Extensions of Time Spectral Methods for Practical Rotorcraft Problems

Abstract

For flows with strong periodic content, time-spectral methods can be used to obtain time-accurate solutions at substantially reduced cost compared to traditional time-implicit methods which operate directly in the time domain. In their original form, time spectral methods are applicable only to purely periodic problems and formulated for single grid systems. A wide class of problems involve quasi-periodic flows, such as maneuvering rotorcraft problems, where a slow transient is superimposed over a more rapid periodic motion. Additionally, the most common approach for simulating combined rotor-fuselage interactions is through the use of a dynamically overlapping mesh system. Thus, in order to represent a practical approach for rotorcraft simulations, time spectral methods that are applicable to quasi-periodic problems and capable of operating on overlapping mesh systems need to be formulated. In this paper, we propose separately an extension of time spectral methods to quasi-periodic problems, and an extension for overlapping mesh configurations. In both cases, the basic implementation allows for two levels of parallelism, one in the spatial dimension, and another in the time-spectral dimension, and is implemented in a modular fashion that minimizes the modifications required to an existing steady-state solver. Results are given for three-dimensional quasi-periodic problems on a single mesh, and for two-dimensional periodic overlapping mesh systems.

Time-Spectral Method for Overlapping Meshes

“…Overset solvers typically employ a spatial smoothing operation to populate the solution within hole cuts with non zero data in case such points are inadvertently queried. Mavriplis et al [15] outlined a general Time-Spectral solver for relative motion by taking advantage of this common feature. In this approach, Laplace's equation is solved over the domain of blanked spatial nodes using the data on the hole cut fringe as the boundary condition.…”

“…These approaches prove worthy for simple configurations but are not general solutions for the case of arbitrary relative motion. Mavriplis et al [15] demonstrated a general approach to treat dynamically-blanked nodes by applying Laplacian smoothing to populate blanked data using the solution on the boundaries of hole cuts. In the current work, a hybrid Time-Spectral scheme capable of consistently treating dynamically-blanked nodes resulting from general relative motion between overset grids is developed and implemented within NASA's OVERFLOW solver.…”

Algorithmic Advanced for the Adaptive Non-Linear Frequency Domain Method.

“…Therefore, the effect of nonlinear harmonic coupling would not be considered. On the other hand, in the nonlinear harmonic method, known as Harmonic Balance , 13,15,16 Non-Linear Frequency Domain (NLFD), 29,30,34,35 and Time Spectral, 5,6,11,12,26,27,44,53 all the harmonic equations are solved coupled. Besides, there is no restriction on the amplitude of the perturbation terms.…”

An Extension of the Time-Spectral Method to Overset Solvers

“…One approach is to fill the blanked nodes with solution data via spatial averaging and proceed with the standard Time-Spectral method (cf. [17]). While attractive for its simplicity, this approach is inconsistent.…”