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Table 1: Bionic wing planforms adopted for the upcoming numerical simulations smooth LE-smooth TE (i.e., real Mobula alfredi planform), wavy LE-wavy TE, wavy LE- smooth TE, smooth LE-wavy TE, as summarized in Table 1 (illustrated in Fig. 3). With the aid of these hydro-planforms, hydrodynamic effects of these prominent geometric features such as the evolution of vortical structures, flow separation evolutions, and post-stall behavior of these 'swimming wings' can be assessed, as discussed in the present paper.

Table 1 Bionic wing planforms adopted for the upcoming numerical simulations smooth LE-smooth TE (i.e., real Mobula alfredi planform), wavy LE-wavy TE, wavy LE- smooth TE, smooth LE-wavy TE, as summarized in Table 1 (illustrated in Fig. 3). With the aid of these hydro-planforms, hydrodynamic effects of these prominent geometric features such as the evolution of vortical structures, flow separation evolutions, and post-stall behavior of these 'swimming wings' can be assessed, as discussed in the present paper.

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2. CHIMERICAL MANTA RAY BODY MODELS
2. CHIMERICAL MANTA RAY BODY MODELS
In general, geometric deficiencies can be present in the manta ray's external morpholo g g p y rp gy (eidonomy) d ue to injuries or bites on T.E. of their pectoral fins caused by predator's attacks (e.g. sharks/mammals), boat strikes while feeding or swimming close to the oceanic water surface. As explained in detail by Stevens et al., manta rays exhibit a noticeable capability to hese body wounds and regenerate large portions of the missing flesh [8]. Many examples of manta rays with these types of injuries have been observed by Stevens et al. over quickly heal he years in t he Ma dives and Mozambique manta ray populations [8]. As mentioned earlier, one of the famous examples with a 'geometric deficiency’ at T.E. is a reef manta ray (Mobula alfredi), namely 'Babaganoush.' The manta ray has been injured by a speedboat strike and has been observed for t arge and deep injuries at T.E. in November 2018 [14]. However, the manta was incredibly healed in the next show-up in May 2019, as observed by' The Manta Trust.’ In the present paper, the injured hydrodynamic consequences of these kinds of ‘geometric deficiencies’ (Fig. 3-e). he first time in the Maldives by 'The Manta Trust' research team having body planform of 'Babaganoush' in May 2019 is considered to assess
In general, geometric deficiencies can be present in the manta ray's external morpholo g g p y rp gy (eidonomy) d ue to injuries or bites on T.E. of their pectoral fins caused by predator's attacks (e.g. sharks/mammals), boat strikes while feeding or swimming close to the oceanic water surface. As explained in detail by Stevens et al., manta rays exhibit a noticeable capability to hese body wounds and regenerate large portions of the missing flesh [8]. Many examples of manta rays with these types of injuries have been observed by Stevens et al. over quickly heal he years in t he Ma dives and Mozambique manta ray populations [8]. As mentioned earlier, one of the famous examples with a 'geometric deficiency’ at T.E. is a reef manta ray (Mobula alfredi), namely 'Babaganoush.' The manta ray has been injured by a speedboat strike and has been observed for t arge and deep injuries at T.E. in November 2018 [14]. However, the manta was incredibly healed in the next show-up in May 2019, as observed by' The Manta Trust.’ In the present paper, the injured hydrodynamic consequences of these kinds of ‘geometric deficiencies’ (Fig. 3-e). he first time in the Maldives by 'The Manta Trust' research team having body planform of 'Babaganoush' in May 2019 is considered to assess
iy Indonesian Journal of Engineering and Science, Vol. 2, No. 3, 2021 https://doi.org/10.51630/ijes.v213.25
iy Indonesian Journal of Engineering and Science, Vol. 2, No. 3, 2021 https://doi.org/10.51630/ijes.v213.25
Fig. 5. Computational grid generation around the planform with wavy LE-wavy TE
Fig. 5. Computational grid generation around the planform with wavy LE-wavy TE
Low-aspect ratio wings possess different characteristics compared to the high-aspect- ratio ones with long spans. By decreasing the aspect ratio (defined as AR=b/c, where b is the wingspan and c is the averaged chord of the wing), trailing/tip vortices become more influential over a large portion of the wing and modify the aero/hydrodynamic performance of the wing. As a result, by decreasing AR, the lift slope decreases [27]. Here, turbulent flows over a low-aspect-ratio wing (AR=1) with NACA 0012 airfoil sections are simulated at a high Reynolds number Re ~1.5x10° (Fig. 7). In this regard, a well-converged grid with about 1 million elements is utilized. The computational domain is extended to 4 and 10 times the wingspan in x and x° directions, respectively. In addition, the domain is extended 3 times of the wing span in the lateral directions to minimize the boundary effects. Fig. 7. Formation of the tip vortices on a low-aspect-ratio wing with NACA 0012 airfoil
