Large-scale volumetric flow visualization of the unsteady wake of a flapping-wing micro air vehicle

Qualitative smoke visualisation has proved instrumental in revealing particular flow structures, such as the occurrence of leading edge vortices (LEVs) on insect wings, in, for example, hawkmoths (Ellington et al. 1996) and butterflies (Srygley and Thomas 2002). Planar particle image velocimetry (PIV) provided further quantitative information on the flow structures near the flapping wings as well as in the (near) wake, from observations on natural flyers and flapping mechanisms. Important aspects of flapping flight were thus quantified, such as the characterization of the LEV structure on insect-scale wings (Birch and Dickinson 2001) and the clap-and-fling interaction between two wings (Lehmann et al. 2005). These flow features were also found to occur in actual flyers, such as the vortical structures generated by birds (Hedenström et al. 2006) and flapping-wing MAVs (De Clercq et al. 2009). By combining the information obtained in several planes along the span, a reconstruction of the three-dimensional wake flow can be proposed (Spedding et al. 2003; Bomphrey et al. 2006; Groen et al. 2010; Ren et al. 2013). A more accurate representation of the 3D flow structure can be obtained from dense multi-plane 2C/3C data, by phase-synchronizing sequentially acquired planes, such as carried out for the flow generated by a flapping-wing mechanism (Lu and Shen 2008; Carr et al. 2013) and also for reconstruction of the flow in the wake of the DelFly MAV (Percin et al. 2014, 2017; Deng and van Oudheusden 2016). Evidently, this procedure is laborious and, furthermore, depends critically on cycle repeatability, which does not make it likely a suitable procedure for animal studies, although it was successfully applied for the investigation of butterflies by Fuchiwaki et al. (2013).

With the availability of high-speed PIV, a simpler yet more approximate approach has become common for characterizing flapping-wing wakes. Here, a convection model based on Taylor’s hypothesis is used to reconstruct the three-dimensional wake structure from the time-resolved data obtained in a single spanwise-oriented wake plane behind the flapping wings. This approach assumes that the flow structures that are generated by the flapping wings and measured in the wake plane are convected downstream without distortion and at a constant velocity, equal to that of the free stream, thus neglecting the diffusion of the wake structures as well as their deformation as a result of the induced velocities and wing motion. This procedure has been widely applied for the wake investigations of animals (Hedenström et al. 2009; Johansson and Hedenström 2009; Hubel et al. 2010; Muijres et al. 2011) and also for MAVs (Percin et al. 2014; Deng and van Oudheusden 2016). This allowed to identify the specific wake structures of different animal species and their dependence on flight regime while further providing a means to quantify how the circulation and spanwise distribution of lift of the wings varies over the flapping cycle.

The accuracy of this wake reconstruction method evidently depends critically on the reliability of the convection model underlying the Taylor’s hypothesis, and may be violated when the distorting influence of the induced velocities becomes significant. Bomphrey et al. (2012) used high-speed volumetric tomographic PIV to reconstruct the wake of a desert locust in tethered conditions. The measurement volume in the experiment (60 × 80 × 4 mm³) had a limited thickness of 4 mm oriented in the longitudinal direction, to be able to cover the wake in width and height. This made the use of Taylor’s hypothesis again necessary to propagate the flow information downstream to describe the full-wake length. Analysis of the results revealed that this procedure introduces errors on wake morphology, which may lead to erroneous force calculations based on such information. After correcting for this deformation by realigning the subsequent wake elements, the shape of the wake structures was found to be changed significantly and it was concluded that the volumes captured at subsequent time intervals do not reliably compose the actual wake shape. Instead, a large volumetric imaging technique would be desired to properly capture the longitudinal development of the wake.

