Optimization and manipulation of acoustical vortices generated by annularly distributed sparse sources

The method of the generation of acoustical vortices with annularly distributed sparse sources is proposed and it is also optimized for field manipulation. Theoretical derivations and analyses of acoustic pressure and phase as well as vibration velocity of the generated acoustical vortices are conducted. By changing the parameters of source number, frequency and transmission distance, 3-D pressure distributions of acoustical vortices are simulated. It is proved that the radius of acoustical vortices is mainly determined by the wave length of the sources. The higher the frequency is, the more concentrated energy of acoustical vortices with smaller radius can be generated. It is also demonstrated that the pressure peak of acoustical vortices increases with the increase of source number, while decreases for increased propagation distance. Meanwhile, the linearity of the circular phase distribution of acoustical vortices enhances for increased source number, longer wave length and bigger transmission distance. In addition, with the experimental setup using 3/4/6/8 sources, the measured radial and circular distributions of pressure and phase agree well with the numerical results, and the rotation of the suspended foam disk also demonstrates the existence of angular momentum transfer of acoustical vortices. The favorable results of property analysis and parameter optimization for acoustical vortices provide the basis for particle manipulation in biomedical engineering.