Quasi-steady Lift Research Articles

Revealing the mechanism and scaling laws behind equilibrium altitudes of near-ground pitching hydrofoils

A classic lift decomposition (Von Kármán & Sears, J. Aeronaut. Sci., vol. 5, 1938, pp. 379–390) is conducted on potential flow simulations of a near-ground pitching hydrofoil. It is discovered that previously observed stable and unstable equilibrium altitudes are generated by a balance between positive wake-induced lift and negative quasi-steady lift while the added mass lift does not play a role. Using both simulations and experiments, detailed analyses of each lift component's near-ground behaviour provide further physical insights. When applied to three-dimensional pitching hydrofoils the lift decomposition reveals that the disappearance of equilibrium altitudes for ${A{\kern-4pt}R}\ {\rm (aspect\ ratio)} <1.5$ occurs due to the magnitude of the quasi-steady lift outweighing the magnitude of the wake-induced lift at all ground distances. Scaling laws for the quasi-steady lift, wake-induced lift and the stable equilibrium altitude are discovered. A simple scaling law for the lift of a steady foil in ground effect is derived. This scaling shows that both circulation enhancement and the velocity induced at a foil's leading edge by the bound vortex of its ground image foil are the essential physics to understand steady ground effect. The scaling laws for unsteady pitching foils can predict the equilibrium altitude to within $20\,\%$ of its value when $St\ {\rm (Strouhal\ number)} < 0.45$ . For $St \ge 0.45$ there is a wake instability effect, not accounted for in the scaling relations, that significantly alters the wake-induced lift. These results not only provide key physical insights and scaling laws for steady and unsteady ground effects, but also for two schooling hydrofoils in a side-by-side formation with an out-of-phase synchronization.

Lift enhancement by a flapped trailing edge at low Reynolds number: A frequency response approach

The capability of an oscillating trailing edge flap to enhance the lift generated by a rigid NACA-0012 airfoil at 2.1×104 Reynolds number is investigated. Experiments are performed at two angles of attack, namely α0=0∘ that represents a fully attached flow and α0=10∘ that represents a near-stall flow condition. The presented data and analysis cover sinusoidal oscillations of the flap at five reduced frequencies between k=0.02 and 0.12, and three oscillating amplitudes δA=5∘, 8° and 10° relative to the airfoil’s angle of attack. Enhancement to the mean lift, lift-to-drag ratio, and unsteady lift dynamics are discussed. The validity of quasi-steady formulation of Leishman’s model in predicting the lift is quantitatively assessed in light of the measurements. The unsteady lift dynamics generated by flap oscillations are modeled by constructing frequency response functions with the quasi-steady lift as the input and unsteady lift as the output. The experimentally determined gain variations are compared with analytically-derived gain functions. The effects of rate and amplitude of flap oscillations on lift cycle variations are examined using aerodynamic hysteresis response.

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.

Dynamic modeling and simulation for transmission line galloping

This paper presents a new dynamic model for the simulation of power-transmission-line galloping. The energy approach using the assumed mode method was used to derive equations of motion for a single transmission line and double transmission lines connected by spring spacers. Equations of motion are expressed in matrix form, which simplifies numerical analysis and saves computational time. The dynamic models were verified experimentally by comparing theoretical natural frequencies with measured natural frequencies of real transmission lines installed in the test site. Accelerometers and a CCD camera were used to measure vibrations, and an image processing technique was used to trace a circular target mounted on the line. Experimental results are in good agreement with theoretical results, which validate the dynamic models derived in this study. Galloping forces were modeled by assuming quasi-steady aerodynamic lift and drag, which enabled us to predict the galloping phenomena. Numerical simulation results are presented.

Conditional stability of particle alignment in finite-Reynolds-number channel flow