A variety of volumetric flow measurement techniques have been reported in the literature, as reviewed recently by Discetti and Coletti (2018), but most techniques have important restrictions on the achievable volume, especially for experiments in air. Therefore, apart from generic flapping-wing configurations (e.g., David et al. 2012; Cheng et al. 2014; van de Meerendonk et al. 2018), volumetric visualization studies of full-scale true flyers are quite scarce. Langley et al. (2014) applied synthetic aperture PIV (SA-PIV) for the investigation of the flow around a butterfly, in a single volume of size 330 cm³. Henningsson et al. (2015) performed a tomographic PIV (tomo-PIV) measurement of the wake of a desert locust in a domain of 200 × 240 × 58 cm³ (length × span × height), corresponding to a volume of 2800 cm³, which allowed to capture the full extent of the wake cycle. To the authors’ knowledge, this constitutes presently the largest single-volume flapping-wing visualization experiment in air.

The DelFly MAV (Fig. 1) is a flapping-wing MAV concept with a tip-to-tip wingspan of 28 cm and a nominal mass of around 20 g. It features a biplane configuration, with wings moving alternately towards and away from each other when flapping (see Fig. 2) to generate both thrust and lift, taking advantage of the clap-and-fling wing–wing interaction effect, which in the case of flexible deforming wings is rather to be interpreted as a “clap-and-peel” (De Clercq et al. 2009; Armanini et al. 2016; Percin et al. 2016, 2017). Flow measurements to characterize the DelFly MAV have been performed under tethered conditions, using planar (2C and stereo) PIV. De Clercq et al. (2009) carried out time-resolved stereoscopic PIV measurements around the wings of a DelFly model, flapping at 13 Hz in a quiescent environment representing a hover flight configuration, in a plane at 75% semi-span. The measurements provided a characterization of the wing deformations, including the occurrence of the clap-and-fling interaction. The presence of the LEV during instroke and outstroke was confirmed, although its visualization during most of the flapping motion was optically obstructed by the wings. To resolve this issue, Groen et al. (2010) performed phase-locked stereo-PIV measurements with data acquisition triggered when the wing surface is aligned normal to the illumination plane, for a given phase of the flapping motion. With this approach, the existence of an LEV during the flapping motion was explicitly revealed. Measurements carried out at different spanwise positions showed that the LEV had an approximately conical shape up to about 86% of the wingspan, where it was speculated to be connected to the tip vortex. To obtain more detailed three-dimensional information on the flow structure around the wings and in the near wake, phase-synchronized multi-plane measurements were performed by (Percin et al. 2014, 2017; Deng and van Oudheusden 2016). In addition to the true spatial reconstruction of the wake, also the spatio-temporal wake reconstruction using Taylor’s hypothesis was investigated, which may be assumed to be reasonable for a forward-flight configuration at zero angle of attack (Percin et al. 2014; Deng and van Oudheusden 2016). This allowed to visualize the main structures in the wake, notably the tip vortices generated by the four wings and the starting trailing edge vortex connected to the tip vortex. With this approach, it was also possible to assess the effect of the reduced frequency on the interaction between the vortex structures. It was concluded that an increase in reduced frequency leads to a stronger interaction between the vortices, which is linked as well with the enhancement of the clap-and-fling mechanism. Comparing the spatio-temporal reconstruction with the true structure of the wake obtained from the spatial interpolation, very similar characteristics were observed. This was interpreted by the authors as a justification of the convection model, while some detail differences were attributed to the non-uniform convection velocity in the near wake. However, the use of Taylor’s hypothesis fails to represent the wake at more realistic flight conditions, where the angle of attack is quite high and the interaction between the velocities induced by the wings and the free stream is too complex to be accounted for by a simple uniform convection model. Free-flight visualizations of the DelFly (del Estal Herrero et al. 2018; Karasek et al. 2019) give, furthermore, clear evidence that in slow forward flight, the wake is predominantly aligned along the body axis direction, making the assumption of convection in the free stream direction unrealistic.

