Sally Bane Explosion Dynamics Laboratory Directed by Professor Joseph Shepherd Graduate Aerospace Laboratories (GALCIT) Ae104b Lecture February 9, 2010

Sally Bane

Explosion Dynamics Laboratory

Directed by Professor Joseph Shepherd

Graduate Aerospace Laboratories (GALCIT)

Ae104b LectureFebruary 9, 2010

Shadowgraph and Schlieren Techniques

2

Schlieren Visualization

• optical techniques have been used for decades to study inhomogeneous media

• Robert Hooke (1635-1703) – “Father of the optics of inhomogeneous media”, invented the schlieren method

• many different optical techniques for studying fluid flow

• will focus on the classic schlieren technique

Schlieren image of explosion in hydrogen-air

3

Basic Concepts: Light Propagation Through Inhomogeneous Media

Schlieren and Shadowgraph Techniques

allow us to see the phase differences in light

Q: Why do stars “twinkle”?

A: atmosphere is inhomogeneous – disturbances due to turbulence etc. change the air density

→ change in the refractive index

→ rays of starlight bend, wave front of the light is wrinkled

→ star not a point, but fluctuates (“twinkles”) on the time scale of the atmospheric disturbances

4


Refractive Index: describes how the speed of light changes upon interacting with matter

c

cn 0

medium in thelight of speed :

m/s 103 vacuumain light of speed :

000292.1 e.g.

1 index refractive :

80

c

xc

n

n

air

Gases: linear relationship between n and the gas density

kn 1

/gcm 23.0 e.g.

tcoefficien Dale-Gladstone :

density gas :

tyrefractivi :1

3

airk

k

n

5


Increase air density by two orders of magnitue → 2.3% increase in n!

Refractive index only very weakly dependent on density

→ k = 0.23 cm3/g = 2.3 x 10-4 m3/kg

Require very sensitive optics!

6


What does “schlieren” mean?

Schliere (singular of schlieren):

German for “streak,” “striation,” or “cord”

gradient disturbance of inhomogeneous transparent media

object that has a gradient in the index of refraction, i.e.

y

n

x

n

or

7


Example schliere: Laminar Candle Plume

y

x

2

11

x

n

x

n

12

The gas in the plume is hotter and less dense than the surrounding gas, so

and therefore

12 nn

producing a gradient in the x-direction

8


Increasing n

Negative vertical refractive-index

gradient dn/dy < 0

y

z

x

t = 0 t = t

y1

y2

z1 = (c0/n1)t

z1

z2

z2 = (c0/n2)tand

Planar wave front

Rays (normal to wave front)

z = ct = (c0/n)t

Since n2 > n1, c2 < c1 so

z2 < z1

9


Increasing n

Negative vertical refractive-index

gradient dn/dy < 0

y

z

x

t = t

RESULT:

Refracted wave front

Huygen’s Principle:

Light rays, always normal to the local speed of light, are bent

toward the zone of higher refractive index (zones of higher

density in gases).

10


y

z

x

y

y1

y

y2 (c0/n2)t

z1

z2

Distance wave front moves in time t:

tn

ctc 0

dn/dy < 0

Refraction angle:

y

tnctnc

)/(/

tan 1020

z

Also:

0c

nzt

z

y

nn

nn

n

21

21

11


y

z

x

y1

y

y2 (c0/n1)t

z1

z2

0 , 0 zydn/dy < 0

z

dy

dn

ndz

d 1

Because is a very small angle, it is approximately equivalent to dy/dz, the slope of the refracted ray.

y

n

nz

y

1

2

2

x

n

nz

x

1

2

2

and

Curvature of refracted ray

y

12


y

z

x

y1

y

y2 (c0/n1)t

z1

z2

dn/dy < 0

z

For a 2D schliere of length L along the optical axis (z):

dzy

n

ny

1 dz

x

n

nx

1and

So the angular ray deflection in the x and y directions are:

y

n

n

Ly

0

x

n

n

Lx

0

and

Refraction caused by gradients of n, not overall level of n!

y

13

Shadowgraphy

Only need a light source, a schlieren object, and screen on which the shadow is cast

*point light source

schliere

extra illumination

less illumination

*point light source

Denser sphere (i.e. a bubble)

lens

screen

screenScreen

14

Shadowgraphy

Screen

Dark circle due to light refracted from outline of sphere

Light circle due to refracted light from the outline illuminating this part of the screen

Gradient back to background illumination due to non-uniform refraction of rays as the light wave travels down the optical axis (x)

15

Shadowgraphy

Uniform shift of

illumination

z

y

z

y

Nonuniform illumination

see some shadow, but don’t get outline of the schliere

as move down optical path (z-direction),

so all rays shift the same!

constant yn

as move down optical path (z-direction),

so rays shift non-uniformly

constant 22 yn

Variation of gradients critical!