Finite-size neutrally buoyant particles in a channel flow are known to accumulate at specific equilibrium positions or spots in the channel cross-section, if the flow inertia is finite at the particle scale. Experiments in different conduit geometries have shown that while reaching equilibrium locations, particles tend also to align regularly in the streamwise direction. In this paper, the force coupling method was used to numerically investigate the inertia-induced particle alignment, using square-channel geometry. The method was first shown to be suitable to capture the quasisteady lift force that leads to particle cross-streamline migration in channel flow. Then the particle alignment in the flow direction was investigated by calculating the particle relative trajectories as a function of flow inertia and of the ratio between the particle size and channel hydraulic diameter. The flow streamlines were examined around the freely rotating particles at equilibrium, revealing stable small-scale vortices between aligned particles. The streamwise interparticle spacing between aligned particles at equilibrium was calculated and compared to available experimental data in square-channel flow [Gao et al., Microfluid. Nanofluid. 21, 154 (2017)]. The new result highlighted by our numerical simulations is that the interparticle spacing is unconditionally stable only for a limited number of aligned particles in a single train, the threshold number being dependent on the confinement (particle-to-channel size ratio) and on the Reynolds number. For instance, when the particle Reynolds number is ≈1 and the particle-to-channel height size ratio is ≈0.1, the maximum number of stable aligned particles per train is equal to 3. This agrees with statistics realized on the experiments of [Gao et al., Microfluid. Nanofluid. 21, 154 (2017)]. It is argued that when several particles are hydrodynamically connected moving as a unique structure (the train) with a steady streamwise velocity, large-scale hydrodynamic perturbations induced at the train scale prohibit small-scale vortex connection between the leading and second particles, forcing the leading particle to leave the train.

Reciprocal theorem for the prediction of the normal force induced on a particle translating parallel to an elastic membrane

When an elastic object is dragged through a viscous fluid tangent to a rigid boundary, it experiences a lift force perpendicular to its direction of motion. An analogous lift mechanism occurs when a rigid symmetric object translates parallel to an elastic interface or a soft substrate. The induced lift force is attributed to an elastohydrodynamic coupling that arises from the breaking of the flow reversal symmetry induced by the elastic deformation of the translating object or the interface. Here we derive explicit analytical expressions for the quasi-steady state lift force exerted on a rigid spherical particle translating parallel to a finite-sized membrane exhibiting a resistance toward both shear and bending. Our analytical approach proceeds through the application of the Lorentz reciprocal theorem so as to obtain the solution of the flow problem using a perturbation technique for small deformations of the membrane. We find that the shear-related contribution to the normal force leads to an attractive interaction between the particle and the membrane. This emerging attractive force decreases quadratically with the system size to eventually vanish in the limit of an infinitely-extended membrane. In contrast, membrane bending leads to a repulsive interaction whose effect becomes more pronounced upon increasing the system size, where the lift force is found to diverge logarithmically for an infinitely-large membrane. The unphysical divergence of the bending-induced lift force can be rendered finite by regularizing the solution with a cut-off length beyond which the bending forces become subdominant to an external body force.

Three-Dimensional Modeling of a Fin-Actuated Robotic Fish With Multimodal Swimming

Dynamical model is always an important factor in controller design for robots. Existing models of robotic fish typically incorporate only planar motion, rarely considering spatial motion. This paper formulates a complete three-dimensional (3-D) dynamic model for the robotic fish actuated by pectoral and caudal fins, in which the fluid forces mainly contain quasi-steady lift and drag, gravity and buoyancy, and waterjet strike force. The critical lift and drag of flapping fins are derived with an explicit 3-D angle of attack. Taking a bioinspired central pattern generator as the system actuation, our model can produce multimodal maneuvers, including forward/backward swimming, turning, and ascending/descending, as well as complicated motions, such as rolling and spiraling. Motions simulated in a 3-D environment are experimentally validated with a free-swimming robotic fish. Furthermore, systematic comparisons between simulations and experiments are conducted over a wide range of the control parameter space for beating frequency, amplitude, and offset. The overall results demonstrate the effectiveness and the versatility of the developed 3-D dynamic model in the prediction of the robot trajectory, velocity, and attitude.

Measurement and modeling of lift enhancement on plunging airfoils: A frequency response approach

A frequency response approach is taken to model unsteady aerodynamics resulting from plunging oscillations of an airfoil. The oscillations range covers high angles of attack (up to 65°) and reduced frequencies (up to 0.95) with particular attention to the range of flow nonlinearities over which lift enhancement is observed. Experiments were performed in a wind tunnel on an airfoil section at a Reynolds number of 80,000. Airfoil acceleration and lift force data were used to determine the frequency response functions between the measured unsteady lift and the quasi-steady lift. The results show enhanced lift amplitude over the stall regime at a reduced frequency of 0.7. The flow dynamics associated with this observation were identified from water tunnel experiments. Particular attention is paid to the flow separation and consequent formation and convection of the leading edge vortex. An optimization-based system identification approach is performed to represent the unsteady lift by a fourth-order dynamical system. This representation is suitable for sensitivity, dynamics and control analyses especially for applications where unsteady aerodynamics can be exploited for the purpose of lift enhancement.

