Tagging molecular clouds in turbulent air

Citation for published version (APA):Mirzaei, M. (2013). Tagging molecular clouds in turbulent air. Technische Universiteit Eindhoven.https://doi.org/10.6100/IR760959

DOI:10.6100/IR760959

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Tagging Molecular Clouds in Turbulent Air

Copyright c⃝2013 Mehrnoosh (Maria) MirzaeiCover: Nimbus Green Room, 2013Cover design: Berndnaut Smilde, courtesy of the artist and Ronchini Gallery(http:www.ronchinigallery.com), London, UK.Printed by CPI-Wöhrmann Print Service, Zutphen, the Netherlands.

CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVENMirzaei, Mehrnoosh (Maria)Tagging molecular clouds in turbulent airby Mehrnoosh (Maria) Mirzaei. - Eindhoven: Technische Universiteit Eindhoven,2013. - Proefschrift.

A catalogue record is available from the Eindhoven University of TechnologyLibraryISBN: 978-90-386-3495-1

Tagging Molecular Clouds in Turbulent Air

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan deTechnische Universiteit Eindhoven, op gezag van derector magnificus, prof.dr.ir. C.J. van Duijn, voor een

commissie aangewezen door het College voorPromoties in het openbaar te verdedigen

op donderdag 21 november 2013 om 16.00 uur

door

Mehrnoosh Mirzaei

geboren te Ghaemshahr, Iran

Dit proefschrift is goedgekeurd door de promotoren en de samenstelling van depromotiecommissie is als volgt:

voorzitter: prof.dr.ir. G.M.W. Kroesen1e promotor: prof.dr. L.P.H. de Goeycopromotoren: dr. N.J. Dam

dr.ir. W. van de Waterleden: prof.dr. J.J. ter Meulen (RUN)

prof.dr. W. van der Zande (RUN)adviseur: dr. E. Calzavarini (Université de Lille)

This work is part of the research programme of the Foundation for FundamentalResearch on Matter (FOM), which is part of the Netherlands Organization forScientific Research (NWO).

Contents

1 Introduction 11.1 The Ubiquitous Nature of Turbulence . . . . . . . . . . . . . . . . . 11.2 Turbulent Flow Diagnostics:

An Experimentalist’s Perspective . . . . . . . . . . . . . . . . . . . . 41.2.1 Mechanical Techniques . . . . . . . . . . . . . . . . . . . . . 41.2.2 Opto-Mechanical Techniques . . . . . . . . . . . . . . . . . . 51.2.3 All-Optical Techniques . . . . . . . . . . . . . . . . . . . . . 6

1.3 Contribution of this thesis . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Turbulent Flows and Molecular Tagging Velocimetry, Basic Facts 92.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Molecular Tagging Velocimetry (MTV) . . . . . . . . . . . . . . . . . 10

2.2.1 MTV: Mechanism A . . . . . . . . . . . . . . . . . . . . . . . 112.2.2 MTV: Mechanism B . . . . . . . . . . . . . . . . . . . . . . . 122.2.3 MTV: Mechanism C . . . . . . . . . . . . . . . . . . . . . . . 122.2.4 MTV: Mechanism D . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Basic Facts of Turbulence . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Interaction with Molecular Diffusion . . . . . . . . . . . . . . . . . 17

2.4.1 Simple Kinetic Description of Tracer Diffusion . . . . . . . . 182.4.2 Tracer Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 Air Photolysis and Recombination Tracking (APART) for Turbulence 253.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2 Rayleigh Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3 APART Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3.1 Molecular Diffusion Experiment . . . . . . . . . . . . . . . . 333.3.2 Intensity Decay of the LIF Patterns . . . . . . . . . . . . . . 333.3.3 Broadening of the LIF Patterns . . . . . . . . . . . . . . . . . 35

3.4 Results of Turbulent Mixing Experiments using APART . . . . . . . 36

6 Contents

3.4.1 Jet-Induced Turbulence Characteristics . . . . . . . . . . . . 363.4.2 Broadening of the tagged patterns in turbulence . . . . . . . 39

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4 Laser-Induced Phosphorescence of Biacetyl Molecules 454.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.2 The Biacetyl Molecule . . . . . . . . . . . . . . . . . . . . . . . . . . 474.3 Experimental Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . 504.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.4.1 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 524.4.2 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5 Lead Atoms as Heavy Flow Tracers 635.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.2 Experimental Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . 655.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.3.1 Lead Emission Spectrum . . . . . . . . . . . . . . . . . . . . 705.3.2 Lead Luminescent Lifetime in Weakly Turbulent Flow . . . 725.3.3 Turbulent Mixing Experiment . . . . . . . . . . . . . . . . . . 755.3.4 Chemical Reaction Test . . . . . . . . . . . . . . . . . . . . . 765.3.5 Intensity Decay and Line Widening . . . . . . . . . . . . . . 80

5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6 Molecular Diffusion and Turbulent Dispersion 856.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866.2 Interaction of Turbulent and Molecular Dispersion . . . . . . . . . . 876.3 Numerical simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 896.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.4.1 Setup and data analysis . . . . . . . . . . . . . . . . . . . . . 936.4.2 Experimental results . . . . . . . . . . . . . . . . . . . . . . . 96

6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 976.6 Derivation of equation for Gaussian blobs . . . . . . . . . . . . . . . 100

Summary 103

Bibliography 105

Acknowledgement 113

Curriculum Vitae 115

Chapter1Introduction

1.1 The Ubiquitous Nature of Turbulence

Turbulent flow of fluid is a fascinating phenomenon, the understanding of whichis one of the most nagging, frustrating and important problems in all of classicalphysics. It is a fact that most fluid flows are turbulent: the smoke of a fire, abruptwind changes, flow of steam, flow inside a jet engine and flow over an airfoil areall examples of turbulence in our daily life. In fact, it pervades many aspects ofour lives such that it becomes very hard not to be intrigued. Furthermore, theproblem’s complexity and our insufficient knowledge, makes it an attractive re-search topic around the globe. The present study aims to further the understand-ing of turbulent flows using an experimental approach. We start this thesis witha brief review of the main highlights in the evolution of ideas associated with theproblem of turbulence and its treatments. In the remaining of this introduction,we will briefly overview a few experimental approaches to the turbulent flowproblem. At the end of this chapter, the outline of this thesis will be presented.

It appears that turbulence was already recognized as a distinct fluid behav-ior by at least 500 years ago, by the time of da Vinci, who in 1507 named thephenomenon he observed in swirling flow “la turbolenza”, described in the fol-lowing picture: “Observe the motion of the surface of the water, which resemblesthat of hair, which has two motions, of which one is caused by the weight of thehair, the other by the direction of the curls; thus the water has eddying motions,one part of which is due to the principal current, the other to the random andreverse motion” [72]. Yet there seems to have been no substantial progress in un-derstanding turbulence until the late 19th century, beginning with Boussinesq inthe year 1877. His hypothesis [8] that turbulent stresses are linearly proportionalto mean strain rates is still the cornerstone of most turbulence models. Osborne

2 1.1 The Ubiquitous Nature of Turbulence

Reynolds was the first to systematically investigate the transition from laminar toturbulent flow by injecting a dye streak into flow through a pipe having smoothtransparent walls. In his seminal paper [70] of 1894, he clearly distinguishedbetween two possible flow regimes, laminar and turbulent and argued that thedimensionless parameter which controlled the transition from one regime to theother had to be [47]

Re =ρUL

µ=

ULν

, (1.1)

which is now called the “Reynolds number”. In this equation, ρ is the densityof the fluid, µ the dynamic viscosity of the fluid, ν the kinematic viscosity of thefluid, U the velocity scale (i.e., the mean flow down the pipe) and L is a typicallength scale (i.e., the diameter of the pipe). Therefore, Re expresses the relativeimportance of inertial and viscous forces.

Following Reynolds’ introduction of the random nature of turbulence and hisproposed use of statistics to describe turbulent flows, essentially all subsequentanalyses continued along these lines. The next major steps in the analysis ofturbulence were taken by G. I. Taylor during the 1920s. In his 1935 paper [81],Taylor very explicitly presented the assumption that turbulence is a random phe-nomenon and then proceeded to introduce statistical tools for the analysis of ho-mogeneous, isotropic turbulence [47]. Taylor proposed a probabilistic-statisticalapproach based on averaging over ensembles of individual realizations, althoughhe soon replaced ensemble averages by time averages at a fixed point in space.The assumption that they are equivalent is nowadays called the “Taylor hypothe-sis”. Taylor also used the idealized concept (originally introduced by Lord Kelvinin 1887) of statistically homogeneous, isotropic turbulence. Homogeneity andisotropy imply that spatial translations and rotations, respectively, do not changethe average values of physical variables [16]. Lewis F. Richardson was anotherinfluential fluid dynamicist of the early 20th century. Richardson performed thefirst numerical computation for predicting the weather condition (on a hand cal-culator!). He also proposed (1926) a pictorial description of turbulence called a“cascade”, in which nonlinearity transforms large-scale velocity circulations (oreddies, or whorls) into circulations at successively smaller scales (sizes) until theyreach such a small scale that the circulation of the eddies is efficiently dissipatedinto heat by viscosity. Richardson captured this energy cascade in a poetic take-off as follows [71]:

“Big whorls have little whorls,which feed on their velocity,And little whorls have lesser whorls,And so on to viscosity.”

Introduction 3

A. N. Kolmogorov followed Richardson’s idea of the energy transport fromlarge to small eddies. He wrote only few papers on turbulence theory, most ofthem in the decade from 1940 to 1950 [33, 34, 35, 36, 37]. In all, they contain lessthan thirty pages, but their influence on the field has been so profound that it isa source of permanent wonder to fluid mechanicists to learn that Kolmogorov isknown preliminary as a statistician by most scientists. Since all the investigationsin this thesis are based on Kolmogorov theory of turbulence, we will discuss itin detail in Chapter 2; for now, we shall continue with the problem of turbulenceand its possible treatments.

The equation, which is now almost universally believed to embody the physicsof all fluid flows (within the confines of the continuum hypothesis), including tur-bulent ones, is called “The Navier–Stokes Equation”, and was introduced in theearly to mid 19th century by George Stokes in England and Claude-Louis Navierin France. This equation for a fluid with constant density ρ and constant kine-matic viscosity ν is

∂u∂t

+ (u · ∇)u = −∇Pρ

+ ν∇2u, (1.2)

with ∇ · u = 0, which is a statement of fluid incompressibility and with suitableconditions imposed at the boundaries of the flow. The variable u(x, t) is the (in-compressible) fluid velocity field, and P(x, t) is the pressure field determined bythe preservation of incompressibility [47]. The Navier-Stokes equation is basedon the following assumptions:

• Newton’s second law applied to a continuum;

• a constitutive law, called Newton’s law of viscosity, which relates shearstresses in a fluid to the rate of distortion of fluid elements;

• the conservation of mass (i.e., what flows in must flow out).

Thus, the left side of equation 2 is the acceleration of the fluid, and the rightside is the sum of the forces per unit mass on a unit volume of the fluid: thepressure force and the viscous force arising from momentum diffusion throughmolecular collisions. Remarkably, a deceptively simple equation representing asimple physical concept describes enormously complex phenomena. Neverthe-less, the equation is too hard to be solved analytically for most situations, al-though numerical attempts have proved that a global solution (i.e., valid for alllater times) exists, but may not be unique, and it has been proved that unique so-lutions exist which may not be global (i.e., they are guaranteed to exist as uniquesolutions only for a finite time) [74]. Therefore the problem of investigating tur-bulent mixing at Kolmogorov scale is essentially still open.

41.2 Turbulent Flow Diagnostics:

An Experimentalist’s Perspective

1.2 Turbulent Flow Diagnostics:An Experimentalist’s Perspective

Thus far, we discussed the theoretical and numerical perspective of the turbu-lence problem. In fact, comprehensive theoretical and numerical models andsimulations have been developed during past decades, to the stage of being ableto quantitatively predict turbulence. However, in order to validate and furtherdevelop efficient numerical models, there is a continuous need of experimentaldata. In this section, an overview is given of various experimental approaches tothe turbulence problem.

1.2.1 Mechanical Techniques

Two major mechanical instruments used for flow velocity measurements are PitotTube and Hotwire Anemometer. The Pitot tube (named after Henri Pitot in 1732)measures a fluid velocity by converting the kinetic energy of the flow into po-tential energy. It uses a differential pressure principle for the measurement usingthe known or measured static pressure and total pressure differences known asthe dynamic pressure. Pressure can be measured using a manometer or pressuretransmitter. The device is also known as the “Prandtl Tube”. The advantages ofa standard Pitot tube are ruggedness, small finite area, reliability and ability toperform in dusty, corrosive and hot atmospheres. For example, it is used in in-dustry to measure the velocities in ducts and tubing, where measurements by ananemometer would be difficult to obtain. The Pitot tube can be inserted througha small hole in the duct with the Pitot connected to a U-tube water gauge or someother differential pressure gauge for determining the velocity inside the ductedwind tunnel. However, its main disadvantage is its lack of precision at low ve-locities, below 3.5 m/s [23].

The hot-wire anemometer consists of a sensor (a small electrically heated wireexposed to the fluid flow), and of electronic equipment, which performs thetransformation of the sensor output into a useful electric signal. As the fluidvelocity increases, the rate of the heat flow from the heated wire to the flow in-creases. Thus, a cooling effect on the wire occurs, causing its electrical resistanceto change. Typical dimensions of the heated wire are 5 µm in diameter and 1 to3 mm in length. Some advantages of this technique are good spatial resolution(measures the flow in a precise location), quick response to changes in the flow(with appropriate control circuitry) and two-phase flow measurement capability.On the other hand, it is quite a costly technique, orientation sensitive, fragile andthe “wire” can accumulate debris in a dirty flow, break or burn [13].

Introduction 5

In conclusion, mechanical techniques are in general “intrusive techniques”, asthey need to be inserted at the exact location in the flow in order to be able tomeasure the flow parameters, thus, they perturb the flow characteristics.

1.2.2 Opto-Mechanical Techniques

Opto-mechanical techniques do not rely on photonics alone for flow measure-ments but require macro-size seeding (i.e., injection of tracers). The two mostcommon ones for turbulent flow diagnostics are Particle Image Velocimetry (PIV)and Laser Doppler Anemometry (LDA).

Particle Image Velocimetry (PIV) is a whole–field technique providing instan-taneous velocity vector measurements in a cross-section of a flow. A pulsed lasersheet illuminates small seeding particles carried by the flow. The positions of par-ticles during two consecutive laser pulses are recorded by a double-frame CCDcamera. Local flow velocity is calculated from displacement of the particles be-tween the two light pulses. The whole flow field is divided into elementary cells(interrogation windows), in which the average displacement of particles is calcu-lated on the basis of cross-correlation analysis. The dynamic range of measuredvelocities depends on the time between pulses. The technique is applicable tovelocities ranging from millimeters per second up to transsonic.

In LDA, the flow is seeded with small, neutrally buoyant particles that scatterlight. The particles are illuminated by monochromatic laser light. The scatteredlight is shifted in frequency due to the particle motion, and the beat frequencyis detected by a photomultiplier tube, an instrument that generates a currentin proportion to absorbed optical power, and then amplifies that current. Themotion-coordinated difference between the incident and scattered light frequen-cies is called the “Doppler shift”.

PIV and LDA, as essentially non-intrusive techniques, can be applied to highspeed and boundary layer studies of fluids. An advantage of PIV compared toother velocimetry techniques is that it allows the direct measurement of eithertwo or three-dimensional instantaneous velocity vectors over a planar domain.However, as with all measurement techniques, there are several uncertainties thatcan, if not mitigated, degrade the quality of a PIV-LDA experiment. A fundamen-tal issue here is the “bias error”. In brief, velocity bias is caused by the larger pas-sage rate through the measurement volume of fast tracer particles than of slowones. In case of a time-dependant velocity field, averages will bias towards thelarger velocities. Although random errors also exist in PIV-LDA experiments,they can be rendered negligible when the PIV-LDA fields are averaged in eitherspace or time over a suitably large ensemble. Bias errors, on the other hand, arecertainly not random in space and time and can therefore degrade not only the

61.2 Turbulent Flow Diagnostics:

An Experimentalist’s Perspective

accuracy of instantaneous PIV-LDA results, but also any statistic computed frombiased PIV-LDA ensembles. Among all non-avoidable bias errors in a PIV-LDAmeasurement, “peak locking”, the biasing of particle displacements toward in-teger pixel values, is one of the most significant ones. It is attributable to boththe choice of sub-pixel estimator and under-resolved optical sampling of the par-ticle images [12]. Furthermore, in both techniques, the size of the interrogationarea should be small such that there is no significant velocity gradient within theinterrogation area.

1.2.3 All-Optical Techniques

The two major all-optical flow measurement techniques are called Molecular Tag-ging Velocimetry (MTV) and Filtered Rayleigh Scattering (FRS) techniques. Thechief advantage of these techniques is that they do not require seeding of externalparticles at all, but rely on light scattering off the molecules making up the flowthemselves.

Molecular Rayleigh scattering (RS) is the result of quasi-elastic light scatter-ing off (gas) molecules. When light from a single frequency laser beam passesthrough a gas, the scattered light is shifted in frequency by the Doppler effectdue to both the bulk motion of the molecules and the random (thermal) motionof individual molecules. The optical frequency spectrum contains informationabout the flow density, bulk velocity and temperature. One of the main disad-vantage of the technique is that the Doppler shifts are very small with respectto the wavelength of the incident light; the technique thus needs sophisticatedspectral filtering [54].

Whereas FRS can be thought of as a molecular variant of LDA, being based onDoppler shifted scattered light, MTV is displacement-based, and kind of a molec-ular variant of PIV. MTV relies on molecules that can be turned into long lifetimetracers upon excitation by photons of an appropriate wavelength. Typically, apulsed laser is used to “tag” the regions of interest, and those tagged regions areinterrogated at successive times within the lifetime of the tracer. The measuredLagrangian displacement vector provides the estimate of the velocity vector. Thistechnique can be thought of as essentially the molecular counterpart of ParticleImage Velocimetry (PIV) and complements it where the use of seed particles iseither not desirable or may lead to complications connected to tracking the flow,density mismatch, particle seeding density or strong out-of-plane motions [38].Since all measurements of this thesis were performed using the MTV technique,we shall discuss the principles and points of argument in detail in Chapter 2.

Introduction 7

1.3 Contribution of this thesis

The small scales of turbulence are elusive due to lack of experimental access. Inthis study, we specifically address this lacuna by performing molecular mixingstudies down to the smallest relevant scales in a strongly turbulent flow, with theultimate goal of not being thwarted by molecular diffusion. To achieve this goal,we performed a systematic survey of the available options. “Red Thread” of thestudy is the quest for suitable MTV tracers.

As mentioned, the objective of this study was to find a suitable tracer to beused in our laser diagnostics experiments of gas-phase turbulent fluids at verysmall scales, i.e., scales of the order of Kolmogorov length scale. The introduc-tion presented in this chapter was intended to review the turbulence problem ingeneral and current experimental treatments to the problem. To find the suitablecandidate for our purpose, we first investigated the basic physics of the molecu-lar diffusion and turbulent dispersion and listed the ideal tracer’s characteristics.Chapter 2 provides a summary of this literature study, which also intends tomotivate the need for this laboratory study and the potential usefulness of the re-sults. Molecular tagging velocimetry technique, as the cornerstone of this thesiswill be elaborated in Chapter 2 as well.

In Chapter 3 we studied turbulent mixing phenomena using a recently in-vented scheme called APART (Air Photolysis And Recombination Tracking). It isa molecular tagging velocimetry scheme based on creating nitric oxide (NO) mo-lecules out of O2 and N2 molecules in the focus of a strong UV laser beam. Despiteall of its advantages, which will be discussed in Chapters 2 and 3, APART suffersfrom very light molar mass of its tracers, NO molecules. To overcome this prob-lem, based on the theory explained in Chapter 2, we started to search for heaviertracers to be used in combination with heavier gases as carrier flow.

The results of flow measurements using heavier tracers are presented in thenext two chapters. Chapter 4 is dedicated to the investigation of the applicabilityof biacetyl as a tracer for our jet-turbulence experiments. For this purpose, someexperiments were done to find the optimal experimental conditions, which shedmore light on the suitability of biacetyl. Although there has been a modest up-surge in the investigation of biacetyl properties for flow diagnostics, especiallyconcerning its laser-induced fluorescence and phosphorescence characteristics,all of these were limited to demonstrating a “proof of principle”. Our researchhas uncovered a few fundamental limitations, which imply that biacetyl may notbe an applicable tracer for many laser diagnostics turbulence experiments afterall.

Since the results of our measurements using biacetyl as a tracer revealed thata phosphorescent molecule might not be an ideal option for our study, we con-

8 1.3 Contribution of this thesis

tinued our tracer exploration on atoms. In fact, atoms lack both vibrational androtational degrees of freedom, so the electronic transition strength is concentratedin a single transition and makes the excitation/detection process much easier.Considering all of the requirements, we investigated heavy metal compounds,with the idea of photodissociating the compound and unleashing the heavy metalatom in the first step, and conducting laser-induced florescence measurementson the created atom in the second step. In Chapter 5, we present the first andpreliminary results of turbulent mixing phenomenon using “lead nitrate” mole-cules as tracers. Our research showed that lead atoms could potentially be usedas tracers for laminar and turbulent flows diagnostics measurements. In fact,their quite high molecular weight (207 g/mol) and fair chemical reactivity makethem a good candidate for gas phase flow study. Nevertheless, the result of thisstudy can only be considered as a first step investigation to their applicability forMTV measurements in weakly turbulent flows. More measurements consideringpractical adjustments, especially the seeding mechanism, are needed for a solidconclusion on their suitability for our purpose.

Following the discussion on the dispersion of written lines in Chapter 2, wepresented the results of a numerical study in Chapter 6. Our study showed that asimple linear equation can be written for the evolution of the size of tiny Gaussianpuffs in a turbulent flow field. The question there is if this can predict wideningof lines written using the APART technique. To this aim, the linear evolutionequation is integrated in a numerical turbulent velocity field, which is publiclyavailable as a database.

This thesis come to an end with a Summary, which is dedicated to summariz-ing the main features presented in the thesis and rendering the final conclusionson the turbulence mixing phenomena at Kolmogorov scale. Suggestions for fu-ture upgrades of the turbulent flow diagnostics, using MTV technique are alsoprovided in this chapter.

Chapter2Turbulent Flows andMolecular Tagging

Velocimetry, Basic Facts

10 2.1 Introduction

2.1 Introduction

In this chapter, we elaborate on Molecular Tagging Velocimetry (MTV) technique,as the cornerstone method on which this study is based. We will demonstrate thatMolecular Tagging Velocimetry allows us to create flow tracers in user-specifiedpatterns at user-specified locations in space and time, and provide a relativelycomprehensive list of different MTV mechanisms including supporting and op-posing arguments.

It worth noting that unlike tracer particles which have a macroscopic size,molecular tracers diffuse. It will turn out that understanding the competitionbetween molecular diffusion and turbulent dispersion is important for MTV im-plementation, therefore, we will end this chapter with a brief description of dif-fusion.

2.2 Molecular Tagging Velocimetry (MTV)

Molecular tagging velocimetry (MTV) is an all-optical technique to measure fluidflow velocities without particle seeding. An impression of the state-of-the-art canbe obtained from the collection of papers written by Koochesfahani [33, 38, 39].The basis of this all-optical technique consists of two steps: in the first step, anensemble of molecules (a line or a grid) is labeled such that it is different fromthe carrier gas. This ensemble will then move with the flow and will be de-formed by its gradients. The second step is then visualizing the tagged mole-cules, which gives information on the location of the molecules. With the initialposition known, a velocity can be assigned to each point of the ensemble.

In fluid mechanics, there are several very accurate and proven methods for ve-locimetry, so there should be some good reasons to explore a new technique likeMTV. Indeed, as MTV has some major advantages in comparison to other (rathertraditional) techniques like Particle Image Velocimetry (PIV), Laser Doppler Ane-mometry (LDA) and hot-wire velocimetry. First of all, MTV techniques haveproven to allow measurements of velocities in inhospitable environments, likejet engines and high pressure vessels while techniques like pitot and hot-wirevelocimetry and PIV will not, or barely, work under these circumstances. Mostother possible advantages arise from the freedom of being able to create tracersat the desired location and the desired instant. As mentioned in Section 1.2.2,traditional optical velocimetry suffers from the problem of velocity bias whilemolecular tagging velocimetry technique allows us, in theory, to write patternsat will. In brief, velocity bias is caused by the larger passage rate through themeasurement volume of fast tracer particles than of slow ones. In case of a time-

Turbulent Flows and Molecular Tagging Velocimetry, Basic Facts 11

dependent velocity field, average will bias towards the larger velocities.This means that we are not dependent on particles that traverse the measure-

ment volume, but instead we have comparable control of the position and timeat which tracers are introduced to the flow. This makes the MTV technique, otherthan LDA and PIV [88], insensitive to velocity bias errors. Furthermore, standardtechniques like hot-wire velocimetry and LDA are point-wise measurements. Inorder to measure space-dependent spatial structures, their usage is based on Tay-lor’s hypothesis of frozen turbulence. In this hypothesis, one assumes that theadvection caused by turbulence to be negligible and therefore the advection ofturbulence past a fixed point may be taken to be entirely caused by the meanflow; spatial structures can thus be derived from time-dependent signals. How-ever, fluctuations of the convecting velocity and several other phenomena cancause distortion of statistics that result from the usage of Taylor’s frozen tur-bulence. These distorting phenomena have been discussed by Fisher et al [19],Lumley [82] and others. With MTV, we are capable of measuring true spatiallyseparated velocities.

