Experimental setup for probing a von Karman type flow of normal and superfluid helium

Transcription

1 Journal of Low Temperature Physics - QFS2009 manuscript No. (will be inserted by the editor) Experimental setup for probing a von Karman type flow of normal and superfluid helium D. Schmoranzer L. Skrbek Received: date / Accepted: date Abstract An experimental setup for probing a von Karman type flow of normal and superfluid 4 He generated inside a cm 3 brass box by counter-rotating discs with blades has been designed and tested. The generated steady and decaying flow of both normal and superfluid liquid 4 He can be probed simultaneously by vibrating quartz forks and by measuring pressure fluctuations. Additionally, the vortex line density in von Karman superflow can be sensed by attenuation of second sound. We describe the setup, present and discuss the available preliminary data and outline planned experiments that thanks to a possibility of simultaneous detection by three independent complementary techniques ought to bring new results in studies of quantum turbulence and its classical counterpart. Keywords Quantum turbulence Superfluid helium von Karman flow PACS PACS Jv PACS dk 1 Introduction Quantum turbulence [1,2] a most general way of flow of a quantum fluid that involves dynamics of a tangle of quantized vortices as well as its classical counterpart represent a challenging field of investigation from both fundamental and practical point of view. Although quantum turbulence in superfluid He II at finite temperature must differ significantly from that in normal He I, which is a classical fluid, while He II exhibits two-fluid behaviour and flow of its superfluid component (superflow) is subject to severe quantum restrictions, in some cases one observes surprising similarities, such as the existence of an inertial part of Kolmogorov form in their energy spectra [3,4] or striking similarity between decaying quantum and classical turbulence [5 7]. In order to study these similarities and differences experimentally, it is desirable to choose a type of flow that can be generated in the same way both in He I and in He II and Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, Prague, Czech Republic Tel.: Fax: skrbek@fzu.cz

2 2 Fig. 1 (Color online) An assembled (a) second sound sensor based on the gold-plated nuclepore membrane, mechanically stretched over a delrin ring, forming a capacitor with the opposite brass electrode (b) pressed against it by a spring. Detailed view of one of the bare quartz tuning forks sealed with Stycast 1860 to the brass wall (c) and the geometric configuration (e) of three forks inside the cell oscillating at different frequencies (32 khz, 77.5 khz, and 100 khz). The photograph of the lower part of the cryogenic insert showing the brass cell (d). The driving stainless steel shaft is connected to the gearbox via soft bellows. probed simultaneously in situ using various complementary techniques available in steady-state and/or decaying flows again both in He I and in He II. Based on our previous investigations, we have chosen a mechanical probe a vibrating quartz fork [8 12] and a piezoelectric pressure sensor, similar as was successfully used by previous investigators. Additionally, the vortex line density in a von Karman superflow can be sensed by attenuation of second sound, a technique which has been utilized in our Laboratory over recent years [7, 13]. This publication does not represent any serious study of physics underlying quantum or classical turbulent flow, it is rather a progress report reflecting current state of development. It shows, nevertheless, that our aim to study complementary quantum and classical turbulent flows in situ by means of chosen techniques could be accomplished.

