Explanation for ball hovering in a vertical stream

[rcgldr]

Example video I made a few years go:



Note that most of the air interacting with the ball flows around the ball, as demonstrated near the end of the video where a tube is used to prevent flow around the ball, causing the ball to shoot upwards.

The main point of this post is the explanation for the self stability of the ball to remain centered in the stream, even when the stream is tilted significantly.

One explanation I often read states that the pressure in the higher speed middle of the stream is less than the pressure on the slower speed outer portions of the stream, so the ball tends to hover in the lower pressure zone. The issue with this idea is that the impact effects of the flow with the ball result in the change in momentum being greater at the center of the ball where a small portion of the flow stops in a stagnation zone, than the change in momentum of the air impacting the ball away from the center of the ball.

It's my belief that the ball's stability is due to Coanda / Magnus effect. Say the flow around the the outer surface of the ball tends to follow the surface of a the ball for a nearly fixed angle of deflection, detaching away from the ball somewhere along the upper surface of the ball. The flow at the sides of the stream diverges outwards, while the flow in the center of the stream remains vertical (until it collides with the ball). If the ball shifts to one side of the stream, then the flow on the oustide of the stream has a greater angle from vertical than the flow on the inside of the stream. Since the flow remains attached for the same angle of displacement, the flow on the outside stream detaches sooner with less horizontal deflection than the flow on the inside of the stream. The net result is that the wake of the flow is diverted outwards. There is a Newton third law pair of forces involved with the Coanda / Magnus effect, the off center ball exterting an outwards force on the air, diverting the wake of air outwards coexistant with the air exerting an inwards force on the ball. I believe this inwards force of the air on an off centered ball is why the ball returns back to the center of the stream and why the ball's position within the stream is stable.

 

[CWatters]

It's my belief that the ball's stability is due to Coanda / Magnus effect.

http://en.wikipedia.org/wiki/Coandă_effect

A spinning ping pong ball is held in a diagonal stream of air by the Coandă Effect. The ball "sticks" to the lower side of the air stream, which (in combination with the Magnus effect) stops the ball from falling down. The jet as a whole keeps the ball some distance from the jet exhaust, and gravity prevents it from being blown away.

 

[rcgldr]

A spinning ping pong ball

As seen in the video the ping pong ball doesn't need to spin to remain stable, even in a diagonal stream.

After reading the side article on the Wiki Coanda effect, showing the ping pong ball being stable in a diagonal stream, the explantion is Coanda effect (the point I've been making) in combination with Magnus effect also occurring when the ball ends up spinning in the "right" direction. My point is that the Coanda effect alone is sufficient for stability, and Magnus effect is a minor contributor, since I can reverse the angle of the diagonal stream, and in spite of the ball initially spinning the "wrong way", it remains stable.

What's missing from the side article is noting that the stream is expanding (larger cross sectional area) as it slows down (mass flow is somewhat constant, there is interaction due to viscosity with the surrounding air). The expanding stream means the outer portions of the stream are angled outwards relative to the stream, while the inner portions are angled less outwards. It's this difference in angle relative to the stream combined with Coanda effect that results in an offset ball producing an outwards wake and experiencing an inwards corrective force.