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Centripetal Acceleration Reaction: An Effective and Robust Mechanism for Flapping Flight in Insects.

Zhang C, Hedrick TL, Mittal R - PLoS ONE (2015)

Bottom Line: Despite intense study by physicists and biologists, we do not fully understand the unsteady aerodynamics that relate insect wing morphology and kinematics to lift generation.Furthermore, unlike the lift due to vorticity, centripetal acceleration reaction lift is insensitive to Reynolds number and to environmental flow perturbations, making it an important contributor to insect flight stability and miniaturization.This force mechanism also has broad implications for flow-induced deformation and vibration, underwater locomotion and flows involving bubbles and droplets.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical Engineering, the Johns Hopkins University, Baltimore, Maryland, United States of America.

ABSTRACT
Despite intense study by physicists and biologists, we do not fully understand the unsteady aerodynamics that relate insect wing morphology and kinematics to lift generation. Here, we formulate a force partitioning method (FPM) and implement it within a computational fluid dynamic model to provide an unambiguous and physically insightful division of aerodynamic force into components associated with wing kinematics, vorticity, and viscosity. Application of the FPM to hawkmoth and fruit fly flight shows that the leading-edge vortex is the dominant mechanism for lift generation for both these insects and contributes between 72-85% of the net lift. However, there is another, previously unidentified mechanism, the centripetal acceleration reaction, which generates up to 17% of the net lift. The centripetal acceleration reaction is similar to the classical inviscid added-mass in that it depends only on the kinematics (i.e. accelerations) of the body, but is different in that it requires the satisfaction of the no-slip condition, and a combination of tangential motion and rotation of the wing surface. Furthermore, the classical added-mass force is identically zero for cyclic motion but this is not true of the centripetal acceleration reaction. Furthermore, unlike the lift due to vorticity, centripetal acceleration reaction lift is insensitive to Reynolds number and to environmental flow perturbations, making it an important contributor to insect flight stability and miniaturization. This force mechanism also has broad implications for flow-induced deformation and vibration, underwater locomotion and flows involving bubbles and droplets.

No MeSH data available.


Related in: MedlinePlus

Components of the instantaneous lift coefficient over one flapping cycle for the (a) hovering hawkmoth at Re = 1000, and the (b) fruit fly at Re = 100. The stroke is divided into two phases: downstroke (D) and upstroke (U). Lift coefficient is defined as CF = F/(ρAβ2f2L2) where F is force, ρ is the fluid density, A and L the wing area and wing length respectively, and β and f the stroke amplitude and frequency respectively. The vortex-induced lift (VIL) Fω exhibits a large and distinct peak near mid-downstroke for both wings. In upstroke both wings generate positive VIL, but the magnitudes are significant only for the hawkmoth.
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pone.0132093.g002: Components of the instantaneous lift coefficient over one flapping cycle for the (a) hovering hawkmoth at Re = 1000, and the (b) fruit fly at Re = 100. The stroke is divided into two phases: downstroke (D) and upstroke (U). Lift coefficient is defined as CF = F/(ρAβ2f2L2) where F is force, ρ is the fluid density, A and L the wing area and wing length respectively, and β and f the stroke amplitude and frequency respectively. The vortex-induced lift (VIL) Fω exhibits a large and distinct peak near mid-downstroke for both wings. In upstroke both wings generate positive VIL, but the magnitudes are significant only for the hawkmoth.

Mentions: Fig 2 shows the time variations of the total lift coefficient (which corresponds to the vertical direction x2) and its three significant components (FκI, Fω, and Fσ) for the two cases studied here. Table 1 summarizes the time-averaged values of these components over one flapping cycle. For the hawkmoth wing, the downstroke contributes the majority (70%) of the total lift and the upstroke, 30%. As described in detail in our previous paper [9], the simulations of the hovering hawkmoth reproduce both the mean as well as time-variation of the lift quite accurately when compared to the experimental estimates obtained from the body acceleration of the animal during flight. In contrast to hovering flight of the hawkmoth, the fruit fly in slow climbing flight modeled here, generates all of its weight support during the downstroke, with the upstroke and wing rotation periods generating a small net negative lift force. Thus, compared to the idealized hovering kinematics [7] or kinematics measured from freely hovering flies [11], which produce similar magnitude lift in upstroke and downstroke and, depending on rotation phase, substantial forces during wing rotation, the tilted stroke plane kinematics adopted by the fly recorded here differ markedly in the time course of force production within a stroke. However, when re-dimensionalized for comparison with the whole-body kinematics of the fruit fly (described above), our simulation predicts a net upward force of 1.83 × 10−5N, or 124% of the 1.48 × 10−5N calculated from whole-body kinematics and body mass. Note that our whole-body kinematics does not include the drag due to upward motion, so the computed 1.48 × 10−5N upward force is expected to underestimate the force actually produced by the fly. Thus, although the flapping kinematics used by the fly here are distinct from typical hovering, they also produce force sufficient to support the weight of the fly and even account for its slight upward acceleration. It is not clear why the fly used wing kinematics distinct from those typically recorded from hovering animals, but it may be the case that tilting the stroke plane down and concentrating force production at the phase of the stroke cycle when the wing is moving downward improves efficiency during climbing flight. The figure and the table indicate that the viscosity-induced lift force is nearly negligible for the hawkmoth and it generates a non-negligible (25%) but net-negative lift contribution for the fruit fly. This is consistent with the order-of-magnitude higher Reynolds number for the hawkmoth. The rest of the discussion will focus on the vortex-induced and kinematic lift components.


