Helicopter Rotor Flow Analysis Using Mapped Chebyshev Pseudospectral Method and Overset Mesh Topology

Im, Dong Kyun; Choi, Seongim Sarah

Helicopter Rotor Flow Analysis Using Mapped Chebyshev Pseudospectral Method and Overset Mesh Topology

dc.contributor.author	Im, Dong Kyun	en
dc.contributor.author	Choi, Seongim Sarah	en
dc.contributor.department	Aerospace and Ocean Engineering	en
dc.date.accessioned	2018-05-21T12:44:00Z	en
dc.date.available	2018-05-21T12:44:00Z	en
dc.date.issued	2018-05-15	en
dc.date.updated	2018-05-20T07:04:04Z	en
dc.description.abstract	Unsteady helicopter rotor flows are solved by a Chebyshev pseudospectral method with overset mesh topology which employs Chebyshev polynomials for solution approximation and a Chebyshev collocation operator to represent the time derivative term of the unsteady flow governing equations. Spatial derivative terms of the flux Jacobians are discretized implicitly while the Chebyshev spectral derivative term is treated in explicit form. Unlike the Fourier spectral method, collocation points of standard Chebyshev polynomials are not evenly distributed and heavily clustered near the extremities of the time interval, which makes the spectral derivative matrix ill-conditioned and deteriorates the stability and convergence of the flow solution. A conformal mapping of an arcsin function is applied to redistribute those points more evenly and thus to improve the numerical stability of the linear system. A parameter study on the condition number of the spectral derivative matrix with respect to the control parameters of the mapping function is also carried out. For the validation of the proposed method, both periodic and nonperiodic unsteady flow problems were solved with two-dimensional problems: an oscillating airfoil with a fixed frequency and a plunging airfoil with constant plunging speed without considering gravitational force. Computation results of the Chebyshev pseudospectral method showed excellent agreements with those of the time-marching computation. Subsequently, helicopter rotor flows in hovering and nonlifting forward flight are solved. Moving boundaries of the rotating rotor blades are efficiently managed by the overset mesh topology. As a set of subgrids are constructed only one time at the beginning of the solution procedure corresponding to the mapped Chebyshev collocation points, computation time for mesh interpolation of hole-cutting between background and near-body grids becomes drastically reduced when compared to the time-marching computation method where subgrid movement and the hole-cutting need to be carried out at each physical time step. The number of the collocation points was varied to investigate the sensitivity of the solution accuracy, computation time, and memory. Computation results are compared with those from the time-marching computation, the Fourier spectral method, and wind-tunnel experimental data. Solution accuracy and computational efficiency are concluded to be great with the Chebyshev pseudospectral method. Further applications to unsteady nonperiodic problems will be left for future work.	en
dc.description.version	Published version	en
dc.format.mimetype	application/pdf	en
dc.identifier.citation	Dong Kyun Im and Seongim Choi, “Helicopter Rotor Flow Analysis Using Mapped Chebyshev Pseudospectral Method and Overset Mesh Topology,” Mathematical Problems in Engineering, vol. 2018, Article ID 9745862, 20 pages, 2018. doi:10.1155/2018/9745862	en
dc.identifier.doi	https://doi.org/10.1155/2018/9745862	en
dc.identifier.uri	http://hdl.handle.net/10919/83366	en
dc.language.iso	en	en
dc.publisher	Hindawi	en
dc.rights	Creative Commons Attribution 4.0 International	en
dc.rights.holder	Copyright © 2018 Dong Kyun Im and Seongim Choi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.	en
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	en
dc.title	Helicopter Rotor Flow Analysis Using Mapped Chebyshev Pseudospectral Method and Overset Mesh Topology	en
dc.title.serial	Mathematical Problems in Engineering	en
dc.type	Article - Refereed	en
dc.type.dcmitype	Text	en