Saffman–Taylor instability in eccentric cylinders at gaseous cavitation

A flow of silicon fluid in the gap between eccentric cylinders was studied experimentally.The condition of gaseous cavitation inception during the rotation of internal cylinder was considered.It was shown that at reduction of the gap between cylinders Saffman–Taylor instability appeared on surface of the internal cylinder and then gaseous cavitation was observed.Possibility of one uniform gas formation appearance under this type of instability was demonstrated.

Acoustic radiation force and torque on a lossless eccentric layered fluid cylinder

Exact analytical equations and computations for the longitudinal and transverse acoustic radiation force and axial torque components for a lossless eccentric liquid cylinder submerged in a nonviscous fluid and insonified by plane waves progressive waves(of arbitrary incidence in the polar plane)are established and computed numerically.The modal matching method and the translational addition theorem in cylindrical coordinates are used to derive exact mathematical expressions applicable to any inner and outer cylinder sizes without any approximations,and taking into account the interaction effects between the waves propagating in the layer and those scattered from the cylindrical core.The results show that longitudinal and transverse radiation force components arise,in addition to the emergence of an axial radiation torque component acting on the non-absorptive compound cylinder due to geometrical asymmetry as the eccentricity increases.The computations demonstrate that the axial torque component,which arises due to a geometrical asymmetry,can be positive(causing counterclockwise rotation in the polar plane),negative(clockwise rotation)or neutral(rotation cancellation)depending on the size parameter of the cylinder and the amount of eccentricity.Furthermore,verification and validation of the results have been accomplished from the standpoint of energy conservation law applied to scattering,and based on the reciprocity theorem.

Eccentricity and thermoviscous effects on ultrasonic scattering from a liquid-coated fluid cylinder

Calculation of the scattered field of the eccentric scatterers is an old problem with numerous applications. This study considers the interaction of a plane compressional sound wave with a liquid-encapsulated thermoviscous fluid cylinder submerged in an unbounded viscous thermally conducting medium. The translational addition theorem for cylindrical wave functions, the appropriate wave field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in the form of infinite series. The analytical results are illustrated with a numerical example in which the compound cylinder is insonified by a plane sound wave at selected angles of incidence in a wide range of dimensionless frequencies. The backscattered far-field acoustic pressure amplitude and the spatial distribution of the total acoustic pressure in the vicinity of the cylinder are evaluated and discussed for representative values of the parameters characterizing the system. The effects of incident wave frequency, angle of incidence, fluid thermoviscosity, core eccentricity and size are thoroughly examined. Limiting case involving an ideal com- pressible liquid-coated cylinder is considered and fair agreement with a well-known solution is established.

An Experimental and Numerical Study of Natural Convection Heat Transfer in Horizontal Annuli between Eccentric Cylinders

Natural convection heat transfer in eccentric annuli made of two isothermal horizontal circular cylinders is numerically investigated. Bipolar coordinates are used for the eccentric annuli. The governingequations are transformed into finite difference equations (FDE) by the central difference approach.Heat transfer and flow convection pattern results are simulated for 5.0≤RaL≤1.0×105, withPr = 0.3 - 100, Do/Di = 1.25 - 5.0, andε= 0.01-0.95. The axis of the inner cylinder lies onan inclined plane with θp= 0°- 180°.A Mach-Zehnder interferometer is used for the experimentalstudy. The range is for RaL = 5.3×102-2.41×104, with Do/Di = 2.0, 2.5 and 3.125,ε= 0.0-0.85,and θp= 0°-180°.Air is used as the medium. Comparison of the numerical results with the experimental data shows good agreement.

Rotational Flow in a Narrow Annular Gap Based on Lattice Boltzmann Method

For comprehensive characteristics of flow in a gas bearing,lattice Boltzmann method(LBM)is applied for study of the two-dimensional flow between two eccentric cylinders with the inner one rotating at a high speed.The flow pattern and circumferential pressure distribution are discussed based on critical issues such as eccentricity ranging from 0.2 to 0.9,clearance ratio varying from 0.005 to 0.01 and rotating speed in the range of 3×104—1.8×105 r/min.The analysis and discussion on the circumferential pressure distribution affirmed the quasilinear relation between the extremum pressure and rotating speed.Furthermore,a high eccentricity and small clearance ratio contributes most to the fluctuation of the circumferential pressure distribution.The flow pattern inside the channel exhibits separation vortex under a large eccentricity.The conclusions drawn in this work give rise to prediction of the flow pattern in the gas bearing which is beneficial for evaluating the performance of as well as instructing the design and development.