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Two examples of bio-inspired AUVs that combine front and back flipper oscillation (tandem arrangement) as a means of propulsion: (a) a pure pitching motion (Long et al., 2006); (b) a combination of rolling and pitching (Weymouth et al., 2017). A simplified version of the latter kinematics is used in this study.
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In this work, we describe the impact of aspect ratio ( $AR$ ) on the performance of optimally phased, identical flapping flippers in a tandem configuration. Three-dimensional simulations are performed for seven sets of single and tandem finite foils at a moderate Reynolds number, with thrust producing, heave-to-pitch coupled kinematics. Increasing...
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... roll, coupled motion, etc. Most of these tetrapodal swimmers (see Figure 1) are electric-powered, designed for a wide range of depths (1-100 m) and can reach velocities of 0.5-2 m s −1 (Licht, Polidoro, Flores, Hover, & Triantafyllou, 2004;Long, Schumacher, Livingston, & Kemp, 2006;Weymouth et al., 2017), which are comparable to modern propeller-driven, ocean-going AUVs of a similar size and weight (Yuh, 2000). ...
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... investigate the relative augmentation of thrust for the back foil in more detail, we examine C T,b * (from (2.9a,b)) in Figure 10(a). It can be seen that there is a sharp increase in this ratio for AR ∼ [2,4] (from C T,b * = 1.3 to C T,b * = 1.45) and the ratio seems to level out around AR = 4 (at ...
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... there are no further benefits beyond AR = 4 in terms of relative augmentation, although there is still a benefit in the overall thrust produced by the pair of flippers. Interestingly, Figure 10(b) shows that the relative efficiency í µí¼ b * (which is the ratio of efficiency of the back foil to the front foil) remains practically unchanged, showing minor growth of approximately 2.4 % throughout the entire range of AR (see Figure 10b). This has been reported in recent studies of in-line foils (Arranz et al., 2020;Broering & Lian, 2015) for a range of harmonic motions and can be linked to the St A being already optimised for maximum efficiency on both flippers (similarly to the single foil cases). ...
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... there are no further benefits beyond AR = 4 in terms of relative augmentation, although there is still a benefit in the overall thrust produced by the pair of flippers. Interestingly, Figure 10(b) shows that the relative efficiency í µí¼ b * (which is the ratio of efficiency of the back foil to the front foil) remains practically unchanged, showing minor growth of approximately 2.4 % throughout the entire range of AR (see Figure 10b). This has been reported in recent studies of in-line foils (Arranz et al., 2020;Broering & Lian, 2015) for a range of harmonic motions and can be linked to the St A being already optimised for maximum efficiency on both flippers (similarly to the single foil cases). ...
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... above observations can be linked to the flow field development between the two foils. This is evident in Figure 11, where the wakes of tandem arrangements for AR = 2 and AR = 8 are compared (animations of these test cases can be found in the supplementary material). As mentioned previously, wingtip effects are proportionally higher in the wake of AR = 2 compared to AR = 8 (Figures 11a and 11b) resulting in the break-up of the foils' shed vortices (Figures 11c and 11d). ...
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... is evident in Figure 11, where the wakes of tandem arrangements for AR = 2 and AR = 8 are compared (animations of these test cases can be found in the supplementary material). As mentioned previously, wingtip effects are proportionally higher in the wake of AR = 2 compared to AR = 8 (Figures 11a and 11b) resulting in the break-up of the foils' shed vortices (Figures 11c and 11d). Specifically, the break-up of the LEV shed from the front foil means that the back foil does not experience a coherent wake across its span, which limits the benefits derived from wake recapture. ...
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... is evident in Figure 11, where the wakes of tandem arrangements for AR = 2 and AR = 8 are compared (animations of these test cases can be found in the supplementary material). As mentioned previously, wingtip effects are proportionally higher in the wake of AR = 2 compared to AR = 8 (Figures 11a and 11b) resulting in the break-up of the foils' shed vortices (Figures 11c and 11d). Specifically, the break-up of the LEV shed from the front foil means that the back foil does not experience a coherent wake across its span, which limits the benefits derived from wake recapture. ...
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... the break-up of the LEV shed from the front foil means that the back foil does not experience a coherent wake across its span, which limits the benefits derived from wake recapture. Therefore, although a ∼30 % increase in thrust can be noteworthy (Figure 10a for AR = 2), it is still far away from the optimal cases reported here or found in the literature (Akhtar, Mittal, Lauder, & Drucker, 2007;Boschitsch, Dewey, & Smits, 2014;Joshi & Mysa, 2021;Lagopoulos, Weymouth, & Ganapathisubramani, 2020;Muscutt et al., 2017aMuscutt et al., , 2017bXu et al., 2017). It should also be noted that a similar performance deterioration of inline flapping due to 3-D associated effects has been witnessed within insect-like concepts, where lower Re C and S C have been used (Arranz et al., 2020). ...
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... should also be noted that a similar performance deterioration of inline flapping due to 3-D associated effects has been witnessed within insect-like concepts, where lower Re C and S C have been used (Arranz et al., 2020). However, the propulsive enhancement derived from Figure 11. Snapshots of normalised vorticity at t/T = 1 for tandem configurations, where the flow structures are visualised by using iso-surfaces with 0.14 % of Q max . ...
