduction in the overall fluctuation amplitude. With an optimal gap ratio and angle of attack, the collective behavior of plates in side-by-side arrangement can be advantageous to enhance lift-generation performance.

Numerical and experimental study of the flow around a 4:1 rectangular cylinder at moderate Reynolds number

This paper presents the results of investigations into the flow around a rectangular cylinder with a chord-to-depth ratio equal to 4. The studies are performed through wind tunnel dynamic pressure measurements along a cross section combined with two-dimensional Unsteady Reynolds-Averaged Navier-Stokes (urans) and three-dimensional Delayed-Detached Eddy Simulation (ddes). These experimental and numerical studies are complementary and combining them allows a better understanding of the unsteady dynamics of the flow. These studies aim mainly at determining the effects of the rectangle incidence and freestream velocity on the variation of the flow topology and the aerodynamic loads, and at assessing the capability of the industrially affordable urans and ddes approaches to provide a sufficiently accurate estimation of the flow for different incidences. The comparison of experimental and numerical data is performed using statistics and Dynamic Mode Decomposition. It is shown that the rectangular cylinder involves complex separation-reattachment phenomena that are highly sensitive to the Reynolds number. In particular, the time-averaged lift slope c¯lα increases rapidly with the Reynolds number in the range 7.8×103≤Re≤1.9×104 due to the modification of the time-averaged vortex strength, thickness and distance from the surface. Additionally, it is shown that both urans and ddes simulations fail to accurately predict the flow at all the different incidence angles considered. The urans approach is able to qualitatively estimate the spatio-temporal variations of vortices for incidences below the stall angle α=4∘. Nonetheless, urans does not predict stall, while ddes correctly identifies the stall angle observed experimentally.

Estimating lift from wake velocity data in flapping flight

The application of the Kutta–Joukowski (KJ) theorem to estimating the lift of a flying animal based on wake velocity fields often leads to significant underprediction of the lift, which is known as the wake momentum paradox. This work attempts to answer the puzzling question on whether the KJ theorem is legitimate in its use for complex viscous unsteady wakes generated by flapping wings. The limitations in applying the KJ theorem to flapping wings are quantitatively examined through numerical simulations of viscous incompressible flows over three flapping wing models. The three flapping wing models studied in this work are a flapping wing with a fixed wingspan, a flapping wing with a dynamically changing wingspan and a dihedral flapping wing. The KJ theorem fails to give a satisfactory prediction of the time-averaged lift unless an effective span length is correctly computed. We propose a wake-sectional Kutta–Joukowski (WS-KJ) model to predict the time-averaged lift, where the effective span length is computed based on the time-averaged distance between the streamwise vorticity centroids in the right and left half sides of the Trefftz plane. The WS-KJ model incorporates the spatial evolutionary effects of the complex vortex structures in the wake and significantly improves the prediction of the time-averaged lift. The physical foundation for such improvement is explored. In addition, the time-dependent amplitude and phase changes of the unsteady lift are discussed as the fluid acceleration effect.

Influence of wake confinement and buoyancy on flow past a square cylinder

A study of vortex shedding from a square cylinder with wake confinement is carried out for the gap ratio (G/D) in the range 0.1–12.0 for 30 ≤ Re ≤ 150. Wake confinement is achieved by placing the cylinder near a moving wall. The critical Reynolds number (Recr) for the onset of vortex shedding first decreases and then increases with a decrease in the gap-ratio. The influence of mean velocity in the gap and shear-layer formed on the moving wall during the transition of wake from steady to an unsteady state are investigated. In contrast to the case of a stationary wall, vortex shedding in the present case is observed even for quite low values of the gap ratio (G/D = 0.1). It is observed that the destabilization tendency of flow increases for G/D > 0.3. The influence of buoyancy on the vortex shedding for the given configuration is also examined for 0.1 ≤ G/D ≤ 1 and for −1 ≤ Ri ≤ 1, where buoyancy effects are introduced by heating or cooling the cylinder. Unlike the case of a stationary wall, dual roles of buoyancy have been observed. It acts as a stabilizing mechanism at low gap ratios while it destabilizes the flow at large gap ratios. Further, the influence of baroclinic production of vorticity on the flow is investigated. In the gap region, it is positive for Ri > 0 and negative for Ri < 0. Streamlines, vorticity and temperature contours and Nusselt number for different values of G/D, Re and Ri are presented. It was observed that the time-averaged drag coefficient increased with Ri and the time-averaged lift coefficient decreased with Ri except for G/D = 0.1. For G/D = 0.1, the time-averaged lift coefficient was found to increase with Ri.