# The Development and Analysis of a Multistage Spraying Method for Liquids in an Ultrasonic Field
## 3 Ultrasonic Emitter  
An ultrasonic emitter in the form of a hollow bending-oscillating cylinder (tubular emitter) was developed for the practical implementation of the proposed multistage ultrasonic spraying technique. The emitter is a cylinder with a stepped-variable cross-section, which generates bending-diametral vibrations at a frequency above 20 kHz. The hollow shape of the cylinder was chosen for this emitter in order to ensure the self-focusing of ultrasonic vibrations in the internal cavity on the axis of the cylinder. The application of this type of emitter enables the generation of a regular structure of vibrations of great length. Liquid droplets consistently passing the maximums of standing wave velocity inside the cylindrical emitter will deform and collapse until they reach the minimum possible particle size for the sound pressure level generated by the emitter. To ensure sufficient ultrasonic vibration intensity at high ultrasonic frequencies, a multi-package transducer with radially spaced Langevin transducers can be used as the piezoelectric transducer [26]. An estimation of acoustic and geometric parameters and calculation of the emitter vibration waveform were performed using modal analysis in the finite element modeling system (ANSYS package, ver. 19.2). The tetrahedral type of finite element was used for the estimation and analysis of the performance of an ultrasonic emitter exposed to a volumetric stress state. When the modal analysis was performed, the convergence of numerical results for different emitter designs was analyzed. A modeling result that corresponded to a finite element model with a minimized number of finite elements, the increase in which results in a change in the main values of the design parameters (e.g., the natural frequency of vibrations) by no more than 0.2-0.5%, was considered satisfactory. Figure 2 shows a drawing of the tubular emitter and the waveform of its vibrations obtained from the results of the estimations. The ultrasonic field generated by the tubular emitter was estimated by finite element analysis in ANSYS. The harmonic acoustics module of harmonic acoustic analysis was used. During modeling, the boundary conditions were set on the basis of the obtained design data specifying cylindrical emitter parameters (the frequency of vibrations and distribution of the vibration amplitudes of the emitting surface). The scope of the calculation domain was limited by the inner surface of the tubular emitter. The boundary conditions were set at the ends of the estimated area: radiation boundary. During the estimations of the acoustic field, the iterative variation of tubular emitter dimensions was carried out to ensure the standing wave mode in the inner space of the emitter. Figure 3 shows the results of the estimations of distribution of the sound pressure generated in the emitter and a picture of the manufactured emitter. The results of estimations show that conditions and a sufficient sound pressure level in the volume of the multistage spraying chamber (more than 190 dB) are available for the implementation of multistage spraying. Three sound pressure maxima were formed along the emitter axis. Thus, a droplet moving inside the emitter will undergo up to three stages of disintegration. The sound pressure level was measured inside the fabricated emitter to confirm the estimations. The measurements were carried out with a noise meter/vibro-meter Ekofizika-110A (OKTAVA-ElektronDizayn, Moscow, Russia) with a microphone VMK-401 (Vibropirbor, Yaroslavl, Russia). The measurements showed that the sound pressure level formed inside the tubular emitter was within 170...182 dB. The measurements were carried out at maximum power consumption. Figure 2: Ultrasonic tubular emitter: (**a**) tubular emitter drawing; (**b**) vibration waveform.