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Mestrado Integrado em Engenharia Mecânica Aerodynamics

1st Semester 2012/13

Exam “1ª época”, 18 January 2013 Name : Time : 8:00 Number: Duration : 3 hours 1st

Part : No textbooks/notes allowed 2nd

Part : Textbooks allowed

1st Part

Indicate if the sentences are true (T) or false (F) in the empty squares. For each theme, any

combination of true and false is possible. The classification of each answer is the following:

Correct answer 0.25 marks.

Empty square 0 marks.

Incorrect answer -0.15 marks

1. The Reynolds-Averaged Navier-Stokes equations

require a turbulence model to match the number of unknowns with the number of

equations.

allow the determination of instantaneous velocity components.

cannot be applied to flows including separation.

are appropriate for the calculation of flows at low Reynolds numbers.

2. The aerodynamic centre of a lifting foil

is the location around which the pitching moment is maximum.

can only be determined for an ideal fluid.

requires a linear variation of the lift coefficient with the angle of attack to exist.

can never coincide with the pressure centre.

3. The figure below presents the neutral stability curves of laminar boundary

profiles.

Ri corresponds to the transition

Region D corresponds to the unstable region of velocity profile

Region C is typical of adverse pressure gradient flows

The variable plotted in the vertical axe

applied to the velocity profile

4. The figure below illustrates the lift and drag coefficients of an airfoil whitout high

devices and with four different flaps (plain

angle of attack α.

Lines E and 1 correspond to the airfoil without flaps.

Three of the high-lift devices have boundary

Lines D and 5 correspond to the split

The plain and split flaps have similar deflections

The figure below presents the neutral stability curves of laminar boundary

corresponds to the transition Reynolds number.

Region D corresponds to the unstable region of velocity profile A.

Region C is typical of adverse pressure gradient flows.

ble plotted in the vertical axe is related to the frequency of the perturbations

applied to the velocity profile.

The figure below illustrates the lift and drag coefficients of an airfoil whitout high

devices and with four different flaps (plain, split, slotted and Fowler) as a function of the

correspond to the airfoil without flaps.

lift devices have boundary-layer control.

to the split flap.

have similar deflections.

The figure below presents the neutral stability curves of laminar boundary-layer velocity

is related to the frequency of the perturbations

The figure below illustrates the lift and drag coefficients of an airfoil whitout high-lift

as a function of the

5. The figure below presents the pressure distribution (ideal fluid) on the upper and lower

surfaces of a Joukowski a

which the lift coefficient is larger or equal

The upper surface corresponds to the solid lines

The airfoil has positive camber, but it has no t

The pitching moment around the centre of the airfoil for the angle attack corresponding

to lines C is positive.

The area between the solid and dashed lines (upper and lower surfaces) plotted in the

figure is exactly equal to the lift coefficient for the three angles of attack.

6. The figure below presents the total shear

region of a turbulent boundary

ν is the kinematic viscosity

ν

ξ τ yu= .

2

τρuA = .

uvB ρ−= .

The plot corresponds to zero pressure gradient

The figure below presents the pressure distribution (ideal fluid) on the upper and lower

Joukowski airfoil at three angles of attack (including zero degrees)

which the lift coefficient is larger or equal than 0.

The upper surface corresponds to the solid lines.

The airfoil has positive camber, but it has no thickness.



equal to the lift coefficient for the three angles of attack.

The figure below presents the total shear-stress ( uvyutotal ρµτ −∂∂= )

region of a turbulent boundary-layer ( τu is the friction velocity, y is the distance to the wall

is the kinematic viscosity and ρ is the fluid density).

The plot corresponds to zero pressure gradient flow.

The figure below presents the pressure distribution (ideal fluid) on the upper and lower

irfoil at three angles of attack (including zero degrees) for



) in the near-wall

is the distance to the wall,

7. The figure below presents the drag coefficient

for two airfoils at three Reynolds number

Reynolds numbers with roughness applied to the airfoil surface

None of the airfoils exhibits a range of angles of attack that leads to pressure

distributions without suction peak.

The lowest Reynolds number of the smooth airfoils corresponds to lines

The increase of dC with the application of roughness on the surface is due only to the

friction resistance.

If the range of Reynolds numbers

for the two airfoils should not change significantly

8. The figure below presents the drag coefficient

circular cylinder as a function of the

Line A corresponds to the drag coefficient

For Reynolds numbers smaller than

For Reynolds numbers larger than those included in the plot,

again horizontal.

For 410Re = , the vortex shedding frequency of a 20cm cylinder imersed in a flow

with an undisturbed velocity of 10m/s is

The figure below presents the drag coefficient dC as a function of the lift coefficient

for two airfoils at three Reynolds numbers between 106 and 10

7 and for one of the

Reynolds numbers with roughness applied to the airfoil surface.

one of the airfoils exhibits a range of angles of attack that leads to pressure

ibutions without suction peak.

number of the smooth airfoils corresponds to lines A

with the application of roughness on the surface is due only to the

numbers increases to 108 to 10

9, the shape of the lines

for the two airfoils should not change significantly.

