Instantaneous Aerodynamic Forces Research Articles

A numerical study on the aerodynamic effects of dynamic twisting on forward flight flapping wings

To better understand the secret of natural flying vertebrates such as how humming-birds twist their wings to achieve superb flight ability, we presented a numerical investigation of dynamic twisting based on a hummingbird-like flapping wing model. Computational fluid dynamic simulations were performed to examine the effects of dynamic twisting on the unsteady flow field, the generation of instantaneous aerodynamic forces, and the time-averaged aerodynamic performance. This research reveals the details of leading-edge vortices (LEVs) and the underlying mechanisms behind the positive effects of wing torsion. The results demonstrated that wing torsion can effectively maintain the favorable distribution of effective angle of attack along the wing spanwise, resulting in a higher time-averaged thrust and vertical force. Further, the proper parameters of dynamic twisting can also improve the propulsive efficiency in forward flight. Dynamic twisting also showed a superior ability in controlling the airflow separation over the wing surface and maintaining the stability of the LEV. The amplitudes of effective angle of attack associated with the highest peak thrust and the maximum thrust-to-power at different advanced ratios were also explored, and it was found that the amplitudes decrease with increasing advanced ratio. To improve the efficiency during larger advanced ratio, specific modifications to the pitching of the wing were proposed in this work. The research in this paper has promising implications for the bio-inspired flapping wing.

A simple model of wake capture aerodynamics.

Flapping wings may encounter or 'capture' the wake from previous half-stroke, leading to local changes in the instantaneous aerodynamic force on the wing at the start of each half-stroke. In this paper, I developed a simple approach to integrating prediction of these wake capture effects into existing analytical quasi-steady models for hovering insect flapping flight. The local wake flow field is modelled as an additional induced velocity component normal to the stroke plane of the flapping motion that is blended/switched in at the start of each half-stroke. Comparison of model results against experimental data in the literature shows satisfactory agreement in predicting the wake capture lift and drag variations for eight different test cases. Sensitivity analysis shows that the form of the translation velocity time history has a significant effect on the magnitude of wake capture forces. Profiles that retain high translational velocity right up to stroke reversal evoke a much larger effect from wake capture compared with sinusoidal. This result is significant because while constant flapping translation velocity profiles can be generated in the laboratory, the very high accelerations required near stroke reversals incur high mechanical cost that prevents practical adoption in nature or engineered flapping flight vehicles.

Effect of spanwise folding on the aerodynamic performance of three dimensional flapping flat wing

Bird flight incorporates complex multi-degree-of-freedom motions, such as flapping, pitching, twisting, and folding. The aerodynamic mechanism of these complex movements, especially the coupled flapping-folding motion, still lacks in-depth understanding. In this study, the flapping-folding motion is numerically investigated based on a three-dimensional two-section flapping plate with various folding parameters. Different folding amplitudes, phase angles between flapping and folding, and mean folding angles are considered under a preset flapping motion. Kinematics of different flapping-folding motions is analyzed to establish the relationship between the motion and aerodynamic characteristics. The aerodynamic forces and flow structures are also compared. It is found that the folding motion affects the horizontal projection area of the wing, which primarily dominates the trend of lift variation. The folding motion mainly affects the development of the leading-edge vortex on the outer part of the wing by changing the local tangential velocity and the effective angle of attack, which in turn affects the instantaneous aerodynamic forces. A larger folding amplitude will cause an obvious phase shift on lift force and generate more thrust force. An increase in the phase angle between flapping and folding will reduce the lift amplitude, but a small phase angle is beneficial for thrust. A negative mean folding angle can enhance lift during downstroke and reduce negative lift in upstroke, thus significantly increasing the mean lift force, indicating a potential advantage of folding motion in lift generation. The research in this paper is helpful to understand the flight mechanism of birds and to design a micro-air vehicle with bio-inspired flapping kinematics.

Active control of separated flow on a symmetric airfoil by pitching oscillation

Experiments are conducted on the control of massively separated flow over a symmetric airfoil by imposing pitching oscillation at smaller amplitudes. Two symmetric airfoils of different thickness to chord ratios are considered to account for the effect of thickness and the stall-type on flow control. Instantaneous aerodynamic forces and moments are calculated by integrating surface and wake pressure distributions. Time-resolved particle image velocimetry and unsteady pressure measurements are carried out simultaneously to characterize the flow field over the pitching airfoil. The results presented here provide an insight into flow dynamics and the dynamic response of a stalled airfoil to pitching oscillation at different reduced frequencies. The present research adopts a dynamical system approach and attempts to estimate an optimum pitching oscillation frequency for better flow control on a stalled airfoil. The adopted methodology can be used to determine the optimal value of input parameters pertaining to flow control on a flat plate/wing by any unsteady excitation. Besides, a novel data-driven aerodynamic model has been developed on a Fourier basis for a symmetrical airfoil undergoing pitching oscillation at the post-stall regime.

