Deterministic unsteady and aeroelastic flow simulations with high-order FVM schemes

Abstract

During the last few years, unsteady and aeroelastic simulations have become a standard part of CFD computations in aeronautical applications. They are usually used with various types of turbulent models the most of which are derived from system of the Reynolds-Averaged Navier–Stokes equations (RANS). However, the RANS system itself is derived using time-averaging and hence it neglects certain type of unsteadiness in its own nature. Therefore it is necessary to investigate what is the ability of the contemporary numerical methods (i.e. combinations of numerical schemes and turbulence models) to simulate various types of unsteady flows. The authors carried out a series of numerical tests of two types of unsteady flows in external aerodynamics. Namely the transonic compressible flow over harmonically oscillating NACA 0012 aerofoil and subsonic compressible flow over the same aerofoil with oscillations induced by the flow itself (i.e. considering the aeroelastic interaction). Three different high-order finite volume schemes with various contemporary turbulence models were chosen for the testing. In the first researched case the computations were carried out using: the Modified Causon’s scheme “as reported by Furmanek and Kozel (Kybernetika 45(4):567–579, 2009)” (derived from TVD form of the classical MacCormack scheme) and the solver edge developed by the Swedish defence and research agency FOI (n-stage Runge–Kutta scheme, central differences with Jameson’s artificial dissipation, geometric multigrid, implicit residual smoothing). The tested models of turbulence were: the one-equation Spalart–Allmaras model, the two-equation Kok’s TNT model and the EARSM model. Unfortunately, none of these models produced results able to serve as a reliable numerical simulation of the first researched case. The main cause is probably the interaction between the turbulent boundary layer and shock-wave formed on the top side of the aerofoil. For the purpose of further investigation the Modified Causon’s scheme was adapted for modelling aeroelastic interaction between aerofoil and flow with one degree of freedom. Results of this simulation correspond better to the real flow, but it is necessary to carry out another tests to find out what is the exact cause of the observed problems.