> Once the cross sectional area through which a stream of air passes
> is increasing at a rate greater than 5 degrees, the flow becomes
> turbulent and the Bernoulli principle ceases to apply.

had 7 degrees written down here, hmm, gata find the source...
this also applys to increasing pressure in a "ram air" induction too :-)

Rob,

 

The generally accepted cone diffuser angle for the onset of separation is indeed 7 degrees for fully developed flow. The lowest energy loss is found at about 5 degrees for this condition. Angles exceeding 40 - 60 degrees are actually worse than a step change due to recirculation. Cone angles up to 10 degrees are still quite efficient but the losses increase rapidly as the angle increases.

 

However, in the inlet of your cowl the flow is not fully developed, as this represents the inlet of the "duct". In this region the optimum cone angle is closer to 4 degrees, but the losses are about 50% of what they would be for the fully developed condition. A cone angle of about 15 degrees will have roughly the same efficiency as would 10 degrees in the fully developed condition. Sources are: White, Fluid Mechanics and Panton, Incompressible Flow.

 

The transition to fully developed flow takes place over around 10 diameters, depending upon Reynolds number. The entrance condition data are probably correct for about 3 duct diameters.

 

This exposes a common error in entrance diffuser design. While it is certainly desirable to have a radiused transition to prevent "tripping" the flow, continuing an expanding radius beyond the optimum angle throughout the length of the diffuser is counter productive. If it is necessary to over expand the diffuser, it will be most efficient to generate the majority of the over expansion in the up stream half of the duct. Thus the cone angle should be greatest just inside the entrance and gradually decrease toward the engine in this case.

 

Rob