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

Controlled spherical deuterium droplets as Lagrangian tracers for cryogenic turbulence experiments

The study of the smallest scales of turbulence by (Lagrangian) particle tracking faces two major challenges: the requirement of a 2D or 3D optical imaging system with sufficiently high spatial and temporal resolution and the need for particles that behave as passive tracers when seeded into the flow. While recent advances in the past decade have led to the development of fast cameras, there is still a lack of suitable methods to seed cryogenic liquid helium flows with mono-disperse particles of sufficiently small size, of the order of a few micrometers, and a density close enough to that of helium. Taking advantage of the surface tension, we propose two different techniques to generate controlled liquid spherical droplets of deuterium over a liquid helium bath. The first technique operates in a continuous mode by fragmenting a liquid jet, thanks to the Rayleigh-Taylor instability. This results in the formation of droplets with a diameter distribution of 2 ± 0.25DN, where DN is the diameter of the jet nozzle (DN = 20 μm in the present experiment). This method offers a high production rate, greater than 30 kHz. The second technique operates in a drop-on-demand mode by detaching droplets from the nozzle using pressure pulses generated using a piezoelectric transducer. This approach yields a much narrower diameter distribution of 2.1 ± 0.05DN but at a smaller production rate, in the range 500 Hz-2 kHz. The initial trajectories and shapes of the droplets, from the moment they are released from the nozzle until they fall 3 mm below, are investigated and discussed based on back-light illumination images.

Second sound resonators and tweezers as vorticity or velocity probes: Fabrication, model, and method

An analytical model of open-cavity second sound resonators is presented and validated against simulations and experiments in superfluid helium using a new resonator design that achieves unprecedented resolution. The model incorporates diffraction, geometrical misalignments, and flow through the cavity and is validated using cavities operated up to their 20th resonance in superfluid helium. An important finding is that resonators can be optimized to selectively sense either the quantum vortex density carried by the throughflow-as typically done in the literature-or the mean velocity of the throughflow. We propose two velocity probing methods: one that takes advantage of misalignments between the tweezers' plates and other that drives the resonator non-linearly, beyond a threshold that results in the self-sustainment of a vortex tangle within the cavity. A new mathematical treatment of the resonant signal is proposed to adequately filter out parasitic signals, such as temperature and pressure drift, and accurately separate the quantum vorticity signal. This elliptic method consists in a geometrical projection of the resonance in the inverse complex plane. Its effectiveness is demonstrated over a wide range of operating conditions. The resonator model and elliptic method are being utilized to characterize a new design of resonators with high resolution, thanks to miniaturization and design optimization. These second-sound tweezers are capable of providing time-space resolved information similar to classical local probes in turbulence, down to sub-millimeter and sub-millisecond scales. The principle, design, and microfabrication of second sound tweezers are being presented, along with their potential for exploring quantum turbulence.

Fabrication of freestanding Pt nanowires for use as thermal anemometry probes in turbulence measurements

We report a robust fabrication method for patterning freestanding Pt nanowires for use as thermal anemometry probes for small-scale turbulence measurements. Using e-beam lithography, high aspect ratio Pt nanowires (~300 nm width, ~70 µm length, ~100 nm thickness) were patterned on the surface of oxidized silicon (Si) wafers. Combining wet etching processes with dry etching processes, these Pt nanowires were successfully released, rendering them freestanding between two silicon dioxide (SiO₂) beams supported on Si cantilevers. Moreover, the unique design of the bridge holding the device allowed gentle release of the device without damaging the Pt nanowires. The total fabrication time was minimized by restricting the use of e-beam lithography to the patterning of the Pt nanowires, while standard photolithography was employed for other parts of the devices. We demonstrate that the fabricated sensors are suitable for turbulence measurements when operated in constant-current mode. A robust calibration between the output voltage and the fluid velocity was established over the velocity range from 0.5 to 5 m s^-1 in a SF₆ atmosphere at a pressure of 2 bar and a temperature of 21 °C. The sensing signal from the nanowires showed negligible drift over a period of several hours. Moreover, we confirmed that the nanowires can withstand high dynamic pressures by testing them in air at room temperature for velocities up to 55 m s^-1.