Let us now elaborate on different types of MTV techniques. Different MTV ap-proaches can be categorized in four mechanisms. In this section, we will brieflydiscuss these mechanisms and their probable advantages and disadvantages. Thefundamentals of these four mechanisms can be found in Fig. 2.1. As can be seen,all mechanisms are based on the chemistry of molecules in electronic excitedstates, so the difference comes from the different detection approaches.

2.2.1 MTV: Mechanism A

Let us start with mechanism A, which is called Laser-Induced PhotochemicalAnemometry (LIPA) and has been originally introduced by Miller [55] for vi-sualizing flows. It relies on measuring the absorbance of an image produced bya photochromic dye. This dye is turned absorbing by illumination using a laser,after which the written pattern is distorted and translated by the moving fluid.Using of photochromic chemicals requires two photon sources (two lasers), onefor writing the absorbing dye pattern, and one for visualizing the deformed pat-tern.

LIPA has been mostly used for liquid phase flow diagnostics, due to the largesize and mass of the photochromic dye molecules. The advantages of this tech-nique are the long lifetime and reversibility of the tracers. However, becausethe image is produced by a change in absorbance, the difference between inci-dent and transmitted light must be measured, which dramatically complicatesthe data collection and analysis process.

12 2.2 Molecular Tagging Velocimetry (MTV)

Figure 2.1: K and K∗ refer to the molecule at ground and electronic excited staterespectively, while N indicates the formation of a new molecule. Solid arrows depictradiative transitions and wavy arrows depict non-radiative ones. ISC refers to inter-system crossing [39].

2.2.2 MTV: Mechanism B

Mechanism B, known as Raman Excitation plus Laser-Induced Electronic Fluo-rescence (RELIEF) was initially designed by Miles and co-workers [50, 51, 52, 59]for unseeded air flow diagnostics. In RELIEF, vibrationally excited oxygen is cre-ated by Stimulated Raman Scattering (SRS) and functions as tag. Since this vibra-tionally excited oxygen molecule is long-lived, it can be excited to an electronicexcited state, the relaxation of which is an emissive process and can be interro-gated. The requirement of three frequencies (i.e., two for tagging and one to inter-rogate) makes RELIEF one of the most sophisticated MTV techniques, however,it has been successfully used for gas phase flow diagnostics [53].

2.2.3 MTV: Mechanism C

For mechanism C, there are various possibilities due to the production of dif-ferent N species (see Fig. 2.1). PHANTOMM, first introduced by Lempert etal. [42, 43, 44, 45], is an acronym for Photo-Activated Non-intrusive TrackingOf Molecular Motion. This mechanism is for liquid and gas phase flow diag-nostics. In fact, PHANTOMM is the luminescent counterpart for LIPA. In bothtechniques, an initial excitation is used to produce a tracer. In LIPA the tracer

Turbulent Flows and Molecular Tagging Velocimetry, Basic Facts 13

is absorbing, and hence tracked by the detection of transmitted light, whereasin PHANTOMM the tracer is tracked by detecting emitted light. Since the dyemolecule can be excited multiple times, multiple photons can be detected from anindividual activated dye over time durations which are short with respect to thefluid motion. However, the luminescent dye is produced irreversibly by cleavageof a covalent bond, therefore the tracer can be used just once. Another techniquebased on mechanism C is called Hydroxyl Tagging Velocimetry (HTV) and hasoriginally been introduced by Pitz and co-workers [65, 66, 67]. In this technique,OH radicals are produced by single-photon dissociation of vibrationally excitedwater molecules, the OH is subsequently visualized by LIF. Their technique hasbeen implemented in H2-air flames [86]. In another technique, called Ozone Tag-ging Velocimetry (OTV), Pitz and co-workers created ozone from oxygen mole-cules [65, 67, 85], which needs two sources of photons.

The creation of NO by irradiating air is another example of mechanism C. Theadvantage of this tracer in comparison to other small tracers is its stability andlong lifetime, that is of the order of seconds, and it can therefore be implementedin relatively slow flow experiments. Nitric oxide can be produced in several dif-ferent approaches, by dissociating NO2 molecules in the focus of a 308 nm XeClexcimer laser [62], by dissociation of tert-butyl nitride [40], or by irradiating airwith an intense ArF laser beam. The latter is known under the acronym of APART(Air Photolysis And Recombination Tracking), and has been developed in ourgroup over the last ten years [7, 15, 79, 84]. Within mechanism C, one can also in-clude the reverse approach such as photobleaching, where instead of releasing aluminescent tracer, a non-luminescent species is produced from fluorescent dyes,thereby creating a “negative” image. Another technique of this type (negativeimage) is based on using Laser-Enhanced Ionization (LEI) method, which relieson the excitation of an atom or molecule to an excited state near to its ionizationlimit. A second photon then is needed to ionize the atom or molecule, thus pro-ducing a depletion of the neutral species, which is typically fluorescent. As wealready mentioned, bright background makes the implementation and data anal-ysis of techniques based on “negative images” quite challenging and limits theoverall dynamic range of the approach; nevertheless, MTV experiments based onthese techniques have been successfully conducted [73, 76].

2.2.4 MTV: Mechanism D

Mechanism D, which is sometimes considered as the most straightforward tech-nique in MTV, is based on phosphorescence. In fact, among all other taggingmethods, the use of phosphorescent molecules as tracers has some advantages.In this mechanism, a single laser is used to produce a luminescent excited state

14 2.3 Basic Facts of Turbulence

and the image can be detected by directly monitoring long-lived phosphores-cence from the tracer upon its radiative return to its ground state. The overallapproach of mechanism D is very similar to LIF (Laser Induced Fluorescence)whereas here the tracer has a long lifetime which permits sufficient displacementof the luminescent tagged regions. The emission of a photon returns the moleculeback to its ground state, from which the tracer may be re-excited, thus the tracer isre-usable. However, all of these molecules have a limited luminescence lifetime,which is a serious restriction for turbulence measurements.

Another disadvantage of techniques based on mechanism D is the reactionwith other molecules. In fact, quenching is an issue pervading most measure-ments and the most problematic quencher in engineering applications is oxygen.Although, one can make unquenchable tracers by connecting small molecularsubunits for liquid-phase flow diagnostics [56, 58, 64], when it comes to the gas-phase flow diagnostics, the number of possible suitable candidates shrinks dra-matically. Among a few suitable candidates, biacetyl and acetone are two famousand more applicable ones.

2.3 Basic Facts of Turbulence

As mentioned in Chapter 1, the objective of this study was to find a suitable tracerto be used in our laser diagnostics experiments of gas-phase turbulent fluids atvery small scales, i.e., scales of the order of Kolmogorov length scale. We dis-cuss the general characteristics of turbulent flows and Kolmorogov theory in thissection.

Providing an accurate definition of turbulence is quite tough, but what seemsto be generally agreed upon is that: “turbulence is a chaotic flow, i.e., a flow whichis sensitive to its initial conditions”; however the term “chaotic” does not implypurely stochastic (non-deterministic); indeed, it is argued that turbulence is de-terministic (i.e., the current state permits prediction of a future state) because theNavier-Stokes equations are deterministic, although the time scale for predictionmay be extremely short. A more definitive and precise definition of turbulencemay only come, when the phenomenon is fully understood. Nevertheless, sev-eral characteristic properties of a turbulent flow can be listed as below:

Irregularity and Unpredictability: A turbulent flow is irregular both in spaceand time, displaying unpredictable, random patterns.

Statistical Order: From the irregularity of a turbulent motion, there emergesa certain statistical order. Mean quantities and correlations are regular and pre-dictable.

Wide Range of Active Scales: A wide range of scales of motion are active and

Turbulent Flows and Molecular Tagging Velocimetry, Basic Facts 15

display an irregular motion, yielding a large number of degrees of freedom.Mixing and Enhanced Diffusivity: The fluid particles undergo complicated

and convoluted paths, causing intense mixing of different parts of the fluid. Thismixing significantly enhances diffusion, increasing the transport of momentum,energy, heat, and other advected quantities.

Vortex Stretching: When a moving portion of fluid also rotates transversallyto its motion, an increase in speed causes it to rotate faster, a phenomenon called“vortex stretching”. This causes that portion of fluid to become thinner and elon-gated, and fold and intertwine with other such portions. This is an intrinsicallythree-dimensional mechanism which plays a fundamental role in turbulence andis associated with large fluctuations in the vorticity field [74].

To appreciate Kolmogorov’s phenomenological description of turbulence, letus start with introducing the concept of an eddy, which is a patch of fluid concep-tually separated from the rest of the flow, with a size l and a characteristic internalvelocity difference ul. As this eddy moves with the flow, it will be influenced bytwo types of forces: inertial forces and the viscous forces. The ratio of these twoforces is represented by a dimensionless value called the “Reynolds number”:

Re =Inertial forcesViscous forces

=ul lν

, (2.1)

when Re ≪ 1, the inertial forces are negligible, i.e., the analytic solution to theNavier-Stokes equation corresponding to laminar flow can often be found. Onthe other hand, in case of Re ≫ 1, the fluid flow is highly fluctuating in space andtime, corresponding to turbulent flow, i.e., there are no stable stationary solutions.

The significance of Kolmogorov’s insights was to recover Richardson’s ideathat eddies could be arranged in a hierarchy of sizes, along which they decayedinto one another. For large Reynolds numbers, the nonlinear term dominatesthe viscosity according to the dimensional analysis, but this is valid only for thelarge-scale structures. Kolmogorov remarked that the smaller members of this hi-erarchy are so far removed from the forces that maintain turbulence at the largestscales that they should eventually become independent of the mechanism, as wellas statistically homogeneous and isotropic. In this cascade process, the inertialterm is responsible for the transfer of energy to smaller and smaller scales untilsmall enough scales are reached for which viscosity becomes important. At thosesmallest scales, kinetic energy is finally dissipated into heat. He then proposedthat the statistical regime of these small-scale eddies is universal; the “equilib-rium range” is defined as the range of scales in which this universality holds.Figure.2.2 illustrates the eddy breakdown process in which energy is transferredto smaller eddies and so on until the smallest scales are reached and the energyis dissipated by viscosity.

16 2.3 Basic Facts of Turbulence

Stirring

l0

h

Flow of

energy

Molecular dissipation

Figure 2.2: The Energy Cascade Picture of Turbulence. This figure represents a one-dimensional simplification of the cascade process The eddies are purposely shown tobe “space filling” in a lateral sense as they decrease in size.

Kolmogorov noted next that the largest eddies in a turbulent flow, whosecharacteristic scales are defined as the “integral length” l0 and velocity ul0 , haveReynolds numbers of the order of that of the flow, which is always large in tur-bulence; viscosity is therefore “unimportant” in their evolution and they do notdissipate energy. As a consequence, their energy needs to pass to other scalesof the representation when the eddies break up. He assumed that in the inertialrange eddies with length scale l transfer kinetic energy to smaller eddies dur-ing their characteristic time scale, also known as “circulation time”. If ul is theircharacteristic velocity, then τl = l/ul is their circulation time, so that the kineticenergy transferred from these eddies during this time is [74]

ε ∼u2

lτl

=u3

ll

. (2.2)

In statistical equilibrium, the energy lost to the smaller scales equals the energygained from the larger scales, and that should also equal the total kinetic energydissipated by viscous effects. Hence, ε l = ε and

ε ∼u3

ll

. (2.3)

In three-dimensional turbulence, the energy is transferred from larger to smallerscales, continuously decreasing the Reynolds number of the eddies until the pointat which [82]

Re =ulν

= 1. (2.4)

Turbulent Flows and Molecular Tagging Velocimetry, Basic Facts 17

At this point, viscosity becomes important and the energy is dissipated. Thesmallest length scale, l = η, (“Kolmogorov length”) and the smallest velocityscale of these viscous eddies, u = vk, (“Kolmogorov velocity”) can then be com-puted from equations 2.3 and 2.4 as follows

η =

(ν3

ε

)1/4

(2.5)

andvk = (νε)1/4. (2.6)

The turnover time of the eddy (“Kolmogorov time”), is then

τη =η

vk=

(ν

ε

)1/2. (2.7)

In summary, at these time and length scales (τη, η), viscous dissipation balancesthe energy flux ε, and the velocity field is smooth.

It is worth noting that velocimetry is used to measure gradients in turbulence,for example to measure Reynolds stresses. For this purpose, the velocity fieldmust be resolved to scale η. As in MTV velocities are inferred from displacements,these displacements must be measured during time intervals not longer than τη.In the next two sections we will discuss issues regarding time intervals in moredetail.

2.4 Interaction with Molecular Diffusion

Imagine we write a line of tagged molecules with a Gaussian cross section, n(r) ∝exp(−r2/∆2). If the width of the line, ∆, would be smaller than the Kolmogorovlength scale, η, the line will be wrinkled due to the turbulence, with the smallestwrinkles having size η. At the same time, this line will broaden due to moleculardiffusion. The final line width can be computed as follows

∆2 = ∆20 + 4Dt, (2.8)

with ∆0 as the initial line width, t as the time interval between the writing andreading of the line, and D as diffusion constant. In the case of MTV, tagged mo-lecules diffuse into the gas of untagged ones. If tagged molecules have a simi-lar weight and size as the other molecules, the diffusion of mass approximatelyequals the diffusion of momentum. This ratio

ν/D = Sc (2.9)

18 2.4 Interaction with Molecular Diffusion

is known as the “Schmidt number”, with ν as the kinematic viscosity of the fluidand D as the molecular diffusion. In normal gases like air, the Schmidt numberis of the order of unity. This has a remarkable consequence on the observabilityof the smallest eddies in turbulence: wrinkles in material lines that are due tothe smallest eddies will always be blurred by diffusion. Now let us compute thewidening of a line after one small-eddy turnover time τη

∆(τη) = (4Dτη)1/2 = (4ν|Sc|−1τη)

1/2 = (4ν|Sc|−1(ν/ε)1/2)1/2 = 2η|Sc|−1/2.(2.10)

Therefore, if Sc ≤ 1, after one smallest-eddy turnover time (τη), the width ofthe line (the radius of the object), will always be at least twice as the Kolmogorovlength, which irons out wrinkles of that size. This simple fact implies that thesmall scale in any turbulent flow remains unresolved. This implies that for trac-ers with Schmidt number equal to one, velocimetry is possible, but the velocityfield is always seen through the filter of molecular diffusion. In other words, inturbulence, we are sensitive to the velocity fluctuations on inertial-range scalesonly. The case of Schmidt number one tracers in air is special, it stands both forthe dispersion of small tracer molecules and for the diffusion of heat. Still, bothfor velocimetry and for the study of turbulent mixing, it would be extremely de-sirable to be able to alter the Schmidt number. This will allow us to resolve thevelocity field down to smaller scales, and to study turbulent mixing in anotherregime of Schmidt numbers. In the next two sections, we will investigate the roleof molecular diffusion effect on finding the ideal tracer (and technique) to be usedin our laser diagnostics study of turbulent fluids.

2.4.1 Simple Kinetic Description of Tracer Diffusion

In this section, we discuss an elementary treatment of mutual diffusion using themomentum–transfer method [68]. Assume a mixture of two ideal gases, in whichwe call gas type 1 and gas type 2. When there is a gradient in the concentrationof a constituent, there is a gradient in the partial pressure of each gas (becausepi = nkBT), while the total pressure p = p1 + p2 must remain constant. Nowconsider a thin “slice” of gas of unit area and thickness |dz| in the case of one–dimensional diffusion along the z−direction. The gas of type 1 contained in theslice is subject to a net force dp1 in the z direction, which corresponds to a changein the total z component of momentum of the molecules of type 1. Since there isno motion of the gas as a whole, viscous shear stresses are not set up; meaningthat there will be no variation in the transport velocity of either type of moleculeat right angles to the concentration gradient, and no transport of z momentum inthe x or y directions.

Turbulent Flows and Molecular Tagging Velocimetry, Basic Facts 19

At atmospheric pressures, when the mean free path is much smaller than thedimensions of the apparatus, collisions with the walls are very infrequent com-pared to collisions with other molecules of the gas. The total z component ofmomentum of the molecules of type 1 in the thin slice is unaltered by (elastic)collisions between type 1 molecules according to the law of conservation of mo-mentum. We conclude that the net force dp1 is entirely associated with the ex-change of z momentum between gas 1 and gas 2. As a result of unlike moleculescollisions, there will be a net transfer of z momentum from one gas to the other,and the net force dp1 is equal to the transfer taking place per unit time in thethin slice. Correspondingly, dp2, which is equal to −dp1, represents the reactionforce of the second gas. If we denote by M12 the average amount of z momentumtransferred from gas 1 to gas 2 per unit of volume and per unit of time, it followsthat

dp1 = kBT dn1 = −M12 dz. (2.11)

The momentum–transfer treatment of mutual diffusion is based on this equa-tion and involves a kinetic expression for M12. We now calculate the averagenumber of unlike collisions taking place in unit volume per unit time and the av-erage momentum transferred per collision between unlike molecules. The prod-uct of these two averages will represent M12 approximately but not exactly, sincethe average of a product is not in general equal to the product of the averagevalues of the factors.

Now consider a molecule of type 1 moving among molecules of type 2 withdensity n2. Denoting the molecular diameters by σ1 and σ2, we see that the crosssection of the sphere of influence for unlike collisions is πσ2

12 where σ12 = (σ1 +

σ2)/2 is the average molecular diameter. The number of collisions per unit timebetween molecule 1 of gas 1 flying with average relative velocity v12 through gas2 is n2 πσ2

12v12. Therefore, the number of all collisions of molecule 1 per unit timeand per unit volume is

n1 n2 v12πσ212. (2.12)

We take the simple approach that on average the relative velocity is

v212 = ⟨(v1 − v2)

2⟩ = ⟨v21⟩+ ⟨v2

2⟩ = kBT(m−11 + m−1

2 ) =kBTm∗

, (2.13)

with m∗ the reduced mass, m∗ = (m1 m2)/(m1 + m2).We next consider the average momentum transferred in a collision between

two unlike molecules. Let us denote by u1 the (macroscopic) diffusive transportvelocity of gas 1. If the diffusion takes place in the z direction, then u1 is themean z−component of the velocity of molecules 1. These transport velocities

20 2.4 Interaction with Molecular Diffusion

must satisfy the constraint that there is no net flow of molecules

n1 u1 + n2 u2 = 0. (2.14)

Momentum is transfered between the unlike gases by collisions between un-like molecules. These elastic collisions must conserve momentum and kineticenergy. If v′1 is the velocity of molecule 1 after a head–on collision, elementarykinematics teaches us that its momentum change is m1(v1 − v′1) = 2m∗(v1 − v2),again in terms of the reduced mass m∗. This allows us to express the momentumchange, and thus the force of gas 1 on gas 2, in terms of the macroscopic velocitiesu, M12 = 2m∗(u1 − u2). Notice that this is an approximate argument, as it takesmacroscopic velocities to the molecular level, and no proper average is done.

We now find the average momentum transfer between the gases as the prod-uct of the collision rate and the momentum change per collision,

dp1

dz= kBT

dn1

dz= −M12 = −2m∗(u1 − u2) n1n2v12πσ2

12. (2.15)

Zero mean flow (Eq. 2.14) further implies that (u1 − u2) = u1n1+n2

n2. So that Eq.

2.11 becomes

kBTdn1

dz= −2m∗

n1 + n2

n2u1 n1 n2 v12πσ2

12 = −2m∗(n1 + n2)v12πσ212 n1u1. (2.16)

This equation relates the gradient of n1 to the flux n1u1, which is nothing elsethan the diffusion equation,

n1u1 = −D12dn1

dz(2.17)

so that

D12 =

(kBTm∗

)1/2 12 n π σ2

12. (2.18)

A more sophisticated treatment of the hard–sphere collisions leads to the expres-sion that we shall use from now on

D12 =38

(kBT

2πm∗

)1/2 1n ([σ1 + σ2])/2)2 . (2.19)

It only differs in the numerical prefactor from the result of the simple treatment.The emergence of the reduced mass owes to the momentum exchange in col-

lisions between unequal partners, and in the requirement of vanishing numberflux. The point is that even heavy molecules need to move when there is a con-centration gradient, otherwise a pressure difference would arise in the gas con-tainer. The consequence is that the diffusion of a heavy tracer is determined bythe molecular mass of the light buffer gas. When m1/m2 ≫ 1, m∗ = m2, and viceversa. Therefore, an arbitrarily small molecular diffusion of a tagged moleculecan only be reached by increasing its diameter, and not just by increasing its mass.

Turbulent Flows and Molecular Tagging Velocimetry, Basic Facts 21

2.4.2 Tracer Diffusion

Turbulent flows impose restrictions on the application of molecular tagging ve-locimetry (MTV); these restrictions are related to the length- and time scales inturbulence which need to be resolved and the length and time scales of MTV. Inthis section, we will contrast this issue with the properties of a few common tur-bulent flows that can be created in the laboratory. The time scale of MTV is thelifetime of the tagged molecule, while the length scale is the distance over which atagged molecule straggles during a turbulence time scale. It will turn out that thislength scale, which is often overlooked, is essential for the application of MTV inturbulent flows.

For application of luminescent tracers in turbulent flows, a few key require-ments have to be fulfilled. Typically, the interest is in the statistical properties ofthe small-scale motion, such as the Reynolds stresses. As already been mentionedin section 2.3, in turbulence the smallest relevant length scale is the Kolmogorovlength η and the smallest relevant time scale is the Kolmogorov time τη. To mea-sure gradients of the velocity field, the spatial resolution should match η, whilevelocities are deduced from displacements of tagged molecules during τη.

Therefore, the phosphorescence lifetime tphos should, at least, be equal to τη.Turbulence flow, with root-mean-square velocity u, may or may not have a meanvelocity U. To make our argument quantitative, we shall consider turbulent flowswith U/u≫ 1, U/u ∼ 1, and U = 0.

In turbulent flows, the smallest length and time scales are determined by thedissipation rate ε. Within the Kolmogorov picture, ε follows from the large-scalemotion through the relation

ε = Cεu3

L, (2.20)

where u is the turbulent (fluctuating) velocity, L is the integral length scale andCε is a constant O(1) which its value depends on the particular flow. Using thedissipation rate, one can determine the Taylor microscale λ, that gauges the extentof correlations, and the Kolmogorov time scale τη and length scale η as follows:

η = (ν3

ε)1/4, (2.21)

λ = (5νq2

ε)1/2, (2.22)

τη = (ν

ε)1/2, (2.23)

where ν is the kinematic viscosity, and q2 the kinetic energy per unit mass of theturbulent fluctuations. The integral and Kolmogorov length scales are related to

22 2.4 Interaction with Molecular Diffusion

flow U(ms−1) u(ms−1) ε(m2s−3) λ(m) Reλ τη(s) η(m) te(s)1 12 1.2 2.0 1.3× 10−2 1000 2.7× 10−3 2.0× 10−4 2.0× 10−5

2 0 0.86 11.3 3.8× 10−3 218 1.2× 10−3 1.3× 10−4 1.5× 10−4

3 40 10 4.7× 104 0.18 460 1.8× 10−5 1.6× 10−5 4× 10−7

Table 2.1: Characteristics of typical turbulent flows that can be realized in the labora-tory, with U as mean flow velocity, u as rms velocity, ε as dissipation rate, λ as Tay-lor’s microscale, Reλ as Taylor-based Reynold’s number, τη Kolmogorov time scale, η

as Kolmogorov length scale and te as emisiion time: (1) turbulence in the efflux of asmall jet [7], (2) zero mean flow turbulence driven by synthetic jets [30], (3) turbulencein a windtunnel [57]. All flows have a large enough Reynolds number and a sizableinertial range to display a Kolmogorov spectrum, E(k) ∼ k−5/3.

the Taylor-based Reynolds number by

Lη= C15−3/4R3/2

eλ = C−3/2ε R3/4

e . (2.24)

We will now use these relations to consider the characteristics of the inducedturbulence in relation with the type of the tagging methods. In particular, wewant to know which combination of turbulence creation and tagging methodwill give us the optimal experimental data. To achieve this goal, we have roughlytwo choices: we can either induce turbulence with mean flow or without meanflow. Let us now consider three typical turbulent flows which are used commonlyin fundamental studies of turbulence, namely turbulent flow in a wind tunnelgenerated by an active grid [57], turbulence created by a jet [7], and finally tur-bulence generated acoustically using loudspeakers, which does not have a meanflow [30]. Table 1 represents and compares the typical flow parameters for thesethree different methods of turbulence creation.

Let us contrast the derived flow conditions with those in Table 2.1. First, thephosphorescence time tphos should be larger than the Kolmogorov time τη. Sec-ond, the exposure time te, should be small such as to prevent motion unsharpness.Specifically, a tracer should move over less than a Kolmogorov scale η during theexposure time. For flows with a mean velocity this implies te ≈ η/U, whilst forflow without a mean velocity, the exposure time should satisfy te ≈ η/u. Startingfrom the condition in Table 2.1, let us now study how our requirements changewhen flow parameters such as the mean velocity, U, turbulent velocity u or thesize L of the experiment change. Therefore, we explicitly write the dependence

Turbulent Flows and Molecular Tagging Velocimetry, Basic Facts 23

of Reλ, η and τη on these two parameters:

Reλ = l1/2u1/2151/2ν−1/2C−1/2ε (2.25)

η = l1/4u−3/4ν3/4C−1/4ε (2.26)

τη = l1/2u−3/2ν1/2C−1/2ε (2.27)

This implies how the phosphorescent time tphos and exposure time te dependon the size L of the experiment (which we take to be the integral length scale),tphos & τη ∝ l1/2 u−3/2 and for the exposure time te in turbulence without amean velocity te ≤ η/u ∝ L1/4 u−7/4, while for flows with a mean velocity te .η/U ∝ L1/4 u−3/4U−1. These dependencies imply that, for a given integral lengthscale L, large turbulent velocities give short turbulence times, and many turnovertimes can be observed in a phosphorescence time. However, with increasing u,the exposure time, and thus the number of collected photons, decreases rapidly.If intensity is a problem, molecular tagging in turbulence with a large mean flowis problematic.