The above considerations motivate the (large-scale) volumetric imaging to properly capture the longitudinal development of the wake, under realistic conditions that are representative of actual flight. With the wing span of the Delfly being ~ 30 cm and typical wake structures ~ 20–25 cm in length (del Estal Herrero et al. 2018, see also Sect. 3.3), the minimum volume requirements would amount to around 20,000 cm³. This cannot be achieved by regular tomo-PIV, in view of the volume restrictions, which has been reported as being typically no more than 100 cm³ for low-repetition-rate systems in air (Scarano 2013; Scarano et al. 2015). Exceptionally large tomo-PIV measurement volumes, using a powerful laser illumination of about 1 J/pulse, were reported in the studies of Fukuchi (2012) on a cylinder wake and Henningsson et al. (2015) on the wake of a desert locust, achieving volume sizes of around 2800 cm³. An important step towards substantially increasing the dimensions of the measurement volume has been achieved with the introduction of helium-filled soap bubbles (HFSB) as tracer particles, which are of sub-millimetre size and have a light-scattering capability of typically 10⁴ times that of micron-sized droplet seeding (Scarano et al. 2015). Large-scale experiments using HFSB have been reported, amongst others, by Kühn et al. (2011) using tomo-PIV in a convection cell (56,000 cm³) and Huhn et al. (2018) using Lagrangian particle tracking of a jet flow at 4 m/s (54,000 cm³). Earlier experiments have shown that the use of HFSB is not detrimental to the operation of the DelFly (del Estal Herrero et al. 2018), although occasional cleaning of the wings is required, which, therefore, makes it a feasible option for the current purpose as well. In the present investigation, the particular strategy to achieve the required large-scale measurement volume to visualize the entire wake extent of the DelFly is combining the HFSB seeding with a robotic PIV system based on coaxial illumination and imaging (Schneiders et al. 2018; Jux et al. 2018); more details are given in Sect. 2.3.

In addition to the realization of a full-wake visualization, a second objective of the current work is to compare the experiments carried out in a tethered configuration in a wind tunnel with free-flight visualization experiments. Earlier DelFly studies have compared the aerodynamic forces derived from flight tests to balance data taken under similar conditions in the wind tunnel (Caetano et al. 2015; Karasek et al. 2016). In general, good agreement was found, especially for the thrust force in the direction along the body longitudinal axis. However, larger differences were found in the wing stroke direction, which were attributed to structural vibrations of the MAV body, which affect the force balance measurements depending on the clamping position. For the free-flight measurements in the current study, the same procedure is followed as for the preliminary free-flight visualization experiments described in (Karasek et al. 2019), by combining the PIV visualization with a position-control system for autonomous flight in the wind tunnel environment.

The DelFly MAV used in the experiments is shown in Fig. 1, together with the layout and dimensions of one of the half-wings. The MAV has a configuration with two full-span wings, arranged in cross configuration with a dihedral angle of 12°, that flap in counter motion. The wings have a span of 280 mm and mean chord of 80 mm. The wing kinematic motion is illustrated in Fig. 2, which shows that during one flapping cycle, the wings periodically move away and towards each other, which is referred to as the outstroke and instroke phases of the cycle, respectively. To assist the discussion of the results, the flapping cycle has been divided in eight phases (indicated as I, II, etc.) equally spaced in time over the cycle. The maximum angle between the wings (reached in the phase indicated as V) is 87°. The wings are made of 15 µm Mylar foil and are reinforced with carbon-fibre leading edge spars and wing stiffeners. As a result, the wings are highly deformable, which is a characteristic that was found to enhance the aerodynamic performance significantly (Percin et al. 2016). The DelFly is, furthermore, equipped with conventional horizontal and vertical tail planes and corresponding control surfaces, elevator, and rudder (see Fig. 1a), which make it a stable and controllable MAV platform relying on tail actuation. The weight of the DelFly is approximately 25 g and the distance from the leading edge of the wings to the trailing edge of the tail is about 215 mm. The tail has a span of 170 mm and is made from 2 mm-thick polystyrene sheet; it was painted black for the experiments to avoid unwanted reflections from its surfaces. This treatment was not applied to the wings of the DelFly, as the paint could change considerably the stiffness and the weight of the wings, and thus affect the flight behaviour. However, as the current interest lies primarily in the characterization of the wake structures, light reflections from the wings as well as their possible obstruction of the measurement domain are no direct concern.

