explorer@rpi.edu (James C Krok) (06/25/91)
From: James C Krok <explorer@rpi.edu>
There's been some talk about drag on objects lately, and being
a grad student in aerospace engineering, boy, do I know my drag! But
seriously, I hope this hasn't already been posted, as I'm about 130
articles behind by now. I also hope that this doesn;'t fall outside
the charter (welcome back, Bill!).
This is hard to explain without pictures, but here goes. The type
of flow that occurs around objects is governed by a parameter called the
Reynold's number. It is the ratio of inertia forces to viscous forces
in a flow, and is defined:
(rho)*(V)*(D)
--------------
(mu) rho=fluid density
V=freestream velocity
D=diameter or length, depending
on situation
mu=fluid viscosity
At low Re, viscosity dominates and smooths out any perturbations in
the flow, giving laminar flow. While this type of flow provides for low
surface friction, the velocity profile it produces does not have
sufficient energy near the surface of the object to stay attached down
its back side. This creates the wake shown in the previous post.
This wake is a low pressure region, and hence gives high "form drag".
At high Re, inertia takes over, and small perturbations in the flow
can amplify, causing the flow to go turbulent. This creates much skin
drag, but the flow has much more energy near the surface. This allows the
flow to stay attached further down the back side of the golf ball. In this
case, the reduction in form drag greatly outweighs the increase in skin
drag. Thus, the dimples on the golf balls are there to assist in generation
of turbulence.
I can't remember what the transition Re is for a sphere, but for a
flat surface, it is about 500,000. This is measured down the length of
the surface (the parameter D, that is), and the actual transition number
varies due to freestream effects.
In the case of other objects, such as rockets, you don't want
turbulent flow until the very end of the body, so you can minimize skin
friction. At the end of the rocket, you want a turbulent flow so it
can stay better attached to the base of the rocket. Generally, this
doesn't have to be artificially induced; the transition to turbulent
flow will occur somewhere on the body on its own. Giving the flow a
better surface to stay attached to doesn't hurt, either; i.e. the idea of
the cone at the end of the rocket coming into place after the engine
expires. Bullets are "boattailed" for this very reason. A boattail is
a truncated cone on the tail of the projectile, making it look like a
boat. Unfortunately, adding a boattail increases the aerodynamic
instability of the projectile.
The laminar-flow aerfoil on the P-51 Mustang is a good example of
laminar-turbulent transition. The widest part of that airfoil occurs
as far back as possible, encouraging the flow to remain laminar. The
airfoil then contracts in thickness where the flow is turbulent, helping the
flow penetrate the adverse pressure gradient on the rear part of the
wing.
I tried to keep this brief (unsuccessfully), and managed to leave out
a lot of stuff in the process (whats an adverse pressure gradient?).
Please feel free to e-mail me, or better yet, find a book on fluid
mechanics or aerodynamics. The practical stuff that I have mentioned
here is pretty easy to understand, and the problem of flow around a
sphere in particular is a classic one. Or, if you're in the Troy area,
feel free to stop by and see me in person!
-J. Chris Krok Rensselaer Polytechnic Institute
Explosion Dynamics Laboratory Troy, NY
Troy Building