Derivated turbulence model to predict harmonic loads in transonic separated flows over a bump

Nowadays, frequency-domain time-linearized flow solvers are widely employed for aerospace engineering applications like turbomachinery or wing aeroelacticity. Due to substantial savings in the computational costs compared to the classical time-nonlinear methods, these methods are promising in the context of industrial design process in aeronautics. Nevertheless, the timelinearized solution is often relying on the assumption of frozen turbulence which can lead to significant discrepancies in the unsteady flow prediction, especially when the steady flow exhibits strong shock-wave boundary layer interactions. In the present paper, we propose to account for effects of the turbulence on the unsteady field by linearizing the k-? turbulence closure of Wilcox. To this end, an Automatic Derivation Tool is applied to the discretized Reynolds Average Navier-Stokes solver Turb'Flow™. The resulting time-linearized LRANS solver Turb'Lin™is used to computed the unsteady response of forced shock-wave motion in a transonic nozzle due to harmonic back pressure fluctuations. The accuracy of the present methodology is assessed by comparison with time-nonlinear and harmonic-balance solutions for both weak and strong shock-wave turbulent boundary layer interactions forced by an excitation frequency equal to 500 Hz.