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

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.= Hz

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

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

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

Another flow: project NS2 bis Ligne hauts Reynolds NEF 7 Moteu r Pompe  location : CEA Grenoble  T range :1,5 - 4 K  Mass flow 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,…

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

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

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

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

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

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

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

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)

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

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)