Centripetal Acceleration Reaction: An Effective and Robust Mechanism for Flapping Flight in Insects.

Zhang C, Hedrick TL, Mittal R - PLoS ONE (2015)

Components of the instantaneous lift coefficient over one flapping cycle for the (a) hovering hawkmoth at Re = 1000, and the (b) fruit fly at Re = 100. The stroke is divided into two phases: downstroke (D) and upstroke (U). Lift coefficient is defined as CF = F/(ρAβ2f2L2) where F is force, ρ is the fluid density, A and L the wing area and wing length respectively, and β and f the stroke amplitude and frequency respectively. The vortex-induced lift (VIL) Fω exhibits a large and distinct peak near mid-downstroke for both wings. In upstroke both wings generate positive VIL, but the magnitudes are significant only for the hawkmoth.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4529139&req=5

pone.0132093.g002: Components of the instantaneous lift coefficient over one flapping cycle for the (a) hovering hawkmoth at Re = 1000, and the (b) fruit fly at Re = 100. The stroke is divided into two phases: downstroke (D) and upstroke (U). Lift coefficient is defined as CF = F/(ρAβ2f2L2) where F is force, ρ is the fluid density, A and L the wing area and wing length respectively, and β and f the stroke amplitude and frequency respectively. The vortex-induced lift (VIL) Fω exhibits a large and distinct peak near mid-downstroke for both wings. In upstroke both wings generate positive VIL, but the magnitudes are significant only for the hawkmoth.
Mentions: Fig 2 shows the time variations of the total lift coefficient (which corresponds to the vertical direction x2) and its three significant components (FκI, Fω, and Fσ) for the two cases studied here. Table 1 summarizes the time-averaged values of these components over one flapping cycle. For the hawkmoth wing, the downstroke contributes the majority (70%) of the total lift and the upstroke, 30%. As described in detail in our previous paper [9], the simulations of the hovering hawkmoth reproduce both the mean as well as time-variation of the lift quite accurately when compared to the experimental estimates obtained from the body acceleration of the animal during flight. In contrast to hovering flight of the hawkmoth, the fruit fly in slow climbing flight modeled here, generates all of its weight support during the downstroke, with the upstroke and wing rotation periods generating a small net negative lift force. Thus, compared to the idealized hovering kinematics [7] or kinematics measured from freely hovering flies [11], which produce similar magnitude lift in upstroke and downstroke and, depending on rotation phase, substantial forces during wing rotation, the tilted stroke plane kinematics adopted by the fly recorded here differ markedly in the time course of force production within a stroke. However, when re-dimensionalized for comparison with the whole-body kinematics of the fruit fly (described above), our simulation predicts a net upward force of 1.83 × 10−5N, or 124% of the 1.48 × 10−5N calculated from whole-body kinematics and body mass. Note that our whole-body kinematics does not include the drag due to upward motion, so the computed 1.48 × 10−5N upward force is expected to underestimate the force actually produced by the fly. Thus, although the flapping kinematics used by the fly here are distinct from typical hovering, they also produce force sufficient to support the weight of the fly and even account for its slight upward acceleration. It is not clear why the fly used wing kinematics distinct from those typically recorded from hovering animals, but it may be the case that tilting the stroke plane down and concentrating force production at the phase of the stroke cycle when the wing is moving downward improves efficiency during climbing flight. The figure and the table indicate that the viscosity-induced lift force is nearly negligible for the hawkmoth and it generates a non-negligible (25%) but net-negative lift contribution for the fruit fly. This is consistent with the order-of-magnitude higher Reynolds number for the hawkmoth. The rest of the discussion will focus on the vortex-induced and kinematic lift components.

Bottom Line: Despite intense study by physicists and biologists, we do not fully understand the unsteady aerodynamics that relate insect wing morphology and kinematics to lift generation.Furthermore, unlike the lift due to vorticity, centripetal acceleration reaction lift is insensitive to Reynolds number and to environmental flow perturbations, making it an important contributor to insect flight stability and miniaturization.This force mechanism also has broad implications for flow-induced deformation and vibration, underwater locomotion and flows involving bubbles and droplets.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical Engineering, the Johns Hopkins University, Baltimore, Maryland, United States of America.

ABSTRACT
Despite intense study by physicists and biologists, we do not fully understand the unsteady aerodynamics that relate insect wing morphology and kinematics to lift generation. Here, we formulate a force partitioning method (FPM) and implement it within a computational fluid dynamic model to provide an unambiguous and physically insightful division of aerodynamic force into components associated with wing kinematics, vorticity, and viscosity. Application of the FPM to hawkmoth and fruit fly flight shows that the leading-edge vortex is the dominant mechanism for lift generation for both these insects and contributes between 72-85% of the net lift. However, there is another, previously unidentified mechanism, the centripetal acceleration reaction, which generates up to 17% of the net lift. The centripetal acceleration reaction is similar to the classical inviscid added-mass in that it depends only on the kinematics (i.e. accelerations) of the body, but is different in that it requires the satisfaction of the no-slip condition, and a combination of tangential motion and rotation of the wing surface. Furthermore, the classical added-mass force is identically zero for cyclic motion but this is not true of the centripetal acceleration reaction. Furthermore, unlike the lift due to vorticity, centripetal acceleration reaction lift is insensitive to Reynolds number and to environmental flow perturbations, making it an important contributor to insect flight stability and miniaturization. This force mechanism also has broad implications for flow-induced deformation and vibration, underwater locomotion and flows involving bubbles and droplets.

No MeSH data available.


Related in: MedlinePlus