Dynamics of a rigid cylinder near a plane boundary in the radiation field of an acoustic wave

An approach is described for investigation of the interaction between a rigid body and a viscous fluid boundary under acoustic wave propagation. The influence of the liquid on the rigid body is determined as a mean force, which is a constant in the time component of the hydrodynamic force. This enables the use of a previously developed technique for calculation of pressure in a compressible viscous liquid. The technique takes into account the second-order terms with respect to the wave field parameters and is based on investigation of a system of initially nonlinear hydromechanics equations that can be simplified with respect to the wave motion parameters of the liquid. It has proven possible to retain the second-order terms for determination of stresses in the liquid without having to solve the system of nonlinear equations. The stresses can be expressed in terms of parameters found in the solution of the linearized equations of the compressible viscous liquid. In this way, the solution of linearized equations is expressed in terms of a scalar and vector potentials. The problem statement is derived for a rigid cylinder located near a rigid flat wall under the effects of a wave propagating perpendicular to the wall. The solution for this particular example is obtained.     

Interaction of an acoustic shock wave with a cylindrical piezoceramic shell located near a plane boundary

Institute of Mechanics of the Ukrainian Academy of Sciences, Kiev (Ukraine). Translated from Prikladnaya Mekhanika, Vol. 29, No. 4, pp. 46–54, April, 1993.     

Dynamics of a spherical particle near a flat liquid boundary under acoustic radiation forces

The effect of radiation forces on a spherical particle near a flat liquid boundary is studied. The force is established to depend on the density ratio, the distance to the boundary, and the acoustic field parameters. The motion of a spherical particle under the action of radiation forces is described Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 30–41, November 2008.     

Grouping of suspended particles in a standing acoustic wave field

Assuning a snall difference in phase densities averaged equations have been obtained for the motion of a two-phase medium in a standing acoustic wave field. The force causing the relative motion of the phases has been determined. On the basis of the averaged equations obtained the dynamics of the redistribution of particles in the suspension in a plane standing acoustic wave has been studied.Translated from Izvestiya Akadenii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 81–88, September–October, 1984.The authors wish to thank S. A. Regirer for his interest in this work and for useful advice.     

Wiener-Hopf analysis of an acoustic plane wave in a trifurcated waveguide

In this paper, we have made Wiener-Hopf analysis of an acoustic plane wave by a semi-infinite hard duct that is placed symmetrically inside an infinite soft/hard duct. The method of solution is integral transform and Wiener-Hopf technique. The imposition of boundary conditions result in a 2 × 2 matrix Wiener-Hopf equation associated with a new canonical scattering problem which is solved by using the pole removal technique. In the solution, two infinite sets of unknown coefficients are involved that satisfy two infinite systems of linear algebraic equations. These systems of linear algebraic equations are solved numerically. The graphs are plotted for sundry parameters of interest. Kernel functions are also factorized.     

Axial acoustic radiation force on a rigid cylinder near an impedance boundary for on-axis Gaussian beam

This work presents a theoretical model to calculate the acoustic radiation force on a rigid cylindrical particle immersed in an ideal fluid near a boundary for an on-axis Gaussian beam. An exact solution of the axial acoustic radiation force function is derived for a cylindrical particle by applying the translation addition theorem of cylindrical Bessel function. We analyzed the effects of the impedance boundary on acoustic radiation force of a rigid cylinder immersed in water near an impedance boundary with particular emphasis on the radius of the rigid cylinder and the distance from the cylinder center to impedance boundary. Simulation results reveal that the existence of particle trapping behavior depends on the choice of nondimensional frequency as well as the offset distance from the impedance boundary. The value of the radiation force function varies when the cylinder lies at the different position of the on-axis Gaussian beam. For the particle with different radius, the acoustic radiation force functions vary significantly with frequency. This study provides a theoretical basis for acoustic manipulation, which may benefit to the improvement and development of the acoustic control technology.     