16

Example Shadowgraphs

Shock wave diffraction around wedge (Settles 2001)

Oil globs in water (Settles 2001)

Sphere flying at M=1.7 (Merzkirch 1987)

He/N2 mixing layer (Settles 2001)

17

Shadowgraphy vs. Schlieren Imaging

Less sensitive except for special cases (e.g. shock waves)

More sensitive in general

Schlieren Imaging Shadowgraphy

Focused optical image formed by a lens

Requires cutoff of the refracted light

Illuminance level responds to ∂n/∂x and ∂n/∂y

Schlieren image displays the deflection angle

Not an image but a shadow

No cutoff of refracted light

Responds to second spatial derivative, ∂2n/∂x2 and ∂2n/∂y2

Shadowgraph displays ray

displacement

More difficult to set up – use lamps, mirrors, lenses

Extremely easy to setup, occurs naturally

18

Schlieren System – Point Light Source

*point light source

lens lens

schliere in test section

screen

• merely a projector, imaging opaque objects in the test section

deflected rays miss the focus

focused back to same point

on screen

19

Schlieren System – Point Light Source

*point light source

lens lens

schliere in test section

screen

knife-edge

• translating phase difference causing a vertical gradient ∂n/∂y to amplitude of light on the screen

• refracts many rays in many directions – all downward deflected rays get blocked, painting at least a partial picture

• gives black and white image

Brighter point on screen

20

Schlieren System – Extended Light Source

extended light source

lens lens

knife-edge

• the light source is first collimated by a lens then refocused by the second lens

• an inverted image of the light source is formed at the knife-edge

• the extended light source can be considered as an array of point sources – each “point source” forms a schlieren beam that focuses to a corresponding point in the light source image (extreme rays shown in cartoon above)

• knife-edge blocks a portion of the image of the extended light source

• another lens focuses an inverted image of the test area on the screen

screen

21



lens lens

knife-edge

• each “point source” in the extended light sources illuminates every point in the test section → each point in test section is illuminated by rays from the entire extended source

• when focused to knife-edge, each point in test section produces an entire “elemental” source image to the “composite” image at the knife-edge

• e.g. if insert a pinhole in the test section, would still see an image of the extended source, but much weaker in intensity than the “composite” image

screen

22



lens lens

knife-edge

IMPORTANT POINT:

• with no schliere present, if we advance the knife-edge to block more the “composite” image of the extended light source → block each “elemental” source image equally

screen

therefore blocking equal amount of light from every point in the test area

Screen darkens uniformly! This is how you know your alignment is good and that you are at the true focus!

23



lens lens

knife-edge

• consider one point in the test area to be subject to refraction by the schliere

• since all of the “point sources” on the extended light source contribute a ray to this point, a group of rays from all “point sources” is deflected (dashed lines in cartoon)

• this group of rays are focused to produce an “elemental” image of the light source at the knife-edge but the image is displaced due to the refraction

• the group of rays is returned to the same relative position on the screen by the third lens → true image of the schliere at the screen

screen

NOW PLACE A SCHLIERE IN THE TEST AREA

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• the displacement of the “elemental” source image separates the rays refracted by the schliere from the rays that provide the background illuminance

• because the refracted light is separated, can have a different amount of cut-off by the knife edge → recombined in the schlieren image at the screen → variations in the illumination with respect to the background

Many points of varying illuminance

schlieren image that shows the shape

and strength of the schliere

Note: using an extended light sources gives continuous gray-scale schlieren images!

