Seediscussions,stats,andauthorprofilesforthispublicationat:https://www.researchgate.net/publication/225284744

MeasuringLagrangianaccelerationsusinganinstrumentedparticle

ARTICLE·JUNE2012

DOI:10.1088/0031-8949/2013/T155/014063·Source:arXiv

CITATIONS

3

READS

47

5AUTHORS,INCLUDING:

RobertZimmermann

EcolenormalesupérieuredeLyon

11PUBLICATIONS77CITATIONS

SEEPROFILE

LionelFiabane

NationalResearchInstituteofScienceand…

8PUBLICATIONS27CITATIONS

SEEPROFILE

RomainVolk

EcolenormalesupérieuredeLyon

54PUBLICATIONS971CITATIONS

SEEPROFILE

Jean-FrancoisPinton

EcolenormalesupérieuredeLyon

182PUBLICATIONS4,689CITATIONS

SEEPROFILE

Availablefrom:RomainVolk

Retrievedon:05February2016

Measuring Lagrangian accelerations using an instrumented particle

R. Zimmermann,1 L. Fiabane,1 Y. Gasteuil,2 R. Volk,1 and J.-F. Pinton1

1Laboratoire de Physique, ENS de Lyon, UMR CNRS 5672, Université de Lyon, France∗2smartINST S.A.S., 46 allée d’Italie, 69007 Lyon, France

(Dated: August 13, 2012)

Accessing and characterizing a flow impose a number of constraints on the employed measurementtechniques; in particular optical methods require transparent fluids and windows in the vessel.Whereas one can adapt apparatus, fluid and methods in the lab to these constraints, this is hardlypossible for industrial mixers. We present in this article a novel measurement technique which issuitable for opaque or granular flows: an instrumented particle, which continuously transmits theforce/acceleration acting on it as it is advected in a flow. Its density is adjustable for a wide range offluids and because of its small size and its wireless data transmission, the system can be used both inindustrial and scientific mixers allowing a better understanding of the flow within. We demonstratethe capabilities and precision of the particle by comparing its transmitted acceleration to alternativemeasurements, in particular in the case of a turbulent von Kármán flow. Our technique shows tobe an efficient and fast tool to characterize flows.

I. INTRODUCTION

Experimental fluid dynamics research in the labconsists of an interplay of suitable flow generationdevices, working fluids, measurement techniquesand analysis, with goals ranging from fundamentalresearch in statistical / non-linear physics to theoptimization of mixers in industrial R&D depart-ments. In this endeavor, very significant progresshas been achieved during the last decade with theadvent of space and time resolved optical tech-niques based on high speed imaging [1]. However,direct imaging is not always possible especially inindustry: opaque vessels, non-transparent fluids,environmental constraints among other things maybe limiting factors. Even if the fluid is transparent,the injection of tracer particles might be still notallowed or unsuitable due to bio-medical or foodregulations, or due to the chemical properties ofthe fluid. While techniques using other kinds ofprobing waves (e.g. acoustics [2]) have been de-veloped, a direct resolution of the Eulerian flowpattern is not always possible. In this context,Lagrangian techniques provide an interesting al-ternative particularly for problems related to mix-ing [3, 4].

Lagrangian tracers with a temperature sensi-tive dependance have been used in the studyof Rayleigh-Bénard convection [5], a problem forwhich our group has developed instrumented par-ticles [6–9]. The approach was to instrument aneutrally buoyant particle in such a way that itmeasures the temperature fluctuations during itsmotion as it is entrained by the flow, while trans-mitting the data via radio frequency to a lab opera-

