Fast Multipole Accelerated Unsteady Vortex Lattice Method Based Computations

Kebbie-Anthony, Abu; Gumerov, Nail A.; Preidikman, Sergio; Balachandran, Balakumar; Azarm, Shapour

doi:10.2514/1.i010690

Cited by 4 publications

(3 citation statements)

References 24 publications

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“…As enhancements, the current aerodynamic model can be extended by incorporating a growth core-vortex scheme in order to handle tandem configurations of harvesters (Bhagwat and Leishman, 2002; Roccia et al, 2018). In addition, the use of the fast multipole method to rapidly compute the velocity contribution from the time-varying wakes will also be desirable (Kebbie-Anthony et al, 2019). Regarding the structural model, one can conclude that a significant limitation is the lack of consideration of nonlinearities, which are necessary to conduct more detailed studies on the dynamic behavior of the piezo-aeroelastic system, such as detection of quasiperiodic motions, intermittence, determination of SHB points, and chaos.…”

Section: Numerical Resultsmentioning

confidence: 99%

Computational study on aerodynamically coupled piezoelectric harvesters

Roccia

Verstraete

Ceballos

et al. 2020

Journal of Intelligent Material Systems and Structures

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In this work, the authors present a two-dimensional computational model for predicting the aeroelastic response as well as the output power of vertically arranged harvesters by taking into account all aerodynamic interactions. The piezo-aeroelastic framework consists of the following: (1) an aerodynamic model based on the unsteady vortex-lattice method to compute the aerodynamic forces; (2) a discrete parameter model for each harvester with 3 degrees of freedom (plunge motion, pitch motion, and the voltage generated by the piezoelectric effect); (3) an inter-model connection to exchange information between models at each time step; and (4) a numerical scheme based on the Hamming’s fourth-order predictor–corrector method to integrate all the governing equations in the time domain. The results obtained allow us to infer new insights into the flutter onset as well as the post-critical behavior of harvester arrangements. An interesting finding is that the flutter speed is significantly decreased as the distance between the harvesters is reduced. The results suggest the strong possibility of effective energy extraction at low flow speeds using properly distributed harvester arrangements. However, in post-critical conditions, the output power is significantly enhanced as the free-stream speed is increased.

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Section: Numerical Resultsmentioning

confidence: 99%

Computational study on aerodynamically coupled piezoelectric harvesters

Roccia

Verstraete

Ceballos

et al. 2020

Journal of Intelligent Material Systems and Structures

Self Cite

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“…Willis et al 14 achieve this with the fast multipole method (FMM), which they applied to an unsteady panel method. This is the main inspiration for the method introduced in this paper and has been applied to the UVLM by Wales et al 15 The most recent FMM UVLM implementation is by Kebbie-Anthony et al 16,17 The method requires the conversion of UVLM vortex filaments into vortex particles, at which point the FMM can be implemented with a Lamb-Helmholtz decomposition. 18 The effect of a group (agglomeration) of vortex particles is then estimated using a multipole expansion, allowing for a tree structure to be built that describes the wake in varying levels of agglomeration.…”

Section: Introductionmentioning

confidence: 93%

“…14 This means that the wake can effectively have full refinement close to the point, and progressively less refinement further away from the point, which saves computation time while minimizing the difference in the solution. Kebbie-Anthony et al show that the UVLM FMM can achieve O(n) computations 17 ; however, the procedure is reasonably complex to implement, and its performance is sensitive to several parameter values.…”

Section: Introductionmentioning

confidence: 99%

The double‐tree method: An O(n) unsteady aerodynamic lifting surface method

Jones

Dunning

Maheri

2020

Numerical Methods in Fluids

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Summary Two new methods for reducing the computational cost of the unsteady vortex lattice method are developed. These methods use agglomeration to construct time‐saving tree structures by approximating the effect of either a group of vortex rings or query points. A case study shows that combining the two new O(n·log n) tree methods together results in an O(n) method, called the double‐tree method. Other case studies show that the trade‐off between accuracy and speed can be easily and reliably controlled by the agglomeration cutoff distance. For a flat plate with 5 × 200 panels analyzed over 20 time steps, the double‐tree method is 7 times faster than the unsteady vortex lattice method with a <5% difference in the force distribution and total lift coefficient. The case studies suggest that the computational benefit will increase for the same level of accuracy if the size of the problem is increased, making the method beneficial for full‐aircraft analysis within optimization or dynamic load analysis, where the computational cost of the unsteady vortex lattice method can be large.

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