Expert: Paul Soderman - 4/20/2011

Question
When an adverse pressure gradient results in flow separation and formation of a wake region, the pressure in the wake tends to be lower than the pressure upstream, thereby resulting in a drag. Can you please explain qualitatively why the pressure in the wake tends to be lower than the pressure upstream? I have not been able to find a convincing answer to this.

Thank you

Answer
Vishaal
You raise a good question.  When you speak of the pressure in the wake I assume you are speaking of the flow on or near the airfoil because far downstream the wake pressure becomes equal to the local atmospheric pressure.  Some energy is lost in the turbulence and viscosity of the the separated flow.  But more importantly, whenever we have flow separation we have an unsteady shedding of vorticity. On a cylinder or sphere, that shedding manifests in a vortex street. As each vortex leaves the airfoil it imparts a strong velocity on the rear side of the cylinder that reduces the local surface pressure and results in a drag increase.  That drag force oscillates in time as the upper and lower vortices shed. (See Schlichting:  Boundary-Layer Theory.)  A similar thing happens with airfoils. Although the steady lift is decreased by the reduction in low pressure in the separated region on the airfoil upper surface, the unsteady loading from shed vorticity causes the pressure drag to increase (see Katz and Plotkin:  Low-Speed Aerodynamics section 15.4.1 for flow visualization of separated flow on an airfoil.)  The unsteady drag forces alternates from the upper to lower surface. In fact, a strong vortex street can form in an airfoil wake as I discovered during wind tunnel studies of airfoil noise generation (Soderman and Allen:  Microphone Measurements In and Out of Airstream - Ch 1 in Aeroacoustic Measurements, T. Mueller (Ed.) Springer).  Airfoils can sing.

In a related phenomenon - the drag of airfoils with blunt trailing edges, S. Hoerner (Fluid-Dynamic Drag) shows the strong correlation with blunt trailing edge size and drag.  He attributes the drag to a jet-pump effect where the flow outside the wake near the trailing edge induces low pressures on the blunt trailing edge.  Drag can be very complicated and dependent on many things.
Paul