Acoustic Mode Velocimetry

A substantial challenge of the turbulent liquid metal experiments we perform is to get global constraints on the velocity field that is generating the magnetic field patterns and fluctuations we observe. Classic measurement techniques for turbulent flows tend to use optical methods, and prediction of the turbulent velocity field in some states is difficult to impossible with current numerical simulations even on state-of-the-art computing hardware. 

Acoustic Mode of the Sun

Solar Acoustic Mode, Courtesy of Wikimedia Commons

With suitable seeding particles in the flow, ultrasound doppler velocimetry is a useful technique to measure velocities in opaque liquid metals, but this technique has limitations for full flow mapping in the 3m system. It can only measure the component of the velocity along the ultrasound beam axis and has a fundamental limit on the product of maximum measureable velocity and maximum depth over which the velocity profile can be measured. We need to measure velocities of several meters per second, which generally translates to 10cm-30cm measuring depth, a small fraction of the 3m shell gap. Lower frequencies (longer ultrasound wavelengths) help this, but require larger particles that perform poorly as tracers in low-viscosity turbulent flow. It is unlikely that we can use ultrasound velocimetry to probe the mean velocity profile throughout the entire sphere.

Dan Lathrop, Santiago Triana, and I have been working on a technique to measure the global azimuthal velocity profile in liquid metals using the frequency shifts of resonant acoustic modes in a container full of moving fluid. This technique is inspired by the field of helioseismology, where comparison of measured acoustic mode oscillation frequencies are compared to calculations to infer velocities inside the sun.

Actual implementation in the 3m experiment itself is still in development. The main remaining challenge is strong acoustic excitation inside the hot and chemically difficult molten sodium environment. But we have conducted several proof-of-concept experiments in the same geometry in air, where we can use commodity audio hardware to make some progress and test the technique. 

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30cm Proof-of-Concept Setup

The proof-of-concept experiment is a stationary 30cm stainless steel sphere with a concentric, rotating 10cm copper inner sphere driven by a DC motor. This experiment was a sodium experiment at one time, a small-scale version of the 3m experiment, but it's been decommissioned for a while. 

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Electret Microphone Array, Lower Hemisphere

The experiment is outfitted with an amplifier and speaker to drive acoustic exciation and with an array of microphones positioned at known azimuthal and polar angles to measure the acoustic mode response. We acquire many microphones simultaneously with a multi-channel sound card so that we can cross-correlate signals to check the modes' spatial structure against what we expect from calculations. 

 

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Conventional Hot Film Velocity Meter

In addition to the acoustic instrumentation, we have a calibrated air velocity meter that uses a hot film sensing element. In this way we can directly measure the angular velocity profile in the experiment to validate our technique. To measure turbulent fluctuations (we can't help it, and it's potentially useful in analyzing some aspects of the acoustics) I added a faster hot film sensor using the thermal anemometry system I designed, and calibrated the mean response against the TSI air velocity meter.

helioseis_lg.pngMeasured Spectra, Stationary and Spinning Inner Sphere

We are analyzing and preparing a full report of the results of these experiments, but the spectra shown above are a taste of those results. We are using a slowly varying frequency chirp generated by MATLAB, amplified, and played into the excitation speaker. The darkest blue curve in the response above is measured with the inner sphere stationary. Adding rotation of the inner sphere causes each spectral peak to split into two peaks shifted in a way that's related to the flow profile in the sphere. Modes with higher azimuthal wavenumber are split more, generally speaking, but the splittings also involve a geometrical factor related to the mode intensity profile. 

By measuring many mode splittings, we can derive a system of equations for an internal flow profile estimate using the modes' predicted frequencies and amplitude patterns inside the sphere. As with many inverse problems of this type, there are uniqueness and other issues, and this is all a work in progress. But we have found very good agreement in the forward calculation where we predict the frequency splittings of different modes using the conventionally measured velocity profiles, and that's a good start.