Why Does Air Break Up into Swirls Behind a Blunt Body in Fast Motion?

[Bashyboy]

At the moment, I am reading about fluids and the drag force. There is one particular paragraph that I would like help with, specifically the part in red:
"Here we examine only cases in which air is the fluid, the body is blunt (like
a baseball) rather than slender (like a javelin), and the relative motion is fast
enough so that the air becomes turbulent (breaks up into swirls) behind the body."

Why does the air break up into swirls behind the body?

 

[Bashyboy]

Also, in the next paragraph the author begins talking about an equation for the force of drag, D = 1/2C\rho Av^2. How was the equation found? The describe the variable A as "effective cross-sectional area," what does that mean?

 

[boneh3ad]

"Here we examine only cases in which air is the fluid, the body is blunt (like a baseball) rather than slender (like a javelin), and the relative motion is fast enough so that the air becomes turbulent (breaks up into swirls) behind the body."

Why does the air break up into swirls behind the body?

Well, because of viscosity, a fluid must have zero velocity near a surface (relative to that surface). This gives rise to what is called the boundary layer. In a simplified sense, as the air moves around the ball, the boundary layer doesn't have enough energy in it to make its way completely around the back end and ends up separating from the surface. When the boundary layer separates from the surface, it creates essentially a low pressure, recirculating bubble between it and the surface. There are essentially two vortices such as these that form for a circular cylinder (a similar but less complicated case compared to a ball). For low values of the Reynolds number (low velocities), which denotes the ratio of inertial forces to viscous forces, these vortices are stable and remain attacked to the back of the object. At a certain value of the Reynolds number, the system becomes unstable and the vortices begin shedding in an alternating pattern.

This is a fairly complicated problem and it sounds like you don't have any prior fluids experience so I will leave it at this simplified explanation for the time being.

Also, in the next paragraph the author begins talking about an equation for the force of drag, D=1/2CρAv2. How was the equation found? The describe the variable A as "effective cross-sectional area," what does that mean?

That equation is essentially empirical where you find a value for C_D through experiments. There are a handful of cases where it can be calculated approximately, but in general, you need to find that from experiments. The meaning of A depends on what sort of drag you are looking at. For pressure drag, it is the frontal area of the object. For viscous drag it would be the wetted area, etc, though that equation is of limited use for viscous drag.

 

[slowwisekelly]

all the equation on friction

 

[Bashyboy]

Well, because of viscosity, a fluid must have zero velocity near a surface (relative to that surface). This gives rise to what is called the boundary layer. In a simplified sense, as the air moves around the ball, the boundary layer doesn't have enough energy in it to make its way completely around the back end and ends up separating from the surface. When the boundary layer separates from the surface, it creates essentially a low pressure, recirculating bubble between it and the surface. There are essentially two vortices such as these that form for a circular cylinder (a similar but less complicated case compared to a ball). For low values of the Reynolds number (low velocities), which denotes the ratio of inertial forces to viscous forces, these vortices are stable and remain attacked to the back of the object. At a certain value of the Reynolds number, the system becomes unstable and the vortices begin shedding in an alternating pattern.

This is a fairly complicated problem and it sounds like you don't have any prior fluids experience so I will leave it at this simplified explanation for the time being.



That equation is essentially empirical where you find a value for C_D through experiments. There are a handful of cases where it can be calculated approximately, but in general, you need to find that from experiments. The meaning of A depends on what sort of drag you are looking at. For pressure drag, it is the frontal area of the object. For viscous drag it would be the wetted area, etc, though that equation is of limited use for viscous drag.

Thank you for that explanation, though most of it was a bit above my understanding. You are right in supposing that have not any experience with fluids, but I'll keep this webpage saved for the time being until I have learned about them.