Ultrasonic field modeling by distributed point source method for different transducer boundary conditions

Several investigators have modeled ultrasonic fields in front of transducers by Huygens-Fresnel superposition principle that integrates the contributions of a number of point sources distributed on the transducer face. This integral solution, also known as the Rayleigh integral or Rayleigh-Sommerfeld Integral solution, assumes the strengths of the point sources distributed over the transducer face. A newly developed technique called distributed point source method (DPSM) offers an alternative approach for modeling ultrasonic fields. DPSM is capable of modeling the field for prescribed source strength distribution as well as for prescribed interface conditions with unknown source strengths. It is investigated how the ultrasonic field in front of the transducer varies in different situations: (1) when the point source strengths are known, (2) when the point source strengths are unknown but obtained from the interface condition that only the normal component of the transducer velocity is continuous across the fluid-solid interface, (3) when all three components of velocity are assumed to be continuous across the interface for the no-slip condition, and (4) when the pressure instead of the velocity is prescribed on the transducer face. Results for these different interface conditions are compared with the analytical solutions along the central axis.