Computational analysis of high resolution unsteady airloads for rotor aeroacoustics

The study of helicopter aerodynamic loading for acoustics applications requires the application of efficient yet accurate simulations of the velocity field induced by the rotor's vortex wake. This report summarizes work to date on the development of such an analysis, which builds on the Constant Vorticity Contour (CVC) free wake model, previously implemented for the study of vibratory loading in the RotorCRAFT computer code. The present effort has focused on implementation of an airload reconstruction approach that computes high resolution airload solutions of rotor/rotor-wake interactions required for acoustics computations. Supplementary efforts on the development of improved vortex core modeling, unsteady aerodynamic effects, higher spatial resolution of rotor loading, and fast vortex wake implementations have substantially enhanced the capabilities of the resulting software, denoted RotorCRAFT/AA (AeroAcoustics). Results of validation calculations using recently acquired model rotor data show that by employing airload reconstruction it is possible to apply the CVC wake analysis with temporal and spatial resolution suitable for acoustics applications while reducing the computation time required by one to two orders of magnitude relative to that required by direct calculations. Promising correlation with this body of airload and noise data has been obtained for a variety of rotor configurations and operating conditions

Stationary biparametric ADI preconditioners for conjugate gradient methods

In the present article we determine optimal stationary biparametric ADI preconditioners for the conjugate gradient methods when applied for the solution of a model problem second order elliptic PDE. The PDE is approximated by 5- and 9-point stencils. As was proved in Hadjidimos and M. Lapidakis [Optimal alternating direction implicit preconditioners for conjugate gradient methods, (http://www.math.uoc.gr/similar to hadjidim/hadlap05.ps)] the problem of determining the best ADI preconditioner is equivalent to that of determining the optimal extrapolated (E) ADI method. So, analytic expressions are found for the optimal acceleration and extrapolation parameters for both discretizations where those for the 9-point stencil ones are new. Finally, numerical examples run using other well-known preconditioners show that the ADI ones we propose are very competitive. (C) 2006 Elsevier B.V. All rights reserved