From the data measured for configuration 3TC, information on the longitudinal velocity is extracted in a single wake plane (Fig. 7). The wake plane is located at 10 mm downstream of the trailing edge of the tail and its particular position is indicated by the orange line in the top and side views depicted in Fig. 14. The information is given in the body reference frame, with the x-component set along the body of the DelFly and y the spanwise direction (see also Fig. 6). In the plots, the position of the DelFly is schematically indicated by a black outline to relate the flow field results with the position of the wings. The flapping cycle has been divided into eight phases to show the behaviour of the flow structures and their evolution over the flapping cycle (see Fig. 2). The flapping cycle is defined to start when the wings are closed and the outstroke is going to start (phase I). Note, however, that the flow measured in the observation plane is not corresponding to the instantaneous position of the physical wings at that precise moment, in view of the convective delay between the wing position and the visualization plane. Therefore, to assist the interpretation of these flow fields, a “virtual wing position” (hence, flapping phase) is introduced, which has been deduced from the information of the change in crossflow velocity along the wingbeat cycle. In the setup of these experiments, the CVV system was positioned at the starboard side of the DelFly (i.e., positive y, see Fig. 3) which leads to a better tracking of the particles on that side, because the particles that are closer to the laser source will scatter more light as the intensity decreases with the fourth power of the distance. As a consequence, having more particles tracked contributes to a higher accuracy in that measuring side.

Regarding the accelerated flow region, represented by the red areas of relatively high longitudinal velocity, its evolution along the flapping cycle can be observed in Fig. 7. The first phase (Fig. 7-I) of the cycle corresponds to the start of the outstroke. There is no clear acceleration region in the wake, for the reason that the wings are closed (see also Fig. 2). It is seen in Fig. 7-II that a high-velocity region has drastically increased in size with respect to the previous phase, due to the opening of the wings. The deformation of the wings plays a major role in this effect due to the “peeling” action. To illustrate the wing deformation during the clap-and-peel process, video images of the corresponding phases are depicted in Fig. 8, with the approximate chordwise shape of the two wings indicated by the orange lines.

The acceleration region keeps increasing during phases III and IV as the wings are still opening further. On phase V, when the instroke has started, the flow acceleration that is generated by the wings reaches its maximum, again due to the deformation of the wings and the “clap” effect that is created as the wings start moving together (see Fig. 8-left). During the following phases, from VI to VIII, the acceleration region reduces its size and it is concentrated into two different regions, one near the body of the DelFly and the other near the tip of the wings. The flow at the first location follows the direction of the body, while the second acceleration region has a lateral component of velocity directing the flow outward along the wings (Fig. 9). The outward velocity occurs as a consequence of the deformation of the wings. The deformation along the wing is restricted because of the presence of the stiffeners, as shown in Fig. 1; this may explain why the acceleration region at the end separates in two. In the most outward part of the wing, apart from the expected chordwise deformation, there is a spanwise deformation of the wing which is the probable cause of the observed flow acceleration in the lateral direction.

Figure 10 displays the longitudinal vorticity ω_x (i.e., in the direction of the MAV body axis) for the subsequent phases of the flapping cycle. The first observation is that there are two main counter-rotating vortices originating from the tips of the DelFly during the entire flapping cycle. According to lifting line theory, this implies that positive lift is generated during the entire flapping cycle, which is crucial for the MAV to provide the necessary lift to maintain its altitude. Lift is defined as the force generated perpendicular to the free stream, so the vertical force in an absolute reference frame. The vortices are shed by the lower pair of wings during the outstroke and by the upper wings during the instroke. This finding leads to the conclusion that the main vortices are always shed by the wing that is moving in the direction opposite to that of the free stream when the relative velocity of the wing with respect to the flow is higher and the majority of the force is generated. Considering the wings moving along with the flow, the velocity experienced by the wing surface is reduced significantly. Assuming that the effective flapping-induced velocity produced by the wing is located at two-thirds of the wing span (\(b = 14 \;{\text{cm}}\)), it is estimated that the total velocity seen by the wing moving against the flow is more than three times larger than the one seen by the wing going in the free-stream direction.

