lecture # 07: laminar and turbulent flowshuhui/teaching/2015sx/class-notes/aere344... · laminar...

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Dr. Hui Hu

Dr. Rye M Waldman

Department of Aerospace Engineering

Iowa State University

Ames, Iowa 50011, U.S.A

Lecture # 07: Laminar and Turbulent Flows

AerE 344 Lecture Notes

Sources/ Further reading: Munson, Young, & Okiishi, “Fundamentals of Fluid Mechanics,” 4th ed, Ch 8

Tropea, Yarin, & Foss, “Springer Handbook of Experimental Fluid Mechanics,” Part C Ch 10

Kundu & Cohen, “Fluid Mechanics,” 3rd ed, Chs 3 & 13

Tritton, “Physical Fluid Dynamics,” 2nd ed, Chs 2, 19–21


Turbulence

“Big whorls have little whorls

That feed on their velocity,

And little whorls have lesser whorls

And so on to viscosity.”

-LF Richardson

Leonardo Da Vinci


Reynolds’ experiment

DUReReynolds number:

Empirically, when Re < 1000, laminar flow,

and when Re > 3000, turbulent flow.

ReC ~ critical Reynolds number above

which flow exhibits turbulent

characteristics

For external flows (e.g., flow around airfoil)

(ReC)L ~ 3 ∙ 105

For internal flows (e.g., pipe flow)

(ReC)δ ~ 3 ∙ 103

From Pradtl: boundary layer (δ) vs body

size (L) scales like L/δ ~ (Re)L1/2.

Thus (Re)L / (Re)δ ~ 102.


Turbulence

ReLU

Reynolds number:

At the large scales, the flow is determined

by the reference length scale, L, and the

reference time scale, τ0 = L/U.

The small length scales are governed by

the Kolmogorov scales η = (ν3 / ε)1/4, and

τη = (ν / ε)1/2.

ε is the turbulent energy dissipation rate.

Scaling:

For a flow with Re ~ 10,000:

Flow scales span 3 orders of magnitude in

length and 2 orders of magnitude in time.

Turbulent flows contain a vast range of

length and time scales that must be

resolved!!! Difficult!!


Laminar Flows and Turbulence Flows

• Laminar flow, sometimes known as streamline flow, occurs

when a fluid flows in parallel layers, with no disruption

between the layers. Viscosity determines momentum

diffusion.

– In nonscientific terms laminar flow is "smooth," while

turbulent flow is "rough."

• Turbulent flow is a fluid regime characterized by chaotic,

stochastic property changes. Turbulent motion dominates

diffusion of momentum and other scalars. The flow is

characterized by rapid variation of pressure and velocity in

space and time.

– Flow that is not turbulent is called laminar flow


VDRe

Turbulent flows in a pipe


Characterization of Turbulent Flows

'';' wwwvvvuuu

Tt

t

Tt

t

Tt

t

dttzyxwT

wdttzyxvT

vdttzyxuT

u0

0

0

0

0

0

),,,(1

;),,,(1

;),,,(1


Turbulence intensities

0'0';0' wvu

0)'(0)'(;0)'(1

)'( 2222

0

wvdtuT

u

Tt

t

o


Turbulent Shear Stress

y

ulam

Laminar flows:

''vuy

uturblam

Turbulent flows: ''vuturb

(a) laminar flow (b) turbulent flow


Laminar Flows and Turbulence Flows

AU

DCd

2

2

1

DURe


Flow Around A Sphere with laminar and turbulent boundary

layers


Aerodynamics of a golfball

Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved! X/D

Y/D

-101234

-1

0

1

2

U m/s: -10 -5 0 5 10 15 20 25 30 35 40

X/D

Y/D

-101234

-1

0

1

2 U m/s: -10 -5 0 5 10 15 20 25 30 35 40

X/D

Y/D

-101234

-1

0

1

2 U m/s: -10 -5 0 5 10 15 20 25 30 35 40

Smooth ball Rough ball Golf ball

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

-2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

smooth-ballrough-ballgolf-ball

Distance (X/D)

Ce

nte

rlin

e V

elo

city (

U/U

)

Laminar and turbulent flows

Re=100,000


Automobile aerodynamics


Automobile aerodynamics

Mercedes Boxfish Vortex generator above a Mitsubishi rear window

http://www.recumbents.com/car_aerodynamics/diffuser.jpg

http://upload.wikimedia.org/wikipedia/en/2/2b/Truck_aerodynamics.jpg

http://www.cartuningcentral.com/wp-content/uploads/2008/07/ferrari-aerodynamics.gif


Aerodynamic performance of an airfoil

X/C *100

Y/C

*10

0

-20 0 20 40 60 80 100 120

-40

-20

0

20

40

60

vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5

shadow region

GA(W)-1 airfoil

25 m/s

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 2 4 6 8 10 12 14 16 18 20

CL=2

Experimental data

Angle of Attack (degrees)

