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State‐Space Representation of Vortex Wakes by the Method of Lines

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The method of lines (MOL) is applied to the equations of helicopter rotor vortex wakes, and converts the governing partial differential equations into a system of ordinary differential equations (ODEs). These ODEs can then be coupled to other ODEs modeling helicopter dynamics, for time‐marching simulations or to extract linearized models. The MOL is applied to a simplified set of wake equations that has an analytical solution. Because these simplified equations neglect key wake physics, the study is only a first step toward applying MOL to realistic models. Therefore, the conclusions only apply to the simplified problem considered. The results show that the MOL is a suitable method to formulate vortex wake models in state‐space form. The solutions are accurate and numerically stable. Refining the space discretization increases the stiffness of the ODE, but explicit solvers can still be used. Computational efficiency increases when the accuracies of space and time discretizations are matched, that is, the local error tolerance set for the time solver is matched with the order of accuracy of the space discretization. Formulas of several orders were used in the space discretization. In all cases, the explicit ODE solver used (DE/STEP) was much more computationally efficient than another, implicit ODE solver (DASSL). Linearized state‐space wake models can be easily obtained. The MOL could also provide a systematic methodology to extract state‐space models from computational fluid dynamics formulations, and therefore to increase the accuracy of helicopter simulation models.
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Document Type: Research Article

Affiliations: Department of Aerospace Engineering, University of Maryland, College Park, MD

Publication date: 2005-04-01

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  • The Journal of the American Helicopter Society is the world's only scientific journal dedicated to vertical flight technology. It is a peer-reviewed technical journal published quarterly by AHS International and presents innovative papers covering the state-of-the-art in all disciplines of rotorcraft design, research and development. (Please note that AHS members receive significant discounts on articles and subscriptions.)

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