Modelling and control of separation bubbles in transitional turbomachinery flows

In turbomachinery flows, the boundary-layer can remain laminar up to 70% of the chord length, due to a relatively low local Reynolds number on the blade. The high free-stream turbulence intensity penetrates into the laminar boundary-layer by the combined action of turbulence diffusion and pressure fluctuations, and triggers the transition process to a turbulent state. This transition process is said to be of bypass type, in contrast to the natural transition occuring at low free-stream turbulence intensity, in which case transition is preceded by the linear growth of Tollmien-Schlichting waves, well described by the linear stability theory. In an industrial context, statistical Reynolds-Averaged Navier-Stokes models are commonly used to describe the effects of turbulence, because of their low computational cost compared to other approaches such Direct Numerical Simulation, Large Eddy Simulation or hybrid methods. Low-Reynolds-number turbulence models are able to mimic the transition process via the diffusion of turbulence into the boundary layer, but the position and rate of growth of the transition is often poorly predicted. Consequently, the modelling of the transition process must be explicitly aided by using empirical correlations to describe the transition point and an intermittency factor γ, which defines the laminar (γ = 0) and turbulent (γ = 1) regions. In the present work, EVM (Eddy-Viscosity Models) are being used. The classical approach consists of multiplying the eddy-viscosity by the intermittency factor to define the effective eddy-viscosity in the transitional flow. An approach, proposed by Mayle & Schulz [2], is to use a transport equation for the laminar fluctuating kinetic energy to model the growth of non-turbulent fluctuating energy before the transition onset. This is a modelling element that is being developed further and integrated into a turbulence-modelling framework based on a non-linear eddy-viscosity formulation. The above approach is oriented towards modelling transition in attached flow. However, in highly-loaded conditions on blades, the adverse pressure gradient acting on the boundary-layer can result in the laminar or transitional boundary layer separating and possibly reattaching on the blade, in which case a recirculation zone forms above the blade surface. Such separated regions are the source of high losses and should be avoided. As regards transition, the new feature introduced by