The transient electromagnetic field from an antenna near the plane boundary between two dielectric halfspaces

Summary In a preceding publication of the present author expressions were derived to describe the pulse field from a vertical electric antenna placed near the plane boundary of two semi-infinite diëlectrics. These expressions appeared to be integrals on a finite range in the complex plane and were derived for the field in both media. The analysis of the field also gave information about the time of arrival of the several pulse-fronts.In the present paper the field is studied in more detail, and with the aid of suitable approximations more specific results are obtained, such as logarithmic field singularities.Also a discussion of the pulse analogon to the Zenneck wave in the time harmonic case has been included.     

Vibration of an underground pipe in a field of a plane harmonic wave

Moscow. Institute of Irrigation. Translated from Prikladnaya Mekhanika, Vol. 24, No. 5, pp. 38–43, May, 1988     

Experimental study on a non-dilute two-phase coflowing jet: Dynamics of particles in the near flow field

The dynamics of particles in multi-phase jets has been widely studied due to its importance for a broad range of practical applications. The present work describes an experimental investigation on an initially non-dilute two-phase jet, aimed at improving the understanding in this field. A two-color PDPA has been employed to measure simultaneously the velocity and size of particles. The measurements are post-processed to check the reliability of the results and to derive information on particle volume flux as an indication of their concentration. Acoustic forcing is applied in order to control coherent structures, which are responsible for mixing and transport phenomena, and also to get phase-locked measurements. Phase-averaged statistics enabled to freeze the jet structure, not visible in the time-averaged data. The results along the jet centerline confirm that drag forces and the spread angle of the jet initially control particle dispersion, very near the nozzle exit (x/D < 4). However, as the vortical structures evolve forming tongue-shaped structures, the total particle volume flux is augmented when these structures connect with the main stream (x/D > 5). This is due to an increase of the number of smaller size particles, even when a decrease of the number of larger size particle is observed. Further analysis at five cross-stream sections across two consecutive vortices confirm that small particles are convected around the coherent structure and then incorporated to the main stream, increasing the particle concentration at the jet core. On the other hand, the number of larger particles (as well as their contribution to axial volume flux) starts to decay in regions of high azymuthal vorticity. This behaviour is partly ascribed to the transversal lift force, associated to the large spatial gradients observed in these regions. Saffman and Magnus forces have been estimated to be comparable or even greater than radial drag forces. The results suggest that the Saffman force might accelerate particles in radial direction, inducing a high radial volumetric flow rate from high to low axial velocity regions.     

Acoustic radiation force on an elastic cylinder in a Gaussian beam near an impedance boundary

Acoustic radiation force (ARF) is studied by considering an infinite elastic cylinder near an impedance boundary when the cylinder is illuminated by a Gaussian beam. The surrounding fluid is an ideal fluid. Using the method of images and the translation-addition theorem for the cylindrical Bessel function, the resulting sound field including the incident wave, its reflection from the boundary, the scattered wave from the elastic cylinder, and its image are expressed in terms of the cylindrical wave function. Then, we deduce the exact equations of the axial and transverse ARFs. The solutions depend on the cylinder position, cylinder material, beam waist, reflection coefficient, distance from the impedance boundary, and absorption in the cylinder. To analyze the effects of the various factors intuitively, we simulate the radiation force for non-absorbing elastic cylinders made of stainless steel, gold, and beryllium as well as for an absorbing elastic cylinder made of polyethylene, which is a well-known biomedical polymer. The results show that the impedance boundary, cylinder material, absorption in the cylinder, and cylinder position in the Gaussian beam significantly affect the magnitude and direction of the force. Both stable and unstable equilibrium regions are found. Moreover, a larger beam waist broadens the beam domain, corresponding to non-zero axial and transverse ARFs. More importantly, negative ARFs are produced depending on the choice of the various factors. These results are particularly important for designing acoustic manipulation devices operating with Gaussian beams.     