∗Electronic address: robert.zimmermann@ens-lyon.org

tor in real time. Meaningful information regardingthe statistics of thermion plumes have been ob-tained, with excellent agreement with other tech-niques [5] and direct numerical simulations [10].In the work reported here, we built upon this ap-proach to instrument the particle such that onegets flow parameters directly from the measure-ments (in [6], one had to simultaneously film theparticle motion). We equip the particle with a 3-axis accelerometer, whose measurements are sam-pled at a rate equal to 316 Hz and transmitted tothe lab operator. This particle is intended for tur-bulent flows. Thanks to its radio transmission it issuitable for opaque fluids or apparatuses withoutaccess for optical measurement techniques. Its con-tinuous operation is also advantageous over Par-ticle Tracking Techniques which have to operatein chunks as the memory of the tracking camerasis necessarily limited. Moreover and in contrastto tracer particles this instrumented particle canbe easily re-extracted from the apparatus after theexperiment. However, as the particle is advectedin a flow it rotates and consequently continuouslychanges its orientation with respect to the labo-ratory frame. Thereby the signals of the 3D ac-celerometer are altered in a non-trivial way, anddetailed characterization and methods to extractmeaningful information from the acceleration sig-nals are needed. We present here the preliminaryresults of this characterization.

This article is organized as follows: first, wepresent the instrumented particle and additionaltechniques needed for its characterization (sec-tion II). In section III, we present an analysis ofthe results obtained in two different configurations:First, a simple pendulum with the particle at-tached at the end of a stiff arm, then the particleadvected in a fully turbulent flow. In order to ver-ify that the transmitted acceleration is well related

2

to its motion, we compare the results to simultane-ous alternative measurements. Finally, we discusslimitations and perspectives of this new measure-ment technique (section IV).

II. “SMART PARTICLES”

The apparatus described in the following is de-signed and built by smartINST S.A.S., a youngstartup situated on the ENS de Lyon campus. Thedevice consists of a spherical particle (the so-calledsmartPART) which embarks an autonomous cir-cuit with 3D-acceleration sensor, a coin cell and awireless transmission system; and a data acquisi-tion center (the so-called smartCENTER), whichacquires, decodes, processes and stores the signalof the smartPART (see Fig. 1). The ensemble –smartPART and smartCENTER – measures, dis-plays and stores the three dimensional accelerationvectors acting on the particle as it is advected inthe flow. The accelerations are observed in a mov-ing and rotating coordinate system and consist offour contributions: gravity, translation, noise andpossibly a weak contribution of the rotation aroundthe center of the particle itself.

A. Design & Technical Details

a. Sensor: The central component of theparticle is the ADXL 330 (Analog Device) – athree axis accelerometer. This component be-longs to the category of micro-electro-mechanicalsystems (MEMS). Each of the three axes returnsa voltage proportional to the force acting on asmall, movably mounted mass-load suspendedby micro-fabricated springs. The three axesof the ADXL 330 are decoupled and form anorthogonal coordinate system attached to thechip package. From this construction arises apermanent measurement of the gravitationalforce/acceleration g ≡ 9.8 m/s2 · eg = g · eg. Eachaxis has a guaranteed minimum full-scale rangeof ±3 g; however, we observe a typical range of±3.6 g = 35 m/s2 per axis. The sensor has to becalibrated to compute the physical accelerationsfrom the voltages of the accelerometer.

b. smartPART: The signals from the ADXL330 are first-order low-pass filtered at fc = 160 Hzand then digitized at 12 bits and 316 Hz samplingrate. A multiplexer prior the signal digitizationinduces a small time shift between the compo-nents of 0.64 ms. The output is then reshapedinto small packets and send via radio frequency.The ensemble is powered by a coin cell. A voltage

regulator ensures a stable supply voltage and thusa constant quality of the measurement. A Hallswitch allows one to power-down most compo-nents; thereby, the battery is only used duringexperiments. Depending on the power needed totransmit the acceleration signals, a particle oper-ates continuously for 6 to 36 hours. The ADXL330 is soldered to the printed circuit board suchthat it is situated close to the geometrical centerof the particle. The particle itself is sphericalwith a diameter of 25 mm. The capsule walls aremade of Polyether-ether-ketone (PEEK) which isknown for its excellent mechanical and chemicalrobustness. It is leak-proof and its density can bematched to fluids by adding extra weight (namelyTungsten paste) to the particle’s interior; withinthe density range of 0.8− 1.4 g/cm3 a relativedensity match of better than 10−4 is achievable.The particle is thus suited for most experimentsin water and water-based solutions. It shouldbe noted that the mass distribution inside theparticle is neither homogeneous nor isotropic: inparticular its center of mass does not coincide withthe geometrical center, making it out-of-balance.In practice this results into a pendulum-likemotion of the particle in the flow. Nevertheless,the imbalance can be adjusted to some extent byadding patches of Tungsten paste to its interior,and the particles we use are carefully preparedsuch that they are neutrally buoyant, avoid anypendulum-like behavior and rotate easily in theflow.