Study on Galloping Oscillation of Iced Catenary System under Cross Winds

This paper mainly aims at revealing the nature of the galloping oscillation of iced catenary system under cross winds. The aerodynamic force on the iced catenary system is assumed to be quasi-steady, and then the quasi-steady aerodynamic lift and drag coefficients are completed in FLUENT. By fitting the discrete simulation data, the expression of the vertical aerodynamic force is further obtained. According to the Den Hartog vertical galloping mechanism, the stability of iced catenary is discussed and the initial icing angle corresponding to the critical stability is obtained. On this basis, the dynamic model of the simple iced catenary system under cross winds is established. The partial differential vibration equation of the system is converted into the ordinary differential equation by the Galerkin method and then numerically solved. The condition of the unstable catenary motion in simulation is in agreement with that from theoretical stability analysis. In addition, the effects of structural damping, initial icing angle, and wind velocity on the system responses are investigated.

Lift calculations based on accepted wake models for animal flight are inconsistent and sensitive to vortex dynamics

There are three common methods for calculating the lift generated by a flying animal based on the measured airflow in the wake. However, these methods might not be accurate according to computational and robot-based studies of flapping wings. Here we test this hypothesis for the first time for a slowly flying Pacific parrotlet in still air using stereo particle image velocimetry recorded at 1000 Hz. The bird was trained to fly between two perches through a laser sheet wearing laser safety goggles. We found that the wingtip vortices generated during mid-downstroke advected down and broke up quickly, contradicting the frozen turbulence hypothesis typically assumed in animal flight experiments. The quasi-steady lift at mid-downstroke was estimated based on the velocity field by applying the widely used Kutta–Joukowski theorem, vortex ring model, and actuator disk model. The calculated lift was found to be sensitive to the applied model and its different parameters, including vortex span and distance between the bird and laser sheet—rendering these three accepted ways of calculating weight support inconsistent. The three models predict different aerodynamic force values mid-downstroke compared to independent direct measurements with an aerodynamic force platform that we had available for the same species flying over a similar distance. Whereas the lift predictions of the Kutta–Joukowski theorem and the vortex ring model stayed relatively constant despite vortex breakdown, their values were too low. In contrast, the actuator disk model predicted lift reasonably accurately before vortex breakdown, but predicted almost no lift during and after vortex breakdown. Some of these limitations might be better understood, and partially reconciled, if future animal flight studies report lift calculations based on all three quasi-steady lift models instead. This would also enable much needed meta studies of animal flight to derive bioinspired design principles for quasi-steady lift generation with flapping wings.

Experimental investigation of single small bubble motion in linear shear flow in water

The motion of small bubble in a simple shear flow in water was experimental studied. Stable shear flow with low turbulence level was achieved with curved screen and measured using LDV. The bubbles were captured by high speed camera and the captured images were processed with digital image routine. The bubble was released from a capillary tube. The instantaneous bubble position, bubble velocity and forces were obtained based on the captured parameters. The quasi-steady lift coefficient was determined by the linear fitting of the bubble trajectory of several cycles. The results indicated that the lateral migration was coupled with the zigzag motion of bubble in the present experiment. The bubble migrated to the left side and its quasi-steady lift coefficient was negative. Good repeatable results were observed by measurements of 18 bubbles. The bubble motion in shear flow in water was first experimental studied and negative lift force was observed in the present study condition. The lift coefficient decreased when shear stress magnitude or bubble diameter increased in the present experiment condition.

The lateral migration of relative large bubble in simple shear flow in water

The lateral migration of relative large bubble in shear flow was essential for two phase flow modeling when relative large bubble was presented. To better understand the lift force for relative large bubble, the single air bubble motions with diameter ranged from 10mm to 20mm in shear flow in water were captured by high speed camera. The linear shear flow with low turbulence intensity was achieved by curved screen. The bubbles were collected in an inverted semi-spherical cup and released by rotating the cup. The lateral migration velocity and quasi-steady lift force were obtained by linear fitting of bubble trajectories. Reproducible results were obtained by measurements of many bubbles. The results showed that bubble shape parameters, rising velocity and drag force were stayed at same level in shear flow as in still water. The relative large bubble migrated to left side and the lift force was negative. A critical bubble diameter of 15mm was observed which was near the boundary between oblate bubble and spherical cap bubble. When the bubble equivalent diameter was lower than the critical value, the lift coefficient was decreasing with the increasing of shear stress magnitude. When the bubble diameter was larger than the critical diameter, the lift coefficient was monotonically decreased with the bubble equivalent diameter and the shear stress magnitude had no effect in the present experiment condition. The comparison with existing study revealed that the present lift correlations were not able to predict the values and new models were needed.

