Lecture # 07: Laminar and Turbulent Flowshuhui/teaching/2018-08F/AerE344/class-notes/AerE... · Munson, Young, & Okiishi, “Fundamentals of Fluid Mechanics,” 4th ed, ... Conventional

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

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

Sources/ Further reading: Schlichting, “Boundary Layer Theory,” any ed

White, “Viscous Fluid Flow,” 3rd ed.

Kundu & Cohen, “Fluid Mechanics,” 3rd ed.


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

ula m

Laminar flows:

''vuy

utu rblam

Turbulent flows: ''vutu rb

(a) laminar flow (b) turbulent flow


Quantification of Boundary Layer Flow

y

Uu 99.0

, yat

Displacement thickness:

Momentum thickness:


Boundary Layer Theory

X

X

X

X

f

X

X

X

X

C

XU

Re

664.0

Re

72.1*

Re

0.5

Re

328.1

Re

0

y

p

X

Y Blasius solution for laminar

boundary layer:

wa ll

wy

U


Boundary Layer Theory

5/1

5/1

)(Re

37.0

)(Re

074.0

Re

X

X

f

X

X

C

XU

0

y

p

X

Y

Turbulent boundary layer:

wa ll

wy

U


Boundary Layer Flows

wa ll

wy

U

X

Y

Which one will induce more

drag?

Laminar boundary layer?

Turbulent boundary layer?


Boundary Layer Flows

wa ll

wy

U

Which one will induce more drag?

Laminar boundary layer? Turbulent boundary layer?


Laminar Flows and Turbulent Flows

AU

DCd

2

2

1

DURe


Flow Around A Sphere with laminar and Turbulence

Boundary Layer


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

Laminar and turbulent flows

Re=100,000 -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

)


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


Flow Separation on an Airfoil


Conventional vs Laminar Airfoils

• Laminar flow airfoils are usually thinner than the

conventional airfoil.

• The leading edge is more pointed and its upper

and lower surfaces are nearly symmetrical.

• The major and most important difference

between the two types of airfoil is this, the

thickest part of a laminar wing occurs at 50%

chord while in the conventional design the

thickest part is at 25% chord.

• Drag is considerably reduced since the laminar

airfoil takes less energy to slide through the air.

• Extensive laminar flow is usually only

experienced over a very small range of angles-of-

attack, on the order of 4 to 6 degrees.

• Once you break out of that optimal angle range,

the drag increases by as much as 40%

depending on the airfoil


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)


Active flow control: Plasma actuators

Corke et al, Annu. Rev. Fluid Mech.

2010. 42:505–529

Use methods to actively control boundary

layer separation:

•Suction

•Blowing

•Plasma actuators: Applies a body force

acting on weakly ionized air to couple

momentum into the flow

•Synthetic Jets


Active flow control: Synthetic jets

Synthetic jets: zero mass flux

actuators that inject momentum into

the flow

Glezer & Amitay, Annu. Rev. Fluid Mech.

2002. 34:503–29


Passive flow control: Shark Skin

Dean & Bhushan, Phil. Trans. R.

Soc. A (2010) 368, 4775–4806


Vortex Structure over Riblets


Shark Skin


Shark Skin Swimming Suits


y

x

Lab 6: Airfoil Wake Measurements and Hotwire Anemometer

Calibration

1 2

2

2

2

Forces on CV = Fluid momentum change

ˆForces on CV: ( ) ( )

Since , ( )

Momentum change: ( ) ( )

[

X X up

CS

up

X

X

F D pndA D p dA p y dA

p p p y p

F D

U y U y U dA F D

UD U

2

2

( ) ( )(1 )]

y U ydA

U U

2

2

2

2 2

2

( ) ( )[ (1 )]

1 1

2 2

2 ( ) ( ) [ (1 )]

D

D

U y U yU dA

U UDC

U C U C

U y U yC dy

C U U

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

NOTE: We will be using the GA(W)-1 airfoil from the previous lab for the wake pressure

measurements

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

Documents

Lecture # 07: Laminar and Turbulent Flowshuhui/teaching/2018-08F/AerE344/class-notes/AerE... · Munson, Young, & Okiishi, “Fundamentals of Fluid Mechanics,” 4th ed, ... Conventional