Effect of Pitch Parameters on Aerodynamic Forces of a Straight-Bladed Vertical Axis Wind Turbine with Inclined Pitch Axes

Pitch regulation plays a significant role in improving power performance and achieving output control in wind turbines. The present study focuses on a novel, pitch-regulated vertical axis wind turbine (VAWT) with inclined pitch axes. The effect of two pitch parameters (the fold angle and the incline angle) on the instantaneous aerodynamic forces and overall performance of a straight-bladed VAWT under a tip-speed ratio of 4 is investigated using an actuator line model, achieved in ANSYS Fluent software and validated by previous experimental results. The results demonstrate that the fold angle has an apparent influence on the angles of attack and forces of the blades, as well as the power output of the wind turbine. It is helpful to further study the dynamic pitch regulation and adaptable passive pitch regulation of VAWTs. Incline angles away from 90° lead to the asymmetric distribution of aerodynamic forces along the blade span, which results in an expected reduction of loads on the main shaft and the tower of VAWTs.

Vortex flow aerodynamics behind a symmetric airfoil at low angles of attack and Reynolds numbers

The low Reynolds number aerodynamics is important to investigate for micro air vehicle applications. The current paper covers numerical simulations to present the downstream development of the wake patterns and detailed analysis of the vortices generated at the downstream of NACA 0012 airfoil around the critical angle of attack where the instantaneous vortex patterns are oscillatory and differ from the mean vortex pattern for low Reynolds numbers ranging from 1000 to 4000. The instantaneous and mean aerodynamic forces, pressure and skin friction coefficients, and vorticity values are compared in addition to the path of the vortex centers, their longitudinal and lateral spacings, Kármán spacing ratios, and distortion ratios at the wake of the airfoil in regard to the different Reynolds numbers investigated. The streamwise and crosswise velocities of the vortex cores and relative velocities at different transverse locations are also discussed and presented in detail. The correlations between different non-dimensional numbers (St, Re, Ro) are obtained at these low Reynolds numbers investigated.

Aerodynamic effects of bio-inspired corrugated wings on gliding and hovering performances

Recently, numerous studies have been conducted to clarify the effects of corrugation wing on aerodynamic performances. The effects of the corrugation patterns and inclination angles were investigated using computational fluid dynamic method in gliding and hovering flight at Reynolds numbers of order 104. The instantaneous aerodynamic forces and the vorticity field around the wing models were provided to research the underlying mechanisms of aerodynamic effects of corrugated wing models. The findings can be concluded as follows: (1) the corrugation patterns have different effects on aerodynamic performance. The effect of noncamber corrugated wing is to decrease the lift and increase drag compared with a flat-plate when the angle of attack is less than 25° during gliding flight. The corrugated wing with a camber (corrug-2) after the valleys enhances the aerodynamic forces when angle of attack is higher than 35°. The valley inclination angle has limited effect on aerodynamic forces in gliding flight. (2) The lift forces of different corrugation patterns show significantly asymmetric during the upstroke and downstroke. The main reason leads to this phenomenon is the case that two sides of the corrugated wings are not symmetric around the pitching axis. The corrugated wing with only two valleys (corrug-1) changes the lift and drag very slightly. Corrug-2 produces larger peak during downstroke and smaller peak during upstroke. The increase in the inclination angle has limited effect on the aerodynamic forces. The possible reason for these small aerodynamic effects might be that the corrugated wings are smoothed by small vortices trapped in valleys. The main reason for the significant difference between plate and corrug-2 is that the recirculating vortices trapped in the saddle and hump reduce the pressure above the wing surface.

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.

Aerodynamic effects of corrugation configurations in sweeping- pitching flight

Some insects possess corrugated wings, which distinguish from the ordinary airfoils. It is important to research the corrugation effect on the aerodynamic performances. A series of corrugated wing models were designed based on former research in represent study to find out the underlying mechanisms. The effects of the corrugation pattern and inclination angle were studied using computational fluid dynamic (CFD) method during hovering flight at Reynolds numbers in the order of 104. The instantaneous aerodynamic forces and the vorticity field around the wing models were provided. The findings are as follows: (1) the results of this paper show that patterns of corrugation have different effect on aerodynamic performances. The corrugated wing like Corrug-1 changes the lift and drag very slightly compared with a flat-plate. The corrugation patterns like Corrug-2 and 3 of wing model reduce the lift and drag force. (2) the increase in the inclination angle has limited effect the aerodynamic forces. The inclination angles like corrug-3 and 4 produce almost the same forces.

