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From this page:

Spillage drag, as the name implies, occurs when an inlet "spills" air around the outside instead of conducting the air to the compressor face. The amount of air that goes through the inlet is set by the engine and can change with altitude and throttle setting. The inlet is usually sized to pass the maximum airflow that the engine can ever demand and, for all other conditions, the inlet will spill the difference between the actual engine airflow and the maximum air demanded. As the air is spilled over the external cowl lip, the air is accelerated and the pressure decreases. This produces a lip suction effect, which partially cancels out the drag due to spilling.

I understand most of the above, except starting from "This produces a lip suction effect..."

If I'm getting this right, the unwanted air, stuck in the inlet, leaves the inlet moving forward, spills out, sucking the airframe with it, thus negating some of the drag caused by the spillage?

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Yes, your last sentence gets it about right. Just one detail: Air does not move "forward" to flow out again once it has entered the intake - which air goes where is all settled ahead of the intake. Never forget, though, that this effect is small and spillage leaves a net drag component.

When compared to a sharp-lipped intake as used on supersonic planes, subsonic intakes are more forgiving for a mismatch between capture area (area of the stream tube which goes into the engine) and the actual intake lip area. Below I tried to fake the flow around an intake lip using Inkscape and added blue and red shading to indicate pressure. The core flow gets compressed ahead of the intake (blue shade, diverging streamlines) while the outer flow is pushed to the outside of the intake lip by the increasing pressure and now has to follow the contour of the intake. Like with air flowing around the upper side of an airfoil, the air is accelerated (converging flow lines) and a suction peak forms on the intake lip (red shading). This suction peak sits on the forward-facing part of the intake lip and provides some suction.

The sharp intake lip of a surpersonic intake would produce separated flow under the same conditions with a considerable increase in drag.

Schematic intake flow pattern

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