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5 Skin Friction Drag and Streamlined Flows
Fluids have a property commonly known as
viscosity, which characterizes the relative ease
with which the fluid can be deformed (i.e,
viscosity is a measure of how well the fluid
molecules “stick” to one another). A high
viscosity fluid requires a larger shear force to
deform than a low viscosity fluid. There
is a relationship that describes the effects of
viscosity on that shear force:
Equation 2
Where tau is the shear force, m is the fluid
viscosity, and the ratio du-dy is the velocity
gradient (change in velocity relative to the
change in distance) perpendicular to the surface
of the solid body. Looking at Equation 2,
we can see that as the viscosity of the fluid
increases, the shear force, or skin friction
drag, increases. Similarly, when there is
a higher velocity gradient there is higher skin
friction.
5.1.1
Reynolds Number Dependence
There is a common term used in aerodynamics that
describes the relationship between the viscous
forces and the inertial forces for a given fluid
and solid object. Viscous forces have been
briefly described already. Inertial forces
can be thought of as those forces that are
related to the fluid’s velocity field. In
equation form, the Reynolds number is defined
as:
Equation 3
Where r is the fluid density and L is a length
scale (diameter of cylinder, cyclist chest
width, chord length of a 2-d airfoil, length of
a flat plate in the direction of the flow,
etc...).
Low Reynolds numbers (not necessarily less than
1, anything on the order of 1,000 is a low
Reynolds number) mean that viscous forces will
dominate the flow. For example, the flow over a
flat plate with a Reynolds number of 1 (r, m, L,
and u equal to 1) means that the viscous forces
of the fluid are large compared to the inertial
forces. The low Reynolds number means that
boundary layer has a smooth and gradual
transition from the surface to the free-stream.
The viscous fluid forces “suck” the molecules of
the fluid together resisting the inertial
shearing forces, and overall drag remains low.
There is negligible pressure drag due to the
absence of a wake, and therefore, the shear
force developed by the boundary layer is the
primary contributor to the overall drag on the
object. Low Reynolds number flows have
very small overall drag due to the small skin
friction drag and negligible pressure drag.
Inertial forces, however, dominate high Reynolds
number flows where large velocity gradients are
present. In high Reynolds number flows,
the viscous forces of the fluid molecules are
too small to successfully resist the shearing
action of the high velocity (and high inertia)
of the free-stream flow. Large changes in
velocity over very small distances are present
in these flows and, as a result, high skin
friction drag is created.
Using the same flat plate example as before but
with a Reynolds number of 300,000 (r, m, L = 1,
u = 300,000) it is easy to see that a much
larger change in velocity from the wall to the
free-stream takes place (zero to 300,000 as
opposed to 0 to 1). Recalling Equation 2,
it can be shown that the large velocity gradient
will result in large shearing forces. The
skin friction drag generated in high Reynolds
number flows is significantly greater than in
low Reynolds number flows. These types of
high Reynolds numbers are never generated during
normal bike riding conditions. Skin
friction concerns should, therefore, not drive
design feature choices in the bluff body
geometries encountered on bikes/riders.
5.1.2
Transition to Turbulence
When the boundary layer changes from a laminar
flow to a turbulent flow it is referred to as
transition (see Figure 3). Everyone who
has seen a candle, match, or cigarette burn in
still air has witnessed a transition to
turbulence. Near the flame, the smoke
streams upward in a steady smooth flow.
The stream of hot air remains organized in
laminar (tightly layered) sheets of smoothly
varying velocities. As the smoke travels
away from the flame, the Reynolds number of the
flow increases (because the “L” in Equation 3 is
increasing). At a certain distance away
from the flame, the smoke begins to swirl and
mix violently with the rest of air in the room.
This violent mixing of the smoke and the still
air surrounding it signals that a transition
from the smooth laminar flow near the flame to
the turbulent flow away from the flame has
occurred.
Figure 3. Transition to turbulence in a
plume of smoke.
For a large number of flows, transition takes
place at a Reynolds number of approximately
500,000. It should be realized though that
transition does not naturally occur at one
single Reynolds number, rather, it occurs over a
range of Reynolds numbers (Figure 4 below).
500,000 is a widely accepted value that ensures
transition has occurred for many flows (flat
plates, 2-d cylinder, sphere, etc..).
5.1.3
Laminar Flow
Laminar flow generally refers to the properties
of the boundary layer surrounding an object in a
moving fluid. In a laminar flow, there is
no mixing of the boundary layer flow and the
free-stream flow. The velocity gradients
within the layer are small. As a result,
skin friction drag in a laminar flow is minimal.
