Cantilever anemometer based on a superconducting micro-resonator: Application to superfluid turbulence

Turbulence in superfluid helium is unusual and presents a challenge to fluid dynamicists because it consists of two coupled, interpenetrating turbulent fluids: the first is inviscid with quantized vorticity, and the second is viscous with continuous vorticity. Despite this double nature, the observed spectra of the superfluid turbulent velocity at sufficiently large length scales are similar to those of ordinary turbulence. We present experimental, numerical, and theoretical results that explain these similarities, and illustrate the limits of our present understanding of superfluid turbulence at smaller scales. He.) Besides the lack of viscosity, another major difference from ordinary (classical) fluids such as water or air is that, in helium, vorticity is constrained to vortex line singularities of fixed circulation κ = h=M, where h is Planck's constant, and M is the mass of the relevant boson (M = m 4 , the mass of He, the vortex core radius ξ ≈ 10 −10 m is comparable to the interatomic distance. Thus, quantization of circulation results in the appearance of another characteristic length scale: the mean separation between vortex lines, ℓ. In typical experiments (both in 4 He and 3 He), ℓ is orders of magnitude smaller than the scale D of the largest eddies but is also orders of magnitudes larger than ξ.There is a growing consensus (2) that superfluid turbulence at large scales R ℓ is similar to classical turbulence if excited similarly, for example by a moving grid. The idea is that motions at scales R ℓ should involve at least a partial polarization (3-5) of vortex lines and their organization into vortex bundles that, at such large scales, should mimic continuous hydrodynamic eddies. Therefore, one expects a classical Richardson-Kolmogorov energy cascade, with larger "eddies" breaking into smaller ones. The spectral signature of this classical cascade is indeed observed experimentally in superfluid helium. In the absence of viscosity, in superfluid turbulence the kinetic energy should cascade downscale without loss, until it reaches scales R ∼ ℓ, where the discreteness becomes important. It is also believed that the energy is further transferred downscales by the interacting Kelvin waves (helical perturbation of the individual vortex lines) where it is radiated away by thermal quasiparticles (phonons and rotons in 4 He). Although this scenario seems reasonable, crucial details are yet to be established. Our understanding of superfluid turbulence at scales of the order of ℓ is still at infancy stage, and what happens at scales below ℓ is a question of intensive debates. The "quasiclassical" region of scales, R ℓ, is better understood, but still less than classical hydrodynamic turbulence. The main reason is that at nonzero temperatures (but still below the critical temperature), superfluid helium is a two-fluid system. According to the theory of Landau and Tisza (6), it consists of two interpenetrating components: the inviscid superfluid, of density ρ s and velocity u s (associated to the quantum ground stat...

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“…SI-2, lower left sketch). Preliminary spectral measurements with a resolution of 100 μm have been recently reported (23).…”

Section: Discussionmentioning

confidence: 99%

Experimental, numerical, and analytical velocity spectra in turbulent quantum fluid

Barenghi

L’vov

Roche

2014

Proc. Natl. Acad. Sci. U.S.A.

109

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“…where E is the Young modulus of silicon oxide [18]. The pressure load induced by the motion of the fluid impinging on the cantilever normally can be written…”

Section: Calibration Of the Strain Gaugementioning

confidence: 99%

“…Five years ago, we have extended this technique of cantilever-based anemometry to the case of low temperature liquid helium flows [18]. We then proposed a method based on a superconducting micro-resonator patterned onto the cantilevered beam.…”

Section: Turbulent Velocity Fluctuationsmentioning

confidence: 99%

A local sensor for joint temperature and velocity measurements in turbulent flows

Salort

Rusaouen

Robert

et al. 2018

Review of Scientific Instruments

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We present the principle for a micro-sensor aimed at measuring local correlations of turbulent velocity and temperature. The operating principle is versatile and can be adapted for various types of flow. It is based on a micro-machined cantilever, on the tip of which a platinum resistor is patterned. The deflection of the cantilever yields an estimate for the local velocity, and the impedance of the platinum yields an estimate for the local temperature. The velocity measurement is tested in two turbulent jets: one with air at room temperature which allows us to compare with well-known calibrated reference anemometers, and another one in the GReC jet at CERN with cryogenic gaseous helium which allows a much larger range of resolved turbulent scales. The recording of temperature fluctuations is tested in the Barrel of Ilmenau which provides a controlled turbulent thermal flow in air. Measurements in the wake of a heated or cooled cylinder demonstrate the capability of the sensor to display the cross correlation between temperature and velocity correctly.

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“…Silicon micro-cantilevers have today applications in many areas of measurement, as chemical and biological sensors, 1 mass detectors, 2,3 flow meters, 4,5 or force sensors. 6 Thanks to their industrial production with tight tolerances, and the ability to integrate a sharp tip in the fabrication process, they are, for example, ubiquitous in atomic force microscopy (AFM).…”

Section: Introductionmentioning

confidence: 99%

Resonance frequency shift of strongly heated micro-cantilevers

Sandoval

Geitner

Bertin

et al. 2015

Journal of Applied Physics

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In optical detection setups to measure the deflection of micro-cantilevers, part of the sensing light is absorbed, heating the mechanical probe. We present experimental evidences of a frequency shift of the resonant modes of a cantilever when the light power of the optical measurement set-up is increased. This frequency shift is a signature of the temperature rise and presents a dependence on the mode number. An analytical model is derived to take into account the temperature profile along the cantilever; it shows that the frequency shifts are given by an average of the profile weighted by the local curvature for each resonant mode. We apply this framework to measurements in vacuum and demonstrate that huge temperatures can be reached with moderate light intensities: a 1000 °C with little more than 10 mW. We finally present some insight into the physical phenomena when the cantilever is in air instead of vacuum.

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Cantilever anemometer based on a superconducting micro-resonator: Application to superfluid turbulence

Cited by 20 publications

References 34 publications

Experimental, numerical, and analytical velocity spectra in turbulent quantum fluid

Experimental, numerical, and analytical velocity spectra in turbulent quantum fluid

A local sensor for joint temperature and velocity measurements in turbulent flows

Resonance frequency shift of strongly heated micro-cantilevers

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