2.5 Conclusions

Laser diagnostic techniques like MTV have found widespread applications influid mechanics over the past decades as they enable us to investigate severaldifferent aspects of turbulence process.

In this thesis, we will consider three different MTV techniques. In Chapter 3,we will discuss the APART technique, that is based on the creation of NO mo-lecules which are visualized by LIF. The lifetime of these tracers is large, whichmakes them suitable for each flow in Table 2.1. Another technique, which willbe discussed in Chapter 4, involves phosphorescent biacetyl molecules, with aphosphorescent lifetime of 1.5 ms in oxygen-free flows. We will also present ourpreliminary experimental results on lead atoms as new tracers in our turbulentflow diagnostic investigation in Chapter 5.

At first view, one might assume that the length scales are determined by theRayleigh length of the focussed laser beam and the width of the focus. This caneasily match the smallest turbulent scales η in the windtunnel and synthetic–jetdriven flows, while the smallest length scale η = 15 µm can be matched onlyapproximately. Nevertheless, it will appear in the following chapters that morerelevant length scales are set by the (reaction) dynamics of the molecular tracers.

Chapter3Air Photolysis and

Recombination Tracking(APART) for Turbulence

In this chapter, we study turbulent velocimetry and turbulent mixing phe-nomena using a novel scheme called APART (Air Photolysis And Recombi-nation Tracking). APART is a molecular tagging velocimetry scheme basedon creating nitric oxide (NO) molecules out of O2 and N2 molecules in thefocus of a strong UV laser beam. The created pattern can be visualized a fewmicroseconds later with the help of another UV laser beam. Using this tech-nique, we are capable of investigating turbulent mixing phenomena at verysmall scales (scales comparable to the Kolmogorov length scale). To considerthe effects of molecular diffusion and turbulent dispersion at this scale, weneed to reach the appropriate resolution, that is, the pattern width shouldbe comparable to the Kolmogorov length scale. Although the initial patternwidth is mainly determined by the size of the focus, it can be changed "rela-tively" by changing the Kolmogorov length η. We achieved this by changingthe rms velocity in our experiment. The Kolmogorov length scale η dependson the turbulent velocity u as η ≈ u−3/4, hence, when u decreases, η in-creases. In this way we are able to study turbulence down to the Kolmogorovscale.

26 3.1 Introduction

3.1 Introduction

All investigations of this chapter were done by means of a scheme named APART(Air Photolysis And Recombination Tracking). This scheme has been introducedby the members of our group a couple of years ago [7]. In this scheme, nitricoxide is created locally in an air flow in the waist region of a mildly focused ArFlaser beam. At an adjustable time interval (∆t) later, the advected NO distribu-tion is probed by planar LIF in the γ-bands, induced by a pulsed dye laser. Sincethis tagging scheme requires only N2 and O2 molecules, it can be used in am-bient air as well as in any air flow system, hence does not require any seeding.Furthermore, since NO is a stable molecule, written patterns can, in principle, befollowed almost indefinitely. In comparison to other MTV techniques which pos-sess the advantage of using native air molecules as tracers, like RELIEF (Ramanexcitation plus laser-induced electronic fluorescence), APART is significantly eas-ier to set up, because it does not require a dual-wavelength beam for tagging.

Nevertheless, our knowledge of the photochemical pathway in which NO iscreated is still incomplete. Investigations show that photo-excitation by the ArFexcimer laser results in excited O2 being created in the B-state, which easily dis-sociates into atomic oxygen, or in some cases, ionizes to O+

2 by absorption ofadditional photons [7]. The same tagging wavelength causes nitrogen to end upin certain ionized and excited states. Besides these species that are assumed to becritical in NO production, many other products are reported to be created dur-ing photolysis, such as ozone (O3). These and other species which are present inthe air after the tagging process, will now chemically interact to ultimately createground-state nitric oxide.

As a molecular tagging velocimetry technique, APART suffers from limitedprecision due to molecular diffusion. In general, all molecular tagging velocime-try methods of gas flow diagnostics are affected by the gradual blurring of thewritten patterns through molecular diffusion. In case of a turbulent flow, molec-ular diffusion poses a fundamental limit on the resolution of the smallest scalesin the flow. Since the NO tracer molecules have mass comparable to N2 and O2,mass will approximately diffuse at the same rate as momentum, i.e., the Schmidtnumber is approximately 1. As the size of the smallest eddies (the Kolmogorovlength scale) is determined by the diffusion of momentum (the kinematic vis-cosity), the tagged NO pattern will broaden to one Kolmogorov length in oneKolmogorov time (small-eddy turn over time). On the other hand, the turbulentwrinkles of written patterns can be only visualized several microseconds (equiv-alent to a couple of Kolmogorov times) after the creation process. Therefore, atdelay times after which the LIF patterns are being read, they are already too muchbroadened for observation of turbulent wrinkles.

APART 27

3.2 Rayleigh Experiment

Flow diagnostics experiments which use the APART technique under laminarflow conditions show an enhanced spreading rate of the written patterns, whichwas ascribed to the heat deposited in writing [7]. For a pattern of NO moleculeswith a Gaussian density profile, ρt(y) ∝ exp(−y2/σ2), the Gaussian width σ(τ)

after writing should increase as

σ(τ)2 = σ(0)2 + 4Dmolτ,

where Dmol is the mass diffusion constant of NO, Dmol = 1.8× 10−5 m2s−1. In-stead, it was found that at short times, τ . 30 µs, the width σ(τ)2 increasednon–linearly and asymptotically approached diffusive behavior with diffusionconstant Dmol ≈ 2.6× 10−5 m2s−1.

The enhanced spreading of the pattern was explained by the following courseof events: upon writing the deposited laser power causes a jump in temperature,resulting in a radially outward convective flow of the NO tracers. This was corro-borated by a simple analytically solvable model and assuming a temperature riseat writing of 100 K. The enhanced radial transport, therefore, is the consequenceof both molecular diffusion and convection.

Focusing a laser beam in a small volume of the air (in principle) should notaffect the gas as long as the light is not absorbed. In case of an excimer laser,however, the Schumann–Runge bands of oxygen will very efficiently absorb theincoming photons, thereby raising the local temperature. Knowledge of the tem-perature in the focus of the excimer laser beam is very useful in this case since itprovides information on the creation process, and will pose a limit on the intru-siveness of the APART technique as well. If there would be a strong increase ofthe temperature, this will change the flow conditions which needs to be avoided.The temperature can be measured in different ways, in our experiment we in-ferred it from the density of our LIF patterns using Rayleigh scattering. Here wewill further quantify this effect by directly measuring the temperature of the airusing Rayleigh scattering.

Patterns of NO molecules were created through photosynthesis. We used abroad–band ArF laser (Λ Physik, LPX 150) operated at λ = 193 nm with a pulseenergy of about 100 mJ/pulse and a pulse duration of 18 ns. To make a verysharp narrow pattern, we selected a part of the beam by means of an aperture;this selected beam had a minimum waist diameter (FWHM) of about 70 µm af-ter having been tightly focused in the air using a composite lens, optimized forexcimer laser beams, with focal length of f = 250 mm. Rayleigh scattering wasmeasured using a frequency-doubled Nd:YAG (Quanta Ray, SpectraPro 150) laser

28 3.2 Rayleigh Experiment

Figure 3.1: Experimental setup to measure the temperature upon creation of the NOtracer molecules using a pulsed ArF excimer laser. After a delay time τ, the Nd:YAGlaser is fired and the Rayleigh scattering is visualized using the gated intensified cam-era.

with λ = 532 nm. Except for the reading laser and an extra camera for the ob-servation of the depth of the intersected laser beams, a typical APART setup wasemployed to have exactly the same condition as an APART experiment. The im-ages were captured using a PIMAX II ICCD camera (1024× 1024 pixels), cooledby a Peltier element. The intensifier could be gated or triggered to open and closewithin 5 ns or more. It was controlled by an ST–133 controller with pulse gen-erator (PTG). An extra camera was placed perpendicular to the axis of the othercamera and the dye and excimer laser beams, to observe these beams from above.It was used to focus the dye laser in a way that it has the minimum depth per-pendicular to the excimer laser beam.

The experiments were done by first registering a background Rayleigh imageIB(x, y) using the dye laser, without firing the excimer laser. This backgroundimage was used to correct for the intensity profile of the Nd:YAG laser. Next,Rayleigh images I(x, y) were taken at time τ after NO tracers were written withthe excimer laser. The relative Rayleigh images IR(x, y) = I(x, y)/IB(x, y) shownin Fig. 3.2 quantify the density change. What is also explicitly visible in thisfigure is the existence of two pressure waves on the two sides of the excimer laser

APART 29

3.0 3.2 3.4 3.60.8

0.9

1.0

1.1

y (mm)

I(a

rb.

uni

ts)

3.0 3.2 3.4 3.6y (mm)

3 sm

1 sm

1 sm 3 sm

x

y

(a)

(b)

(c) (d)

Figure 3.2: (a, b) Rayleigh images IR(x, y) of air in which NO patterns were written.The images IR were taken at delay times τ = 1, 3 µs after pulsing the excimer laser. (c,d) Full curves indicate the horizontally averaged relative intensity of (a, b) after cor-rection for the slight inclination angle of the patterns; dashed lines indicate Gaussianfits. At τ = 1 µs two pressure waves can be clearly observed; they are much fainter atτ = 3 µs.

beam. These waves travel with the velocity of sound. They carry away possiblepressure variations due to tagging, so that the density changes observed in Fig.3.2(c,d) directly translate into temperature changes.

The sloping trend in the intensity profile is due to the alignment of the laserbeam. To avoid damaging the camera (by overexposure), we aligned the lasersin a way that the focus point would be very close to the camera field of view butnot within it, hence, the right hand side of the pattern which is closer to the focuspoint has a higher intensity.

The images IR were horizontally averaged after correcting for the slight incli-nation angle of the excimer laser beam; these averages are shown in Fig. 3.2(c,d).Due to the normalization of IR, the cross sections directly indicate the relativetemperature change due to tagging. In Fig. 3.2(a,b) the pressure pulse can clearlybe seen, but it is no longer visible after 10 µs. The strongest turbulence realized inour experiments has a Kolmogorov time τη = 17 µs, so that there is no interaction

30 3.2 Rayleigh Experiment

0 20 40 60 800

20

40

60

τ (µ s)

∆T

(K)

0 20 40 60 800

2

4

6

*10 -9

τ (µ s)

σ2

(m2

)

(a) (b)

Figure 3.3: (a) Temperature rise above ambient ∆T(τ) computed from the depth a(τ)of the density profile of Fig. 3.2(c,d). (b) Squared width σ2 of Gaussian fits of thedensity profile as a function of delay time τ. Dashed line: fit of σ(τ)2 = σ(0)2 + 4DTτ,with DT = 1.34× 10−5 m2s−1.

between the smallest turbulent eddies and the pressure wave due to tagging.

By fitting the density profiles to Gaussians,IR(y) = 1− a(τ) exp((y− y0)

2/σ(τ)2), where a(τ) is the relative density change,σ(t) its Gaussian width and y0 its center, we can follow the temporal evolutionof temperature and width. Two of these fits are shown in Fig. 3.2, however, wenotice that the density profile at small delay times differs from a pure Gaussian.The temperature rise above ambient ∆T(τ) is shown in Fig. 3.3(a). It was com-puted from the depth a(τ) of the density profiles using ∆T(τ) = a(τ) T, withT = 273 K. At a delay time τ = 1 µs, it is seen that ∆T ≈ 50 K, in agreementwith what was found earlier by us using our simple convection model. Thesquared width σ2 of Gaussian fits of the density profile as a function of delaytime τ is shown in Fig. 3.3(b). It can be represented well using a diffusive behav-ior σ(τ)2 = σ(0)2 + 4DTτ, with DT = 1.34× 10−5 m2s−1.

The value of the found temperature diffusion constant DT = 1.34× 10−5 m2s−1

is surprising, as it is smaller than the mass diffusion constant Dmol = 2.6 ×10−5 m2s−1 of tagged NO molecules that was determined by LIF experiments,and comparable to the unperturbed mass diffusion constant of NO, Dmol = 1.8×10−5 m2s−1. In the context of our convection model, we predicted that tempera-ture and mass should be affected in exactly the same way, assuming that the un-perturbed mass diffusivity of NO and temperature diffusivity of air are the same.However, in our model we assumed the same Gaussian profile for the initial tem-perature rise and the NO concentration. As we do not know the precise chemicalpathway of NO tagging, this assumption may only be approximate. Further, theprofiles of Fig 3.2(c,d) show that the initial temperature profiles deviate from asimple Gaussian.

APART 31

In conclusion, we have further quantified the intrusiveness of APART, demon-strating that at the turbulence time scales of interest, the effects of increased tem-perature can be considered harmless.

3.3 APART Experiment

APART is based on "photosynthesis" of NO molecules which are created out of N2

and O2 molecules in the focus of a strong UV laser. The created pattern needs tobe visualized, which in the case of NO, could be done by UV LIF, thus in APARTwe always need two UV lasers with appropriate wavelengths, one for writingpatterns and the other one for reading them.

A schematic overview of the experimental setup is given in Fig. 3.4. Thepulsed ArF excimer laser creates a pattern of NO particles and the jet–inducedturbulent flow displaces and wrinkles the patterns. A short while later, the pulseddye laser induces the NO molecules to fluoresce, and the ICCD camera collects

Figure 3.4: Experimental setup for APART measurements. The pulsed ArF excimerlaser creates a pattern of NO particles and the flow displaces and wrinkles these pat-terns. The pulsed dye laser visualizes the NO molecular fluorescence, while the ICCDcamera collects fluorescence signals from the readout area. A filter in front of thecamera suppresses elastically scattered ArF laser light.

32 3.3 APART Experiment

fluorescence from the readout area. In order to fully characterize the turbulence,we use one of the most commonly studied free shear flows, the axi-symmetricalfree turbulent jet. The jet consists of a pressure chamber and a 10 cm diameterdiffuser that smoothly goes over into a 1 cm diameter orifice.

For the strongest turbulence studied, the exit velocity of the air jet was near–sonic, U ≈ 200 m/s, and it slowed down to a mean velocity of U ≈ 30 m/s at themeasurement location. The experiments were performed about 40 nozzle diam-eters downstream (along the y−axis) of the orifice where the turbulent jet flowbecomes self–preserving. The mean velocity could be changed by varying thepressure of the jet. In the self–preserving regime there is a fixed relation betweenthe turbulent velocity u and the mean velocity U. In our experiments, the largestU recorded was 31 ms−1, for which u = 8 ms−1. Since the Kolmogorov scaleη decreases with increasing u, at the smallest u, η was approximately the initial(Gaussian) width of the tagged molecular cloud, while at the largest velocity, thewidth of the cloud was three times larger than η.

Measuring the pattern width is a challenge. The reason is that patterns aredistorted by the turbulent flow, which also redistributes the NO molecules alongthe patterns, so that patterns may develop holes. The backbone of these wrinkledpatterns was determined using the technique of active contours. If the 2D back-bone was x(s), the intensity of pattern cross sections I(y′) is determined alongpatterns perpendicular to x(s). These intensity cross-sections have a Gaussianprofile, I(y′) = a + b exp(−y′

2/σ2), where the pattern center is at y′ = 0. This

defines the (Lagrangian) pattern width σ. For a pattern written along the x–axisin still air, the y′ direction coincides with the y–axis. In the case of molecular dif-fusion only, the Gaussian width increases in time as σ2 = σ(0)2 + 4Dmolt, withDmol the diffusion constant.

The writing of patterns has already been described in Section 3.2. For read-ing the written patterns, a Nd:YAG-pumped dye laser (Sirah PrecisionScan) wasmixed with the frequency tripled wavelength of the Nd:YAG laser (λ = 355 nm)to obtain radiation with a wavelength of λ = 226 nm. The 226 nm beam was usedto excite the R21(17.5) pattern in the A ← X(0, 0) system (γ−bands) of NO andthe resulting emission from the A−state was detected by a camera system. In allexperiments of this chapter, the dye laser beam was aligned anti-collinearly to theexcimer laser beam, perpendicular to the flow direction (Fig. 3.4).

A high intensity laser beam is needed to be able to measure very tiny fluctu-ations of the written patterns accurately, hence we weakly focused the dye laserbeam. It was done using a lens with focal length f=1000 mm where the focal pointwas before the readout area. By changing the position of the focus nearer to or far-ther from the readout area the intensity could be regulated to result in sufficient

APART 33

signal while still encompassing the written pattern. In this way, the diameterof the probe beam waist at the measurement volume could be varied between2 mm to 5 mm. At the largest delay time between writing and reading process(∆t = 80 µs), the rms pattern displacement was approximately 0.7 mm, whichindeed fits inside the beam waist of the reading laser. The intensity profile of thedye laser could be mapped using the random displacements of the tagged pat-terns; we will come back to this below. Fluorescence was recorded as describedabove, without the top view camera. A custom lens (Bernard Halle Nachfl.) wasused in front of the camera with a fixed focus of 250 mm. When the objective andimage distance were set for minimal aberrations, a region of 5.68× 5.68 mm2 wasimaged onto the CCD chip. Since the resolution of the chip was 1024 pixels, thespatial resolution of each image would be 5.55 µm per pixel.

The light incident on the camera was filtered using a custom long-pass fil-ter (Laser Optik) with low transmittance (nearly 0%) at 226 nm and high trans-mittance (95%) above, thereby effectively removed Rayleigh-scattered light fromboth lasers while transmitting most of the NO fluorescence (A(0) → X(ν ≥ 1)).Examples of written patterns in two different conditions, without flow (laminar)and with flow (turbulent) are shown in Fig. 3.5 and Fig. 3.8, respectively. Eachimage was measured using single pulses of both excimer and dye lasers.

3.3.1 Molecular Diffusion Experiment

In order to test our image capturing procedure, we performed a set of measure-ments in laminar flow to measure the molecular diffusion coefficient of our tracerin the carrier gas, which in this case would be the molecular diffusion coefficientof NO molecules in ambient air. The experiment was done using the facilitiesshown in Fig. 3.4, except that, in this case we did not use the jet, i.e., the exper-iment was done in still air. To delimit the acquired signal to NO molecule fluo-rescence and discard the scattered light, the ICCD chip was open for only 100 ns.Images of tagged patterns were registered at different delay times after firing theexcimer laser, starting from 10 µs as the shortest and continued until 80 µs.

A narrow initial pattern was made with a narrow cylindrical laser beam, usinga composite lens (f=250 mm) in front of the excimer laser in combination with anaperture of 1 mm radius. A few patterns are shown in Fig. 3.5.

3.3.2 Intensity Decay of the LIF Patterns

The necessity of single laser shot measurements in turbulence makes the intensityof the LIF pattern one of the most significant parameters of LIF measurements.Fig. 3.6 summarizes the intensity of LIF patterns of NO molecules at various delay

34 3.3 APART Experiment

0 10 µs

20 µs 40 µs

80 µs

Figure 3.5: Laser-induced fluorescence (LIF) patterns of NO molecules at differentdelay times after firing the excimer laser. The experiment was done in still air. Im-ages are single laser shot measurements and the widening of the patterns is due tomolecular diffusion. The width of each image is 1024 pixels (5.68 mm).

times. It was found that the excimer laser beam power gradually decreases dur-ing the measurement, due to decreasing efficiency of its operating gases. There-fore, we decided to record a reference pattern (at ∆t = 10 µs) immediately beforerecording each delay time pattern. Fig. 3.6(a) depicts the intensity of all recordedpatterns (references and delayed ones) in one graph, the gradual decrease of theintensity of the reference patterns while the experiment progressed is clearly vis-ible in this graph.

To calculate the intensity of patterns at different delay times, we scaled allreference patterns to the same intensity. Fig. 3.6(a) illustrates the intensities ofwritten patterns at different delay times after excimer laser firing. Each point inthese graphs represents the integrated intensity of 1× 103 individual single lasershots.

Fig. 3.6(b) shows the pattern intensity, normalized by that of the correspond-ing reference pattern. The intensity decay averaged over the extent of the patternsin Fig. 3.6(b) is shown in Fig. 3.6(c). Just after creation of the NO molecules their

APART 35

0 2 4 60

1

2

3

´10 3

x (mm)

Inte

nsi

ty(a

rb.

uni

ts)

1

2

3

4

567

8

0 2 4 60

0.5

1.0

x (mm)0 50 100

0.4

0.6

0.8

1.0

t (ms)

Rel

ativ

ein

ten

sity

(a)

(b) (c)

120 sm

80

40

20

Figure 3.6: Intensity of the patterns written in still air at different delay times. (a)The reference patterns at t = 10 µs indicated by 1,3,5,7; their intensity decreases inthe course of the experiment due to degradation of the working gases in the excimerlaser. The patterns at delays 120 µs, 80 µs, 40 µs and 20 µs are indicated by 2,4,6 and8, respectively. At each delay time, an average was taken over 4 × 103 laser shots.(b) Intensity divided by the intensity of the corresponding reference line. (c) Relativeintensity as a function of delay time, averaged over the pattern.

LIF intensity drops to a small value with a time constant of u 54 µs. Perhaps thisrelatively fast decay is due to the presence of O3 which is also created during thewriting phase of APART.

3.3.3 Broadening of the LIF Patterns

In still air, the width σ of the transverse Gaussian density profile of written pat-terns, ρt(y) ∼ exp(−y2/σ2) increases diffusively as

σ2mol(t) = σ2

mol(t0) + 4Dmol(t− t0),

where σ2mol(t) is the squared width of the cloud relative to its point of release,

σ2mol(t0) is the squared width of the cloud at the point of release, Dmol is the molec-

36 3.4 Results of Turbulent Mixing Experiments using APART

ular diffusion coefficient of the medium and t− t0 is the delay time between writ-ing and reading processes. A measurement of the width of the patterns written instill air, therefore, provides the diffusion coefficient. The purpose of experimentsin laminar flow is to study the influence of the writing process on molecular diffu-sion. In these experiments, average pattern widths were determined over 4× 103

laser shots.The reference patterns were registered at t0 = 10 µs. Since the excimer laser

intensity decreases gradually during the measurement, patterns with too low in-tensity were discarded. At the last measurements of an experimental run, thisaffected approximately half of the patterns. Fig. 3.7(a) shows the width of nor-malized patterns at various delay times. Especially at longer delay times, thewidth shows a maximum near the pattern center, at the location of the focus ofthe excimer beam. At this spot, the pattern broadens faster due to the local rise oftemperature which is associated with the writing process. In Fig. 3.7(b) we plotthe relative squared pattern width ∆2(t) = σ2

mol(t)− σ2mol(t0), with the delay time

of the reference pattern as t0 = 10 µs. Clearly, the pattern broadens diffusively,but the diffusion coefficient depends on x. It is largest where the initial widthis largest. At the pattern center, we measure Dmol = 2.43× 10−5 m2s−1, whichagrees with the value reported in Bominaar et al. [7], while at the leftmost loca-tion we measure Dmol = 1.7× 10−5 m2s−1, which is close to the literature value ofthe NO diffusion constant Dmol = 1.8× 10−5 m2s−1. The variation of Dmol alongthe tagged pattern is shown in Fig. 3.7(c).

3.4 Results of Turbulent Mixing Experiments usingAPART

3.4.1 Jet-Induced Turbulence Characteristics

After retrieving the molecular diffusion coefficient of NO molecules in still air, weperformed single shot LIF measurements of NO molecules in a turbulent mixingflow using the set-up shown in Fig. 3.4. Fig. 3.8 illustrates a few single shot LIFpatterns under different turbulent flow conditions.

In an axi-symmetric incompressible and isothermal turbulent jet which haswell-documented scaling properties [13], the mean flow depends on the distancefrom the orifice in a characteristic way. In fact, at a particular location relative tothe nozzle, there is a fixed ratio between mean and fluctuating velocity. This self-preserving area starts at about 20 nozzle diameters downstream of the nozzle.This ratio, which is called Cu = u/U, reflects a constant relative turbulence in-tensity which shows that the jet is self-preserving. Furthermore, when the value

APART 37

´

(a) (b)

(c)

0 2 4 60.4

0.6

0.8

1.0

1.2

10 -4

x (mm)

s(m

)

1

2

3

4

5

6

7

8

0 0.5 1.0 10 -40

0.5

1.0

10 -8

t (s)

D2

(m2

)

0 2 4 60

1

2

3

10 -5

x (mm)

D(m

2s-1

)

´

´

´

1

1

2

2

3

1

2

Figure 3.7: (a) Gaussian width σ of patterns written in still air at different delaytimes. The meaning of the numbers near the patterns is the same as in Fig. 3.6. Thelarge width near the center is due to the focus of the writing laser. (b) Full patternsindicate relative width ∆2(t) = σ2

mol(t)− σ2mol(t0), where t0 = 10µs is the delay of the

reference patterns. Dashed lines show fits ∆2(t) = 4 D (t − t0). Curves 1 and 2 areaveraged over the x-intervals, indicated as grey regions in (a,c), curve 3 is an averageover the entire horizontal extent of the pattern. (c) Variation of diffusion coefficientalong the pattern.

of Cu has been determined (together with the value of Cε, the dimensionless dis-sipation constant), it can be used to infer the small-scale velocities, hence we canestimate the turbulent dissipation ε from a measurement of u only.