Lift

Co

eff

icie

nt,

C

l

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 2 4 6 8 10 12 14 16 18 20

Experimental data

Angle of Attack (degrees)

Dra

g C

oe

ffic

ien

t,

Cd

X/C *100

Y/C

*10

0

-40 -20 0 20 40 60 80 100 120 140

-60

-40

-20

0

20

40

60

vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5

shadow region

GA(W)-1 airfoil

25 m/s

Airfoil stall

Airfoil stall

Before stall

After stall

cV

DCd

2

2

1

cV

LCl

2

2

1


Flow Separation and Transition on Low-Reynolds-number

Airfoils

• Low-Reynolds-number airfoil (with Re<500,000)

aerodynamics is important for both military and

civilian applications, such as propellers, sailplanes,

ultra-light man-carrying/man-powered aircraft, high-

altitude vehicles, wind turbines, unmanned aerial

vehicles (UAVs) and Micro-Air-Vehicles (MAVs).

• Since laminar boundary layers are unable to

withstand any significant adverse pressure gradient,

laminar flow separation is usually found on low-

Reynolds-number airfoils. Post-separation behavior

of the laminar boundary layers would affect the

aerodynamic performances of the low-Reynolds-

number airfoils significantly

• Separation bubbles are usually found on the upper

surfaces of low-Reynolds-number airfoils .

Separation bubble bursting can cause airfoil stall at

high AOA when the adverse pressure gradients

become too big.


-0.10

-0.05

0

0.05

0.10

0.15

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

X/C

Y/C

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0

0.5

1.0

1.50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

AOA = 06 degAOA = 08 degAOA = 09 degAOA = 10 degAOA = 11 degAOA = 12 degAOA = 14 deg

X / C

CP

Separation point

Transition

Reattachment point

Surface Pressure Coefficient distributions (Re=68,000)

Typical surface pressure distribution when a laminar

separation bubble is formed (Russell, 1979)

7.5

8.0

8.5

9.0

9.5

10.0

10.5

11.0

11.5

12.0

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Transition

Reattachment

Separation

X/C

AO

A (

degr

ee)

GA (W)-1 airfoil

(also labeled as NASA LS(1)-0417 )


Laminar Separation Bubble on a Low-Reynolds-number Airfoil

PIV measurement results at AOA = 10 deg, Re=68,000

X/C*100

Y/C

*10

0

-5 0 5 10 15 20 25 30 35

0

5

10

-18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0 10.0 14.0 18.0

10 m/sGA (W)-1 airfoil

Spawisevorticity

X/C*100

Y/C

*10

0

-5 0 5 10 15 20 25 30 35

0

5

10

U m/s: 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0

GA (W)-1 airfoil

reattachmentseparation

X/C*100

Y/C

*10

0

18 20 22 24 26 28 30 32 343

4

5

6

7

8

9

10

11

U m/s: 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00

10 m/s

Reattachment

X/C*100

Y/C

*10

0

18 20 22 24 26 28 30 32 343

4

5

6

7

8

9

10

11

-25.0 -20.0 -15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 20.0 25.0

SpanwiseVorticity(1/s * 10

3)

10 m/s

Instantaneous flow field Ensemble-averaged flow field

(Hu et al., ASME Journal of Fluid Engineering, 2008)


Stall Hysteresis Phenomena

• Stall hysteresis, a phenomenon where stall inception and stall recovery do not occur at the same

angle of attack, has been found to be relatively common in low-Reynolds-number airfoils.

• When stall hysteresis occurs, the coefficients of lift, drag, and moment of the airfoil are found to be

multiple-valued rather than single-valued functions of the angle of attack.

• Stall hysteresis is of practical importance because it produces widely different values of lift coefficient

and lift-to-drag ratio for a given airfoil at a given angle of attack. It could also affect the recovery from

stall and/or spin flight conditions.

Increasing AOA

decreasing AOA

AOA – Angle of Attack

Lift

coeffic

ient

Lift coefficient curve of a “typical” airfoil Lift coefficient curve with stall hysteresis

AOA – Angle of Attack

Increasing AOA

decreasing AOA

Lift

coeffic

ient


Measured airfoil lift and drag coefficient profiles

-0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

-4 -2 0 2 4 6 8 10 12 14 16 18 20

AOA increasingAOA decreasing

Angle of Attack (degree)

Lift

Co

eff

icie

nt,

Cl

Hysteresis

loop

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

-4 -2 0 2 4 6 8 10 12 14 16 18 20

AOA increasingAOA decreasing


Dra

g C

oe

ffic

ien

t, C

d

Hysteresis loop

• The hysteresis loop is clockwise in the lift coefficient profiles, and counter-clockwise in the drag coefficient

profiles.

