> Oh, yes, forgot. A definitive explanation of turbulence.
When I see hot rodders tossing around the term turbulence, I find they often
confuse it with pressure separation which a completely separate effect. Flow
separation and turbulence are NOT the same thing. They also seem to think
that turbulence is worse than laminar flow but that's not necessarily the case.
When laminar flow can be maintained, it does have less drag than the turbulent
flow. However, laminar flow can only (passively) be maintained by to slender
bodies, like airfoil sections, and then only sometimes. For low drag on a
shape that will not sustain laminar flow, you want to eliminate flow separation.
Inducing turbulence is a great way to do this.
The profile drag of an object can be split into two components:
Cd = Cdf + Cdp
where
Cd = profile drag coefficient
Cdp = pressure drag coefficient due to flow separation
Cdf = skin friction drag coefficient due to surface roughness
in the presence of laminar/turbulent flow
The drag which comprises the Cdf component is caused by the shear stress
induced when air molecules collide with the surface of a body. A smooth
surface will have a low Cdf. Also, the Cdf is lower for laminar flow and
higher for turbulent flow. Cdp, on the other hand, is caused by the
fore-and-aft pressure differential created by flow separation. Often
(usually?) Cdp is lower for turbulent flow and higher for laminar flow.
In many cases, inducing turbulence will dramatically decrease the pressure
drag component, decreasing the overall drag. Airplanes use this trick all
the time.
Back in the 19th century, when scientists were just beginning to study the
field of aerodynamics, an interesting observation was made with respect to
the drag of a cylinder. Since a cylinder is symmetric front-to-back (and
top-to-bottom), their early theories predicted it should have no drag (or
lift). If you plot the (theoretical) pressure distribution along the
surface of the cylinder (remembering that pressure acts perpendicular to a
surface) and decompose it into horizontal (drag) and vertical (lift)
components, you'll find that the pressure on the front face of the cylinder
(from -90 to +90 degrees) and the pressure on the rear face ( from +90 to
+270 degrees) are equal in magnitude but opposite in direction, exactly
canceling each other out. Therefore, there should be no drag (or lift).
However, if you actually measure the pressure distribution, you'll find
there are considerably lower pressures on the rear face, resulting in
considerable drag. This difference between predicted and observed drag
over a cylinder was particularly bothersome to early aerodynamicists who
termed the phenomenon d'Alembert's paradox. The problem was due to the
fact that the original analysis did not include the effects of skin
friction at the surface of the cylinder. When air flow comes in contact
with a surface, the flow adheres to the surface, altering its dynamics.
Conceptually, aerodynamicists split airflow up into two separate regions,
a region close to the surface where skin friction is important (termed the
boundary layer), and the area outside the boundary layer which is treated
as frictionless. The boundary layer can be further characterized as
either laminar or turbulent. Under laminar conditions, the flow moves
smoothly and follows the general contours of the body. Under turbulent
conditions, the flow becomes chaotic and random.
It turns out that a cylinder is a very high drag shape. At the speeds
a high performance street car travels, a cylinder has a drag Cd of
approximately 0.4. By comparison, an infinite flat plate sets the upper
limit with a Cd of 1.0. An efficient shape like an airfoil (that is aligned
with the airflow, i.e. is at 0 degrees angle of attack) may have a Cd of
0.005 to 0.01. Think about what this means. An airfoil that is 40 to 80
inches tall may have approximately the same drag as a 1 inch diameter cylinder.
Luckily, there are easy ways of reducing a cylinder's drag. Another thing
the early aerodynamicists noticed was that as you increased the speed of
the air flowing over a cylinder, eventually there was a drastic decrease in
drag. The reason lies in different effects laminar and turbulent boundary
layers have on flow separation. For reasons I won't get into here, laminar
boundary layers separate (detach from the body) much more easily than
turbulent ones. In the case of the cylinder, when the flow is laminar, the
boundary layer separates earlier, resulting in flow that is totally
separated from the rear face and a large wake. As the air flow speed is
increased, the transition from laminar to turbulent takes place on the front
face. The turbulent boundary layer stays attached longer so the separation
point moves rearward, resulting in a smaller wake and lower drag. In the
case of the cylinder, Cd can drop from 0.4 to less than 0.1.
You don't have to rely on high speeds to cause the boundary layer to "trip"
from laminar to turbulent. Small disturbances in the flow path can do the
same thing. A golf ball is a classic example. The dimples on a golf ball
are designed to promote turbulence and thus reduce drag on the ball in
flight. If a golf ball were smooth like a ping pong ball, it would have
much more drag. So instead of waxing your car, maybe you should let it get
hail damaged
If you look closely, you'll notice that some Indy and F1 helmets have a
boundary layer trip strip to reduce buffeting. It seems odd but promoting
turbulence can reduce buffeting by producing a smaller wake.
Another consequence of skin friction on a cylinder is that you can generate
substantial lift with a spinning cylinder. By spinning a cylinder you can
speed up the flow over the top and slow down flow under the bottom, resulting
in a lift producing pressure differential. I think this phenomenon is known
as the Magnus effect. BTW, the spinning tires on F1 and Indy cars are *huge*
sources of drag.
Technically speaking, separated flow is not turbulent, even though it is
random and chaotic (and very draggy). The laminar and turbulent concepts
apply only to the boundary layer, which is only a few inches thick. Beyond
the boundary layer, flow is treated as frictionless (inviscid). The boundary
layer is very important since it determines skin friction drag and the
tendency towards pressure separation (turbulent boundary layers are *less*
likely to detach). There is a drag increase associated with the transition
from laminar to turbulent flow but it is usually small compared to the drag
increase associated with separated flow.
This brings up another important aerodynamic term, the Reynolds number, which
is defined as:
Re_x = (Rho * V * X)/Mu
where:
Re_x = Reynolds number at location x (a dimensionless quantity)
Rho = freestream air density
V = freestream flow velocity
x = distance from the leading edge
Mu = freestream viscosity, a physical property of the gas (or liquid)
involved, varies with temperature, at standard conditions mu is
approximately 3.7373x10E-07 slug/(ft*sec) for air.
The location along the body at which the flow transitions from laminar to
turbulent determines the critical Reynolds number. Below this number, the
flow is laminar, above it is turbulent. Since the Reynolds number varies
linearly with the location along the body and with velocity, the faster you
go, the farther forward the transition point moves. At cruising speed on a
typical jet airliner, only a small region near the leading edge may be
laminar. Slow speed gliders with very slender (but still with rounded, blunt,
leading edges) may maintain laminar flow over most of the wing surface but
this is not the case for most practical aircraft. Note that glider wings
are typically designed with very short chord lengths (x distances) to help
promote laminar flow. Laminar flow is desirable when there is no pressure
separation.
Dan Jones