Pharos University ME 253 Fluid Mechanics II

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Pharos UniversityME 253 Fluid Mechanics II

• Flow over bodiesLift and Drag

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External External Flows

• Bodies in motion, experience fluid forces and
  moments.
• Examples include aircraft, automobiles,
  buildings, ships, submarines, turbo machines.
• Fuel economy, speed, acceleration, stability, and
  control are related to the forces and moments.

Airplane in level steady flight drag thrust
lift weight.
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Flow over immersed bodies

• flow classification
• 2D, axisymmetric, 3D
• bodies
• streamlined and blunt

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Airplane

• Upper surface
• (upper side of wing)
• low pressure
• Lower surface (underside of wing) high pressure

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Lift and Drag

• shear stress and pressure integrated over body
  surface
• drag force component in the direction of
  upstream velocity
• lift force normal to upstream velocity

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AIRFOIL NOMENCLATURE

• Mean Chamber Line Points halfway between upper
• and
  lower surfaces
• Leading Edge Forward point of mean chamber line
• Trailing Edge Most reward point of mean chamber
  line
• Chord Line Straight line connecting the leading
  and trailing edges
• Chord, c Distance along the chord line from
  leading to trailing edge
• Chamber Maximum distance between mean chamber
  line
• and chord line

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AERODYNAMIC FORCE

• Relative Wind Direction of V8
• We used subscript 8 to indicate far upstream
  conditions
• Angle of Attack, a Angle between relative wind
  (V8) and chord line
• Total aerodynamic force, R, can be resolved into
  two force components
• Lift, L Component of aerodynamic force
  perpendicular to relative wind
• Drag, D Component of aerodynamic force parallel
  to relative wind

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Pressure Forces acting on the Airfoil
Low Pressure High velocity
High Pressure Low velocity
Low Pressure High velocity
High Pressure Low velocity
Bernoullis equation says where pressure is high,
velocity will be low and vice versa.
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Relationship between L and p
V?
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Relationship between L and p(Continued)
Divide left and right sides by
We get
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Pressure Coefficient Cp
From the previous slide,
The left side was previously defined as the
sectional lift coefficient Cl.
The pressure coefficient is defined as
Thus,
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• Fluid dynamic forces are due to pressure and
  viscous forces.
• Drag component parallel to flow direction.
• Lift component normal to flow direction.

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Drag and Lift

• Lift and drag forces can be found by integrating
  pressure and wall-shear stress.

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Drag and Lift

• Lift FL and drag FD forces fn ( ? , A,V )
• Dimensional analysis lift and drag coefficients.
• Area A can be frontal area (drag applications),
  plan form area (wing aerodynamics).

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Example Automobile Drag bile Drag
CD 1.0, A 2.5 m2, CDA 2.5m2
CD 0.28, A 1 m2, CDA 0.28m2

• Drag force FD1/2?V2(CDA) will be 10 times
  larger for Scion XB
• Source is large CD and large projected area
• Power consumption P FDV 1/2?V3(CDA) for both
  scales with V3!

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Drag and Lift

• If CL and CD fn of span location x.
• A local CL,x and CD,x are introduced.
• The total lift and drag is determined by
  integration over the span L

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Friction and Pressure Drag

• Fluid dynamic forces pressure and friction
  effects.
• FD FD,friction FD,pressure
• CD CD,friction CD,pressure

Friction drag
Pressure drag
Friction pressure drag
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Flow Around Objects
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Streamlining

• Streamlining reduces drag by reducing
  FD,pressure,
• Eliminate flow separation and minimize total drag
  FD

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Streamlining
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CD of Common Geometries

• For many shapes, total drag CD is constant for Re
  gt 104

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CD of Common Geometries
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CD of Common Geometries
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Flat Plate Drag

• Drag on flat plate is due to friction created by
  laminar,
• transitional, and turbulent boundary layers.

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Flat Plate Drag

• Local friction coefficient
• Laminar
• Turbulent
• Average friction coefficient
• Laminar
• Turbulent

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Cylinder and Sphere Drag
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Cylinder and Sphere Drag

• Flow is strong function of Re.
• Wake narrows for turbulent flow since turbulent
  boundary layer is more resistant to separation.
• ?sep, lam 80º
• ?sep,Tur 140º

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Lift

• Lift is the net force (due to pressure and
  viscous forces) perpendicular to flow direction.
• Lift coefficient
• Abc is the planform area

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Characteristics of Cl vs. a
Stall
Cl
Slope 2p if a is in radians.
a a0
Angle of zero lift
Angle of Attack, a in degrees or radians
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EXAMPLE AIRFOIL STALL
Lift
Angle of Attack, a
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Effect of Angle of Attack

• CL2?? for ? lt ?stall
• Lift increases linearly with ?
• ObjectiveMaximum CL/CD
• CL/CD increases until stall.

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Effect of Foil Shape

• Thickness and camber affects pressure
  distribution and
• location of flow separation.

