Shape, Structure, and Kinematic Parameterization of a Power-Optimal Hovering Wing

Stanford, Bret; Kurdi, Mohammad; Beran, Philip S.; McClung, Aaron

doi:10.2514/6.2010-2963

Cited by 18 publications

(10 citation statements)

References 18 publications

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“…(20), (21), (35), (36), (46), and (52), the coefficient for the instantaneous power required is obtained from the relation…”

Section: An Alternate Flapping-airfoil Propulsion Modelmentioning

confidence: 99%

“…Recently, most investigations of wing flapping have focused on experimental studies 9-24 and numerical solutions that use either potential-flow theory [25][26][27][28][29][30][31][32][33][34][35][36][37] or computational fluid dynamics (CFD). [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54] Because the Theodorsen 7 model appears to be applicable over the range of frequencies and amplitudes that are of interest in practical flapping flight, this model is often used for comparison in CFD and experimental studies, 44,47,55,56 which show varying degrees of agreement with the Theodorsen model.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Propulsion Theory of Flapping Airfoils, Comparison with Computational Fluid Dynamics

Hunsaker

Phillips

2015

53rd AIAA Aerospace Sciences Meeting

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The thrust, required power, and propulsive efficiency of a flapping airfoil as predicted by the well-known Theodorsen model are compared with solutions obtained from gridresolved inviscid computational fluid dynamics.A straight-forward summary of Theodorsen's flapping airfoil model is presented using updated terminology and symbols. This shows that both axial and normal reduced frequencies are of significant importance. The axial reduced frequency is based on the chord length and the normal reduced frequency is based on the plunging amplitude. Computational fluid dynamics solutions are presented over the range of both reduced frequencies typically encountered in the forward flight of birds. It is shown that computational results agree reasonably well with those predicted by Theodorsen's model at low flapping frequencies. An alternate model is also developed, which shows that the time-dependent aerodynamic forces acting on a flapping airfoil can be related to two unknown Fourier coefficients. The computational results are correlated with algebraic relations for these Fourier coefficients, which can be used to predict the thrust, required power, and propulsive efficiency for airfoils with sinusoidal pitching and plunging motion.

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“…(20), (21), (35), (36), (46), and (52), the coefficient for the instantaneous power required is obtained from the relation…”

Section: An Alternate Flapping-airfoil Propulsion Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Propulsion Theory of Flapping Airfoils, Comparison with Computational Fluid Dynamics

Hunsaker

Phillips

2015

53rd AIAA Aerospace Sciences Meeting

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“…Isogai and Harino 7 optimized the thickness distribution of the leading edge spar from a Kite Hawk UAV but did not address the planform in their work. Stanford, et al 8 optimized the thickness and planform of a flapping wing. They parameterized the planform by dividing the wing into a series of blade elements and then varying the chord length of each of the blades.…”

Section: Introductionmentioning

confidence: 99%

Aeroelastic Shape Optimization of a Pluging Plate

Stewart¹,

Patil²,

Canfield³

et al. 2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

2
0
1
0

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In this paper, aeroelastic shape optimization is performed on flapping micro air vehicle (MAV) wings in forward flight. The aeroelastic model tightly couples the structural plate finite element model with an unsteady vortex lattice method aerodynamic model. A gradient-based optimizer is used to maximize the cycle-average thrust generated by the wing while minimizing the power requirements. The multiobjective optimization is performed using the -constraint method. The optimizer creates wings that maximize the span while the chord is limited by the power constraint. Nomenclatureα instantaneous angle of attack ∆t time step size η, ξ area coordinates of the DKT element Γ b vector of bound vorticies Γ w vector of wake vorticies ρ fluid density A b matrix of influence coefficients from the bound vorticity A e area of the e th finite element A w matrix of influence coefficients from the wake B DKT strain-displacement relationship matrix C s proportional structural damping D b DKT stress-strain relationship matrix F aero vecotr of aerodynamic forces acting on the wing F inertia vecotr of inertial forces acting on the wing g gravitational constant h rigid body motion at the nodes h CP vector of rigid-body velocity at the control points K s structural stiffness matrix for the DKT elements L lift m number of triangular elements in the structure M s structural mass matrix for the DKT elements m wing mass of the wing P in input power q vector of the global nodal degrees of freedom T thrust t h thickness of the plate T α,qmatrix that converts nodal deformation to control point rotations T a,cp matrix that converts pressure at the control points to nodal forces T V,q matrix that converts the nodal velocities to velocities at the control points V s velocity of the air acting on the wing due to the rate of the deformation V kin velocity of the air acting on the wing due to the prescribed kinematic motion

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“…Stanford, et al [9] optimized the shape, structure, and kinematics of a flexible hovering wing by modeling the wing as a series of beam elements.…”

Section: Introductionmentioning
confidence: 99%

Aeroelastic Shape Optimization of a Flapping Wing
Stewart
¹
,
Patil
²
,
Canfield
³

et al. 2014
10th AIAA Multidisciplinary Design Optimization Conference
6
0
2
0
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This paper presents the theory and results for the shape and structural optimization of a plate-like flapping wing. The aeroelastic system is analyzed by coupling an unsteady vortex lattice aerodynamics model with a plate finite element model. The assumptions in the aerodynamic model allow the system of equations to be reduced to a set of constantcoefficient, ordinary differential equations. The forcing of the flapping motion is timeperiodic so the steady-state periodic response can be calculated with the inversion of a single matrix -greatly reducing the computational cost. The design variables are the shape parameters from the modified Zimmerman method as well as the polynomial coefficients that describe the wing thickness. A multiobjective optimization is performed using the -constraint method where the power is the secondary objective function and is treated as a nonlinear constraint while the cycle-averaged thrust is the primary objective function. A case study with wing mass as a secondary objective function is also performed. This allows the wing deformation to increase without being constrained by the input power. Nomenclature α instantaneous angle of attack α 0 angle of attack of the rigid body with respect to the freestream velocity ∆P change in pressure on the wing ∆t time step size Downloaded by KUNGLIGA TEKNISKA HOGSKOLEN KTH on July 30, 2015 | http://arc.aiaa.org |

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Shape, Structure, and Kinematic Parameterization of a Power-Optimal Hovering Wing

Cited by 18 publications

References 18 publications

Propulsion Theory of Flapping Airfoils, Comparison with Computational Fluid Dynamics

Propulsion Theory of Flapping Airfoils, Comparison with Computational Fluid Dynamics

Aeroelastic Shape Optimization of a Pluging Plate

Aeroelastic Shape Optimization of a Flapping Wing

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