c. smartCENTER: The signals from thesmartPART are received by an antenna connectedto the smartCENTER, which contains radio re-ception, processing and display units. It demod-ulates and decodes in real-time the received rawsignal into a time-series of raw voltages of theADXL 330. The physical acceleration sensed bythe smartPART aSP can then be computed:

aSP =

a1a2a3

=

(A1 −O1)/S1

(A2 −O2)/S2

(A3 −O3)/S3

, (1)

where Ai, Oi and Si are the measured raw signal,the offset and the sensitivity of each axis, respec-tively. Offset and sensitivity have to be calibratedbeforehand; the procedure is described in the fol-lowing section. The resulting time-series are savedfor further processing.

3

Multiplexer &A/D Conversion

µCon

trolle

r

Hall Switch

Battery &Regulator

RF – Modulation

ADXL 330x y z

smartPART

User Interfaceto display

and save a(t)x y z

Receiver &Acquisition

Decoding & Preprocessing

smartCENTER

b)

c)

a)

Figure 1: a) and b) : the instrumented particle (smartPART ) and its data control & acquisition unit(smartCENTER). The coin cell is 20mm in diameter. c) The diagram sketches the measurement of the

acceleration, its transmission to and the processing by the smartCenter.

B. Calibration and robustness

The offset and sensitivity of the ADXL 330 haveto be calibrated to convert the measured voltagesinto a physical acceleration. The axes of the ac-celerometer form an orthogonal coordinate systemaccording to Eq. (1). At rest one observes onlygravity projected onto the sensor at an arbitraryorientation. The observed raw values define con-sequently a translated ellipsoid (for simplicity weset |g| ≡ 1):

aSP ·aSP =∑i

(Ai −Oi)2

S2i

= g2 = 1 . (2)

Eq. (2) can be arranged to:

1 =∑i

(ξiA

2i − 2 ξi+3Ai

), (3)

with ξi six parameters containing offset and sen-sitivity. A sufficient number of measurementswith different orientations define a set of equationswhich is solved using a linear least squares tech-nique. Offset and sensitivity are then

Oi =ξ3+iξi

and Si =

√1 +

∑i

(ξ23+i/ξi

)ξi

. (4)

We find that the particle at rest has an averagenoise of σx = σy = 0.006 g and σz = 0.008 g, giving|σ| =

√∑i σ

2i = 0.012 g, where g is the magnitude

of gravity. An analysis using the residuals showeda slightly higher resolution of σx = σy = 0.005 gand σz = 0.003 g, and |σ| = 0.008 g. These valuesare thus the absolute errors of our measurement.

The ADXL 300 has among other things beenchosen for its weak temperature dependance: itsoffset typically varies by 10−3 g/◦C, and its sensi-tivity by 0.015 %/◦C. Digitizing and transmissionunit were verified to be temperature independent.Consequently, the total temperature dependenceof the smartPART is given by its accelerometer.For high precision measurements, it is advised tocalibrate the particle at experiment temperatureshortly before the actual experiment.

We noticed a small drift of the order of 0.005 g/hfor the z−axis. No drift was observed for the x−and y−axes. Since a voltage regulator ensures astable supply voltage of the circuit, this drift stemsmost likely from the internal construction of the ac-celerometer. Owing to the continuous data trans-mission of the instrumented particle, one flow con-figuration can be characterized in approximately30 minutes. Hence, the little drift of the z−axiscan be neglected.

Considering the mechanical robustness, thesmartPART survived several days in a von Kár-

4

mán mixer and neither contacts with the wall norwith the sharp edged blades of the fast rotatingpropellers damaged its function or shell.