As we performed our experiments at about 40 nozzle diameters downstreamfrom the jet exit, that is, in the self-preserving region, the turbulent velocity u inour experiment is expected to be proportional to the mean velocity [87]. Fig. 3.9shows the ratio u/U in our experiment, and the slope of the diagram gives thevalue of Cu. Each point in this diagram represents approximately 103 individualpatterns which were recorded at various delay times and under different turbu-lence conditions.

38 3.4 Results of Turbulent Mixing Experiments using APART

U=0 m/s

U=5 m/s

U=17 m/s

U=40 m/s

U=48 m/s

U=3 m/s

U=8 m/s

U=26 m/s

U=44 m/s

U=56 m/s

Figure 3.8: Single-shot Laser-induced fluorescence (LIF) patterns of NO moleculesrecorded under different turbulent flow conditions. The experiment was done ath=0.4 m downstream of jet orifice. The jet was operated by high pressure air. Thewidth of each image is 1024 pixels (5.68 mm).

In addition to Fig. 3.9, Fig. 3.10 shows the variation of rms velocity of our jet-induced turbulence flow along the pattern length. The small variation of u alongthe pattern which is inside the internal range of the jet, confirms the homogeneityof the created turbulent flow.

A point of concern is the extent of the dye laser beam, which is used for read-ing the written NO patterns. It should be concentrated in order to maximize theLIF intensity, but wide enough to embrace the patterns advected in the turbulentflow field. A map of the intensity can be made using these fluctuating patterns.At each (x, y) location in Fig. 3.11 the summed intensity over 103 written patterns

APART 39

Figure 3.9: The turbulent velocity versus the mean velocity. Each point is based on103 single laser shot patterns.

is plotted, divided by the number of times this location was visited. Practically,the image is coarse grained in pixels, and we count the number of times that thefitted line backbone falls in a pixel. There is a small angle between the dye laserand the excimer laser beam. The dye laser intensity remains approximately uni-form over the region visited by the fluctuating patterns, indicating that the beamwidth suffices to embrace these patterns.

3.4.2 Broadening of the tagged patterns in turbulence

In Chapter 6, we will sketch a framework for understanding the joint action ofturbulent dispersion and molecular diffusion. At short times and small distances,turbulent dispersion leads to an exponentially fast separation of two points,

d(t) = d0 eγt/τη (3.1)

where d0 is their initial separation, and γ is a Lyapunov exponent. Briefly, it willbe argued that dispersion and diffusion can be added such that

σ2(t) = σ2(t0) exp(2γ(t− t0)/τη) + 4Dmol(t− t0),

with γ the Lyapunov exponent, γ = (2/15)1/2, which follows from dimensionalarguments. At short times, when the exponential can be expanded, this leads to

40 3.4 Results of Turbulent Mixing Experiments using APART

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

8

9

10

u (m

s-1)

Position (mm)

Figure 3.10: Variation of the rms velocity along the LIF pattern. Each point is basedon 4× 103 single laser shot patterns integrated over a region of interest of 128 pixels.From bottom to top, different patterns correspond to mean velocities U ranging from 1to 32 ms−1. The smoothness and small slope of the patterns confirms the homogeneityof our jet-induced turbulence.

an effective diffusion constant

D = Dmol + σ2(t0)γ/2τη. (3.2)

The purpose of the experiments is to measure D for increasing turbulent veloc-ities u. If Eq.3.2 holds, according to equations 2.3 and 6.12 the total dispersionshould increase with increasing u as u3/2. However, at the same time the Kol-mogorov length η decreases, at the largest value of u = 10 m/s, η = 16 µm, whichis is a factor 3 smaller than the width of the initially written line. At u = 2 m/s, η

is approximately the initial width. If lines are wrinkled on scales which are a fewtimes η, we may under-resolve the turbulent fluctuations and may underestimatethe line dispersion.

The experiments were done as follows. At each setting of the jet mean ve-locity 103 reference lines were registered at a delay time t0 = 10 µs. From theselines we measured the initial Gausian width σ(t0). Immediately following theseexperiments we registered 103 lines at delay times t, with t = 40 µs at the low-est u, decreasing to t = 20 µs at the largest turbulent velocity. Both referenceand delayed mean line widths are shown in Fig. 3.12(a). The width of the initialline does not vary significantly from run to run, and we take σ(t0) = 61 µm

APART 41

0 2 4 6

3.0

3.5

4.0

x (mm)

y (m

m)

Figure 3.11: Intensity map of the dye laser beam averaged 103 times at the delay timet = 20 µs, advected in a turbulent flow with u = 8.9 ms−1. Locations that were nevervisited are painted black.

as defence value in the central part of the written lines. From the mean linewidth at longer delay times t we measure the effective diffusion coefficient asD = σ(t)− σ(t0)/4(t− t0). The result is shown in Fig. 3.12(b). There is a signifi-cant variation of D with x, and we take the average over the central region of thewritten line. This average is shown in Fig. 3.12(c).

In Fig. 3.12(c) we also compare the measured effective diffusion constant as afunction of the turbulent velocity u with the prediction of Eq. 3.2, using σ(t0) =

61 µm and Dmol = 2.8× 10−5 m2s−1, which was obtained from Fig. 3.7. We findgood agreement with the prediction, except at the lowest turbulence level.

The agreement is striking as it demonstrates that at the times considered, theeffects of molecular diffusion and turbulent dispersion may be added. Also, thatpossible averaging due to under resolution of the turbulent length scales is notimportant. The discrepancy at the lowest u is surprising as the delay t is largestthere, the width increase is largest and the error should be smallest.

3.5 Conclusion

In this chapter we discussed turbulent velocimetry and turbulent mixing phe-nomena using a novel scheme called APART (Air Photolysis And RecombinationTracking). This scheme has been introduced by members of our group a few

42 3.5 Conclusion

10 -4s

(m)

10 -5

D(m

2s-1

)

´´

0 2 4 6

0.6

0.8

1.0

x (mm)0 2 4 6

2

4

6

x (mm)

0 5 100

2

4

6

u (m/s)

D(m

2s-1

)

10 -5´

(b)(a)

(c)

Figure 3.12: (a) Variation of the initial (lower lines) and final width (upper lines) ofwritten lines as a function of position along the line for increasing turbulent veloci-ties u. The initial time delay is t = 10 µs. Since the final delay times t decrease withincreasing u, u increases from top to bottom. (b) Effective diffusion coefficient D mea-sured from the width increase in (a). (c) Dots indicate D averaged over the grayedinterval in (b), the error bars indicate the rms variation over this interval. Line: pre-diction using Eq. 3.2 with σ(t0) = 61 µm and Dmol = 2.8× 10−5 m2s−1.

years ago [7]. Using this technique, we investigated turbulent mixing phenom-ena at very small scales (scales comparable to the Kolmogorov length scale). Sincethe early flow diagnostic experiments using the APART technique under laminarflow conditions showed an enhanced spreading rate of the written patterns, wefirst investigated this effect which was ascribed to the heat deposited in writing.In our investigation using the Rayleigh scattering technique, we further quanti-fied the intrusiveness of APART, demonstrating that at the turbulence time scalesof interest, the effects of increased temperature can be considered harmless.

We then performed a set of measurements in laminar flow to measure themolecular diffusion coefficient of our tracer in the carrier gas, which in this case

APART 43

would be the molecular diffusion coefficient of NO molecules in ambient air. Weconsidered a pattern registered at 10 µs as our reference pattern, because beforethis time the tagged pattern anomalously broadens due to a local rise of temper-ature. After this time the squared line widths increase linearly with time untilt u 100 µs, but with a diffusion constant depending on x. It is largest where theinitial width of the line is largest. These values were taken as reference values inthe case of turbulence dispersion.

Although the pattern width is mainly determined by the size of the focus, itcan be changed "relatively" by changing the Kolmogorov length η. We achievedthis by changing the rms velocity in our experiment. The Kolmogorov lengthscale η is inversely proportional to rms velocity u as η ≈ u−3/4, hence, whenwe increase the rms velocity, the Kolmogorov length scale decreases. Our ex-periments show that the total effective diffusion coefficient of NO molecules inturbulent air increases by increasing the rms velocity of the turbulent flow and isconsistent with the theoretical prediction. Further research on the joint interac-tion of molecular diffusion and turbulent dispersion will be presented in Chapter6.

Chapter4Laser-Induced

Phosphorescence of BiacetylMolecules

We measure the evolution of line profiles consisting of phosphorescing bi-acetyl molecules. These molecules form a commonly used probe in molec-ular tagging velocimetry. For relatively large laser power, the evolution ofthese line profiles are determined not by molecular diffusion, but by thetriplet–triplet annihilation reaction of excited biacetyl molecules. We identifya new reaction pathway, and present a model for the observed line shapes.The rapid widening of tagged lines of biacetyl molecules due to chemical re-action restricts this MTV technique to large–scale turbulent motion in gasesof comparable molecular weight.

46 4.1 Introduction

4.1 Introduction

This chapter is dedicated to the investigation of the applicability of biacetyl mo-lecules as tracers in turbulence experiments. As mentioned in Chapter 3, despiteall the advantages of APART for flow tracing, it features a few drawbacks. One ofthese is related to the NO tracer molecules having a relatively small mass, hencethe luminescent pattern broadens very quickly, i.e., mass diffusion and momen-tum diffusion live on the same time scale. A second issue concerns the local flowheating, due to the tracer creation by focussed ArF excimer laser light. To over-come the first problem, based on the theory explained in Chapter 2, we startedto search for heavier tracers to be used in combination with heavier gases as car-rier flow. According to Eq. 2.19, this will lead to a smaller mutual diffusion co-efficient and consequently, less intrinsic broadening of the luminescent patterns.This should enable us to study flow features in turbulence very close to the small-est length scales in turbulence.

The issue of local heating requires a technique that involves less heat inputin the medium during tracer creation. From this point of view, the use of phos-phorescent tracers is particularly advantageous: most of the photon energy inputinto the medium is re-emitted, and so does not contribute to heating. Moreover,by looking at (long-lived) phosphorescence we also circumvent the need for asecond visualization laser, which makes the whole setup considerably more user-friendly.

Molecular tagging measurement using biacetyl laser-induced fluorescence orphosphorescence is quite an old method in gas flow diagnostics. Biacetyl hasbeen suggested for visualizing structures and measuring velocity by Epstein in1974. He performed the first experiment in fluid mechanics with biacetyl as atracer, and quantitatively measured the three dimensional density distribution ina transonic compressor rotor [17]. The first experiment in turbulence (unsteadyflow) was reported by McKenzie and coworkers in 1979. They demonstrated alaser-induced fluorescence technique for the measurement of the relative time-dependent density fluctuations in unsteady or turbulent flows [48]. Gas phasevelocimetry using biacetyl phosphorescence was subsequently reported by Hilleret al. [25].

All mentioned studies, however, concentrated on the gross flow structure, andnot so much on the small details. Thus, it was still an open question whether ornot biacetyl would perform as a suitable flow tracer down to the Kolmogorovscale in turbulent flow. Based on the promising results of earlier studies, the ini-tial intention of our study was to find out whether biacetyl could be the “perfecttracer” for small scale turbulent flow diagnostics. Our study however revealedthat lines of tagged triplet biacetyl molecules widen not only through molecu-

Biacetyl 47

lar diffusion, but also through triplet-triplet annihilation (TTA) collisions. Be-cause the decay of the intensity depends quadratically on the local density, thehigh-density line center decays more rapidly than the line wings, resulting inan apparent line widening and a loss of accuracy of the position of the line. Itappeared that this effect is much more severe than that due to molecular dif-fusion, thus effectively incapacitating the use of biacetyl for molecular taggingvelocimetry in turbulence. In this way, MTV using biacetyl is restricted to flowswith rather large length scales; an example is described in the work of Stier andKoochesfahani [80]. In this Chapter we will present our experimental results onthe time-dependent transverse shape of written lines and discuss models for thisdynamical behavior.

4.2 The Biacetyl Molecule

Biacetyl has always received a lot of attention because of its phosphorescence inthe gas, liquid and solid phases [18, 24]. It also has a relatively low triplet energy(about 20000 cm−1) [20], which makes it a suitable candidate for triplet energytransfer studies [2, 69, 78]. In fact, it has some unique properties that make itsuitable for flow field diagnostics as well. It has a relatively high vapor pressure(5.3 kPa at room temperature) with no obvious condensation below 2.7 kPa [48],meaning that it can be easily added to the flow of a gas. It is nontoxic and com-monly used as an additive in dairy products. Its continuous broad absorptionband in the UV and visible range (250-470 nm) [80] makes it a convenient candi-date for LIF or LIP techniques. This continuous absorption band is depicted inFig. 4.1.

As can be seen in the figure, two broad absorption maxima occur at λ ≈270 nm and λ ≈ 420 nm. The photophysics that occurs after excitation will bediscussed in some detail later in this chapter, but the basic idea is as follows (seealso Fig. 4.2): Excitation occurs in the singlet system, but efficient intersystemcrossing results in a large fraction of electronically excited molecules ending upin the triplet manifold. From there, they can relax back to the (singlet) groundstate by photon emission, but as this is a slow process (phosphorescence), the ex-cited triplet molecules are susceptible to perturbation due to interaction with theenvironment, that is, intermolecular collisions.

The excitation of biacetyl in either of the absorption bands gives rise to bothfluorescence and phosphorescence emission; the latter is included in Fig. 4.1.The natural phosphorescence lifetime of biacetyl is about 1.52 ms [78], but theobserved lifetime can be considerably lower due to a variety of reasons. Colli-sional deactivation of the triplet state is a major cause of reduced phosphores-

48 4.2 The Biacetyl Molecule

Figure 4.1: Low-resolution absorption (solid line) and emission (dashed line) spectraof biacetyl in the gas phase (modified from Stier [80].)

cence lifetime. Molecular oxygen, which possesses a triplet ground state and twolow-lying singlet states (a1∆g and b1Σ+

g at 7882 cm−1 and 13,121 cm−1, respec-tively [41], is a particularly effective collision partner [25]. Consequently, to makeuse of the phosphorescence property of biacetyl, it must be used in an O2-freeenvironment and nitrogen is usually used as carrier gas.

Almy and Anderson [1] were among the first to study the lifetime of biacetylfluorescence experimentally. They also investigated the quenching of biacetylby oxygen. Comprehensive studies on photochemical processes of biacetyl weredone by the group of Noyes [60, 77] afterwards. They looked at the detailedmechanism of the primary process and its relationship to the singlet and tripletexcited states, which varies with wavelength [77] and temperature [60]. Later on,Garabedian, Doms and Sidebottom investigated the triplet-triplet annihilation inbiacetyl vapor. Sidebottom and coworkers [78] studied the lifetime of excitedbiacetyl singlet and triplet molecules in vapor phase experiments. They excitedbiacetyl with low-energy laser pulses of various wavelengths, and showed thatthe lifetime of the triplet state (phosphorescence lifetime) is independent of theexcitation wavelength and of the biacetyl pressure. They also considered the exci-tation intensity dependence of the phosphorescence quenching in biacetyl vapor,excited at 436.5 nm, and demonstrated that the rates of phosphorescence decayafter high intensity excitation deviate markedly from the rates observed at lowintensities [2]. The conclusion from all these was that triplet biacetyl moleculesare very efficiently deactivated by collisions with other triplet biacetyl molecu-les. Both collision partners then are lost for phosphorescence, and the process is

Biacetyl 49

S1

E (eV)

0

2

3

1

T1

S0

k1

kST

kdiss415.9 nm(2.98 eV)

k2

522 nm(2.37 eV)

570 nm(2.17 eV)

Figure 4.2: Photophysical processes in biacetyl laser excitation, starting with laserexcitation in the singlet system. Solid and dashed lines indicate radiative processes,wavy lines indicate non-radiative processes. Horizontal fat lines indicate effectiveenergy levels, but these in fact correspond to broader bands.

therefore known as triplet-triplet annihilation.In continuation of flow field diagnostics experiments, Jian-Bang and coworkers

proposed a new method for measuring the density, temperature and velocity ofN2 gas flow by laser-induced biacetyl phosphorescence [31]. They investigatedthe characteristics of the laser-induced phosphorescence of biacetyl mixed withN2 both in static gas and in one-dimensional pipe flow. Their theoretical andexperimental investigation showed that the temperature and density of N2 gasflow could be measured by observing the lifetime and initial intensity of biacetylphosphorescence. In their experiments, they also showed that the phosphores-cence lifetime is a function of temperature, but independent of density and con-centration. They claimed that the velocity could be measured by observing thetime of flight of the phosphorescent gas after pulsed laser excitation. Based ontheir studies [32], Hu and coworkers performed instantaneous, quantitative, pla-nar measurements of fluid flow, using biacetyl fluorescence and phosphorescenceemission [26, 27].

Concerning the phosphorescence characteristics of biacetyl, let us look at theluminescence of this molecule in more detail, on the basis of the energy levelscheme of Fig. 4.2. At the excitation wavelength employed, i.e., 416 nm, biacetylis raised to its first excited singlet state upon absorption of a photon. The sin-glet molecule can then cross over into the triplet manifold, or it can return tothe ground state via fluorescence, internal conversion or collisional quenching.Within the triplet manifold, molecules are expected to quickly relax down to thelowest vibrational state. From there, the molecule may return to the ground stateby phosphorescence or collisional quenching, or it may suffer dissociation. Colli-

50 4.3 Experimental Facilities

sional quenching may occur by collisions between triplet biacetyl molecules witheach other (the double wavy arrow in Fig. 4.2), or with other molecules (the sin-gle wavy arrow). It will turn out that the former process very probably leads todissociation of biacetyl, yielding products that are themselves efficient quenchersof triplet biacetyl. This will be discussed in more detail in the modelling sec-tion. Fluorescence and phosphorescence are both luminescent processes whileinternal conversion and collisional quenching are not. Moreover, due to the veryshort lifetime of the fluorescence emission (≈ 10 ns), phosphorescence is the onlyprocess that can be used in most flow visualization experiments. The followinglist of reactions summarizes the above considerations (with modification, fromSidebottom [78]):

Bi + hν → 1Bi (4.1a)1Bi → 3Bi (4.1b)3Bi → Bi + hνphos (4.1c)

3Bi + M → Bi (4.1d)3Bi + 3Bi → Bi∗ + Bi (4.1e)3Bi + Bi∗ → Bi + M (4.1f)

In these equations, Bi stands for the biacetyl molecule in the electronic groundstate, 1Bi indicates electronically excited biacetyl in the singlet system and 3Bias the first-excited triplet biacetyl molecule. Since the ratio of phosphorescenceto fluorescence yield is about 60 : 1 [61], we have neglected the vibrationallyexcited singlet-state biacetyl i.e., 1Bi→ Bi + h νflu. Furthermore, as the vibrationalrelaxation is very efficient and fast compared to the phosphorescence process, wetake it as being essentially instantaneous. In fact, we assumed that every act ofabsorption leads to a triplet biacetyl molecule in its ground vibrational state.

4.3 Experimental Facilities

For excitation of biacetyl, we chose a wavelength of λexc = 416 nm, close tothe absorption maximum [80]. Radiation of this wavelength was obtained byRaman-shifting the frequency-tripled output of a Nd:YAG laser (SpectraPhysicsPro 250-10) in a cell filled with 0.8 MPa of hydrogen, H2. The experimental setupis sketched in Fig. 4.3. The laser output is focused into the 80 cm long Raman cellby means of an f = 600 mm quartz lens. The exiting beams are collimated byan f = 500 mm lens, and the various orders were spatially separated by meansof a Pellin Broca prism. The 1st Stokes component was selected by means of adiaphragm, and focussed in the center of the test cell by various optics. Where

Biacetyl 51

Figure 4.3: The schematic of experimental facilities used for biacetyl measurements.

appropriate, the beam profile was cleaned by means of a spatial filter consistingof a pinhole between two positive lenses. Unless indicated otherwise, for the ex-periments we typically used a laser pulse energy in the order of a few µJ/pulse,which in fact, was too low for us to measure with the available equipment. Dif-fusion experiments were performed with two laser pulse energies, that we willdesignate by ‘high’ and ‘low’ power, respectively, the former being sufficientlyhigh for the TTA process to play a role, whereas in the experiments with ‘low’power there was no evidence for a discernable role of TTA.

As the diffusion experiments were performed in still gas, averaging couldbe employed to increase the signal-to-noise ratio. In addition, we increased thecamera exposure time te along with the write-read delay time t, such that te =

0.1 t. This approximately compensated for the decrease of the phosphorescencesignal with increasing delay time, the latter ranging from 0.5 to 500 µs.

The test cell was equipped with three quartz windows of 60 mm free aper-ture, arranged in a horizontal T-configuration, and could be evacuated by meansof a small rotary pump (Edwards XDS-10) equipped with a zeolite vapor trap

52 4.4 Results and Discussion

in its exhaust. The laser beam passed through the cell into a beam dump at theexit, and phosphorescence was collected unfiltered in the perpendicular directionby means of an intensified CCD camera (Princeton Instruments, PIMAX-2, 10242

pixels or ICCD-576G/RB-E, 5122 pixels, both 16 bit dynamic range) equippedwith a UV Nikor f/4.5 105 mm lens or a fixed-focus fast camera lens (B. Halle,f /2.5, 250 mm focal length). The camera field of view typically amounted to9.3 mm, corresponding to 9.1 µm/pixel. Timing of camera and laser was con-trolled by means of a Stanford Research Systems DG535 delay generator.

Analytical grade biacetyl (> 99% purity) was purchased from Sigma-Aldrich,and used as is. It was kept in a sealed erlenmeyer flask during the experiments.Carrier gas (N2, He, or SF6) was bubbled through the liquid and introduced intothe center of the test cell by means of a 1 mm diameter, circular nozzle in theend of a slightly thicker stainless steel tube, positioned just above the focus of theexcitation beam. By means of appropriate throttle valves, this setup allowed toperform stationary flow measurements at varying background pressure, as wellas still gas measurements.

4.4 Results and Discussion

4.4.1 Experimental Results

As mentioned in Chapter 2, the widening of written lines in MTV, or the blur-ring of more complicated patterns poses a fundamental limit on the accuracy ofthe velocity measurements. When the typical size of patterns is smaller than thetypical size of the flow structure, we expect that blurring is caused by moleculardiffusion which depends on the properties of both tracer and those of the carriergas. As explained there, the mutual diffusion coefficient depends on the reducedmass and the mean collisional cross-section. Paradoxically, little is gained by in-creasing the mass of the tracer molecule while keeping the collision cross-sectionsthe same. The largest effect on the mutual diffusion coefficient is through the col-lision cross-section: tracer molecules with an increasing size have a decreasingmutual diffusion coefficient.

In order to test the influence of the ambient gas on the evolution of the lineshape, we wrote tagged lines of triplet biacetyl molecules in He, N2 and SF6 car-rier gases at pressures of 0.5 and 1 bar. As mentioned, we determine the diffusioncoefficient of biacetyl by measuring the widening of the phosphorescent pattern(line); therefore, we tag the initial pattern as the reference and acquire the delayedimage after an appropriate delay time. Since the measurement was done in staticcondition, sufficient time was needed to observe distinguishable widening of the

Biacetyl 53

(a)

(b)

( c)

Figure 4.4: Time series images of laser-induced phosphorescent of tagged biacetylmolecules in static (a) helium, (b) nitrogen and (c) sulfur hexafluoride; all at P=1 bar.Each image is an average over 50 consecutive single laser shots. Images were scaledindividually.

54 4.4 Results and Discussion

x

y1 sm

50 sm

0 2 4 6 8

0 2 4 6 8x (mm)

Figure 4.5: Phosphorescing lines of triplet biacetyl molecules in still SF6 carrier gasat 1 bar for two delay times since excitation of the triplet molecules. At t = 50 µsafter creation, the line has widened considerably. The broadening, and the slight de-pression of the concentration in the center are due to the triplet–triplet annihilationreaction.

pattern, i.e., mostly tens of microseconds. We accumulated 50 images of singlelaser shots at each delay time. Fig. 4.4 depicts the results of laser-induced phos-phorescence of biacetyl molecules in He, N2 and SF6, at atmospheric pressure(P=1 bar) and different delay times. It’s worth to note that at the smaller delaytime we essentially probe the profile of the excitation beam through fluorescence.

The absolute initial number density n0 of triplet biacetyl molecules is notknown precisely in our experiments. It is determined by the vapor pressure of theground–state molecules, the energy of the 420 nm laser pulse, and the absorptionlength of the laser light. At ambient temperature T = 300 K, the vapor pressureof biacetyl molecules corresponds to a gas–phase density of 1.3× 1024 m−3, butwe do not know the concentration after the bubbling system. Therefore, we willchoose a value of n0 that fits the cross section of the tagged line. Two types ofexperiments were done: experiments in which the laser pulse energies were largeenough for the TTA process to be relevant (“high” power), and experiments atvery small pulse energies (“low” power) to measure the widening of lines due tomolecular diffusion only.

To have a better view, an enlarged view of typical tagged molecules is illus-trated in Fig. 4.5. The carrier gas in this case was SF6 gas at 1 bar. As can be seenat a delay time of 50 µs, the width of the line has increased, while the line profiledevelops a dip in the center. This behavior was also observed in other carriergases at 1 bar, but the central dip in the line profile in He carrier gas was smallest(see Fig. 4.4).

