# Are there rocket nozzles that use non-elliptical shapes?

I was reading this question: Why the non-symmetric design of rocket nozzles?

Which got me thinking, have there been any nozzles that don't end in an ellipse? Even the one in that question ends in a conic section, which is an ellipse. Perhaps maybe a notched ellipse, or a square? I realize that these are impractical for various reasons, but I don't doubt somebody has done experiments with non-elliptical nozzles.

A couple short-comings I would assume with non-elliptical nozzles would be:

• Potentially difficult (impossible?) gimbal.
• Incorrectly vectored thrust.
• Less concentrated thrust (possibly?).

(Feel free to correct/add to any of the above assumptions, because they are indeed assumptions).

If the answer is no, can someone give a quick-and-dirty why about the elliptical shape of all nozzles compared to something like a square?

Yes, aerospike engines don't have to be elliptical, since their "nozzle boundary" is just a line of equal pressure.

Even the little nozzles at the top of the ramp appear to be rectangular.

As far as why normal nozzles are circular, it allows for a nice smooth expansion. Flow in ducts with corners has a lot of nonuniformities.

The author states in reference to the secondary velocities

Maximum velocities about 1 1/2 percent of the axial centerline velocity occur along the walls near the corner. Along the diagonal they reach 1 percent. Near the center of the duct the secondary velocities are very small.

Source

A bit of explanation

In a circular cross section tube the speed of material through the tube is lowest near the sides due to drag. The speed increases as you move away from the edges with highest speeds in the center. This results in a parabolic speed profile. Now in a square tube the regions near a corner are influenced by 2 sides so the speed will be even slower there. As you move away from the sides a speed profile much like a circular tube will develop. What you will end up with is that the majority of the material will be flowing in a circular region inside the square. The conclusion would be why pay for and carry around the corners, they do not flow nearly as much flow as the center region.

• Could you explain what the last picture actually represents? It looks really cool and I want to understand it. Also the link you gave is behind a paywall. Commented Oct 25, 2018 at 4:59
• @Ingolifs This paper appears to be the one that OrganicMarble linked to (or at rather a pre-print version of it). Commented Oct 25, 2018 at 6:46
• @Ingolifs rewrote to use a non-paywalled paper and add some explication. Commented Oct 25, 2018 at 14:31