Flat Plate Wing Research Articles

Experimental Exploration of Bioinspired Planar Wingtip Devices for a Flat-Plate Wing in the Low Reynolds Number Regime

Experimental Exploration of Bioinspired Planar Wingtip Devices for a Flat-Plate Wing in the Low Reynolds Number Regime

Unsteady Lift Produced by a Flat-Plate Wing Translating Past Finite Obstacles

The unsteady lift of a high-angle-of-attack, flat-plate wing encountering finite-length obstacles is studied using towing-tank force measurements and flow visualization. The wing translates from rest and at 1 chord traveled interacts with a rectangular channel, ceiling, or ground. The angle of attack, obstacle length, and height to the obstacle are varied. As the channel gap height decreases, circulatory-lift peaks attributed to leading-edge vortices (LEVs) become larger, and for the second peak onward occur earlier, from wing blockage enhancing the flow speed. Larger and earlier LEVs are visualized, supporting this, as are secondary vortices off the channel. The lift reduces while exiting a channel, being lowest afterward if exiting during a lift peak. For ceilings, the first circulatory-lift peak increases for smaller LE-to-ceiling gaps, but for 0.5 chord gaps or less, later maxima are below the no-obstacle case yet still earlier. For grounds, with lower wing height the first circulatory-lift peak is larger but the second peak’s behavior varies with angle of attack, and lift decreases near the ground end. Grounds affect peak timing the least, indicating less influence on the LEV. The lift rises slightly ahead of channels and ceilings, and often lowers before channels and grounds end, providing warnings.

Enhancement of aerodynamic performance of a bristled wing by elliptic cylinders

Enhancing the aerodynamic performance of bristled wings is an important topic for small flying robotics. This paper numerically investigates this situation at very low Reynolds numbers by using elliptic cylinders as the bristles instead of circular cylinders. Optimal configuration of the bristled wing with five elliptic cylinders is obtained, which corresponds to the maximum lift. The results show that, compared with the case of circular cylindrical bristles, the aerodynamic performance of the elliptical bristles can be enhanced effectively. The enhancement can be more significant as the aspect ratio of the ellipses increases and the gap width decreases. The bristled wing generates more lift compared to a flat-plate wing with a length five times that of the major axis of an ellipse. For the cases that the attack angle α for the whole wing is equal to those for the elliptical bristles θ, the optimal attack angle for ellipses maximizing the total lift force of the five-bristle model is between 40° and 45°. For α ≠ θ with the Reynold number Re ≪ 0.1, the optimal ellipse attack angle is between 40° and 45°. For α ≠ θ with Re∼ 1, the optimal ellipse attack angle deviates heavier from the range between 40° and 45° at some α values and reaches approximately 32° at α = 20°. This paper can lay a foundation for optimal design of small flying robotics and enhancement of flow through porous structures in future.

Navigating vortex gust interactions and mitigations by plunging wings

Inspired by the stability achieved by biological flapping-winged fliers in gusty environments, we conducted particle image velocimetry studies on the interactions between plunging wings and large-scale vortex gusts. Our experiments involved a flat plate wing performing sinusoidal plunging motions at various frequencies, resulting in Strouhal numbers (St) ranging from 0 to 0.5 within which biological fliers commonly operate. This range of St corresponded to reduced frequencies (k) between 0 and 0.79 at a chord Reynolds number of 2000. The gust structures, generated periodically by pitching vanes, traveled downstream to the wing. We observed the vortex interactions between wing-induced vortices [particularly the boundary layer and the leading-edge vortex (LEV)] and the gusts. Additionally, we quantified the gusts' effects on the local flow around the wing by calculating the circulation within a control region attached to the plunging wing. The wing-induced vorticity merged momentarily with gusts of the same-sign vorticity. In contrast, opposite-sign gusts not only increased the circulation of the wing-induced vortices but also led to the LEV detaching faster. While gusts had the potential to significantly alter the flow around the wings, the plunging wings sometimes managed to avoid the gusts due to their transverse motion. Furthermore, the prolonged presence of the stronger LEVs near the wing, which are characteristic of plunging wings at higher St and k, could deflect the gusts away, reducing their impact on the vorticity and circulation within the control region. These findings illustrate how robust flapping kinematics can mitigate the effects of vortex gusts.