Reduced-order unsteady aerodynamic models at low Reynolds numbers

AbstractIn this paper we develop reduced-order models for the unsteady lift on a pitching and plunging aerofoil over a range of angles of attack. In particular, we analyse the pitching and plunging dynamics for two cases: a two-dimensional flat plate at$\mathit{Re}= 100$using high-fidelity direct numerical simulations and a three-dimensional NACA 0006 aerofoil at$\mathit{Re}= 65\hspace{0.167em} 000$using wind-tunnel measurements. Models are obtained at various angles of attack and they are verified against measurements using frequency response plots and large-amplitude manoeuvres. These models provide a low-dimensional balanced representation of the relevant unsteady fluid dynamics. In simulations, flow structures are visualized using finite-time Lyapunov exponents. A number of phenomenological trends are observed, both in the data and in the models. As the base angle of attack increases, the boundary layer begins to separate, resulting in a decreased quasi-steady lift coefficient slope and a delayed relaxation to steady state at low frequencies. This extends the low-frequency range of motions that excite unsteady effects, meaning that the quasi-steady approximation is not valid until lower frequencies than are predicted by Theodorsen’s classical inviscid model. In addition, at small angles of attack, the lift coefficient rises to the steady-state value after a step in angle, while at larger angles of attack, the lift coefficient relaxes down to the steady-state after an initially high lift state. Flow visualization indicates that this coincides with the formation and convection of vortices at the leading edge and trailing edge. As the angle of attack approaches the critical angle for vortex shedding, the poles and zeros of the model approach the imaginary axis in the complex plane, and some zeros cross into the right half plane. This has significant implications for active flow control, which are discussed. These trends are observed in both simulations and wind-tunnel data.

双分裂导线次档距振荡的气动力模型与解析

次档距振荡是分裂导线特有的一种振动现象，由前端导线的尾流引起后端导线的振动。导线绕流其实质是流体的圆柱绕流，通常条件下将在尾流区产生卡门涡街。本文建立了一种理想的卡门涡街模型，在对该模型进行数学解析的基础上，提出了双分裂导线中后端导线绕流的准定常气动力数学表达式，并通过与经典风洞实验所得的气动力系数对比修正该表达式的相关系数，为解决导线绕流问题提出了新的方法。 Subspan oscillation is a unique phenomenon to split conductors, in which the flowing of upward conductor causes downward conductor’s vibration. The essence of the flowing around a conductor is the flowing around a cylinder. Karman vortex street will emerge downstream usually. With ahypothetical modal of Karman vortex street being set up in this paper, a mathematical expression of its quasi-steady drag and lift is founded on the base of the analysis of this modal. Then relative coefficient in aforementioned is amended according to the data acquired from wind tunnel testing. Thus a new idea is proposed to solve the question of the flowing around conductors.

Rolling/sliding of a particle on a flat wall in a linear shear flow at finite Re

Recently Lee and Balachandar proposed analytically-based expressions for drag and lift coefficients for a spherical particle moving on a flat wall in a linear shear flow at finite Reynolds number. In order to evaluate the accuracy of these expressions, we have conducted direct numerical simulations of a rolling particle for shear Reynolds number up to 100. We assume that the particle rolls on a horizontal flat wall with a small gap separating the particle from the wall ( L = 0.505) and thus avoiding the logarithmic singularity. The influence of the shear Reynolds number and the translational velocity of the particle on the hydrodynamic forces of the particle was investigated under both transient and the final drag-free and torque-free steady state. It is observed that the quasi-steady drag and lift expressions of Lee and Balachandar provide good approximation for the terminal state of the particle motion ranging from perfect sliding to perfect rolling. With regards to transient particle motion in a wall-bounded shear flow it is observed that the above validated quasi-steady drag and lift forces must be supplemented with appropriate wall-corrected added-mass and history forces in order to accurately predict the time-dependent approach to the terminal steady state. Quantitative comparison with the actual particle motion computed in the numerical simulations shows that the theoretical models quite effective in predicting rolling/sliding motion of a particle in a wall-bounded shear flow at moderate Re.