Looking more in detail to the different phases, two strong counter-rotating tip vortices are retrieved in phase I of the cycle (starting of the outstroke) that have been generated by the upper wings during the previous instroke. These tip vortices (wake structures A in Fig. 10) interact with the wings while they are closed, and then with the tip vortices generated by the lower wings during the outstroke, resulting in a major tip vortex structure with the same sign for the entire cycle, as it can be clearly appreciated in the 3D views that will be shown in Sect. 3.2. The tip vortex structure in phase II is quite elongated, as is also the case for phase III. The shape of the tip vortices along the outstroke will be further discussed in Sect. 3.2. Several smaller vortices, indicated by the label B, start to appear in phase II, but they are not yet defined until phase III. The crossflow going over the wings from tip to root needs to be redirected once it reaches the root, generating these vortices.

In phase IV, the wings are completely open, indicating the transition from the outstroke to the instroke. According to wing theory, a lifting surface of finite span will generate tip and root vortices at the extremities of the surface, that are aligned with the free-stream direction. This same concept can be applied to flapping wings, similar to propeller theory. In this way when the upper wings start to generate lift, a spanwise-aligned starting vortex is produced that is followed by the generation of counter-rotating tip and root vortices. From Fig. 9, phases IV and V, the evolution of root and tip vortices can be confirmed (wake structures C and A, respectively). Visualization of the starting vortex is performed by analysis of the spanwise vorticity. In Fig. 11, such a plot is presented for phase V, where the starting vortex can be seen at the upper side of the DelFly. The vorticity in that region has a negative sign which means that positive circulation, and therefore, positive lift is being generated. The starting vortex can only be clearly seen at the beginning of the instroke, because at the beginning of the outstroke, a strong interaction between the wings occurs, so the change in circulation of the wings is not significant. On the lower side of Fig. 11, however, the opposite behaviour is found in a large area with high positive y-vorticity. It corresponds to the trailing edge vortices shed from the lower wings when they stop producing lift. The trailing edge vortex generated by a lifting surface is indeed of opposite sign to that of the starting vortex.

In phase V, the wings are completely open, which causes the crossflow along the lower wings to be maximum; hence, the secondary vortices formed on the upper part of the DelFly are enhanced. Then the peak vorticity of these vortices diminishes drastically when the wings come closer together, as the flow is now directed away from the root, and towards the tips. In the same way, the root vortices also experience a decrease in strength and they nearly disappear at phase VIII, as the wings are approximately closed and the DelFly resembles a fixed wing vehicle. The tip vortices, where the highest flapping-induced velocity can be found, still maintain their strength throughout the final phases of the cycle.

Considering again configuration 3TC, the vortex structures identified in the previous section are now discussed by means of their three-dimensional representation. First, a complete three-dimensional visualization of the entire wake is shown in Fig. 12, for one specific phase (an animation for the full cycle is provided as online supplementary material). It can be observed that the wake displays a good level of symmetry with respect to the centreline plane of the DelFly. Therefore, although data are available for the full span of the wake, in the following discussions only the structures at one side (corresponding to positive y) are shown, to facilitate visual interpretation.

