Investigation of transition to turbulence at low Reynolds numbers using Implicit Large Eddy Simulations with a Discontinuous Galerkin method

Abstract

The present work predicts the formation of laminar separation bubbles at low Reynolds numbers and the related transition to turbulence. In addition to being one of the first Implicit Large Eddy Simulation studies using a high-order Discontinuous Galerkin method, unique attention is given to the boundary layer characteristics thus contributing to the understanding of low Reynolds number flows and the related separation-induced transition. Furthermore, a preliminary transition model suitable for such flows is introduced and its underlying concept proven valid. The flow around an SD7003 infinite wing at an angle of attack of 4 is first considered at Reynolds numbers of 10,000, 22,000, and 60,000. At the lowest Reynolds number studied, the ow remains laminar and two dimensional with a periodic vortex shedding. For higher Reynolds numbers, the flow is highly unsteady and exhibits a separation bubble on the upper surface over which ow transitions to turbulence. Tollmien-Schlichting waves are observed in the boundary layer upstream of separation, and their streamwise amplification factor shows they are responsible for transition. The major effects of cross-flow on low Reynolds number transition are studied by comparing the flows over the same infinite wing at different sweep angles. Projecting the results along a common two-dimensional equivalent direction, it is established that the cross-flow cannot be decoupled from the streamwise evolution at intermediate sweep angles due to strong non-linear interactions that take place after the laminar boundary layer separates. Hence, for separation-induced transition at low Reynolds numbers, it is not possible to treat streamwise and cross-flow instabilities independently for wings with sweep angles between about 10 and 40, and predicting the mixed transition cannot be reduced to treating the disturbances of each component separately. An important presumption to be adopted in the study of unsteady flows for MAVs and animal locomotion is thus that the type of transition (TS dominated, cross-flow dominated, or mixed) is a priori unknown as soon as the flow is slightly misaligned with the wing's chord.