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... findings can be further quantified by computing the spanwiseaveraged circulation of the LEV for the back flipper at different aspect ratios. As shown in Figure 12(a), wake recapture allows the formation of a noticeably larger and stronger LEV compared with those shed by the front foil. However, its compactness/coherence is more dependent on flipper elongation, which alters the LEV circulation with AR (see Figure 12b). ...
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... shown in Figure 12(a), wake recapture allows the formation of a noticeably larger and stronger LEV compared with those shed by the front foil. However, its compactness/coherence is more dependent on flipper elongation, which alters the LEV circulation with AR (see Figure 12b). Note that the circulation is computed based on a given box size and further information on the effect of box size on the computation of this circulation is in Appendix B. For low AR, the vortex appears to be diffused due to interactions between the main LEV and the tip. ...
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... to the findings of § 3.1, values of C Y,max follow a saturating pattern with increasing flipper elongation (see Figure 13b). Furthermore, by comparing peaks C Y,f and C Y,b , we notice relatively higher values for the latter. ...
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... previous sections revealed a lack of coherence in the shed vortices of AR ≤ 4. Another critical feature of low-AR flippers is the tendency of consecutive LEVs to travel further apart from the centreline, leading to more divergent streams ( Dong et al., 2006;Shao et al., 2010). Indeed, Figure 14 shows that the distance of successive vortices, normal to the hind foil's chord, is larger at AR = 2 compared to AR = 8. This, combined with their aforementioned low cohesion, means that colliding with the back foil is both less probable and less critical for the latter's performance. ...
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... foil simulations were performed, starting from í µí¼ = 0 • and progressing at increments of Δí µí¼ = 45 • until í µí¼ = 315 • , while the single foil was found to produce C t,f ∼ 0.675. Figure 15 shows that the modification of the hind foil's thrust, due to interaction with the incoming wake, follows a cosine-like curve with respect to the phase lag, as shown in similar studies (Muscutt et al., 2017a). Clearly, optimal C * T,b is found for í µí¼ = 0 • and therefore it is chosen for all the simulations presented in the current study. ...
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... foil simulations were performed, starting from í µí¼ = 0 • and progressing at increments of Δí µí¼ = 45 • until í µí¼ = 315 • , while the single foil was found to produce C t,f ∼ 0.675. Figure 15 shows that the modification of the hind foil's thrust, due to interaction with the incoming wake, follows a cosine-like curve with respect to the phase lag, as shown in similar studies (Muscutt et al., 2017a). Clearly, optimal C * T,b is found for í µí¼ = 0 • and therefore it is chosen for all the simulations presented in the current study. ...
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... this study, circulation is calculated via the integration of vorticity over a rectangular cell (see Figure 16a). As we focus on the LEV analysis, the size and location of this area should be optimised to enclose the exact size of the vortex while minimising ambient interference. ...
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... we focus on the LEV analysis, the size and location of this area should be optimised to enclose the exact size of the vortex while minimising ambient interference. Therefore, after visually choosing an initial location, we gradually increase the area of integration until the overall circulation begins to drop (see Figure 16b). Having finalised the size of the box, we re-evaluate its location by moving its centre towards the y and x axis until a position of maximum circulation is identified. ...
Citations
... Majority of the computational research conducted on flapping foils has been two-dimensional (Wu et al., 2020) and the three-dimensional spanwise as well as end effects have not been taken into consideration. Recent works by Lagopoulos et al. (2021); Arranz et al. (2020);Jurado et al. (2022) have studied the effect of aspect ratio of the foil on propulsive performance. However, the conditions under which three-dimensional (3D) flow effects become important are yet to be studied in detail for tandem foils. ...
In this study, we present two and three-dimensional numerical investigation to understand the combined effects of the non-dimensional heave amplitude varying from 0 to 1 and the pitch amplitude ranging from 0° to 30° on the propulsive performance for a single and tandem foil system at Reynolds number 1100 and reduced frequency 0.2. We initially present a systematic analysis on the thrust generation due to the kinematic parameters for a single foil. The significance of effective angle of attack and the projected area of the foil has been emphasized in explaining the dynamics of lift and drag forces and their relationship with the propulsion. We next investigate the relation between the streamwise gap and kinematic parameters on propulsion for the tandem foil system. We show that the propulsive performance strongly depends on the upstream wake interacting with the downstream foil, and the timing of the interaction due to the gap between the foils. Through a control volume analysis, the time-averaged pressure and streamwise velocity have been investigated to explain the effect of kinematic parameters on the hydrodynamic forces. Typically in the literature, the formation of jet in the wake has been attributed to thrust generation. However, in this study, we emphasize and show the significance of the time-averaged pressure in the wake apart from the streamwise velocity (jet) for predicting the thrust forces. The study is concluded with a three-dimensional demonstration of the tandem foils to understand the possible three-dimensional effects due to the large amplitude flapping and wake-foil interaction.
