Closed-Form Expressions for Cycle-Averaged Aerodynamic Quantities at an Airfoil Section of an Avian Flapping Wing

Bhattacharjee, Diganta; Subbarao, Kamesh

doi:10.2514/6.2019-0565

Cited by 1 publication

(10 citation statements)

References 17 publications

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“…The power requirement calculations were also carried out without accounting for the drag and that lead to unrealistic propulsive efficiency estimates (Paranjape et al 7 ). Bhattacharjee and Subbarao 18 recently derived analytical cycle-averaged force expressions for a flapping airfoil. A suitable drag model was integrated in the framework proposed by Bhattacharjee and Subbarao.…”

Section: Literature Reviewmentioning

confidence: 99%

“…A suitable drag model was integrated in the framework proposed by Bhattacharjee and Subbarao. 18 Utilizing the results, a hypothesis was presented regarding the choice of Strouhal numbers for avian-scale cruising flight.…”

Section: Literature Reviewmentioning

confidence: 99%

“…In this section, the formulation required for the calculation of cycle-averaged forces, power, and propulsive efficiency is provided. While, the formulation given in Bhattacharjee and Subbarao 18 addressed the 2 D airfoil, this paper addresses the extensions to the finite wing.…”

Section: Preliminariesmentioning

confidence: 99%

“…The detailed representation of the rotation matrices for the right and left wings are given in Bhattacharjee and Subbarao. 18…”

Section: Rotation Matricesmentioning

confidence: 99%

“…where _ hðyÞ is aligned with the z R or z L axes and _ zðyÞ is aligned with the z B axes (see Figure 3 in Bhattacharjee and Subbarao 18 ) The local AoA at a section are given by…”

Section: Flapping Kinematics and Strouhal Numbermentioning

confidence: 99%

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A flight mechanics-based justification of the unique range of Strouhal numbers for avian cruising flight

Bhattacharjee

Subbarao

2020

Proceedings of the Institution of Mechanical Engineers, Part G:

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In this paper, analytical expressions for cycle-averaged aerodynamic forces generated by flapping wings are derived using a force model and flapping kinematics suitable for the forward flight of avian creatures. A strip theory-based formulation is proposed and the analytical expressions are found as functions of the amplitude of twist profile, mean twist angle, the flow separation point on the upper surfaces of the wings, and Strouhal number. Numerical results are obtained for a rectangular planform as well as for a representative avian wing planform. Utilizing these results, it is shown that there exists a narrow Strouhal number range where cycle-averaged net thrust, lift, and lift to drag ratio are optimal for a given flow pattern over the upper surfaces of the wings. This narrow Strouhal number range, found to be between 0.1 and 0.3, corresponds to the cruising range for a large number of avian creatures, as documented in current literature. An explanation, based on force constraints and local optimization in aerodynamic force generation, is provided for the unique range of Strouhal numbers utilized in avian cruising flight. The results and the approach outlined in the paper can be utilized to design efficient bio-inspired flapping vehicles.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

“…The detailed representation of the rotation matrices for the right and left wings are given in Bhattacharjee and Subbarao. 18…”

Section: Rotation Matricesmentioning

confidence: 99%

“…where _ hðyÞ is aligned with the z R or z L axes and _ zðyÞ is aligned with the z B axes (see Figure 3 in Bhattacharjee and Subbarao 18 ) The local AoA at a section are given by…”

Section: Flapping Kinematics and Strouhal Numbermentioning

confidence: 99%

See 3 more Smart Citations