A Log-w Turbulence Model Formulation for Flutter Analysis with Harmonic Balance

Abstract

When considering flutter problems, unsteady effects in turbulence quantities are often not taken into account when using time-linearized methods. However, several studies have demonstrated that it can be necessary to resolve those effects in certain cases. The harmonic balance method is inherently able to capture the time dependent behaviour of the turbulence model. However, the method can suffer from instabilities due to problems in the turbulence model. As a possible solution, a logarithmic formulation of the w equation of the Wilcox k-w model is applied to the Harmonic Balance method in this paper. The combination is validated using a flutter computation of the NACA 3506 airfoil. One of the operating points exhibits significant oscillations in a shock induced separation. Resolving the unsteady behaviour of the boundary layer proved to be crucial to obtain a converged solution with the harmonic balance method. Both model variants were able to achieve satisfactory results. However, the log(w) model variant was able to provide advantages in accuracy and convergence.