Biacetyl 55

-1 0 10

0.5

1.0

I(a

rb.

uni

ts)

-1 0 1

-.2 0 0.20.7

0.8

0.9

1.0

y (mm)

I(a

rb.

uni

ts)

(b)(a)

(c)

t

Figure 4.6: Line profiles Iy(y) of phosphorescent biacetyl molecules measured in SF6

gas at 0.5 bar. (a) At time delay t = 0, full lines shows the data, dashed line a fit of aLorentz profile, Iy(y) = (πσ)−1(1 + y2/σ2)−1, with σ = 6.5× 10−5 m. (b) Profiles atincreasing time delays, t = 0, 0.2, 0.5, 1, 2, 5, 10, 20, 50 and 100 µs. (c) Enlargement ofthe central region; the arrow points to increasing delay time. The profiles have beennormalized so that their maximum is 1.

The evolution of the observed line profiles is shown in Fig. 4.6. As demon-strated in Fig. 4.6(a), the fluorescence at zero time delay can in this case be repre-sented well by a Lorentzian profile, Iy(y) = (πσ)−1(1 + (y− y0)

2/σ2)−1, whereσ is the line width and y0 the line center. The evolution of a dip in the line centercan be clearly seen. We will argue below that this feature is due to a new quench-ing process of excited biacetyl molecules, thus revealing yet unknown details ofthe chemistry of triplet molecules.

The squared half–maximum width increment ∆2 of a Gaussian line grows dif-fusively as ∆2(t) = σ2

1/2(t)− σ21/2(0) = 16 ln 2 D t, with D the molecular diffusion

coefficient, and σ1/2 the full line width at half maximum. From now on we willcharacterize the widening of tagged biacetyl lines using ∆2(t).

Fig. 4.7 shows ∆2(t) for all our experiments at relatively large laser pulse en-ergies in He, N2 and SF6 carrier gas at 0.5 and 1 bar. All curves approximatelycollapse, which indicates that line widening of tagged biacetyl molecules is notinfluenced by the carrier gas, i.e., not through diffusion, but by interaction among

56 4.4 Results and Discussion

0 50 1000

2

4

6

8

*10 -7

t (µs)

∆2 (

m2

)

Figure 4.7: Time dependence of full–width half maximum increment ∆2. Triplet–biacetyl lines were written in He, N2 and SF6 buffer gases at pressures of 0.5 and 1bar. The dashed line indicates the line widening due to molecular diffusion in the 0.5bar He carrier gas.

biacetyl molecules only. At large times, the rise of ∆2(t) is much faster than thatof molecular diffusion, with the fastest growth in the low–pressure He gas. Thisasymptote is included in Fig. 4.7. We will now analyze the dynamical behav-ior of the profiles in terms of reaction equations for the triplet molecular density(Eq. 4.1).

4.4.2 Data Analysis

According to the processes Eqs. (4.1c, 4.1d), and (4.1e), in which the excited tripletdensity decays due to radiation, collisions with other molecules M and triplet mo-lecules 3Bi, the time–dependent radial concentration of triplet biacetyl molecules,ΘB, should be described by

∂θB

∂t= −k1θB − k2θ2

B + D∇2θB (4.2)

where k1 is the rate constant of linear decay, which includes radiation and quench-ing due to collisions with other molecules, such as oxygen. In an oxygen–freeenvironment the lifetime of triplet molecules is k−1

1 = 1.5 ms, but k1 rapidly in-creases with increasing oxygen concentration, k1 = 670 + 220 pO2 , with pO2 theoxygen pressure [78] in N m−2.

The rate constant k2 embodies the triplet-triplet annihilation reaction Eq. 4.1d.Its value, k2 = 1.39× 10−15 s−1 m−3, has been determined by Badcock and co-workers [2] using an experimental technique similar to ours. The information

Biacetyl 57

used was the temporal decay of the integrated line intensity. Due to the quadraticdependence on the concentration, this technique needs accurate information onthe line profile. The acoustic–optical technique in the study of Hunter et al. [28]yielded k2 = 7.6× 10−16 s−1 m−3, which is approximately half that of Badcock’swork [2]. Surprisingly, these values are larger than the hard–sphere molecu-lar collision rate, which indicates that TTA collisions are relatively efficient [1].We conclude that k2 is not known very well; in this study we take the valuek2 = 1.39× 10−15 s−1 m−3.

We assume that the initial density is rotationally symmetric such that∫ ∞

0θB(r, t = 0) 2πr dr = n0, (4.3)

is the total number of excited triplet molecules per unit length along the laserbeam. We also assume that the radial density profile θB(r, t) is proportional to theradial intensity profile Ir(r, t). What is observed in the experiment is the chord–integrated intensity profile Iy(y, t), which follows from the radial profile throughthe Abel transform,

Iy(y) =∫ ∞

y

Ir(r)(r2 − y2)1/2 r dr. (4.4)

The observed initial profile Iy(y, t = 0) is close to a Lorentzian (Fig. 4.6(a)), forwhich the inverse Abel transform can be done exactly, and

θB(r, 0) =n0

2πσ21

(1 + r2/σ2)3/2 . (4.5)

Starting from the initial profile, the time–dependent density profiles θB(r, t) canbe computed, but to compare them to the observed line profiles, they must againbe Abel transformed.

The last term on the right–hand side of Eq. (4.2) represents the effect of molec-ular diffusion, D∇2θB = D 1

r∂∂r (r

∂θB(r,t)∂r ). In the absence of molecular diffusion,

an ordinary differential equation results, with the analytic solution

θB(r, t) =k1θB(r, 0)e−k1t

k1 + k2θB(r, 0)(1− e−k1t). (4.6)

For long times, t≫ k−11 , the concentration is θB(r, t) = e−k1t/(k2/k1 + θB(r, 0)−1),

which becomes independent of the initial concentration, θB(r, t) = (k1/k2)e−k1t,if the initial concentration is large, θB(r, 0)≫ k1/k2. In that case, there is an initialdecay from the initial value, dθB/dt|t=0 ≈ −k1k2θ2

B(r, 0), which becomes steeperas the initial concentration increases. For short times, t ≪ k−1

1 and large initialconcentration, θB(r, t) ∼ t−1.

58 4.4 Results and Discussion

-1 0 10

0.5

1.0

y (mm)

I (ar

b. u

nits

)

-1 0 1y (mm)

-1 0 1y (mm)

(a) (b) (c)

Figure 4.8: Dots are measured line profiles in N2 carrier gas at 1 bar, at time delayst = 0, 50 and 100 µs, for frames (a), (b), and (c), respectively. Full lines are computedprofiles using Eqs. (4.7, 4.8).

If the initial concentration θB(r, 0) has a single maximum, as in our experi-ments, this first–order process cannot explain the observation of a dip growingin the center of the measured profile, and additional processes are needed. Thisconclusion remains unaltered when molecular diffusion is included, although ananalytic solution of Eq. (4.2) is no longer possible.

In order to explain the dip growing into the central portion of the written lineof phosphorescent biacetyl molecules, a mechanism that efficiently removes 3Bimolecules in locations where they are abundant is required. We consider twosuch mechanisms, differing in the fate of the collision partners in 3Bi− 3Bi colli-sions (the TTA events).

In the first case both collision partners end up in the ground state, and all ex-cess energy is liberated in the form of heat, raising the temperature of the carriergas. This locally increases the thermal decomposition of 3Bi. Concheanainn &Sidebottom report results on the decomposition of thermalized biacetyl triplets,which they, somewhat oxymoronically, call a “unimolecular pressure–dependentprocess” [14]. Relevant for our experiments is the temperature dependence oftheir high-pressure limiting rate constant kdiss, kdiss(T) = 2×1011exp(−7000/T),with T in K. It turns out that the temperature rise of the carrier gas is too small toexplain the enhanced decay of θB in the line center. Moreover, the observed diphardly depends on the carrier gas (He, N2, SF6), while their heat capacity differsapproximately by a factor of 3.

In the second mechanism, one of the collision partners ends up in the groundstate, while the other one dissociates into fragments. The dissociation productsare assumed to be efficient collisional quenchers of 3Bi, thus locally reducing the3Bi density. Highly internally excited biacetyl is likely to dissociate into two acetylfragments, CH3CO, with the excess energy raising the temperature. The quench-

Biacetyl 59

0 50 1000

2

4

6

8

*10 -7

t (µs)

∆2 (

m2

)

Figure 4.9: Full line is the computed line width ∆2(t) using Eqs. (4.2). Dashed line isthe computed line width without molecular diffusion. The dots are the same data asin Fig. 4.7.

ing efficiency of the dissociation product (which could also be a secondary prod-uct, resulting from a chemical reaction of the primary dissociation product) isunknown, and treated as a free variable in the model presented below.

We assume that each triplet–triplet annihilation collision produces two radi-cals, and that these radicals, with concentration θR, are not consumed. This sim-ple model results in the following equations for the concentrations

∂θB

∂t= −k1θB − k2θ2

B − k3θR θB + D∇2θB (4.7)

∂θR

∂t= k2θ2

B + D∇2θR (4.8)

The system of equations was solved numerically, with initial condition Eq. (4.5)and θR = 0. The initial density n0 was chosen such that n0 = 2.9× 1013 m−1, whilethe rate constant k3 = 0.1 k2 was chosen as best fit to the experimental intensityprofiles. The computed profiles are shown in Fig. 4.8; they agree well with theline profiles measured in N2 carrier gas at 1 bar, but in view of the choice of n0

and k3, this agreement can only be called qualitative.The squared relative widths ∆2(t) of the computed profiles are shown in Fig. 4.9,

and compared to the measurements. With our choice of n0, the width of the modelprofile agrees with the experiment at t = 100 µs. We conclude that the overalltime dependence of the model line shapes matches the experiment well.

Even at pulse energies of ≈ 2 µJ of Fig. 4.7, the widening of the lines is almostcompletely determined by the triplet–triplet annihilation process, with a smalleffect of molecular diffusion. For even smaller pulse energies, the nonlinearity ofbiacetyl tagging is depleted and ∆2(t) increases diffusively, as is illustrated in Fig.

60 4.5 Conclusion

0 200 4000

1

2

´10 -7

t (ms)

D2

(m2

0.02 0.05 0.1 0.2

10 -5

10 -4

1/m* (a.u.) -1

D(m

2s-1

)

) He

(a) (b)

N2

SF6

Figure 4.10: Widening of lines of tagged biacetyl molecules at low laser pulse energy.(a) Open circles connected by full lines show ∆2 measured in He, N2 and SF6 car-rier gas; the dashed lines are fits ∆2(t) = 16 ln 2 D t. (b) Open circles are measureddiffusion coefficients, dots are diffusion coefficients computed from Eq. (4.9).

4.10. Our results are consistent with the simple kinetic arguments mentioned inChapter 2, i.e., the mutual diffusion coefficient of biacetyl is smallest in SF6, theheaviest carrier gas, and largest in He, the lightest carrier gas.

The diffusion coefficients of excited triplet biacetyl molecules can be measuredfrom the linear dependence on t of ∆2 and have been compared to the simplehard–sphere coefficient for diffusion of biacetyl molecules into the carrier gas [11]

D12 =38

(kBT

2πm∗

)1/2 1n ([σ1 + σ2])/2)2 (4.9)

where the index 1 points to biacetyl and 2 to the carrier gas, σ1 and σ2 are themolecular radii of the two gases, m∗ is the reduced mass, m∗ = (m1 m2)/(m1 +

m2), and where we ignored the contribution of self–diffusion of the dilute bi-acetyl gas to line widening. Little is known about the radius of the excited bi-acetyl molecule; we have used the value σ1 = 2.9 × 10−10 m from Almy andAnderson [1]. Fig. 4.10(b) illustrates that the measured and computed diffusioncoefficients agree in their dependence on the reduced mass m∗, but all measureddiffusion coefficients are a factor ≈ 2.5 smaller than the computed ones. It sug-gests that the radius of the excited biacetyl is approximately twice as large as wasestimated by Almy and coworkers [1].

4.5 Conclusion

The loss of accuracy due to broadening of written patterns is a serious problem ofmolecular tagging velocimetry. In fact, for tagged tracers with Schmidt number

Biacetyl 61

one, when mass diffuses at the same rate as momentum, diffusional broadeningposes a fundamental limit on the application of MTV in turbulence. Small–scaleturbulent motion can only be resolved by using molecules which diffuse slower.Because of the presence of the reduced mass m∗ in the expression for the mutualdiffusion coefficient (Eq. (4.9)) the size of these molecules is more important thantheir mass. Heavy molecular tracers may move slower, but their diffusion in alight gas is determined by the mass of the light constituent. When m1/m2 ≫ 1,m∗ = m2, and vice versa. Therefore, an arbitrarily small molecular diffusion of atagged molecule can only be reached by increasing its diameter, not by increasingits mass.

Biacetyl is a relatively complex molecular tracer, which diffuses slower thanthe O2 and NO molecular tracers of other techniques [7, 15, 50, 51, 52, 59, 79, 84].However, the accuracy of biacetyl tagging is not set by its diffusion, but by chem-ical reaction of the excited molecules. Due to nonlinear processes, the line width(expressed in terms of its width at half maximum) increases much more quicklythan through molecular diffusion. Of course, this is a function of the initial lineprofile; line widening is relatively rapid for the Lorentzian beam used in our ex-periment, it will be slower for Gaussian beams and would be absent for a perfecttophat profile; however, diffraction prohibits such a profile for narrow lines. Weconclude that molecular tagging with biacetyl only works when visualizing largelength scales. Perhaps more interesting would be to use triplet biacetyl as a modelchemical reagent in turbulent flows.

Chapter5Lead Atoms as Heavy Flow

Tracers

We evaluate the usage of heavy atoms as molecular tracers for velocime-try in air. Lead tracers were created by photo–fragmentation of lead nitratemolecules, and made visible using laser–induced fluorescence. We studythe lifetime of the tracer luminescence in laminar flow environments withand without oxygen. We finally measure the widening of lines written in(slightly) turbulent flows. In its current state, the method is limited by theseeding mechanism.

64 5.1 Introduction

5.1 Introduction

Up to now, none of the examined candidates for molecular flow tracing couldembody all desired characteristics of an ideal tracer, that is, an atom or moleculethe distribution of which can be visualized with the following properties:

1. Sufficient signal to noise ratio: Because we want to study structures in tur-bulent flow, measurements must be done on the basis of single laser shots,without averaging.

2. Sufficiently long lifetime: We require structures to evolve over up to a fewKolmogorov time scales after tracer creation. The lifetime of the tracershould therefore exceed the smallest time scales in the flow, in our case typ-ically several tens of microseconds.

3. Its production should not interfere with the flow. This was seen to be one ofthe issues in the NO production via the APART scheme.

The results of our measurements using biacetyl as a tracer revealed that aphosphorescent molecule might not be an ideal option for our study, since thetriplet-triplet annihilation effect causes anomalies in the spatial distribution of thetracer. Hence, we figured that we might focus our tracer exploration on atoms.In fact, atoms have neither vibrational nor rotational degrees of freedom, so theelectronic transition strength is concentrated into single transitions, which makesthe excitation process much easier.

Besides its luminescent properties, the ideal tracer should meet some otherrequirements. The tracer produced in the APART scheme (NO molecule) hasvery light molar mass, consequently its Schmidt number is close to one and masswill diffuse at the same rate as momentum. Since the size of the smallest ed-dies (the Kolmogorov length scale) is determined by the diffusion of momentum(the kinematic viscosity), the tagged NO pattern will broaden to one Kolmogorovlength in one Kolmogorov time (small-eddy turn over time), hence the LIF pat-terns become too broad for observation of turbulent wrinkles. To overcome thisdisadvantage, we need to use a heavier precursor, which can either be in the gasphase or can easily be converted into the gas phase.

Considering these requirements, we have investigated heavy metal compounds.The idea was to photodissociate the compound and unleash the heavy metal atomin the first (‘write’) step, then conduct laser-induced fluorescence measurementson the created atom in the second step, very much like in the APART scheme. Thismeans that two laser beams are needed to accomplish this experiment. Therefore,the laser frequency availability has to be considered as an extra demand. Among

Lead 65

the heavy metal atoms which meet our requirements, some of them are highlyaggressive, some have an absorption frequency which is not available in our lab-oratory and some have very high boiling point which makes it quite difficult toconvert them into the gas phase. Our investigation of a heavy metal compoundfinally ended up with the lead nitrate molecule, Pb(NO3)2, after the discovery ofan experimental study of flame and post flame gases in combustion technologyusing lead vapor as tracer.

In this study, Buckley and coworkers [9] accomplished single shot measure-ments of lead vapor in a flame using an excimer laser fragmentation fluorescencespectroscopy (ELFFS) technique. The two laser frequencies which they used forphoto-fragmentation of lead nitrate molecules (λ = 193 nm) and lead atom ex-citation (λ = 283 nm) were both available in our laboratory. Besides, the highsolubility of lead nitrate molecules in water (52 g/100 mL, 20◦) [63] provides theopportunity of having a non-flammable solution; which is of great advantage,since the flammable solutions (e.g. lead nitrate in methanol or ethanol) can beeasily ignited by the excimer laser beam. The spectrometry of lead atoms rele-vant for this study is illustrated in Fig. 5.2. This chapter will describe the exper-imental investigation of turbulent and non-turbulent flows using laser-inducedfluorescence of lead atoms.

5.2 Experimental Facilities

This section elaborates on the experimental facilities used in different experi-mental runs. In this study, we used an excimer laser fragmentation fluores-cence method as has been used in combustion technology for detection of var-ious species in flames [9]. We used a 193 nm beam of an ArF laser, with a rep-etition rate of 10 Hz and pulse duration of 20 ns FWHM to photo-fragment thelead compound, Pb(NO3)2, into lead atoms and nitrate molecules. The photo-fragmentation process is illustrated in Fig. 5.1. The lead atom is what we areinterested in for use as a tracer in our flow, assuming that we can excite it with anappropriate wavelength and detect its luminescence.

To create the appropriate LIF wavelength a Nd:YAG-pumped dye laser oper-ated on Rhodamine 6G was used. This dye has a peak efficiency at the wave-length required for Pb-atom excitation, around 566 nm. The laser beam wasfrequency-doubled in a KDP crystal. Using a spectrometer, a series of preliminarytests were conducted to find the optimum excitation wavelength, which accord-ing to the lead energy level diagram depicted in Fig. 5.2.(a) is around 283.3 nm.The excitation-emission spectrum relevant for this case is shown in Fig. 5.2.(b).As can be seen, lead has two emission peaks at 365 nm and 405 nm respectively,

66 5.2 Experimental Facilities

and there is no detectable interference from other species.

To resolve the smallest length scales in turbulence, the width of the writtenpattern should be comparable to the Kolmogorov length scale η, which in ourcase is a few tens of micrometers. This width is determined by the beam widthof the excitation laser. To make a narrow cylindrical excimer laser beam, we useda composite lens ( f = 250 mm) in combination with an aperture of 1 mm radius.Further details of the experimental set-up can be found in Fig. 5.3. As is depicted,we used a combination of two cylindrical lenses in the dye laser beam to make athin light sheet at the position of the excimer laser beam focus in the air.

An important part of the experimental set-up were the flow facilities. Since westudy turbulence in gas phase, our tracer needs to be in the gas phase as well. Aswe mentioned in the introduction section, the lead nitrate compound was chosenbased on a successful experimental study in combustion technology [9]. In theirinvestigation, Buckley and co-workers used lead atoms produced from photo-fragmented lead nitrate molecules as tracers to study post flame gases. Leadatoms in their case were liberated by passage of the compound through the flamefront. In our case (without flame), we had to think of an appropriate approachto bring lead nitrate molecules into the gas phase. Finding a good solvent andusing an atomizer seemed to be the easiest and most practical approach to thisproblem.

Considering the solubility of lead nitrate in different liquids such as ethanol,methanol and water, a set of preliminary test experiments were performed inmethanol and water and at different concentrations. Lead nitrate crystals solved

Figure 5.1: Laser-induced photo-fragmentation scheme of lead nitrate.

Lead 67

(a)

(b)

Figure 5.2: (a) Lead energy levels [9], (b) excitation-emission spectrum, the verticalaxis shows the excitation wavelength while the horizontal axis represents the emittedfluorescent wavelength range.

in water with a concentration of 6000 ppm provided fluorescent signal with ade-quate signal to noise ratio, hence this setting was used for the final experimentalruns.

To bring it into the gas phase, we tried different seeding methods using a bub-bler, a nebulizer and an atomizer. The latter seemed to be the most successfulway of seeding in our case. Although we have recognized afterwards that thisapproach will likely not provide just individual lead atoms but also generatesclouds of lead nitrate crystals instead, due to its efficiency and simplicity, all ofour experiments were done using a six-jet atomizer (TSI 9306 atomizer). Fig. 5.4depicts the assembly of the atomizer with a detailed view of one of the six in-dividual particle generator atomizers within the liquid reservoir. To have theoptimum S/N ratio, all 6 jets of the atomizer were used in all measurements.

The operating principle of the atomizer is simple. As can be seen, the carriergas (pressurized air or nitrogen in our case) forms a high-velocity jet through a0.3 mm diameter orifice. The pressure drop from this jet draws liquid up througha narrow tube. The liquid is then broken up into droplets by this high-velocity

68 5.2 Experimental Facilities

Figure 5.3: Schematic of experimental facilities for lifetime and turbulent mixing mea-surements. The jet can easily be exchanged for a laminar flow generator, if desired.

air-jet. In this study, the input pressure of the carrier gas (air or nitrogen) wasalways set to 340 kPa (3.4 bar). For our input pressure, the aerosol flow-rate perjet was approximately 11 L/min with a mean droplet diameter of approximately0.3 µm for water solutions.

Experiments were done at two different conditions, that will be called weakand moderate turbulence. As shown in Fig. 5.3, a standard jet with well-documentedscaling properties [29] was used to create turbulence. An overpressure of P=300 Pa(3 mbar) and an upper limit of P=40 Pa (0.4 mbar) were used for the experimentsin strong and weak turbulence, respectively.

The last part of the experimental set up was the flow visualization section. AnICCD (intensified charge coupled device) camera (Princeton Instruments) wasused to detect the fluorescence from the excited lead atoms, and was placed at90 ◦ to the focused laser sheet. The camera worked at 10 Hz with resolution of1024 × 1024 pixels, combined with UV-sensitivity and a 16 bit dynamic range.A custom-made lens (Bernhard Halle Nachfl.) was used with a fixed focus of250 mm and f/2.5. To reject the collection of elastically scattered laser light by thecamera, a spectral high-pass filter with cut off wavelength of 375 nm was placedin front of the detector. The field of view defined by the laser sheet with a focusedcamera was 9.3× 9.3 mm2.

Lead 69

A digital delay generator (SRS DG535) was used to set the required delaybetween the Nd:YAG and excimer lasers and the ICCD camera. The delay timebetween writing the patterns (the excimer laser shots) and reading them (dyelaser shots), was varied depending on the experimental situation. In both casesof weak and moderate turbulence, we have been able to carry out single-shotmeasurements.

A surprising aspect of turbulence measurements was that in case of weak tur-bulence, lead atoms could survive for quite a long time in ambient air and wewere able to capture fluorescence images with a delay time of tens of microsec-onds, but in the case of moderate turbulence, lead atoms could only survive fora few microseconds after the writing process. This difference has defied explana-tion up to now.

A possible explanation for the finite lifetime of the lead atoms is chemistry, thechemical reaction between lead atoms and oxygen in air. To check this hypothesis,we performed a series of test experiments with lead as the tracer and two differentcarrier gases, air and nitrogen. These experiments were performed in the setupof Fig. 5.3 but in a laminar flow, in order to avoid ambient air entrainment.

A detailed view of the laminar flow generator and the experimental set up isdepicted in Fig. 5.5 and Fig. 5.6. As it is shown in Fig. 5.5, the carrier gas and

Figure 5.4: Schematic drawing of the atomizer assemblies.

70 5.3 Results and Discussion

the seeded tracers all went into the laminar flow generator via the same entrance.Fig. 5.5.b. illustrates the central part of the assembly, the porous plate.

(a) (b)

Figure 5.5: Schematic drawing of the laminar flow generator.

The initial idea behind using a laminar flow generator for this experimentis as follows: considering the dimensions of the porous plate (30 × 30 mm) incomparison to the size of our LIF pattern (9.3× 9.3 mm), by blowing a small flowof nitrogen (mixed with lead nitrate molecules) and observing the LIF patternnot too far downstream of the center of the porous plate, one can assume thatthere is no oxygen present there. Therefore, this experiment was done once withair and again with nitrogen as carrier gas, 1.5 cm above the porous plate center.The results of all the experiments using the laminar flow generator are shown inSection 5.3.4.

5.3 Results and Discussion

5.3.1 Lead Emission Spectrum

A first step in examining a molecule’s suitability as an MTV tracer is to perform aset of photochemical test experiments. These measurements will provide exper-imental data on tracer properties such as its lifetime and visibility, the optimumwavelength for the photo-fragmentation and excitation process, and the range oflaser power needed to photodissociate or excite the sample. The experimentalfacilities for performing these test runs is as shown in Fig. 5.3 (with laminar flowgenerator), except that for acquiring an emission spectrum, a spectrometer wasused in front of the ICCD camera. The purpose of using a spectrometer was to

Lead 71

validate that the luminescent signal is indeed LIF signal coming from lead atomscreated by excimer-laser-induced photo-fragmentation of the lead nitrate com-pound. As we discovered later, the dye laser beam can also photo-dissociate thelead nitrate molecule and create and excite lead atoms by itself. Therefore, fromnow on, by ‘LIF pattern’ we mean the laser-induced fluorescence of lead atomsproduced by the excimer laser only.