Impact of Different Nose Lengths on Flow-Field Structure around a High-Speed Train

In this study, the time-averaged and instantaneous slipstream velocity, time-averaged pressure, wake flows, and aerodynamic force of a high-speed train (HST) with different nose lengths are compared and analyzed using an improved delayed detached-eddy simulation (IDDES) method. Four train models were selected, with nose lengths of 4, 7, 9, and 12 m. To verify the accuracy of the numerical simulation results, they were compared with wind tunnel test results. The comparison results show that the selection of the numerical simulation method is reasonable. The research results show that with increasing nose length, the peak values of the time-averaged slipstream velocity of the trackside position (3 m from the center of track and 0.2 m from the top of rail) and the platform position (3 m from the center of track and 0.2 m from the top of rail) decrease continuously, and show a trend of rapid reduction at first, and then a slow decrease. As the nose length increased from 4 to 12 m, the time-averaged slipstream velocity at the trackside position and platform position are decreased by 57% and 19.5%, respectively. At a height of 1.6 m from the top of the rail, ΔCP max (maximum pressure coefficient), |ΔCP min| (the absolute value of minimum pressure coefficient), and ΔCP (pressure change coefficient) decrease with increasing nose length, which is similar to the peak value of time-averaged slipstream velocity, decreasing rapidly at first and then slowly. As the nose length increased from 4 to 12 m, decreases of ΔCP max, |ΔCP min|, and ΔCP by 26.5%, 58.5%, and 44.8% were shown, respectively. Different nose lengths also have a significant impact on wake flow.

The actuator cell model for the Darrieus wind turbine

Development of existing and innovative aerodynamic models for the Darrieus wind turbine has become very popular in recent years. Since research in the field of aerodynamics of the Darrieus concept is very limited, the development of simplified aerodynamic methods is very difficult. Therefore, the major objective of the present study is to present the concept of a new aerodynamic model for the Darrieus wind turbine – the actuator cell model (ACM). Aerodynamic loads are added to the unsteady incompressible Navier-Stokes equations as momentum source terms. The source terms are computed basing on instantaneous aerodynamic forces taken from the literature. The numerical results of wake structure computed by ACM are compared with the experimental data. Agreement between the numerical results of velocity profiles and the experimental data is reasonably good.

Comparison of Aerodynamic Forces and Moments Calculated by Three-dimensional Unsteady Blade Element Theory and Computational Fluid Dynamics

AbstractIn previous work, we modified blade element theory by implementing three-dimensional wing kinematics and modeled the unsteady aerodynamic effects by adding the added mass and rotational forces. This method is referred to as Unsteady Blade Element Theory (UBET). A comparison between UBET and Computational Fluid Dynamics (CFD) for flapping wings with high flapping frequencies (>30 Hz) could not be found in literature survey. In this paper, UBET that considers the movement of pressure center in pitching-moment estimation was validated using the CFD method. We investigated three three-dimensional (3D) wing kinematics that produce negative, zero, and positive aerodynamic pitching moments. For all cases, the instantaneous aerodynamic forces and pitching moments estimated via UBET and CFD showed similar trends. The differences in average vertical forces and pitching moments about the center of gravity were about 10% and 12%, respectively. Therefore, UBET is proven to reasonably estimate the aerodynamic forces and pitching moment for flight dynamic study of FW-MAV. However, the differences in average wing drags and pitching moments about the feather axis were more than 20%. Since study of aerodynamic power requires reasonable estimation of wing drag and pitching moment about the feather axis, UBET needs further improvement for higher accuracy.

On the aerodynamic forces on heaving and pitching airfoils at low Reynolds number

The influence that the kinematics of pitching and heaving 2D airfoils has on the aerodynamic forces is investigated using direct numerical simulations and a force decomposition algorithm. Large-amplitude motions are considered (of the order of one chord), with moderate Reynolds numbers and reduced frequencies of order $O(1)$, varying the mean pitch angle and the phase shift between the pitching and heaving motions. Our results show that the surface vorticity contribution (viscous effect) to the aerodynamic force is negligible compared with the contributions from the body motion (fluid inertia) and the vorticity within the flow (circulation). For the range of parameters considered here, the latter tends to be instantaneously oriented in the direction normal to the chord of the airfoil. Based on the results discussed in this paper, a reduced-order model for the instantaneous aerodynamic force is proposed, taking advantage of the force decomposition and the chord-normal orientation of the contribution from vorticity within the flow to the total aerodynamic force. The predictions of the proposed model are compared with those of a similar model from the literature, showing a noticeable improvement in the prediction of the mean thrust, and a smaller improvement in the prediction of the mean lift and the instantaneous force coefficients.

