Viscoacoustic model for near-field ultrasonic levitation

Abstract

Ultrasonic near-field levitation allows for contactless support and transportation of an object over vibrating surface. We developed an accurate model predicting pressure distribution in the gap between the surface and levitating object. The formulation covers a wide range of the air flow regimes: from viscous squeezed flow dominating in small gap to acoustic wave propagation in larger gap. The paper explains derivation of the governing equations from the basic fluid dynamics. The nonreflective boundary conditions were developed to properly define air flow at the outlet. Comparing to direct computational fluid dynamics modeling our approach allows achieving good accuracy while keeping the computation cost low. Using the model we studied the levitation force as a function of gap distance. It was shown that there are three distinguished flow regimes: purely viscous, viscoacoustic, and acoustic. The regimes are defined by the balance of viscous and inertial forces. In the viscous regime the pressure in the gap is close to uniform while in the intermediate viscoacoustic and the acoustic regimes the pressure profile is wavy. The model was validated by a dedicated levitation experiment and compared to similar published results.

Viscoacoustic squeeze-film force on a rigid disk undergoing small axial oscillations

“…Practical applicability of either theory in hydrodynamic bearings is further complicated because equilibrium separation distances are typically unknown prior to operation, which yields uncertainty in the choice of the needed analytical framework. Melikhov et al (2016) addressed this problem by numerically computing the levitation force for a compressible squeeze-film system with arbitrary Stokes number. In determining the time-averaged pressure distribution across the slender film, Melikhov et al (2016) imposed a Robin boundary condition that enforces strictly acoustic wave propagation at its edge, which yielded a model that demonstrates reasonable agreement between theoretically predicted and experimentally determined levitation heights h o .…”

“…Melikhov et al (2016) addressed this problem by numerically computing the levitation force for a compressible squeeze-film system with arbitrary Stokes number. In determining the time-averaged pressure distribution across the slender film, Melikhov et al (2016) imposed a Robin boundary condition that enforces strictly acoustic wave propagation at its edge, which yielded a model that demonstrates reasonable agreement between theoretically predicted and experimentally determined levitation heights h o . To the best of our knowledge, a complete viscoacoustic theoretical analysis of the axisymmetric squeeze-film problem that accounts for the existence of the edge flow region is yet to be developed.…”

Benefits of controlled inclination for contactless transport by squeeze-film levitation

“…As shown by Melikhov, Chivilikhin, Amosov, and Jeanson (2016) and , the flow dynamics in the thin air layer of a squeeze-film system is characterized by three principal time scales -that of the driving oscillations t o = 𝜔 −1 , viscous diffusion across the film t v = h 2 o /(𝜇 a /𝜌 a ) and acoustic pressure equilibration along the film t a = a/ p a /𝜌 a -which enter in the theoretical description through two non-dimensional parameters, the relevant Stokes number S = t v /t o (or, equivalently, the associated Womersley number S 1/2 ) and a compressibility number C = t a /t o . As shown by Taylor and Saffman (1957), the description simplifies in configurations for which t v t o , whereby inertial forces are negligibly weak compared with viscous shear.…”

“…As shown by Melikhov, Chivilikhin, Amosov, and Jeanson (2016) and Ramanarayanan et al. (2022), the flow dynamics in the thin air layer of a squeeze-film system is characterized by three principal time scales – that of the driving oscillations , viscous diffusion across the film and acoustic pressure equilibration along the film – which enter in the theoretical description through two non-dimensional parameters, the relevant Stokes number (or, equivalently, the associated Womersley number ) and a compressibility number .…”

Incompressible Squeeze-Film Levitation

“…A limited number of studies attempted to derive a unified viscoacoustic theory that works across the viscous and acoustic regimes. Melikhov et al [19] developed a viscoacoustic model and identified the different operating regimes for air squeeze films as a function of the levitation height, confirming a purely viscous regime for typical squeeze film levitation systems. Ramanarayanan et al [20] proposed another unified theory which described critical parametric conditions that causes levitation forces to switch to adhesion forces in air squeeze film systems.…”