For streamlined bodies not susceptible to large
pressure drag, laminar flow is desirable (highly
tapered head tubes, downtubes, leading surfaces
of helmets). The overall drag of the
object will be less since the skin friction for
laminar flow is less than the skin friction for
a turbulent flow. There are several things
that can be done to help maintain a laminar flow
over a solid body for as long as possible.
5.1.3.1
Promoting Laminar Flow
The most important variable in promoting a
laminar flow over a streamlined body is the
surface roughness. The smoother the
surface of the object is, the longer the
boundary layer will remain laminar.
Surface roughness churns up the fluid within the
boundary layer and hastens the transition to
turbulence. For example, if a uniform flow
were blown over a smooth flat plate and also a
flat plate that had tiny grains of sand glued to
the surface, the smooth plate would maintain a
laminar boundary layer, and correspondingly less
drag, for a longer distance. This theory
is what has been driving helmet design and
skinsuit design up to this point (with a few
notable exceptions in the helmet arena).
Another tool at the disposal of engineers is
altering the geometry of the object.
Shaping the object in such a way that a
favorable pressure gradient (as the flow travels
along the surface the pressure is decreasing) is
set up on the surface for as long as possible is
desirable. A favorable pressure
gradient is usually formed up until the point of
maximum thickness on the object. After the
point of maximum thickness an unfavorable, or
adverse, pressure gradient is formed which tends
to induce turbulence. Laminar flow wings
have a peak thickness that is further downstream
than a typical commercial aircraft wing due to
its longer favorable pressure gradient and
laminar flow inducing characteristics.
The length of the object in the direction of the
flow (chord length for wings) also affects
laminar flow properties. A shorter length
means the flow cannot reach high Reynolds
numbers and transition cannot take place.
There is a practical limit that this technique
can be employed, but in general, the shorter the
streamwise length, the more laminar the flow.
Engineers of the long distance airplane
“Voyager” developed laminar flow wings, which
used smooth, short chord, favorable pressure
gradient wings to fly around the world on one
tank of gas. Gliders, since they have no
on board power, also use these techniques on
their wings.
5.1.4
Turbulent Flow
Turbulent flow is characterized by the unsteady
mixing of the free-stream flow and the boundary
layer. The injection of high momentum
fluid into the boundary layer increases the
velocity gradient near the surface, which
increases the skin friction drag. With
streamlined objects, this turbulent flow is
undesirable since the skin friction component of
drag is increased. However, with bluff
bodies, (where wakes and large separated regions
are present) turbulent flows can be
advantageous. It is this theory that Nike
is basing its “Swift-Spin Body Suit” on.
6 Pressure Drag and Bluff Body Flows
All prior discussions have focused primarily on
flows that are dominated by skin friction drag.
Flows that are dominated by the pressure, or
form, component of drag are sometimes referred
to as bluff bodies. The flow around a
cyclist’s torso, upper arms, and legs can be
described as bluff body type of flows. In
these types of flows, the skin friction drag is
negligible since there are large regions of the
flow on the leeward side (side of the body that
is downstream of the maximum point of thickness)
that are separated. These separated
regions on bluff bodies are also referred to as
wakes.
Figure 5. Separated flow about a cylinder
– leeward side is to the right, windward to the
left.
The leeward side of the body has a lower
pressure than the windward side of the body.
This pressure differential results in a force
that is directed against the direction of
travel, thus, the term “pressure drag”.
6.1
Velocity Profile in the Boundary Layer
The fundamental process that causes a wake to
form is an adverse pressure gradient. The
boundary layer on a flat plate will never leave
the surface and form a wake. A flat plate
has no pressure gradient to cause this to
happen. However, a bluff body, such as a
cyclist’s torso, has definite, and severe,
pressure gradients.
On the windward side of a bluff body (upstream
of the point of maximum thickness) a favorable
pressure gradient is in place. As a
particle in the flow passes along the windward
surface, the pressure is dropping, causing the
particle to accelerate. This favorable
gradient keeps the boundary layer energized and
the flow is “sucked” on to the body. Once
the point of maximum thickness is reached the
flow continues onto the leeward side of the
body. It is on the leeward side of the
object that an adverse pressure gradient is
present and separation of the flow becomes
possible
6.1.1
Separation and Wakes
Separation occurs when an adverse pressure
gradient slows the flow in the boundary layer
such that the stream-wise component of velocity
(velocity parallel to the surface) goes to zero,
as shown in Figure 6. The perpendicular
component of velocity “lifts” or “separates” the
flow off the surface and a wake is created.