The figure below presents the drag coefficient DC and the Strouhal

circular cylinder as a function of the Reynolds number, Re.

s to the drag coefficient.

numbers smaller than 50, there is no vortex shedding.

numbers larger than those included in the plot, lines A and

, the vortex shedding frequency of a 20cm cylinder imersed in a flow

with an undisturbed velocity of 10m/s is 10≅f Hz.

as a function of the lift coefficient lC

and for one of the

one of the airfoils exhibits a range of angles of attack that leads to pressure

A.

with the application of roughness on the surface is due only to the

the shape of the lines obtained

Strouhal number S of a

and B become

, the vortex shedding frequency of a 20cm cylinder imersed in a flow

Mestrado Inte

Exam “1ª época”, 18 January 2013 Name :Time : 8:00 Number:

Duration : 3 hours 1st

Part : No textbooks/notes allowed2nd

Part : Textbooks allowed

1. The figure above presents the aerodynamic

zero angle of attack, assume that the friction resistance coefficient of the airfoil may be

estimated from a zero pressure gradient flat plate boundary

number (with identical boundary

transition from laminar to turbulent flow is instantaneous, i.e. critical

equal to transition Reynolds number

×= − /s,m1051.1 25

arν

Mestrado Integrado em Engenharia MecânicaAerodynamics

1st Semester 2012/13

época”, 18 January 2013 Name :8:00 Number:

o textbooks/notes allowed extbooks allowed

2nd Part

The figure above presents the aerodynamic coefficients of a NACA 63009


estimated from a zero pressure gradient flat plate boundary-layer at the same Reynolds

number (with identical boundary-layers on the two sides of the airfoil).

transition from laminar to turbulent flow is instantaneous, i.e. critical Reynolds

Reynolds number.

transitioncritical ReRe == ,kg/m2.1 3

arρ

grado em Engenharia Mecânica

época”, 18 January 2013 Name : 8:00 Number:

NACA 63009 airfoil. For


layer at the same Reynolds

ers on the two sides of the airfoil). Assume that

Reynolds number

For angle of attack equal to zero

a) In conditions of natural transition

boundary-layer.

b) Is it possible to estimate the

forced at the leading edge for both sides of the airfoil

answer.

c) For the flow with natura

supplemented by an eddy

The flow solver available includes the standard

model. Which model is the best choice to perform the calculation?

justification to your answer

d) Estimate the minimum relative roughness

friction drag coefficient

2. Consider the steady, bi-dimensional, potential and incompressible flow

cylinder. The radius of the cylinder is 1m and its centre is located at

coordinate system ζ=ξ+

04.00 2 ≤≤ a . The uniform incoming flow makes an angle

axe ξ and the magnitude of the velocity is

vortex with the required intensity to guarantee that there is a stagnation point at the

intersection of the cylinder with the

a) Write the complex potential that represents the flow as a function of the constant

the angle of attack α. Indicate clearly what is the coordinate system adopted.

angle of attack equal to zero and Reynolds number of 3×106:

In conditions of natural transition, estimate the minimum size of the region with laminar

Is it possible to estimate the pressure drag coefficient of the airfoil when transition is

forced at the leading edge for both sides of the airfoil? Justify quantita

natural transition, the Reynolds-Averaged Navier-

eddy-viscosity turbulence model are going to be solved numerically.

The flow solver available includes the standard k-ε model and the SST version of

model. Which model is the best choice to perform the calculation?

your answer.

Estimate the minimum relative roughness ( crε ) on the airfoil surface that makes the

independent of the Reynolds number.

dimensional, potential and incompressible flow

cylinder. The radius of the cylinder is 1m and its centre is located at

+iη. 2a is a positive constant smaller or equal than 0.

The uniform incoming flow makes an angle α, (|α|<π/4),

and the magnitude of the velocity is U∞. At the centre of the cylinder, there is a line


intersection of the cylinder with the positive real axe, ξ=b.

Write the complex potential that represents the flow as a function of the constant

Indicate clearly what is the coordinate system adopted.

region with laminar

coefficient of the airfoil when transition is

quantitatively your

Stokes equations

viscosity turbulence model are going to be solved numerically.

version of the k-ω

model. Which model is the best choice to perform the calculation? Give a clear

) on the airfoil surface that makes the

around a circular

cylinder. The radius of the cylinder is 1m and its centre is located at ( )2i,0 a of the

is a positive constant smaller or equal than 0.04,

/4), with the real

At the centre of the cylinder, there is a line


Write the complex potential that represents the flow as a function of the constant 2a and

Indicate clearly what is the coordinate system adopted.

b) Determine the range of angles of attack ( minα and maxα ) that guarantees the existence of a

stagnation point (( ) ( )

11

11,

== pCpCηξ ) with a real coordinate smaller or equal than -0.985 and an

absolute value of the imaginary coordinate of that same point below 0.2 (( )

985.01

1−≤

=pCξ

and ( ) 2.01

1 <=pCη ). Select the value of 2a that leads to the largest value of maxα .

Consider the Karmán-Treftz conformal mapping given by

( ) ( )( ) ( )

96.1andiwith =+=−−+

−++= kyxz

bb

bbkbz

kk

kk

ζζ

ζζ

that transforms the cylinder into an airfoil.

c) Determine the value of 2a that leads to the highest lift coefficient at zero degrees angle of

attack ( )( )0formax

=αlC and determine the equation that relates lC to α for that value

of 2a .

d) For the value of 2a of the previous question and zero lift angle, determine the maximum

and minimum values of the pressure coefficient in the transformed (airfoil) plane and

its location.

3. A finite wing of a glider has an aspect ratio of Λ=14, a mean chord of 1.5m, no twist and

its section is a NACA 63009 airfoil ( lC and dC given in the figure of problem 1). Assume

that the circulation along the span is elliptic and that the drag coefficient of the glider is

equal to the drag coefficient of the wing.

a) For the wing section, determine the pitching moment coefficient around the centre of the

airfoil and the location of the pressure centre.

b) If the glider is flying at constant speed in a region without wind, estimate the minimum

loss of altitude for each km flown.

c) In the conditions of question b), estimate at what angle of attack is the wing operating.

d) In the conditions of question b), determine the relation between the weight and the speed

of the glider.

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