Knife-edge

a

a

Undisturbed composite source image

Weak source image

displaced by schlieren

object

25


Knife-edge

a

a

Undisturbed composite source image

Weak source image displaced

by schlieren object

Sensitivity:

Constrast:a

f

E

EC ys

differential illuminance at an image point

background illuminance

focal length of the schlieren lens

refraction angle

:E

:E

:sf

:ySensitivity: d

dC

d

dS

input

output

a

fS s

Larger focal length = better sensitivity

More obstruction of source image = better sensitity

26

Z-Type Schlieren Arrangement

camera

knife-edge

parabolic mirrorparabolic mirror

light sourcecondenser

lenspinhole or slit

test area

Most common arrangement: easy to set-up, allows for a schlieren mirror with long focal length (high sensitivity) and large field-of-views

27

Cool Schlieren Images

Bullet and candle flame (Settles 2001)

Glass fibers (Settles 2001)

Projectile fired at Mach 4.75 in reactive

H2/air mixture – cyclic detonation behind the shock

(Settles 2001)

28


Removing frozen pizza from case

(Settles 2001)

Blackjack dealer and players

(Settles 2001)

Space heater (Settles 2001)

29


Image of a T-38 at Mach 1.1 (Leonard M. Weinstein, NASA Langley Research Center) – taken using a telescope, the sun, and a cutoff, field of view of 80 m!

30


3D schlieren of a glass figurine (Settles 2001)

Color schlieren of the space

shuttle orbiter in supersonic wind

tunnel test (Settles 2001)

Color schlieren of a gun firing 0.22 caliber bullet

(Settles 2001)

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Important Equations

Equations:

Gaussian Lens Equation:

243121

111 and

111

fxxfxx

Constraints:

For Real Image: 0, 32 xx

2311 and fxfx

Table Size:

Lxxxx 4321

where L is limited by the size of the optics table

Magnification:3

4

1

2

1

2

0

1 and x

x

y

y

x

x

y

y

I

II

13

24

0

2

xx

xx

y

yM I Total

Magnification

x1 f1

x2 x3 x4

f2

y0

yI1

yI2

Lens 1 Lens 2Knife-edge

Object (FOV)

Inverted object image

Object image

32

Important Equations

Must Satisfy:

13

24

243

121

111

111

xx

xxM

fxx

fxx

Under the Constraints:

Lx

fx

fx

ii

4

1

23

11

SUMMARY

x1 f1

x2 x3 x4

f2

y0

yI1

yI2

Lens 1 Lens 2Knife-edge

Object (FOV)

Inverted object image

Object image

33

How My Schlieren Setup Works

Light source (Xe arc lamp)

Optical assembly

Vertical slit (razor blades)

Achromatic lens (to collimate the light)

f = 200 mm

Aperture (to make 1” Ø beam)

Baffle (to block stray light)

Flat mirror

Flat mirror

Test section (1” Ø field-

of-view)

Concave mirror (schlieren lens) f = 1000 mm

Flat mirrors

Flat mirror

Knife-edges (razor blades)

High-speed camera (no additional

focusing lens used)

34


Camera Side:

x1

f

x2

yOyI

Schlieren “Lens” (concave mirror)

Knife-edges

Object (1” Ø field-of-view)

Inverted object image on

camera CCD

f

Equations:

fxx

111

21

1

2

x

x

y

yM

O

I

Knowns: mm 1000f

Diameter Beam

CCD Camera of SizeM

625.0in. 1

in. 8/5

1

2

Unknowns: 21 , xx

35


fxx

xx 1

21

12

12 Mxx

1

2 fMx

M

Mxx

xMx 11

111

11

12 into

3

3Invert fM

Mx

11

Solve for x1:

mm 1000625.0

625.0111

fM

Mx mm 26001 x

Then from :2 mm 2600625.012 Mxx mm 16252 x

Remember: Sensitivity is proportional to the focal length so f should be as large as possible!

36

Setting Up a Schlieren System:Step-by-Step (1)

Step 1: Calculate the required distances between he object, schlieren lens, focusing lens, and camera based on the equations on the previous slide and the focal lengths of your lenses

Step 2: Set up the light source, any flat mirrors, and test section with windows in place if applicable

Step 3: Set up a laser in the place where the camera will go

Step 4: Turn on the laser and ensure that the beam is straight in both the vertical and horizontal directions along the optical axis (line to next mirror)

Side View Top View

ylaser

ruler or height gauge

optical axis (z)

z

x

laser

right angle ruler

optical axis (z)

37


Step 5: Adjust any mirrors on this side of the set-up to direct the laser to the test section, ensuring that the beam stays the same height the whole way (use a ruler or a height gauge to test this at every mirror)

