Lecture # 16: Review for Final Exam - Iowa State Universityhuhui/teaching/2014Fx/class-notes/AerE344... · AerE 344 Lecture Notes . ... • Index of refraction: O ... • Mensor Digital

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

Hui Hu

Department of Aerospace Engineering, Iowa State University

Ames, Iowa 50011, U.S.A

Lecture # 16: Review for Final Exam

AerE 344 Lecture Notes


AerE343L: Dimensional Analysis and Similitude

Commonly used non-

dimensional parameters:

force tension surface

force inertial WeNumber,Weber

force inertial

force lcentrifugaStr Number, Strohal

forcelity compressib

force inertialM Number,Mach

forcegravity

force inertial

lgFr Number, Froude

force viscous

force inertialRe number, Reynolds

force inertial

force pressureEu number,Euler

2

2

lV

V

l

c

V

V

VL

V

p

Similitude:

• Geometric similarity: the model

have the same shape as the

prototype.

• Kinematic similarity: condition

where the velocity ratio is a

constant between all corresponding

points in the flow field.

• Dynamic similarity: Forces which

act on corresponding masses in the

model flow and prototype flow are

in the same ratio through out the

entire flow


Measurement Uncertainties

• “Error” is the difference between the experimentally-determined value and its true value;

therefore, as error decreases, accuracy is said to increase.

• Total error, U, can be considered to be composed of two components:

– a random (precision) component,

– a systematic (bias) component,

– We usually don’t know these exactly, so we estimate them with P and B, respectively.

222 PBU

X

True value

X=100

Bias error

precision error

measured value

X=101

Repeatability Precision Error

Reproducibility Both Bias and Precision Errors

truemtruemeasurederror AAEAAA true

error

relativeA

AE


Measurement Uncertainties

pppV

BernoulliVpp

statictotal

statictotal

2)(2

)(,2

1 2

222

RRR PBU

Uncertainty in velocity V:

J

i

i

i

R

J

i

i

i

R PX

RPB

X

RB

1

2

2

1

2

2 ;

M

j

ii jBB

1

2

For a large number of

samples (N>10) ii SP 2

N

kkii

N

k

ikii XN

XXXN

S1

21

1

2 1;

1

1


Pressure Measurement Techniques

• Deadweight gauges:

• Elastic-element gauges:

• Electrical Pressure transducers:

• Wall Pressure measurements

– Remote connection

– Cavity mounting

– Flush mounting

• Pressure Measurements inside Flow Field:


)(2

)(,2

1

0

2

0

stat

stat

ppV

BernoulliVpp

• Advantage:

• Simple

• cheap

• Disadvantage:

• averaged velocity only

• Single point measurements

• Low measurement accuracy

Velocity measurement techniques – Pitot –Static Probe


Velocity measurement techniques – Hotwire Probe

• Advantage:

• High accuracy

• High dynamic response

• Disadvantage:

• Single point measurements

• Fragile, easy to broke

• Much more expansive

compared with pitot-static

probe.

Flow Field

Current flow

through wire

The rate of which heat is removed from the

sensor is directly related to the velocity of

the fluid flowing over the sensor

V

• Constant-current anemometry

• Constant-temperature anemometry

),(2

www TVqRi

dt

dTmc


AerE311L: The nature of light

• Light as electromagnetic waves.

• Light as photons.

• Color of light

• Index of reflection

1/ 0

vcn

sm /3x10c 8

0


Shadowgraph and Schlieren technique

• Index of refraction:

• Depend on variation of index of refraction in a transparent medium and the resulting effect on a light beam passing through the test section

• Shadowgraph systems: are used to indicate the variation of the second derivatives (normal to the light beam) of the index of refraction.