Downstream of this separation point is a region
of flow reversal, in which there is a
re-circulation of the fluid in a direction
opposite of the free-stream and the low pressure
on the surface of the body does not recover.
With a bluff body, flow separation is difficult
to avoid and minimization of this phenomenon
through streamlining and/or boundary layer
control is highly advantageous.
Figure 6. Velocity profile in the boundary
layer and separation.
6.2 Reynolds Number
Since the Reynolds number is the ratio of
inertial forces to viscous forces, a flow in
which the viscous forces dominate (low to
moderate Reynolds number) will lead to lower
overall drag. Low Reynolds numbers flows,
however, are not very practical and for the most
part are not widely seen in commercial
applications. For the majority of flows
(with a few important exceptions), bluff body
and streamlined included, as the Reynolds number
increases the overall drag increases (see
Equation 1).
6.3 Laminar Flow
With laminar flow and streamlined bodies, the
Reynolds numbers are low and the viscous forces
are dominant. When the geometry of the
object changes to a bluff body, in which large
adverse pressure gradients are present, a
laminar flow is undesirable. The low
energy contained in the laminar boundary layer
is not able to resist these large pressure
gradients effectively, and as a result,
separation with a laminar boundary layer occurs
much sooner than with a turbulent boundary
layer. Laminar boundary layers should be
avoided when the geometry of the object is
considered to be a bluff body due to the large
wakes and correspondingly high-pressure drag
values that result.
6.4
Turbulent Flow
Turbulent flow is desired on bluff-bodied
objects. Even though there is a
corresponding increase in the skin friction
component of drag with a turbulent boundary
layer, the pressure drag can be significantly
decreased. The turbulent boundary layer
and its violent mixing with the high momentum
free-stream fluid is better able to resist
adverse pressure gradients. As a result,
separation is delayed and the size of the wake
on the leeward side of the body is reduced.
With a reduced wake, the high-pressure zone on
the leeward side is smaller and the overall drag
force is decreased. Several important
geometries in fluid dynamics clearly show the
effects of a turbulent boundary layer and its
effect on the reduction of overall drag.
The sphere and the 2-d cylinder are two classic
examples of how a turbulent boundary layer leads
to a smaller wake and less overall drag.
A natural transition to turbulence occurs once a
Reynolds number of ~500,000 has been achieved.
On streamlined surfaces or surfaces where
laminar flow is desired, the boundary layer is
allowed to develop naturally. With bluff
bodies, however, it is sometimes desirable to
induce a turbulent flow to hasten the benefits
of reduced pressure drag. This
portion of the field of fluid dynamics is
sometimes referred to as boundary layer control.
7 Boundary Layer Control –
Inducing Turbulence
Often times it is desirable to prematurely
induce turbulence in the boundary layer.
This procedure, called tripping the boundary
layer, involves placing artificial flow
turbulence creators on the surface of the body.
This technique is used in the small-scale wind
tunnel setting to ensure full-scale flow
behavior on lower Reynolds number models.
There are several methods of controlling the
boundary layer that are used, which include
vortex generators, trip strips, and surface
roughness.
7.1 Vortex Generators
Vortex generators work by creating a streamwise
vortex, which mixes the high momentum
free-stream flow into the low momentum boundary
layer. A large-scale streamwise vortex can
be seen on the wing tips of aircraft as seen in
Figure 7). The high-pressure undersurface
air wraps around the tip of the wing to meet the
low-pressure top surface air. When this
curling action is added to the streamwise
velocity of the aircraft (forward velocity), a
3-d helix of spinning air is created. This
swirling air is called a streamwise vortex.
Vortex generators operate on a much smaller
scale, but the streamwise vortexes they create,
inject high momentum free-stream air into the
boundary layer through their twirling action
(see Figure 8). These features are placed
on aircraft wings to improve lift, by delaying
separation, at the high angles of attack seen
during take-off and landing. The vortex
generators on wings are usually placed in a row
just forward of the maximum thickness and take
the shape of a small sheet metal tab placed at
an angle relative to the oncoming flow.
The drawback to this method is that it is
dependent on orientation. The layout of
the vortex generators must be carefully designed
and flow misalignments will decrease
performance.
7.2 Trip
Strips
A less elegant and much lower tech method for
inducing boundary layer turbulence is a trip
strip. A trip strip is a surface feature
that extends past the boundary layer into the
free stream and is usually place perpendicular
to the flow. As the free stream flow
passes over the strip (usually a wire, wall, or
series of 3-d columns of material) a localized
separated flow is created that mixes the high
momentum free-stream fluid into the boundary
layer. Descente had a skinsuit available
in the early to mid 90’s that incorporated some
of these types of features in the shoulder
region. This product was never really
accepted by the marketplace.
