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Novel experimental apparatus to visualise low-temperature flows This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2011 J. Phys.: Conf. Ser. 318 092029 (http://iopscience.iop.org/1742-6596/318/9/092029) Download details: IP Address: 216.47.136.20 The article was downloaded on 22/05/2013 at 14:40 Please note that terms and conditions apply. View the table of contents for this issue, or go to the journal homepage for more Home Search Collections Journals About Contact us My IOPscience

Novel experimental apparatus to visualise low-temperature flows

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Novel experimental apparatus to visualise low-temperature flows

This article has been downloaded from IOPscience. Please scroll down to see the full text article.

2011 J. Phys.: Conf. Ser. 318 092029

(http://iopscience.iop.org/1742-6596/318/9/092029)

Download details:

IP Address: 216.47.136.20

The article was downloaded on 22/05/2013 at 14:40

Please note that terms and conditions apply.

View the table of contents for this issue, or go to the journal homepage for more

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Novel experimental apparatus to visualise

low-temperature flows

Marco La Mantia, Milos Rotter and Ladislav SkrbekDepartment of Low-Temperature Physics, Faculty of Mathematics and Physics,Charles University in Prague, V Holesovickach 2, 180 00 Praha 8, Czech Republic

E-mail: [email protected]

Abstract. The first laboratory in Europe for the visualisation of liquid helium flows iscurrently being established at the Charles University in Prague. The use of such a valuableexperimental tool for the analysis of cryogenic flows of normal and superfluid 4He is introducedand its specific features discussed. More importantly, it is shown that the newly implementedflow visualisation equipment is potentially capable of obtaining new results, that is, furtherunderstanding of the underlying physics.

1. Introduction

Flow visualisation techniques have been recently employed at very low temperatures for theanalysis of various liquid helium flows (Zhang & Van Sciver, 2005; Bewley et al., 2006).Quantitative techniques, such as PIV (Particle Image Velocimetry) and PTV (Particle TrackingVelocimetry), have been indeed proven very useful in many scientific and industrial areas ofresearch (Raffel et al., 2007). However, such promising experimental tools are still in theirbeginning in the investigation of cryogenic flows and the ways to optimise them are yet to befully investigated due to a number of difficulties, e.g., the optical access to the helium bath andchoice of suitable tracers.

The most common fluids used in cryogenic fluid mechanics research are gaseous and liquid4He. At the pressure of 1 bar 4He is a gas, if the temperature is larger than 4.2 K. At lowertemperatures it becomes liquid and, if the temperature is larger than 2.17 K, liquid 4He is callednormal helium or He I. This fluid is characterised by extremely low values of the kinematicviscosity (of the order of 10−4 cm2/s), compared to those of air (of the order of 10−1 cm2/s) andwater (of the order of 10−2 cm2/s) (Niemela & Sreenivasan, 2006). If the temperature decreasesfurther, liquid He changes dramatically its properties and is called He II or superfluid helium. Itsviscosity can be considered null at 0 K, i.e. the fluid is assumed inviscid in the zero-temperaturelimit. Besides, its behaviour cannot be accounted for by just using the Navier-Stokes equation.

The unique properties of He II can be described by the two-fluid model, e.g., see Tilley &Tilley (1990); La Mantia et al. (2010). It is assumed that He II is made of two fluids, the normaland superfluid component of He II. The former is viscous and carries entropy while the latteris inviscid and does not carry entropy. The total density ρ of He II is defined as the sum ofthe densities of its normal and superfluid components, ρn and ρs, respectively, and dependsweakly on temperature. The densities ρn and ρs have instead a much stronger dependence on

13th European Turbulence Conference (ETC13) IOP PublishingJournal of Physics: Conference Series 318 (2011) 092029 doi:10.1088/1742-6596/318/9/092029

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temperature. The ratio between ρs and ρ increases steeply as the temperature decreases and,for example, is equal to 0.986 at 1.1 K (Vinen & Niemela, 2002). In other words, He II can beoften considered entirely superfluid at temperatures below 1 K. To highlight the uniqueness ofHe II, an example can be made on the basis of the just sketched two-fluid model. If a volume ofHe II is suitably heated, the normal component flows away from the heater while the superfluidcomponent moves towards the heater in order to have a zero-mass flow rate, that is, to conservethe mass of He II. This phenomenon is called thermal counterflow and has no equivalent inclassical fluid mechanics.

