Optical techniques for density (andconcentration) measurements in

fluid mechanicsJ. Kristian Sveen

jks@math.uio.no

Dept. of Mathematics, University of Oslo

Optical density meas. tech. – p.1/35

Overview

1. Density/concentration measured optically?

2. Focus on applications in Fluid Mechanics

Concept

Refractive index - densityMean density along line of sight

Use a passive tracer � concentration of tracer givesdensity/concentration of fluid

2D slice (or 3D using a scanning system)

Optical density meas. tech. – p.2/35

Example

Laser light passing through fluid w. strong densitygradient

see Merzkirch [1974], Merzkirch and Peters [1992]

Optical density meas. tech. – p.3/35

Deflection of light rays

Constant second derivative

Constant density gradient

Constant density

see Merzkirch [1974]

Optical density meas. tech. – p.4/35

What do we see?

Looking through a fluid

Incident light disturbance

Photographicdevice

∆yθ t

t*

Shadowgraph - measure

���

Schlieren - measure

�

Mach-Zendner Interferometer - measure phase-shift��� � ��� � � � �� � ��

Optical density meas. tech. – p.5/35

See the light

Method

Shadowgraph

Schlieren

Interferometry

Easy

Difficult

What we measure

Second derivative

of densityFirst derivative

Density

of density

Optical density meas. tech. – p.6/35

Shadowgraph

Optical density meas. tech. – p.7/35

Shadowgraph

Pionered by Dvorak (1880)

*Light Source

Lens Lens

Measurementsection (w optical disturbance)

Lens

Photographicdevice

Shadowgraph – p.8/35

Shadowgraph

Picture copied from Merzkirch (1974)Shadowgraph – p.9/35

Schlieren

Shadowgraph – p.10/35

Schlieren

Attributed to Focault (1859) and Toepler (1864) (dep.on national preference)

Used by Focault to check quality of lenses and mirrors

Elaborated by Toepler

Now often referred to as the “Toepler method”

Schlieren – p.11/35

Schlieren

Idea: Introduce knife edge at focal pointlight bent down is removed � darker-spotslight bent up is kept � brighter-spots

Direction of density gradient known

*Light Source

Lens Lens

LensPhotographicdevice

Knife edge

Measurementsection (w optical disturbance)

Schlieren – p.12/35

Schlieren - example

Schlieren – p.13/35

Schlieren in the digital world

Shadowgraph - sensitive to changes in secondderivative of density

Idea: compare two subsequent images

Construct first derivative by “integration”

Schlieren – p.14/35

Schlieren in the digital world contd

Motion in density field distorts background pattern

Schlieren – p.15/35

Synthetic Schlieren

Dalziel et al. [2000], Sutherland et al. [1999, 2003],Onu et al. [2003]

Using different background patterns1. Lines (horizontal or vertical)2. Regular pattern (dots individually tracked)3. Irregular pattern (using pattern matching)

Using different algorithms for pattern matching

Problem - regularity in pattern limits maximal recoverable dis-

placement

Schlieren – p.16/35

Synthetic Schlieren

Examples of background patterns:

1 2

Schlieren – p.17/35

Synthetic Schlieren

The relationship between the displacement and thedensity is given by (Dalziel et al. [2000]):

��� � ��� � � � ���

� �

��

and

� � � ��� � � � ���

� �

��

where - width of tank,

�distance from tank to

pattern (to increase sensitivity),

� � ��� �� �

,

� � �

g cm � � and � the density fluctuations

Schlieren – p.18/35

Synthetic Schlieren

Applied to measurements of internal waves in a linearstratification

2ρ

ρ1

Density field (perturbation)Setup

Schlieren – p.19/35

Background Orientated Schlieren (BOS)

Meier [1999], Richard and Raffel [2001], Klinge et al.[2003]

Essentially the same as Dalziel et al. [2000]

Cross correlation (w FFT) for pattern matching

Applied to measurements in air

Schlieren – p.20/35

BOS - continued

Displacement fields proportional to

� � �� and

� � �� .

Schlieren – p.21/35

BOS example

Rising Helium from a container (or: the coffee cupexperiment)

Courtesy of F. Klinge, DLR

Schlieren – p.22/35

Industrial applications

Example: Structured Light - used to measure 3Dobjects:

Method currently in use at Kongsberg Automotive -Automatic inspection of aluminium car-parts.

Picture from Sintef Materials Technology - used without permissionSchlieren – p.23/35

Structured light continued

Should be applicable in the fluid mechanics lab:High speed camera (2000 fps, 1Mpix), viewing fromabove3D, high resolution, surface wave measurements

Schlieren – p.24/35

Industrial applications

Pattern matching approaches used widelyMpeg encoding of digital moviesObject recognitionRobotics Vision - automatic car parking:

Schlieren – p.25/35

Comments on the pattern matching

So far:

Absolute differences

Cross correlation (full or FFT-based)

Squared differences

Other approaches may be applicable:

Differential approaces (often used in Optical Flow):

��� � � � �� � � �

Intensity (

�

) conservedSmall displacements (generally <1 pixel)

Schlieren – p.26/35

Laser Induced Fluorescence

Schlieren – p.27/35

Laser Induced Fluorescence (LIF)