The development of the topology obtained for different phases of the cycle is sketched to give an overview of the variation of the structures, while they are convected. In Fig. 13, the different vortices are identified, as well as the distinction between instroke and outstroke, indicated by the grey/white colour bands in the figure. The latter division has been obtained from visual inspection of the vortical shapes in accordance with the reasoning presented in Sect. 3.1. It may be reminded here again that the x-axis is aligned with the body axis, so the upward deflection of the wake that can be observed in the side view is the result of the body inclination with respect to the free-stream direction (body angle \(\alpha_{b} = 31^\circ\) in this case).

The large tip vortex structures that were already mentioned in Sect. 3.1 can be clearly recognized in Fig. 13. The shape of the convected tip vortex seems to be straight with respect to the DelFly body during the instroke, while it is deflected downwards during the outstroke, which was also seen in Fig. 10 on phases II and III. During the outstroke, the lower wing is the one that is generating the tip vortex, which agrees with the downward movement of the vortex. Another reason for the shape of the vortex on the outstroke comes from the fact that the convection velocity is lower in this part of the cycle (Fig. 7), especially in the tip area, where the air is being redirected towards the root. Therefore, the vortex does not travel away as rapidly along the x-direction in the first stages of the outstroke. In addition, the vortex is moved slightly towards the centre of the wake due to the crossflow that appears. This also explains that the instroke structures are longer than the ones generated during the outstroke (the grey area is shorter than the white area), similar as in Percin et al. (2014).

The wake topology is highly affected by the different convection velocities that are experienced throughout the flapping cycle in different locations in the wake (Fig. 7). This makes the analysis of the wake evolution more complex. The vortices generated by the flapping wings are not convected in the direction of the body of the DelFly, neither in the direction of the freestream. There is a combination between the freestream and the effect of the varying induced flow generated throughout the cycle. The result is that the angle of the wake varies as the structures travel away from the wings. With downstream distance the importance of the induced flow acceleration decreases, and the wake convection velocity will become more uniform and closer to the free-stream velocity. However, this situation is not reached within the measuring volume studied and, instead, it will be assumed that over the measured region the angle of the wake is approximately constant. The value of this wake angle is computed by taking the information of the wake at two different spanwise-oriented planes that are spaced in the x-direction, such that they correspond to the same phase of subsequent flapping cycles. A correlation between the x-vorticity values of both planes provides a measure of the average displacement of the vortex structures during the length of a flapping cycle. This procedure is carried out for each of the eight phases, as shown in Sect. 3.1. The result for each phase varies, so only the correlations with a signal to noise ratio \({\text{SNR}} > 2.9\) were considered. For the current configuration (3TC), the mean angle of the wake with respect to the longitudinal body direction is established to be approximately 15°, which agrees with a visual inspection of the side view in Fig. 13, and clearly different from the body angle (31°). The angle of the wake in the lateral direction is not so easily verified visually, but the cross-correlation procedure computes an outwards movement of the wake structures at an angle of 2°. The outward velocity that was presented in the previous section has an influence on the movement of the wake, which slightly moves away from the centre plane.

The evolution of the wake over three different phases during the flapping cycle can be seen in Fig. 14, where the wake plane location corresponding to the information depicted in Sect. 3.1 is also indicated (orange line). The assumption of a constant wake angle seems to be reasonable when looking at the side views for the different phases. Starting from phase II that has been explained in detail before, phase V shows clearly the starting vortex linked to the root and tip vortices during the instroke. The secondary vortex created during the outstroke moves upwards and inwards, as visible in, respectively, the side and top views. As can be expected, the vortex structures become more diffuse, as they convect downstream, which can be seen when looking at the root vortex for phase II, which is not so prominent as in phase V. The peak vorticity of all vortex structures also decreases. On phase VII, the vortex structures from the instroke have moved downstream and the trailing edge vortex from the lower wings is seen below the root vortex. The secondary vortex seems to interact with small vortices generated before. This interaction probably originates before this point, but the reason behind this interaction was not studied in detail.