Besides, the superfluid component of He II can be described as a quantum fluid, that is,by a macroscopic wave function, see again Tilley & Tilley (1990); La Mantia et al. (2010) forfurther details. This leads to the result that superfluid flow is irrotational, i.e. ω = curl vs =0, where ω is the flow vorticity and the superfluid velocity vs is proportional to the gradient ofthe wave function phase. It follows that for a simply connected fluid region the circulation ofthe superfluid velocity is null. If the region is instead multiply connected, the circulation is notnull and equal to an integer multiple of the quantum of circulation k, which is the ratio of thePlanck constant and 4He atomic mass, i.e. k = 9.98 10−4 cm2/s (Vinen & Niemela, 2002). Thisresult can be seen as a quantum restriction to the superfluid motion. In other words, quantisedvortices - line singularities where the superfluid density is null - can exist in superfluid helium.These vortices usually arrange themselves in a tangle and such a tangle of quantised vorticesconstitutes what is generally called quantum turbulence.

The description of superfluid helium (He II) as a quantum fluid is specifically relevant forthe implementation of flow visualisation techniques at low temperatures. For example, thecomplex interactions between tracer particles, quantised vortices and macroscopic eddies incryogenic flows are far from being completely understood and novel experiments are requiredto verify the current theoretical understanding of these coupled phenomena, e.g., see Sergeev &Barenghi (2009); Van Sciver & Barenghi (2009). Moreover, the interesting and puzzling resultsrecently obtained in overseas laboratories (Zhang & Van Sciver, 2005; Bewley et al., 2006) areposing more questions than giving clear answers, e.g., the mechanisms of particles trapping intothe quantised vortices cores and the vortical structures observed around cylinders in thermalcounterflow deserve further attention and study. These outcomes show consequently the needof more detailed experimental analyses by flow visualisation, which is being proven as a veryvaluable technique to study cryogenic flows.

2. Experimental set-up

In order to fulfil such a need of new experimental data we are currently establishing the firstlaboratory in Europe for flow visualisation at low temperatures. Experimental investigation ofselected cryogenic flows over wide ranges of governing dynamical parameters, spanning fromlaminar to developed turbulent regime, using all forms of cryogenic 4He as working fluids arebeing planned. All these classical and quantum flows will be mainly probed by using quantitativeflow visualisation techniques, i.e. PIV and PTV. The cryogenic flows will be obtained by variousmeans. Flows around bodies oscillating in stationary fluid will be studied, due to their relativesimplicity of implementation at low temperatures. A bellows system (Babuin et al., 2010) willbe used to generate flows of various velocities around bluff bodies and heaters will be employedto obtain thermal counterflow, the aim of these experiments being also the comparisons ofdynamically similar flows in normal and superfluid 4He.

The flow visualisation equipment, which already is available in our laboratory, consists of thefollowing parts. A custom-made low-loss cryostat equipped with five sets of 25 mm diameterwindows that minimise the heat input into the helium bath, enabling horizontal as well asvertical optical access, was designed and manufactured, see Figure 1. A seeding system with a

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fast computer-controlled valve to supply the helium bath with the desired amount of hydrogenand deuterium micron-sized solid tracers was built and is being tested. These low-temperaturerelated parts are to be used with an off-the-shelf 5 W continuous wave solid state laser, a veryfast digital camera (up to 6273 fps at full resolution, i.e. 1 MP) and relevant hardware andsoftware to implement the PIV and PTV techniques for cryogenic flows, purchased from DantecDynamics.

100

100

50

150

Ø 25

Ø 500

(a) (b)

Figure 1. (a) Sketch of the low-loss optical cryostat (not to scale, dimensions in mm); (b)Cryostat optical tail.

Our facility is being designed to perform novel experiments, that is, not to be just a copyof existing systems but to be potentially capable of obtaining new results. For example, themuch faster camera will most likely allow a more detailed analysis of cryogenic flows’ dynamics,compared to Zhang & Van Sciver (2005); Bewley et al. (2006). As already mentioned, thecomplex interactions between tracer particles, quantised vortices and macroscopic eddies couldbe studied experimentally in unprecedented detail and, for example, the theoretical models thatpredict the conditions for particles’ trapping into the quantised vortices’ cores verified. Thismay also have an impact on the study of turbulent multiphase flows, which is a very activefield of research in classical fluid mechanics, e.g., see Poelma & Ooms (2006); Balachandar &Eaton (2010). Besides, the PTV technique, especially chosen to study quantum flows, has so farbeen rarely used for such applications and the use of PIV also appears controversial for thesepeculiar flows. In other words, particularly for turbulent flows, it is not completely clear if andwhen the PIV computed velocities are those of the normal component of He II or those of thesuperfluid portion of it or a mixture of the two. A plausible option would then be to follow theparticles in their motion to have a closer look at the flow dynamics. Moreover, the possibilityof using PIV and PTV for the same flow would definitely allow a further insight into this openissue. However, a number of technical difficulties have to be tackled. For example, even thoughthe set-up was carefully designed, the seeding system needs to be tuned in order to obtain themost suitable tracers. The PIV and PTV equipment is also currently being tested on various

13th European Turbulence Conference (ETC13) IOP PublishingJournal of Physics: Conference Series 318 (2011) 092029 doi:10.1088/1742-6596/318/9/092029

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experiments in water, such as well-known flows past bluff bodies and around oscillating objects,see next Section. The first results at low temperatures are expected in the coming months.More precisely, thermal counterflow experiments are being planned, similar to those discussedin Zhang & Van Sciver (2005), as well as experiments on cryogenic flows around oscillatingobjects, such as cylinders and spheres, which to our best knowledge have not been yet analysedby visualisation.