III. ACCELERATION SIGNALS

As mentioned previously, the smartPART trans-mits in real-time the accelerations acting on theparticle as it is advected in the flow. The noise-to-signal ratio being small, we neglect the noise fromhere on. The contributions consist therefore of:gravity, translation, and rotation of the particle.We now test the accuracy of the particle signals intwo different experimental configurations by com-parison with alternative measurements.

A. 2D pendulum

A pendulum is a simple and well-known case,ideal to measure the resolution of the particle.A stiff pendulum with 60 cm long stiff arm isequipped with a position sensor returning thedeflection angle ϕ of the arm. The particle isfixed at known length, l, with a known arbitraryorientation to the arm. The fact that a rotation ofthe particle around its center is restricted, impliesthat the contribution from the rotation of theparticle around is center is known. Measuring aSPat rest (ϕ = 0◦) and at several arbitrary positionsone can determine the axis of rotation of the arm.Once this vector is known the measured accel-eration signal is rotated/re-expressed such thatay points with the arm, ax with the movement,and az with the axis of rotation. Note that bydefinition the latter does not change when thependulum moves. The signal seen by the particleis a two-dimensional problem and fully describedas a function of the deflection angle ϕ:

ax(ϕ) = g sinϕ+ l ϕ ,

ay(ϕ) = g cosϕ+ l ϕ2 .(5)

In the limit of the small angle approximation,this simplifies to the well-known oscillations of fre-quency ω:

ax(ϕ) ≈ −lω2 sinωt ,

ay(ϕ) ≈ g +l ω2

2(1 + cos 2ωt) .

(6)

The simultaneous measurement of the angle, ϕ(t),and the particle’s signal, aSP(t), enables us to com-pare the two signals without any other approxima-tion or fit than Eq. (5).

60 65 70 75 800.8

0.9

1

1.1

1.2

1.3

a y (a

rm) [

g]

60 65 70 75 800.1

0.05

0

0.05

0.1

a x (m

ov) [

g]60 65 70 75 80505

x 10 3

a z [g

]time [s]

Figure 2: Comparison of the particle’s signal aSP(t)(•) to the theoretical curves based on the position

sensor (—). ay points with the arm and ax measuresthe force in direction of the movement. No force isexerted along the z−axis (the green lines represent

the uncertainty of the calibration). Note, thatacceleration is measured in g = 9.8m/s2 .

Fig. 2 shows aSP(t) for several periods of thependulum, measured by the smartPART and bythe position sensor. The agreement between thetwo signals is very good, and in particular betterthan the uncertainty of the calibration. Hence, theLagrangian acceleration of the smartPART corre-sponds well to its actual motion in this simple case.We now move on to more complicated motions.

B. Fully developed (3D) turbulence

The instrumented particle is intended for thecharacterization of complex/turbulent flows. Suchflows exhibit strong, intermittent variations in theacceleration. To verify the suitability of the smart-PART for these conditions, we now investigate itsmotion in a fully turbulent mixer while tracking itwith an independent optical technique.

Namely, we use a von Kármán water flow: aswirling flow is created in a square tank by twoopposing counter-rotating impellers of radius R =9.5 cm fitted with straight blades 1 cm in height.The flow domain in between the impellers has char-acteristic length H = 20 cm ∼= 2R (see Fig. 3) andthe vessel is built with transparent flat side walls,allowing direct optical measurements over almostthe whole flow domain. Blades on the impellers

5

b)

cam

era

von-Kármán mixer

camera

c)

a)

smartPART

impellers

cooling circuitsmartCENTER

Figure 3: Experimental setup: a) picture of the apparatus; b) sketch of the arrangement; c) a texturedinstrumented particle at different orientations.

a x [m/s

2 ]a y [m

/s2 ]

9.4 9.6 9.8

a z [m/s

2 ]

time [s]9.4 9.6 9.8

time [s]

particle framelab frame

Figure 4: A sample trajectory of the instrumented particle seen by the camera (—) or smartPART (•), it isfprop = 3Hz. The absolute orientation enables us to re-express the camera measurement of the particle (lab

frame) in the moving frame of the particle and vice-versa. In the former gravity is subtracted and in the particleframe gravity is represented by the red line.

