Introduction to Aerospace Engineering

Home , Boundary layer, Jaap Eden

Lecture slides

Challenge the future 1 Introduction to Aerospace Engineering Aerodynamics 7&8

Prof. H. Bijl ir. N. Timmer 7 & 8. Laminar and turbulent flows Anderson 4.15 - end of chapter 4.

Osborne Reynolds Ludwig Prandtl

1842-1912 1874-1953 Subjects lecture 7 & 8

• Viscous flows • Laminar boundary layers • Turbulent boundary layers • Transition • Separation

3 Viscous flow

Up till now we have only dealt with frictionless flow. What is the effect of friction ? ….

Inviscid flow (No friction) Viscous flow (friction) NO DRAG FINITE DRAG

4 Viscous flow

In real life the flow at the surface adheres to the surface because of friction between the gas and the solid material:

Right at the surface the velocity is zero

5 Boundary layer

Friction force Boundary layer (exaggerated) V

In the vicinity of the surface there is a thin region of retarded flow: the boundary layer The pressure through the boundary layer in a direction perpendicular to the surface is constant

6 Viscous flow

Inside the boundary layer Bernoulli’s law is not valid!!!!!!

7 Viscous flows Shear stress can be Boundary layer written as : velocity profile τ = μ dU w   boundary layer  dy y=0 thickness, δ shear stress, τw (schuifspanning)  skin friction drag

μ = absolute viscosity coefficient or viscosity Air at standard sea level : μ=1.789*10-5 kg/ms)

8 Viscous flows, some definitions δ V∞ x

==ρ∞∞ V x V ∞ x Reynolds number : Re x μ∞∞ν dimensionless, and varies linearly with x

Laminar flow : streamlines are smooth and regular and a fluid element moves smoothly along a streamline Turbulent flow : streamlines break up and a fluid element moves in a random irregular way

9 Laminar boundary layer, boundary layer thickness

Consider flat plate flow. What is boundary layer thickness δ

and skin friction drag Df at location x?

V∞ δ

δ = 5.2 x From laminar boundary layer theory : Rex

Thus δ is proportional to : √x (parabolically)

10 Laminar boundary layer, skin friction drag

τw x dx L 1 (unit width) width)

Total force = total pressure force + total friction force

Total friction force on element dx is: τw(x)⋅dx⋅1 = τw(x) dx

L τ Total skin friction drag is: D f =  w dx o

11 Laminar boundary layer, skin friction drag For the skin friction coefficient we find from laminar boundary layer theory : τ w τ w 0.664 c f = ρ = = x 1 2 q∞ Rex ∞V ∞ 2

C τ x Thus fx and w decrease as increases The skin friction at the beginning of the plate is larger than near the trailing edge.

To calculate the total aerodynamic force we must integrate!

12 Laminar boundary layer, skin friction drag L L L dx 0.664 q∞ dx D f = c f . q∞ dx = 0.664q∞ =   x  V ∞ /ν x o o Rex o

dx  =  x -1/2 = 2 x x 0.664 q∞ 1.328q∞ L Df = 2 L = V∞ / ν∞ V∞ L/ ν∞ Df Define total skin friction drag coefficient as Cf = q∞S 1.328 L 1.328.L 1.328 = = C = Cf ⋅ f ReL S ReL L 1 ReL

13 Results for a turbulent boundary layer

δ turbulent δ laminar

Due to the action of turbulence : no exact solution for turbulent boundary layers ! From experiments : 0.37x δ = Note : C varies as L-1/5 for turbulent flow 0.2 f Rex while it changes as L-1/2 for laminar flow. 0.074 C = Thus the friction in a turbulent boundary layer f 0.2 ReL is larger than in a laminar flow

14 Transition

Osborne Reynolds (1842-1912)

Pipe flow experiment

15 Transition

Re > 2300 : transition from laminar to turbulent flow

Osborne Reynolds (1842-1912)

Development of turbulent flow in pipes observed and sketched by Reynolds (from his original paper)

16 Transition

Cf transition turbulent

laminar

17 Transition

Flat plate flow

18 Transition

Flow visualization experiment

19 Transition

Tollmien- Three-dimensional Fully Schlichting vortex turbulent waves breakdown flow

Stable U∞ laminar flow

Growth of Generation of Span wise vorticity turbulent spots

20 Ludwig Prandtl (1875-1953)

•Boundary Layer theory (1904) •Wing theory (1918 - 1919) •Contributions to the theory of supersonic flow & turbulence •Development of wind tunnels and other aerodynamic equipment •Theory of plasticity and of meteorology.

21 • Prandtl and his water tunnel (TU Hannover 1904)

22 • FLOW OVER A PLATE WITH A SEMI-CIRCULAR LEADING EDGE

Zhiyin Yang and Peter Voke

Fluids Research Center, University of Surrey, U.K. The image represents the results of a hybrid DNS/LES (by Zhiyin Yang and Peter

Voke) computation of separation, transition and reattachment of the flow over a plate with a semicircular leading edge

23 Transition

Skin friction y ∂ (mm) τ = μ u ∂y laminar

turbulent

u/V transition V

Flat plate flow

24 Transition transition

V turbulent laminar

xcr

The critical Reynolds number at which transition occurs is difficult to find. It should be found from experimental data applicable for the given problem

25 Laminar-Turbulent Transition on airfoils

Transition “point”

Laminar Turbulent B.L. B/L V

Laminar boundary layer: thin, low skin friction drag Turbulent boundary layer: thick, high skin friction drag

26 transition

turbulent laminar

Airfoil model vertically spanning the wind tunnel

27 Laminar flow favourable

τ < τ We have seen that : wla minar wturbulent

Vast majority of flows is TURBULENT ! => We may adapt the geometry of the airfoil such that it favors laminar flow. We then have Laminar flow airfoils.