3. Water flows’ analyses

Figure 2 displays the mean vorticity field for a slightly bent water jet, directed downwards, ascalculated by the Dynamic Studio software (200 images were taken at the maximum frame rateand a two-dimensional PIV analysis with micron-sized buoyant particles was performed). It canbe noted that the camera field of view is quite small, ca. 4 cm2. Besides, the Reynolds numberis equal to ca. 18,000, the jet diameter being approximately 12 mm and its mean velocity vm

≈ 1.5 m/s. In other words, such a flow field could not have been probed with a much slowercamera. Besides, it is worth mentioning that the clock-wise region of vorticity can be explainedby considering that the jet was slightly bent to the left of the field of view.

2 4 6 8 10 12 14 16 18 20 22 24

2

4

6

8

10

12

14

Vorticity [1/s]

X [mm]

Y [

mm

]

-562.5

-420.2

-277.9

-135.6

6.7

149.0

291.2

433.5

575.8

718.1

860.4

1002.7

1145.0

Figure 2. Mean vorticity field [1/s] for a slightly bent water jet (Re ≈ 18,000).

In Figure 3 particles’ tracks for a flow past a circular cylinder are plotted. They werecomputed by using a procedure appropriately developed to process the results obtained bythe Dynamic Studio software (100 images were taken at the maximum frame rate, micron-sizedbuoyant particles were used, as above). The cylinder, placed at the left of the field of view, wasin a water jet, directed horizontally from the left to the right, slightly bent downwards. TheReynolds number is equal to ca. 1,000, as the cylinder diameter d = 5 mm and jet mean velocityvm ≈ 0.2 m/s. The colour code for the tracks indicates the minimum number of points for thetracks shown in that colour. For example, there are ca. 1,400 tracks with at least 25 points andca. 290 with at least 75 points. It can be seen that the recirculation zone behind the cylinder iswell captured by this visualisation technique.

13th European Turbulence Conference (ETC13) IOP PublishingJournal of Physics: Conference Series 318 (2011) 092029 doi:10.1088/1742-6596/318/9/092029

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0 2 4 6 8 10 12 14 16 18 20 22 24

0

2

4

6

8

10

12

14

16

Y [m

m]

X [mm]

25 50 75

Figure 3. Particles’ tracks for the flow past a cylinder in a slightly bent water jet (Re ≈ 1,000);the legend indicates the minimum number of points for the tracks shown in that colour.

-6 -4 -2 0 2 4 6

1E-3

0.01

0.1

1

10

PD

F %

V

25

50

75

PIV

Figure 4. PDF of the vertical velocity V of the flow past a cylinder in a slightly bent waterjet (Re ≈ 1,000), shown as a percentage of the total number of points of the considered type ofanalysis (tracks’ colour code as in Figure 3, cyan diamonds correspond to PIV data).

Figure 4 shows the PDF of the vertical component V of the fluid velocity for the same jetflow past the 5 mm diameter cylinder. It is displayed as a percentage of the total number ofpoints of the considered type of tracks (the colour code is as in Figure 3). V , negative if directed

13th European Turbulence Conference (ETC13) IOP PublishingJournal of Physics: Conference Series 318 (2011) 092029 doi:10.1088/1742-6596/318/9/092029

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downwards and normalized by using the corresponding standard deviations, was estimated foreach point of the tracks from the points’ positions and time between frames. The verticalvelocity PDF obtained from a two-dimensional PIV analysis of the same flow field, displayedas a percentage of the total number of calculated vectors, is also shown (the velocity was againnormalized by using the corresponding standard deviation): the agreement with the PTV datais fairly good, as expected for such a classical flow. Besides, it is not surprising to observe thatthe PDF shape is influenced by the chosen type of flow analysis. From a more general pointof view, this shape can be linked to specific flow features, e.g., it is clearly seen that the waterjet is slightly bent downwards. Such a procedure was indeed developed in order to be appliedto the study of specific features of cryogenic flows, e.g., the normal and superfluid flow fieldsthat have been reported in thermal counterflow experiments, e.g., see again Sergeev & Barenghi(2009); Van Sciver & Barenghi (2009).

