Development of an Improved Unsteady Low Mach Number Navier-Stokes Simulation Module for Rotorcraft Aerodynamics

Accurate and efficient modeling of rotorcraft flowfields is challenging due to a combination of unsteady flow dynamics and a large disparity in Mach numbers. Preconditioning techniques used to alleviate numerical stiffness from low Mach numbers in steady flows have not performed as well in unsteady environments since preconditioning parameters that are optimal for efficiency are detrimental to the level of spatial dissipation necessary for accuracy. A unified flux formulation is proposed here where the optimal scaling required for spatial accuracy is independent of the preconditioning required for time-accuracy thus providing a framework that is valid over a broad range of flow conditions. An additional objective of our effort is the formulation of a more comprehensive"unsteady"preconditioning methodology when multiple time scales are present that would account for both for the unsteady frequencies associated with local flow fluctuations, as well as system wide frequencies such as the blade passage frequency. In this effort, we will test and validate proposed unsteady flux formulations on unit problems with analytical solutions, while its application to rotorcraft flowfields and implementation in the Helios rotorcraft computational framework will be undertaken in the follow-on Phase II effort.