A theory on leading-edge vortex stabilization by spanwise flow

Natural flyers are capable of producing excessive lift via a stabilized leading-edge vortex (LEV), which appears to linger above the wing for a longer duration than it could in an equivalent two-dimensional flow. Previous studies found this stabilization behaviour closely related to a spanwise flow along the LEV axis; however, it is still debatable how the spanwise flow influences the LEV stability. In this work, potential flow theory is adopted to model an LEV attached to a flat-plate wing. To account for the spanwise flow effect, we propose a finite-area sink (FAS) model which allows the dynamical interaction between co-located LEV and spanwise flow. Through linear stability analysis of the dynamical system associated with the LEV movement, we arrive at a stable spiral-sink type of equilibrium, which is the first mathematical evidence supporting LEV stabilization by spanwise flow. It is further concluded that the LEV stability can be enhanced by either increasing the strength or decreasing the cross-section area of the spanwise flow.

Examination and Prediction of the Lift Components of Low Aspect Ratio Rectangular Flat Plate Wings

An investigation of the lift components present over low aspect ratio rectangular wings is presented. Wing aspect ratios ranging from 0.5 to 3 are examined using published experimental results and analytic analysis methods. The methods are based on the fundamental decomposition of Polhamus; that is, lift is attributed to a potential flow lift component coupled with a vortical lift component stemming from the leading and side edges of the flat plate wing. The analysis suggests a low sensitivity to Reynolds numbers spanning three orders of magnitude and brings into doubt the realization of a leading edge vortex lift component for wings with unswept leading edges under steady state conditions. The analytic prediction method of Purvis is shown to provide close accord with all experimental data sets when lift contributions caused by a leading edge vortex are excluded.

Vortex force decomposition—forces associated with individual elements of a vorticity field

The impulse theory used to calculate the force from a vorticity distribution in two-dimensional, incompressible flow, is re-cast with the aim of approximating, to a first order, the forces generated by a specific flow feature, such as a free vortex passing by an object. To achieve this, the force acting on the body is split up into several core contributions. The first component arises from the time variation of the body’s boundary layer. The second is generated by the advection of any free vorticity located in the flowfield by the object’s boundary layer vorticity. The final force contribution is due to new vorticity being shed. To test the theory, it is applied to two multi-body flowfields consisting of a circular cylinder and a flat plate wing at incidence in close proximity. Force balance measurements and planar particle image velocimetry data are simultaneously obtained at Reynolds numbers of 10,000 and 20,000. The forces acting on the cylinder are successfully recovered from the vorticity data using the derived formulation, verifying its accuracy. Subsequently, the proposed force formulation is used to create force heat maps that demonstrate how the location of a leading edge vortex affects its force contribution around a pitching NACA-0021 wing translating at a Reynolds number of 10, 000.

Effect of marginal variation of aspect ratio and frequency with kinematic asymmetry on flow field around flapping rigid wing in hover

Phase-locked two dimensional particle image velocimetry (PIV) measurements are used to capture flow field around rigid flat plate wings undergoing main flapping motion (hover) with water as fluid medium in quiescent condition. Experiments are conducted using asymmetric upper-lower stroke single degree of freedom main flapping motion. Two different aspect ratio (AR) 1.5 and 1.0 rectangular wings at 1.5 Hz and 2.0 Hz flapping frequency and chord based Reynolds number of the order of 104 are studied. To achieve the desired aspect ratio, wing span is varied while wing chord remains fixed. Flow features for downstroke and upstroke are comparable for all four cases investigated. This includes vortex shedding from wingtip during wing stroke, vorticity intensification caused due to vortex stretching which occurs more dominantly for AR = 1.0, occurrence of KH instability in shear layer formed due to wing sweep and added mass effect due to the flow dragged by flapping wing. Vortex filamentation and fragmentation phenomena are observed during downstroke and upstroke respectively due to faster downstroke and slower upstroke. Rossby number, which is the ratio of inertial to Coriolis force is significant for rotational flapping wing. With increase in Rossby number there is a reduction in the spanwise flow over wing which influences strength of wingtip vortex at beginning of a stroke. It is found that spanwise flow for AR = 1.5 is stronger than AR = 1.0 and consequently the strength of wingtip vortex is higher for higher aspect ratio. However, peak vorticity is higher for AR = 1.0 due to vortex stretching effect which is expected to be more dominant at lower AR due to three dimensional effects. Effect of marginal variation in wing aspect ratio, flapping frequency with kinematic asymmetry are studied using velocity field, vorticity (ωz) contours, λ2 criterion, peak vorticity variation and its spatial distribution as well as kinetic energy variation of the flow field. Kinetic energy distribution and its connection with wake capture is explored.