In Figure 5 the instantaneous vorticity field generated by a cylinder oscillating in still wateris plotted, as calculated by the Dynamic Studio software (the images were taken at 1000 fps,micron-sized buoyant particles were used, as above). The cylinder was oscillating vertically (thelowest position of the cycle was just above the bottom of the field of view) and the vorticityfield was computed just after the cylinder left the field of view moving upwards. The Reynoldsnumber Re ≈ 120, as the cylinder diameter d = 5 mm and its mean velocity vm ≈ 0.024 m/s.The oscillation frequency was set to ca. 0.6 Hz and its amplitude to 0.02 m. Vortices rotatingin opposite direction were consecutively shed by the cylinder, resembling a Von Karman vortexstreet. Besides, the weak clock-wise vortex at the bottom left of the figure was shed at the endof the previous stroke, when the cylinder reached its lowest position, and pushed away while thecylinder moved upwards.

2 4 6 8 10 12 14 16 18 20 22 24

2

4

6

8

10

12

14

X [mm]

Y [m

m]

-52.5

-44.4

-36.3

-28.2

-20.2

-12.1

-4.0

4.1

12.2

20.3

28.3

36.4

44.5

Vorticity [1/s]

Figure 5. Instantaneous vorticity field [1/s] for the flow past an oscillating cylinder (Re ≈ 120).

Figure 6 displays the instantaneous vorticity standard deviation ωsd as a function of thecylinder oscillation frequency f : an almost linear relationship is found (the vorticity fields wereestimated by the Dynamic Studio software at the same point of the oscillating cycle, whenthe cylinder just left the field of view moving upwards). In other words, the strength of thevortices shed by the moving cylinder increases almost linearly with the oscillation frequency.

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Besides, a transition between two different shedding regimes was observed around 0.35 Hz,which corresponds to Re ≈ 70. For lower oscillation frequencies two spatially symmetric regionsof counter rotating vorticity were continuously shed behind the cylinder. For larger frequenciesa vortex shedding regime similar to that shown in Figure 5 was found instead, i.e. vortices ofopposite sign were consecutively shed by the cylinder. Such a flow instability cannot howeverbe seen in Figure 6, as the vorticity standard deviation is not influenced by the shed vortices’positions in the wake but just by their strength.

0.01 0.1 1 10

0.1

1

10

100

ωsd [1

/s]

f [Hz]

Figure 6. Instantaneous vorticity standard deviation as a function of the cylinder oscillationfrequency (Re ranging approximately between 10 and 300).

Further investigations, at different oscillation velocities and by using different cylinder sectiongeometries, e.g., square instead of circular, are being currently performed and planned, theiraim being also a systematic study of the characteristics of the wake shed by oscillating bodies(Schmoranzer et al., 2010; La Mantia & Dabnichki, 2011; Schmoranzer et al., 2011). This is infact relevant for the analysis of the flow around quartz tuning forks, which are fast oscillatorsextensively used as sensors in low temperature research (Schmoranzer et al., 2010, 2011).

However, the results presented in this Section are well known, at least qualitatively, e.g.,see Jeon & Gharib (2004) and references therein. The main purpose of these experiments inwater is to explore the capabilities of the visualisation system that is soon going to be usedto analyse various cryogenic flows, as detailed in the previous Section. More precisely, it wasbriefly shown that the chosen visualisation apparatus appears to be well suited for the task ofanalysing cryogenic flows, especially for that of experimentally studying in unprecedented detailthe complex interactions between tracer particles, quantised vortices and macroscopic eddies.

4. Conclusions

In summary, the use of flow visualisation at low temperature appears to be a very promisingexperimental tool that is certainly capable of improving our general knowledge of classical andquantum flows. The flow instabilities, fine details of the transition to turbulence and propertiesof developed and decaying classical and quantum turbulent flows could be studied systematically

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over wide ranges of dynamical parameters by using cryogenic helium, a remarkable working fluidwith well-known, unique and easily tunable properties.

Acknowledgments

We would like to thank Simone Babuin, Gregory Bewley, Tymofiy Chagovets, Veronika Pilcova,David Schmoranzer, Frantisek Soukup, Josef Sebek, Vaclav Uruba and Bohumil Vejr for fruitfuldiscussions and valuable help. Besides, we acknowledge the support of COST Action MP0806,MS 0021620834 and GACR P203/11/0442.

References

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Balachandar, S. & Eaton, J.K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. FluidMech. 42, 111–133

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Schmoranzer, D., Kral’ova, M., Pilcova, V., Winen, W.F. & Skrbek, L. 2010Experiments relating to the flow induced by a vibrating quartz tuning fork and similarstructures in a classical fluid. Phys. Rev. E 81, 066316

Schmoranzer, D., La Mantia, M., Sheshin, G., Gritsenko, I., Zadorozhko, A.,Rotter, M. & Skrbek, L. 2011 Acoustic emission by quartz tuning forks and otheroscillating structures in cryogenic 4He fluids. J. Low Temp. Phys. 163, 317–344

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