Load-estimation techniques for unsteady incompressible flows

In a large variety of fluid-dynamic problems, it is often impossible to directly measure the instantaneous aerodynamic or hydrodynamic forces on a moving body. Examples include studies of propulsion in nature, either with mechanical models or living animals, wings, and blades subjected to significant surface contamination, such as icing, sting blockage effects, etc. In these circumstances, load estimation from flow-field data provides an attractive alternative method, while at the same time providing insight into the relationship between unsteady loadings and their associated vortex-wake dynamics. Historically, classical control-volume techniques based on time-averaged measurements have been used to extract the mean forces. With the advent of high-speed imaging, and the rapid progress in time-resolved volumetric measurements, such as Tomo-PIV and 4D-PTV, it is becoming feasible to estimate the instantaneous forces on bodies of complex geometry and/or motion. For effective application under these conditions, a number of challenges still exist, including the near-body treatment of the acceleration field as well as the estimation of pressure on the outer surfaces of the control volume. Additional limitations in temporal and spatial resolutions, and their associated impact on the feasibility of the various approaches, are also discussed. Finally, as an outlook towards the development of future methodologies, the potential application of Lagrangian techniques is explored.

A numerical study on the aerodynamic performance and the self-starting characteristics of a Darrieus wind turbine considering its moment of inertia

Self-starting characteristics is a challenging issue in the field of Darrieus-type vertical axis wind turbines. Traditionally, the numerical simulations were performed at several constant rotational velocities for the turbine and the generated torques were reported for each rotational velocity, neglecting the effects of the turbine inertia on the transient start-up motion of the turbine. In the current study, a numerical method is proposed to study the self-starting characteristics of a Darrieus wind turbine, considering the turbine moment of inertia. The simulation starts from the initial stationary state and continues until the final steady-periodic condition. At each time step, the instantaneous rotational velocity of the turbine is computed based on the Newton’s second law, according to the instantaneous aerodynamic and mechanical forces acting on the turbine. Results indicate that as the rotor inertia increases, it takes a longer time for the turbine to reach its final velocity, in a manner that, the turbine might even fail to reach the final condition and the rotation halts. Results also show that as the rotor inertia decreases, the oscillations amplitude of the turbine rotational velocity increases. This can enable the turbine to pass higher resistant torques than those computed based on the traditional method.

A computational study on the influence of insect wing geometry on bee flight mechanics.

ABSTRACTTwo-dimensional computational fluid dynamics (CFD) is applied to better understand the effects of wing cross-sectional morphology on flow field and force production. This study investigates the influence of wing cross-section on insect scale flapping flight performance, for the first time, using a morphologically representative model of a bee (Bombus pensylvanicus) wing. The bee wing cross-section was determined using a micro-computed tomography scanner. The results of the bee wing are compared with flat and elliptical cross-sections, representative of those used in modern literature, to determine the impact of profile variation on aerodynamic performance. The flow field surrounding each cross-section and the resulting forces are resolved using CFD for a flight speed range of 1 to 5 m/s. A significant variation in vortex formation is found when comparing the ellipse and flat plate with the true bee wing. During the upstroke, the bee and approximate wing cross-sections have a much shorter wake structure than the flat plate or ellipse. During the downstroke, the flat plate and elliptical cross-sections generate a single leading edge vortex, while the approximate and bee wings generate numerous, smaller structures that are shed throughout the stroke. Comparing the instantaneous aerodynamic forces on the wing, the ellipse and flat plate sections deviate progressively with velocity from the true bee wing. Based on the present findings, a simplified cross-section of an insect wing can misrepresent the flow field and force production. We present the first aerodynamic study using a true insect wing cross-section and show that the wing corrugation increases the leading edge vortex formation frequency for a given set of kinematics.

The impact of pitch motion of a platform on the aerodynamic performance of a floating vertical axis wind turbine

The flow-field around the offshore floating vertical axis wind turbines (OF-VAWTs) is affected by the six-degrees of freedom (6-DOF) movement of the platforms. Understanding the impact of a certain DOF motion on the aerodynamics is beneficial to the design of wind turbines. In this paper, the aerodynamics and performance of a scale OF-VAWT in pitch motion are investigated. The computational fluid dynamics (CFD) method with the turbulence model of improved delayed detached eddy simulation (IDDES) and the overset mesh technique are employed to analyze the characteristics of pitch motion of wind turbines. The CFD model is verified by the experimental data from available literature when the turbine has no-pitch motion. Then, the aerodynamic forces, power, and wake of an OF-VAWT in periodical pitch motion are analyzed. Because of the varying wave loads, an unsteady aerodynamic analysis considering the pitch motion with different periods and amplitudes is performed. The results show that the pitch motion can improve the power output of the OF-VAWTs, and enlarge the variation ranges of aerodynamic force coefficients. Meanwhile, the graphs of the vortex structure show that the complex flow interaction emerges around the rotor blades. Additionally, the power coefficient and the instantaneous aerodynamic forces coefficients sensitively change with different pitching periods and pitching amplitudes.

