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

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

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

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

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

Drag on a surface – 2 types

• Pressure stress/ distribution > form drag

• Shear stress > skin friction drag

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

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

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) !!

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

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

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 )

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)

• https://www.youtube.com/watch?v=sV_6E

1Lh7yo

• https://www.youtube.com/watch?v=CdE7I

T-EsZ0

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

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)

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

Note that vortex shedding is reflected in unsteady drag force on the structure

(Tacoma bridge collapse)

Lift next week...