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What type of supersonic intake does the Dassault Rafale use? Is it a Pitot Intake? It cannot be a Ramp Intake, nor can it be a Spike Intake / Cone Intake, and it does not seem as a Diverterless Supersonic Inlet either.
Are there any explanations for the half-circular shape of the two intakes?

Sources for supersonic intake types: NASA Website, Aviation.SE Answers 1 and 2, Lockheed Martin CODE ONE Magazine

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It is a pitot intake, and the round shape makes the intake tube lighter. It is a pressure vessel, after all, because the intake converts flow speed into pressure and slows the flow of air to the engines down to approximately half of the speed of sound.

Placing the intake squarely at the side would make them less efficient (a classic example for this would be the Blackburn Buccaneer). The bulging fuselage above effects a pre-compression of the flow at supersonic speed, especially at higher angle of attack when thrust is needed most. To put them together under the fuselage (Eurofighter style) would cause interference in single-engine mode and would require a higher landing gear. The chosen shape is the best compromise for a lightweight and efficient intake for a two-engined aircraft.

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The semi-ventral pitot air intakes is a compromise between Ventral and Side Mounting where the intakes and their ducts are placed on the lower corner of the fuselage. In order to prevent interaction in case of single engine failure Rafale uses two semi-circular air intakes on the windward side, separated by the body.

Intakes are separated from the fuselage so as to avoid capturing the fuselage boundary layer (layer of air where air slows from high velocity relative to aircraft at its edge to standstill at the surface itself) as boundary layer, if enters engine, impairs pressure recovery and increases distortion, thus lowering intake performance; space between intake and fuselage is called external boundary layer bleed. This space is repartitioned, and expansion waves from it energize canard root vortex. Engine cooling duct is also located in this layer. In case the Rafale is equipped with stronger engine, intakes can be enlarged.

The architecture of the air intakes along with the nose and main undercarriages gives the capability for a large store to be carried under the fuselage, which is essential to achieve certain Air-to-Ground missions

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