Measurement of acoustic streaming in a standing wave using laser Doppler anemometry

by Thompson, Michael W.

Laser Doppler anemometry (LDA) with burst spectrum analysis (BSA) is used to study the acoustic streaming generated in a cylindrical standing-wave resonator filled with air. The air column is driven sinusoidally at a frequency of approximately 310 Hz, and the resultant acoustic-velocity amplitudes are less than 1.3 m/s at the velocity antinodes. The axial component of fluid velocity is measured along the resonator axis, across the diameter, and as a function of acoustic amplitude. The velocity signals are post-processed using the Fourier averaging method [Sonnenberger et al., Exp. Fluids 28, 217–224 (2000)]. Equations are derived for determining the uncertainties in the resultant Fourier coefficients. The time-averaged velocity-signal components are seen to be contaminated by significant errors due to the LDA/BSA system. In order to avoid these errors, the Lagrangian streaming velocities are determined using the time-harmonic signal components and the arrival times of the velocity samples. The observed Lagrangian streaming velocities are consistent with Rott’s theory [N. Rott, J. Appl. Math. Phys. (ZAMP) 25, 417–421 (1974)], indicating that the dependence of viscosity on temperature is important. The onset of streaming is observed to occur within approximately 5 s after switching on the acoustic field. The influences of a thermoacoustically induced axial temperature gradient and fluid inertia on the streaming are investigated using this same method. The axial component of Lagrangian streaming velocity is measured along the resonator axis and across the diameter at acoustic-velocity amplitudes of 2.7 m/s, 4.3 m/s, 6.1 m/s, and 8.6 m/s at the velocity antinodes. Measurements are repeated with the resonator either wrapped in foam insulation, surrounded by a water jacket, or suspended within an air-filled tank, in order to vary the magnitude of the axial temiii perature gradient. A significant correlation is observed between the temperature gradient and the behavior of the streaming: as the magnitude of the temperature gradient increases, the magnitude of the streaming decreases and the shape of the streaming cell becomes increasingly distorted. The decay of the streaming after switching off the acoustic field is also affected by the presence of a temperature gradient. iv