The initial purpose of using a burner was to duplicate the results of Buck-ley’s report [9], i.e., doing the experiment in a flame; the result of this measure-ment is similar to Fig. 5.2. We then used the burner as a laminar flow generator.The focused excimer laser beam with λ = 193 nm crossed the laminar flow ofair and supplemented by a mist of lead nitrate solution, 1.5 cm downstream theporous plate center. The dye laser wavelength was scanned over the range ofλ = 281.5 nm to λ = 283.5 nm. The spectrometer observed the fluorescent sig-nal 50 ns after firing the excimer laser. The result of this test run is illustrated inFig. 5.2. In this figure, the vertical coordinate represents the excitation frequencyof lead atoms while the horizontal axis represents the emission wavelength. Twoemission peaks assigned at λ = 365 nm and λ = 405 nm are in perfect agreementwith Buckley’s results. As illustrated in Fig. 5.2, the optimum lead LIF signal wasobserved at λ = 283.39 nm as the excitation wavelength. The dye laser outputpower was set to 8 mJ/pulse in subsequent experiments.

Figure 5.6: Close-up view of chemical test experiment facilities.

72 5.3 Results and Discussion

Figure 5.7: (a) First four images are consecutive images of laser-induced fluorescenceof lead atoms produced by excimer laser at h=10 cm above the jet and ∆t = 50 ns, lastimage in the row is the laser-induced fluorescence of lead atoms produced by the dyelaser itself (that is, without excimer laser pulse) at the same height ; (b) Fitted intensityprofile of the above patterns.

5.3.2 Lead Luminescent Lifetime in Weakly Turbulent Flow

As already mentioned, we study weak turbulence, which comes with a long Kol-mogorov time. The tracer lifetime should then be of the order of several Kol-mogorov time scales to be able to observe wrinkles in the LIF patterns, that is,in this case several tens of microseconds. So, our next goal was to identify thelifetime of lead atoms in our flow conditions.

The experimental set-up to measure the lifetime of lead atoms is shown inFig. 5.3. The two laser beams were focused in the center of the jet, 10 cm down-stream along the jet axis. The gas flow had a gauge pressure of 39 Pa (0.39 mbar)at the exit of the jet. A camera gate time of 100 ns was used, and we step thedelay times after the creation process, starting from 50 ns as the shortest and con-tinuing to longer delays until the LIF pattern was barely distinguishable from thebackground.

We acquired 50 images of single (write/read) laser shots at each delay time.In Fig. 5.7.(a), one can see four consecutive images of write/read laser shots atthe shortest delay time, ∆t = 50 ns, after subtraction of the dye laser-inducedfluorescence. The last image of the row is the background due to laser-inducedfluorescence of lead atoms which are produced by dye laser in the absence of the

Lead 73

Figure 5.8: Close up view of excimer laser-induced fluorescence pattern of leadatoms.

excimer laser pulse. To have a better view of these patterns, an enlarged versionof a typical captured image is illustrated in Fig. 5.8. As it is distinctly visible,the LIF pattern is not homogeneous, but contains portions with irregular struc-tures. From now on, we denote the most irregular and bulky structures as lumpsand less irregular, smaller ones as grains. Although all these irregular structureswere initially assumed to be dust particles vaporized by the laser beams, they arein fact lead nitrate crystals in the solid phase, according to a series of test mea-surements which revealed that their existence requires simultaneous operation ofexcimer and dye lasers. To put it differently, they are associated with clouds oflead atoms. Considering the seeding approach we used for turning lead nitratecrystals into the gas phase, this effect is perhaps not too surprising. The atomizercreates a mist of the solution, the water evaporates, so small crystallites will re-main and be advected. Besides the lumpy structures, the grainy structure of theLIF pattern is also related to the density of lead nitrate clusters in our flow. In con-clusion, one can consider all inhomogeneities of the LIF patterns as a drawbackof our seeding method; i.e., our seeding apparently does not provide a homoge-neous density distribution of lead atoms in the flow. Nevertheless, the existenceof smaller irregularities (grains) is not disturbing, but it is the presence of lumpsthat might give rise to abnormal broadening of the patterns.

As a consequence of this inhomogeneity, the data analysis needed to be donepartially manually. To avoid the inhomogeneities, we selected a region of interest

74 5.3 Results and Discussion

equivalent to 10 pixels in each image and performed all the data analysis on sucha region of interest. One region of interest is indicated by a rectangular bar inFig. 5.7.(a) as an example. Considering the non-uniformity of the dye laser beamshape along the horizontal axis due to the optical alignment, such a region ofinterest needs to be (as much as possible) at the same part of the pattern in all 50images. On the other hand, the lumpy structure of lead atoms might occur at anyposition along the pattern, therefore, the selection of region of interest was donemanually at all captured images. Subsequently, we averaged the region of interestin the horizontal dimension and made a vertical cross-section of the LIF pattern,perpendicular to the laser beam propagation. Fig. 5.7.(b) shows the Lorentzianfit on the cross-sections of each individual image. Such a fit will provide us theintegrated intensity of the LIF pattern and its width.

Figure 5.9: (a) Consecutive images of laser-induced fluorescence of lead atoms pro-duced by excimer laser at h=10 cm above the jet and ∆t = 20 µs,(b) Fitted-intensityprofile of the above patterns, image 4 was discarded due to its poor fit quality .

The same analysis was accomplished on the image series of each delay time,although at longer delay times, the captured images suffer from the lower signalto noise ratio which, as a consequence, leads to poor quality fits. It is worthwhileto note that due to the fast evolution of the turbulent eddies in time, the LIFimages need to be captured in single laser shots and we can not overcome thepoor S/N ratio problem by accumulating a series of images. When in some casesthe fitting process failed, the related image was discarded. Fig. 5.9.(a) illustrates 4consecutive images of lead LIF at ∆t = 20 µs and its fitted vertical cross-sections.

Lead 75

In this particular case, image 4 in the series was discarded due to the poor fitquality. Another major difference of these images in comparison to short delaytime images is the disappearance of irregular structures, in which we believe isdue to the high reactivity of these structures.

As mentioned, the lumps are actually made of clouds of lead nitrate crystals(in solid phase). Firing the excimer laser beam would heat them up and breakthem into fragments. These fragments will then chemically react with the speciesof carrier gas and could no longer be visualized by the dye laser beam.

5.3.3 Turbulent Mixing Experiment

Experiments in a moderately turbulent flow were done in the turbulent jet, withP=294 Pa (2.9 mbar); the results of these experimental runs are discussed in thepresent section. The flow field of the jet was characterized earlier at a distanceof 40 cm above the nozzle exit (Chapter 3). The present experiments are donecloser to the jet orifice at h = 0.1 m, with the flow properties inferred from thosemeasured at h = 0.4 m using the scaling documented in Wygnanski [87] and Hus-sein [29]. Table 5.1 summarizes the characteristics of both "weak" and "moderate"turbulence experiments at our working height h = 0.1 m.

flow h(m) U(m/s) u(m/s) ε(m2/s3) Reλ τη(s) η(m)

"Weak turbulence" 0.1 18 4.8 5× 103 3× 102 5.3× 10−5 2.8× 10−5

"Moderate turbulence" 0.1 31 8.4 2.8× 104 4× 102 2.3× 10−5 1.1× 10−6

Table 5.1: Characteristics of the turbulence jet flows used in the experiments withlead tagging. The flow properties were inferred from those measured at h=0.4 m, asdescribed Chapter 3, using scaling arguments from [87] and [29].

At each delay time, 200 single shot images were captured. Fig. 5.10 andFig. 5.11 illustrate 4 image sequences of these experiments at the shortest andlongest delay time, respectively. Similar to the experimental runs for measur-ing the lifetime in Section 5.3.1, the figures show four images of consecutive leadLIF at each delay time, with fitted vertical cross-section profile. An important andeasily recognizable difference between these results and the lifetime runs (Fig. 5.7and Fig. 5.9) is the improved homogeneity of the LIF patterns. This is a result ofturbulent mixing, which as an advantage, makes the data analysis process con-siderably easier; since the same region of interest can (in principle) be used for all200 images and allows automated data treatment.

Another surprise of these results is the small luminescent intensity of leadatoms in the presence of turbulence. As shown in fig. 5.11, the signal to noise

76 5.3 Results and Discussion

Figure 5.10: (a) The first four images are consecutive images of laser-induced fluo-rescence of lead atoms produced by the excimer laser at h=10 cm above the jet and∆t = 50 ns, the last image in the row is the laser-induced fluorescence of lead atomsproduced by the dye laser at the same height, which was used as background imagein the data processing; (b) Fitted intensity profile of the above patterns.

ratio is already poor at ∆t = 1 µs, hence, this is the longest delay time at whichwe could capture an LIF image.

5.3.4 Chemical Reaction Test

As mentioned in the experimental facilities section, the idea behind this experi-ment was to examine our hypothesis about the probable correlation between thelifetime of the lead atoms and their chemical reactivity. To evaluate our hypothe-sis, we decided to perform a series of test experiments with lead atoms as tracersand air and nitrogen as carrier gases. This experiment was performed using thesetup shown in Fig. 5.3, but now with the laminar flow generator.

An input pressure of 340 kPa (3.4 bar) of air or nitrogen was used to operatethe atomizer. We captured 50 consecutive images of laser-induced fluorescenceof lead atoms at different delay times after lead creation by the ArF laser. The firstset of images was acquired at 20 ns after excimer laser shot and the measurementwas continued until the time that the excimer induced fluorescence signal wasjust barely recognizable from the image background. Since the experiment wasperformed in laminar flow, we could now average over 50 images at each delaytime. Fig. 5.12 presents the results of this experiment in air.

Lead 77

In Fig. 5.12.(a), one can see 10 images of excimer laser-induced fluorescence oflead atoms captured at different delay times after the excimer laser shot, startingfrom ∆t = 20 ns as the shortest and ends up with ∆t = 50 µs as the longest de-lay time. A difference between these images and those presented in Sections 5.3.1and 5.3.3 is the laser-induced fluorescence of lead atoms produced by the dyelaser. The last image of Fig. 5.12.(a) shows the profile of laser-induced fluores-cence of lead atoms excited (solely) by the dye laser in laminar flow measure-ments. Contrary to the jet-experiments, the background is now inhomogeneous.The reason for this difference in dye-laser-induced background is unknown, butclearly a different technique had to be used in the data processing to account forthis background.

Fig. 5.13. illustrates the major complication of the data analysis. This figureshows the cross-section of each image along the vertical axis. The intensity profilehas a relatively narrow peak standing on a pedestal. The kind of narrow peak inthe profile arises from the LIF signal of lead atoms released from the lead nitratemolecules by radiation from the excimer laser, and derives its width from thewidth of the excimer laser beam. The broad pedestal is due to the fluorescence oflead nitrate molecules induced solely by the dye laser.

For analyzing these images, we divided each image into three areas, as de-picted in Fig. 5.13. This figure is an enlarged vertical cross-section shown in

Figure 5.11: (a) Consecutive images of laser-induced fluorescence of lead atoms pro-duced by excimer laser at h=10 cm above the jet and ∆t = 1 µs; (b) Fitted-intensityprofile of the above patterns; image 3 was discarded due to the poor fit quality.

78 5.3 Results and Discussion

20 ns 100 ns 200 ns 500 ns 1 µs 2 µs

5 µs 10 µs 20 µs 50 µs

(a)

(b)

( c)

Figure 5.12: (a) Time series of ten laser-induced fluorescent patterns of lead atomsproduced by excimer laser in laminar air flow. The last image is the laser-inducedfluorescence of lead atoms produced by the dye laser. Each image is an average over50 consecutive single laser shots. Note that images were scaled individually, (b) Ver-tical cross-section of the above patterns at the binned region of interest indicated, (c)Fitted-intensity profile of the excimer LIF images shown in section (a) after the dyelaser-induced fluorescence subtraction.

Lead 79

0 100 200 300 400 500 600 700 800 900 10001500

2000

2500

3000

Area 2.2

Area 2.1

Area 1

Figure 5.13: Cross-section profile of a typical excimer laser-induced fluorescence pat-tern of lead atoms in air in details. Area 1 is considered as constant background, area2.1 is regarded to laser-induced fluorescence of lead atoms produced by the dye laserand area 2.2 is the laser-induced fluorescence of lead atoms created by the excimerlaser beam.

Fig. 5.12.(b). The three areas in this figure are defined as follows:1. Area 1 is equivalent to the top and bottom of each image in Fig. 5.12.(a).

This area has been considered as constant background.2. We divided the central part of each image in Fig. 5.12.(a). in two parts:area 2.1. is taken to be the inner part of the center containing a narrow line

that is considered to be the laser-induced fluorescence of lead atoms produced bythe focused excimer laser beam and

area 2.2. as the outer part of the center which is considered to be the laser-induced fluorescence of lead atoms produced by the dye laser beam.

To analyze these data, we decided to first subtract the constant background(area 1) from each image, then separate area 2.1 and area 2.2 and fit a line-shapefunction to each part individually. First, the dye laser profile (area 2.1) was fittedto a line-shape function and the integrated intensity retrieved from this fittingprocess was subtracted from the LIF profile shown in Fig. 5.12.(b). For this pur-pose, we used a skewed Gaussian as fitting function, a selection based on the factthat such a function resulted in a nice fit result. Such a fit is shown in Fig. 5.13 inred.

These subtracted profiles were then fitted to another line-shape function whichprovides us with the integrated intensity and width of each LIF pattern. Fig. 5.12.(c)

80 5.3 Results and Discussion

shows these graphs of excimer laser-induced profiles of lead patterns, binnedover 10 horizontal pixels and fitted to a line-shape function. In these graphs, they-axis shows the intensity of LIF pattern in arbitrary units while the x-axis repre-sents the central part of Fig. 5.12.(a) (area 2) which is assumed to be the excimerlaser-induced fluorescence of lead atoms in pixels.

Nevertheless, one can realize that even after all of these subtraction processes,the graphs of Fig. 5.12.(c) still consist of several features, which are more pro-nounced at long delay times due to the poor signal to background ratio, i.e., thebackground is not fitted very well. The central peak (with a center at around150 pixel) was considered as the excimer laser-induced component in all of the10 graphs. Two other features of each graph are: a smaller peak (with a center ataround 60 pixel) and a valley of negative intensity (at around 190). These featuresare in fact due to the irregular shape of the dye LIF pattern and are not correctlyremoved by the subtraction process. It is also apparent that due to this inhomo-geneity, our program fails to fit at long delay times; hence, for these images, theintegrated intensity and width of the LIF pattern were derived manually.

To check the chemical reactivity of lead atoms, the experiment was repeatedwith nitrogen as carrier gas under the same experimental conditions. Resultsof this experiment are shown in Fig. 5.14. As it is illustrated in Fig. 5.14.(b) thesame data analysis was accomplished for the data on lead in nitrogen. Majordifferences between the lead LIF air results and nitrogen results are as follows:

1. The tracer lifetime is longer in nitrogen than in air.2. The appearance of less extra features in Fig. 5.14.(b) shows that the subtrac-

tion process of dye LIF contribution was more effective in this case.In the next section of this chapter, we are going to evaluate the results of lead

laser-induced fluorescence measurements performed under various experimen-tal conditions.

5.3.5 Intensity Decay and Line Widening

This section is dedicated to the results of data analysis of all LIF experiments per-formed in laminar and turbulent flow, using lead as a tracer. The necessity of sin-gle laser shot measurements in turbulence makes the intensity of the LIF patternone of the most significant parameters of LIF measurements. Fig. 5.15 summa-rizes the intensity decay of LIF patterns under different experimental conditions.

To retrieve the integrated intensity of LIF patterns at a specific delay time, wederived the area under the fit for that delay time. Each point in Fig. 5.15 repre-sents an average of the integrated intensity over the number of acquired images,i.e., 50 images in case of laminar flow and 200 images in case of turbulence. Asillustrated in the figure, the LIF pattern of lead survives much longer in nitrogen

Lead 81

20 ns 100 ns 200 ns 500 ns 1 µs 2 µs

5 µs 10 µs 20 µs 50 µs 100 µs

(a)

(b)

Figure 5.14: (a) Time series of ten laser-induced fluorescent patterns of lead atomsproduced by excimer laser in laminar nitrogen flow. The last image is the laser-induced fluorescence of lead atoms produced by the dye laser. Each image is an aver-age over 50 consecutive single laser shots. Note that images were scaled individually.(b) Fitted-intensity profile of above images after dye LIF subtraction.

82 5.3 Results and DiscussionI

(arb

. u

nits)

Figure 5.15: Intensity decay of lead laser-induced fluorescent patterns as a functionof delay time after firing the excimer laser, on linear (a) and logarithmic (b) time axes.

than in air, under the same experimental conditions in laminar flow. The rela-tively slow decay of the intensity in nitrogen can undoubtedly be related to thelower reaction rate of nitrogen molecules in comparison to oxygen.

Nevertheless, the LIF pattern has approximately the same intensity decay rateunder laminar and slightly turbulent flow conditions, which is in fact of no sur-prise considering the similar conditions (overall pressure) in these experimentalruns. However, the intensity has its fastest decay (shortest tracer lifetime) in thepresence of moderate turbulence.

An issue concerning the LIF patterns is the trend of the intensity decay versusdelay time. It seems that the intensity decay consists of two phases: short delaytimes and long delay times. Fig. 5.15(b) illustrates these two phases. It is alsoshown that the intensity has far slower decay at short delay times rather thanlonger ones, which might imply that the photo-chemical creation process is stillunder development.

Another parameter which is of critical importance in our measurements isthe width of the laser-induced fluorescent pattern. As it has been explained inChapter 2, by calculating the initial and final widths of the LIF patterns and con-sidering the delay time between the writing and reading process, we can extractthe mutual diffusion (dispersion) coefficient of the tracer in the flow.

As it is depicted in Fig. 5.16, the widening of the LIF patterns is slowest un-der the condition of the laminar flow experiment and is pretty much the samein air and in nitrogen. On the other hand, the lines written in weak turbulenceseem to broaden faster than the laminar flow data, which is in agreement withour expectation that weak turbulence enhances the widening process. Besides,

Lead 83

0 10 20 30 40 500.000.020.040.060.080.100.120.140.160.180.200.220.240.260.280.30

wid

th2 (m

m2 )

t ( s)

weak turbulence, air moderate turbulence, air laminar, air laminar, nitrogen

Figure 5.16: (a) Square width of lead laser-induced fluorescent patterns under differ-ent experimental conditions versus the delay time between creation and detection.

it seems that the widening process happens in two phases, i.e., short and longdelay times. This is illustrated in Fig. 5.16(b) with delay time on a logarithmicaxis. Apparently, the LIF patterns preserve the same width at short delay times,i.e., hundreds of nanoseconds. It seems that the creation process is still underdevelopment at this time scale. However, at about 1 µs after the excimer laserhas fired, the patterns face an extremely fast broadening and the molecular dif-fusion coefficient retrieved from these broaden patterns is far above the expectedvalue. We believe that this broadening is ballistic and is not due to moleculardiffusion. In fact, when the focused excimer laser beam crosses the flow, it injectsa lot of energy into the flow. Part of this energy will break the molecular bondingof lead nitrate molecules and create lead atoms. The excess part, however, willheat up the flow; since the center of the laser beam has the highest energy, theexcited lead atoms at the center of the pattern will blow away, an artifact whichleads into the broadening of the luminescent patterns. The smooth behavior ofthe width increase at short delay times implies that the chemical process of leadatoms creation is still under development, however, as time passes, the excessenergy transforms into the heat which warms up the flow. Therefore, the fastwidening of the patterns at long delay times is likely due to the thermal expan-sion of LIF patterns as a result of the high energy excimer laser shot, and can beconsidered an essential drawback of our diagnostic method.

84 5.4 Conclusions

5.4 Conclusions

In this chapter, we have demonstrated laser diagnostics measurements of lami-nar and turbulent gas flows using lead atoms as tracers. Single-laser-shot MTVmeasurements under different flow conditions illustrate that lead atoms couldbe considered as tracers for laminar and turbulent flows diagnostics measure-ments. In fact, their quite high molecular weight (207 g/mol) and fair chemicalreactivity make them a beneficial candidate for gas phase flow study. Neverthe-less, the result of this study can only be considered as a first step investigation totheir applicability for MTV measurements in weakly turbulent flows. Suggestionof practical adjustments which could lead to improved efficiency of experimentsare:

- Using a heavier and less reactive carrier gas, like SF6, to avoid chemicalreaction of created lead atoms with active quenchers like O2.

- Performing measurement in a big container filled with lead nitrate mist, tocreate a homogenous distribution of lead atoms in diagnosed flow.

- Using a different seeding method which provides individual lead nitratemolecules (instead of clouds) will also provide more homogenous distribution oflead atoms.

- Using lead nitrate molecules instead of lead nitrate crystals, to prevent thecreation of lumpy structures.

As a disadvantage, laser-induced fluorescence of lead atoms approach suffer-ers from the fact that lead atoms needs to be created under photo-fragmentationprocess, this makes the method an aggressive technique. Firing a high-energylaser beam into the flow will (under any circumstance) spread excess (unwanted)heat into the flow, which will consequently have abnormal effects on LIF patterns.

Chapter6Molecular Diffusion and

Turbulent Dispersion

We discuss the joint action of turbulent dispersion and molecular diffusionon the spreading of Gaussian puffs of a passive scalar. We describe the re-sults of a numerical simulation of a linear equation for the size of a Gaussiancloud, driven by a strongly turbulent velocity field which is computed bydirect numerical simulation. Surprisingly, analytical results of this equationinvolving a constant velocity field, can be compared well to the results of thesimulations. In the experiments the widening of lines with Gaussian crosssections was measured and compared to the theoretical framework. A re-markable finding of the experiments is that the observed rate of spreadingagrees very well with the numerical simulations. It also leads to the conjec-ture that, at least for short times, turbulent dispersion is aided by moleculardiffusion.

86 6.1 Introduction

6.1 Introduction

Imagine a situation where at t = 0 we release a puff of contaminant into a field ofturbulence, say dye released into a mixing tank. Two mechanisms will act on thiscloud of particles, molecular diffusion and turbulent dispersion. There is littlethat we can say a priori about the cooperation of these two effects, whether theyreinforce or suppress each other. Understanding this issue is extremely impor-tant, as it is at the basis of turbulent mixing at the smallest scales. It is at thesescales where chemical reactions take place.

The very first attempt to measure this interaction was done by Townsend [83]and Mickelsen [49]. They both reported that for long time, accelerated moleculardiffusion is negligible, so that molecular diffusion makes only an independentcontribution to the total dispersion. However, it turns out that all their measure-ments were done on scales of the order of the integral scale and their conclusionneed not hold for the small scales. Later on Saffman [75] calculated the role of in-teraction on the dispersion of the centroid of a particle cloud relative to its pointof release and the dispersion of the cloud relative to its centroid. He showed thatalthough the interaction increases the dispersion of a point of the cloud relativeto its centroid, the dispersion of the centroid of the cloud is reduced by a greateramount; so in total, the dispersion relative to the point of release is reduced.

Despite Saffman’s argument about the destructive effect of turbulence andmolecular diffusion interaction, Mazzino and Vergassola [46] showed numeri-cally that this interaction is not necessarily destructive. They assumed an oscil-lating Lagrangian correlation function and based on perturbation theory, theyshowed that the constructive effect associated with anticorrelated regions can in-deed be stronger than the decorrelating effect of Saffman’s argument. So com-petition between these two effects makes it possible to have either constructiveor destructive interaction, depending on the specific flow correlations. Whetherthese anticorrelated regions would really play a role in the interaction or not, isstill an open question. The present Chapter is concerned with a numerical andexperimental investigation of the effect of molecular diffusion and turbulent dis-persion.

In the absence of molecular diffusion, small clouds expand due to the strain-ing action of the velocity field. Their rate of expansion should be the rate of sepa-ration of a pair of points. Pair separation has been studied extensively, mostly inthe context of direct numerical simulations of turbulence. If we denote by δ thedistance between two particles, then

δ(t) = δ0 eγ t/τη ,

where δ is the spreading rate, which for asymptotically long times and vanishing

Molecular motion in turbulence 87

δ0 can be viewed as a Lyaponov exponent.For the value of such an exponent γ, Biferale et al. [6] found γ = 0.12 at

a Taylor–based Reynolds number Reλ = 280. This value depends on the initialseparation δ0 of the pair, it ranges from γ = 0.24 at δ0/η = 1.2 to γ = 0.15 atδ0/η = 9.8 [5]. Using the same numerical approach, Bec et al. obtained γ = 0.14at Reλ = 185 [3]. At much smaller values of Reλ = 93, Girimaji and Pope foundγ = 0.14, while at Reλ = 56, Kida and Goto found γ = 0.13 [21]. An experimentalvalue has been provided by Guala et al. who found λ = 0.21 at Reλ = 50, withinitial particle separation δ0/η = 5 [22]. Summarizing, the value of the largestLyapunov exponent γ that has been reported in the literature is around γ = 0.14,but can be as large as γ = 0.24. It is not clear whether this variation reflects aReynolds number dependence. The main interest of Kida and Goto [21] was inthe stretching of material lines. Naively one would say that a line would stretchat the same rate as random infinitesimal line elements, i.e., with the Lyapunovexponents, however, these line elements are correlated and the stretching rate ofan entire line was found to be 0.17.