Low-aspect ratio wings possess different characteristics compared to the high-aspect- ratio ones with long spans. By decreasing the aspect ratio (defined as AR=b/c, where b is the wingspan and c is the averaged chord of the wing), trailing/tip vortices become more influential over a large portion of the wing and modify the aero/hydrodynamic performance of the wing. As a result, by decreasing AR, the lift slope decreases [27]. Here, turbulent flows over a low-aspect-ratio wing (AR=1) with NACA 0012 airfoil sections are simulated at a high Reynolds number Re ~1.5x10° (Fig. 7). In this regard, a well-converged grid with about 1 million elements is utilized. The computational domain is extended to 4 and 10 times the wingspan in x and x° directions, respectively. In addition, the domain is extended 3 times of the wing span in the lateral directions to minimize the boundary effects. Fig. 7. Formation of the tip vortices on a low-aspect-ratio wing with NACA 0012 airfoil
Fig. 7 shows the formation of the wingtip vortices over the low-aspect-ratio wing at AoA equals to12°. In this regard, a tracer particle study has been performed. To do so, the tracer particles, about 300 water spherical particles with a diameter of 0.0001 m, are continually released from the wing surface and convected downstream by the background flow field having the same velocity as the local flow field). For the calculations, ideal reflection has been applied for fluid particle-solid interactions, e.g., in the separation zones on the wing. As shown in Fig. 7, tip vortices extend far downstream with a spiral motion visualized by tracer particles colored by axial velocity. Intersections of the counter-rotating tip vortices are also visible on a plane positioned x/b=4 downstream of the wing visualized by iso-contours of vorticity, @, =+100 1/s. Fig. 8 depicts the lift coefficient curve versus AoA for the adopted wing compared to the experimental curve measured by Chen et al. [28] and the theoretical curve by Lowry and Polhamus [29], which exhibits a perfect agreement.
Fig. 7 shows the formation of the wingtip vortices over the low-aspect-ratio wing at AoA equals to12°. In this regard, a tracer particle study has been performed. To do so, the tracer particles, about 300 water spherical particles with a diameter of 0.0001 m, are continually released from the wing surface and convected downstream by the background flow field having the same velocity as the local flow field). For the calculations, ideal reflection has been applied for fluid particle-solid interactions, e.g., in the separation zones on the wing. As shown in Fig. 7, tip vortices extend far downstream with a spiral motion visualized by tracer particles colored by axial velocity. Intersections of the counter-rotating tip vortices are also visible on a plane positioned x/b=4 downstream of the wing visualized by iso-contours of vorticity, @, =+100 1/s. Fig. 8 depicts the lift coefficient curve versus AoA for the adopted wing compared to the experimental curve measured by Chen et al. [28] and the theoretical curve by Lowry and Polhamus [29], which exhibits a perfect agreement.
iy Indonesian Journal of Engineering and Science, Vol. 2, No. 3, 2021 https://doi.org/10.51630/ijes.v2i3.25 Fig. 9. An initial manta-ray-inspired test case; Top: grid generation, Bottom: formation of
iy Indonesian Journal of Engineering and Science, Vol. 2, No. 3, 2021 https://doi.org/10.51630/ijes.v2i3.25 Fig. 9. An initial manta-ray-inspired test case; Top: grid generation, Bottom: formation of
Fig. 10. Lift coefficient versus AoA for the initial manta-inspired planform (test case)
Fig. 10. Lift coefficient versus AoA for the initial manta-inspired planform (test case)
The effects of AoA variations on the evolution of tip/trailing vortices for these planforms are shown in Fig. 11 via tracer particle dynamics. As one can see in the figure, by increasing AoA, tip vortices are getting more distorted and tilted upward. Furthermore, Iso-contours of vorticity defined by the axial vorticity, @,=+1 1/s, at a plane positioned at x/b=2 also show that by increasing AoA, cross-sections of tip/trailing vortices are getting larger and more intensified. For example, Fig. 12 shows the formation and evolution of the vortical structures by increasing AoA for the bio-inspired wing planforms with smooth LE-smooth TE (I) compared to wavy LE-wavy TE (II). The vortical structures are captured here by Az -criterion (Ao=-1). As one can see in the figure, a pair of wall-bounded horseshoe vortices with a relatively large scale (comparable to the planform chord) is generated over the wing at a = 12°. By increasing AoA, the vortex pairs become more significant and finally merge at a = 36° and produce a large dominant vortical structure over the planform. As it is also evident in the figure, the presence of L.E. and T.E. undulations modify formation, pattern, and evolution of the minor and major vortical structures at all AoAs.