• Schlieren Systems: are used to indicate the variation of the first derivative of the index of refraction

1/ 0

vcn

shadowgraph depicting the flow generated by a bullet

at supersonic speeds. (by Andrew Davidhazy )

Schlieren images of the muzzle blast and

supersonic bullet from firing a .30-06 caliber

high-powered rifle (by Gary S. Settles )


Visualization of a Schockwaves using Schlieren technique

Before turning on the Supersonic jet

After turning on the Supersonic jet


Schlieren vs. Shadowgraph

Shadowgraph

• Displays a mere shadow

• Shows light ray displacement

• Contrast level responds to

• No knife edge used

Schlieren

• Displays a focused image

• Shows ray refraction angle, • Contrast level responds to

• Knife edge used for cutoff

yn

2

2

y

n


Particle Image Velocimetry (PIV)

• To seed fluid flows with small tracer particles (~µm), and

assume the tracer particles moving with the same velocity as

the low fluid flows.

• To measure the displacements (L) of the tracer particles

between known time interval (t). The local velocity of fluid

flow is calculated by U= L/t .

A. t=t0 B. t=t0+10 s

Classic 2-D PIV measurement

C. Derived Velocity field X (mm)

Y(m

m)

-50 0 50 100 150

-60

-40

-20

0

20

40

60

80

100

-0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.9

5.0 m/sspanwisevorticity (1/s)

shadow region

GA(W)-1 airfoil

t=t0 t

LU

t= t0+t

L

• Advantage:

• Whole flow field measurements

• Non-intrusive measurements

• Disadvantage:

• Low temporal resolution

• Very expansive compared with

hotwire anemometers and pitot-

static probes.


PIV System Setup

Illumination system

(Laser and optics)

camera

Synchronizer

seed flow with

tracer particles

Host computer

Particle tracers: to track the fluid movement.

Illumination system: to illuminate the flow field in the interest region.

Camera: to capture the images of the particle tracers.

Synchronizer: the control the timing of the laser illumination and

camera acquisition.

Host computer: to store the particle images and conduct image processing.


Advanced PIV techniques

Measurement region

80mm by 80mm

Laser sheet with P-polarization direction

Lobed nozzle

650mm

650mm

25 0

250

Synchronizer

cylinder lens

Host computer

high-resolution

CCD camera 3

Double-pulsed

Nd:YAG Laser set A

Polarizer cube

Polarizing beam splitter cubes

Mirror #3

Mirror #4

Half wave (/2) plateMirror #1

Mirror #2

high-resolution

CCD camera 1

Laser sheet with

S-polarization direction

S-polarized laser beamP-polarized

laser beam

high-resolution

CCD camera 2

high-resolution

CCD camera 4

Double-pulsed

Nd:YAG Laser set B

• Stereoscopic PIV technique

• Dual-plane stereoscopic PIV technique

• 3-D PTV technique

• Holograph PIV techniques

• Defocus PIV technique

Camera 1 Camera 2

Laser Sheet

1

2

Z

X

Stereo PIV technique


Laminar Flows and Turbulent Flows

'';' wwwvvvuuu

...),,,(1 0

0

Tt

t

dttzyxuT

u

0'0';0' wvu

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

)'( 2222

0

wvdtuT

u

Tt

t

o


Boundary Layer Flow

y

Uu 99.0

, yat Displacement thickness:

Momentum thickness:


Review of Quasi-1D Nozzle Flow

u

duM

A

dA)1( 2

M<1 M>1

Throat

M=1

u increasing

M>1 M<1

Throat

M=1

u decreasing


1st, 2nd and 3rd critic conditions

1st critic

condition

2st critic

condition

3st critic

condition

P0 in

crea

sin

g

P0 in

crea

sin

g


Streamlines (experiment)

Lab #1: Flow visualization by using smoke wind tunnel

• Path line

• Streak lines

• Streamline


2

2

1*

*

VC

qC

ppp

T

EA

Test section

Contraction

section

A

E

V

Settling

chamber

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140

Linear curve fittingExperimental data

P = PA-P

E (Pa)

q =

0.5

*V

2

Lab#02: Wind Tunnel Calibration


Lab #3: Pressure Sensor Calibration and Uncertainty Analysis

• Task #1: Pressure Sensor Calibration experiment

– A pressure sensor – Setra pressure transducer with a range of +/- 5 inH2O

• It has two pressure ports: one for total pressure and one for static (or reference) pressure.

– A computer data acquisition system to measure the output voltage from the manometer.

