NACA0012 — DNS Approach

Abstract

The objective of the present study is to analyse the main compressibility terms involved in the modelling of the turbulence kinetic energy equation for the upper transonic flow regime that is of priority interest for the aeronautical industry. It is well known that mostly the modelling of this equation comes from incompressible flow assumptions and for a long time it was admitted that compressibility effects become significant only beyond Mach numbers higher than 4 (Morkovin hypothesis). However, this stands only for steady flows. In case of unsteady boundary-layer-shock wave interaction and of appearance of recirculation regions near the wall, the van Driest law and Morkovin hypothesis for the turbulent fluctuations are no longer valid. For these reasons, it is also well known that the attempts to predict transonic flows in the upper transonic regime by simply ‘transposing’ the turbulence modelling hypotheses from the incompressible flow give very poor prediction of the shock position and of the drag coefficient. There are few developments for modelling of compressibility effects (Sarkar, (1992), (1995), Zeman, (1990)) among other. However, these developments had given poor improvements in the prediction of transonic flows around bodies. The aim of the present study is to address the terms to be modelled in the energy equation as well as to evaluate these terms in their exact form and according to the different suggested modelled assumptions in order to investigate the efficiency of the modelling assumptions. This can be done essentially by means of a DNS database, because the experimental measurement of compressibility effects is very difficult, although there remains the restriction for DNS concerning the low Reynolds number range of their realisation. IMFT has provided in the FLOMANIA programme a detailed DNS data base for the unsteady transonic flow around a NACA0012 wing at zero angle of incidence. Furthermore, the study of onset of the turbulent motion in its early stages has been carried out for the incompressible flow around a NACA0012 wing at 20°. In previous studies of the same research group (Bouhadji and Braza (2003a,b)) it had been shown that the increase of the Mach number in the upper transonic regime causes a natural amplification of a von Kàrmàn instability and of a strong shock-boundary layer and shock-vortex interaction near the trailing edge. Therefore, this test case is an ideal one for the investigation of compressibility terms under the effect of unsteadiness, for aerodynamic flows around bodies. Thanks to a fully parallelised version of the EMT2/IMFT code ICARE and to the use of a consequent grid size and small time step, it has been possible to perform DNS at Reynolds numbers 5,000 to 10,000 for the flow around the NACA0012 wing. The outcomes of this study are described in the following.