Drag Assessment for Boundary Layer Control Schemes with Mass Injection

The present study considers uniform blowing in turbulent boundary layers as active flow control scheme for drag reduction on airfoils. The focus lies on the important question of how to quantify the drag reduction potential of this control scheme correctly. It is demonstrated that mass injection causes the body drag (the drag resulting from the stresses on the body) to differ from the wake survey drag (the momentum deficit in the wake of an airfoil), which is classically used in experiments as a surrogate for the former. This difference is related to the boundary layer control (BLC) penalty, an unavoidable drag portion which reflects the effort of a mass-injecting boundary layer control scheme. This is independent of how the control is implemented. With an integral momentum budget, we show that for the present control scheme, the wake survey drag contains the BLC penalty and is thus a measure for the inclusive drag of the airfoil, i.e. the one required to determine net drag reduction. The concept of the inclusive drag is extended also to boundary layers using the von Karman equation. This means that with mass injection the friction drag only is not sufficient to assess drag reduction also in canonical flows. Large Eddy Simulations and Reynolds-averaged Navier-Stokes simulations of the flow around airfoils are utilized to demonstrate the significance of this distinction for the scheme of uniform blowing. When the inclusive drag is properly accounted for, control scenarios previously considered to yield drag reduction actually show drag increase.