Difficulty Understanding 'Drag Crisis' (transitionary period from laminar to turbulent flow)

[lebronJames24]

Homework Statement

similar to my previous post, this isnt a specific question, but more so a topic that I have to cover in a slideshow

Relevant Equations

no necessary equation, but the drag equation is relevant so 1/2 p v^2 Cd A

Ok so far, from my understanding, during the transitionary period from laminar to turbulent flow, an object is in drag crisis. For my application, I am attempting to understand this phenomena for a knuckleball in soccer. I am trying to understand what properties of fluids are responsible for this phenomena.

On a more general question, I do not understand how the quick steep drop in the force of drag on a graph is significant to this phenomena.

Lastly, I have attached a graph of a drag force vs relative reynolds number graph. Am i correct in saying that if all the variables for the reynolds number are held constant aside from velocity, then the circled parts of the graph represent the velocity at which a ball would knuckle? (assuming that the graph is one of a soccer ball)

Last, last thing - how does the surface of a ball affect the drag crisis? I have attached a second graph of two different golf balls with different surfaces having different lines. Why is this?

 

[Arjan82]

You conglomerate several concepts that shouldn't be conglomerated. Let's untangle a few concepts first:

• Laminar/Turbulent flow in this application refers to the state of the boundary layer around an object. The boundary layer is a thin layer adjacent to the surface from which the flow velocity decreases rapidly to zero at the wall. For the laminar flow case the flow in this layer is 'layered' (laminate like, hence the name). The communication between these layers is dominated by viscosity. The flow velocity is smooth and virtually (but not exactly) zero in wall normal direction. Turbulent flow on the other hand behaves much more erratic. The flow in the boundary layer now moves in 'eddies', or somewhat swirly but at an average still parallel to the surface (of course). However the instantaneous velocity in wall normal direction can now be substantial (some small percentage of the main flow velocity). This means that there occurs much more 'mixing' between the 'velocity layers' (now in average sense) of the boundary layer. Besides the Reynolds number the surface condition (smooth, rough, with seems, etc.) has a large influence on when the boundary layer becomes turbulent.
• The drag crisis is a name for a part in the drag vs Reynoldsnumber curve where the drag decreases sharply with increasing Reynolds number, i.e. the part you've put a yellow circle around. This effect most notably occurs for spheres and cylinders. The reason is that before the drag crisis the boundary layer separates (i.e. stops moving along the surface of the object) before it transitions to turbulent flow, after the drag crisis the boundary layer first 'trips' (i.e. becomes turbulent) and then separates. Since a turbulent boundary layer separates much later than a laminar one because a turbulent boundary layer is much more able to mix momentum in wall-normal direction compared to laminar flow, the turbulent flow follows the surface of the ball or cylinder for longer. This significantly reduces the size of the wake behind the ball/cylinder which reduces the drag significantly. Note that it is not true that *every* object is in 'drag crisis' when the boundary layer trips to turbulent flow. It is not true for air foils, flat plates or blunt bodies with sharp edges. It can only occur on objects where the point of flow separation is influenced significantly by the transition to turbulence. See picture: left before drag crisis, right is after drag crisis.
  
• A knuckleball is a ball (mostly baseball, but also soccer and maybe other sports) where the ball moves through the air with minimal rotation. If the ball has some surface artifacts, like a seem, the flow around the left side of the ball might transition to turbulence (due to the seem) but around the right side it does not. This introduces a force imbalance in the direction normal to its direction. But when the ball rotates slightly this may be reversed, which causes the ball to wobble. This makes it very difficult to deal with such balls.

So this also answers the question of why the drag curves are different for a smooth and a rough ball. The boundary layer around a rough ball transitions to turbulence earlier, and therefore the drag crisis occurs at a lower Reynolds number. Also, a rough ball has more surface friction once the boundary layer is turbulent, so after the drag crisis the rough ball has a higher drag coefficient.