Turbulent interactions for rotating blades and wakes

Modelling and asymptotic analysis of the fully turbulent flow produced on a rotating blade system or cut-disk are described, the cut-disk being a thin disk with a significant amount of solidity removed. This is based on addressing the Reynolds-averaged Navier–Stokes equations in three-dimensional boundary-layer form together with an eddy-viscosity model, with the flow structure being analyzed for high Reynolds numbers. Interaction between blades and wakes plays a substantial part. The relationship between the present three-dimensional flow and the two-dimensional or axisymmetric flow over an isolated blade and a rotating disk is considered and leads to the finding that for the most part the flow on a cut-disk is, to leading order, the same as that on a rotating disk. A physical parameter, the disk solidity, plays an important role linking these two flows. The limiting case of low disk solidity yields the flow past an isolated blade locally, with global wake effects acting to provide the necessary azimuthal periodicity. This low-solidity limit also permits more analytical solutions which show agreement with numerical findings.