Time-harmonic Navier–Stokes computations of forced shock-wave oscillations in a transonic nozzle

• Alternatives to time-domain RANS solvers are investigated to compute unsteady flows.
• Time-linearized and time domain Fourier solvers are considered.
• These linear/non-linear methodologies are applied to transonic nozzle flows.
• Both back-pressure fluctuations and vibrating test objects are studied.

This study focuses on the development of frequency-based Reynolds-Averaged Navier–Stokes methods in the presence of harmonic excitations. Two different methodologies are proposed to alleviate the problem of high computational costs of conventional time-domain time-nonlinear approaches due to the capture of the long transients. A time-linearized approach is adopted using either the simple frozen-turbulence-scales assumption or the full linearization of the turbulence model. In order to account for nonlinear coupling between harmonics, a flexible time-domain Fourier-based solver is derived from a Reynolds-Averaged Navier–Stokes solver based on a local dual time stepping technique. Various flow regimes, involving forced shock-wave oscillations due to an elliptical cam placed at the nozzle exit and forced vibrations of test objects, are investigated to assess the robustness and the computational efficiency of the two frequency-based approaches in the presence of recirculating flows.