Small disturbance Navier-Stokes method: Efficient tool for predicting unsteady air loads

Regarding industrial aeroelastic applications, the otherwise common yet computationally expensive procedure of time-accurately solving the unsteady Reynolds-averaged Navier-Stokes (RANS) equations is presently not feasible. However, a numerical method based on the small disturbance formulation of these governing equations can provide an efficient means for predicting aerodynamic loading. With this alternative approach the initial unsteady problem is reduced to a formally steady one for the perturbation part under specification of a time law, thus allowing a solution in the frequency domain. A detailed derivation of the small disturbance Navier-Stokes equations on the theoretical basis of the triple decomposition is presented for high-Reynolds-number flow restricted to harmonic behavior. Validation of the resultant numerical method FLM-SD.NS is performed with a transonic test case for each the NACA 64A010 and NLR 7301 airfoil, respectively, undergoing sinusoidal pitch oscillations. Computational results are in good agreement with experimental data, as well as time-accurate RANS solutions provided by the comparative solvers FLM-NS and FLOWer. Reductions in computational time up to an order of magnitude in relation to FLM-NS are observed.