The interaction of a gravity current with a circular cylinder mounted above a wall: Effect of the gap size

Abstract The flow of a gravity current past a circular cylinder mounted above a bottom wall is studied by means of two-dimensional Navier–Stokes simulations. The investigation focuses on the effects of the gap size on the forces acting on the cylinder. The interaction of the current with the cylinder can be divided into an impact, a transient, and a quasisteady stage. During the impact stage, the gravity current meets the cylinder, and the drag increases towards a maximum, while the lift undergoes a drastic fluctuation which increases noticeably with the gap size. During the quasisteady stage, the flow past the cylinder resembles that observed in constant-density boundary layer flows past cylinders: Karman vortex shedding is observed for sufficiently large gap sizes, while a vorticity cancellation mechanism is responsible for the suppression of vortex shedding at small gap sizes. On the other hand, interesting differences that distinguish the gravity current case from the constant-density case are the presence in the gravity current flow of a component of the mean quasisteady lift due to buoyancy, and another component from the deflection of the wake towards the wall by the constriction of the dense fluid flow downstream of the cylinder, as well as the cancellation of vortex shedding for all gap sizes when the ratio of the channel depth to lock height is decreased from 5 to 1.

Sports ball aerodynamics: A numerical study of the erratic motion of soccer balls

The application of the commercial CFD code, FLUENT, to sports ball aerodynamics was assessed and a validated 3D analysis technique was established for balls that have been scanned with a 3D laser scanner or drawn in CAD. The technique was used to examine the effects of surface geometry on the aerodynamic behaviour of soccer balls by comparing the flow around different balls and predicting the aerodynamic force coefficients. The validation process included performing CFD studies on 3D smooth spheres and various soccer balls, and comparing the results to wind tunnel tests and flow visualisation. The CFD technique used a surface wrapping meshing method and the Reynolds Averaged Navier–Stokes approach with the realizable k-ε turbulence model, which was found to be able to predict the drag, lift and side force coefficients ( C D , C L and C S ) reliably, to compare the wake behaviour, and to give good pressure distributions near the stagnation point. The main limitations of the technique with the available computational resources were its inability to accurately predict boundary layer transition or growth, but despite this, several conclusions could be drawn regarding soccer ball aerodynamics. C D was not significantly different between balls. C L and C S were found to be significantly affected by the orientation of the ball relative to its direction of travel, meaning that balls kicked with low amounts of spin could experience quasi-steady lift and side forces and move erratically from side-to-side or up and down through the air. For different balls, C D , C L and C S were predicted and their variation with orientation entered into a modified trajectory simulation program. The erratic nature of this type of kick was found to vary with details of the surface geometry including seam size, panel symmetry, number, frequency and pattern, as well as the velocity and spin applied to the ball by the player. Exploitation of this phenomenon by players and ball designers could have a significant impact on the game.

Influence of wing kinematics on aerodynamic performance in hovering insect flight

The influence of different wing kinematic models on the aerodynamic performance of a hovering insect is investigated by means of two-dimensional time-dependent Navier–Stokes simulations. For this, simplified models are compared with averaged representations of the hovering fruit fly wing kinematics. With increasing complexity, a harmonic model, a Robofly model and two more-realistic fruit fly models are considered, all dynamically scaled atRe= 110. To facilitate the comparison, the parameters of the models were selected such that their mean quasi-steady lift coefficients were matched. Details of the vortex dynamics, as well as the resulting lift and drag forces, were studied.The simulation results reveal that the fruit fly wing kinematics result in forces that differ significantly from those resulting from the simplified wing kinematic models. In addition, light is shed on the effect of different characteristic features of the insect wing motion. The angle of attack variation used by fruit flies increases aerodynamic performance, whereas the deviation is probably used for levelling the forces over the cycle.

Geometric Methods for Modeling and Control of Free-Swimming Fin-Actuated Underwater Vehicles

In this paper, techniques from geometric mechanics and geometric nonlinear control theory are applied to modeling and construction of trajectory tracking algorithms for a free-swimming underwater vehicle that locomotes and maneuvers using a two-link actuated ldquotailrdquo and independently actuated ldquopectoral finrdquo bow planes. Restricting consideration of fluid forces to the simple effects of added mass and quasi-steady lift and drag, the resulting system model can be expressed in a control-affine structure. With particular choices of oscillatory actuation of the four system joints, maneuvers such as swimming forward, in and out of plane turning, surfacing, and diving can be constructed. Further, the vehicle and model can generate agile maneuvers such as snap turns. Trajectory tracking can then be produced using state error feedback. The methods are demonstrated both in simulation and in experiment using the University of Washington prototype fin-actuated underwater vehicle.

Unsteady Wing Characteristics AtLow Reynolds Number

Unsteady Wing Characteristics AtLow Reynolds Number