Experimental and Numerical Study of Acoustic Streaming in Mid-Air Phased Arrays

Technical Summary: Experimental and Numerical Study of Acoustic Streaming in Mid-Air Phased Arrays

Problem Statement
Mid-air acoustic streaming, the steady fluid motion induced by ultrasound, is a critical factor in the performance of airborne ultrasonic technologies. While extensively studied in liquid media and microchannels, the streaming behavior within airborne phased-array transducers (PATs) remains poorly understood. This lack of understanding poses challenges for applications relying on precise control of air, such as haptic feedback, acoustic levitation stability, odor delivery, and volumetric displays. Existing measurement methods, such as hot-wire anemometers, are prone to inaccuracies due to nonlinear acoustic field interactions. Consequently, there is a need for a comprehensive characterization of streaming dynamics in single- and multi-focus acoustic fields to optimize system design.

Methodology
The study employs a dual approach combining Particle Image Velocimetry (PIV) experiments with numerical simulations to investigate streaming dynamics.

• Experimental Setup: A 16×16 open-type air-coupled transducer array (Murata MA40S4S) operating at 40 kHz was used. The array was placed at the bottom of a smoke-filled chamber (using mosquito coil smoke as tracers). A 5W green laser illuminated the particles in the xz-plane, and a high-speed camera (240 Hz) captured particle displacements. Data processing was performed using PIVlab in MATLAB to calculate streaming velocity fields.
• Numerical Modeling: The acoustic pressure field was modeled using a 3D Huygens' principle approach, superimposing contributions from all transducers. Phase shifts were calculated for focused beams, Bessel beams, and multi-focus fields (using an iterative backpropagation algorithm).
• Streaming Force Calculation: The acoustic streaming force was derived from the acoustic intensity vector. Two distinct attenuation mechanisms were incorporated into the models to compare their efficacy:
  1. Thermoviscous attenuation: Calculated via the Stokes-Kirchhoff relation.
  2. Atmospheric attenuation: Calculated using relaxation frequencies for nitrogen and oxygen.
• Simulation Implementation: The calculated streaming forces were exported and applied as volume forces in COMSOL Multiphysics 6.2. A 2D mirror symmetry model with laminar flow assumptions was used to simulate the flow fields, which were then compared against experimental data.

Key Results

• Velocity Magnitudes: Experimental measurements revealed streaming velocities exceeding 0.4 m/s in single-focus configurations and up to 0.3 m/s in multi-focus setups.
• Grating Lobes: A distinct feature observed in experiments was the presence of strong lateral jets induced by grating lobes, which contribute significantly to the lateral flow structure.
• Model Accuracy (Central vs. Lateral Flow):
  • The 2D mirror symmetry models effectively captured the central streaming flow, showing reasonable agreement with experimental data, particularly when using the atmospheric attenuation model.
  • However, the models performed poorly in replicating the lateral flow characteristics, specifically the grating lobe-induced jets. The thermoviscous model significantly underestimated both central and lateral flows, while the atmospheric model improved central flow prediction but still underestimated grating lobe intensity.
• Parametric Dependencies:
  • Focal Distance: Maximum velocity generally increased with focal distance, a trend that became more pronounced at higher input voltages (5 V, 8 V, 10 V).
  • Cone Angle (Bessel Beams): At higher voltages, experimental data aligned with the thermoviscous model at small cone angles but shifted toward atmospheric model predictions as the cone angle increased.
• Transient Response: Analysis of the temporal behavior showed that rise times (time to reach mean velocity) were approximately 0.8–1.2 seconds, while fall times (decay after power-off) ranged from 2.5 to 5 seconds. Higher voltages resulted in higher steady-state velocities and faster dissipation rates.
• Multi-Focus Configurations: For closely spaced focal points (±10 mm and ±30 mm), experimental and numerical results showed good agreement, with flow fields combining into unified jets. However, for widely separated focal points (±50 mm), the simulation failed to replicate the experimental flow direction, predicting straight upward flow where experiments showed outward orientation. Additionally, simulations predicted vortex formation near walls that were not observed experimentally.

Significance and Contributions
The paper provides a systematic framework for understanding the interplay between acoustic field design and streaming dynamics in mid-air phased arrays. By validating experimental PIV data against numerical models, the study highlights the limitations of current 2D symmetry models and weakly nonlinear formulations in capturing complex lateral flow features like grating lobes.

The findings offer practical guidance for optimizing ultrasonic technologies:

• Design Optimization: The study clarifies how focal distance and beam geometry influence streaming strength, aiding in the design of systems for haptics and levitation.
• Modeling Guidance: It identifies that while simplified 2D models are sufficient for predicting central flow, they are inadequate for lateral flow and widely separated multi-focus fields. This suggests a need for refined attenuation models, better boundary condition assumptions, and full 3D simulations for high-fidelity applications.
• Application Impact: The results contribute to improving the stability of levitation systems and the precision of haptic and odor display technologies by accounting for the fluid dynamic effects of acoustic streaming.

The authors conclude that while the current modeling approach is effective for central flow in specific configurations, future work must address the discrepancies in side-lobe modeling and transition to full 3D simulations to fully characterize these complex phenomena.