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

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.

Simplified Aeroelastic Model for Fluid Structure Interaction between Microcantilever Sensors and Fluid Surroundings

Fluid-structural coupling occurs when microcantilever sensors vibrate in a fluid. Due to the complexity of the mechanical characteristics of microcantilevers and lack of high-precision microscopic mechanical testing instruments, effective methods for studying the fluid-structural coupling of microcantilevers are lacking, especially for non-rectangular microcantilevers. Here, we report fluid-structure interactions (FSI) of the cable-membrane structure via a macroscopic study. The simplified aeroelastic model was introduced into the microscopic field to establish a fluid-structure coupling vibration model for microcantilever sensors. We used the finite element method to solve the coupled FSI system. Based on the simplified aeroelastic model, simulation analysis of the effects of the air environment on the vibration of the commonly used rectangular microcantilever was also performed. The obtained results are consistent with the literature. The proposed model can also be applied to the auxiliary design of rectangular and non-rectangular sensors used in fluid environments.

Hot-wire anemometry for superfluid turbulent coflows

We report the first evidence of an enhancement of the heat transfer from a heated wire to an external turbulent coflow of superfluid helium. We used a standard Pt-Rh hot-wire anemometer and overheat it up to 21 K in a pressurized liquid helium turbulent round jet at temperatures between 1.9 K and 2.12 K. The null-velocity response of the sensor can be satisfactorily modeled by the counterflow mechanism, while the extra cooling produced by the forced convection is found to scale similarly as the corresponding extra cooling in classical fluids. We propose a preliminary analysis of the response of the sensor and show that-contrary to a common assumption-such sensor can be used to probe local velocity in turbulent superfluid helium.

Planarised optical fiber composite using flame hydrolysis deposition demonstrating an integrated FBG anemometer

This paper reports for the first time a planarised optical fiber composite formed using Flame Hydrolysis Deposition (FHD). As a way of format demonstration a Micro-Opto-Electro-Mechanical (MOEMS) hot wire anemometer is formed using micro-fabrication processing. The planarised device is rigidly secured to a silicon wafer using optical quality doped silica that has been deposited using flame hydrolysis and consolidated at high temperature. The resulting structure can withstand temperatures exceeding 580K and is sensitive enough to resolve free and forced convection interactions at low fluid velocity.

Superfluid high REynolds von Kármán experiment

The Superfluid High REynolds von Kármán experiment facility exploits the capacities of a high cooling power refrigerator (400 W at 1.8 K) for a large dimension von Kármán flow (inner diameter 0.78 m), which can work with gaseous or subcooled liquid (He-I or He-II) from room temperature down to 1.6 K. The flow is produced between two counter-rotating or co-rotating disks. The large size of the experiment allows exploration of ultra high Reynolds numbers based on Taylor microscale and rms velocity [S. B. Pope, Turbulent Flows (Cambridge University Press, 2000)] (Rλ > 10000) or resolution of the dissipative scale for lower Re. This article presents the design and first performance of this apparatus. Measurements carried out in the first runs of the facility address the global flow behavior: calorimetric measurement of the dissipation, torque and velocity measurements on the two turbines. Moreover first local measurements (micro-Pitot, hot wire,…) have been installed and are presented.

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

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.

Dynamics of quantum turbulence of different spectra

Turbulence in a superfluid in the zero-temperature limit consists of a dynamic tangle of quantized vortex filaments. Different types of turbulence are possible depending on the level of correlations in the orientation of vortex lines. We provide an overview of turbulence in superfluid (4)He with a particular focus on recent experiments probing the decay of turbulence in the zero-temperature regime below 0.5 K. We describe extensive measurements of the vortex line density during the free decay of different types of turbulence: ultraquantum and quasiclassical turbulence in both stationary and rotating containers. The observed decays and the effective dissipation as a function of temperature are compared with theoretical models and numerical simulations.