3 3 2 Experimental setup Von Karman flow is generated by rotating the two discs of diameter 8.5 cm, each fitted with five blades, located at opposite sides of the cm 3 brass cell, see Fig. 1. Both discs are driven simultaneously to rotate in mutually opposite directions by a Maxon engine placed at the top flange of the cryogenic insert and connected to the cell via a hollow stainless steel shaft fitted with soft bellows. The gears located on the box ensure sufficient rotation speeds of the discs (corresponding to velocities up to 1 m/s) with reasonably low rotation velocity of the shaft itself. Three different techniques were employed for the detection and/or characterization of turbulence in the cell. Classical turbulence can be probed by three different quartz tuning forks as well as by a PCB Piezotronics low temperature piezoelectric pressure probe. These sensors provide us with complementary information, because while the forks measure directly the force acting on a body oscillating at a single frequency (currently, forks oscillating at 32 khz, 77.5 khz and 100 khz are installed), the dynamical pressure sensor allows us to construct the power spectrum of turbulent fluctuations by Fourier transforming its time domain signal. The pressure sensor is located on the outside of the cell and connected to its interior by a thin z-shaped tube. The orifice of the tube is positioned about 1 cm away from one of the two rotating discs and oriented so that it faces the incoming mean flow. The sensor is operated using a PCB charge amplifier and signal conditioner to provide maximum accuracy. Quantum turbulence can be probed in our setup using the two above mentioned types of sensor and, additionally, by second sound attenuation. Two second sound transducers with gold-plated nuclepore membranes (see detail in Fig. 1) are located in the center of two opposing sides of the box. However, this preliminary report is concerned mainly with tests and measurements in He I, and second sound will not be discussed here any further. The cell is also fitted with two RuO 2 thermometers, one on the inside and one on the outside, which can be used for monitoring and stabilizing temperature, together with a heater in the open helium bath and a LTC temperature controller. Temperature stabilization routines were not employed during the presented preliminary measurement conducted in He I at 4.2 K, but are essential for any measurement in He II, as our tests indicate that the rotating gears and discs dissipate significant energy. 3 Preliminary data and discussion Based on our previous study [12], where the bare quartz fork was placed in front of a capillary in a streaming counterflow jet, we have placed three forks inside the box, exposed them to the flow due to counter-rotating discs and tested their response as a function of the rotation velocity. Fig. 2 shows the typical data from a bare fork [14] oscillating at 32 khz at room temperature. There are two features worth commenting. First, the linewidth measured with discs at rest is stable and reproducible, providing that one allows enough time (up to half hour) for the swirling fluid inside the box to settle. However, at all finite measured velocities the linewidth becomes significantly larger. Qualitatively the same feature was observed in He II, where, however, the linewidth becomes strongly temperature dependent and an accurate measurement requires careful temperature control. Second, at velocities of the disc approaching about 0.4 m/s, the observed linewidth starts to increase dramatically. Note that similar increase in linewidth was observed

4 4 f deviation (Hz) v R (cm/s) f (Hz) v R (cm/s) 15 f (Hz) v N (cm/s) Fig. 2 (Color online) Upper panel: The linewidth f of the fork oscillating inside the turbulent box in He I at 4.2 K, plotted versus the velocity, v R, of the counter-rrotating discs at their perimeter. Each data point represents an average of ten independent measurements. The inset shows the corresponding deviation of f. Lower panel: The linewidth f of the fork oscillating in a counterflow jet of He II streaming from a capillary plotted versus the normal fluid velocity inside it - the fork was placed about 2 mm from its outlet [12]. The solid (red) line is a linear fit through the data. in our previous work [12], when the fork of the same type was placed in He II inside a counterflow jet streaming from the capillary 2 mm away (see the bottom panel of Fig. 2). It is noteworthy that in both cases the flow velocities (in He II case of its normal component) at which the linewidth starts to grow are similar in magnitude, although any direct comparison is hardly possible. It must be kept in mind that cavitation might occur in the vicinity of the fork s prongs as its peak velocity reaches about 1 m/s [15], although in the case of cavitation, the observed electrical signal was distinctly different in character which did not show here. Fig. 3 shows the preliminary power spectra obtained using the pressure sensor in He I at rest and at various values of perimeter velocity of the counter-rotating discs as