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End Effects of Wing Tips

• Tip vortex created by flow from high-pressure
  side to low-pressure side of wing.
• Tip vortices from heavy aircraft far downstream
  and pose danger to light aircraft.

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Lift Generated by Spinning
Superposition of Uniform stream Doublet Vortex
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Drag Coefficient CD
Stokes Flow, Relt1
Supercritical flow turbulent B.L.
Relatively constant CD
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Drag

• Drag Coefficient

with
or
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DRAG FORCE

• Friction has two effects
• Skin friction due to shear stress at wall
• Pressure drag due to flow separation

Total drag due to viscous effects Called Profile
Drag
Drag due to skin friction
Drag due to separation


Less for laminar More for turbulent
More for laminar Less for turbulent
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COMPARISON OF DRAG FORCES
d
d
Same total drag as airfoil
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AOA 2
40
AOA 3
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AOA 6
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AOA 9
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AOA 12
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AOA 20
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AOA 60
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AOA 90
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Drag Coefficient of Blunt and Streamlined Bodies

• Drag dominated by viscous drag, the body is
  __________.
• Drag dominated by pressure drag, the body is
  _______.

streamlined
Flat plate
bluff
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Drag

• Pure Friction Drag Flat Plate Parallel to the
  Flow
• Pure Pressure Drag Flat Plate Perpendicular to
  the Flow
• Friction and Pressure Drag Flow over a Sphere
  and Cylinder
• Streamlining

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Drag

• Flow over a Flat Plate Parallel to the Flow
  Friction Drag

Boundary Layer can be 100 laminar, partly
laminar and partly turbulent, or essentially 100
turbulent hence several different drag
coefficients are available
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Drag

• Flow over a Flat Plate Perpendicular to the Flow
  Pressure Drag

Drag coefficients are usually obtained
empirically
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Flow past an object
Character of the steady, viscous flow past a
circular cylinder (a) low Reynolds number flow,
(b) moderate Reynolds number flow, (c) large
Reynolds number flow.
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Drag

• Flow over a Sphere and Cylinder Friction and
  Pressure Drag (Continued)

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Streamlining

• Used to Reduce Wake and hence Pressure Drag

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Lift

• Mostly applies to Airfoils

Note Based on planform area Ap
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Lift

• Induced Drag

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Experiments for Airfoil Lift Drag

• Examine the surface pressure distribution and
  wake velocity profile on airfoil 2-D
• Compute the lift and drag forces acting on the
  airfoil
• Pressure coefficient
• Lift coefficient

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• Test Facility
• Wind tunnel.
• Airfoil
• Temp. sensor
• Pitot tubes
• Pressure sensors
• Data acquisition

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Test Design

• Airfoil in a wind tunnel with
• free- stream velocity of 15 m/s.
• This airfoil has
• Forces normal to free stream Lift
• Forces parallel to free stream Drag
• Top of Airfoil
• - The velocity of the flow is greater
• than the free-stream.
• - The pressure is negative
• Underside of Airfoil
• - Velocity of the flow is less than the
• free-stream.
• - The pressure is positive
• This pressure distribution contribute
• to the lift Drag

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Pressure taps positions
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• The lift force, L on the Airfoil will be find
  by integration of the
• measured pressure distribution over the
  Airfoils surface.

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Data reduction

• Calculation of lift force
• The lift force L Integration of the measured
  pressure over the airfoils surface.
• Pressure coefficient Cp where, pi surface
  pressure measured, P pressure in the
  free-stream
• U8 free-stream velocity,
• ? air density
• pstagnation stagnation pressure
• by pitot tube,
• L Lift force, b airfoil span,
• c airfoil chord

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Drag Force

• The drag force, D on the Airfoil
  Integration of the momentum loss using the axial
  velocity profile in the wake of the Airfoil.

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Data reduction

• Calculation of drag force
• The drag force D integration of the momentum
  loss
• The velocity profile u(y) is measured ui at
  predefined locations
• U8 free-stream velocity,
• ? air density
• pstagnation Stagnation pressure
• by Pitot tube,
• D Drag force, b airfoil span,
• c airfoil chord

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Velocity and Drag Spheres
General relationship for submerged objects
Spheres only have one shape and orientation!
Where Cd is a function of Re
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Sphere Terminal Fall Velocity
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Sphere Terminal Fall Velocity (continued)
General equation for falling objects
Relationship valid for spheres
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Drag Coefficient on a Sphere
1000
100
Stokes Law
Drag Coefficient
10
1
0.1
0.1
1
10
102
103
104
105
106
107
Re500000
Reynolds Number
Turbulent Boundary Layer
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Drag Coefficient for a SphereTerminal Velocity
Equations
Valid for laminar and turbulent
Laminar flow R lt 1
Transitional flow 1 lt R lt 104
Fully turbulent flow R gt 104
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Example Calculation of Terminal Velocity
Determine the terminal settling velocity of a
cryptosporidium oocyst having a diameter of 4 mm
and a density of 1.04 g/cm3 in water at 15C.
Reynolds