Transient leading-edge vortex development on a wing rolling in uniform flow

Plenoptic particle image velocimetry and surface pressure measurements were used to analyse the early development of leading-edge vortices (LEVs) created by a flat-plate wing of aspect ratio 2 rolling in a uniform flow parallel to the roll axis. Four cases were constructed by considering two advance coefficients, $J=0.54$ and 1.36, and two wing radii of gyration, $R_g/c=2.5$ and 3.25. In each case, the wing pitch angle was articulated such as to achieve an angle of attack of $33^{\circ }$ at the radius of gyration of the wing. The sources and sinks of vorticity were quantified for a chordwise rectangular control region, using a vorticity transport framework in a non-inertial coordinate system attached to the wing. Within this framework, terms associated with Coriolis acceleration provide a correction to tilting and spanwise convective fluxes measured in the rotating frame and, for the present case, have insignificant values. For the baseline case ( $J=0.54, R_g/c=3.25$ ), three distinct spanwise regions were observed within the LEV, with distinct patterns of vortex evolution and vorticity transport mechanisms in each region. Reducing the radius of gyration to $R_g/c=2.5$ resulted in a more stable vortex with the inboard region extending over a broader spanwise range. Increasing advance ratio eliminated the conical vortex, resulting in transport processes resembling the mid-span region of the baseline case. Although the circulation of the LEV system was generally stronger at the larger advance coefficient, the shear-layer contribution was diminished.

Long-term two-dimensional analysis of the flow field around a hovering flapping flat-plate wing

Long-term two-dimensional analysis of the flow field around a hovering flapping flat-plate wing

Aerodynamic Efficiency Enhancement of Delta Wings for Micro Air Vehicles Using Shape-Optimization

The performance of fixed-wing micro air vehicles (MAVs) is impaired due to their small size, operating speeds, and altitude leading to limited lift, aerodynamic efficiency (lift-to-drag ratio), and low gust resilience. Nonslender delta wings have high stall angle and maneuverability, which are desirable features for MAVs. However, the aerodynamic efficiency of delta-winged MAVs is low, thus impacting the overall performance. We optimize the aerodynamic efficiency of a flat-plate delta wing using the adjoint-based aerodynamic shape optimization method coupled with incompressible Reynolds-averaged Navier–Stokes equations. The optimization improves the aerodynamic efficiency from 6.2 to 10.2 at 5° angle of attack while satisfying lift and moment constraints. The optimized wing is significantly cambered, and the axial cross section reveals that a circular arc can approximate the optimized wing airfoil. A parametric study of the circular camber delta wings with a 0–7.5% camber-to-chord ratio reveals that an increase in camber leads to linear growth in the lift, whereas the drag shows a quadratic growth. Consequently, an optimum camber exists at 2.5% for maximizing the aerodynamic efficiency (9.3); the wing has aerodynamic characteristics closely resembling the optimized wing, thus revealing that the essence of the efficiency optimization process is to identify the optimal camber distribution.

The wing−wing interaction mechanism of bristled wing pair in fling motion

Smallest flying insects commonly have bristled wings and use novel aerodynamic mechanisms to provide flight forces, such as the fling mechanism. In the fling motion, the left and right wings are initially parallel to each other, and then the wings rotate around the trailing edge and “open” to form a V shape. Previous studies lacked the detailed flow around bristles, so the interaction mechanism of the two bristled wings in the fling motion was not well understood. In the present study, we obtained the detailed flow around each bristle numerically and revealed the interaction mechanism of two bristled wings. The results are as follows. During the fling, the vertical force of the bristled wings is similar to that of the corresponding flat-plate wings, but the drag of the bristled wings is much smaller. When the initial distance between wings is small, the opening drag of the bristled wings can be one order of magnitude smaller than that of the flat-plate wings. This is due to the different wing–wing interaction mechanisms of the two types of wings: for the flat-plate wings, during the fling motion, a “cavity” is created between the wings, producing a very large drag on the wings; for the bristled wings, there are gaps between the bristles and Stokes flows move through the gaps; thus, the cavity effect is much weaker. Very low “opening” drag may be one of the advantages of using bristled wings for the smallest insects.

Aerodynamics of two parallel bristled wings in low Reynolds number flow

Most of the smallest flying insects use bristled wings. It was observed that during the second half of their upstroke, the left and right wings become parallel and close to each other at the back, and move upward at zero angle of attack. In this period, the wings may produce drag (negative vertical force) and side forces which tend to push two wings apart. Here we study the aerodynamic forces and flows of two simplified bristled wings experiencing such a motion, compared with the case of membrane wings (flat-plate wings), to see if there is any advantage in using the bristled wings. The method of computational fluid dynamics is used in the study. The results are as follows. In the motion of two bristled wings, the drag acting on each wing is 40% smaller than the case of a single bristled wing conducting the same motion, and only a very small side force is produced. But in the case of the flat-plate wings, although there is similar drag reduction, the side force on each wing is larger than that of the bristled wing by an order of magnitude (the underlying physical reason is discussed in the paper). Thus, if the smallest insects use membrane wings, their flight muscles need to overcome large side forces in order to maintain the intended motion for less negative lift, whereas using bristled wings do not have this problem. Therefore, the adoption of bristled wings can be beneficial during upward movement of the wings near the end of the upstroke, which may be one reason why most of the smallest insects adopt them.

