An overset time-spectral method for relative motion [electronic resource]

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 flow is achieved. Such flows, while unsteady in the time domain, are invariant in the frequency domain. As such, the governing equations can 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 unsteady 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 initial transients in physical time and because of the spectral convergence properties of the Fourier series. This dissertation extends the Time-Spectral method to overset flow solvers in a general manner. 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 within the impermeable boundaries of solid bodies. Since the infinite support of the complex exponential basis functions prevents direct application of the standard Time-Spectral method, a novel hybrid Time-Spectral method has been developed that expands the temporal variation at dynamically-blanked nodes in an alternative manner. Investigation of a number of strategies to handle dynamically-blanked nodes is described. However, the proposed scheme is extensible by construction to enable the incorporation of future improvements with minimal effort. The hybrid Time-Spectral discretization has been incorporated within NASA's well-established three-dimensional implicit Reynolds-averaged Navier-Stokes (RANS) solver OVERFLOW. Details concerning the implicit approximate factorization scheme, turbulence modeling, multigrid acceleration and dealiasing are addressed with respect to the Time-Spectral implementation. The augmented Time-Spectral OVERFLOW solver is validated by direct comparison with the existing time-accurate solver for a variety of numerical experiments. A series of two-dimensional oscillating airfoil cases are included to assess the ability of the hybrid Time-Spectral scheme to handle high-frequency, transonic and turbulent flows. The relatively inexpensive two-dimensional test cases serve as meaningful model problems that are used to uncover solution strategies for more expensive realistic three-dimensional flows. The thesis concludes with a pair of three-dimensional calculations of the quarter-scale V-22 Tilt Rotor Aeroacoustic Model (TRAM) in hover and forward (edgewise) flight. The Time-Spectral hover simulation matches the time-accurate calculation using a single harmonic. Significantly more temporal modes and dealiasing are required to accurately compute the forward flight case because of its more active, high-frequency wake.

Keywords: Aeronautics and Astronautics.
Advisor: Jameson Antony
Alonso Juan José
Pulliam T. H. (Thomas H.)