Idea: Add a visual tracer (indicator) � function ofconcentration

Pankow et al. [1984], Asher and Pankow [1989]

Koochesfahani [1984], Koochesfahani and Dimotakis[1985, 1986]

Walker [1987]

LIF – p.28/35

LIF - howto

Flow illuminated by thin sheet of light formed by a laserand optics

Add fluorescent dyeDye absorbs laser lightre-emits light at longer wavelengthcommonly used dyes: Rhodamine 6G, RhodamineB, Fluorescein Disodium, ++

CCD camera w filter records flowFilter removes all light except the fluorescentThe light intensity directly related todensity/concentration

LIF – p.29/35

LIF - calibration and use

At low concentration levels ( � � ��� � � � �) there is a linearrelationship between signal and dye concentration:

� � � � � where

�

is signal, � a constant,�

concentration and

�

laser light intensity

Calibration consists of determining � at each camerapixel

In use:� � � � � �

The above holds for density measurements - slight difference for temperature

LIF – p.30/35

LIF - some references

Papantoniou and List [1989], Law and Wang [1999] -Buoyant jet. Related to mixing and entrainment of arising buoyant jet (for example discharges fromoil-platforms)

Turbulent jets: Guillard et al. [1998], Westerweel et al.[2002]

Concentration profiles on the air/seainterface: Münsterer and Jähne [1998]

Oxygen concentration in air: Miles and Lempert [1997]

LIF – p.31/35

LIF - some more references

Deusch and Dracos [2001] - 3D field using a scanningmirror system.

Sakakibara and Adrian [1999]:

LIF – p.32/35

LIF - example

Liao and Cowen [2003], motivated by the workof Koehl et al. [2001]

Purpose: how can lobsters smell?How to find the source of polution etcSolve the “inverse problem” of turbulent diffusion inthe environment

Image showing the far-field of a plume:

LIF – p.33/35

LIF - example contd

Koehl et al. [2001] - Lobster sniffing

Rapid flickagainst current

Slow returnalong current

Current

LIF – p.34/35

Summary

Briefly reviewed Schlieren (BOS and ’synthetic’)methods and LIF

Provide quantitative information aboutconcentration/density fields

Non-intrusive, whole-field methods

Generally 2D - but extensions to 3D possible for LIF

LIF – p.35/35

References

W. E. Asher and J. F. Pankow. Direct observation of con-centration fluctuations close to a gas/liquid interface.Chem. Engrg. Sci., 44:1451–1455, 1989.

S. B. Dalziel, G. O. Hughes, and B. R. Sutherland.Whole-field density measurements by ’syntheticschlieren’. Exp. Fluids, 28(4), 2000.

S. Deusch and T. Dracos. Time resolved 3d passive scalarconcentration-field imaging by laser induced floures-cence (lif) in moving liquids. Meas. Sci. Tech., 12,2001.

F. Guillard, R. Fritzon, J. Revstedt, C. Tragard, M Alden,and L. Fuchs. Mixing in a confined turbulent imping-ing jet using planar laser induced fluorescence. Exp.Fluids, 25:143–150, 1998.

F. Klinge, T. Kirmse, and J. Kompenhans. Applicationof quantitative background oriented schlieren (bos): in-vestigation of a wing tip vortex in a transonic wind tun-nel. In Proceedings of PSFVIP-4, Chamonix, June 3-5,2003.

M. A. R. Koehl, J. R. Koseff, J. P. Crimaldi, M. G. Mc-Cay, T. Cooper, M. B. Wiley, and P. A. Moore. Lobster

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sniffing: Antennule design and hydrodynamic filteringof information in an odor plume. Science, 294:1948–1951, 2001.

M. Koochesfahani. Experiments on turbulent mixing andchemical reactions in a liquid mixing layer. PhD thesis,California Institute of Technology, 1984.

M. M. Koochesfahani and P. E. Dimotakis. Laser inducedfluorescence measurements of mixed fluid concentra-tion in a liquid plane shear layer. AIAA J., 23(11):1700–1707, 1985.

M. M. Koochesfahani and P. E. Dimotakis. Mixing andchemical reactions in a turbulent liquid mixing layer. J.Fluid Mech., 170:83–112, 1986.

A. W.-K. Law and H. Wang. Simultaneous velocity andconcentration measurements of buoyant jet dischargeswith combined dpiv and plif. In Jayawardena Lee andWang, editors, Environmental Hydraulics, 1999.

Q. Liao and E. A. Cowen. Experimental investigation onthe growth of a scalar plume in a turbulent boundarylayer. To be submitted, 2003.

G. E. A. Meier. Hintergrund schlierenmessverfahren.Deutsche Patentanmeldung, DE 199 42 856 A1, 1999.

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W. Merzkirch. Flow visualization. Academic Press,1974.

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J. Sakakibara and R. J. Adrian. Whole field measurementof temperature in water using two-color laser inducedfluorescence. Exp. Fluids, 26:7–15, 1999.

B. R. Sutherland, S. B. Dalziel, G. O. Hughes, and P. F.Linden. Visualization and measurement of internalwaves by ’synthetic schlieren’. part 1. vertically oscil-lating cylinder. J. Fluid Mech., 390:93–126, 1999.

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