Unsteady aerodynamics of a model bristled wing in rapid acceleration motion

Tiny insects with bristled wings perform the “rowing” motion: the wings accelerate rapidly from zero-velocity to certain reference velocity at 90° angle-of-attack, and the drag produced in this motion provides the weight-supporting force. A flat-plate wing will produce a large drag in such a motion, but it is unknown whether a bristled wing could do so. Here, we study this problem using numerical simulation and simple model wings. The acceleration is large: the wing translates only about half the wing chord length to reach the reference velocity. The following is shown. The bristled wing can produce a very large unsteady drag peak and large time-averaged drag as a flat-plate wing does; the time-averaged drag is about 2.5 times as large as the quasi-steady value. The force production mechanisms are different between the two wings: for the flat-plate wing, because of the large acceleration, the added-mass and the strong free vorticity in the flow produce a large pressure difference between the windward and leeward surfaces of the plate, resulting in large drag (surface frictional force has negligible contribution). Yet for the bristled wing, although the acceleration of the wing is large, a bristle needs to translate about 80 diameters to reach the reference velocity; thus, the effect of acceleration is very weak. Each bristle operates in a quasi-steady Stokes flow and the large drag of the bristled wing is due to the very large surface pressure and frictional forces on each bristle, generated by the strong viscous effect of the Stokes flow (the drag is equally contributed by the surface pressure and frictional forces).

Unsteady Aerodynamic Response of a Flat Plate Encountering Large-Amplitude Sharp-Edged Gust

This study presents numerical findings of the response of a flat plate to transverse, sharp-edged gusts at a low Reynolds number (). A split velocity method was implemented in a three-dimensional Navier–Stokes solver to simulate a rigid flat plate wing at steady velocity and 0° angle of incidence encountering a sudden sharp-edged gust. The gust perturbations in the flow domain were prescribed to the grid points, and source terms were added to the governing equations to account for the full interaction between the wing and the gust. Two sharp-edged gust profiles are considered: 1) a top-hat profile gust of finite width and 2) a step profile gust of infinite width. The gust amplitude varies from 4 to 120% of the freestream velocity (). The split velocity method was found to be capable of capturing the physical phenomenon of flat plate undergoing sharp-edged gust, and the predicted lift coefficient is found to be in good agreement with that of experiments. The duration and magnitude of the wing–gust interaction were both found to affect the airfoil response. In the step gust encounter, the lift behaves similarly to that predicted by the Küssner’s model for small-amplitude gusts where . The lift buildup is nonlinear for larger gust amplitudes where . Convolution with the computed step gust response shows good agreement with the simulated response during long and large gust encounters. However, both computational fluid dynamics and Küssner-convolution-based methods fail to predict the exit phase from gust and the recovery to a steady-state value.

Experimental and Numerical Studies on Static Aeroelastic Behaviours of a Forward-Swept Wing Model

The static aeroelastic behaviours of a flat-plate forward-swept wing model in the vicinity of static divergence are investigated by numerical simulations and wind tunnel tests. A medium fidelity model based on the vortex lattice method (VLM) and nonlinear structural analysis is proposed to calculate the displacements of the wing structure with large deformation. Follower forces effect and geometric nonlinearity are considered to calculate the deformation of the wing by finite element method (FEM). In the wind tunnel tests, the divergence dynamic pressure is predicted by the Southwell method, and the static aeroelastic displacement is measured by a photogrammetric method. The results obtained by the medium fidelity model calculations show reasonable agreement with wind tunnel test results. A high fidelity model based on coupled computational fluid dynamics (CFD) and computational structural dynamics (CSD) predicts better results of the wing tip displacement when the freestream dynamic pressure is approaching the divergence dynamic pressure.