6.2 Interaction of Turbulent and Molecular Disper-sion

Molecular diffusion will proceed independently of the turbulent motion only solong as the size ∆ of the cloud remains small compared to the size η of the smallesteddies of the turbulence, ∆ ≪ η. Then the total dispersion will be the sum of thetwo effects,

∆2(t) =⟨

Y2(t)⟩+ 4Dmolt (6.1)

Where⟨Y2(t)

⟩is the total dispersion due to turbulence which is equal to

⟨Y2(t)

⟩=

2∫ t

t0

∫ t′

t0⟨v(t′) v(t′′)⟩dt′ dt′′, where v(t) is the velocity of a fluid parcel and ⟨v(t′) v(t′′)⟩

is its time correlation. The second part of equation 6.1 represents molecular dif-fusion, with Dmol the molecular diffusion coefficient of the tracers.

To measure the molecular diffusion contribution in Eq. (6.1), the pattern widthneeds to be much less than the Kolmogorov length scale, so that velocity gradi-ents over the pattern can be ignored. When the turbulent velocity of a turbulentflow decreases, the related Kolmogorov length scale η will increase. Therefore,we can increase the Kolmogorov length scale η by reducing the turbulent veloc-ity u in experiments. In this way the width of our written line becomes smallerthan η and we are able to solely measure the molecular diffusion part. To mea-sure the turbulent dispersion part of Eq. (6.1), one must perform the experimentwith a much heavier tracer which has a much smaller Brownian motion.

88 6.2 Interaction of Turbulent and Molecular Dispersion

The interaction between turbulent dispersion and molecular diffusion can beinvestigated from two points of view: one is its effect on the dispersion of the cen-troid of a spreading cloud and another one involves the dispersion of the cloudrelative to its centroid, that is, the dispersion of the cloud in the Lagrangian frame.Saffman [75] argues that the interaction will decrease the dispersion of the centroidof the cloud (relative to the point of release) from

⟨Y2(t)

⟩to⟨

Y2(t)⟩− 2

9 Dmol ω2 t3,

where ω2 is the mean squared turbulent fluid vorticity, ω2 = τ−2η , and the an-

gular brackets denote an average over both the Brownian trajectory and real-izations of the turbulent velocity field. The point is that the velocity correla-tion of a Brownian particle which samples local velocity gradients contributesa term

⟨u∇2u

⟩< 0. In the Langrangian frame, however, Saffman [75] uses

Townsend’s [83] solution and cites an increase of the Gaussian cloud spreadingby 8/9Dmω2t3, however, a contribution due to the velocity gradients in over thecloud, 2/3∆2

0 (t/τη)2 was (inadvertently) omitted in his paper [75].Let us now briefly summarize the results from these two distinct points of

view. We assume that the cloud has a Gaussian shape with Gaussian size ∆ suchthat in one dimension the concentration field is C(x, t) ∝ exp(−x2/∆(t)2). In theLagrangian frame, the size of such a cloud with respect to its centroid increasesas

∆2(t) = ∆2(0) + 23 ∆2

0(t/τη)2 + 4Dmolt + 8

9 Dmt3/τ2η

= ∆2(0) + 23 ∆2

0(t/τη)2 + 4Dmolt (1 + 2

9(t/τη)2). (6.2)

The interaction is reflected by the term 29(t/τη)2, in our experiments, t/τη . 3,

so that the interaction, which increases the diffusive term from 4Dmt to 12 Dmt,which should be well observable.

From the Eulerian point of view, where we consider the spreading of a cloudwith respect to its point of origin,

∆2(t) = ∆2(0) +⟨

Y2(t)⟩+ 4Dmolt− 2

9 Dmolω2t3

= ∆2(0) +⟨

Y2(t)⟩+ 4 Dmol t

(1− 1

18(t/τη)2)

(6.3)

At times shorter than the Lagrangian integral time scale,⟨Y2(t)

⟩= 2 u2 t2. The

interaction between turbulence and molecular diffusion will decrease the effectof molecular diffusion from 4 Dmolt to 2 Dmolt at the longest delay times in ourexperiments. However, the term due to turbulent dispersion is much larger thanthe one due to molecular diffusion, and it will be impossible to observe the inter-action effect in Eq. (6.3).

Molecular motion in turbulence 89

The arguments presented here are qualitative, and are based upon assump-tions about the (Lagrangian) statistics of the velocity field. In the next section wewill resort to numerical simulations, allowing for the full detail of Lagrangianturbulent diffusion.

6.3 Numerical simulations

The equation for the evolution of the concentration C(x, t) of a passive scalar in aturbulent velocity field, 1

∂C∂t

+ (u.∇) = Dmol∇2C, (6.4)

is linear, but the concentration field C(x, t) inherits highly nontrivial statisticsfrom the velocity field u(x, t) by which it is advected, dx/dt = u(x, t).

For small Gaussian clouds it is possible to derive an interesting corollary ofEq. (6.4) that contains both the action of turbulent strain and molecular diffusion.Let us assume that at the moment of release the cloud has a Gaussian profile,C(x) ∝ exp(−xTΓ−1x), which is centered at x = 0 and has sizes determinedby the principal axes of the matrix Γ; in one dimension, Γ11 = σ2. The mannerin which this cloud spreads and deforms in the turbulent velocity field u(x, t) isdescribed by an equation for Γ,

dΓ

dt= 4Dmol I + AΓ + ΓAT, (6.5)

where the elements of the matrix A are the velocity gradients, Ai,j = ∂ui/∂xj, I isthe unit matrix, and Dmol is the molecular diffusion coefficient. For completeness,the details of the derivation, which originates from Tennekes and Lumley [82] areprovided in Section 6.6.

In Eq. (6.5) it is assumed that the size of the Gaussian remains so small that thevelocity field may be linearized. At the largest Reynolds numbers in our experi-ment, Reλ ≈ 500, the width of the initially written line is σ0 ≈ 3η, while the line isobserved during a time τ ≈ 3τη, when its width has increased to σ ≈ 7η. There-fore, we believe that our experiment remains in the linear regime where Eq. (6.5)applies. In our experiment the initially written cloud is a line with Gaussian crosssection. A projection of this line onto a plane perpendicular to the line of sightis followed in time. Let us assume that this line is composed of Gaussian balls.As time evolves, these balls will be stretched to ellipsoids, with their long axis

1The results presented in this section was mainly done by Enrico Calzavarini, who kindlyagreed to share his unpublished work.

90 6.3 Numerical simulations

pointing in the direction of fastest growth. Therefore, it is tempting to associatethe intermediate eigenvalue of Γ to the transverse width of the lines.

The dimensionless form of Eq. (6.5),

dΓ

dt= 4I + AΓ + ΓA

T, (6.6)

with dimensionless time t/τη, squared size Γ = Γ/Dmolτη = Γ/Sc η2, and A =

A/τη, illustrates that for a given velocity field with a given strain rate A(t), theinitial squared size Γ0 of the Gaussian blob is the only remaining parameter, withthe effect of molecular diffusion being largest for the smallest initial sizes. It isuseful and instructive to discuss the solutions of Eq. 6.6 for a few model situationsin which the gradient matrix A is assumed constant [10].

If A contains a single non–zero matrix element, Axy = s, it can be shownreadily that

Γxx(t) = Γ0 + 4Dmolt + sΓ0t2 + 43 Dmols2t3

Γyy(t) = Γzz(t) = Γ0 + 4Dmolt (6.7)

Γxy(t) = Γyx(t) = sΓ0t + 2Dmolst2.

The t3 dependence of Γxx owes to the combined action of diffusion and strain.The squared size of a diffusive cloud increases as Dmolt, while it is torn apartballistically by the gradients according to (st)2. The resulting growth with timeis the product of these two factors.

The more general case, with strain organized as Axy = Ayx = s displaysboth diffusive spreading and exponential growth. As Calzavarini et al. haveshown, it is possible to solve in this case for the matrix Γ(t), which now has 4nonzero elements, with the direction of fastest growth determined by the largesteigenvalue of Γ [10],

Γ1(t) = Γ0e2st +Dmol

s

(e2st − 1

)≈ Γ0 + 4(Γ0s/2 + Dmol)t = Γ0 + 4 D t, (6.8)

which defines an effective diffusion coefficient, D = Dmol + Γ0s/2. The dimen-sional estimate for the shear rate in isotropic turbulence is s = ⟨(∂yux)2⟩1/2 =

(2/15)1/2τ−1η , which leads to the prediction, D = Dmol + (2/15)1/2Γ0/2τη. We

notice that the effective diffusion also depends on the (squared) initial size of thespot Γ0. Most importantly, however, our model implies a particular combina-tion of the effects of molecular diffusion and turbulent dispersion, such that forshort times it is the sum of diffusive and exponential spreading. In general, whenthe gradients must be taken along the path of a fluid parcel in turbulence, it is aquestion whether these two effects are additive.

Molecular motion in turbulence 91

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

Cor

r(t)

t/τη

Reλ= 400 , uidiujdiui

Reλ= 180 , uidiujdiui

Figure 6.1: Time correlations of the longitudinal, i = j and transverse i = j velocitygradients along a Lagrangian trajectory. The transverse gradients are more persistentin time.

Let us now summarize the results of the numerical simulations. The numeri-cal integration of Eq. 6.6 is done for the gradients A(t) that have been computedin a direct numerical simulation of the Navier–Stokes equations on a periodic do-main at Reλ = 400 and 180, which corresponds to spatial grids of 20483 and 5123

points, respectively [4].

The turbulent dispersion of the Gaussian spot is driven by the gradients Aalong the Lagrangian path of the fluid parcel. The elements of Ai,j can be sepa-rated crudely into the ones involving strain, the longitudinal i = j, and the onesinvolving rotation, the transverse i = j. The time correlations of these matrix ele-ments along a Lagrangian trajectory are shown in Fig. 6.1 [10]. It appears that thetransverse gradients are much more persistent in time, which suggests the stronginfluence of small–scale vortical events. As these events act in a more correlatedfashion that the strain events, we conclude that the dispersion of the cloud sizein Eq. 6.5 is dominated by the transverse gradients. In isotropic turbulence, thedimensional estimate for the root–mean–square magnitude of these gradients is(2/15)1/2 τ−1

η . It will turn out that this number also provides the correct orderof magnitude for the size increase of Gaussian puffs in the numerical simulationsand the width increase of Gaussian lines in the experiment.

Fig. 6.2(a) [10] shows that the analytical solutions of the Gaussian equation,Eq. (6.8), can actually be identified in the numerical results. In particular, whenthe initial squared size of the blob Γ0 = 0, the increase with t3 can be seen, whilefor the largest squared size, Γ0 = 8 η2, the quadratic increase prevails. This resultis remarkable, because the velocity gradients are now the actual fluctuating ones

92 6.3 Numerical simulations

0 2 40

50

100

0.1 110 -4

10 -3

10 -2

0.1

1

10

10 2

t /th

Γ0

= 0.5

Γ0

= 8 Γ 1Γ 2

5

(a) (b)Γ

-Γ 0

<>

4 t

-x x

Figure 6.2: Average blob sizes in a turbulent flow. (a) Effect of the initial conditions onthe matrix element Γ11, for initial sizes Γ0 = 0.5, and Γ0 = 8, respectively. The effect ofmolecular diffusion has been subtracted. Dashed lines: ⟨Γ11(t)⟩− Γ0− 4t = 4

3 s2 t3 and⟨Γ11(t)⟩ − Γ0 − 4t = s Γ0 t2 for Γ0 = 0.5, and Γ0 = 8, respectively, with s = (2/15)1/2.The matrix Γ has been made dimensionless by the Kolmogorov length η, as Γ/η2. Asthe initial size of the blob increases, the initial growth slows down, shifting from a t3

to a t2 behavior. This behavior is the same as that seen in simple analytical solutionsEq. 6.8, which were derived for a constant value s of the gradient Axy. (b) Solid linesare largest and next largest eigenvalues of Γ, for Γ0 = 8, dashed line is Eq. 6.8.

from a direct numerical simulation of turbulence, and are not constant, such asassumed in Eq. (6.8).

Another striking result from the direct numerical simulations of the velocityfield concerns the statistics of the fluctuating gradients along a Lagrangian tra-jectory. As is well–known, the (small–scale) gradients in strong turbulence arehighly intermittent, and have a probability density function which strongly de-viates from Gaussian. The results are shown in Fig. 6.3 [10]. It appears that theprobability density function (PDF) of the transverse gradients Ai =j is much moreintermittent than the one from the longitudinal gradients Aii. We also notice theclear dependence on the Reynolds number; the intermittency becomes strongerwith increasing Reynolds number.

In Section 6.4 we will present results on the fluctuations of the Gaussian widthof lines, which enables us to discuss the relation between the statistics of the gra-dients and the statistics of Gaussian blob sizes.

Molecular motion in turbulence 93

10-810-710-610-510-410-310-210-1100

-20 -10 0 10 20

PDF(

di u

i )

di ui /< di ui >rms

Reλ = 400

Reλ = 180

exp(-x)

10-810-710-610-510-410-310-210-1100

-20 -10 0 10 20

PDF(

di u

j )

di uj /< di uj >rms

Reλ = 400

Reλ = 180

exp(-x)

Figure 6.3: Probability density function (PDF) of the diagonal ∂iui and off–diagonal∂iuj gradient matrix elements. Not that the PDF of the diagonal matrix elements isskewed, while that of the off–diagonal elements is symmetric.

6.4 Experiments

6.4.1 Setup and data analysis

The experimental setup is similar to the one which has already been describedin the preceding chapters of this thesis, but for completeness we will start thediscussion in this Section with a brief recapitulation of the used techniques. Aschematic view of the experimental setup is shown in Fig. 6.4. Writing thin linesin the turbulent air flow was done by focusing the beam of an ArF excimer laser(λ = 193 nm) with a pulse energy of about 40 mJ/pulse using an optimized lens.The tagged line has a waist diameter of about 50 µm. Along this focus NO isformed over a length of approximately 1 cm. Therefore, the line extends outsidethe 6.4× 6.4 mm2 field of view of the camera. The duration of the writing laserpulse is a few tens of ns, which is instantaneous on the time scale of the turbu-lence. The reading laser is fired with delays ranging from 3 µs to as much as50 µs with respect to the tagging laser. This frequency-mixed Nd:YAG-pumped

94 6.4 Experiments

dye laser is operated at a wavelength of 226 nm to visualize the created NO tag-ging molecules. The probe laser excites the γ-bands of NO, and the resulting LIFemission from the excited (A) state is detected with the camera system. In theexperiments the dye laser beam is aligned anti-collinearly to the excimer beamand both travel perpendicular to the mean flow direction. The beam diameterwas adjusted to result in maximal intensity while still encompassing the writtenline. Also the reading of the deformed line is instantaneous on the time scale ofthe turbulence.

The UV fluorescence radiation from the NO molecules is observed with anintensified gated CCD camera. The light incident on the camera is filtered usinga high-pass filter that removes Rayleigh scattered light from both lasers whiletransmitting most of the NO fluorescence. The write-read delay t is controlled bytiming the respective laser pulses using a multi-channel delay generator (StanfordDG535), which also synchronizes the camera gate to the read laser pulse. Thecamera images are captured using a high speed frame grabber and then storedfor off–line processing.

The wrinkled and widened lines of the deformed patterns are traced usingan image processing technique based on active contours which finds their back-bone [7]. Next, the profiles of perpendicular sections are determined by fittingGaussian to the line intensity I(y, s) = I(s) exp(−y2/σ(s, t)2) where y is mea-sured perpendicular to the line center, σ(s) is the line width, and s is the chordlength. It is these lines that we view as small-scale clouds; they have a diameterσ(s, t) comparable to the Kolmogorov scale η. Notice that σ2 should be com-pared to Γ in Sec. 6.3. We follow these clouds in the Lagrangian frame, and wecollect the statistical properties of σ(s, t) for increasing delay time t between writ-ing and reading. The various image processing steps are illustrated in Fig. 6.4.The nitric oxide tracer molecules which are created in this experiment have amolecular mass that is comparable to that of the indigenous air molecules. Asa consequence, the mass diffusion rate Dmol = 2.42 × 10−5 m2s−1 of the traceris comparable to the kinematic viscosity of air, ν = 1.5× 10−5 m2s−1; their ratiodefines the Schmidt number, Sc = ν/Dmol = 0.62.

In our experiment a strongly turbulent air flow emerges from a jet, with di-ameter L = 0.1 m. In the field of view of the camera, 40 jet diameters or 0.4 mdownstream, the flow is approximately homogeneous and isotropic, with typicalmean velocity U = 46 m/s, root-mean-square velocity u = 12 m/s, Taylor-scaleReynolds number Rλ = 500, Kolmogorov scale η = 14 µm, and Kolmogorovtime τη = 14 µs. The mean and turbulent velocities can be measured well fromthe displacement of the tagged lines, but since their initial width is a few timesthe Kolmogorov length η, the gradients needed for an estimate of the dissipa-

Molecular motion in turbulence 95

pulsed dye laser226 nm, reading

pulsed excimer laser193 nm,writing

x

y turbulentjet flow

camera

2

5

4 1

3

-1 0 10

1

2

y (mm)

I(a

rb.

uni

ts)

0 2 4 60

100

200

300

y (mm)

σ(m

m)

(b) (c)

(a)

Figure 6.4: Experimental setup for molecular tagging. The beam of an ArF excimerlaser (1) at λ = 193 nm is focussed into the 6.4× 6.4 mm2 field of view (2) by a lens (3).A while later the created NO molecules are illuminated by a light pulse from the dyelaser (4) at λ = 226 nm. This wavelength is blocked by an absorption filter (5), whichtransmits the induced fluorescence. The UV image is registered by a gated, intensifiedcamera (6). The inset illustrates the processing of a registered line at a time delay oft = 30 µs, which consists of the following steps. (a) The backbone of the line is foundusing active contours. (b) Is the Gaussian width along the line, (c) is a Gaussian fit ofa perpendicular section (indicated by the white line in (a)).

96 6.4 Experiments

0 1 2 30

0.5

1.0

10 3

y (mm)

I(a

rb.

uni

ts)

0 0.5 1.010 -9

0

1

2

3

410 -7

t 2 (s)

s2

(m2)

(a) (b)´

´

´

Figure 6.5: The width of averaged lines as a function of the delay time t betweenwriting and reading. (a) Full lines are measured profiles at t = 0.2, 15 and 30 µs(t/τη = 0, 1.1, 2.1). The intensities at different time delays cannot be compared.Dashed lines are Gaussian fits I(y) ∝ exp(−y2/σ2). (b) Dots are widths σ(t)2− σ(0)2,dashed line is σ2(t)− σ(0)2 = 2 u2 t2, with u = 12 m s−1.

tion rate ϵ were measured using hot–wire anemometry, together with the scalingϵ = Cϵu3/L of a self–preserved turbulent jet flow; for Cϵ we found Cϵ = 0.47.

6.4.2 Experimental results

Lines were written at t = 0, and imaged at time delay t, where t ranged from0.2 to 50 µs; this was repeated 4× 103 times. The time between two subsequentwritten lines is 100 ms, which is much larger than any turbulence time scale, sothat all 4× 103 lines at a given time delay t may be considered independent. Atotal of 5.2× 104 images was analyzed.

The simplest approach is to superpose all images at a given time delay t. Thiscorresponds to the mean dispersion of a cloud in the Eulerian frame. If the con-centration profile of such a cloud is Gaussian, C(y) ∝ exp(−y2/σ2), its Gaussianwidth σ should increase as σ2(t) = σ(0)2 + 4 Dmol t + 2u2 t2. This behavior isillustrated in Fig. 6.5, which shows that the accumulated lines have a Gaussianprofile, but that their width increases slightly faster than the prediction. We alsonotice that for the accumulated lines the effect of molecular diffusion is irrelevant.The width is a factor of 5 larger than the width of the individual lines, and at longdelay times t, the profile of the reading laser starts to be felt.

The dispersion of clouds in the Lagrangian frame is shown in Fig. 6.6. A strik-ing result is that the measured effective diffusion coefficient D = 6.8 m2s−1 agreeswith the estimate Dmol + (2/15)1/2Γ0/2 ∗ τη = 6.9 m2s−1.

However, the long term exponential increase, which can be seen in Γ1(t) ofEq.6.8, or the long time behavior of the simpler addition of molecular diffusion

Molecular motion in turbulence 97

0 2 4*10 -50

1

2

*10 -8

t (s)

σ2 (

m2

)

Figure 6.6: Dots connected by line is the dependency of the average width ⟨σ2⟩on the time delay τ between writing and reading lines. The error bars indicatethe variation of σ2 along the written line. Dashed line shows ⟨σ2(t)⟩ = 4Dt, withD = 6.8 m2s−1. The dash–dotted line indicates σ2(t) = 4 Dmol t + σ2(0) exp(2γt/τη),with γ = (2/15)1/2.

and turbulent dispersion appears to be faster than what is observed experimen-tally.

The stretching and squeezing of Gaussian blobs is caused by the local gradi-ents of the turbulent flow. In strong turbulence, these gradients are highly non–Gaussian, with exponential tails of the PDF. The question is if this property isinherited by the shape fluctuations of Gaussian blobs. These fluctuations weremeasured at two delay times, t = 15 µs (t/τη = 1.1) and t = 30 µs (t/τη = 2.1),the result is shown in Fig. 6.7. The results show that the PDF of Gaussian widthsis close to lognormal, with exponential tails growing with increasing delay time.Surprisingly, the anomalous statistics of the local gradients is not inherited by themeasured blob shape fluctuations. The fluctuations, ⟨(σ− ⟨σ⟩)2/⟨σ⟩2 as a func-tion of delay time t/τη increase approximately proportional to delay time t. Theydo not vanish at small delay times because of pixel noise in the registered images.

6.5 Conclusion

In this Chapter we discussed the spreading of (Gaussian) blobs under the jointaction of turbulent dispersion and molecular diffusion. Many years ago, Saffmanpredicted that molecular diffusion suppresses the effect of turbulent dispersionin the laboratory (Eulerian) frame of reference. The results of such an experi-ment are shown in Fig. 6.5. Clearly, for our Schmidt number unity molecules, thespreading of a cloud with respect to the origin is dominated by turbulent motion,

98 6.5 Conclusion

0 2 410 -5

10 -4

10 -3

10 -2

0.1

1

σ/<σ>

PD

F

-2 -1 0 1 2log(σ/<σ>)

0 1 2 3 40

0.05

0.10

0.15

t/τ η

<σ2

>/<

σ>2

- 1

(a) (b)

(c)

Figure 6.7: (a) Histogram of relative widths σ/⟨σ⟩ at time delays τ = 15 and 30 µs.(b) Same as (a), but now on logarithmic horizontal axis. The dashed lines indicatelognormal distributions, P(σ) ∝ exp(−σ2/∆2), with Gaussian widths ∆ = 0.23, and0.26. (c) Fluctuations of Gaussian widths, ⟨(σ− ⟨σ⟩)2/⟨σ⟩2 as a function of delay timet/τη .

and the predicted effect of the joint action of turbulence and molecular diffusionit too small to be observed. Also, we must realize that the turbulent contributionto the predicted σ2(t) = σ(0)2 + 4 Dmol t + 2u2 t2 can only hold for times muchshorter than the Lagrangian integral time.

More interesting is the widening of Gaussian lines, which is by itself a La-grangian quantity. For short times numerical simulations and experiments agreeon a value for the Lyapunov exponent, λ = (2/15)1/2 ≈ 0.37, which is muchlarger than the values cited in the literature so far. A caveat of course is that theLyapunov exponent is a long–time average, times which we cannot reach in theexperiment.

Finally, it is not sure whether the measured line widening should be comparedto the largest Γ1 or next largest Γ2 eigenvalue of Γ. Fig. 6.2(b) shows that theline widening with the effective diffusion D (Eq. 6.8), which is actually observedexperimentally, lies between Γ1 and Γ2. We have argued that the rate of increaseof the transverse width of lines should be compared to Γ2. Also, an average of thelocal expansion over a material line, as is done in the experiment, is not the same

Molecular motion in turbulence 99

as an average of the expansion of randomly picked Gaussian blobs, as is done inthe numerical approach.

The ultimate conclusion of this Chapter is that diffusion aids turbulent disper-sion.

100 6.6 Derivation of equation for Gaussian blobs

6.6 Derivation of equation for Gaussian blobs

An analytic equation can be formulated for the widening of Gaussian clouds.This attractive model can provide an important framework for understandingthe widening of tagged lines in our experiment. The model does not solve theadvection–diffusion equation for arbitrary distributions of the concentration, butrestricts these distributions to Gaussian profiles. The advection–diffusion equa-tion is

∂ρ

∂t+ (u · ∇)ρ = D∇2ρ, (6.9)

We now introduce a Lagrangian variable ξi = xi − Xi(t), where dXidt = ui(Xi, t),

therefore we define ρ′(ξ, t) = ρ(Xi + ξi, t) and

∂ρ′

∂t=

∂ρ

∂t+ Xi

∂ρ

∂xi.

Substitution in equation 6.9 results in

∂ρ′

∂t+ (ui − Xi)

∂ρ′

∂ξi= D

∂2ρ′

∂ξ j∂ξ j.

We now make a linear approximation of the velocity field around the Lagrangiantrajectory, ui − Xi ≈ ξk(∂ui/∂ξk) so that

∂ρ

∂t+ ξk

∂ui

∂ξk

∂ρ

∂ξi= D

∂2ρ

∂ξ j∂ξ j.