Simulation of particles released near the wall in a turbulent boundary layer

A direct numerical simulation was used along with a Lagrangian particle tracking technique to study particle motion in a horizontal, spatially developing turbulent boundary layer along an upper-wall (with terminal velocity directed away from the wall). The objective of the research was to study particle diffusion, dispersion, reflection, and mean velocity in the context of two parametric studies: one investigated the effect of the drift parameter (the ratio of particle terminal velocity to fluid friction velocity) for a fixed and finite particle inertia, and the second varied the drift parameter and particle inertia by the same amount (i.e. for a constant Froude number). A range of drift parameters from 10⁻⁴ to 10⁰ were considered for both cases. The particles were injected into the simulation at a height of four wall units for several evenly distributed points across the span and a perfectly elastic wall collision was specified at one wall unit.Statistics collected along the particle trajectories demonstrated a transition in particle movement from one that is dominated by diffusion to one that is dominated by gravity. For small and intermediate sized particles (i.e. ones with outer Stokes numbers and drift parameters much less than unity) transverse diffusion away from the wall dominated particle motion. However, preferential concentration is seen near the wall for intermediate-sized particles due to inhomogeneous turbulence effects (turbophoresis), consistent with previous channel flow studies. Particle–wall collision statistics indicated that impact velocities tended to increase with increasing terminal velocity for small and moderate inertias, after which initial conditions become important. Finally, high relative velocity fluctuations (compared to terminal velocity) were found as particle inertia increased, and were well described with a quasi-one-dimensional fluctuation model.     

The field near the wave front in a Cauchy-Poisson problem

A study is made of the asymptotic behavior of the Green's function of the Cauchy—Poisson problem in the far zone near the wave front, i.e., for r c₀t, where is the maximal group velocity of a surface wave. It is shown that the solution to this problem given in the book by LeBlond and Mysak [1] is incorrect, and the correct asymptotic behavior, expressed in terms of the square of an Airy function, is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 173–174, March–April, 1984.We thank Yu. L. Gazaryan for interest in the present work.     

Acoustic radiation force on a rigid cylinder in an off-axis Gaussian beam near an impedance boundary

The exact equations of the axial and transverse acoustic radiation force functions of a Gaussian beam arbitrarily incident on an infinite rigid cylinder close to an impedance boundary and immersed in an ideal fluid are deduced by expressing the incident wave, the scattering wave and the boundary reflected wave in terms of the cylindrical wave function. The effects of the beam waist, the sound reflection coefficient, the cylinder position and the distance from the impedance boundary on the acoustic radiation force are studied using numerical simulations. The simulation results show that the amplitude of the acoustic radiation force function increases with beam width. Moreover, the values of the acoustic radiation force in both the axial and transverse directions reach those of a plane wave when the beam width is considerably larger than the wavelength of the Gaussian beam. The properties of the impedance boundary and the position of the cylinder in the Gaussian beam have a considerable effect on the magnitude and direction of the force. The simulation results, particularly in the case of a transverse force, indicate the presence of a negative acoustic radiation force that is related to the nondimensional frequency and position of the cylinder in the Gaussian beam.     

The lateral migration of solid particles in a laminar flow near a plane

The lateral inertial migration of a solid spherical particle suspended in a laminar flow over a vertical wall is considered theoretically. Formulae for the migration velocity are obtained for both neutrally buoyant and non-neutrally buoyant particles and also for the case of zero flow over the wall. Situations in which the particle is either free to rotate or prevented from rotating are considered. Such results are found to agree qualitatively with known experimental data.     

Effect of a plane acoustic pressure wave on a reinforced cylindrical shell

Translated from Prikiadnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 110–116, September–October, 1992.     

Structure of artificial disturbances induced by an external acoustic field in a supersonic boundary layer

The wave structure of the artificial disturbances generated by an external acoustic field in a supersonic boundary layer is investigated. The disturbances are classified with respect to phase velocity. Disturbances whose phase velocity in the direction of flow is greater than unity and waves located at the boundary of the discrete and continuous spectra are detected.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 82–86, May–June, 1989.