Previous studies (Percin et al. 2014) have indicated that the interaction between the vortices in the wake of a flapping-wing system is affected by the reduced frequency. However, in their investigation, the body angle was set to zero, resulting in symmetric conditions for top and bottom wings, while the investigated range of reduced frequencies spanned from 0.47 to 1.17. As such, the conditions investigated by Percin et al. (2014) are not representative of realistic slow forward flight, in contrast to the conditions considered in the present study (see Table 1). To assess the impact of the flight condition on the wake structure, the three investigated configurations (1TC, 2TC, and 3TC) are compared, where the reduced frequency of configuration 1TC is five times higher than that of configuration 3TC, being 6.5 and 1.3, respectively. It should be noted, however, that in this case, the configurations not only differ in the value of the reduced frequency, but also in the body inclination with respect to the free-stream direction, such as to represent realistic flying conditions of the MAV.

The 3D wake topology for each of the configurations is presented in Fig. 15, for a specific phase in the cycle. An animation of the entire cycle can be found in the supplementary material available online. There are large differences between the topologies shown, but some similarities can still be observed. The major vortex structure appreciated in all three configurations is the tip vortex. The tip vortex in case 1TC is no longer a smooth structure throughout the flapping cycle, but it has a distinct shape for instroke and outstroke. During the instroke, the tip vortex and the starting vortex cannot be distinguished, forming a single oblique vortex that starts close to the root of the DelFly and moves outwards as the instroke develops. The tip vortex generated during the outstroke is shorter than for the instroke, as it was the case for configuration 3TC, and it follows a straighter path with respect to the body of the MAV. A second tip vortex structure generated during the instroke on the lower part of the DelFly can be seen for configuration 1TC. This indicates that the lower wing is producing a vertical force. However, the x-vorticity of this structure is negative, which indicates that negative lift is being generated. This can be confirmed from the analysis of the y-vorticity which has positive values for the lower wing during the instroke (figure not shown as it is similar to Fig. 11). However, in this case, it is not the trailing vortex that is shed but the starting vortex related to a sudden change in lift generation. The strength of this vortex is smaller than the one measured for the tip vortex of the upper wing, which can be understood from their different relative velocities with respect to the flow, so the total resulting lift force remains positive. Another vortex structure that appears for configuration 1TC is located on the upper part of the instroke tip vortex. This vortex is not present close to the wings, but as the wake travels downstream, the vortices interact strongly with each other. The outstroke tip vortex seems to interact with the tip vortex of the following instroke. When looking at configuration 2TC, the wake topology is more similar to the one of configuration 3TC. There is a clear tip vortex, while a starting vortex can also be seen. The shape, however, is more curved rather that straight as in the case of configuration 3TC, which means that the wake of configuration 2TC starts to look more similar to that of configuration 1TC.

No root vortex is observed for configurations 1TC and 2TC for any phase of the flapping cycle. Due to the relatively high flapping frequency, the flow at the root of the wings is constantly changing and the dominant component is the crossflow. Therefore, it is conjectured that the root vortex is not present, as it is not generated as fast as the change in wing conditions happens. As the crossflow is augmented, the secondary vortex is strengthened, while also its length changes from one configuration to the other. It is hypothesized that the deformation of the wings is an important contributing factor in this. As the flapping frequency increases, the deformation of the wings is enhanced and the phase lag between the leading edge and the trailing edge of the wings increases (Percin et al. 2016). This allows for the secondary vortex to last for a longer time, as the wings do not close completely until later in the flapping cycle. The secondary vortex seems to be generated closer to the root on configurations 1TC and 2TC than in configuration 3TC in both y- and z-directions. The fact that it is closer in the z-direction is likely due to the reduction of the free-stream component, so the convection of the vortices is much more influenced by the flow acceleration induced by the wings. This causes the angle of the wake with respect to the body to be smaller.