Design and computational fluid dynamics analysis of bio-inspired non slender cropped delta wingsuit

This study examines the effect of bio-inspired serrations on aerodynamic performance of a Non Slender cropped delta wingsuit model. In this study, Gottingen 228 aerofoil is used for designing the wingsuit model having AR of 1.00 using CAD software Solidworks. Ansys Fluent solver has been utilised to solve the Reynolds Averaged Navier–Stokes (RANS) equations with a k− $$\omega$$ turbulence model. The flow velocity was kept at 45 m/s with Re ~ 2.6 × 106 and angle of attack was varied from 0° to 45°. Computations revealed that the wingsuit with serrations in comparison with clean basemodel had a notable increase in maximum lift coefficient. The results were compared with the experimental and CFD results of existing literature in the open domain. The serrated non slender delta wingsuit performs extremely well giving a lift coefficient of 2.74 and $$C_{{\text{L}}}$$ / $$C_{{\text{D}}}$$ of 9.72. The results were validated by comparing them with flat plate and non slender cropped delta wing results available in the existing literature. A good agreement in terms of trends was obtained for $$C_{{\text{L}}}$$ and $$C_{{\text{D}}}$$ which indicates that proposed wingsuit should perform well aerodynamically under typical wingsuit flying conditions.

Aerodynamics of two-dimensional bristled wings in low-Reynolds-number flow

The smallest flying insects commonly possess bristled wings and use drag to provide flight forces. A bristled wing, with a wing area about 10% of that of a flat-plate wing, operating at the relevant Reynolds number of 5–15, produces a drag close to the plate wing. How this is done is not well understood. Here, detailed flows around each of the bristles are investigated numerically using simple model wings, and the following results are shown. (1) The drag production mechanism of the bristled wing is different from that of the plate wing: For the plate wing, the flow is blocked by the wing, giving a small positive pressure on the windward surface, and there exists a pair of weak vortices on the wing back, giving a small negative pressure on the leeward surface; the drag is due to the pressure forces (the frictional stress has almost no contribution). For the bristled wing, each bristle operates in a creeping flow and produces thick and strong shear layers. Strong viscous force generates a very large pressure difference between the windward and leeward surfaces of each bristle and very large frictional stress on the bristle surface, resulting in a large drag on each bristle, and the drag is equally contributed by the pressure and frictional forces. (2) Due to the flow-interference effect, when the bristle number reaches a certain value, a further increase in bristles has little effect on force production but has the disadvantage of increasing wing mass; this means that for a bristled wing of miniature insects, the distribution density of the bristles will not be too large, which agrees with observations.

On the effect of boundary condition uncertainty on robust topology optimization of aerospace structures

Uncertainty quantification (UQ) within topology optimization (TO) is a growing trend, with designers recognizing that deterministic analysis does not reflect the natural variabilities found in real-world structural performance. Thus far the majority of works have dealt with uncertain loading and material properties; however, minimal research has considered uncertain boundary conditions (BCs), which play a vital role for static and dynamic analysis involving compliance and natural frequency objectives and/or constraints. BCs uncertainty is studied in this paper by assuming a random percentage of a cantilever can be freed to rotate and/or translate in space. This is firstly demonstrated through a case study on a flat plate wing where the frequency gap between two modes is maximized, and secondly through optimizing the wing of a sensorcraft where compliance is minimized. A robust objective is formulated via a weighted sum of the mean and standard deviation, which is approximated efficiently using a Non-Intrusive Polynomial Chaos Expansion (NIPC). Both studies demonstrate the pitfalls of a deterministic optimum in dealing with uncertain BCs, and how using Robust TO (RTO) can effectively reduce the variance and worst-case performance of the objective. Experimental validation for the flat plate wing is also undertaken to ensure practical feasibility of the RTO topologies and to provide motivation to study BCs uncertainty further.

A novel lightweight aerodynamic design for the wings of hypersonic vehicles cruising in the upper atmosphere

Base on the concept of molecular mean free paths in high-altitude rarefied aerodynamics, a novel conceptual lightweight design is proposed and applied to the aerodynamic design of wings of hypersonic vehicles cruising in the upper atmosphere between 120 km to 300 km. The lightweight scheme proposed here is promising in hypersonic vehicles cruising in the upper atmosphere in the sense that it is able to not only reduce the weight of a wing by about 14%, but also save the material by the same amount. A comprehensive aerodynamic analysis indicates that the lightweight aerodynamic design can apply to a wide range of cruising altitudes and Mach numbers. In comparison with the conventional flat-plate wing, the lightweight wing always has smaller drags and larger effective lift-to-drag ratios, proving the feasibility of lightweight design for hypersonic vehicles at high altitudes. Moreover, as the cruising altitude is increased, the lightweight wing has even better lift and lift-to-drag-ratio performances, further demonstrating the excellent promise of lightweight wings for hypersonic vehicles cruising in the upper atmosphere. This lightweight design concept is of great value because the region of the upper atmosphere is relatively unexplored, and hypersonic vehicles cruising in this region can be used for high-resolution earth surveillance, accurate gravity/magnetic field mapping, and global ocean climate exploring.