Aerodynamics

Masters of Mechanical Engineering

Aerodynamics

Professor: Luís Eça

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

Aerodynamics

Masters of Mechanical Engineering

Balance of a generic property

(“Conservation equation”)

Property ξ fξ

Mass 1 —

Momentum Forces

EnergyHeat

Work

vr

gzv

ue ++=2

2