Although the observed wake topologies qualitative confirm these conclusions, an accurate quantitative characterisation can only partly be achieved, as the quality of the wake reconstructions reduces when moving from configuration 3TC towards 1TC. A number of characteristic parameters of the wake have been collected in Table 2: the wake length corresponding to a single flapping cycle (L), the maximum longitudinal velocity \((U_{{b_{\text{MAX}} }} )\), and the maximum longitudinal vorticity (\(\omega_{{x_{\text{MAX}} }}\)), both defined in the body frame of reference. The wake length of a flapping cycle has been computed by determining the difference between the location of the start of the instroke, which is defined as the time when the starting vortex is shed. This length is retrieved by visual means from the flow visualization, and should be treated as an approximate value. The values of maximum velocity and vorticity are computed, selecting only regions where more than 1200 particles have been tracked on the same slice as the contour plots, as shown in Sect. 3.1.

Based on the wake cycle length \(L\) observed in the visualizations, a mean convective velocity has been calculated, according to: \(U_{\text{conv}} = L f_{\text{flap}}\). As can be seen in Table 2, the effective convection velocity is much different from the free-stream speed, being substantially higher due to the flapping-induced flow. For configuration 3TC, the maximum induced velocity, \(U_{{b_{\text{MAX}} }}\), is nearly twice the free-stream velocity, while the estimated mean convection speed is about 40% higher than the free-stream velocity, and close to the average value of \(U_{{b_{\text{MAX}} }}\) and \(U_{\infty }\). The differences between the convection velocity and free-stream velocity become progressively pronounced for decreasing free speed (increasing reduced frequency), their ratio becoming about 2 (for 2TC) to 4 (for 1TC). Together with the wake alignment observed in Fig. 15, these results clearly illustrate the invalidity of Taylor’s hypothesis for low flight speeds, which combine a high value of the reduced frequency with a large body angle. For comparison, also the reduced frequency \(k_{\text{conv}}\) based on the convective velocity has been computed, which is seen to display a much smaller variation than the reduced frequency based on the free-stream speed. The maximum values of the longitudinal vorticity (\(\omega_{x}\)) occur always in the tip vortex structure across all phases analysed. The highest maximum value occurs for configuration 3TC, as more force is generated on the wings than for the other configurations. The overall maximum value along the flapping cycle is found at the beginning of the outstroke, when the wings are close together and coming apart from each other, which can relate to the interaction of the tip vortex from the previous instroke that combines its strength with the following vortex generated by the lower wing.

To finalize the analysis, the comparison between tethered and free-flight experimental conditions is investigated using configurations 3TC and 3FC. The reduced frequency for both cases is very similar, albeit that the flapping frequency for case 3FC is about 10% higher than for case 3TC. This affects the length of the wake for a flapping cycle, as seen in Fig. 16, yielding approximately 27 cm and 24 cm for configurations 3TC and 3FC, respectively. Such result is consistent with the difference in flapping frequency, as very similar values of the convection velocity are obtained (see Table 2). The vortex structures that can be appreciated for free-flight are not captured with the same level of detail as for the tethered condition, and only the main structure, namely, the tip vortex, can be clearly seen. The root vortex is one of the structures that are not visible for configuration 3FC, whereas they are well defined for configuration 3TC.

The dynamic motion of the DelFly is inherent to the free-flight tests, as it is flying around a set point with small deviations from it. The largest deviations are found in the lateral direction which can reach a variation of 20 cm. Using the information from the flight tracking system, the position deviations are corrected for, to be able to process the data with the phase-averaging procedure. However, the motion of the DelFly, especially the lateral component which also involves the heading of the Delfly with respect to the free stream, changes the precise position and the orientation of the wake and to some extent the way the vortex structures are shed. This translates in fluctuations of the position of the individual wake structures that cause the smaller structures to be spread out over the volume, such that they are no longer detectable in the phase-averaged visualisation. The larger structures still remain visible but, as seen in Fig. 16, the core is larger due to this “blurring” of the vortex and the x-vorticity reached is smaller than for tethered conditions. The overall shape of the tip vortex, however, is still very similar to the vortex structure found in tethered conditions, indicating that the structures generated in both cases follow the same trend.