1. A Miniature Second Sound Probe I - MOTIVATION & SENSORS DEVEL. PROGRAM II -2nd SOUND SENSOR IN STATIC HELIUM III -2nd SOUND SENSOR IN FLOW IV-FIRST RESULTS Sensor validation + Preliminary physics results Cryogenic Turbulence Group Center for Research on Very Low Temperature (CRTBT) Grenoble, France

2. Motivation : scaling laws of superfluid/quantum turbulence Approach : local & dynamical sensors for 4 He above 1.3 K T=1,4 K T=2,3 K T=2,08 K Reference result : Pitot pressure fluctuations by Maurer & Tabeling, 1998 Space resol.= 1.2mm (outer diam.) Time resol.= 1-800 Hz

3. Pressure sensors (under operation and/or test) Commercial sensor (Maurer-Tabeling’s approach)  DC-1kHz bandwidth / mm spatial resolution Home-made silicon membrane sensor : very sensitive + differential  objective : DC-few kHz bandwidth / 0.5 mm spatial resolution

4. Temperature sensors (under development)  objective : DC-1MHz bandwidth / few  m spatial resolution Superconducting transition edge thermometer (Al) Supporting frame is a delicate issue (non invasive for the flow) « our traditional frame » :  5  m glass fiber Fully micromachined process on a Kapton membrane (under develop.) 30  m thermometer spot  m thermometer spot

5. Flow T = 1.5 K  superfluid ratio = 88% V = 0.05-1 m/s  Re = V.  /   = 10 4 - 2.10 5 (mass flow = 40 g/s) Axis propeller local probes pipe (T.Didelot PhD) Pitot tube (mean velocity) Screens Honeycomb

6. Another flow: project NS2 bis Ligne hauts Reynolds NEF 7 Moteu r Pompe  location : CEA Grenoble  T range :1,5 - 4 K  Mass flow :400g/s @ 1.5 K 600g/s for T > 1.8 K  Grid turbulence ( R ~350 )  Collaboration :  CEA : flow operation (Girard, Rousset,…)  CRTBT : instruments (Roche, Chabaud, Hébral, Thibault, Diribarne(PhD),Gauthier(PhD )  LEGI (Gagne, Baudet)  Theoretical / Numerical : Castaing, Barenghi, Vassilicos, Daviaud,…

7. Miniature second sound probe Attenuation ~ Vortex line density ~ (inter-vortex spacing) -2 Anisotropic sensor Thermometer Heater HELIUM FLOW

8. Heater and Thermometer supports Design/micromachining : H. Willaime, P. Tabeling, Microfluidic group, ESPCI O. Français, L. Rousseau, Micromachining center, ESIEE Effective surface = 1mm*1mm Thermometer (Al) (transition edge ~ 1.5K) Heater (Cr) Side view : thermometer and heater facing each others Tip thickness = 15  m

9. Assembling 4 wires measurements Cavity size : 1mm*1mm*300  m Thickness ~ 15  m Gap ~ 300  m

10. How to choose the Heater driving current ? Steady counter-flow  Induced turbulence ?if yes : sensor is invasive Heater Joule effect (sin) 2 = DC+AC Second sound attenuation W T1 T2 Superfluid / Normal

11. Choosing the Heater driving current Evidence of « T1 » transition found at expected the critical heat flux density Driving current was set-up below this transition (…but doesn’t seem critical) T1 transition laminar turbulent

12. Second sound resonance modes without flow Fondamental mode :f 0 = 40 kHz (expected ~ V 2nd son / 2.Gap ~ 35 kHz) Dynamical response :n.f 0 / Q > 4 kHz Linear propagation :sinus signal received on thermometer (negligible distorsion) Received signal amplitude is what we expect

13. Resonance modes with a flow Frequency shift negligeable Limited defocusing since V flow << V 2nd sound (and can be compensated) in the following, the fondamental mode of resonance was chosen

14. From Measured signal to Vortex Line Density (VLD) Based on rotating bucket experiments (Hall & Vinen 1956, …) + Vortex Tangle Isotropy hypothesis First order relation is : VLD(t) ~ (6.f 0.  / B.  0.Q). (A 0 /A(t) -1) with : A 0 /Aattenuation of amplitude Bmutual friction constant f 0 resonant frequency Qquality factor (general relation : for ex. see Stalp thesis, 1998)

15. Time / Space resolution Electronic Bandwidth: DC-1kHz Typical velocity : 1 m/s electronic resolution~ (1m/s*1kHz) -1 = 1 mm ~ sensor size Structures larger than sensor and/or slower than time of flight thru sensor 300  m 1 mm

16. Acknowledgement Colleagues : Students : Collaboration : Many inputs from B. Castaing (ENS Lyon) B. Chabaud - B. Hébral T. Didelot (PhD), F.Muzellier, F. Gauthier P. Tabeling, H. Willaime (ESPCI) O. Français, L. Rousseau (ESIEE)