Favorable pressure gradient

laminar flow airfoil

Favorable pressure gradient

28 Flow Separation

Why is it important? When does it occur ?

CFD example

29 Alternating separating vortices on a cilinder (Karman street)

30 Unsteady behavior of construction due to separation

31 Flow separation

separation point

Separation due to a positive pressure gradient

32 Separation

From: Van Dyke: “An Album of fluid motion”

aluminum powder in water

33 Flow Separation

Effect of pressure pressure distribution without separation distribution

strong adverse -Cp separated flow pressure gradient

moderate adverse pressure gradient

attached flow

-1.0

34 DU 91-W2-250

35 -4 C p α = 0 degr. -3

-2

-1

1 x/c (%) 0 20406080100

36 -4 C p α = 2.6 degr. -3

-2

-1

1 x/c (%) 0 20406080100

37 -4 C p α = 5.6 degr. -3

-2

-1

1 x/c (%) 0 20406080100

38 -4

Cp α = 7.2 degr. (l/d)max -3

-2

-1

1 x/c (%) 0 20406080100

39 -4

Cp α = 9.2 degr. (Cl,max) -3

-2

-1

1 x/c (%) 0 20406080100

40 -4

Cp α = 9.2 degr. (Cl,max) -3 transition

-2

-1 Separation at x/c=92%

1 x/c (%) 0 20406080100

41 -4

Cp -3 α = 9.2 degr. (Cl,max) -2 α = 7.2 degr. (l/d)max -1

1 x/c (%) 0 20406080100

42 -4

Cp -3

-2 Separation at x/c=35%

18.2 degr. -1

1 x/c (%) 0 20406080100

43 Flow Separation Why is it important ?

Loss in lift (airfoil) Increase in pressure drag Generation of unsteady loads

Example : Interaction of separated vortex flow with vertical stabilizer (F18)

44 Flow Separation • Effect of turbulence

u/U Turbulent boundary layer has more flow kinetic energy near the surface. Thus flow separation may be postponed.

laminar

turbulent

Boundary layer

45 Viscous drag

Drag due to viscous effects = friction drag + pressure drag = profile drag

C = C + C Dp Dpressure Dfriction

46 Influence of the Reynolds number

a Re=300000 Cd high b

Re=650000 Cd lower c ≈ Re=1200000 Cd Cd(b)

47 Effect on CD of shape and Re-no.

48 Pressure drag

Drag distribution Pressure drag on Cylinder Friction drag

V θ

49 Two objects with the same drag force

5 (ReD=10 )

diameter D V

10D

50 51 Artificial transition

Flow over a sphere

free transition artificial transition Re = 15000 Re = 30000

52 Artificial transition

53 Use in sports: example 1 :speed skating

Effect of zigzag strips

54 lower leg 1.4

Cd 1.2

smoothsmooth cilinder cylinder 1

0.8

0.6 coolmax 0.4

0.2

0 0 100,000 200,000 300,000 400,000 Reynoldsgetal

Measured drag characteristics of different fabrics on a cylinder

55 lower leg 1.4

Cd 1.2 smooth cilinder 1

0.8

0.6 coolmax 0.4

0.2

0 0 100,000 200,000 300,000 400,000 Reynoldsgetal

56 lower leg 1.4

Cd 1.2 smooth cilinder 1

0.8

0.6 coolmex 0.4

0.2

0 0 100,000 200,000 300,000 400,000 Reynoldsgetal

57 lower leg

1.4 smooth cilinder

1.2

0.8

coolmax+strips coolmax 0.6

0.4

0.2

0 0 100,000 200,000 300,000 400,000 Reynolds no.

58 59 Position of the strips

60 Gianni Romme

World records speed skating men 5000 m:

8.36.6 Jaap Eden Hamar 1894 6.34.96 J. Olav Koss Hamar 1994 6.30.62 Gianni Romme H’veen 1997* 6.22.20 Gianni Romme Nagano 1998 6.21.49 Gianni Romme Galgary 1998 Current: 6.03.32 Sven Kramer Galgary 2007

Result: 8.4 seconds off WR * First on clap skates

61 Experimenting with aerodynamics

Cathy Freeman, 400 m. gold medalist, Sydney Olympics 2000

62 Example 2

Case study :

Usain Bolt 100m men world record holder

63 Measured effect of strips on the total aerodynamic drag:

• strips on lower legs -3 to -11 %

• strips on the cap -2 to -6 %

64 Location Berlin air density 1.20 kg/m^3 parameters Bolt length 1.96 m mass 86 kg Cd*S-total 0.82 Cd*S-legs 0.246 distance 100 m min sec 09.58 V-average 10.44 m/s

3 P = Cd.S.½.ρ.V

First calculate the required power for the time of 9.58 s P = 560 Watts propulsion (V=10.44 m/s)

65 Pprop = 560 Watts

Location air density 1.20 kg/m^3 parametersBolt length 1.96 m mass 86 kg Cd*S-total 0.806 Cd*S-legs 0.231 -6%

V3 = P /C .S.½.ρ. d 4

Then calculate new V with V =10.479 m/s av reduced drag of legs