Trip strips are usually used in the wind tunnel
where orientation and placement are carefully
controlled. However, there are underwater
applications where this method was used with
success in the real world.
Recent
experiments with a series of longitudinal trip
strips on an underwater cable proved successful
in reducing the size of the wake (as measured by
accelerated submersion velocities). US
Patents have been issued that describe this
method (see patent number 3884173) as it
pertains to underwater cables.
Depending on the design, this method can also be
dependent on orientation of the trip strip.
If incorrectly designed, the boundary layer may
not be tripped or the overall drag may actually
be increased.
7.3 Surface Roughness
The final boundary layer method to be discussed
is the one that is the least dependent on
orientation and it is also the one that is
implemented by Nike engineers in their new
“Swift-Spin” skinsuit. It is also the
theory behind the large dimples in the current
Lazer helmets and the Troxel radius Ti helmets
of the past. A rough surface finish will
cause the transition to turbulence to occur at
lower Reynolds numbers. This method should
be completely independent of orientation
assuming the surface roughness is completely
random.
Careful attention must be taken when
determining the size of the surface roughness
features, however. Too large of a
roughness and the drag might actually increase,
but too small and no gains will be made.
Nike claims that over 50 types of fabric were
investigated during the development of their
suits. It is apparent that they were
trying to dial in the surface roughness for each
particular body feature (torso, upper arms,
legs, etc..).
7.4
2-d Cylinder Flow Redux
Remember the plot that started this whole thing?
The one that showed a large drop off in drag
just past the critical Reynolds number for a 2-d
cylinder? The one that Nike is banking its
R&D dollars on? Now that there has been
some detailed discussion about some fundamental
aerodynamics we can re-investigate this flow and
tie it all together. The flow region with
Reynolds numbers below the critical value is
termed sub-critical.
7.4.1
Sub-Critical Flow
Since the boundary layer in a sub-critical flow
is still laminar it cannot resist the adverse
pressure gradients introduced past the point of
maximum thickness. As a result, the
laminar boundary layer becomes separated from
the surface of the cylinder just aft of the
point of maximum thickness (approximately 90°
clockwise and counter-clockwise from the
stagnation point) and a large wake and a large
low-pressure zone on the leeward side of the
body results. This point on a cyclist is
analagous to where the “love handles” are
located on the lower torso, and just below the
armpits. Even though the boundary layer is
laminar and skin friction is low, the drag on
the cylinder is high due to the large wakes and
the subsequent dominant pressure drag.
7.4.2
Super-Critical Flow
The boundary layer in the super-critical 2-d
flow around a cylinder is turbulent. The
highly energized turbulent boundary layer is
better able to resist the adverse pressure
gradient on the leeward side of the cylinder.
Separation is delayed past the point of maximum
thickness, up to approximately 120° clockwise
and counter-clockwise from the stagnation point.
The resulting smaller wake decreases the size of
the low-pressure zone on the leeward side of the
cylinder and the overall drag is decreased.
Even though the boundary layer has transitioned
into turbulence and the skin friction has
increased, the drag is lower due to the
significantly reduced pressure drag. Nike
engineers have apparently induced a turbulent
boundary on the appropriate body parts of the
USPS riders through clever utilization of finely
tuned and selected surface roughness lycra.
They have therefore claimed to reduce the size
of their wakes and, therefore, their total drag.
8 Summary
Nike implemented boundary layer control features
on selective panels of their new “Swift-Spin
Body Suit” that induce a super-critical flow
around a cyclist’s body. Overall
drag has been claimed to be decreased by simply
putting on their new product.
With the release of the Nike product, Nike is
saying that for the bluff body flows around a
cyclist, where large wakes are present, it is
advantageous to induce turbulent boundary layers
(thus increasing skin friction drag) in order to
take advantage of the super-critical flow
reduction in pressure drag. It is for this
fundamental aerodynamic reason that golf balls
have dimples, and Lance and his US Postal mates
are being offered rougher than normal surface
textured skinsuits (“Swift-Spin
Body Suits”). Cycling history says
that Nike engineers have gotten it all wrong,
but Lance and his team may just prove them right
when they roll onto the streets of Paris - but
first, Nike has to convince Lance to slip one of
these bad boys on!!!
What did the inventors of the
Nike Suits had to say about this article?
Read it
here!
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