5 5 Power (a.u.) cm/s 53 cm/s 37 cm/s 3 cm/s 0 cm/s Frequency (Hz) Fig. 3 (Color online) Steady-state energy spectra of He I flows as detected by the piezoelectric pressure sensor. The bottom (black) line shows the spectrum measured with discs at rest; other spectra correspond to ascending velocities as indicated. The dashed (black) line illustrates the Kolmogorov roll-off exponent of -5/3. indicated. It is evident that the pressure sensor is capable of probing the flow as the background data measured with the discs at rest (it takes rather long time of order minutes for the flow inside the box to decay) lie several orders of magnitude lower than those measured at finite velocities. Moreover, the upper two spectra seem consistent with the famous Kolmogorov -5/3 roll-off exponent up to about 70 Hz. Present higher frequency data are unreliable, most likely due to combined effect of electrical noise, mechanical vibrations, and acoustic resonances occurring along the entry tube of the sensor. Our attempts to acquire similar spectra in He II have so far been less successful. Although some of them do display features consistent with the inertial range of Kolmogorov type with -5/3 roll-off exponent, their quality is generally worse, probably because of temperature gradients and overheating of the interior of the box. 4 Conclusions and future prospects We have designed and manufactured a cryogenic setup for generation of von Karman turbulent flows of both He I and He II. In He I, it can be operated under approximately isothermal conditions up to about 5 revolutions per second, corresponding to the Reynolds number based on the perimeter velocity of the counterrotating discs and

6 6 their mutual distance Re at 4.2 K. In He II, reliable operation of the setup requires an effective pumping system and careful temperature regulation in view of a significant heat input released into the helium bath. Our preliminary data confirm the ability of quartz tuning forks and pressure sensor to detect externally generated cryogenic helium turbulence. Further work, both experimental and theoretical, is needed in order to calibrate these sensors in some known flow and link these measurements with the intensity of turbulence in classical fluids and with the second sound data on vortex line density in He II. For future experiments, several improvements and modifications to our setup proved to be essential. The most important factors for the pressure measurements is to reduce both electrical noise and mechanical vibration levels and to optimize the mounting of the sensor on the cell as well as its connection the the cell s interior. Temperature control needs to be applied efficiently in He II. Acknowledgements We are grateful to L. Doležal for skillful manufacturing of mechanical parts of our home-made cryogenic system, P. Roche for providing an additional pressure sensor and useful discussions and to T.V. Chagovets for help with development of second sound transducers and to P. Skyba for developing and providing an I-V convertor for use with the quartz tuning forks. This research is supported by research plans MS , by GAČR 202/08/0276 and by GAUK 7953/2007. References 1. W. F. Vinen, and J. J. Niemela, J. Low Temp. Phys. 128, 167 (2002). 2. L. Skrbek, Physica C 404, 354, (2004). 3. J. Maurer, and P. Tabeling, Europhys. Lett. 43, 29 (1998). 4. P.E. Roche, P. Diribarne, T. Didelot, O. Francais, L. Rousseau, H. Willaime, Eur. Phys. Lett. 77, (2007). 5. S.R. Stalp, L. Skrbek, and R.J. Donnelly, Phys. Rev. Lett. 82, 4831 (1999). 6. L. Skrbek, J.J. Niemela, and R.J. Donnelly, Phys. Rev. Lett. 85, 2973 (2000). 7. L. Skrbek, A. V. Gordeev, and F. Soukup, Phys. Rev. E 67, (2003). 8. M. Blazkova, D. Schmoranzer, and L. Skrbek, Phys. Rev. E 75, , (2007). 9. R. Blaauwgeers et al., J. Low Temp. Phys., 146, 537 (2007). 10. M. Blažková et al., J. Low Temp. Phys., 150, 525 (2008). 11. M. Blazkova, D. Schmoranzer, L. Skrbek, and W. F. Vinen, Phys. Rev. B 79, (2009). 12. D. Schmoranzer, and L. Skrbek, Journal of Physics: Conference Series 150, (2009). 13. T.V. Chagovets et al., Acta Physica Slovaca, 56, 173 (2006). 14. Forks used in this work have been produced by Fronter Electronics, China, M. Blažková, D. Schmoranzer, and L. Skrbek, Low Temperature Physics 34, 380 (2008).