The effects of AoA variations on the evolution of tip/trailing vortices for these planforms are shown in Fig. 11 via tracer particle dynamics. As one can see in the figure, by increasing AoA, tip vortices are getting more distorted and tilted upward. Furthermore, Iso-contours of vorticity defined by the axial vorticity, @,=+1 1/s, at a plane positioned at x/b=2 also show that by increasing AoA, cross-sections of tip/trailing vortices are getting larger and more intensified. For example, Fig. 12 shows the formation and evolution of the vortical structures by increasing AoA for the bio-inspired wing planforms with smooth LE-smooth TE (I) compared to wavy LE-wavy TE (II). The vortical structures are captured here by Az -criterion (Ao=-1). As one can see in the figure, a pair of wall-bounded horseshoe vortices with a relatively large scale (comparable to the planform chord) is generated over the wing at a = 12°. By increasing AoA, the vortex pairs become more significant and finally merge at a = 36° and produce a large dominant vortical structure over the planform. As it is also evident in the figure, the presence of L.E. and T.E. undulations modify formation, pattern, and evolution of the minor and major vortical structures at all AoAs.
Fig. 12. Formation and evolution of vortical structures versus AoA captured by A» - criterion (A2=-1), colored by axial velocity . Indonesian Journal of Engineering and Science, Vol. 2, No. 3, 2021 https://doi.org/10.51630/ijes.v2i3.25
Fig. 12. Formation and evolution of vortical structures versus AoA captured by A» - criterion (A2=-1), colored by axial velocity . Indonesian Journal of Engineering and Science, Vol. 2, No. 3, 2021 https://doi.org/10.51630/ijes.v2i3.25
Fig. 13. Evolution of separation zones versus AoA for the designed bionic planforms i) Indonesian Journal of Engineering and Science, Vol. 2, No. 3, 2021 https://doi.org/10.51630/ijes.v2i3.25
Fig. 13. Evolution of separation zones versus AoA for the designed bionic planforms i) Indonesian Journal of Engineering and Science, Vol. 2, No. 3, 2021 https://doi.org/10.51630/ijes.v2i3.25
) Indonesian Journal of Engineering and Science, Vol. 2, No. 3, 2021 https://doi.org/10.51630/ijes.v2i3.25 As shown in Fig. 17, lift coefficients of the injured body are modified and exhibit lower/higher values over specific intervals of AoA. Fig. 18 shows intersections of trailing/tip vortices on a plane positioned at x/b=2 visualized by iso-contours of vorticity, @,=+1 1/s, at different AoAs from the back-side of the manta. At a = 24°, dissymmetry of the counter- rotating vortices is more pronounced. By increasing AoA, cross-sections of tip and trailing vortices merger are getting larger and more intensified (Fig. 18).
) Indonesian Journal of Engineering and Science, Vol. 2, No. 3, 2021 https://doi.org/10.51630/ijes.v2i3.25 As shown in Fig. 17, lift coefficients of the injured body are modified and exhibit lower/higher values over specific intervals of AoA. Fig. 18 shows intersections of trailing/tip vortices on a plane positioned at x/b=2 visualized by iso-contours of vorticity, @,=+1 1/s, at different AoAs from the back-side of the manta. At a = 24°, dissymmetry of the counter- rotating vortices is more pronounced. By increasing AoA, cross-sections of tip and trailing vortices merger are getting larger and more intensified (Fig. 18).
Fig. 17. Variations of lift and drag coefficients versus AoA for the injured (blue) and healthy (red) 'Babaganoush' (base (red): planform without LE/ TE undulations)
Fig. 17. Variations of lift and drag coefficients versus AoA for the injured (blue) and healthy (red) 'Babaganoush' (base (red): planform without LE/ TE undulations)
The final important topic is the non-equilibrium state, corresponding to an unbalance generation of forces and moments by the swimming animal. An injured manta ray, such as Babaganoush, experiences unbalance forces and moments exerted on the body, induced by the 'geometric deficiency.' This makes it more difficult for the animal to maintain a so-called ‘trimmed swimming,' similar to the concept of a 'trimmed flight' for an airplane. For example, Fig. 19 shows the absolute values of rolling moments versus AoA exerted on the injured Babaganoush body compared to a healthy one. As one can see the injured animal experiences higher levels of rolling moments at almost all AoAs. Therefore, the injured manta should perform asymmetric flapping and hold asymmetric curvatures to the left and right pectora fins, e.g., dihedral angle, in the gliding and maneuvering phases to maintain the 'trimmed' swimming state.
The final important topic is the non-equilibrium state, corresponding to an unbalance generation of forces and moments by the swimming animal. An injured manta ray, such as Babaganoush, experiences unbalance forces and moments exerted on the body, induced by the 'geometric deficiency.' This makes it more difficult for the animal to maintain a so-called ‘trimmed swimming,' similar to the concept of a 'trimmed flight' for an airplane. For example, Fig. 19 shows the absolute values of rolling moments versus AoA exerted on the injured Babaganoush body compared to a healthy one. As one can see the injured animal experiences higher levels of rolling moments at almost all AoAs. Therefore, the injured manta should perform asymmetric flapping and hold asymmetric curvatures to the left and right pectora fins, e.g., dihedral angle, in the gliding and maneuvering phases to maintain the 'trimmed' swimming state.
Related topics:
Ocean EngineeringZoologyNumerical SimulationsFunctional MorphologyMorphologyManta Ray
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