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Aerodynamics
Masters of Mechanical Engineering
Program
1. Introduction (1st week)
• Aerodynamical forces.
• Flow description. Dependent variables and physicalprinciples that govern the flow
Aerodynamics
Masters of Mechanical Engineering
Program
2. Incompressible, Viscous Flow (2nd to 4th week)
• Laminar thin-shear layers (overview).
• Transition from laminar to turbulent flow.
• Turbulent boundary-layers (overview).
• Three-dimensional boundary-layers.
Aerodynamics
Masters of Mechanical Engineering
Program
3. Incompressible, Ideal Flow (5th to 7th week)
• Euler equations. Bernoulli equation. Irrotacional flow.
• Vorticity and velocity circulation.
• Two-dimensional, incompressible, irrotationalflow. Complex potential and conformal mapping.
• Tri-dimensional potential flow.
Aerodynamics
Masters of Mechanical Engineering
Program
4. Lifting Surfaces (8th to 12th weeks)
• Geometrical definitions.
• Lift and drag coefficients.
• Airfoils.
• Finite wings.
Aerodynamics
Masters of Mechanical Engineering
Program
5. Bluff Bodies (13th week)
• Near and far wake.
• Vortex shedding.
• Strouhal number.
• Vibrations induced by the flow.
Aerodynamics
Masters of Mechanical Engineering
Program for Laboratory
a) Numerical Methods (2nd to 7th week)
• Numerical error.
• Code verification.
• Solution verification.
• Validation.
Aerodynamics
Masters of Mechanical Engineering
Program for Laboratory
b) Experimental Fluid Dynamics (10th to 13th week)
• Experimental uncertainty.
• Blockage effects.
• Experimental determination of aerodynamiccoefficients of an airfoil.
Aerodynamics
Masters of Mechanical Engineering
Bibliography
1. Aerodinâmica Incompressível:FundamentosVasco de Brederode Aerodinâmica Incompressível: ExercíciosIST Press
2. Fluid Flow, A First Course in Fluid Mechanics Sabersky R.H., Acosta A.J., Hauptmann E.G, Gates E.M. Prentice Hall, 4th Edition, 1999.
3. Momentum Transfer in Boundary Layers Cebeci T., Bradshaw P.Hemisphere Publishing Corporation, McGraw-Hill, 1977.
Aerodynamics
Masters of Mechanical Engineering
Bibliography
4. Boundary Layer TheorySchlichting H.
McGraw-Hill, 7th Edition, 1979.
5. Theory of Wing SectionsAbbott I.H., Doenhoff A.E. Von Dover Publications, 1959.
6. Aerodynamics of the Airplane Schlichting K., Truckenbrodt E., Ramm H.J.McGraw-Hill, 1979.
Aerodynamics
Masters of Mechanical Engineering
Bibliography
7. Fluid Mechanics: Problems and SolutionsSpurk J.H.
Springer Verlag, 1997.
Aerodynamics
Masters of Mechanical Engineering
Assessment
• Written exam, N1 (Minimum = 10/20)
• One practical task: Test of an airfoil or
Numerical Calculation (P1)
Practical assignments are to be performed by groups of 3 students.Oral presentation of 15 minutes during the several Lab shifts available
• 2 Questionnaires (Q1 and Q2) (weeks 5 and 9)
Weighted classification=0.5N1+0.2P1+0.15Q1+0.15Q2
Second season exam N2
Weighted classification=0.8N2+0.2P1
Aerodynamics
Masters of Mechanical Engineering
Introduction
Objective: Determine the forces acting on a body
immersed in a flow
Aerodynamics
Masters of Mechanical Engineering
Introduction
Weight
Lift
Drag
Propulsion
For an airplane flying at constant height and speedWeight = Lift
Propulsion = Drag
Aerodynamics
Masters of Mechanical Engineering
Introduction
Lift is the aerodynamic force component in thedirection perpendicular to the undisturbed incoming flow.
Drag is the aerodynamicforce component in the
direction parallel to theundisturbed incoming flow.
Aerodynamics
Masters of Mechanical Engineering
Introduction
Origin of the aerodynamic force:
1. Pressure on the surface of the body
Aerodynamics
Masters of Mechanical Engineering
Introduction
Origin of the aerodynamic force:
2. Shear-stress on the body surface
Transition
TurbulentShear-stress
at the wall
0=
∂
∂=
y
wy
Uµτ
Aerodynamics
Masters of Mechanical Engineering
IntroductionDetermination of the aerodynamic force:
a) Experimental
Aerodynamics
Masters of Mechanical Engineering
IntroductionDetermination of the aerodynamic force:
b) Theoretical (Numerical solution of a mathematical model)
Aerodynamics
Masters of Mechanical Engineering
Description of the flow field
Dependent variables:
• Pressure (1)
• Velocity (3)
• Density (1)
• Temperature (1)
Aerodynamics
Masters of Mechanical Engineering
Description of the flow field
• Fluid is treated as a continuum field
• Equation of state(1)
- Incompressible fluid ρ=constant
- Perfect gas p=ρRT
• Mass Conservation (1)
• Newton’s 2nd law (Momentum balance)(3)
• 1st Law of Thermodynamics (Energy balance)(1)
Aerodynamics
Masters of Mechanical Engineering
Description of the flow field
• Eulerian methodology
- Physical principles applied to a fixed volume in space
- Time derivative includes two contributions
1. Change in time for a fixed positionin space
2. Point to point variation in space for agiven instant in time
Aerodynamics
Masters of Mechanical Engineering
Basic Concepts
• Material Derivative
Generic property→= ),,,( tzyxqq
z
qw
y
qv
x
qu
t
q
Dt
Dq
t
z
z
q
t
y
y
q
t
x
x
q
t
q
Dt
Dq
∂
∂+
∂
∂+
∂
∂+
∂
∂=
∂
∂
∂
∂+
∂
∂
∂
∂+
∂
∂
∂
∂+
∂
∂=
Aerodynamics
Masters of Mechanical Engineering
Basic Concepts
• Gauss’s divergence theorem
Balance of a vector field for an infinitesimal volume
zyx
SV
ez
ey
ex
dSnQdVQ
rrrr
rrrr
∂
∂+
∂
∂+
∂
∂=∇
⋅=⋅∇
→⋅∇ Qrr
Qr
Aerodynamics
Masters of Mechanical Engineering
Basic Concepts
• Gauss’s divergence theorem
Balance of a vector field for an infinitesimal volume→⋅∇ Qrr
Qr
Outlet
Inlet
Outlet –Inlet
Aerodynamics
Masters of Mechanical Engineering
Basic Concepts
• Transformation of the time derivative in a volume that changes in time (V) to a fixed volume (Vo)
Generic property per unit mass
( ) ( ) ⋅+∂
∂=
oo SVVdSnvdV
tdV
Dt
D rrρξρξρξ
→ξ
Aerodynamics
Masters of Mechanical Engineering
Balance of a generic property
(“Conservation equation”)
• Volume changing in time
sources/sinks of property
=VV
dVfdVDt
Dξρξ
→ξf ξ
Aerodynamics
Masters of Mechanical Engineering
Balance of a generic property
(“Conservation equation”)
• Volume fixed in time
• Vo is arbitrary
( ) ( )
( ) ( )
( ) ( ) 0
0
=−⋅∇+∂
∂
=
−⋅∇+
∂
∂
=⋅+∂
∂
ξ
ξ
ξ
ρξρξ
ρξρξ
ρξρξ
fvt
dVfvt
dVfdSnvdVt
o
oo o
V
VV S
rr
rr
rr