AE 2251 AERODYNAMICS

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AE 2251AERODYNAMICS

• DR.V.RAMJEE
• DEAN
• AERONAUTICAL ENGINEERING DEPARTMENT

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UNIT 1

• CONSERVATION EQUATION
• MASS CONSERVED
• CONTINUITY EQUATION
• CARTESIAN COORDINATE
• POLAR COORDINATE

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UNIT 1

• CONSERVATION OF MOMENTUM
• ENERGY EQUATION
• BERNOULLIS EQUATION
• p1/2 R U2 P0

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UNIT 2

• SOURCE
• SINK
• VORTEX
• DOUBLET
• COMBINATION

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UNIT 2

• RANKINE HALF BODY
• RANKINE OVAL
• FLOW PAST A CIRCULAR CYLINDER
• PRESSURE COEEFICIENT
• COMPARISION WITH EXPERIMENT

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UNIT 2

• VORTEX SHEDDING
• REYNOLDS NUMBER
• STROUHAL NUMBER
• SHEDDING FREQUENCY
• APPLICATION

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APPLICATIONS

• CHIMNEY- a group-
• TALL BUILDINGS-
• BRIDGES-
• TOWER-
• CABLE transmission lines-
• ANTENNA-
• Golf ball- cricket ball- s

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RANKINE HALF BODY
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RANKINE OVAL
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Potential Flow
U(q) 2U? sinq
P(q) 1/2 r U(q)2 P? 1/2 r U?2
Cp P(q) - P ?/1/2 r U?2 1 - 4sin2q
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Reynolds Number Dependency
Rd lt 5
5-15 lt Rd lt 40
40 lt Rd lt 150
150 lt Rd lt 300
Transition to turbulence
300 lt Rd lt 3105
3105 lt Rd lt 3.5106
3.5106 lt Rd
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Typical structures interested on VIV
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Vortex shedding
Cross-flow oscillating force
V
Characteristic frequency
fS frequency (Hz) S Strouhal number 0.1850.2
(depending on Re) v flow velocity (m/s) d
cylinder dimeter (m)
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Wind flow on/around buildings
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ALONG ACROSS
Von Karman vortex street
gt 100 m tall Buildings (Holmes)
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View of the CT model inside the tunnel
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Strakes- chimney-
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AERODYNAMIC EXCITATIONS

• PRIMARY SOURCES
• Incoming turbulence, FT
• Vortex shedding, FW
• Motion-induced forces, FM
• F(t) Fturb(t) Fwake(t) FM
• Equation of motion
• MX CX KX FG

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Wind Effects on Bridges
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Length 850 m 2 side span each 335 m
width 12 m Bridge deck plate girder type
07.11.40 Bridge failed (4 months after
construction)Designed to with stand 45m/s
Failed at 19m/sFrequency of vibration changed
from 37 to 14 cycles/minOscillation half an
hour13.7 m sag183 m span broke
Computation of natural frequencies-Necessary
Before failure after failure
reconstructed
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Aerodynamic Coefficients
Aerodynamic Forces and Moments
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Blade Planform - Solidity

• Blade planform is the shape of the flatwise blade
  surface
• Solidity is the ratio of total rotor planform
  area to total swept area
• Low solidity (0.10) high speed, low torque
• High solidity (gt0.80) low speed, high torque

R
a
A
Solidity 3a/A
Slide Courtesy NREL USA
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Airfoil Nomenclaturewind turbines use the same
aerodynamic principals as aircraft
OR
Or
a
V
V
VR Relative Wind
a angle of attack angle between the chord
line and the direction of the relative wind, VR
. VR wind speed seen by the airfoil vector
sum of V (free stream wind) and OR (tip speed).
Slide Courtesy NREL USA
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FLOW VISUALISATION1.HELPS IN BETTER
UNDERSTANDING OF FLUID FLOW2.VORTEX FORMATIONS
AND THE PAIRING OF THE VORTICES CAN BE
OBSERVED
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Conclusion-

• Wind tunnel testing and flow visualization
• Studies reduce drag of buses- trucks- trains-
  trailer trucks- cars-
• Saving of fuel- more profit- by reducing
  aerodynamic drag- at high speed-
• Less pollution , if less fuel is consumed-
• Synergetic benefits- less global warming-

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Applications-

• 1. wind effects on chimneys- towers-
• 2. Buildings- tall medium-short-
• 3. Suspension bridges-
• 4. transmission lines-
• 5. antenna-
• 6. cables- offshore rigs-
• Galloping- flutter- buffeting-

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Rotating cylinder-

• 1.Wings with rotating cylinder- more lift-
• 2. Flettner rotor ship- 1924- with 2 rotors he
  sailed across Atlantic ocean-
• 3. Reduction of drag of trucks-
• 4 Magnus effect in balls- tennis- cricket-