Time-Linearization of the Spalart-Allmaras Turbulence Model

Abstract

This work expands on a reduced-order flow solver used to predict harmonically unsteady flows, which utilizes the time-linearization method. The time-linearization method requires a steady-state flow field from a full-order model flow solver. The time-linearized flow solver then uses the steady-state flow field to predict the unsteady, complex amplitudes of perturbation in the frequency domain. Together, the full-order model and time-linearized flow solvers predict unsteady flows with small harmonic perturbations at a reduced computational cost than an unsteady full-order model simulation. This work explores the limitations of the time-linearized flow solver through various verification and validation tests, with the end goal of implementing a time-linearized Spalart-Allmaras turbulence model to provide closure to the time-linearized Reynolds-Averaged Navier-Stokes equations. The time-linearized flow solver was also used to perform rotordynamic stability analysis of a straight annular gas seal based off the seal used in the High-Pressure Oxidizer Turbo-Pump of the Space Shuttle Main Engine. New features such as a complex grid deformation tool and a complex force integrator were developed for the time-linearized flow solver to simulate complex geometries. Turbulence modeling is required to provide closure for the Reynolds-Averaged Navier-Stokes equations. This research compares two turbulence models for the full-order model flow solver: The Shear Stress Transport turbulence model and the newly implemented Spalart-Allmaras turbulence model. These turbulence models underwent verification and validation tests against cases from NASA’s Turbulence Modeling Resource website along with a turbomachinery blade cascade.