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

Abstract

SUMMARYThe present work predicts the formation of laminar separation bubbles at low Reynolds numbers and the related transition to turbulence by means of Implicit Large Eddy Simulations with a high-order Discontinuous Galerkin method. The flow around an SD7003 infinite wing at an angle of attack of 4 • is considered at Reynolds numbers of 10 000, 22 000, and 60 000 in order to gain insight into the characteristics of the laminar and turbulent regimes. At the lowest Reynolds number studied, the flow remains laminar and two dimensional over the wing surface, with a periodic vortex shedding. For higher Reynolds numbers, the flow is unsteady over the upper wing surface and exhibits a separation bubble along which the flow transitions to turbulence. Tollmien-Schlichting (TS) waves are observed in the boundary layer, and transition is found to be caused by unstable TS modes as revealed by the growth of the stream-wise amplification factor.

Spatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit LES

“…As discussed in [35] , relation (16) leads to the solution of a characteristic polynomial which is quadratic in z and therefore admits (up to) two solutions. These are interpreted as two solution eigenmodes, one physical and another spurious.…”

“…However, especially in industry, the rare use of LES-based approaches have been commonly confined to low-order numerical methods, such as finite volume and finite difference approaches, that are more likely to yield inaccurate results because of the unfavorable diffusion and dispersion properties of the underlying numerics. Most recently, on the other hand, high-order spectral element methods (SEMs) [14] , that have been used for many years in academia within the context of under-resolved simulations of turbulent flows, have been drawing the attention of several researchers and industry practitioners [15][16][17][18][19][20][21] . High-order methods are in fact known to offer numerical benefits over traditional loworder schemes especially when small-scale flow features need to be captured and propagated correctly over long distances [2,22,23] , such as in high-Reynolds number open flows.…”

Low Reynolds Number Flows and Transition

“…The strongest factors affecting transition process are roughness of the wall or surface where the flow passes, adverse pressure gradient and freestream turbulence (Uranga, 2011). Transition is categorized as natural transition, bypass transition, separated flow transition, wake induced transition and reverse transition.…”

On the use of a high-order discontinuous Galerkin method for DNS and LES of wall-bounded turbulence

“…[21,22,23,24,25,26,27,28]). In the absence of an explicit subgrid-scale model, the philosophy behind ILES is to exploit the dissipation properties of the DG scheme to achieve a stable simulation.…”