The effect of the nonlinear velocity and history dependencies of the aerodynamic force on the dynamic response of a rotating wind turbine blade

Existing models for the analysis of offshore wind turbines account for the aerodynamic action on the turbine rotor in detail, requiring a high computational price. When considering the foundation of an offshore wind turbine, however, a reduced rotor model may be sufficient. To define such a model, the significance of the nonlinear velocity and history dependency of the aerodynamic force on a rotating blade should be known. Aerodynamic interaction renders the dynamics of a rotating blade in an ambient wind field nonlinear in terms of the dependency on the wind velocity relative to the structural motion. Moreover, the development in time of the aerodynamic force does not follow the flow velocity instantaneously, implying a history dependency. In addition, both the non-uniform blade geometry and the aerodynamic interaction couple the blade motions in and out of the rotational plane. Therefore, this study presents the Euler–Bernoulli formulation of a twisted rotating blade connected to a rigid hub, excited by either instantaneous or history-dependent aerodynamic forces. On this basis, the importance of the history dependency is determined. Moreover, to assess the nonlinear contributions, both models are linearized. The structural response is computed for a stand-still and a rotating blade, based on the NREL 5-MW turbine. To this end, the model is reduced on the basis of its first three free-vibration mode shapes. Blade tip response predictions, computed from turbulent excitation, correctly account for both modal and directional couplings, and the added damping resulting from the dependency of the aerodynamic force on the structural motion. Considering the deflection of the blade tip, the history-dependent and the instantaneous force models perform equally well, providing a basis for the potential use of the instantaneous model for the rotor reduction. The linearized instantaneous model provides similar results for the rotating blade, indicating its potential application for this scenario, and allowing for the definition of an added damping matrix, applicable for the dynamic analysis of rotating turbine blades.

On the wake pattern of symmetric airfoils for different incidence angles at Re = 1000

In the current study, numerical simulations are performed in order to investigate effects of incidence angle and airfoil thickness on alternating vortex pattern of symmetric airfoils at Re = 1000. This alternating vortex pattern is found to be significantly varying in shape as the incidence angle increases. The results are obtained with 1° increment from 0° to 41° and then with 10° increment from 40° until 180°. The instantaneous and mean vortex patterns are investigated around 2% thick (NACA 0002) and 12% thick (NACA 0012) airfoils. The mean lift, drag, and pitching moment coefficients in addition to Strouhal number are computed and compared with the results available in literature. It is found that the wake behind the airfoil exhibits a continuous vortex shedding pattern below 8° incidence angle for NACA 0002 and below 7° incidence angle for NACA 0012 at Re = 1000. The wake structures are classified into five different modes according to their pattern obtained from instantaneous and mean vorticity fields by also taking into account the amplitude spectrum of the lift coefficient, the instantaneous and mean aerodynamic force coefficients, velocity fields, and the longitudinal and lateral vortex spacings.

Effect of vortex shedding in unsteady aerodynamic forces for a low Reynolds number stationary wing at low angle of attack

This study elucidates the relation between wake vortex shedding and aerodynamic force fluctuations for a low Reynolds number wing from time resolved particle image velocimetry (TR-PIV) experimental measurements. The results reveal a periodic lift and drag variation within the shedding cycle and resolve the frequencies of those fluctuations from a proper orthogonal decomposition (POD) and power spectral density (PSD) analysis. To show the effect of vortex shedding on the body force fluctuations, the evolution of instantaneous aerodynamic forces is compared to the pressure field of the fluid flow and to the vortical structures in the wake of the airfoil. A six step model describing the vortex-force relation is proposed. It shows that changes in lift such as maximum lift and minimum lift are associated with the detachment of a vortex. It also shows that the minimum or local minimum drag value is obtained at the onset formation of a vortex on the airfoil wake. Similarly, the maximum or local maximum drag is obtained at the onset formation of the saddle on the airfoil wake. The model further explains the asymmetry observed in the unsteady drag force evolution. The model can be used to optimize flow control and fluid-structure interaction applications.