Step 6: If there are windows on the test section, check for reflections to ensure the laser is perpendicular to the windows

Tip 1: Try to keep the laser dot as close to the center of the mirrors as possible

Tip 2: The laser light corresponds to approximately the center of the ultimate light beam, so locate the laser beam through the test section where you want the center of the light beam

Incident laser beam

reflection

window

piece of paper

Tip 1: Use a piece of paper to probe all around the incident beam – any reflections will show up on the paper

Tip 2: When it is properly aligned, when you look through the windows all the laser dots will appear in a straight line through the glass

38


Step 7: Adjust any mirrors on the light-source side to direct the laser beam to the light source, ensuring the beam stays the same height and is centered on the mirrors

Step 8: Adjust the height of the light source so that it is at the same height as the laser beam

Step 9: Remove the cover of the light source (make sure it is unplugged and cold!) so you can see the filament or arc bulb.

Step 10: Use the controls on the light source to move the filament or bulb until the laser light hits the center of the filament or bulb. Check for reflections.

Tip 1: The two most common types of light sources are filament and arc light sources, and there are often lenses mounted on the frontTip 2: First, adjust the height of the light source so that the laser beam is centered on the lens on front of light source if presentTip 3: Check for reflections from the lens using the method described before – adjust light source orientation to minimize relfections

39


Step 11: Once alignment of the laser, mirrors, and light source is complete, be sure to secure all the optics in place.

Step 12: One-by-one, add the lenses to the setup.

Step 13: Once the alignment is complete, secure well all of the optical components.

Step 14: Replace the laser with the camera, place the knife-edge at the approximate location of the focus of the schlieren lens, and turn on the light source.

Tip 1: The laser light should go through the center of the lens.Tip 2: Check for reflections using the method described before (probe around the beam with a piece of paper between the incident laser beam and the lens). Get rid of reflections by adjusting the height of the lens and angle of the lens with respect to the laser.

Now the REAL work begins! Remember, the best tool for setting up a good schlieren system is PATIENCE!

40


Step 15: Starting at the light source, very carefully make slight changes to the focusing lens (if one is not included on the light source) to focus the light source down onto the pin-hole or slit.

Step 16: Using a precision translation stage, adjust the distance between the pin-hole or slit and the collimating lens until the beam is collimated. Use an aperture if desired to define the size of the beam

Tip 1: Position the collimating lens (lens 2) one focal length (f2) from the pin-hole or slit first.

Tip 2: Put up a piece of paper a good distance from the lens, then carefully adjust the distance between lens 2 and the pin-hole/slit until the beam on the paper is the same size as at the aperture – then the light is collimated!

f1 f2

light source

lens 1 lens 2

aperture

41


Step 17: After the beam has been collimated, if it is not in the location where you want it in the test area, make adjustments to move the beam.

Step 18: Follow the same procedure to position the image correctly on the camera, heeding the Tips 1 and 2.

Step 19: Find the approximate location of the focus of the schlieren lens, and place the knife-edge there on translation stages.

Step 20: Step the knife-edge in/up to block part of the light – if you are at the focus, the background will become dimmer uniformly. Adjust the location of the knife-edge using the translation stages until you find the focus.

Tip 1: Make horizontal adjustments by moving the mirrors – NOT tilting the mirrors, but actually moving them horizontally. It is a good idea to mount the mirrors on translation stages to allow for this.

Tip 2: Make vertical adjustments by changing the aperture (if you are using one) if possible; if not, change the height of both the lenses and the light source.

42

References & Where to Buy Optics

Reference Books on Schlieren Methods:

G. S. Settles. Schlieren and Shadowgraph Techniques. Springer-Verlag, 2001.

W. Merzkirch. Flow Visualization. 2nd Ed. Academic Press, Inc., 1987.

Where to purchase optical components:

Thorlabs, Inc http://www.thorlabs.com Newport http://www.newport.com Edmund Optics http://www.edmundoptics.com CVI Melles Griot http://www.cvimellesgriot.com

http://www.thorlabs.com/

http://www.newport.com/

http://www.edmundoptics.com/

http://www.cvimellesgriot.com/

Documents

Sally Bane Explosion Dynamics Laboratory Directed by Professor Joseph Shepherd Graduate Aerospace Laboratories (GALCIT) Ae104b Lecture February 9, 2010