day 24: flow around objects - university of...
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Day 24: Flow around objects
case 1) fluid flowing around a fixed
object (e.g. bridge pier)
case 2) object travelling within a fluid
(cars, ships planes)
two forces are exerted between the fluid and the object
related to:
Skin Friction ,
Drag, Lift
case 1) the flow around it is slowed down
while the object experiences a drag force
case 2) the object is slowed down
while the fluid around it is accelerated
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Equivalent “Boundary conditions”
• The object moves with velocity uo
far away from the object, the fluid velocity is 0
• The object is stationary
far away from the object, the fluid velocity is uo.
• Both fluid and object are moving; far away from
the object, the relative fluid velocity is uo.
Consider the relative “free stream velocity” = uo.
plane flying with or against the wind
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Lift / drag • When an object is submerged in a flowing fluid, or the
object moves in a stationary fluid the fluid is forced to flow around the object.
• As a result, the object is subjected to forces perpendicular and parallel to free stream velocity
• Drag:
– forces parallel to free stream velocity
• Lift:
– forces perpendicular to free stream velocity
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The resultant force exerted by the fluid on the object has two
components : parallel to the incoming velocity DRAG
perpendicular to the incoming velocity LIFT
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Drag on a surface alone can be
complicated, velocity dependent
• Consider drag on a
cylinder for different free
stream velocities:
• To model the forces, we
start by focusing on
simple systems
Increasing free
stream velocities
and Reynolds
number
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Drag on a surface – 2 types
• Pressure stress/ distribution > form drag
• Shear stress > skin friction drag
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Total drag
chordchord
D dAdApF sin cos
• force component parallel to the relative (free stream) velocity induced by the fluid on an object
= pressure drag + skin friction
Integral along the chord
length profile
For precise design , we need to consider pressure and skin friction at each point and sum these for total drag.
form drag friction drag
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Shortcuts for total drag
• For less precise design and/or well-known /
well-studied (simple) objects, we rely on
dimensional analysis and experimental
studies for an average coefficient of drag
• Here, A is a reference area, sometimes
“frontal area”
2AV
FC
2
DD
2AVCF 2
DD
from tables
if Re independent
NO
YES
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2D BODY
(sectional drag coeff.)
CD is Reynolds
independent
when flow separation
(thus form drag)
is dominant
L / D>20 : 2D assumptions
note that even if Cd goes down
Fd still increases (prop. to V2) !!
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Shortcuts for total drag
• For less precise design
and/or well-known / well-
studied (simple) objects, we
rely on charts for an average
coefficient of drag
• E.g., cylinders & spheres 2AV
FC
2
DD
2AVCF 2
DD
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flow separation controls the wake region characterized by low pressure
a change of regime (laminar > turbulent) in the boundary layer of the cylinder
retard the separation : the flow in the wake is more mixed, the pressure is not
as low, as the velocity increases
as the upwind – downwind pressure decreases, Cd decreases considerably
laminar >transition > turbulence
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can we control drag by controlling lam > turb transition ?
Yes with surface roughness !
At this RE the smaller Cd is obtained for a rough surface
as the surface roughness increases the
transition occurs earlier (lower Re )
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Other ways to reduce drag ?
• reduce form drag (streamlining)
• reduce frictional drag (materials)
• control laminar turbulence transition
• use roughness in a small range of Reynolds
numbers (e.g. for UAV)
• use surfactants , polymers to change the
apparent flow viscosity at the wall (water)
• use super-hydrophobic surface (water)
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• https://www.youtube.com/watch?v=sV_6E
1Lh7yo
• https://www.youtube.com/watch?v=CdE7I
T-EsZ0
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Drag on a sphere
(important to calculate the terminal velocity of droplets in air
or sediments in water)
d Vμ π3F 0D Stokes drag in the laminar regime for Re<1
2AVCF 2
DD but we also have
Both equations are satisfied when CD = 24/Re
normalized drag decreases with the Reynolds number
(providing the flow stays laminar, same story of the
pipe flow)
lam regine > turbulent
for larger spheres or faster flows, Re increases
as well as Cd (with respect to the laminar case)
)Re15.01(Re
24 687.0DC
for settling velocity, impose Buoyancy +FD = Weight and obtain VS
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vortex shedding vortex shedding is a drag related phenomena , induced by an instability in a
shear layer
a flow region with high velocity gradient
1)
2)
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shear layer
shear layer
shed vortices with predictable periodicity layer
St = n D/ V0 n is the shedding frequency = 1/ Time between vortices
http://www.youtube.com/watch?v=3mclp9QmCGs
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Note that vortex shedding is reflected in unsteady drag force on the structure
(Tacoma bridge collapse)
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Lift next week...