2.9 Wake flow

A wake flow, for instance, is important in the analysis of the inflow to a propeller behind a ship. It is affected by both potential and viscous flow effects. In Chapter 6, we show that the wake generated by an upstream foil provides an important inflow condition to an aft foil of a hydrofoil vessel with a fully submerged foil system. Our analysis in this section is idealized and concentrates on viscous flow effects.

We consider a vertical strut with forward speed U and analyze 2D flow in a horizontal cross-sectional plane. The effect of the free surface is neglected, and the incident flow has zero angle of attack. The flow is described in a coordinate system following the strut (see Figure 2.32). There is then an incident flow with velocity U along the positive x-axis. A wake is generated behind the strut. Even if the flow is laminar in the boundary layer of the strut, the flow in the wake will be turbulent at a small distance behind the foil. The reason is that a laminar wake profile becomes unstable more easily than does a laminar boundary-layer profile (Schlichting 1979). Figure 2.32 illustrates the time-averaged longitudinal velocity profile u in the wake at some distance behind the foil. We express u as

(2.114)

where u ₁ is positive in the wake and zero outside the wake. The wake will be analyzed far away from the strut. This means u ₁