• The aerodynamic hysteresis resulted in significant variations of lift coefficient, Cl, and lift-to-drag ratio, l/d,

for the airfoil at a given angle of attack.

• The lift coefficient and lift-to-drag ratio at AOA = 14.0 deg were Cl = 1.33 and l/d = 23.5 when the angle was

in the increasing angle branch of the hysteresis loop.

• The values were Cl = 0.8 and l/d = 3.66 for the same AOA=14.0 degrees when the angle was at the

deceasing angle branch of the hysteresis loop

GA(W)-1 airfoil, ReC = 160,000


0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

8 9 10 11 12 13 14 15 16 17 18 19 20

AOA decreasing

AOA increasing


Lift

Co

eff

icie

nt,

Cl

PIV Measurement results

X/C *100

Y/C

*10

0

-40 -20 0 20 40 60 80 100 120 140

-60

-40

-20

0

20

40

60

vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5

shadow region

GA(W)-1 airfoil

25 m/s

X/C *100

Y/C

*10

0

-20 0 20 40 60 80 100 120

-40

-20

0

20

40

60

vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5

shadow region

GA(W)-1 airfoil

25 m/s

X/C *100

Y/C

*10

0

-20 0 20 40 60 80 100 120

-40

-20

0

20

40

60

vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5

shadow region

GA(W)-1 airfoil

25 m/s

separation bubble

X/C *100

Y/C

*10

0

-40 -20 0 20 40 60 80 100 120 140

-60

-40

-20

0

20

40

vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5

shadow region

GA(W)-1 airfoil

25 m/s

(Hu, Yang, Igarashi, Journal of Aircraft, Vol. 44. No. 6 , 2007)


0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

8 9 10 11 12 13 14 15 16 17 18 19 20

AOA decreasing

AOA increasing


Lift

Co

eff

icie

nt,

Cl

Refined PIV Measurement Results

X/C *100

Y/C

*10

0

-5 0 5 10 15 20 25 30 35

-10

-5

0

5

10

15

20

25

-18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0

GA(W)-1 airfoil 25 m/s

X/C *100

Y/C

*10

0

-5 0 5 10 15 20 25 30 35

-10

-5

0

5

10

15

20

25

vort: -18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0

GA(W)-1 airfoil 25 m/s

X/C *100

Y/C

*10

0

-5 0 5 10 15 20 25 30 35

-5

0

5

10

15

20

vort: -18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0

GA(W)-1 airfoil25 m/s

X/C *100

Y/C

*10

0

-5 0 5 10 15 20 25 30 35

-10

-5

0

5

10

15

20

vort: -18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0

GA(W)-1 airfoil25 m/s

(Hu, Yang, Igarashi, Journal of Aircraft, Vol. 44. No. 6 , 2007)


y

x

Lab 6: Airfoil Wake Measurements and Hotwire Anemometer

Calibration

2

2

2

2

2

2

;

21

)])(

1()(

[

)]1)(

()(

[

)( Since

)(

)ˆ(

dAU

yU

U

yUUD

dAU

yU

U

yUUDF

DF

pyppp

dAypdApD

dAnpDF

X

X

up

up

CS

XX

2

2

2

2

2

2

)])(

1()(

[2

2

1

)])(

1()(

[

2

1

dyU

yU

U

yU

CC

CU

dAU

yU

U

yUU

CU

DC

D

D

Compare with the drag coefficients obtained based on airfoil surface pressure

measurements at the same angles of attack!


y

x 80 mm

Pressure rake with 41 total pressure probes

(the distance between the probes d=2mm)


Calibration



Calibration

CTA hotwire probe

Flow Field

Current flow

through wire

V

),(2

www TVqRi

dt

dTmc

• Constant-temperature anemometry


Hotwire Anemometer Calibration

0

2

4

6

8

10

12

14

16

18

20

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2

Curve fitting

Experimental data

y=a+bx+cx2+d*x

3+e*x

4 max dev:0.166, r

2=1.00

a=10.8, b=3.77, c=-26.6, d=13.2

voltage (V)

Flo

w v

elo

city (

m/s

)

• Quantify the relationship between the flow velocity and voltage output from the CTA

probe


Required Measurement Results

Required Plots:

• Cp distribution in the wake (for each angle of attack) for the airfoil wake measurements

• Cd vs angle of attack (do your values look reasonable?) based on the airfoil wake

measurements

• Your hot wire anemometer calibration curve: Velocity versus voltage output of hotwire

anemometer (including a 4th order polynomial fit)

Please briefly describe the following details:

• How you calculated your drag—you should show your drag calculations

• How these drag calculations compared with the drag calculations you made in the

previous experiment

• Reynolds number of tests and the incoming flow velocity

lecture # 07: laminar and turbulent flowshuhui/teaching/2015sx/class-notes/aere344... · laminar...

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