6

work similar to a centrifugal pump and add apoloidal circulation at each impeller. For counter-rotating impellers, this type of flow is known toexhibit fully developed turbulence [11]. Within asmall region in the center the mean flow is littleand the local characteristics approximate homoge-neous turbulence. However, at a large scale it isknown to have a large scale anisotropy [12, 13].At a propeller frequency of 3 Hz we estimate aReynolds number based on the Taylor micro-scaleof Rλ = 500± 50.

We optically track the translation and absoluteorientation of the smartPART while simultane-ously acquiring the transmitted acceleration time-series. These optical measurements are then usedas a reference to compare with the instrumentedparticle’s signals. The six-dimensional trackingtechnique (or 6D tracking, 3 components for thetranslation and 3 components for the rotation ofthe particle around its center) is explained in de-tail in [14, 15] and briefly sketched here (Fig. 3).In order to determine the absolute orientation theparticle is textured by hand using black-ink per-manent marker (see Fig. 3c). Acceleration sen-sor and texture are then calibrated/retrieved in-dependently; nevertheless, the accelerometer is ata fixed but unknown orientation with respect tothis texture, i.e. sensor and texture are relatedby a constant rotation matrix. We determine thismatrix by acquiring the acceleration signals of theparticle at arbitrary orientations while addition-ally determining its orientation and the locationof gravity on the texture. The particle is then in-serted into the apparatus, which is illuminated byhigh power LEDs. Its motion is tracked by twohigh-speed video cameras (Phantom V12, VisionResearch) which record synchronously two viewsat approximately 90 degrees. The observation vol-ume is 15 × 15 × 15 [cm3] in size and resolved ata resolution of 4.2 pixel/mm. In our configuration,a camera can store on the order of 14 000 framesin on-board memory, thus limiting the duration ofcontinuous tracks. Therefore, a computer issuesthe recording of 8 bit gray-scale movies at a suffi-ciently high frame rate while controlling the smart-CENTER such that acceleration signal and imagesare synchronized. After extracting the time-seriesof the particle’s position and orientation, one canthen compare the accelerometer’s signal to the mo-tion of the particle.

It should be stressed that the two measure-ment techniques observe the motion of the instru-mented particle in two completely different refer-ence frames. On the one hand, the 6D trackinguses a fixed, non-rotating coordinate system, andis referred to as the lab frame. On the other hand,as the particle is advected and turned in the flow,

it and consequently the embarked accelerometerconstantly rotate their coordinate system with re-spect to the lab frame; the acceleration signal isthus measured in a frame which is continuouslyrotating and not fixed. This frame is referred to asthe particle frame. The acceleration sensor mea-sures the forces acting on it as it moves in the flow.Knowing the absolute orientation of the particle ateach instant we can express the signal of the smart-PART in the lab frame by rotating it such that itcorresponds to a non-rotating particle. Startingfrom the time-series of position and orientation,it is also possible to compute the linear, centrifu-gal and gravitational acceleration/force acting on apoint inside the particle and then project these intothe rotating particle frame. The different compo-nents are then expressed in the frame of the sensor.

Fig. 4 shows a sample trajectory in both coor-dinate systems. The agreement between the twotechniques is remarkable. Furthermore, one ob-serves that the projection of gravity is continuouslychanging: the particle is rotating in a non-trivialway. Deviations between the two techniques stemfrom several experimental errors. First, the posi-tion measurement: bubbles, reflections and otherimpurities alter the measured position of the par-ticle. The acceleration is the second derivate andthus highly sensitive to such events. Second, theorientation measurement: the absolute orientationis needed to change between the reference frames.The uncertainty in the absolute orientation is typ-ically 3◦; that results in a wrong projection ofgravity of ±0.5 m/s2. It further biases the rota-tional forces, as they are derivatives of the ori-entation time-series. Finally, the matrix relatingsensor and texture: this matrix is constant andthus a systematic contribution. The uncertaintyis less than 2◦ – i.e. the error in projecting grav-ity is < 0.3 m/s2. The observed agreement in thelab frame, ∆a = aSP − a6D, between the twotechniques is as follows: all three components of∆a have the same PDF. Surprisingly, the (ab-solute) uncertainty almost doubles by increasingfprop from 2 Hz to 3 Hz. Nevertheless, for 80%of the data the agreement is better than 0.8 m/s2