– A manometer of known accuracy

• Mensor Digital Pressure Gage, Model 2101, Range of +/- 10 inH2O

– A plenum and a hand pump to pressurize it.

– Tubing to connect pressure sensors and plenum

• Lab output:

– Calibration curve

– Repeatability of your results

– Uncertainty of your measurements

Setra pressure

transducer

(to be calibrated)

Mensor Digital

Pressure Gage A computer A plenum hand pump

tubing


Lab#04 Measurements of Pressure Distributions around a Circular Cylinder

2

2

2

2

2

2

sin41)sin2(

1

1

2

1

V

V

V

V

V

PPCp

R

P

Incoming flow

X

Y

-3

-2

-1

0

1

0 100 200 300 400

Angle, Deg.

Cp

Cp distribution around a cylinder

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

0 1 2 3 4 5 6 7

theta (rad ) -->

cp

-->

EFD

CFD

AFD


Lab#05: Airfoil Pressure Distribution Measurements

NACA0012 airfoil with 32 pressure tabs

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

cV

LCl

2

2

1

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


Dra

g C

oe

ffic

ien

t,

Cd

cV

DCd

2

2

1

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

2.0

2.5

3.0

0 1 2 3 4 5 6 7 8 9 10 11 12

X (inches)

Y (

inch

es)

1

5 12 22

25 30 40

47


y

x 80 mm

Pressure rake with 41 total pressure probes

(the distance between the probes d=2mm)

Lab 06: Airfoil Wake Measurements and Hotwire Anemometer

Calibration

y

x

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


Lab 07: Hot wire measurements in the wake of an airfoil y

x

80 mm

Pressure rake with 41 total pressure probes

(the distance between the probes d=2mm)

Hotwire probe

Test conditions:

Velocity: V=15 m/s

Angle of attack: AOA=0, and 12 deg.

Date sampling rate: f=1000Hz

Number of samples: 10,000 (10s in time)

No. of points: 20~25 points

Gap between points: ~0.2 inches

Lab#3

Lab#4


Lab#08: Measurements of Boundary Layer over a Flat Plate

X

Y

Pitot rake

Displacement thickness:

Momentum thickness:

• To conduct velocity profile measurements at 10

downstream locations.

• To determine boundary layer thickness and drag

coefficient based on the velocity measurement

results.

LCd

2Drag coefficient:


Lab#09: Visualization of Shockwaves using Schlieren technique

Under-

expanded

flow

Flow

close to

3rd critical

Over-

expanded

flow

2nd critical –

shock is at

nozzle exit

1st critical –

shock is

almost at the

nozzle throat.

Tank with compressed air Test section


Lab#10: Set Up a Schlieren and/or Shadowgraph System to Visualize a

Thermal Plume

Point Source

Candle plume


Tank with compressed air Test section

Lab#11: Pressure Measurements in a de Laval Nozzle

Tap No. Distance downstream of throat (inches) Area (Sq. inches)

1 -4.00 0.8002 -1.50 0.5293 -0.30 0.4804 -0.18 0.4785 0.00 0.4766 0.15 0.4977 0.30 0.5188 0.45 0.5399 0.60 0.56010 0.75 0.58111 0.90 0.59912 1.05 0.61613 1.20 0.62714 1.35 0.63215 1.45 0.634


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


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


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

Lab#12: PIV measurements of the Unsteady Vortex Structures in the

Wake of an Airfoil


Lab#13: Stereoscopic PIV technique and Applications

Camera 1 Camera 2

Laser Sheet

1

2

Z

X

Displacement vectors in left camera Displacement vectors in right camera

Stereo PIV technique

.deg0.5;000,52Re C

X/C =4.0

X pixel

Yp

ixe

l

0 500 1000 1500

0

200

400

600

800

1000

1200

X pixel

Yp

ixe

l

0 500 1000 1500

0

200

400

600

800

1000

1200

Documents

Lecture # 16: Review for Final Exam - Iowa State Universityhuhui/teaching/2014Fx/class-notes/AerE344... · AerE 344 Lecture Notes . ... • Index of refraction: O ... • Mensor Digital