Next assume that the concentration field takes on the shape of a Gaussiancloud as it is carried along by the turbulent velocity field,

ρ(x, t) =1

π3/2(detΓ)1/2 e−xT Γ−1 x,

where Γ(t) is the variance matrix. In one dimension we recognize a simple Gaus-sian

ρ(x, t) =1

π1/2σe−x2/σ2

,

with σ the Gaussian width. The moments of such a cloud are∫ξpξq ρ dξ = Γpk,

then∂Γpq

∂t+

∫ξp ξq ξk

∂ui

∂ξk

∂ρ

∂ξidξ = D

∫ξpξq

∂2ρ

∂ξ j∂ξidξ. (6.10)

Molecular motion in turbulence 101

Let us call Aik = ∂ui∂ξk

the strain tensor, then taking into account compressibilitywe can write

∂ui

∂ξk

∂ρ

∂ξi=

∂

∂ξi

(ρ

∂ui

∂ξk

). (6.11)

Integrating by parts and realizing that ρ and its derivatives disappear far away,∫ξpξqξk

∂

∂ξi

(ρ

∂ui

∂ξk

)dξ = −

∫ρ

∂ui

∂ξk

∂

∂ξi

(ξpξqξk

)dξ

= −∫

ρ

(ξqξk

∂up

∂ξk+ ξpξk

∂uq

∂ξk+ ξpξq

∂uk∂ξk

)dξ

= −Γqk∂up

∂ξk− Γpk

∂uq

∂ξk,

so that finally∂Γpq

∂t− Γqk Apk − Γpk Aqk = 4D δpq. (6.12)

Simple strain configurations give illustrative solutions for Eq. (6.12), but A(x, t)is a rapidly varying function, and its correlations will determine the dynamicalbehavior of Γpq(t).

Summary

Molecular tagging velocimetry (MTV) is a class of all-optical techniques tomeasure fluid flow velocities without particle seeding. The basis of this techniqueconsists of two steps: in the first step, an ensemble of molecules (a line or a grid)is labeled such that it is different from the carrier gas. This ensemble will thenmove with the flow and will be deformed by its gradients. The second step isvisualization of the tagged molecules, which gives information on their location.With the initial position known, a velocity can be assigned to each point of thewritten structure.

We studied turbulent velocimetry and turbulent mixing phenomena using dif-ferent approaches based on MTV technique. One of these approaches is a novelscheme called APART (Air Photolysis And Recombination Tracking), which isbased on creating nitric oxide (NO) molecules out of O2 and N2 molecules in thefocus of a strong UV laser beam. Despite its advantages, APART suffers fromthe loss of accuracy due to broadening of written patterns, a serious yet com-mon problem of most molecular tagging velocimetry techniques. In fact, this is aproblem of MTV techniques when the tagged tracers have Schmidt number closeto one, which implies that mass diffuses at the same rate as momentum. Thisdiffusional broadening poses a fundamental limit on the application of MTV inturbulence. Small–scale turbulent motion can only be resolved by using mole-cules which diffuse slower. In practice this implies larger, but not necessarilyheavier molecules.

Biacetyl is one of these potentially suitable (heavy and big) tracers which westudied; it is a relatively complex molecular tracer, which diffuses slower than theO2 and NO molecular tracers of other techniques. However, our study showedthat the accuracy of biacetyl tagging is not set by its diffusion, but by chemicalreaction of the excited molecules. Due to nonlinear processes, a tagged patternbroadens much more quickly than through molecular diffusion. Of course, thisis a function of the initial line profile; line widening is relatively rapid for theLorentzian beam used in our experiment, it will be slower for Gaussian beamsand will be absent for a perfect top hat profile. However, diffraction prohibitssuch a profile for narrow lines. Our results show that molecular tagging with bi-acetyl only works when visualizing large length scales. Perhaps more interestingwould be to use triplet biacetyl as a model chemical reagent in turbulent flows.

104

We also investigated the joint action of turbulent dispersion and moleculardiffusion on the spreading of Gaussian puffs of a passive scalar. We describe theresults of a numerical simulation of a linear equation for the size of a Gaussiancloud, driven by a strongly turbulent velocity field which is computed by directnumerical simulation. We found that, surprisingly, analytical results of this equa-tion involving a constant velocity field, can be compared well to the results of thesimulations. In the experiments the widening of lines with Gaussian cross sec-tions was measured and compared to the theoretical framework. We find that theobserved rate of spreading agrees very well with the numerical simulations. Itleads to the conjecture that, at least for short times, turbulent dispersion is aidedby molecular diffusion.

Finally, we can say that in tracing gaseous flow by tracing its constituents, the“own life” of the constituents tends to interfere. Thus, it turned out that MTValso opens opportunities to study the interaction of the tracers with the flow inwhich they are embedded. Numerous recipes can meanwhile be found in the lit-erature to locally create small molecular tracers in gas flows. Any of these willserve to visualize the gross motion of the flow, but the smallest scales will alwaysbe blurred by molecular diffusion. The heavier phosphorescent biacetyl, espe-cially when seeded into a relatively heavy gas like SF6, turns out to be extremelysensitive to itself. This again thwarts its usefulness as a small-scale flow tracer,but on the other hand it provides a means for future research on the interactionof turbulence and chemistry. Other phosphorescent molecules may turn out tobe less prone to self-annihilation (like several examples available for liquid flow).Quite likely, however, these will be heavy molecules that are difficult to get intothe gas phase. This is a problem they share with heavy atom tracers. We havenow studies the photolysis of only one precursor, but there may be alternatives,like the 3-methyl-metals used as CVD feedstock. A major issue to be resolved infuture research is the seeding mechanism: how to get heavy molecules or atomsinto the gas phase without perturbing the flow of interest.

Bibliography

[1] G. M. Almy and S. Anderson. Lifetime of fluorescence in diacetyl and ace-tone. J. Chem. Phys., 8:805–814, 1940.

[2] C. C. Badcock, H. W. Sidebottom, J. G. Calvert, B. R. Rabe, and E. K. Damon.A study of the triplet-triplet annihilation reactionin biacetyl vapor excited at4365 and 25◦. J. Am. Chem. Soc., 94:19–24, 1972.

[3] J. Bec, L. Biferale, G. Boffetta, M. Cencini, S. Musacchio, and F. Toschi. Lya-punov exponents of heavy particles in turbulence. Phys. Fluids, 18:091702,2006.

[4] R. Benzi, L. Biferale, E. Calzavarini, D. Lohse, and F. Toschi. Velocity gradi-ents along particles trajectories in turbulent fows: the refined similarity hy-pothesis in the Lagrangian frame. Phys. Rev. E, 80:066318, 2009. Our datasetis publicly available at: http://data.3tu.nl/repository/uuid:f7cd7b9d-ae4e-498e-92b4-7efe2d350d86.

[5] L. Biferale, G. Boffetta, A. Celani, B. J. Devenish, A. Lanotte, and F. Toschi.Lagrangian statistics of particle pairs in homogeneous isotropic turbulence.Phys. Fluids, 17:115101, 2005.

[6] L. Biferale, G. Boffetta, A. Celani, B. J. Devenish, A. Lanotte, and F. Toschi.Multiparticle dispersion in fully developed turbulence. Phys. Fluids,17:11701, 2005.

[7] J. Bominaar, M. Pashtrapanska, T. Elenbaas, Nico Dam, J. J. ter Meulen, andWillem van de Water. Writing in turbulent air. Phys. Rev. E, 77:046312, 2008.

[8] J. Boussinesq. Essai sur la theorie des eaux courantes. Savant. a l’Acad. Sci.,23:1–680, 1887.

[9] S. G. Buckley, R. F. Sawyer, C. P. Koshland, and D. Lucas. Measurementsof lead vapor and particulate in flames and post-flame gases. Cumbus. andFlame, 128:435–446, 2002.

106

[10] E. Calzavarini. Interaction between molecular and turbulent diffusion, 2013.

[11] C. Chapman and T. G. Cowling. The Mathematical Theory of Non-UniformGases. Cambridge University Press, New York, NY, 1939.

[12] K. T. Christensen. The influence of peak-locking errors on turbulence statis-tics computed from piv ensembles. J. Fluid Mech., 36:484–497, 2004.

[13] G. Comte-Bellot. Hot-wire annemometry. Ann. Rev. Fluid Mech., 8:209–231,1976.

[14] C. O. Concheanainn and H. W. Sidebottom. Temperature dependence of thetriplet lifetime of biacetyl in the gas hase. J. Photochemistry, 80:55–66, 1980.

[15] N. J. Dam, R. J. H. Klein-Douwel, N. M. Sijtsema, and J. J. ter Meulen. Nitricoxide flow tagging in unseeded air. Opt. Lett., 26:36–38, 2001.

[16] R. Ecke. The turbulence problem, an experimentalist’s perspective. LosAlamos Sci., 9:124–141, 2005.

[17] A. H. Epstein. Quantitative density visualization in a transonic compressorrotor. J. of Eng. for Power., 99:460–475, 1977.

[18] K. Eriks, T. D. Hayden, S. Hsi Yang, and I. Y. Chan. Crystal and molecularstructure of biacetyl at -12 and−100◦. J. Am. Chem. Soc., 105:3940–3942, 1983.

[19] M. J. Fisher and P. O. A. L. Davis. Correlation measurements in a non frozenpattern of turbulence. J. Fluid Mech., 18:97–116, 1964.

[20] M. E. Garabedian and D. A. Dows. Vapor–phase biomolecular quenching ofthe triplet state of biacetyl. J. Am. Chem. Soc., 90:2468–2470, 1968.

[21] S. Goto and S. Kida. A lagrangian direct-interaction approximation for ho-mogeneous isotropic turbulence. J. Fluid Mech., 339:287–307, 1997.

[22] M. Guala, B. Lüthi, A. Liberzon, A. Tsinober, and W. Kinzelbach. On theevolution of material lines and vorticity in homogeneous turbulence. J. FluidMech., 533:339–359, 2005.

[23] G. M. Hama and L. C. Curley. Instrumentation for the measurement of lowvelocities with a pitot tube. American Indus. Hygiene Assoc. Journal, 28:204–210, 1967.

[24] J. Heicklen. The fluorescence and phosphorescence of biacetyl vapor andaceton vapor. J. Am. Chem. Soc., 81:3863–3866, 1959.

Bibliography 107

[25] B. Hiller, R. A. Booman, C. Hassa, and R. K. Hanson. Velocity visualizationin gas flows using laser-induced phosphorescence of biacetyl. Rev. Sci. Instr.,55:1964–1967, 1984.

[26] H. Hu and M. M. Koochesfahani. A novel method for instantenous, quantta-tivemeasurement of molecular mixing in gaseous flows. Exp. Fluids, 33:202–209, 2002.

[27] H. Hu and M. M. Koochesfahani. Molecular tagging velocimetry and ther-mometry and its application to the wake of a heated circular cylinder. Mea-sur. Sci. and Tech., 17:1269–1281, 2006.

[28] T. F. Hunter and M. G. Stock. Photophysical processes in the vapour–phasemeasured by the optic–acoustic effect. J. Chem. Soc., Faraday Trans. 2, 70:1010–1021, 1974.

[29] H. J. Hussein, S. P. Gapp, and W. K. George. Velocity measurements in ahigh-reynolds-number, momentum-conserving, axisymmetric, turbulent jet.J. Fluid Mech., 258:31–75, 1993.

[30] W. Hwang and J. K. Eaton. Creating homogeneous and isotropic turbulencewithout a mean flow. Exp. Fluids, 36:444–454, 2004.

[31] L. JianBang, P. Qi, L. ChangSheng, and S. JieRong. Investigation of possibil-ity of flow field diagnostics by laser induced biacetylphosphorescence. Acta.Mechanica. Sinica, 3:370–379, 1987.

[32] L. JianBang, P. Qi, L. ChangSheng, and S. JieRong. Principles of flow fielddiagnostics by laser induced biacetyl phosphorescence. Exp. Fluids, 6:505–513, 1988.

[33] A. N. Kolmogorov. Dissipation of energy in isotropic turbulence. Dokl. Akad.Nauk SSSR, 32:19–21, 1941.

[34] A. N. Kolmogorov. The local structure of turbulence in incompressiblevis-cous fluids at very large reynolds numbers. Dokl. Akad. Nauk SSSR, 30:299–303, 1941.

[35] A. N. Kolmogorov. On the degeneration of isotropic turbulence in an incom-pressible viscous fluids. Dokl. Akad. Nauk SSSR, 31:538–541, 1941.

[36] A. N. Kolmogorov. On the breakage of drops in a turbulent flow. Dokl. Akad.Nauk SSSR, 66:825–828, 1949.

108

[37] A. N. Kolmogorov. A refinment of previous hypotheses concerning the localstructure of turbulence in a viscous incom-pressible fluid at high reynoldsnumber. J. Fluid Mech., 13:82–85, 1962.

[38] M. M. Koochesfahani. Molecular tagging velocimetry (mtv): Progress andapplications. AIAA Paper, 99:3786–3798, 1999.

[39] M. M. Koochesfahani and D. G. Nocera. Molecular tagging velocimetry. InC.Tropea J.Foss and A.Yarin, editors, Handbook of Exp. Fluid Dynamics, chap-ter 5.4. Springer-Verlag, 2007.

[40] S. Krüger and G. Grünefeld. Stereoscopic flow–tagging velocimetry. AppliedPhysics B, 69:509–512, 1999.

[41] P. H. Kruppenie. The spectrum of molecular oxygen. J. Phys. Chem. Ref. Data,1:423–534, 1972.

[42] W. R. Lempert, M. Boehm, N. Jiang, S. Gimelshein, and D. Levin. Compari-son of molecular tagging velocimetry data and direct simulation monte carlosimulations in supersonic micro jet flows. Exp. Fluids, 34:403–411, 2003.

[43] W. R. Lempert and S. R. Harris. Flow tagging velocimetry using caged dyephoto-activated fluorophores. Measur. Sci. and Tech., 11:1251–1258, 2000.

[44] W. R. Lempert, N. Jiang, S. Sethuram, and M. Samimy. Molecular taggingvelocimetry measurements in supersonic microjets. AIAA Paper, 40:1065–1070, 2002.

[45] W. R. Lempert, K. Magee, P. Ronney, K. R. Gee, and R. P. Haughland. Flowtagging velocimetry in incompressible flow using photo-activated nonintru-sive tracking of molecular motion (phantomm). Exp. Fluids, 18:249–257, 1995.

[46] A. Mazzino and M. Vergassola. Interference between turbulent and molecu-lar diffusion. Europhys. Lett., 37:535–540, 1997.

[47] J. M. McDonough. Introductory lectures on turbulence. University of Kentucky,Kentucky, 2007.

[48] R. L. McKenzie, D. J. Monson, and R. J. Exberger. Time-dependent local den-sity measurements in unsteady flows. NASA Technical Memorandom 78555,Ames Research Center, 1979.

[49] W. R. Mickelsen. Measuremnets of the effect of molecular diffusivity in tur-bulent diffusion. J. Fluid Mech., 7:397–400, 1960.

Bibliography 109

[50] R. B. Miles, C. Cohen, J. J. Conners, P. Howard, S. Huang, E. C. Markovitz,and G. Russell. Velocity measurements by vibrational tagging and fluores-cent probing of oxygen. Opt. Lett., 12:861–863, 1987.

[51] R. B. Miles, J. J. Conners, E. C. Markovitz, P. J. Howard, S. Huang, andG. J. Roth. Instantaneous profiles and turbulence statistics of supersonic freeshear layers by raman excitation plus laser-induced electronic fluorescence(relief) velocity tagging of oxygen. Exp. Fluids, 8:17–24, 1989.

[52] R. B. Miles, J. J. Conners, E. C. Markovitz, P. J. Howard, S. Huang, and G. J.Roth. Instantaneous supersonic velocity profiles in an underexpanded sonicair jet by oxygen flow tagging,. Phys. Fluids A, 1:389–393, 1989.

[53] R. B. Miles, J. Grinstead, R. H. Kohl, and G. Diskin. The RELIEF flow taggingtechnique and its application i n engine testing facilities and for helium–airmixing studies. Measur. Sci. and Tech., 11:1272–1281, 2000.

[54] R. B. Miles, W. R. Lempert, and J. N. Forkey. Laser rayleigh scattering. Mea-sur. Sci. and Tech., 12:R33–R51, 2001.

[55] S. Miller. Photochemical reaction for the study of velocity patterns and pro-files, 1962.

[56] M. A. Mortellaro and D. G. Nocera. A turn-on for optical sensing. Chem.Tech., 26:17–23, 1962.

[57] L. Mydlarski and Z. Warhaft. On the onset of high–Reynolds–number grid–generated wind tunnel turbulence. J. Fluid Mech., 320:331–368, 1996.

[58] D. G. Nocera. Not just another pretty shape. New Scientist, 149:24–27, 1996.

[59] A. Noullez, G. Wallace, W. Lempert, R. B. Miles, and U. Frisch. Transversevelocity increments in turbulent flow using the relief technique. J. FluidMech., 339:287–307, 1997.

[60] W. A. Noyes, W. A. Mulac, and M. S. Matheson. Photochemical primaryprocess in biacetyl vapor at 4358 . J. Chem. Phys., 36:880–886, 1962.

[61] H. Okabe and W. A. Noyes. The relative intensities of fluorescence and phos-phorescence in biacetyl vapor. J. Am. Chem. Soc., 79:801–806, 1957.

[62] C. Orlemann, C. Schulz, and J. Wolfrum. NO–flow tagging by photodisso-ciation of NO2. a new approach for measuring small–scale flow structures.Chem. Phys. Lett., 307:15–20, 1999.

110

[63] P. Patnaik. Handbook of Inorganic Chemical Compounds. McGraw-Hill, NewYork, 2002.

[64] Z. Pikramenou, J. A. Yu, R. B. Lessard, A. Ponce, P. A. Wong, and D. G. No-cera. Luminescence from supramolecules triggered by the molecular recog-nition of substrates. Coord. Chem. Rev., 132:181–194, 1996.

[65] R. W. Pitz, T. M. Brown, S. P. Nandula, P. A. Skaggs, P. A. DeBarber, M. S.Brown, , and J.Segall. Unseeded velocity measurement by ozone taggingvelocimetry. Opt. Lett., 21:755–757, 1996.

[66] R. W. Pitz, M. D. Lahr, Z. W. Douglas, J. A. Wehrmeyer, S. Hu, C. D. Carter,K. Y. Hsu, C. Lum, and M. M. Koochesfahani. Hydroxyl tagging velocimetryin a supersonic flow over a cavity. Appl. Opt., 44:6692–6670, 2005.

[67] R. W. Pitz, J. A. Wehrmeyer, L. A. Ribarov, D. A. Oguss, F. Batliwala, P. A.DeBarber, S. Deusch, and P. E. Dimotakis. Unseeded molecular flow taggingin cold and hot flows using ozone and hydroxyl tagging velocimetry. Measur.Sci. and Tech., 11:1259–1271, 2000.

[68] R. D. Present. Kinetic Theory of Gases. McGraw-Hill, York, PA, 1958.

[69] R. E. Rebbert and P. Ausloos. Quenching of the triplet state of acetone andbiacetyl by azoalkanes. J. Am. Chem. Soc., 87:1847–1852, 1965.

[70] O. Reynolds. On the dynamical theory of turbulent incompressible viscousfluids and the determination of the criterion. Phil. Trans., 186:123–161, 1894.

[71] L. F. Richardson. Weather prediction by numerical process. Cambridge Univer-sity Press, London, 1922.

[72] J. P. Richter. The Notebooks of Leonardo Da Vinci. Dover Publications, NewYork, 1970.

[73] J. Rièka. Photobleaching velocimetry. Exp. Fluids, 5:381–384, 1987.

[74] R. M. S. Rosa. Turbulence theories, 2012.

[75] P. G. Saffman. On the effect of the molecular diffusivity in turbulent diffu-sion. J. Fluid Mech., 8:273–283, 1960.

[76] K. F. Schrum, J. M. Lancaster, S. E. Johnston, and S. D. Gilman. Monitor-ing electroosmotic flow by periodic photobleaching of a dilute, neutral fluo-rophore. Anal. Chem., 72:4317–4321, 2000.

Bibliography 111

[77] G. F. Sheats and W. A. Noyes. Photochemical studies. I. the phostochemistryof biacetyl at 3650 and 4358 and its relationship to fluorescence. J. Am. Chem.Soc., 77:1421–1426, 1955.

[78] H. W. Sidebottom, C. C. Badcock, J. G. Calvert, B. R. Rabe, and E. K. Damon.Lifetime studies of the biacetyl excited singlet and triplet states in the gasphase at 25◦. J. Am. Chem. Soc., 94:13–19, 1972.

[79] N. M. Sijtsema, N. J. Dam, R. J. H. Klein-Douwel, and J. J. ter Meulen. Airphotolysis and recombination tracking: A new molecular tagging velocime-try scheme. AIAA Paper, 40:1061–1064, 2002.

[80] B. Stier and M. M. Koochesfahani. Molecular tagging velocimetry (MTV)measurements in gas phase flows. Exp. Fluids, 26:297–304, 1999.

[81] G. I. Taylor. Statistical theory of turbulence. Proc. R. Soc. Lon. A, 151:421–478,1935.

[82] H. Tennekes and J. L. Lumley. A first course in turbulence. MIT Press, USA,1972.

[83] A. A. Townsend. The diffusion of heat spots in isotropic turbulence. Proc.Roy, Soc. London Ser. A, 209:418–430, 1951.

[84] W. P. N. van der Laan, R. A. L. Tolboom, N. J. Dam, and J. J. ter Meulen.Molecular tagging velocimetry in the wake of an object in supersonic flow.Exp. Fluids, 34:531–533, 2003.

[85] J. A. Wehrmeyer, L. A. Ribarov, D. A. Oguss, F. Batliwala, and R. W. Pitz.Flow tagging velocimetry for low and high temperature flow fields. AIAAPaper, 99:0646, 1999.

[86] J. A. Wehrmeyer, L. A. Ribarov, D. A. Oguss, and R. W. Pitz. Flame flowtagging velocimetry with 193 nm H2O. Appl. Opt., 36:6612–6917, 1999.

[87] I. Wygnanski and H. Fiedler. Some measurements in the self-preserving jet.J. Fluid Mech., 38:577–612, 1969.

[88] Zh. Zhang. Velocity bias in lda measurements and its dependence on theflow turbulence. J. Flow Measur. Instr., 13:63–68, 2002.

Acknowledgement

This thesis owes its existence to hard work, patience, inspiration and help ofmany people. First and foremost, I would like to thank Willem van de Water andNico Dam for all their encouragement, patience and support. I deeply indebtedto them for helping me complete this thesis. I am also grateful to Philip de Goeywhom accepted to become my official promoter at the very last stage of my PhDcareer and gave me the opportunity to defend my thesis as a member of his groupat mechanical engineering department of Technical University Eindhoven.

Additionally, I would like to thank the members of my thesis committee, Hanster Meulen, Wim van der Zande and Enrico Calzavarini for their valuable com-ments which are highly appreciated. In addition to their valuable time and com-ments as committee members, I also owe them all a thank individually. I liketo thank Hans as my initial promoter, for giving me the opportunity to do myPhD in his group, a special thank to Wim as my pseudo-supervisor, for his greatsupport after Hans’s retirement, and great appreciation to Enrique, for providingwith his numerical study complementary to my experimental research.

It was the excellent assistance of all technicians of “Molecular and laser physics"and “Molecular and Biophysics" of Radboud University Nijmegen which madethis experimental work possible. My sincere thank to Arjan van Vliet for all hissupport during my frustrating experiments with not so user friendly tracers. Ialso thank Cor Sikkens, Leander Gerritsen and Peter Claus for all their help.

During those four years, I was very grateful to work with three enthusiasticundergraduate students, Thanja Lamberts, Raymund Centeno and Guus Slot-man. I wish them all the best and thank them for bringing great enthusiasm andfun into the laser lab.

My PhD project was made possible by the Foundation for Fundamental Re-search on Matter (FOM). I appreciate their support and help through the careerdevelopment courses that they offered.

My gratitude to all colleagues at “Applied Molecular physics", “Molecularand laser physics" and “Molecular and Biophysics" groups of Radboud universityNijmegen for making it such a friendly place to work. I wish Afric, Andrea, Arjan,Ashim, Bin, Chandan, Dave, Denis A., Dennis G., Dennis M., Devasena, Frans H.,Frans S., Frans W., Gautam, Ine, Jolijn, Juleian, Leo, Magda, Miriam, Raymund,Rink, Robert, Simona, Wim and Zahid all the best.

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I would also like to thank all people at casecade building of Technical Uni-versity Eindhoven with special thanks to Ad Holten and Marjan Rodenburg fortechnical and administrative support. I wish the best for all my PhD studentcolleagues specially Homberto and Ergun.

I am grateful to my current colleagues at VSL too, they were always a greatsource of encouragement during the past one and a half years of preparing thisthesis. A special thank to my daily colleagues Mijndert and Peter for inspiringme with their enormous positive energy. I’m also thankful to Nellie Schipperfor being such a great manager and giving me the opportunity to have flexibleworking hours to finish my PhD project.

I like to dedicate this thesis to my beloved parents Malihe and Behrouz whowere always there for me, the completion of this thesis means a lot to them. Mydeep sense of gratitude to them without whose love, support and encouragementthis work would not have been possible.

Curriculum VitaeApril 29, 1982: Born in Ghaemshahr, Iran

2000–2004: B.Sc. in Applied PhysicsScience Faculty, Mazandaran UniversityBabolsar, Iran

2004–2006: M.Sc. in Atomic and Molecular PhysicsPhysics Faculty, Iran University of Science and TechnologyTehran, Iran

2007–2011: Ph.D. CandidateTurbulence and Vortex Dynamics, Applied Physics FacultyCombustion Technology, Mechanical Engineering FacultyEindhoven University of TechnologyEindhoven, The NetherlandsMolecular and Biophysics, Science FacultyRadboud University NijmegenNijmegen, The Netherlands

2012: Research ScientistVSL, Dutch Metrology InstituteDelft, The Netherlands