Analysis of momentum recovery within the near wake of a cross-flow turbine using Large Eddy Simulation

Momentum recovery within the near wake of a cross-flow turbine is studied, focusing on the different terms of the momentum balance equation. The flow is computed via Large-Eddy Simulation, coupled with an Immersed-Boundary method. Results demonstrate the dominant role of the spanwise flows (oriented along the axis of the turbine) in contributing to momentum recovery within the near wake, especially via advection in the vicinity of its spanwise boundaries and via turbulent transport at inner locations, closer to the mid span. Large streamwise-oriented vortices on the windward side promote momentum recovery into the wake core from its spanwise boundaries, moving the lower-momentum fluid downstream of the turbine from the leeward side towards the windward side, increasing this way the asymmetry of the wake system. Away from the turbine the importance of the spanwise flows declines, compared to that of the cross-stream ones (orthogonal to the axis of the turbine), due to a faster depletion of the spanwise gradients within the wake. As a consequence, the relative importance of the cross-stream flows on further momentum recovery becomes more significant. Meanwhile, as mean gradients decay away from the turbine, turbulent transport contributes more than advection to complete the process of momentum replenishment within the wake.