An Overset Time-Spectral Method for Relative Motion

Speaker: Joshua Leffell, Stanford University
March 13, 2014

Presentation

Abstract

Periodic flow arises in a broad range of aerodynamic applications, including turbomachinery, rotorcraft and flapping-wing configurations. The standard procedure for simulating such flows involves integrating the governing equations forward in time until a statistically-stationary solution is achieved. Recognizing that such flows, while unsteady in the time domain, are invariant in the frequency domain, allows the governing equations to be transformed into a steady set of equations by expanding the temporal variation at every point in space as a truncated Fourier series. The Time-Spectral method is a Fourier pseudospectral scheme developed to exploit this fact while maintaining the ability to resolve the nonlinear dynamics of the governing equations. Fourier collocation techniques have been shown to reduce the computational costs associated with periodic steady-state flows by up to an order of magnitude by obviating the need to simulate through the initial transient in a time-accurate manner and because of the spectral convergence properties of the Fourier series.

This dissertation extends the Time-Spectral method to overset flow solvers. Overset grid technology provides the ability to resolve geometry of arbitrary complexity with structured grids that offer enhanced boundary-layer resolution and efficient data structures. However, relative motion between components results in spatial nodes that lack complete time-histories as they are dynamically removed from the computational domain when located interior to impermeable boundaries. The infinite support of the complex exponential basis functions prevents direct application of the standard Time-Spectral method, so a novel hybrid Time-Spectral scheme has been developed that expands the temporal variation at dynamically-blanked nodes in an alternative manner. The hybrid Time-Spectral scheme has been implemented within NASA's implicit Reynolds-averaged Navier-Stokes solver OVERFLOW and demonstrated on the two- and three-dimensional cases of oscillating airfoils and the quarter-scale V22 Tilt Rotor Aeroacoustic Model (TRAM) in hover and forward flight.

Biography

Joshua Leffell is a Ph.D. candidate in the Department of Aeronautics & Astronautics at Stanford University with co-advisors Professor Antony Jameson of the Aerospace Computing Lab and Thomas Pulliam of NASA Advanced Supercomputing Division at NASA Ames Research Center. Upon graduation, Joshua will start a Postdoc with the US Army Aerodynamics Development Directorate.

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