and 1.6 m/s2, respectively. For comparison, theabsolute value |a6D| has a mean of 2.9 m/s2 and6.6 m/s2 and a standard deviation of 1.8 m/s2 and4.1 m/s2, respectively. The signal of the particleis thus corresponding to the flow, however, its in-terpretation is not simple. In particular, and aftercomparing many different trajectories, it becomesclear that no easy transformation is available toget rid of the rotation of the particle.

By construction the center of the accelerometeris placed at r = 3 mm · ez. A rotation of the par-ticle around its geometric center will thus add a

7

0 0.2 0.4 0.6 0.8 1

10−2

100

fprop= 2 Hzfprop= 3 Hz

Figure 5: Ratio of the rotational forces to the totalforce acting on the particle. The 80% percentile isfound at a ratio of 0.14 and 0.16, respectively.

centrifugal contribution to the measured accelera-tion. This rises the question which term – trans-lation or rotation of the particle – dominates theacceleration signal. To address this question wetake advantage of the 6D-tracking, which enablesus to compute the different forces acting on a pointat r = 3 mm · ez inside the sphere. We can thuscompare the contribution of the translation andthat of the rotation of the particle. Fig. 5 showsthe ratio of the rotational (i.e. centrifugal) accel-eration, arot = ω × ω × r + dω

dt × r to the totalacceleration, atrans + arot, (without gravity). Di-mensional arguments tell that atrans ∝ f2prop andarot ∝ f2prop. Consistently, the PDF of the ratio|arot|/|atrans + arot| differs only little for the twopropeller frequencies. Moreover, it is peaked at5% and the 80% percentile is at a ratio of 14% and16%, respectively. Hence, it is legitimate to neglectthe rotational forces if no 6D tracking is available.

IV. DISCUSSION

In the latter part of this article we studied thebehavior of a large neutrally buoyant sphere in aturbulent flow. Comparing with solid spheres ofthe same size in the same mixer, we find that theparticle in general behaves almost identically [16].In particular (and despite the fact that the in-strumented particle is neutrally buoyant) we ob-serve that it generally stays in a region close tothe impellers. Fig. 6 shows the PDF of positionfor the smartPART. Independent of the impellerspeed it is mostly situated in a torus shape aroundthe propeller, exhibiting a preferential sampling ofthe flow for these large neutrally buoyant spheres.

Moreover, since we investigate large particleswith a size Dpart comparable to the integral lengthscale, Lint, moving through the whole mixer, the

X [m]

r [m

]

−0.06 −0.04 −0.02 0 0.02 0.04 0.06

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

PD

F

0

1

2

3

4

5

6

7

Figure 6: Preferred position of the instrumentedparticle: independent of the propeller speed it is

mostly situated in a torus shape around the propeller.

Kolmogorov assumptions to characterize turbu-lence are no longer valid. For these reasons, thesmartPART can be insufficient to access all detailsof a turbulent flow: some parts of the flow are littleexplored, and some scales of the turbulence mightbe filtered due to the size of the instrumented par-ticle. However, one should bear in mind that thesefeatures of the flow are often accessed by means ofoptical methods whereas the instrumented particleoperates also in environments and fluids which areunsuitable for optical measurement techniques.

Some other experimental constraints should beadditionally stressed here. As previously said, themass distribution inside the particle is neither ho-mogeneous nor isotropic. It is therefore possiblethat the particle is out-of-balance, i.e. that thecenter of mass does not coincide with the geomet-rical center. Such a particle has a strong preferredorientation and wobbles similar to a kicked physi-cal pendulum. The imbalance can be adjusted tosome extent by adding weight to its interior, butthe particle must be prepared very carefully andone must make sure that the particle used is well-balanced and rotates easily in the flow.

