Wave propagation in an acoustic waveguide for ultrasonic phased arrays

We present a simulation of an acoustic waveguide array consisting of 64 circular-shaped ducts with equal lengths. The waveguide reduces the acoustic aperture to an effective element pitch of half lambda. In order to optimize the waveguide geometry regarding sound pressure level and time delay between the channels and directivity, we use the acoustic boundary element method of COMSOL Muliphysics 5.4. The main objective for this work, is to simulate and measure the directivity pattern in the far field region based on the wave propagation inside the waveguide in order to extend our previous simulation of ultrasonic phased arrays. The complexity of the model was reduced using two symmetry planes. The wave propagation is calculated in the frequency domain based on the Helmholtz equation. A finite-sized rigid baffle at the acoustic aperture side of the array, identical to the one used in the measurements, is included. Our model allows visualizing the wave propagation in our waveguide. As the geometry intended, all waveguides emit the ultrasound in phase. Due to a different distribution of the normal velocity of the real transducers, the half power beam width differs only 4° and the side lobe level 3 dB compared to measurements.