Forward propulsion of a rigid plunging airfoil

Arora, Nipun; Jain, Anirudh; Singh, Apoorv; Gupta, Amit; Sanghi, Sanjeev; Aono, Hikaru; Shyy, Wei

doi:10.2514/6.2014-2150

Cited by 2 publications

(10 citation statements)

References 33 publications

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“…The horizontal component of this force will thus be responsible for the forward locomotion along the x-axis. According to Newton's second law, the horizontal position of the plate xp is updated by the following equation The propulsion of a plunging rigid flat plate with a uniform coarse mesh throughout was considered earlier [15]. But an ambiguity was observed in the direction of propulsion of the wing on the commencement of instability as for all parameters except Ref kept constant, in ~50% of the cases the wing moved towards left whereas for the rest it moved towards right.…”

Section: Rigid Plunging Flat Platementioning

confidence: 99%

A shifting discontinuous-grid-block lattice Boltzmann method for moving boundary simulations

Arora

Gupta

Shyy

2015

22nd AIAA Computational Fluid Dynamics Conference

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A translating discontinuous-grid-block model for moving boundaries of finite thickness based on multi relaxation time version of LBM has been developed. In this regard, the execution of this model to simulate moving boundary flows has been demonstrated for the cases of a cylinder in simple shear flow, a single rigid wing executing 'clap and fling' motion, and the propulsion of a plunging flat plate. It is shown that the implementation of a body fitted refined mesh that moves along with the object improves its resolution and reduces the spurious oscillations registered in the force and velocity measurements compared to a single grid block. A number of interpolation schemes of linear, quadratic and cubic natures are assessed around the discontinuous grid interface. This method is highly suitable for problems that (a) involve large domain sizes in which the moving solid keeps traversing indefinitely in one direction, and (b) a high resolution around the body is demanded without the expenditure of additional computational power and memory as with the stationary discontinuous-grid-block. NomenclatureA = plunging amplitude B = discrete velocity space c = lattice velocity C = chord length CD = drag coefficient CL = lift coefficient = kinetic energy f = velocity distribution function (SRT) FD = drag force per unit span FL = lift force per unit span x F = horizontal force on plunging plate G = shear rate H = height of channel = momentum flux K = moment space m = grid refinement ratio mp = mass of plate M = transformation matrix = viscous stress tensor q = energy density 2 Ref = flapping Reynolds number S = diagonal relaxation time matrix t = time T = duration of one cycle u = horizontal translational velocity U = dimensionless translational velocity Up = cylinder horizontal velocity Uw = wall velocity vmax = maximum plunging velocity V = maximum translational velocity Vp = cylinder vertical velocity xb = position vector of the boundary node xf = position vector of the fluid nodes at the interior of domain xs = position vector of solid node xp = horizontal position of flat plate y = instantaneous vertical displacement = dimensionless plunging amplitude f = moments of distribution function f = post collision distribution function (SRT) = post collision distribution function (MRT)  = square of kinetic energy = flapping frequency = single relaxation time = kinematic viscosity c x  = grid size in coarse block f x  = grid size in fine block c t  = time step in coarse block f t  = time step in fine block = mass density ratio

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Section: Rigid Plunging Flat Platementioning

confidence: 99%

A shifting discontinuous-grid-block lattice Boltzmann method for moving boundary simulations

Arora

Gupta

Shyy

2015

22nd AIAA Computational Fluid Dynamics Conference

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“…The detailed description of the SRT as well as MRT uniform grid models, calculation of macroscopic variables (flow field around the wing, i.e. u, v and p) from the distributions, the aerodynamic force evaluation on a rigid plunging airfoil using halfway bounceback method with proper validations is provided elsewhere [9,28]. For the sake of brevity, these details are not repeated here and the focus is rather on presenting the coupling between the fluid and structure solvers.…”

Section: A Fluid Solvermentioning

confidence: 99%

“…According to Newton's second law, the horizontal position of the plate xp can be updated by 2 p x 2 dx =m dt F (9) where m is the mass of the plate and x F is calculated using momentum exchange method as prescribed in Ref. [28]. The horizontal velocity u can be updated by…”

Section: A Plunging Kinematicsmentioning

confidence: 99%

“…As an extension to the propulsion of a plunging rigid flat plate [28], a multi-block (finer mesh) which translates along with the flexible wing has been considered around the structure. The methodology of a moving multi-block LBM is given elsewhere [55].…”

Section: B Computational Domainmentioning

confidence: 99%

“…In most of the studies, either the wing flapped at a fixed position with an oncoming flow or the wing cruised through the flow whose speed could be controlled independently [10][11][12][13][14][15][16][17][18][19]. It is lately that some studies [20][21][22][23][24][25][26][27][28] have been conducted on a self-propelled plunging airfoil (the forward translation is produced only due to heaving motion and both of them are interdependent or coupled) which is more realistic.…”

Section: Introductionmentioning

confidence: 98%

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Propulsion of a Plunging Flexible Airfoil using a Torsion Spring Model

Arora

Gupta

Aono

et al. 2015

33rd AIAA Applied Aerodynamics Conference

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The aim of the present study is to understand the mechanism of propulsion in biological flyers, initially starting from rest, using a computational analysis of the plunging motion of a flexible wing. Simulations are performed on a self-propelled flexible wing unconstrained to move in direction perpendicular to the heaving motion. A two-dimensional lumped torsional flexibility model has been developed for a multi-component system which mimics a real insect wing. Using the lattice-Boltzmann method, this model is used to investigate the role of chordwise flexibility on fluid mechanics associated with forward propulsion. The aerodynamics and vortical wake patterns at different frequencies are investigated for a range of Reynolds number and bending stiffnesses. In addition, the behavior of input power and efficiency with stiffness has been examined. This work is anticipated to pave the way towards an improved understanding of propulsion in biological flyers employing flexible wings and thereby contribute to development of micro-air vehicles employing the same concept. NomenclatureA = plunging amplitude c = length of a link C = chord length E = cycle averaged kinetic energy F = ratio of natural to flapping frequency F = force I = mass moment of inertia K = torsional spring stiffness m = mass of plate Pi = cycle averaged input power Q = centrifugal force matrix R = Coriolis force matrix Ref = flapping Reynolds number Reu = translational Reynolds number St = Strouhal number t = time 2 T = duration of one cycle u = instantaneous translational velocity u = steady translational velocity U = dimensionless translational velocity vmax = maximum plunging velocity V = centre of mass velocity W = cycle averaged input energy xp = horizontal position of flat plate y = instantaneous vertical displacement y = plunging acceleration  = aspect ratio = dimensionless plunging amplitude  = hydrodynamic torque  = plunging efficiency = flapping frequency n  = natural frequency = kinematic viscosity = mass density ratio  = mean angular deflection i  = angular deflection of i th link i  = angular velocity of i th link i  = angular acceleration of i th link = cycle averaged input power coefficient ψ = phase difference between heaving and passive pitching

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Forward propulsion of a rigid plunging airfoil

Cited by 2 publications

References 33 publications

A shifting discontinuous-grid-block lattice Boltzmann method for moving boundary simulations

A shifting discontinuous-grid-block lattice Boltzmann method for moving boundary simulations

Propulsion of a Plunging Flexible Airfoil using a Torsion Spring Model

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