Also, the receiver/demodulation unit of thesmartCENTER works best within a range ofradio power, i.e. particles which are emittingeither too strong or too weak are undesirableand one has to adjust the radio emission of thesmartPART. A stronger radio emission powercan be required, e.g. if the apparatus buildsa Faraday cage (i.e. an electrically-connectedmetal structure surrounds the flow), or if thesignal has to pass a longer distance in morewater or in a bigger apparatus. Solutions witha high conductivity are also likely to damp theradio signal. Naturally, a stronger radio emissionshortens the life time of the battery. Neverthe-less, particles with stronger radio emission still

8

last 6 to 12 hours, which is sufficient in most cases.

To conclude, we presented the working principleof an instrumented particle giving a measure ofthe three components of the Lagrangian accelera-tion. We were able to show that the Lagrangianacceleration of the smartPART corresponds wellto its actual translation and is not biased by apossible rotation of the particle around its center.Work on extracting detailed information on theflow from the acceleration time-series is ongoing.This instrumented particles can shed some lightinto mixers which were not or hardly accessibleup to now. Due to its continuous transmissionone flow configuration can be characterized within∼ 30 min. Apart from its appeal for chemicaland pharmaceutical industry, it might be aninteresting tool to quantify flows in labs.

Acknowledgments

This work was partially supported by ANR-07-BLAN-0155. The authors want to acknowledge thetechnical help of Marius Tanase and Arnaud Rabil-loud for the electronics, and of all the ENS machineshop. The authors also thank Michel Voßkuhle,Mickaël Bourgoin and Alain Pumir for fruitful dis-cussions. Finally, R. Zimmermann warmly thanksthe TMB-2011 committee for assigning the “YoungScientist Award” of the Turbulence Mixing & Be-yond 2011 conference for the work he presentedwithin this article.

[1] C. Tropea, A. Yarin, and J. F. Foss, eds.,Springer Handbook of Experimental Fluid Dynam-ics (Springer-Verlag Berlin-Heidelberg, 2007).

[2] N. Mordant, P. Metz, O. Michel, and J.-F. Pinton,Physical Review Letters 87, 214501 (2001).

[3] F. Toschi and E. Bodenschatz, Annual Review ofFluid Mechanics 41, 375 (2009).

[4] B. Shraiman and E. Siggia, Nature 405, 639(2000).

[5] R. Ni, S.-D. Huang, and K.-Q. Xia, Journal ofFluid Mechanics 692, 395 (2012).

[6] Y. Gasteuil, W. L. Shew, M. Gibert, F. Chillà,B. Castaing, and J.-F. Pinton, Physical ReviewLetters 99, 234302 (2007).

[7] Y. Gasteuil, Ph.D. thesis, École NormaleSupérieure de Lyon (2009).

[8] W. L. Shew, Y. Gasteuil, M. Gibert, P. Metz, andJ.-F. Pinton, Review of Scientific Instruments 78,065105 (2007).

[9] J.-F. Pinton, P. Metz, Y. Gasteuil, and W. L.Shew, Mixer, and device and method for mon-

itoring or controlling said mixer, Patent US2011/0004344 A1 (2009).

[10] J. Schumacher, Physical Review E 79, 056301(2009).

[11] F. Ravelet, A. Chiffaudel, and F. Daviaud, Jour-nal of Fluid Mechanics Digital Archive 601, 339(2008).

[12] N. T. Ouellette, H. Xu, M. Bourgoin, and E. Bo-denschatz, New Journal of Physics 8, 102 (2006).

[13] R. Monchaux, F. Ravelet, B. Dubrulle, A. Chif-faudel, and F. Daviaud, Physical Review Letters96, 124502 (2006).

[14] R. Zimmermann, Y. Gasteuil, M. Bourgoin,R. Volk, A. Pumir, and J.-F. Pinton, Review ofScientific Instruments 82, 033906 (2011).

[15] R. Zimmermann, Y. Gasteuil, M. Bourgoin,R. Volk, A. Pumir, and J.-F. Pinton, Physical Re-view Letters 106, 154501 (2011).

[16] R. Zimmermann, Ph.D. thesis, École NormaleSupérieure de Lyon (2012).