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Source: materialsengineeringconsultant.com and initious.blogspot.com.

Most of the engines are circular except for some that are oval. The oval shape provides a better ground clearance.

Why aren't the intakes square-shaped? Is there some aerodynamic reason for the circular / oval intake shape?

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    $\begingroup$ Why so many down-votes for this question? By the way the two current answers provide interesting details showing the question is a good one. $\endgroup$ – mins Jan 20 '16 at 11:13
  • $\begingroup$ Here are some more discussions: reddit.com/r/askscience/comments/228tuk/… $\endgroup$ – mike Mar 20 at 1:39
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The main purpose of having a square inlet is to have an oblique shock at the entrance so as to decelerate the air to subsonic speed before reaching the compressor. Also, the square inlet ramps are adjustable to produce optimum shock systems over a wide speed ranges. However, they are quite complicated.

The turbofans used in civil airliners operate at subsonic speeds and don't require any shocks for flow deceleration. The circular shape is the best for getting maximum amount of undisturbed airflow into the engine, especially the bypass section. The inlets of high bypass turbofan engines are simple, straight and short with a thick lip.

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Airliner jet intakes are round because the engines are round, and for subsonic flight that's all you need - it's easy and cheap to engineer, provides a clean airflow for the engine and unlike some other shape doesn't present unnecessary frontal area that will only cause drag. You've already identified ground clearance as the reason for a flattened shape on some installations.

Ah, you say, what about Concorde or the Tu144?

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Source: http://www.hitechweb.genezis.eu

Notice that I specified 'subsonic'. Once one reaches supersonic speeds the requirements change. The intake is crucial in controlling airflow into the engine, reducing it's speed to a subsonic level so that the engine can operate efficiently. It's far easier to engineer the required flaps and baffles around a rectangular intake than to do the same with a circular one.

These are the different intake configurations for Concorde at (A) Take-off, (B) Supersonic cruise and (C) Reverse Thrust

enter image description here

(By Nubifer (Own work) [CC0], via Wikimedia Commons)

This is just as true of air intakes on supersonic military aircraft. You'll notice that almost all supersonic military aircraft use some variation of rectangular intakes for this reason.

As with all things aeronautical, there are exceptions. The English Electric Lightning, Mig-21 and the SR-71 (and numerous others) use circular intakes with the geometry adjusted by a movable inlet cone.

You'll find a more detailed discussion of supersonic intakes in this answer

enter image description here enter image description here

"MiG-21 RB23". Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:MiG-21_RB23.JPG#/media/File:MiG-21_RB23.JPG

"Lockheed SR-71 Blackbird" by Judson Brohmer/USAF - NASA Website Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:Lockheed_SR-71_Blackbird.jpg#/media/File:Lockheed_SR-71_Blackbird.jpg

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